diff --git a/.gitignore b/.gitignore index 1abcc3f6..3423d6ec 100644 --- a/.gitignore +++ b/.gitignore @@ -1,5 +1,5 @@ -.DS_Store -*.pyc -*~ -*.png -**/.ipynb_checkpoints +.DS_Store +*.pyc +*~ +*.png +**/.ipynb_checkpoints diff --git a/Chapter1_Introduction/Chapter1_Introduction.ipynb b/Chapter1_Introduction/Chapter1_Introduction.ipynb index cdaae9ba..afdcf1be 100644 --- a/Chapter1_Introduction/Chapter1_Introduction.ipynb +++ b/Chapter1_Introduction/Chapter1_Introduction.ipynb @@ -1,1101 +1,1101 @@ -{ - "metadata": { - "name": "" - }, - "nbformat": 3, - "nbformat_minor": 0, - "worksheets": [ - { - "cells": [ - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Probabilistic Programming\n", - "=====\n", - "and Bayesian Methods for Hackers \n", - "========\n", - "\n", - "#####Version 0.1\n", - "Welcome to *Bayesian Methods for Hackers*. The full Github repository is available at [github/Probabilistic-Programming-and-Bayesian-Methods-for-Hackers](https://github.com/CamDavidsonPilon/Probabilistic-Programming-and-Bayesian-Methods-for-Hackers). The other chapters can be found on the project's [homepage](https://camdavidsonpilon.github.io/Probabilistic-Programming-and-Bayesian-Methods-for-Hackers/). We hope you enjoy the book, and we encourage any contributions!" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Chapter 1\n", - "======\n", - "***" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "The Philosophy of Bayesian Inference\n", - "------\n", - " \n", - "> You are a skilled programmer, but bugs still slip into your code. After a particularly difficult implementation of an algorithm, you decide to test your code on a trivial example. It passes. You test the code on a harder problem. It passes once again. And it passes the next, *even more difficult*, test too! You are starting to believe that there may be no bugs in this code...\n", - "\n", - "If you think this way, then congratulations, you already are thinking Bayesian! Bayesian inference is simply updating your beliefs after considering new evidence. A Bayesian can rarely be certain about a result, but he or she can be very confident. Just like in the example above, we can never be 100% sure that our code is bug-free unless we test it on every possible problem; something rarely possible in practice. Instead, we can test it on a large number of problems, and if it succeeds we can feel more *confident* about our code, but still not certain. Bayesian inference works identically: we update our beliefs about an outcome; rarely can we be absolutely sure unless we rule out all other alternatives. " - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "\n", - "### The Bayesian state of mind\n", - "\n", - "\n", - "Bayesian inference differs from more traditional statistical inference by preserving *uncertainty*. At first, this sounds like a bad statistical technique. Isn't statistics all about deriving *certainty* from randomness? To reconcile this, we need to start thinking like Bayesians. \n", - "\n", - "The Bayesian world-view interprets probability as measure of *believability in an event*, that is, how confident we are in an event occurring. In fact, we will see in a moment that this is the natural interpretation of probability. \n", - "\n", - "For this to be clearer, we consider an alternative interpretation of probability: *Frequentist*, known as the more *classical* version of statistics, assume that probability is the long-run frequency of events (hence the bestowed title). For example, the *probability of plane accidents* under a frequentist philosophy is interpreted as the *long-term frequency of plane accidents*. This makes logical sense for many probabilities of events, but becomes more difficult to understand when events have no long-term frequency of occurrences. Consider: we often assign probabilities to outcomes of presidential elections, but the election itself only happens once! Frequentists get around this by invoking alternative realities and saying across all these realities, the frequency of occurrences defines the probability. \n", - "\n", - "Bayesians, on the other hand, have a more intuitive approach. Bayesians interpret a probability as measure of *belief*, or confidence, of an event occurring. Simply, a probability is a summary of an opinion. An individual who assigns a belief of 0 to an event has no confidence that the event will occur; conversely, assigning a belief of 1 implies that the individual is absolutely certain of an event occurring. Beliefs between 0 and 1 allow for weightings of other outcomes. This definition agrees with the probability of a plane accident example, for having observed the frequency of plane accidents, an individual's belief should be equal to that frequency, excluding any outside information. Similarly, under this definition of probability being equal to beliefs, it is meaningful to speak about probabilities (beliefs) of presidential election outcomes: how confident are you candidate *A* will win?\n", - "\n", - "Notice in the paragraph above, I assigned the belief (probability) measure to an *individual*, not to Nature. This is very interesting, as this definition leaves room for conflicting beliefs between individuals. Again, this is appropriate for what naturally occurs: different individuals have different beliefs of events occurring, because they possess different *information* about the world. The existence of different beliefs does not imply that anyone is wrong. Consider the following examples demonstrating the relationship between individual beliefs and probabilities:\n", - "\n", - "- I flip a coin, and we both guess the result. We would both agree, assuming the coin is fair, that the probability of Heads is 1/2. Assume, then, that I peek at the coin. Now I know for certain what the result is: I assign probability 1.0 to either Heads or Tails (whichever it is). Now what is *your* belief that the coin is Heads? My knowledge of the outcome has not changed the coin's results. Thus we assign different probabilities to the result. \n", - "\n", - "- Your code either has a bug in it or not, but we do not know for certain which is true, though we have a belief about the presence or absence of a bug. \n", - "\n", - "- A medical patient is exhibiting symptoms $x$, $y$ and $z$. There are a number of diseases that could be causing all of them, but only a single disease is present. A doctor has beliefs about which disease, but a second doctor may have slightly different beliefs. \n", - "\n", - "\n", - "This philosophy of treating beliefs as probability is natural to humans. We employ it constantly as we interact with the world and only see partial truths, but gather evidence to form beliefs. Alternatively, you have to be *trained* to think like a frequentist. \n", - "\n", - "To align ourselves with traditional probability notation, we denote our belief about event $A$ as $P(A)$. We call this quantity the *prior probability*.\n", - "\n", - "John Maynard Keynes, a great economist and thinker, said \"When the facts change, I change my mind. What do you do, sir?\" This quote reflects the way a Bayesian updates his or her beliefs after seeing evidence. Even — especially — if the evidence is counter to what was initially believed, the evidence cannot be ignored. We denote our updated belief as $P(A |X )$, interpreted as the probability of $A$ given the evidence $X$. We call the updated belief the *posterior probability* so as to contrast it with the prior probability. For example, consider the posterior probabilities (read: posterior beliefs) of the above examples, after observing some evidence $X$:\n", - "\n", - "1\\. $P(A): \\;\\;$ the coin has a 50 percent chance of being Heads. $P(A | X):\\;\\;$ You look at the coin, observe a Heads has landed, denote this information $X$, and trivially assign probability 1.0 to Heads and 0.0 to Tails.\n", - "\n", - "2\\. $P(A): \\;\\;$ This big, complex code likely has a bug in it. $P(A | X): \\;\\;$ The code passed all $X$ tests; there still might be a bug, but its presence is less likely now.\n", - "\n", - "3\\. $P(A):\\;\\;$ The patient could have any number of diseases. $P(A | X):\\;\\;$ Performing a blood test generated evidence $X$, ruling out some of the possible diseases from consideration.\n", - "\n", - "\n", - "It's clear that in each example we did not completely discard the prior belief after seeing new evidence $X$, but we *re-weighted the prior* to incorporate the new evidence (i.e. we put more weight, or confidence, on some beliefs versus others). \n", - "\n", - "By introducing prior uncertainty about events, we are already admitting that any guess we make is potentially very wrong. After observing data, evidence, or other information, we update our beliefs, and our guess becomes *less wrong*. This is the alternative side of the prediction coin, where typically we try to be *more right*. \n" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "\n", - "### Bayesian Inference in Practice\n", - "\n", - " If frequentist and Bayesian inference were programming functions, with inputs being statistical problems, then the two would be different in what they return to the user. The frequentist inference function would return a number, representing an estimate (typically a summary statistic like the sample average etc.), whereas the Bayesian function would return *probabilities*.\n", - "\n", - "For example, in our debugging problem above, calling the frequentist function with the argument \"My code passed all $X$ tests; is my code bug-free?\" would return a *YES*. On the other hand, asking our Bayesian function \"Often my code has bugs. My code passed all $X$ tests; is my code bug-free?\" would return something very different: probabilities of *YES* and *NO*. The function might return:\n", - "\n", - "\n", - "> *YES*, with probability 0.8; *NO*, with probability 0.2\n", - "\n", - "\n", - "\n", - "This is very different from the answer the frequentist function returned. Notice that the Bayesian function accepted an additional argument: *\"Often my code has bugs\"*. This parameter is the *prior*. By including the prior parameter, we are telling the Bayesian function to include our belief about the situation. Technically this parameter in the Bayesian function is optional, but we will see excluding it has its own consequences. \n", - "\n", - "\n", - "####Incorporating evidence\n", - "\n", - "As we acquire more and more instances of evidence, our prior belief is *washed out* by the new evidence. This is to be expected. For example, if your prior belief is something ridiculous, like \"I expect the sun to explode today\", and each day you are proved wrong, you would hope that any inference would correct you, or at least align your beliefs better. Bayesian inference will correct this belief.\n", - "\n", - "\n", - "Denote $N$ as the number of instances of evidence we possess. As we gather an *infinite* amount of evidence, say as $N \\rightarrow \\infty$, our Bayesian results (often) align with frequentist results. Hence for large $N$, statistical inference is more or less objective. On the other hand, for small $N$, inference is much more *unstable*: frequentist estimates have more variance and larger confidence intervals. This is where Bayesian analysis excels. By introducing a prior, and returning probabilities (instead of a scalar estimate), we *preserve the uncertainty* that reflects the instability of statistical inference of a small $N$ dataset. \n", - "\n", - "One may think that for large $N$, one can be indifferent between the two techniques since they offer similar inference, and might lean towards the computationally-simpler, frequentist methods. An individual in this position should consider the following quote by Andrew Gelman (2005)[1], before making such a decision:\n", - "\n", - "> Sample sizes are never large. If $N$ is too small to get a sufficiently-precise estimate, you need to get more data (or make more assumptions). But once $N$ is \"large enough,\" you can start subdividing the data to learn more (for example, in a public opinion poll, once you have a good estimate for the entire country, you can estimate among men and women, northerners and southerners, different age groups, etc.). $N$ is never enough because if it were \"enough\" you'd already be on to the next problem for which you need more data.\n", - "\n", - "### Are frequentist methods incorrect then? \n", - "\n", - "**No.**\n", - "\n", - "Frequentist methods are still useful or state-of-the-art in many areas. Tools such as least squares linear regression, LASSO regression, and expectation-maximization algorithms are all powerful and fast. Bayesian methods complement these techniques by solving problems that these approaches cannot, or by illuminating the underlying system with more flexible modeling.\n", - "\n", - "\n", - "#### A note on *Big Data*\n", - "Paradoxically, big data's predictive analytic problems are actually solved by relatively simple algorithms [2][4]. Thus we can argue that big data's prediction difficulty does not lie in the algorithm used, but instead on the computational difficulties of storage and execution on big data. (One should also consider Gelman's quote from above and ask \"Do I really have big data?\" )\n", - "\n", - "The much more difficult analytic problems involve *medium data* and, especially troublesome, *really small data*. Using a similar argument as Gelman's above, if big data problems are *big enough* to be readily solved, then we should be more interested in the *not-quite-big enough* datasets. \n" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### Our Bayesian framework\n", - "\n", - "We are interested in beliefs, which can be interpreted as probabilities by thinking Bayesian. We have a *prior* belief in event $A$, beliefs formed by previous information, e.g., our prior belief about bugs being in our code before performing tests.\n", - "\n", - "Secondly, we observe our evidence. To continue our buggy-code example: if our code passes $X$ tests, we want to update our belief to incorporate this. We call this new belief the *posterior* probability. Updating our belief is done via the following equation, known as Bayes' Theorem, after its discoverer Thomas Bayes:\n", - "\n", - "\\begin{align}\n", - " P( A | X ) = & \\frac{ P(X | A) P(A) } {P(X) } \\\\\\\\[5pt]\n", - "& \\propto P(X | A) P(A)\\;\\; (\\propto \\text{is proportional to } )\n", - "\\end{align}\n", - "\n", - "The above formula is not unique to Bayesian inference: it is a mathematical fact with uses outside Bayesian inference. Bayesian inference merely uses it to connect prior probabilities $P(A)$ with an updated posterior probabilities $P(A | X )$." - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "##### Example: Mandatory coin-flip example\n", - "\n", - "Every statistics text must contain a coin-flipping example, I'll use it here to get it out of the way. Suppose, naively, that you are unsure about the probability of heads in a coin flip (spoiler alert: it's 50%). You believe there is some true underlying ratio, call it $p$, but have no prior opinion on what $p$ might be. \n", - "\n", - "We begin to flip a coin, and record the observations: either $H$ or $T$. This is our observed data. An interesting question to ask is how our inference changes as we observe more and more data? More specifically, what do our posterior probabilities look like when we have little data, versus when we have lots of data. \n", - "\n", - "Below we plot a sequence of updating posterior probabilities as we observe increasing amounts of data (coin flips)." - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "\"\"\"\n", - "The book uses a custom matplotlibrc file, which provides the unique styles for\n", - "matplotlib plots. If executing this book, and you wish to use the book's\n", - "styling, provided are two options:\n", - " 1. Overwrite your own matplotlibrc file with the rc-file provided in the\n", - " book's styles/ dir. See http://matplotlib.org/users/customizing.html\n", - " 2. Also in the styles is bmh_matplotlibrc.json file. This can be used to\n", - " update the styles in only this notebook. Try running the following code:\n", - "\n", - " import json, matplotlib\n", - " s = json.load( open(\"../styles/bmh_matplotlibrc.json\") )\n", - " matplotlib.rcParams.update(s)\n", - "\n", - "\"\"\"\n", - "\n", - "# The code below can be passed over, as it is currently not important, plus it\n", - "# uses advanced topics we have not covered yet. LOOK AT PICTURE, MICHAEL!\n", - "%matplotlib inline\n", - "from IPython.core.pylabtools import figsize\n", - "import numpy as np\n", - "from matplotlib import pyplot as plt\n", - "figsize(11, 9)\n", - "\n", - "import scipy.stats as stats\n", - "\n", - "dist = stats.beta\n", - "n_trials = [0, 1, 2, 3, 4, 5, 8, 15, 50, 500]\n", - "data = stats.bernoulli.rvs(0.5, size=n_trials[-1])\n", - "x = np.linspace(0, 1, 100)\n", - "\n", - "# For the already prepared, I'm using Binomial's conj. prior.\n", - "for k, N in enumerate(n_trials):\n", - " sx = plt.subplot(len(n_trials) / 2, 2, k + 1)\n", - " plt.xlabel(\"$p$, probability of heads\") \\\n", - " if k in [0, len(n_trials) - 1] else None\n", - " plt.setp(sx.get_yticklabels(), visible=False)\n", - " heads = data[:N].sum()\n", - " y = dist.pdf(x, 1 + heads, 1 + N - heads)\n", - " plt.plot(x, y, label=\"observe %d tosses,\\n %d heads\" % (N, heads))\n", - " plt.fill_between(x, 0, y, color=\"#348ABD\", alpha=0.4)\n", - " plt.vlines(0.5, 0, 4, color=\"k\", linestyles=\"--\", lw=1)\n", - "\n", - " leg = plt.legend()\n", - " leg.get_frame().set_alpha(0.4)\n", - " plt.autoscale(tight=True)\n", - "\n", - "\n", - "plt.suptitle(\"Bayesian updating of posterior probabilities\",\n", - " y=1.02,\n", - " fontsize=14)\n", - "\n", - "plt.tight_layout()" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "metadata": {}, - "output_type": "display_data", - "png": 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fSy70ej3OnDmD48ePQ6vVokePHs7/8kiV1HTOUyu15chiscBqtbo7DAdsF5Tb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- "text": [ - "" - ] - } - ], - "prompt_number": 5 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "The posterior probabilities are represented by the curves, and our uncertainty is proportional to the width of the curve. As the plot above shows, as we start to observe data our posterior probabilities start to shift and move around. Eventually, as we observe more and more data (coin-flips), our probabilities will tighten closer and closer around the true value of $p=0.5$ (marked by a dashed line). \n", - "\n", - "Notice that the plots are not always *peaked* at 0.5. There is no reason it should be: recall we assumed we did not have a prior opinion of what $p$ is. In fact, if we observe quite extreme data, say 8 flips and only 1 observed heads, our distribution would look very biased *away* from lumping around 0.5 (with no prior opinion, how confident would you feel betting on a fair coin after observing 8 tails and 1 head). As more data accumulates, we would see more and more probability being assigned at $p=0.5$, though never all of it.\n", - "\n", - "The next example is a simple demonstration of the mathematics of Bayesian inference. " - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "##### Example: Bug, or just sweet, unintended feature?\n", - "\n", - "\n", - "Let $A$ denote the event that our code has **no bugs** in it. Let $X$ denote the event that the code passes all debugging tests. For now, we will leave the prior probability of no bugs as a variable, i.e. $P(A) = p$. \n", - "\n", - "We are interested in $P(A|X)$, i.e. the probability of no bugs, given our debugging tests $X$. To use the formula above, we need to compute some quantities.\n", - "\n", - "What is $P(X | A)$, i.e., the probability that the code passes $X$ tests *given* there are no bugs? Well, it is equal to 1, for a code with no bugs will pass all tests. \n", - "\n", - "$P(X)$ is a little bit trickier: The event $X$ can be divided into two possibilities, event $X$ occurring even though our code *indeed has* bugs (denoted $\\sim A\\;$, spoken *not $A$*), or event $X$ without bugs ($A$). $P(X)$ can be represented as:" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "\\begin{align}\n", - "P(X ) & = P(X \\text{ and } A) + P(X \\text{ and } \\sim A) \\\\\\\\[5pt]\n", - " & = P(X|A)P(A) + P(X | \\sim A)P(\\sim A)\\\\\\\\[5pt]\n", - "& = P(X|A)p + P(X | \\sim A)(1-p)\n", - "\\end{align}" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "We have already computed $P(X|A)$ above. On the other hand, $P(X | \\sim A)$ is subjective: our code can pass tests but still have a bug in it, though the probability there is a bug present is reduced. Note this is dependent on the number of tests performed, the degree of complication in the tests, etc. Let's be conservative and assign $P(X|\\sim A) = 0.5$. Then\n", - "\n", - "\\begin{align}\n", - "P(A | X) & = \\frac{1\\cdot p}{ 1\\cdot p +0.5 (1-p) } \\\\\\\\\n", - "& = \\frac{ 2 p}{1+p}\n", - "\\end{align}\n", - "This is the posterior probability. What does it look like as a function of our prior, $p \\in [0,1]$? " - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "figsize(12.5, 4)\n", - "p = np.linspace(0, 1, 50)\n", - "plt.plot(p, 2 * p / (1 + p), color=\"#348ABD\", lw=3)\n", - "# plt.fill_between(p, 2*p/(1+p), alpha=.5, facecolor=[\"#A60628\"])\n", - "plt.scatter(0.2, 2 * (0.2) / 1.2, s=140, c=\"#348ABD\")\n", - "plt.xlim(0, 1)\n", - "plt.ylim(0, 1)\n", - "plt.xlabel(\"Prior, $P(A) = p$\")\n", - "plt.ylabel(\"Posterior, $P(A|X)$, with $P(A) = p$\")\n", - "plt.title(\"Are there bugs in my code?\")" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "metadata": {}, - "output_type": "pyout", - "prompt_number": 6, - "text": [ - "" - ] - }, - { - "metadata": {}, - "output_type": "display_data", - "png": 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mBX11s67X19jLZYj2dsZYv/ZifoyPC1SO7J8fqvizhaytXz8dkpKSEB8fj7ff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\nA/gALRERERE9Ock9+ACg0+lw9uxZVFVVQa1WY9K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- "text": [ - "" - ] - } - ], - "prompt_number": 6 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "We can see the biggest gains if we observe the $X$ tests passed when the prior probability, $p$, is low. Let's settle on a specific value for the prior. I'm a strong programmer (I think), so I'm going to give myself a realistic prior of 0.20, that is, there is a 20% chance that I write code bug-free. To be more realistic, this prior should be a function of how complicated and large the code is, but let's pin it at 0.20. Then my updated belief that my code is bug-free is 0.33. \n", - "\n", - "Recall that the prior is a probability: $p$ is the prior probability that there *are no bugs*, so $1-p$ is the prior probability that there *are bugs*.\n", - "\n", - "Similarly, our posterior is also a probability, with $P(A | X)$ the probability there is no bug *given we saw all tests pass*, hence $1-P(A|X)$ is the probability there is a bug *given all tests passed*. What does our posterior probability look like? Below is a chart of both the prior and the posterior probabilities. \n" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "figsize(12.5, 4)\n", - "colours = [\"#348ABD\", \"#A60628\"]\n", - "\n", - "prior = [0.20, 0.80]\n", - "posterior = [1. / 3, 2. / 3]\n", - "plt.bar([0, .7], prior, alpha=0.70, width=0.25,\n", - " color=colours[0], label=\"prior distribution\",\n", - " lw=\"3\", edgecolor=colours[0])\n", - "\n", - "plt.bar([0 + 0.25, .7 + 0.25], posterior, alpha=0.7,\n", - " width=0.25, color=colours[1],\n", - " label=\"posterior distribution\",\n", - " lw=\"3\", edgecolor=colours[1])\n", - "\n", - "plt.xticks([0.20, .95], [\"Bugs Absent\", \"Bugs Present\"])\n", - "plt.title(\"Prior and Posterior probability of bugs present\")\n", - "plt.ylabel(\"Probability\")\n", - "plt.legend(loc=\"upper left\");" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "metadata": {}, - "output_type": "display_data", - "png": 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w8EBwcDCWLl2KqqoqHDx4EDt37tTY98qVK/jpp59QVlYGCwsL2NjYwMzMDMDt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\nx+Hq6or4+Ph654okIiIiIqKmcc+Evfa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- "text": [ - "" - ] - } - ], - "prompt_number": 7 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Notice that after we observed $X$ occur, the probability of bugs being absent increased. By increasing the number of tests, we can approach confidence (probability 1) that there are no bugs present.\n", - "\n", - "This was a very simple example of Bayesian inference and Bayes rule. Unfortunately, the mathematics necessary to perform more complicated Bayesian inference only becomes more difficult, except for artificially constructed cases. We will later see that this type of mathematical analysis is actually unnecessary. First we must broaden our modeling tools. The next section deals with *probability distributions*. If you are already familiar, feel free to skip (or at least skim), but for the less familiar the next section is essential." - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "_______\n", - "\n", - "##Probability Distributions\n", - "\n", - "\n", - "**Let's quickly recall what a probability distribution is:** Let $Z$ be some random variable. Then associated with $Z$ is a *probability distribution function* that assigns probabilities to the different outcomes $Z$ can take. Graphically, a probability distribution is a curve where the probability of an outcome is proportional to the height of the curve. You can see examples in the first figure of this chapter. \n", - "\n", - "We can divide random variables into three classifications:\n", - "\n", - "- **$Z$ is discrete**: Discrete random variables may only assume values on a specified list. Things like populations, movie ratings, and number of votes are all discrete random variables. Discrete random variables become more clear when we contrast them with...\n", - "\n", - "- **$Z$ is continuous**: Continuous random variable can take on arbitrarily exact values. For example, temperature, speed, time, color are all modeled as continuous variables because you can progressively make the values more and more precise.\n", - "\n", - "- **$Z$ is mixed**: Mixed random variables assign probabilities to both discrete and continuous random variables, i.e. it is a combination of the above two categories. \n", - "\n", - "###Discrete Case\n", - "If $Z$ is discrete, then its distribution is called a *probability mass function*, which measures the probability $Z$ takes on the value $k$, denoted $P(Z=k)$. Note that the probability mass function completely describes the random variable $Z$, that is, if we know the mass function, we know how $Z$ should behave. There are popular probability mass functions that consistently appear: we will introduce them as needed, but let's introduce the first very useful probability mass function. We say $Z$ is *Poisson*-distributed if:\n", - "\n", - "$$P(Z = k) =\\frac{ \\lambda^k e^{-\\lambda} }{k!}, \\; \\; k=0,1,2, \\dots $$\n", - "\n", - "$\\lambda$ is called a parameter of the distribution, and it controls the distribution's shape. For the Poisson distribution, $\\lambda$ can be any positive number. By increasing $\\lambda$, we add more probability to larger values, and conversely by decreasing $\\lambda$ we add more probability to smaller values. One can describe $\\lambda$ as the *intensity* of the Poisson distribution. \n", - "\n", - "Unlike $\\lambda$, which can be any positive number, the value $k$ in the above formula must be a non-negative integer, i.e., $k$ must take on values 0,1,2, and so on. This is very important, because if you wanted to model a population you could not make sense of populations with 4.25 or 5.612 members. \n", - "\n", - "If a random variable $Z$ has a Poisson mass distribution, we denote this by writing\n", - "\n", - "$$Z \\sim \\text{Poi}(\\lambda) $$\n", - "\n", - "One useful property of the Poisson distribution is that its expected value is equal to its parameter, i.e.:\n", - "\n", - "$$E\\large[ \\;Z\\; | \\; \\lambda \\;\\large] = \\lambda $$\n", - "\n", - "We will use this property often, so it's useful to remember. Below, we plot the probability mass distribution for different $\\lambda$ values. The first thing to notice is that by increasing $\\lambda$, we add more probability of larger values occurring. Second, notice that although the graph ends at 15, the distributions do not. They assign positive probability to every non-negative integer." - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "figsize(12.5, 4)\n", - "\n", - "import scipy.stats as stats\n", - "a = np.arange(16)\n", - "poi = stats.poisson\n", - "lambda_ = [1.5, 4.25]\n", - "colours = [\"#348ABD\", \"#A60628\"]\n", - "\n", - "plt.bar(a, poi.pmf(a, lambda_[0]), color=colours[0],\n", - " label=\"$\\lambda = %.1f$\" % lambda_[0], alpha=0.60,\n", - " edgecolor=colours[0], lw=\"3\")\n", - "\n", - "plt.bar(a, poi.pmf(a, lambda_[1]), color=colours[1],\n", - " label=\"$\\lambda = %.1f$\" % lambda_[1], alpha=0.60,\n", - " edgecolor=colours[1], lw=\"3\")\n", - "\n", - "plt.xticks(a + 0.4, a)\n", - "plt.legend()\n", - "plt.ylabel(\"probability of $k$\")\n", - "plt.xlabel(\"$k$\")\n", - "plt.title(\"Probability mass function of a Poisson random variable; differing \\\n", - "$\\lambda$ values\")" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "metadata": {}, - "output_type": "pyout", - "prompt_number": 8, - "text": [ - "" - ] - }, - { - "metadata": {}, - "output_type": "display_data", - "png": 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VuTwxMZFHH300oH385S9/4aabbvK9IV1ddHQ0ffr0AWDZsmVcfPHF9OvXL7jw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\nREQkAI7esZ86dSpffPEFc+fO5dxzzyU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- "text": [ - "" - ] - } - ], - "prompt_number": 8 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "###Continuous Case\n", - "Instead of a probability mass function, a continuous random variable has a *probability density function*. This might seem like unnecessary nomenclature, but the density function and the mass function are very different creatures. An example of continuous random variable is a random variable with *exponential density*. The density function for an exponential random variable looks like this:\n", - "\n", - "$$f_Z(z | \\lambda) = \\lambda e^{-\\lambda z }, \\;\\; z\\ge 0$$\n", - "\n", - "Like a Poisson random variable, an exponential random variable can take on only non-negative values. But unlike a Poisson variable, the exponential can take on *any* non-negative values, including non-integral values such as 4.25 or 5.612401. This property makes it a poor choice for count data, which must be an integer, but a great choice for time data, temperature data (measured in Kelvins, of course), or any other precise *and positive* variable. The graph below shows two probability density functions with different $\\lambda$ values. \n", - "\n", - "When a random variable $Z$ has an exponential distribution with parameter $\\lambda$, we say *$Z$ is exponential* and write\n", - "\n", - "$$Z \\sim \\text{Exp}(\\lambda)$$\n", - "\n", - "Given a specific $\\lambda$, the expected value of an exponential random variable is equal to the inverse of $\\lambda$, that is:\n", - "\n", - "$$E[\\; Z \\;|\\; \\lambda \\;] = \\frac{1}{\\lambda}$$" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "a = np.linspace(0, 4, 100)\n", - "expo = stats.expon\n", - "lambda_ = [0.5, 1]\n", - "\n", - "for l, c in zip(lambda_, colours):\n", - " plt.plot(a, expo.pdf(a, scale=1. / l), lw=3,\n", - " color=c, label=\"$\\lambda = %.1f$\" % l)\n", - " plt.fill_between(a, expo.pdf(a, scale=1. / l), color=c, alpha=.33)\n", - "\n", - "plt.legend()\n", - "plt.ylabel(\"PDF at $z$\")\n", - "plt.xlabel(\"$z$\")\n", - "plt.ylim(0, 1.2)\n", - "plt.title(\"Probability density function of an Exponential random variable;\\\n", - " differing $\\lambda$\");" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "metadata": {}, - "output_type": "display_data", - "png": 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6QRERERERWUiLL+gBQGmnQfjsv8MpMsQw78yy1bi49r9WjKrlYV+cOMytWMyv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\naQlOGgglEERTSOJLHCdOfN3r7Mx5PpyZ2V17fVv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- "text": [ - "" - ] - } - ], - "prompt_number": 12 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "\n", - "###But what is $\\lambda \\;$?\n", - "\n", - "\n", - "**This question is what motivates statistics**. In the real world, $\\lambda$ is hidden from us. We see only $Z$, and must go backwards to try and determine $\\lambda$. The problem is difficult because there is no one-to-one mapping from $Z$ to $\\lambda$. Many different methods have been created to solve the problem of estimating $\\lambda$, but since $\\lambda$ is never actually observed, no one can say for certain which method is best! \n", - "\n", - "Bayesian inference is concerned with *beliefs* about what $\\lambda$ might be. Rather than try to guess $\\lambda$ exactly, we can only talk about what $\\lambda$ is likely to be by assigning a probability distribution to $\\lambda$.\n", - "\n", - "This might seem odd at first. After all, $\\lambda$ is fixed; it is not (necessarily) random! How can we assign probabilities to values of a non-random variable? Ah, we have fallen for our old, frequentist way of thinking. Recall that under Bayesian philosophy, we *can* assign probabilities if we interpret them as beliefs. And it is entirely acceptable to have *beliefs* about the parameter $\\lambda$. \n" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "\n", - "##### Example: Inferring behaviour from text-message data\n", - "\n", - "Let's try to model a more interesting example, one that concerns the rate at which a user sends and receives text messages:\n", - "\n", - "> You are given a series of daily text-message counts from a user of your system. The data, plotted over time, appears in the chart below. You are curious to know if the user's text-messaging habits have changed over time, either gradually or suddenly. How can you model this? (This is in fact my own text-message data. Judge my popularity as you wish.)\n" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "figsize(12.5, 3.5)\n", - "count_data = np.loadtxt(\"data/txtdata.csv\")\n", - "n_count_data = len(count_data)\n", - "plt.bar(np.arange(n_count_data), count_data, color=\"#348ABD\")\n", - "plt.xlabel(\"Time (days)\")\n", - "plt.ylabel(\"count of text-msgs received\")\n", - "plt.title(\"Did the user's texting habits change over time?\")\n", - "plt.xlim(0, n_count_data);" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "metadata": {}, - "output_type": "display_data", - "png": 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h4eGBPn36QAiBdevW4eTJk6aujyTSWu+WtWDu8jB7OZi7HMxdDuYuj9ayV3V3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\ne1WD9KioKJw/fx5Vq1Z9oo3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WLMC7776rakO7d+/GypUr8eyzz8LX1xcAMHv2bEyePBkD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\nxMXFwd7evlCLBbM3nbt372LDhg149dVXCy3TQu4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- "text": [ - "" - ] - } - ], - "prompt_number": 13 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Before we start modeling, see what you can figure out just by looking at the chart above. Would you say there was a change in behaviour during this time period? \n", - "\n", - "How can we start to model this? Well, as we have conveniently already seen, a Poisson random variable is a very appropriate model for this type of *count* data. Denoting day $i$'s text-message count by $C_i$, \n", - "\n", - "$$ C_i \\sim \\text{Poisson}(\\lambda) $$\n", - "\n", - "We are not sure what the value of the $\\lambda$ parameter really is, however. Looking at the chart above, it appears that the rate might become higher late in the observation period, which is equivalent to saying that $\\lambda$ increases at some point during the observations. (Recall that a higher value of $\\lambda$ assigns more probability to larger outcomes. That is, there is a higher probability of many text messages having been sent on a given day.)\n", - "\n", - "How can we represent this observation mathematically? Let's assume that on some day during the observation period (call it $\\tau$), the parameter $\\lambda$ suddenly jumps to a higher value. So we really have two $\\lambda$ parameters: one for the period before $\\tau$, and one for the rest of the observation period. In the literature, a sudden transition like this would be called a *switchpoint*:\n", - "\n", - "$$\n", - "\\lambda = \n", - "\\begin{cases}\n", - "\\lambda_1 & \\text{if } t \\lt \\tau \\cr\n", - "\\lambda_2 & \\text{if } t \\ge \\tau\n", - "\\end{cases}\n", - "$$\n", - "\n", - "\n", - "If, in reality, no sudden change occurred and indeed $\\lambda_1 = \\lambda_2$, then the $\\lambda$s posterior distributions should look about equal.\n", - "\n", - "We are interested in inferring the unknown $\\lambda$s. To use Bayesian inference, we need to assign prior probabilities to the different possible values of $\\lambda$. What would be good prior probability distributions for $\\lambda_1$ and $\\lambda_2$? Recall that $\\lambda$ can be any positive number. As we saw earlier, the *exponential* distribution provides a continuous density function for positive numbers, so it might be a good choice for modeling $\\lambda_i$. But recall that the exponential distribution takes a parameter of its own, so we'll need to include that parameter in our model. Let's call that parameter $\\alpha$.\n", - "\n", - "\\begin{align}\n", - "&\\lambda_1 \\sim \\text{Exp}( \\alpha ) \\\\\\\n", - "&\\lambda_2 \\sim \\text{Exp}( \\alpha )\n", - "\\end{align}\n", - "\n", - "$\\alpha$ is called a *hyper-parameter* or *parent variable*. In literal terms, it is a parameter that influences other parameters. Our initial guess at $\\alpha$ does not influence the model too strongly, so we have some flexibility in our choice. A good rule of thumb is to set the exponential parameter equal to the inverse of the average of the count data. Since we're modeling $\\lambda$ using an exponential distribution, we can use the expected value identity shown earlier to get:\n", - "\n", - "$$\\frac{1}{N}\\sum_{i=0}^N \\;C_i \\approx E[\\; \\lambda \\; |\\; \\alpha ] = \\frac{1}{\\alpha}$$ \n", - "\n", - "An alternative, and something I encourage the reader to try, would be to have two priors: one for each $\\lambda_i$. Creating two exponential distributions with different $\\alpha$ values reflects our prior belief that the rate changed at some point during the observations.\n", - "\n", - "What about $\\tau$? Because of the noisiness of the data, it's difficult to pick out a priori when $\\tau$ might have occurred. Instead, we can assign a *uniform prior belief* to every possible day. This is equivalent to saying\n", - "\n", - "\\begin{align}\n", - "& \\tau \\sim \\text{DiscreteUniform(1,70) }\\\\\\\\\n", - "& \\Rightarrow P( \\tau = k ) = \\frac{1}{70}\n", - "\\end{align}\n", - "\n", - "So after all this, what does our overall prior distribution for the unknown variables look like? Frankly, *it doesn't matter*. What we should understand is that it's an ugly, complicated mess involving symbols only a mathematician could love. And things will only get uglier the more complicated our models become. Regardless, all we really care about is the posterior distribution.\n", - "\n", - "We next turn to PyMC, a Python library for performing Bayesian analysis that is undaunted by the mathematical monster we have created. \n", - "\n", - "\n", - "Introducing our first hammer: PyMC\n", - "-----\n", - "\n", - "PyMC is a Python library for programming Bayesian analysis [3]. It is a fast, well-maintained library. The only unfortunate part is that its documentation is lacking in certain areas, especially those that bridge the gap between beginner and hacker. One of this book's main goals is to solve that problem, and also to demonstrate why PyMC is so cool.\n", - "\n", - "We will model the problem above using PyMC. This type of programming is called *probabilistic programming*, an unfortunate misnomer that invokes ideas of randomly-generated code and has likely confused and frightened users away from this field. The code is not random; it is probabilistic in the sense that we create probability models using programming variables as the model's components. Model components are first-class primitives within the PyMC framework. \n", - "\n", - "B. Cronin [5] has a very motivating description of probabilistic programming:\n", - "\n", - "> Another way of thinking about this: unlike a traditional program, which only runs in the forward directions, a probabilistic program is run in both the forward and backward direction. It runs forward to compute the consequences of the assumptions it contains about the world (i.e., the model space it represents), but it also runs backward from the data to constrain the possible explanations. In practice, many probabilistic programming systems will cleverly interleave these forward and backward operations to efficiently home in on the best explanations.\n", - "\n", - "Because of the confusion engendered by the term *probabilistic programming*, I'll refrain from using it. Instead, I'll simply say *programming*, since that's what it really is. \n", - "\n", - "PyMC code is easy to read. The only novel thing should be the syntax, and I will interrupt the code to explain individual sections. Simply remember that we are representing the model's components ($\\tau, \\lambda_1, \\lambda_2$ ) as variables:" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "import pymc as pm\n", - "\n", - "alpha = 1.0 / count_data.mean() # Recall count_data is the\n", - " # variable that holds our txt counts\n", - "lambda_1 = pm.Exponential(\"lambda_1\", alpha)\n", - "lambda_2 = pm.Exponential(\"lambda_2\", alpha)\n", - "\n", - "tau = pm.DiscreteUniform(\"tau\", lower=0, upper=n_count_data)" - ], - "language": "python", - "metadata": {}, - "outputs": [], - "prompt_number": 14 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "In the code above, we create the PyMC variables corresponding to $\\lambda_1$ and $\\lambda_2$. We assign them to PyMC's *stochastic variables*, so-called because they are treated by the back end as random number generators. We can demonstrate this fact by calling their built-in `random()` methods." - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "print \"Random output:\", tau.random(), tau.random(), tau.random()" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "Random output: 39 10 32\n" - ] - } - ], - "prompt_number": 15 - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "@pm.deterministic\n", - "def lambda_(tau=tau, lambda_1=lambda_1, lambda_2=lambda_2):\n", - " out = np.zeros(n_count_data)\n", - " out[:tau] = lambda_1 # lambda before tau is lambda1\n", - " out[tau:] = lambda_2 # lambda after (and including) tau is lambda2\n", - " return out" - ], - "language": "python", - "metadata": {}, - "outputs": [], - "prompt_number": 16 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "This code creates a new function `lambda_`, but really we can think of it as a random variable: the random variable $\\lambda$ from above. Note that because `lambda_1`, `lambda_2` and `tau` are random, `lambda_` will be random. We are **not** fixing any variables yet.\n", - "\n", - "`@pm.deterministic` is a decorator that tells PyMC this is a deterministic function. That is, if the arguments were deterministic (which they are not), the output would be deterministic as well. Deterministic functions will be covered in Chapter 2. " - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "observation = pm.Poisson(\"obs\", lambda_, value=count_data, observed=True)\n", - "\n", - "model = pm.Model([observation, lambda_1, lambda_2, tau])" - ], - "language": "python", - "metadata": {}, - "outputs": [], - "prompt_number": 17 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "The variable `observation` combines our data, `count_data`, with our proposed data-generation scheme, given by the variable `lambda_`, through the `value` keyword. We also set `observed = True` to tell PyMC that this should stay fixed in our analysis. Finally, PyMC wants us to collect all the variables of interest and create a `Model` instance out of them. This makes our life easier when we retrieve the results.\n", - "\n", - "The code below will be explained in Chapter 3, but I show it here so you can see where our results come from. One can think of it as a *learning* step. The machinery being employed is called *Markov Chain Monte Carlo* (MCMC), which I also delay explaining until Chapter 3. This technique returns thousands of random variables from the posterior distributions of $\\lambda_1, \\lambda_2$ and $\\tau$. We can plot a histogram of the random variables to see what the posterior distributions look like. Below, we collect the samples (called *traces* in the MCMC literature) into histograms." - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "# Mysterious code to be explained in Chapter 3.\n", - "mcmc = pm.MCMC(model)\n", - "mcmc.sample(40000, 10000, 1)" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "output_type": "stream", - "stream": "stdout", - "text": [ - " \r", - "[****************100%******************] 40000 of 40000 complete" - ] - }, - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "\n" - ] - } - ], - "prompt_number": 18 - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "lambda_1_samples = mcmc.trace('lambda_1')[:]\n", - "lambda_2_samples = mcmc.trace('lambda_2')[:]\n", - "tau_samples = mcmc.trace('tau')[:]" - ], - "language": "python", - "metadata": {}, - "outputs": [], - "prompt_number": 21 - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "figsize(12.5, 10)\n", - "# histogram of the samples:\n", - "\n", - "ax = plt.subplot(311)\n", - "ax.set_autoscaley_on(False)\n", - "\n", - "plt.hist(lambda_1_samples, histtype='stepfilled', bins=30, alpha=0.85,\n", - " label=\"posterior of $\\lambda_1$\", color=\"#A60628\", normed=True)\n", - "plt.legend(loc=\"upper left\")\n", - "plt.title(r\"\"\"Posterior distributions of the variables\n", - " $\\lambda_1,\\;\\lambda_2,\\;\\tau$\"\"\")\n", - "plt.xlim([15, 30])\n", - "plt.xlabel(\"$\\lambda_1$ value\")\n", - "\n", - "ax = plt.subplot(312)\n", - "ax.set_autoscaley_on(False)\n", - "plt.hist(lambda_2_samples, histtype='stepfilled', bins=30, alpha=0.85,\n", - " label=\"posterior of $\\lambda_2$\", color=\"#7A68A6\", normed=True)\n", - "plt.legend(loc=\"upper left\")\n", - "plt.xlim([15, 30])\n", - "plt.xlabel(\"$\\lambda_2$ value\")\n", - "\n", - "plt.subplot(313)\n", - "w = 1.0 / tau_samples.shape[0] * np.ones_like(tau_samples)\n", - "plt.hist(tau_samples, bins=n_count_data, alpha=1,\n", - " label=r\"posterior of $\\tau$\",\n", - " color=\"#467821\", weights=w, rwidth=2.)\n", - "plt.xticks(np.arange(n_count_data))\n", - "\n", - "plt.legend(loc=\"upper left\")\n", - "plt.ylim([0, .75])\n", - "plt.xlim([35, len(count_data) - 20])\n", - "plt.xlabel(r\"$\\tau$ (in days)\")\n", - "plt.ylabel(\"probability\");" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "metadata": {}, - "output_type": "display_data", - "png": 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GDx4MBwcHLFy4EFVVVQb5+fj4ICkpCTk5ObCzszP6+MawsDAsWLAAjz/+ON5//33U1NTg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- "text": [ - "" - ] - } - ], - "prompt_number": 22 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### Interpretation\n", - "\n", - "Recall that Bayesian methodology returns a *distribution*. Hence we now have distributions to describe the unknown $\\lambda$s and $\\tau$. What have we gained? Immediately, we can see the uncertainty in our estimates: the wider the distribution, the less certain our posterior belief should be. We can also see what the plausible values for the parameters are: $\\lambda_1$ is around 18 and $\\lambda_2$ is around 23. The posterior distributions of the two $\\lambda$s are clearly distinct, indicating that it is indeed likely that there was a change in the user's text-message behaviour.\n", - "\n", - "What other observations can you make? If you look at the original data again, do these results seem reasonable? \n", - "\n", - "Notice also that the posterior distributions for the $\\lambda$s do not look like exponential distributions, even though our priors for these variables were exponential. In fact, the posterior distributions are not really of any form that we recognize from the original model. But that's OK! This is one of the benefits of taking a computational point of view. If we had instead done this analysis using mathematical approaches, we would have been stuck with an analytically intractable (and messy) distribution. Our use of a computational approach makes us indifferent to mathematical tractability.\n", - "\n", - "Our analysis also returned a distribution for $\\tau$. Its posterior distribution looks a little different from the other two because it is a discrete random variable, so it doesn't assign probabilities to intervals. We can see that near day 45, there was a 50% chance that the user's behaviour changed. Had no change occurred, or had the change been gradual over time, the posterior distribution of $\\tau$ would have been more spread out, reflecting that many days were plausible candidates for $\\tau$. By contrast, in the actual results we see that only three or four days make any sense as potential transition points. " - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "###Why would I want samples from the posterior, anyways?\n", - "\n", - "\n", - "We will deal with this question for the remainder of the book, and it is an understatement to say that it will lead us to some amazing results. For now, let's end this chapter with one more example.\n", - "\n", - "We'll use the posterior samples to answer the following question: what is the expected number of texts at day $t, \\; 0 \\le t \\le 70$ ? Recall that the expected value of a Poisson variable is equal to its parameter $\\lambda$. Therefore, the question is equivalent to *what is the expected value of $\\lambda$ at time $t$*?\n", - "\n", - "In the code below, let $i$ index samples from the posterior distributions. Given a day $t$, we average over all possible $\\lambda_i$ for that day $t$, using $\\lambda_i = \\lambda_{1,i}$ if $t \\lt \\tau_i$ (that is, if the behaviour change has not yet occurred), else we use $\\lambda_i = \\lambda_{2,i}$. " - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "figsize(12.5, 5)\n", - "# tau_samples, lambda_1_samples, lambda_2_samples contain\n", - "# N samples from the corresponding posterior distribution\n", - "N = tau_samples.shape[0]\n", - "expected_texts_per_day = np.zeros(n_count_data)\n", - "for day in range(0, n_count_data):\n", - " # ix is a bool index of all tau samples corresponding to\n", - " # the switchpoint occurring prior to value of 'day'\n", - " ix = day < tau_samples\n", - " # Each posterior sample corresponds to a value for tau.\n", - " # for each day, that value of tau indicates whether we're \"before\"\n", - " # (in the lambda1 \"regime\") or\n", - " # \"after\" (in the lambda2 \"regime\") the switchpoint.\n", - " # by taking the posterior sample of lambda1/2 accordingly, we can average\n", - " # over all samples to get an expected value for lambda on that day.\n", - " # As explained, the \"message count\" random variable is Poisson distributed,\n", - " # and therefore lambda (the poisson parameter) is the expected value of\n", - " # \"message count\".\n", - " expected_texts_per_day[day] = (lambda_1_samples[ix].sum()\n", - " + lambda_2_samples[~ix].sum()) / N\n", - "\n", - "\n", - "plt.plot(range(n_count_data), expected_texts_per_day, lw=4, color=\"#E24A33\",\n", - " label=\"expected number of text-messages received\")\n", - "plt.xlim(0, n_count_data)\n", - "plt.xlabel(\"Day\")\n", - "plt.ylabel(\"Expected # text-messages\")\n", - "plt.title(\"Expected number of text-messages received\")\n", - "plt.ylim(0, 60)\n", - "plt.bar(np.arange(len(count_data)), count_data, color=\"#348ABD\", alpha=0.65,\n", - " label=\"observed texts per day\")\n", - "\n", - "plt.legend(loc=\"upper left\");" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "metadata": {}, - "output_type": "display_data", - "png": 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h+P3334X1JyQkID09Hb169aryPTpnzhxoaWkhISEB69atw+7du2vFMDJCCCG1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\nvIeuDOYuh9nL0PvMllpVCcfB3ajfXwjH/kKox0vdvjZw4P+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- "text": [ - "" - ] - } - ], - "prompt_number": 24 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Our analysis shows strong support for believing the user's behavior did change ($\\lambda_1$ would have been close in value to $\\lambda_2$ had this not been true), and that the change was sudden rather than gradual (as demonstrated by $\\tau$'s strongly peaked posterior distribution). We can speculate what might have caused this: a cheaper text-message rate, a recent weather-to-text subscription, or perhaps a new relationship. (In fact, the 45th day corresponds to Christmas, and I moved away to Toronto the next month, leaving a girlfriend behind.)\n" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "##### Exercises\n", - "\n", - "1\\. Using `lambda_1_samples` and `lambda_2_samples`, what is the mean of the posterior distributions of $\\lambda_1$ and $\\lambda_2$?" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "# type your code here." - ], - "language": "python", - "metadata": {}, - "outputs": [], - "prompt_number": 25 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "2\\. What is the expected percentage increase in text-message rates? `hint:` compute the mean of `lambda_1_samples/lambda_2_samples`. Note that this quantity is very different from `lambda_1_samples.mean()/lambda_2_samples.mean()`." - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "# type your code here." - ], - "language": "python", - "metadata": {}, - "outputs": [], - "prompt_number": 26 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "3\\. What is the mean of $\\lambda_1$ **given** that we know $\\tau$ is less than 45. That is, suppose we have been given new information that the change in behaviour occurred prior to day 45. What is the expected value of $\\lambda_1$ now? (You do not need to redo the PyMC part. Just consider all instances where `tau_samples < 45`.)" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "# type your code here." - ], - "language": "python", - "metadata": {}, - "outputs": [], - "prompt_number": 17 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### References\n", - "\n", - "\n", - "- [1] Gelman, Andrew. N.p.. Web. 22 Jan 2013. [N is never large enough](http://andrewgelman.com/2005/07/31/n_is_never_larg/).\n", - "- [2] Norvig, Peter. 2009. [The Unreasonable Effectiveness of Data](http://static.googleusercontent.com/media/research.google.com/en//pubs/archive/35179.pdf).\n", - "- [3] Patil, A., D. Huard and C.J. Fonnesbeck. 2010. \n", - "PyMC: Bayesian Stochastic Modelling in Python. Journal of Statistical \n", - "Software, 35(4), pp. 1-81. \n", - "- [4] Jimmy Lin and Alek Kolcz. Large-Scale Machine Learning at Twitter. Proceedings of the 2012 ACM SIGMOD International Conference on Management of Data (SIGMOD 2012), pages 793-804, May 2012, Scottsdale, Arizona.\n", - "- [5] Cronin, Beau. \"Why Probabilistic Programming Matters.\" 24 Mar 2013. Google, Online Posting to Google . Web. 24 Mar. 2013. ." - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "from IPython.core.display import HTML\n", - "\n", - "\n", - "def css_styling():\n", - " styles = open(\"../styles/custom.css\", \"r\").read()\n", - " return HTML(styles)\n", - "css_styling()" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "html": [ - "\n", - "\n" - ], - "metadata": {}, - "output_type": "pyout", - "prompt_number": 1, - "text": [ - "" - ] - } - ], - "prompt_number": 1 - }, - { - "cell_type": "code", - "collapsed": false, - "input": [], - "language": "python", - "metadata": {}, - "outputs": [] - } - ], - "metadata": {} - } - ] -} +{ + "metadata": { + "name": "" + }, + "nbformat": 3, + "nbformat_minor": 0, + "worksheets": [ + { + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Probabilistic Programming\n", + "=====\n", + "and Bayesian Methods for Hackers \n", + "========\n", + "\n", + "#####Version 0.1\n", + "Welcome to *Bayesian Methods for Hackers*. The full Github repository is available at [github/Probabilistic-Programming-and-Bayesian-Methods-for-Hackers](https://github.com/CamDavidsonPilon/Probabilistic-Programming-and-Bayesian-Methods-for-Hackers). The other chapters can be found on the project's [homepage](https://camdavidsonpilon.github.io/Probabilistic-Programming-and-Bayesian-Methods-for-Hackers/). We hope you enjoy the book, and we encourage any contributions!" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Chapter 1\n", + "======\n", + "***" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The Philosophy of Bayesian Inference\n", + "------\n", + " \n", + "> You are a skilled programmer, but bugs still slip into your code. After a particularly difficult implementation of an algorithm, you decide to test your code on a trivial example. It passes. You test the code on a harder problem. It passes once again. And it passes the next, *even more difficult*, test too! You are starting to believe that there may be no bugs in this code...\n", + "\n", + "If you think this way, then congratulations, you already are thinking Bayesian! Bayesian inference is simply updating your beliefs after considering new evidence. A Bayesian can rarely be certain about a result, but he or she can be very confident. Just like in the example above, we can never be 100% sure that our code is bug-free unless we test it on every possible problem; something rarely possible in practice. Instead, we can test it on a large number of problems, and if it succeeds we can feel more *confident* about our code, but still not certain. Bayesian inference works identically: we update our beliefs about an outcome; rarely can we be absolutely sure unless we rule out all other alternatives. " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "### The Bayesian state of mind\n", + "\n", + "\n", + "Bayesian inference differs from more traditional statistical inference by preserving *uncertainty*. At first, this sounds like a bad statistical technique. Isn't statistics all about deriving *certainty* from randomness? To reconcile this, we need to start thinking like Bayesians. \n", + "\n", + "The Bayesian world-view interprets probability as measure of *believability in an event*, that is, how confident we are in an event occurring. In fact, we will see in a moment that this is the natural interpretation of probability. \n", + "\n", + "For this to be clearer, we consider an alternative interpretation of probability: *Frequentist*, known as the more *classical* version of statistics, assume that probability is the long-run frequency of events (hence the bestowed title). For example, the *probability of plane accidents* under a frequentist philosophy is interpreted as the *long-term frequency of plane accidents*. This makes logical sense for many probabilities of events, but becomes more difficult to understand when events have no long-term frequency of occurrences. Consider: we often assign probabilities to outcomes of presidential elections, but the election itself only happens once! Frequentists get around this by invoking alternative realities and saying across all these realities, the frequency of occurrences defines the probability. \n", + "\n", + "Bayesians, on the other hand, have a more intuitive approach. Bayesians interpret a probability as measure of *belief*, or confidence, of an event occurring. Simply, a probability is a summary of an opinion. An individual who assigns a belief of 0 to an event has no confidence that the event will occur; conversely, assigning a belief of 1 implies that the individual is absolutely certain of an event occurring. Beliefs between 0 and 1 allow for weightings of other outcomes. This definition agrees with the probability of a plane accident example, for having observed the frequency of plane accidents, an individual's belief should be equal to that frequency, excluding any outside information. Similarly, under this definition of probability being equal to beliefs, it is meaningful to speak about probabilities (beliefs) of presidential election outcomes: how confident are you candidate *A* will win?\n", + "\n", + "Notice in the paragraph above, I assigned the belief (probability) measure to an *individual*, not to Nature. This is very interesting, as this definition leaves room for conflicting beliefs between individuals. Again, this is appropriate for what naturally occurs: different individuals have different beliefs of events occurring, because they possess different *information* about the world. The existence of different beliefs does not imply that anyone is wrong. Consider the following examples demonstrating the relationship between individual beliefs and probabilities:\n", + "\n", + "- I flip a coin, and we both guess the result. We would both agree, assuming the coin is fair, that the probability of Heads is 1/2. Assume, then, that I peek at the coin. Now I know for certain what the result is: I assign probability 1.0 to either Heads or Tails (whichever it is). Now what is *your* belief that the coin is Heads? My knowledge of the outcome has not changed the coin's results. Thus we assign different probabilities to the result. \n", + "\n", + "- Your code either has a bug in it or not, but we do not know for certain which is true, though we have a belief about the presence or absence of a bug. \n", + "\n", + "- A medical patient is exhibiting symptoms $x$, $y$ and $z$. There are a number of diseases that could be causing all of them, but only a single disease is present. A doctor has beliefs about which disease, but a second doctor may have slightly different beliefs. \n", + "\n", + "\n", + "This philosophy of treating beliefs as probability is natural to humans. We employ it constantly as we interact with the world and only see partial truths, but gather evidence to form beliefs. Alternatively, you have to be *trained* to think like a frequentist. \n", + "\n", + "To align ourselves with traditional probability notation, we denote our belief about event $A$ as $P(A)$. We call this quantity the *prior probability*.\n", + "\n", + "John Maynard Keynes, a great economist and thinker, said \"When the facts change, I change my mind. What do you do, sir?\" This quote reflects the way a Bayesian updates his or her beliefs after seeing evidence. Even — especially — if the evidence is counter to what was initially believed, the evidence cannot be ignored. We denote our updated belief as $P(A |X )$, interpreted as the probability of $A$ given the evidence $X$. We call the updated belief the *posterior probability* so as to contrast it with the prior probability. For example, consider the posterior probabilities (read: posterior beliefs) of the above examples, after observing some evidence $X$:\n", + "\n", + "1\\. $P(A): \\;\\;$ the coin has a 50 percent chance of being Heads. $P(A | X):\\;\\;$ You look at the coin, observe a Heads has landed, denote this information $X$, and trivially assign probability 1.0 to Heads and 0.0 to Tails.\n", + "\n", + "2\\. $P(A): \\;\\;$ This big, complex code likely has a bug in it. $P(A | X): \\;\\;$ The code passed all $X$ tests; there still might be a bug, but its presence is less likely now.\n", + "\n", + "3\\. $P(A):\\;\\;$ The patient could have any number of diseases. $P(A | X):\\;\\;$ Performing a blood test generated evidence $X$, ruling out some of the possible diseases from consideration.\n", + "\n", + "\n", + "It's clear that in each example we did not completely discard the prior belief after seeing new evidence $X$, but we *re-weighted the prior* to incorporate the new evidence (i.e. we put more weight, or confidence, on some beliefs versus others). \n", + "\n", + "By introducing prior uncertainty about events, we are already admitting that any guess we make is potentially very wrong. After observing data, evidence, or other information, we update our beliefs, and our guess becomes *less wrong*. This is the alternative side of the prediction coin, where typically we try to be *more right*. \n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "### Bayesian Inference in Practice\n", + "\n", + " If frequentist and Bayesian inference were programming functions, with inputs being statistical problems, then the two would be different in what they return to the user. The frequentist inference function would return a number, representing an estimate (typically a summary statistic like the sample average etc.), whereas the Bayesian function would return *probabilities*.\n", + "\n", + "For example, in our debugging problem above, calling the frequentist function with the argument \"My code passed all $X$ tests; is my code bug-free?\" would return a *YES*. On the other hand, asking our Bayesian function \"Often my code has bugs. My code passed all $X$ tests; is my code bug-free?\" would return something very different: probabilities of *YES* and *NO*. The function might return:\n", + "\n", + "\n", + "> *YES*, with probability 0.8; *NO*, with probability 0.2\n", + "\n", + "\n", + "\n", + "This is very different from the answer the frequentist function returned. Notice that the Bayesian function accepted an additional argument: *\"Often my code has bugs\"*. This parameter is the *prior*. By including the prior parameter, we are telling the Bayesian function to include our belief about the situation. Technically this parameter in the Bayesian function is optional, but we will see excluding it has its own consequences. \n", + "\n", + "\n", + "####Incorporating evidence\n", + "\n", + "As we acquire more and more instances of evidence, our prior belief is *washed out* by the new evidence. This is to be expected. For example, if your prior belief is something ridiculous, like \"I expect the sun to explode today\", and each day you are proved wrong, you would hope that any inference would correct you, or at least align your beliefs better. Bayesian inference will correct this belief.\n", + "\n", + "\n", + "Denote $N$ as the number of instances of evidence we possess. As we gather an *infinite* amount of evidence, say as $N \\rightarrow \\infty$, our Bayesian results (often) align with frequentist results. Hence for large $N$, statistical inference is more or less objective. On the other hand, for small $N$, inference is much more *unstable*: frequentist estimates have more variance and larger confidence intervals. This is where Bayesian analysis excels. By introducing a prior, and returning probabilities (instead of a scalar estimate), we *preserve the uncertainty* that reflects the instability of statistical inference of a small $N$ dataset. \n", + "\n", + "One may think that for large $N$, one can be indifferent between the two techniques since they offer similar inference, and might lean towards the computationally-simpler, frequentist methods. An individual in this position should consider the following quote by Andrew Gelman (2005)[1], before making such a decision:\n", + "\n", + "> Sample sizes are never large. If $N$ is too small to get a sufficiently-precise estimate, you need to get more data (or make more assumptions). But once $N$ is \"large enough,\" you can start subdividing the data to learn more (for example, in a public opinion poll, once you have a good estimate for the entire country, you can estimate among men and women, northerners and southerners, different age groups, etc.). $N$ is never enough because if it were \"enough\" you'd already be on to the next problem for which you need more data.\n", + "\n", + "### Are frequentist methods incorrect then? \n", + "\n", + "**No.**\n", + "\n", + "Frequentist methods are still useful or state-of-the-art in many areas. Tools such as least squares linear regression, LASSO regression, and expectation-maximization algorithms are all powerful and fast. Bayesian methods complement these techniques by solving problems that these approaches cannot, or by illuminating the underlying system with more flexible modeling.\n", + "\n", + "\n", + "#### A note on *Big Data*\n", + "Paradoxically, big data's predictive analytic problems are actually solved by relatively simple algorithms [2][4]. Thus we can argue that big data's prediction difficulty does not lie in the algorithm used, but instead on the computational difficulties of storage and execution on big data. (One should also consider Gelman's quote from above and ask \"Do I really have big data?\" )\n", + "\n", + "The much more difficult analytic problems involve *medium data* and, especially troublesome, *really small data*. Using a similar argument as Gelman's above, if big data problems are *big enough* to be readily solved, then we should be more interested in the *not-quite-big enough* datasets. \n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Our Bayesian framework\n", + "\n", + "We are interested in beliefs, which can be interpreted as probabilities by thinking Bayesian. We have a *prior* belief in event $A$, beliefs formed by previous information, e.g., our prior belief about bugs being in our code before performing tests.\n", + "\n", + "Secondly, we observe our evidence. To continue our buggy-code example: if our code passes $X$ tests, we want to update our belief to incorporate this. We call this new belief the *posterior* probability. Updating our belief is done via the following equation, known as Bayes' Theorem, after its discoverer Thomas Bayes:\n", + "\n", + "\\begin{align}\n", + " P( A | X ) = & \\frac{ P(X | A) P(A) } {P(X) } \\\\\\\\[5pt]\n", + "& \\propto P(X | A) P(A)\\;\\; (\\propto \\text{is proportional to } )\n", + "\\end{align}\n", + "\n", + "The above formula is not unique to Bayesian inference: it is a mathematical fact with uses outside Bayesian inference. Bayesian inference merely uses it to connect prior probabilities $P(A)$ with an updated posterior probabilities $P(A | X )$." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "##### Example: Mandatory coin-flip example\n", + "\n", + "Every statistics text must contain a coin-flipping example, I'll use it here to get it out of the way. Suppose, naively, that you are unsure about the probability of heads in a coin flip (spoiler alert: it's 50%). You believe there is some true underlying ratio, call it $p$, but have no prior opinion on what $p$ might be. \n", + "\n", + "We begin to flip a coin, and record the observations: either $H$ or $T$. This is our observed data. An interesting question to ask is how our inference changes as we observe more and more data? More specifically, what do our posterior probabilities look like when we have little data, versus when we have lots of data. \n", + "\n", + "Below we plot a sequence of updating posterior probabilities as we observe increasing amounts of data (coin flips)." + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\"\"\"\n", + "The book uses a custom matplotlibrc file, which provides the unique styles for\n", + "matplotlib plots. If executing this book, and you wish to use the book's\n", + "styling, provided are two options:\n", + " 1. Overwrite your own matplotlibrc file with the rc-file provided in the\n", + " book's styles/ dir. See http://matplotlib.org/users/customizing.html\n", + " 2. Also in the styles is bmh_matplotlibrc.json file. This can be used to\n", + " update the styles in only this notebook. Try running the following code:\n", + "\n", + " import json, matplotlib\n", + " s = json.load( open(\"../styles/bmh_matplotlibrc.json\") )\n", + " matplotlib.rcParams.update(s)\n", + "\n", + "\"\"\"\n", + "\n", + "# The code below can be passed over, as it is currently not important, plus it\n", + "# uses advanced topics we have not covered yet. LOOK AT PICTURE, MICHAEL!\n", + "%matplotlib inline\n", + "from IPython.core.pylabtools import figsize\n", + "import numpy as np\n", + "from matplotlib import pyplot as plt\n", + "figsize(11, 9)\n", + "\n", + "import scipy.stats as stats\n", + "\n", + "dist = stats.beta\n", + "n_trials = [0, 1, 2, 3, 4, 5, 8, 15, 50, 500]\n", + "data = stats.bernoulli.rvs(0.5, size=n_trials[-1])\n", + "x = np.linspace(0, 1, 100)\n", + "\n", + "# For the already prepared, I'm using Binomial's conj. prior.\n", + "for k, N in enumerate(n_trials):\n", + " sx = plt.subplot(len(n_trials) / 2, 2, k + 1)\n", + " plt.xlabel(\"$p$, probability of heads\") \\\n", + " if k in [0, len(n_trials) - 1] else None\n", + " plt.setp(sx.get_yticklabels(), visible=False)\n", + " heads = data[:N].sum()\n", + " y = dist.pdf(x, 1 + heads, 1 + N - heads)\n", + " plt.plot(x, y, label=\"observe %d tosses,\\n %d heads\" % (N, heads))\n", + " plt.fill_between(x, 0, y, color=\"#348ABD\", alpha=0.4)\n", + " plt.vlines(0.5, 0, 4, color=\"k\", linestyles=\"--\", lw=1)\n", + "\n", + " leg = plt.legend()\n", + " leg.get_frame().set_alpha(0.4)\n", + " plt.autoscale(tight=True)\n", + "\n", + "\n", + "plt.suptitle(\"Bayesian updating of posterior probabilities\",\n", + " y=1.02,\n", + " fontsize=14)\n", + "\n", + "plt.tight_layout()" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "display_data", + "png": 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fSy70ej3OnDmD48ePQ6vVokePHs7/8kiV1HTOUyu15chiscBqtbo7DAdsF5Tb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+ "text": [ + "" + ] + } + ], + "prompt_number": 5 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The posterior probabilities are represented by the curves, and our uncertainty is proportional to the width of the curve. As the plot above shows, as we start to observe data our posterior probabilities start to shift and move around. Eventually, as we observe more and more data (coin-flips), our probabilities will tighten closer and closer around the true value of $p=0.5$ (marked by a dashed line). \n", + "\n", + "Notice that the plots are not always *peaked* at 0.5. There is no reason it should be: recall we assumed we did not have a prior opinion of what $p$ is. In fact, if we observe quite extreme data, say 8 flips and only 1 observed heads, our distribution would look very biased *away* from lumping around 0.5 (with no prior opinion, how confident would you feel betting on a fair coin after observing 8 tails and 1 head). As more data accumulates, we would see more and more probability being assigned at $p=0.5$, though never all of it.\n", + "\n", + "The next example is a simple demonstration of the mathematics of Bayesian inference. " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "##### Example: Bug, or just sweet, unintended feature?\n", + "\n", + "\n", + "Let $A$ denote the event that our code has **no bugs** in it. Let $X$ denote the event that the code passes all debugging tests. For now, we will leave the prior probability of no bugs as a variable, i.e. $P(A) = p$. \n", + "\n", + "We are interested in $P(A|X)$, i.e. the probability of no bugs, given our debugging tests $X$. To use the formula above, we need to compute some quantities.\n", + "\n", + "What is $P(X | A)$, i.e., the probability that the code passes $X$ tests *given* there are no bugs? Well, it is equal to 1, for a code with no bugs will pass all tests. \n", + "\n", + "$P(X)$ is a little bit trickier: The event $X$ can be divided into two possibilities, event $X$ occurring even though our code *indeed has* bugs (denoted $\\sim A\\;$, spoken *not $A$*), or event $X$ without bugs ($A$). $P(X)$ can be represented as:" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\\begin{align}\n", + "P(X ) & = P(X \\text{ and } A) + P(X \\text{ and } \\sim A) \\\\\\\\[5pt]\n", + " & = P(X|A)P(A) + P(X | \\sim A)P(\\sim A)\\\\\\\\[5pt]\n", + "& = P(X|A)p + P(X | \\sim A)(1-p)\n", + "\\end{align}" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We have already computed $P(X|A)$ above. On the other hand, $P(X | \\sim A)$ is subjective: our code can pass tests but still have a bug in it, though the probability there is a bug present is reduced. Note this is dependent on the number of tests performed, the degree of complication in the tests, etc. Let's be conservative and assign $P(X|\\sim A) = 0.5$. Then\n", + "\n", + "\\begin{align}\n", + "P(A | X) & = \\frac{1\\cdot p}{ 1\\cdot p +0.5 (1-p) } \\\\\\\\\n", + "& = \\frac{ 2 p}{1+p}\n", + "\\end{align}\n", + "This is the posterior probability. What does it look like as a function of our prior, $p \\in [0,1]$? " + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "figsize(12.5, 4)\n", + "p = np.linspace(0, 1, 50)\n", + "plt.plot(p, 2 * p / (1 + p), color=\"#348ABD\", lw=3)\n", + "# plt.fill_between(p, 2*p/(1+p), alpha=.5, facecolor=[\"#A60628\"])\n", + "plt.scatter(0.2, 2 * (0.2) / 1.2, s=140, c=\"#348ABD\")\n", + "plt.xlim(0, 1)\n", + "plt.ylim(0, 1)\n", + "plt.xlabel(\"Prior, $P(A) = p$\")\n", + "plt.ylabel(\"Posterior, $P(A|X)$, with $P(A) = p$\")\n", + "plt.title(\"Are there bugs in my code?\")" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "pyout", + "prompt_number": 6, + "text": [ + "" + ] + }, + { + "metadata": {}, + "output_type": "display_data", + "png": 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mBX11s67X19jLZYj2dsZYv/ZifoyPC1SO7J8fqvizhaytXz8dkpKSEB8fj7ff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\nuNDlDn51dTWCg4MNxsS26ABAdnZ2518IvvjiC7z77rui5hE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+ "text": [ + "" + ] + } + ], + "prompt_number": 6 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We can see the biggest gains if we observe the $X$ tests passed when the prior probability, $p$, is low. Let's settle on a specific value for the prior. I'm a strong programmer (I think), so I'm going to give myself a realistic prior of 0.20, that is, there is a 20% chance that I write code bug-free. To be more realistic, this prior should be a function of how complicated and large the code is, but let's pin it at 0.20. Then my updated belief that my code is bug-free is 0.33. \n", + "\n", + "Recall that the prior is a probability: $p$ is the prior probability that there *are no bugs*, so $1-p$ is the prior probability that there *are bugs*.\n", + "\n", + "Similarly, our posterior is also a probability, with $P(A | X)$ the probability there is no bug *given we saw all tests pass*, hence $1-P(A|X)$ is the probability there is a bug *given all tests passed*. What does our posterior probability look like? Below is a chart of both the prior and the posterior probabilities. \n" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "figsize(12.5, 4)\n", + "colours = [\"#348ABD\", \"#A60628\"]\n", + "\n", + "prior = [0.20, 0.80]\n", + "posterior = [1. / 3, 2. / 3]\n", + "plt.bar([0, .7], prior, alpha=0.70, width=0.25,\n", + " color=colours[0], label=\"prior distribution\",\n", + " lw=\"3\", edgecolor=colours[0])\n", + "\n", + "plt.bar([0 + 0.25, .7 + 0.25], posterior, alpha=0.7,\n", + " width=0.25, color=colours[1],\n", + " label=\"posterior distribution\",\n", + " lw=\"3\", edgecolor=colours[1])\n", + "\n", + "plt.xticks([0.20, .95], [\"Bugs Absent\", \"Bugs Present\"])\n", + "plt.title(\"Prior and Posterior probability of bugs present\")\n", + "plt.ylabel(\"Probability\")\n", + "plt.legend(loc=\"upper left\");" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "display_data", + "png": 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w8EBwcDCWLl2KqqoqHDx4EDt37tTY98qVK/jpp59QVlYGCwsL2NjYwMzMDMDt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\nuwBwyy23YLPZ+O6773jrrbd4+eWX3T5mZWUl6en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+ "text": [ + "" + ] + } + ], + "prompt_number": 7 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Notice that after we observed $X$ occur, the probability of bugs being absent increased. By increasing the number of tests, we can approach confidence (probability 1) that there are no bugs present.\n", + "\n", + "This was a very simple example of Bayesian inference and Bayes rule. Unfortunately, the mathematics necessary to perform more complicated Bayesian inference only becomes more difficult, except for artificially constructed cases. We will later see that this type of mathematical analysis is actually unnecessary. First we must broaden our modeling tools. The next section deals with *probability distributions*. If you are already familiar, feel free to skip (or at least skim), but for the less familiar the next section is essential." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "_______\n", + "\n", + "##Probability Distributions\n", + "\n", + "\n", + "**Let's quickly recall what a probability distribution is:** Let $Z$ be some random variable. Then associated with $Z$ is a *probability distribution function* that assigns probabilities to the different outcomes $Z$ can take. Graphically, a probability distribution is a curve where the probability of an outcome is proportional to the height of the curve. You can see examples in the first figure of this chapter. \n", + "\n", + "We can divide random variables into three classifications:\n", + "\n", + "- **$Z$ is discrete**: Discrete random variables may only assume values on a specified list. Things like populations, movie ratings, and number of votes are all discrete random variables. Discrete random variables become more clear when we contrast them with...\n", + "\n", + "- **$Z$ is continuous**: Continuous random variable can take on arbitrarily exact values. For example, temperature, speed, time, color are all modeled as continuous variables because you can progressively make the values more and more precise.\n", + "\n", + "- **$Z$ is mixed**: Mixed random variables assign probabilities to both discrete and continuous random variables, i.e. it is a combination of the above two categories. \n", + "\n", + "###Discrete Case\n", + "If $Z$ is discrete, then its distribution is called a *probability mass function*, which measures the probability $Z$ takes on the value $k$, denoted $P(Z=k)$. Note that the probability mass function completely describes the random variable $Z$, that is, if we know the mass function, we know how $Z$ should behave. There are popular probability mass functions that consistently appear: we will introduce them as needed, but let's introduce the first very useful probability mass function. We say $Z$ is *Poisson*-distributed if:\n", + "\n", + "$$P(Z = k) =\\frac{ \\lambda^k e^{-\\lambda} }{k!}, \\; \\; k=0,1,2, \\dots $$\n", + "\n", + "$\\lambda$ is called a parameter of the distribution, and it controls the distribution's shape. For the Poisson distribution, $\\lambda$ can be any positive number. By increasing $\\lambda$, we add more probability to larger values, and conversely by decreasing $\\lambda$ we add more probability to smaller values. One can describe $\\lambda$ as the *intensity* of the Poisson distribution. \n", + "\n", + "Unlike $\\lambda$, which can be any positive number, the value $k$ in the above formula must be a non-negative integer, i.e., $k$ must take on values 0,1,2, and so on. This is very important, because if you wanted to model a population you could not make sense of populations with 4.25 or 5.612 members. \n", + "\n", + "If a random variable $Z$ has a Poisson mass distribution, we denote this by writing\n", + "\n", + "$$Z \\sim \\text{Poi}(\\lambda) $$\n", + "\n", + "One useful property of the Poisson distribution is that its expected value is equal to its parameter, i.e.:\n", + "\n", + "$$E\\large[ \\;Z\\; | \\; \\lambda \\;\\large] = \\lambda $$\n", + "\n", + "We will use this property often, so it's useful to remember. Below, we plot the probability mass distribution for different $\\lambda$ values. The first thing to notice is that by increasing $\\lambda$, we add more probability of larger values occurring. Second, notice that although the graph ends at 15, the distributions do not. They assign positive probability to every non-negative integer." + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "figsize(12.5, 4)\n", + "\n", + "import scipy.stats as stats\n", + "a = np.arange(16)\n", + "poi = stats.poisson\n", + "lambda_ = [1.5, 4.25]\n", + "colours = [\"#348ABD\", \"#A60628\"]\n", + "\n", + "plt.bar(a, poi.pmf(a, lambda_[0]), color=colours[0],\n", + " label=\"$\\lambda = %.1f$\" % lambda_[0], alpha=0.60,\n", + " edgecolor=colours[0], lw=\"3\")\n", + "\n", + "plt.bar(a, poi.pmf(a, lambda_[1]), color=colours[1],\n", + " label=\"$\\lambda = %.1f$\" % lambda_[1], alpha=0.60,\n", + " edgecolor=colours[1], lw=\"3\")\n", + "\n", + "plt.xticks(a + 0.4, a)\n", + "plt.legend()\n", + "plt.ylabel(\"probability of $k$\")\n", + "plt.xlabel(\"$k$\")\n", + "plt.title(\"Probability mass function of a Poisson random variable; differing \\\n", + "$\\lambda$ values\")" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "pyout", + "prompt_number": 8, + "text": [ + "" + ] + }, + { + "metadata": {}, + "output_type": "display_data", + "png": 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VuTwxMZFHH300oH385S9/4aabbvK9IV1ddHQ0ffr0AWDZsmVcfPHF9OvXL7jw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\n9i2jw9oQXXiKZi2aUzEsBUbY+QEr4s/hk6XkHy0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+ "text": [ + "" + ] + } + ], + "prompt_number": 8 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "###Continuous Case\n", + "Instead of a probability mass function, a continuous random variable has a *probability density function*. This might seem like unnecessary nomenclature, but the density function and the mass function are very different creatures. An example of continuous random variable is a random variable with *exponential density*. The density function for an exponential random variable looks like this:\n", + "\n", + "$$f_Z(z | \\lambda) = \\lambda e^{-\\lambda z }, \\;\\; z\\ge 0$$\n", + "\n", + "Like a Poisson random variable, an exponential random variable can take on only non-negative values. But unlike a Poisson variable, the exponential can take on *any* non-negative values, including non-integral values such as 4.25 or 5.612401. This property makes it a poor choice for count data, which must be an integer, but a great choice for time data, temperature data (measured in Kelvins, of course), or any other precise *and positive* variable. The graph below shows two probability density functions with different $\\lambda$ values. \n", + "\n", + "When a random variable $Z$ has an exponential distribution with parameter $\\lambda$, we say *$Z$ is exponential* and write\n", + "\n", + "$$Z \\sim \\text{Exp}(\\lambda)$$\n", + "\n", + "Given a specific $\\lambda$, the expected value of an exponential random variable is equal to the inverse of $\\lambda$, that is:\n", + "\n", + "$$E[\\; Z \\;|\\; \\lambda \\;] = \\frac{1}{\\lambda}$$" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "a = np.linspace(0, 4, 100)\n", + "expo = stats.expon\n", + "lambda_ = [0.5, 1]\n", + "\n", + "for l, c in zip(lambda_, colours):\n", + " plt.plot(a, expo.pdf(a, scale=1. / l), lw=3,\n", + " color=c, label=\"$\\lambda = %.1f$\" % l)\n", + " plt.fill_between(a, expo.pdf(a, scale=1. / l), color=c, alpha=.33)\n", + "\n", + "plt.legend()\n", + "plt.ylabel(\"PDF at $z$\")\n", + "plt.xlabel(\"$z$\")\n", + "plt.ylim(0, 1.2)\n", + "plt.title(\"Probability density function of an Exponential random variable;\\\n", + " differing $\\lambda$\");" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "display_data", + "png": 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6QRERERERWUiLL+gBQGmnQfjsv8MpMsQw78yy1bi49r9WjKrlYV+cOMytWMyv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\naQlOGgglEERTSOJLHCdOfN3r7Mx5PpyZ2V17fVv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+ "text": [ + "" + ] + } + ], + "prompt_number": 12 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "###But what is $\\lambda \\;$?\n", + "\n", + "\n", + "**This question is what motivates statistics**. In the real world, $\\lambda$ is hidden from us. We see only $Z$, and must go backwards to try and determine $\\lambda$. The problem is difficult because there is no one-to-one mapping from $Z$ to $\\lambda$. Many different methods have been created to solve the problem of estimating $\\lambda$, but since $\\lambda$ is never actually observed, no one can say for certain which method is best! \n", + "\n", + "Bayesian inference is concerned with *beliefs* about what $\\lambda$ might be. Rather than try to guess $\\lambda$ exactly, we can only talk about what $\\lambda$ is likely to be by assigning a probability distribution to $\\lambda$.\n", + "\n", + "This might seem odd at first. After all, $\\lambda$ is fixed; it is not (necessarily) random! How can we assign probabilities to values of a non-random variable? Ah, we have fallen for our old, frequentist way of thinking. Recall that under Bayesian philosophy, we *can* assign probabilities if we interpret them as beliefs. And it is entirely acceptable to have *beliefs* about the parameter $\\lambda$. \n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "##### Example: Inferring behaviour from text-message data\n", + "\n", + "Let's try to model a more interesting example, one that concerns the rate at which a user sends and receives text messages:\n", + "\n", + "> You are given a series of daily text-message counts from a user of your system. The data, plotted over time, appears in the chart below. You are curious to know if the user's text-messaging habits have changed over time, either gradually or suddenly. How can you model this? (This is in fact my own text-message data. Judge my popularity as you wish.)\n" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "figsize(12.5, 3.5)\n", + "count_data = np.loadtxt(\"data/txtdata.csv\")\n", + "n_count_data = len(count_data)\n", + "plt.bar(np.arange(n_count_data), count_data, color=\"#348ABD\")\n", + "plt.xlabel(\"Time (days)\")\n", + "plt.ylabel(\"count of text-msgs received\")\n", + "plt.title(\"Did the user's texting habits change over time?\")\n", + "plt.xlim(0, n_count_data);" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "display_data", + "png": 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h4eGBPn36QAiBdevW4eTJk6aujyTSWu+WtWDu8jB7OZi7HMxdDuYuj9ayV3V3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\ne1WD9KioKJw/fx5Vq1Z9oo3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WLMC7776rakO7d+/GypUr8eyzz8LX1xcAMHv2bEyePBkD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\nxMXFwd7evlCLBbM3nbt372LDhg149dVXCy3TQu4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+ "text": [ + "" + ] + } + ], + "prompt_number": 13 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Before we start modeling, see what you can figure out just by looking at the chart above. Would you say there was a change in behaviour during this time period? \n", + "\n", + "How can we start to model this? Well, as we have conveniently already seen, a Poisson random variable is a very appropriate model for this type of *count* data. Denoting day $i$'s text-message count by $C_i$, \n", + "\n", + "$$ C_i \\sim \\text{Poisson}(\\lambda) $$\n", + "\n", + "We are not sure what the value of the $\\lambda$ parameter really is, however. Looking at the chart above, it appears that the rate might become higher late in the observation period, which is equivalent to saying that $\\lambda$ increases at some point during the observations. (Recall that a higher value of $\\lambda$ assigns more probability to larger outcomes. That is, there is a higher probability of many text messages having been sent on a given day.)\n", + "\n", + "How can we represent this observation mathematically? Let's assume that on some day during the observation period (call it $\\tau$), the parameter $\\lambda$ suddenly jumps to a higher value. So we really have two $\\lambda$ parameters: one for the period before $\\tau$, and one for the rest of the observation period. In the literature, a sudden transition like this would be called a *switchpoint*:\n", + "\n", + "$$\n", + "\\lambda = \n", + "\\begin{cases}\n", + "\\lambda_1 & \\text{if } t \\lt \\tau \\cr\n", + "\\lambda_2 & \\text{if } t \\ge \\tau\n", + "\\end{cases}\n", + "$$\n", + "\n", + "\n", + "If, in reality, no sudden change occurred and indeed $\\lambda_1 = \\lambda_2$, then the $\\lambda$s posterior distributions should look about equal.\n", + "\n", + "We are interested in inferring the unknown $\\lambda$s. To use Bayesian inference, we need to assign prior probabilities to the different possible values of $\\lambda$. What would be good prior probability distributions for $\\lambda_1$ and $\\lambda_2$? Recall that $\\lambda$ can be any positive number. As we saw earlier, the *exponential* distribution provides a continuous density function for positive numbers, so it might be a good choice for modeling $\\lambda_i$. But recall that the exponential distribution takes a parameter of its own, so we'll need to include that parameter in our model. Let's call that parameter $\\alpha$.\n", + "\n", + "\\begin{align}\n", + "&\\lambda_1 \\sim \\text{Exp}( \\alpha ) \\\\\\\n", + "&\\lambda_2 \\sim \\text{Exp}( \\alpha )\n", + "\\end{align}\n", + "\n", + "$\\alpha$ is called a *hyper-parameter* or *parent variable*. In literal terms, it is a parameter that influences other parameters. Our initial guess at $\\alpha$ does not influence the model too strongly, so we have some flexibility in our choice. A good rule of thumb is to set the exponential parameter equal to the inverse of the average of the count data. Since we're modeling $\\lambda$ using an exponential distribution, we can use the expected value identity shown earlier to get:\n", + "\n", + "$$\\frac{1}{N}\\sum_{i=0}^N \\;C_i \\approx E[\\; \\lambda \\; |\\; \\alpha ] = \\frac{1}{\\alpha}$$ \n", + "\n", + "An alternative, and something I encourage the reader to try, would be to have two priors: one for each $\\lambda_i$. Creating two exponential distributions with different $\\alpha$ values reflects our prior belief that the rate changed at some point during the observations.\n", + "\n", + "What about $\\tau$? Because of the noisiness of the data, it's difficult to pick out a priori when $\\tau$ might have occurred. Instead, we can assign a *uniform prior belief* to every possible day. This is equivalent to saying\n", + "\n", + "\\begin{align}\n", + "& \\tau \\sim \\text{DiscreteUniform(1,70) }\\\\\\\\\n", + "& \\Rightarrow P( \\tau = k ) = \\frac{1}{70}\n", + "\\end{align}\n", + "\n", + "So after all this, what does our overall prior distribution for the unknown variables look like? Frankly, *it doesn't matter*. What we should understand is that it's an ugly, complicated mess involving symbols only a mathematician could love. And things will only get uglier the more complicated our models become. Regardless, all we really care about is the posterior distribution.\n", + "\n", + "We next turn to PyMC, a Python library for performing Bayesian analysis that is undaunted by the mathematical monster we have created. \n", + "\n", + "\n", + "Introducing our first hammer: PyMC\n", + "-----\n", + "\n", + "PyMC is a Python library for programming Bayesian analysis [3]. It is a fast, well-maintained library. The only unfortunate part is that its documentation is lacking in certain areas, especially those that bridge the gap between beginner and hacker. One of this book's main goals is to solve that problem, and also to demonstrate why PyMC is so cool.\n", + "\n", + "We will model the problem above using PyMC. This type of programming is called *probabilistic programming*, an unfortunate misnomer that invokes ideas of randomly-generated code and has likely confused and frightened users away from this field. The code is not random; it is probabilistic in the sense that we create probability models using programming variables as the model's components. Model components are first-class primitives within the PyMC framework. \n", + "\n", + "B. Cronin [5] has a very motivating description of probabilistic programming:\n", + "\n", + "> Another way of thinking about this: unlike a traditional program, which only runs in the forward directions, a probabilistic program is run in both the forward and backward direction. It runs forward to compute the consequences of the assumptions it contains about the world (i.e., the model space it represents), but it also runs backward from the data to constrain the possible explanations. In practice, many probabilistic programming systems will cleverly interleave these forward and backward operations to efficiently home in on the best explanations.\n", + "\n", + "Because of the confusion engendered by the term *probabilistic programming*, I'll refrain from using it. Instead, I'll simply say *programming*, since that's what it really is. \n", + "\n", + "PyMC code is easy to read. The only novel thing should be the syntax, and I will interrupt the code to explain individual sections. Simply remember that we are representing the model's components ($\\tau, \\lambda_1, \\lambda_2$ ) as variables:" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import pymc as pm\n", + "\n", + "alpha = 1.0 / count_data.mean() # Recall count_data is the\n", + " # variable that holds our txt counts\n", + "lambda_1 = pm.Exponential(\"lambda_1\", alpha)\n", + "lambda_2 = pm.Exponential(\"lambda_2\", alpha)\n", + "\n", + "tau = pm.DiscreteUniform(\"tau\", lower=0, upper=n_count_data)" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 14 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "In the code above, we create the PyMC variables corresponding to $\\lambda_1$ and $\\lambda_2$. We assign them to PyMC's *stochastic variables*, so-called because they are treated by the back end as random number generators. We can demonstrate this fact by calling their built-in `random()` methods." + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "print \"Random output:\", tau.random(), tau.random(), tau.random()" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Random output: 39 10 32\n" + ] + } + ], + "prompt_number": 15 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "@pm.deterministic\n", + "def lambda_(tau=tau, lambda_1=lambda_1, lambda_2=lambda_2):\n", + " out = np.zeros(n_count_data)\n", + " out[:tau] = lambda_1 # lambda before tau is lambda1\n", + " out[tau:] = lambda_2 # lambda after (and including) tau is lambda2\n", + " return out" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 16 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "This code creates a new function `lambda_`, but really we can think of it as a random variable: the random variable $\\lambda$ from above. Note that because `lambda_1`, `lambda_2` and `tau` are random, `lambda_` will be random. We are **not** fixing any variables yet.\n", + "\n", + "`@pm.deterministic` is a decorator that tells PyMC this is a deterministic function. That is, if the arguments were deterministic (which they are not), the output would be deterministic as well. Deterministic functions will be covered in Chapter 2. " + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "observation = pm.Poisson(\"obs\", lambda_, value=count_data, observed=True)\n", + "\n", + "model = pm.Model([observation, lambda_1, lambda_2, tau])" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 17 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The variable `observation` combines our data, `count_data`, with our proposed data-generation scheme, given by the variable `lambda_`, through the `value` keyword. We also set `observed = True` to tell PyMC that this should stay fixed in our analysis. Finally, PyMC wants us to collect all the variables of interest and create a `Model` instance out of them. This makes our life easier when we retrieve the results.\n", + "\n", + "The code below will be explained in Chapter 3, but I show it here so you can see where our results come from. One can think of it as a *learning* step. The machinery being employed is called *Markov Chain Monte Carlo* (MCMC), which I also delay explaining until Chapter 3. This technique returns thousands of random variables from the posterior distributions of $\\lambda_1, \\lambda_2$ and $\\tau$. We can plot a histogram of the random variables to see what the posterior distributions look like. Below, we collect the samples (called *traces* in the MCMC literature) into histograms." + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# Mysterious code to be explained in Chapter 3.\n", + "mcmc = pm.MCMC(model)\n", + "mcmc.sample(40000, 10000, 1)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + " \r", + "[****************100%******************] 40000 of 40000 complete" + ] + }, + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "\n" + ] + } + ], + "prompt_number": 18 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "lambda_1_samples = mcmc.trace('lambda_1')[:]\n", + "lambda_2_samples = mcmc.trace('lambda_2')[:]\n", + "tau_samples = mcmc.trace('tau')[:]" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 21 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "figsize(12.5, 10)\n", + "# histogram of the samples:\n", + "\n", + "ax = plt.subplot(311)\n", + "ax.set_autoscaley_on(False)\n", + "\n", + "plt.hist(lambda_1_samples, histtype='stepfilled', bins=30, alpha=0.85,\n", + " label=\"posterior of $\\lambda_1$\", color=\"#A60628\", normed=True)\n", + "plt.legend(loc=\"upper left\")\n", + "plt.title(r\"\"\"Posterior distributions of the variables\n", + " $\\lambda_1,\\;\\lambda_2,\\;\\tau$\"\"\")\n", + "plt.xlim([15, 30])\n", + "plt.xlabel(\"$\\lambda_1$ value\")\n", + "\n", + "ax = plt.subplot(312)\n", + "ax.set_autoscaley_on(False)\n", + "plt.hist(lambda_2_samples, histtype='stepfilled', bins=30, alpha=0.85,\n", + " label=\"posterior of $\\lambda_2$\", color=\"#7A68A6\", normed=True)\n", + "plt.legend(loc=\"upper left\")\n", + "plt.xlim([15, 30])\n", + "plt.xlabel(\"$\\lambda_2$ value\")\n", + "\n", + "plt.subplot(313)\n", + "w = 1.0 / tau_samples.shape[0] * np.ones_like(tau_samples)\n", + "plt.hist(tau_samples, bins=n_count_data, alpha=1,\n", + " label=r\"posterior of $\\tau$\",\n", + " color=\"#467821\", weights=w, rwidth=2.)\n", + "plt.xticks(np.arange(n_count_data))\n", + "\n", + "plt.legend(loc=\"upper left\")\n", + "plt.ylim([0, .75])\n", + "plt.xlim([35, len(count_data) - 20])\n", + "plt.xlabel(r\"$\\tau$ (in days)\")\n", + "plt.ylabel(\"probability\");" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "display_data", + "png": 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GDx4MBwcHLFy4EFVVVQb5+fj4ICkpCTk5ObCzszP6+MawsDAsWLAAjz/+ON5//33U1NTg\n5ZdfhlarxeOPP17vem+Xyc2GDx+O0NBQhIWF4eOPP0bbtm3x3nvvobKyEtOnT9evZ+x8uJmvry8K\nCgqQnJwMPz8/tGnTBnZ2drfd1sHBAW+88QbeeOMNKIqC4cOHo7q6GmlpaThy5AiWLFlictt27drh\n4YcfxltvvYWjR4/qh9kAgIuLCzp06IDVq1fD19cXxcXFePXVV2FnZ3fb7+Vm/v7+UBQFH3zwAcLC\nwnD06FG89957RteNjIxEp06d4O3tjQ8//BAlJSWYMWOG0XWffPJJLF++HA8//DAWLlwIf39/FBYW\nIjExEd26dcO4ceMa/JoSkQTmGZpPRM3Fs88+W+epNTd7//33hY+Pj7CxsRH33nuvwZMqTpw4IcaM\nGSM6deokbG1tRefOncWrr74qqqqq9OssXbpUeHh4CCsrKzFs2DD9/K1bt4r+/fsLe3t70bZtWxEc\nHCzee+89/fKbn05jan5VVZV47bXXhIeHh2jVqpXo3r27iI2NNdjmdjcM3igqKkp4eHgIOzs7MXLk\nSPHFF1/UeWrNjdOrVq0SvXv3Fm3bthUODg4iNDRUbN++Xb+/0tJSMWbMGOHk5CQURRFffPHFLWsy\ndrNrVFSUePTRR4W9vb1wd3cXy5cvN9imoKBAPPLII6Jt27bCy8tLxMTE1LnZ9eDBgyIkJETY2dkJ\njUYjzp07JzIzM4VGo9Hf9CiEEL/99psYM2aMcHBwEA4ODuKRRx4RGRkZ+uVr164VNjY2BsfPyckR\nGo1G7N69u16ZGJOfny8mTZoknJ2dhZ2dnRg6dKg4dOiQwTr1udm1qqpKhIWFiXbt2glFUfQ3+Brb\nNjw83OCcFOLPG36Dg4NF69athYuLi7j//vtFTEzMLY8phBDbtm0TiqKIkJCQOst2794tgoKCROvW\nrUXXrl3F5s2b69x8XN/z4eOPPxaenp7Czs5ODBo0SMTHxxtkX3t+fvfdd6J3797C1tZWdO/eXezc\nuVO/D2Ove0lJiZg+fbr+/yMPDw8xfvx4ceTIESHEnb2mRNS0FCEa4VNaiIiIiIhIKo6RJyIiIiJS\nITbyREREREQqxEaeiIiIiEiF2MgTEREREakQG3kiIiIiIhViI09EpHLHjh3DwIED8cMPP7SI4xIR\n0Z/4+EkiIguwYcMGLFmyBIcPH24RxyUiIl6RJyKyCI899hjOnz+PlJSUFnFcIiJiI09EZBFatWqF\nyZMnIyYmxqKP+89//hM9e/aEt7c3vL29ERAQgG7duiE1NVXK8YmImhMOrSEishDHjh1D//79cf78\neTg5Oennz5o1C1FRUVKP+9lnn6GiogJHjhzBJ598Amtr67s+zubNm6HVatGvXz9ER0dj4sSJcHd3\nv+v9EhGpFa/IExFZgKKiIqxZswa9e/fGV199BQCoqqpCVFQUduzYIfW4u3fvRt++ffGPf/wDTk5O\njfZLxIQJE9CvXz8AwL59+9jEE1GLx0aeiEjlTp8+jRkzZmDBggWYNWsWVq1aBQCwsbHBrFmz4Onp\nKfW4WVlZiI2NBQD4+vri3LlzjXrcgoICVFVVNeo+iYjUiI08EZGK/fzzz4iIiMDq1avRtm1bjB07\nFsXFxdi3b99ttz148CASExMb/bhPP/003nzzTQBASkoK/vKXvzTacQFgy5Yt6NOnzx1vT0RkKdjI\nExGpVHZ2NubNm4fNmzejXbt2AP68Cj9nzhx89NFHt91+/fr1mDNnTqMfV6PRwNHREWfOnEFlZSUe\nffTRRjlureTk5Dq/HBARtUS82ZWIyMINGzYMP//8s9Fln3/+OaZOndrox6yoqMCbb76JhQsXwtbW\nVtpxiYhaEl6RJyJqwcrKyppkv2vWrME777wDW1tbfPvtt9KOS0TUkrCRJyKyYCtXrkR6ejoWL16M\n/Px8g2U7duzAiBEjGv2YcXFxmDdvHnx9fdGhQweUlpZKOS4RUUsjbWjNc889hx07dsDV1RVpaWlG\n13nxxRfxww8/wN7eHuvWrUOvXr1klEZEREREpDrSrshPmTIF8fHxJpfHxcXh7NmzSE9Px+rVqzF9\n+nRZpRERERERqY60Rn7QoEFwcXExuXz79u2YPHkyAKBfv364ePEiCgsLZZVHRERERKQqzWaMfF5e\nnsGHlmi1WuTm5pqxIiIiIiKi5qvZNPIAcPNwfUVRzFQJEREREVHzZm3uAmp5eHggJydHP52bmwsP\nD48663377bdo27atzNKIiIiIiJrUlStXMG7cuAZt02wa+bFjx2LlypWYNGkSkpOT4ezsjI4dO9ZZ\nr23btggJCTFDhXdnyZIleO2118xdRovCzOVj5vIxc/mYuXzMXD5mLl9qamqDt5HWyD/xxBPYvXs3\niouL4enpifnz56OqqgoAMG3aNIwZMwZxcXHw8/NDmzZtsHbtWlmlERERERGpjrRGPjY29rbrrFy5\nUkIl5pGdnW3uElocZi4fM5ePmcvHzOVj5vIxc3VoVje7WrLAwEBzl9DiMHP5mLl8zFw+Zi4fM5eP\nmauDtE92bSwJCQmqHCNPRERERGRKamoqhg8f3qBtms3NrndLCIGioiLodDpzl0KSCSHg5OQEBwcH\nc5dCREREJI3FNPJFRUVwdHSEvb29uUshyYQQKC0tRUVFBdq3b6+fn5SUhIEDB5qxspaHmcvHzOVj\n5vIxc/mYuTpYzBh5nU7HJr6FUhQF7du3R0VFhblLISIiIpLGYsbInz9/Hu7u7maoiJoLngNERESk\nVncyRt5irsgTEREREbUkbOTJYiUlJZm7hBaHmcvHzOVj5vIxc/mYuTqwkW/hBgwYgP379zf5cdLT\n0zF48GB4eXnh008/bfLjEREREVk6jpFXsaCgIKxYsQKDBw82dym39cILL8DJyQn/+te/muwYLfEc\nICIiIsvQop8jb0z5ufO4nlfYZPtv7dER9p3N1zgqioI7/T2suroa1tZ39vLfyba5ubkIDQ297Xqr\nVq1CUVER3nrrrTuqjYiIiKilsOhG/npeIY6/Etlk++/x/rx6N/JBQUGYMmUKNmzYgMLCQowZMwbL\nli2Dra0tfvvtN7z88ss4fvw43Nzc8Pbbb+Ohhx4CAERFRWH16tW4fPky3Nzc8MEHH2DQoEH4+9//\njtzcXISFhcHKygqvvPIKJk6ciHnz5iE5ORlt2rTB9OnTERERYVDD1KlTsXHjRvz+++/IyclBSEgI\noqOjMWTIkFvWcfO2ubm50GgMR2aZ2n7cuHHYv38/fv31V7z55pvYtWsXfH19jeYUERGBPn36YNq0\naXB1db2Tl0WPz8CVj5nLx8zlY+byMXP5mLk6cIy8RJs2bcLmzZuRmpqKjIwMfPDBB6iurkZYWBiG\nDx+O9PR0REZGIiIiAmfPnkV6ejo+++wzJCYmIjs7G5s3b4anpycAICYmBlqtFrGxscjOzsbMmTMR\nFhaGnj174uTJk9i6dStiYmKQmJhoUMOWLVuwceNGZGZmwsrKCoqiQFEUVFVVGa0jIyPD6LY3N/G3\n2n7btm3o378/li5diuzsbJNNPPDnXxkmTJiADRs2NGLyRERERJaHjbwkiqIgPDwc7u7ucHZ2xpw5\nc7BlyxYcPHgQ5eXlmD17NqytrTFo0CCMGjUKmzdvhrW1NSorK3H69GlUVVVBq9XC29vb6P4PHTqE\nkpISvPzyy7C2tkbnzp3x9NNPY8uWLQY1REREwN3dHba2tgbbm6pj06ZNt922PtsDqPcwoLCwMMTG\nxtZr3VvhlQT5mLl8zFw+Zi4fM5ePmasDG3mJPDw89P/WarUoKChAfn6+wXwA8PT0RH5+Pnx8fLBo\n0SJERkaiS5cuCA8PR0FBgdF95+TkoKCgAD4+Pvqv5cuXo7i42GQNNzJVx43HM7VtfbdXFMXk9jcq\nLi7GtWvXcOjQoXqtT0RERNQSsZGXKC8vT//v3NxcdOrUCW5ubsjLyzO4Wp2Tk6N/+sqECRMQFxeH\no0ePQlEUzJ8/X7/ejY2xVqtF586dkZmZqf/Kzs7GN998Y1CDqWba3d3daB1ubm633RaAye/jxu3r\nY+fOnUhNTcXcuXOxfv16AMClS5fw3XffYfny5Q3aF5+BKx8zl4+Zy8fM5WPm8jFzdWAjL4kQAp9/\n/jnOnz+PCxcu4MMPP8T48ePRu3dv2NnZITo6GlVVVUhKSsKPP/6I8ePH4+zZs9izZw8qKipga2sL\nW1tbg7HpHTp0QGZmJgAgJCQEDg4OiI6OxrVr16DT6XDy5EkcPny4XvXdqo766NOnz223v93Qmk2b\nNmHv3r2IiIjAuHHjEB8fj+vXr6Nt27YIDg5GZWVlvWohIiIiagnYyEuiKAomTpyICRMmICQkBL6+\nvpg7dy5sbGywfv167Ny5E/7+/nj11VcRExMDPz8/VFZWYsGCBfD390dAQABKS0vx9ttv6/f50ksv\nYdmyZfDx8UFMTAxiY2ORlpaGkJAQ+Pv746WXXsLly5frVd+t6mis7W91Rf/AgQPYtWuX/i8Ojo6O\nePjhhw3G+DcUx/fJx8zlY+byMXP5mLl8zFwdLPoDoUr3H27yx0+2G9CrXusGBwcjOjpaFR/e1Bzl\n5ORg/fr1mDdvnsl1+IFQREREpFb8QKibtPboiB7vm278GmP/JMed/L7JZ+DKx8zlY+byMXP5mLl8\nzFwdLLqRt+/sbtZPXqXGceXKFWzfvh1Hjx7FyZMn0a1bN3OXRERERGR2Fj20hloWngNERESkVncy\ntIY3uxIRERERqRAbebJYfAaufMxcPmYuHzOXj5nLx8zVQVojHx8fj65du8Lf3x+RkXWfJFNcXIyH\nHnoIwcHB6NGjB9atWyerNCIiIiIi1ZEyRl6n06FLly7YuXMnPDw80LdvX8TGxiIgIEC/zrvvvouK\nigosXrwYxcXF6NKlCwoLC2FtbXg/LsfIkyk8B4iIiEitmu0Y+ZSUFPj5+cHb2xs2NjaYNGkStm3b\nZrCOm5sbLl26BAC4dOkS2rdvX6eJJyIiIiKiP0lp5PPy8uDp6amf1mq1yMvLM1jn+eefx4kTJ+Du\n7o6goCBERUU16BhWVlYoLy9vlHpJXYQQKCkpga2trcF8ju+Tj5nLx8zlY+byMXP5mLk6SLnkrSjK\nbddZtGgRgoODsWvXLmRkZGDkyJE4evQoHB0d63UMV1dXFBUV4eLFi3dbbpMoKyuDk5OTucuwSEII\nODk5wcHBwdylEBEREUkjpZH38PBATk6OfjonJwdardZgnf379+PNN98EANx7773w8fHBb7/9hj59\n+tTZ34wZM+Dl5QUAcHJyQmBgIAYOHIiOHTvqf4Os/TQyTrfc6YEDBzarelrCdO285lJPS5mu1Vzq\n4TSnG3uaP8/589wSp9PS0lBWVgYAyM7ORnh4OBpKys2u1dXV6NKlCxISEuDu7o7Q0NA6N7vOmTMH\nTk5OeOedd1BYWIjevXvj2LFjaNeuncG+TN3sSkRERESkVs32Zldra2usXLkSo0aNQrdu3fD4448j\nICAAq1atwqpVqwAAb7zxBg4ePIigoCCMGDECS5curdPEq9nNV86o6TFz+Zi5fMxcPmYuHzOXj5mr\ng7WsA40ePRqjR482mDdt2jT9v++55x589913ssohIiIiIlI1KUNrGhOH1hARERGRpWm2Q2uIiIiI\niKhxsZGXhGPN5GPm8jFz+Zi5fMxcPmYuHzNXBzbyREREREQqxDHyRERERERmxjHyREREREQtBBt5\nSTjWTD5mLh8zl4+Zy8fM5WPm8jFzdWAjT0RERESkQhwjT0RERERkZhwjT0RERETUQrCRl4RjzeRj\n5vIxc/mYuXzMXD5mLh8zVwc28kREREREKsQx8kREREREZsYx8kRERERELQQbeUk41kw+Zi4fM5eP\nmcvHzOVj5vIxc3VgI09EREREpEIcI09EREREZGYcI09ERERE1EKwkZeEY83kY+byMXP5mLl8zFw+\nZi4fM1cHNvJERERERCrEMfJERERERGbGMfJERERERC0EG3lJONbs7pXn5Jv8qi6/Xmd9Zi4fM5eP\nmcvHzOVj5vIxc3WwNncBRPWVvng1yo6eqjPfyr41en/5PqztW5uhKiIiIiLzkDZGPj4+HrNnz4ZO\np0N4eDhTdajBAAAgAElEQVTmzZtXZ51du3bhpZdeQlVVFe655x7s2rWrzjocI2+5Ki+UoTgxGTWV\nVUaX5/xnO6ouXqozv7aRb+3WoalLJCIiImoSdzJGXsoVeZ1Oh5kzZ2Lnzp3w8PBA3759MXbsWAQE\nBOjXuXjxIv7xj3/gxx9/hFarRXFxsYzSqBkR1TqcW7MJVRcvm7sUIiIiomZPyhj5lJQU+Pn5wdvb\nGzY2Npg0aRK2bdtmsM769esxYcIEaLVaAMA999wjozRpONZMPmYuHzOXj5nLx8zlY+byMXN1kNLI\n5+XlwdPTUz+t1WqRl5dnsE56ejpKS0sxbNgw9OnTB1999ZWM0oiIiIiIVEnK0BpFUW67TlVVFVJT\nU5GQkIDy8nL0798f999/P/z9/eusO2PGDHh5eQEAnJycEBgYiIEDBwL4v98gOa3O6WNlf6D6ajkC\n27QDAKRdLQWAW05b6VqhN1BnfwMHDjT799PSpmvnNZd6Wsp0reZSD6c53djT/HnOn+eWOJ2Wloay\nsjIAQHZ2NsLDw9FQUm52TU5Oxrvvvov4+HgAwOLFi6HRaAxueI2MjMS1a9fw7rvvAgDCw8Px0EMP\nYeLEiQb74s2ulquy5CIOPfNKg8fI82ZXIiIiUrtm+4FQffr0QXp6OrKyslBZWYkNGzZg7NixBuuM\nGzcOSUlJ0Ol0KC8vx6+//opu3brJKE+Km6+ctVRXM3ORHrna6FdmTCyqL5c32rGYuXzMXD5mLh8z\nl4+Zy8fM1cFaykGsrbFy5UqMGjUKOp0OU6dORUBAAFatWgUAmDZtGrp27YqHHnoIPXv2hEajwfPP\nP29RjTz9qaaqCvnbE81dBhEREZHqSXuOfGPh0Bp1u3wmE4envN6o++TQGiIiIlK7Zju0hoiIiIiI\nGhcbeUk41kw+Zi4fM5ePmcvHzOVj5vIxc3VgI09EREREpEJs5CW58bmsJAczl4+Zy8fM5WPm8jFz\n+Zi5Okh5ag21LJUXyqArv2Z8oa5GbjFEREREFoqNvCQ3fjqapbt8+necfO0D4wslPiOpJWXeXDBz\n+Zi5fMxcPmYuHzNXBzby1PiEgKjWSTycgKipQWVpmcH8qktXUVlaBk1rW1jbt5ZWDxEREZEMfI48\nNbqS/ak48cpSqce0cXGCYmX8lo/uS+bCMcBPaj1EREREDXEnz5HnFXmyCFUXykwuU9nvqkRERET1\nwqfWSMLnscqXdrUUAKCxsYGoqTH5RY2H57l8zFw+Zi4fM5ePmasDr8iTxTv1djSsTIyR93n+cbjc\nHyS5IiIiIqK7x0ZeEt75LV9gm3YAgGvZ502uU1NZKaucFoHnuXzMXD5mLh8zl4+ZqwOH1hARERER\nqRAbeUk41ky+2jHyJA/Pc/mYuXzMXD5mLh8zVwc28kREREREKsRGXhKONZOvdow8ycPzXD5mLh8z\nl4+Zy8fM1YGNPBERERGRCrGRl4RjzeTjGHn5eJ7Lx8zlY+byMXP5mLk6sJEnIiIiIlIhNvKScKyZ\nfBwjLx/Pc/mYuXzMXD5mLh8zVwc28kREREREKsRGXhKONZOPY+Tl43kuHzOXj5nLx8zlY+bqwEae\nGp3GxtrcJRARERFZPHZckljaWLPivQeRv/lHo8sqii9Irsa4eo2Rt+Lvso3J0s5zNWDm8jFz+Zi5\nfMxcHaQ18vHx8Zg9ezZ0Oh3Cw8Mxb948o+sdOHAA/fv3x8aNGzF+/HhZ5VEDVV24hAsH0sxdxl3L\n+yYOF5KPGl3WfnBfuPQNlFwRERERUf1IuRyp0+kwc+ZMxMfH4+TJk4iNjcWpU6eMrjdv3jw89NBD\nEELIKE0ajjWTrz5j5C+mnsD5LT8Z/bqWmy+hSsvC81w+Zi4fM5ePmcvHzNVBSiOfkpICPz8/eHt7\nw8bGBpMmTcK2bdvqrLdixQpMnDgRHTp0kFEWEREREZFqSWnk8/Ly4OnpqZ/WarXIy8urs862bdsw\nffp0AICiKDJKk4ZjzeTjc+Tl43kuHzOXj5nLx8zlY+bqIGWMfH2a8tmzZ2PJkiVQFAVCiFsOrZkx\nYwa8vLwAAE5OTggMDNSfcLV/CuJ0007fiz/VDl+pbZotbbq55M1pTnOa05zmNKctazotLQ1lZWUA\ngOzsbISHh6OhFCFhMHpycjLeffddxMfHAwAWL14MjUZjcMOrr6+vvnkvLi6Gvb09Pv30U4wdO9Zg\nXwkJCQgJCWnqkhtdUlKS/sWzBPnbE5EeudrcZdxS2tXSu7oq7/fyc3B/7MFGrMjyWdp5rgbMXD5m\nLh8zl4+Zy5eamorhw4c3aBvrJqrFQJ8+fZCeno6srCy4u7tjw4YNiI2NNVjn999/1/97ypQpeOSR\nR+o08URERERE9Ccpjby1tTVWrlyJUaNGQafTYerUqQgICMCqVasAANOmTZNRhlnxt1r5OEZePp7n\n8jFz+Zi5fMxcPmauDlIaeQAYPXo0Ro8ebTDPVAO/du1aGSUREREREakWP9ZSktqbHEie+jxHnhoX\nz3P5mLl8zFw+Zi4fM1cHNvJ0RxSNZT0elIiIiEhtpA2taenUONbs/Lf/xYVfDhtddjUrz+j85oRj\n5OVT43mudsxcPmYuHzOXj5mrAxt5Mqk8Kxcl+1LNXQYRERERGcGhNZJwrJl8HCMvH89z+Zi5fMxc\nPmYuHzNXBzbyREREREQqxEZeEo41k49j5OXjeS4fM5ePmcvHzOVj5urARp6IiIiISIXYyEvCsWby\ncYy8fDzP5WPm8jFz+Zi5fMxcHdjIExERERGpEB8/KQnHmsl3t2PkL/xyBIqV8f9FWrV3QhtfT4ga\nYXS5bcf20Fi3vP+9eJ7Lx8zlY+byMXP5mLk6tLxOg6ieSval3vI5+oqN8f997Du7I/iT+UALbOSJ\niIhIHg6tkYRjzeRr6jHyoqra6FdNVXWTHrc543kuHzOXj5nLx8zlY+bqwEaeiIiIiEiF2MhLwrFm\n8vE58vLxPJePmcvHzOVj5vIxc3XgIN4WrKa6Gvnf/heVpWVGl1/45YjkioiIiIiovtjIS5KUlNT8\nfrsVQMGO3bianmXuSppE2tVSXpWXrFme5xaOmcvHzOVj5vIxc3Xg0BoiIiIiIhViIy8Jf6uVj1fj\n5eN5Lh8zl4+Zy8fM5WPm6sBGnoiIiIhIhdjIS8LnscrX1M+Rp7p4nsvHzOVj5vIxc/mYuTqwkSci\nIiIiUiE28pJwrJl8HCMvH89z+Zi5fMxcPmYuHzNXBzbyREREREQqJLWRj4+PR9euXeHv74/IyMg6\ny7/++msEBQWhZ8+eeOCBB3Ds2DGZ5TUpjjWTj2Pk5eN5Lh8zl4+Zy8fM5WPm6iDtA6F0Oh1mzpyJ\nnTt3wsPDA3379sXYsWMREBCgX8fX1xd79uyBk5MT4uPjERERgeTkZFklEhERERGphrQr8ikpKfDz\n84O3tzdsbGwwadIkbNu2zWCd/v37w8nJCQDQr18/5ObmyiqvyXGsmXwcIy8fz3P5mLl8zFw+Zi4f\nM1cHaY18Xl4ePD099dNarRZ5eXkm1//8888xZswYGaUREREREamOtKE1iqLUe92ff/4Za9aswb59\n+4wunzFjBry8vAAATk5OCAwM1P/mWDumq7lN185rLvXUTh8tPo9rV0v1V69rx5VbwvSNY+RlHt+2\nREFQRSVqqqqxL/kXAMAD9/cHAOxL/gWaVq0weNhQAOZ//Rt7+pNPPlHF/4+WNJ2Wlobp06c3m3pa\nwnTtvOZST0uYvjl7c9fTEqb581zOz++ysjIAQHZ2NsLDw9FQihBCNHirO5CcnIx3330X8fHxAIDF\nixdDo9Fg3rx5BusdO3YM48ePR3x8PPz8/OrsJyEhASEhITJKblRJSUn6F6+5qKmqxuHn/4mr6Vnm\nLqVJpN3wC4psrd06GF+g0SBw2euw8+wktyBJmuN5bumYuXzMXD5mLh8zly81NRXDhw9v0DbWTVRL\nHX369EF6ejqysrLg7u6ODRs2IDY21mCd7OxsjB8/Hv/5z3+MNvFqxv8Z5DPnGPnr+X8YX6Cp/1+m\n1IjnuXzMXD5mLh8zl4+Zq4O0Rt7a2horV67EqFGjoNPpMHXqVAQEBGDVqlUAgGnTpmHBggW4cOGC\n/s/ENjY2SElJkVWiRaqprEL1lXLjCxUFgJQ/yBARERFRI5M2tKaxcGhNw1w/X4S0OYuhu15hdHll\n8QVAXadAvZlzaI1JGgV91y/n0BpqNMxcPmYuHzOXj5nL16yH1pD5VPxRihoTjTwRERERqZPUT3Zt\nyfhbrXzN7mp8C8DzXD5mLh8zl4+Zy8fM1YGNPBERERGRCrGRl+TGZ+CSHDc+R57k4HkuHzOXj5nL\nx8zlY+bqwEaeiIiIiEiF2MhLwrFm8nGMvHw8z+Vj5vIxc/mYuXzMXB3YyBPJZtmfCUVERESSsJGX\nhGPN5GuWY+RrBAq2JyJ73RajX1cyss1d4V3heS4fM5ePmcvHzOVj5urA58gTSZbz9XaTy5yCAyRW\nQkRERGrGK/KScKyZfBwjLx/Pc/mYuXzMXD5mLh8zVwc28pbOii8xERERkSXi0BpJkpKSmuy32yvp\nWcjb+IPRZTWVlaipqGyS4zZ3aVdLeVVesqY8z8k4Zi4fM5ePmcvHzNWBjbwFqKmoRGHcbnOXQURE\nREQScdyFJPytVj5ejZeP57l8zFw+Zi4fM5ePmasDr8irRMUfpdBdvWZ0WU1lleRqqKnoyq/jqolH\nUFq1sUPrTh0kV0RERETNFRt5Se52rNnlk2dx8o0PG7Eiy6fGMfLHX4k0uSxgwaxm38hzTKV8zFw+\nZi4fM5ePmasDh9YQEREREakQG3lJ+FutfGq7Gm8JeJ7Lx8zlY+byMXP5mLk6sJEnIiIiIlIhNvKS\nJCUlmbuEFiftaqm5S2hxeJ7Lx8zlY+byMXP5mLk68GbXZqT6SjmETmd8oaLILYaanev5f6Ds8Emj\ny6ydHNDG10tyRURERGROihBCmLuIhkhISEBISIi5y2gShXG7cW7NJqPLqq+Uo/ryVckVkVr4znwK\n2if+x9xlEBER0R1KTU3F8OHDG7QNr8g3I7pr13E9/w9zl0FEREREKsAx8pJwrJl8HCMvH89z+Zi5\nfMxcPmYuHzNXB2lX5OPj4zF79mzodDqEh4dj3rx5ddZ58cUX8cMPP8De3h7r1q1Dr169ZJXX5NLS\n0vgoJ8kyr19qMY+gLNlzEIqNDYC6I+U0tq1g7dDG6P0XGhtrOPfpAes29o1SB89z+Zi5fMxcPmYu\nHzNXBymNvE6nw8yZM7Fz5054eHigb9++GDt2LAICAvTrxMXF4ezZs0hPT8evv/6K6dOnIzk5WUZ5\nUpSVld1+Jd7Q2qiu1lSbuwRpyo6dRtmx0w3ezrbjPQhZs6jx6qjPeU6NipnLx8zlY+byMXN1kNLI\np6SkwM/PD97e3gCASZMmYdu2bQaN/Pbt2zF58mQAQL9+/XDx4kUUFhaiY8eOMkpsNNVXy3Fm0SpU\nFJUYzC84mYIjmeVodY8zAOMN+9UzWU1fINENdOXXcOn4GWMX8gEADl19YNuhvdyiiIiIqF6kNPJ5\neXnw9PTUT2u1Wvz666+3XSc3N9dsjfz1wmKIauOPglSsrEz14tBYW6NVe2coGsMV/jheCVvXWw/z\ncOjqA4euPndUL9V1aWcBOvzlfnOX0ewV/Wh6HKSdZyeUX883uszKrjVw00Ovss6ko+KPUigaDaqv\nGH/KksbGBq3dXe+8YDKQnZ1t7hJaHGYuHzOXj5mrg5RGXqnnkJGbn4RparvU1NS7rqlJDQ2qM2vu\nY4NxzQyltGTM/O6dLi1q0PoRM/+BEzlZt1+xIPfOCqI6wsPDm//PRAvDzOVj5vIxc/muXLnS4G2k\nNPIeHh7IycnRT+fk5ECr1d5yndzcXHh4eNTZV0Ofr0lEREREZImkPH6yT58+SE9PR1ZWFiorK7Fh\nwwaMHTvWYJ2xY8fiyy+/BAAkJyfD2dlZdePjiYiIiIhkkXJF3traGitXrsSoUaOg0+kwdepUBAQE\nYNWqVQCAadOmYcyYMYiLi4Ofnx/atGmDtWvXyiiNiIiIiEiVFHHzwHQiIiIiImr2+MmuTeC5555D\nx44dERgYaDB/xYoVCAgIQI8ePYx+IBbdOWOZp6SkIDQ0FL169ULfvn1x4MABM1ZoeXJycjBs2DB0\n794dPXr0QHR0NACgtLQUI0eOxH333YcHH3wQFy9eNHOllsNU5q+88goCAgIQFBSE8ePH8/nPjchU\n5rWWLVsGjUaD0lJ+knRjuVXmfB9tGqYy5/to07l+/Tr69euH4OBgdOvWDa+//jqAO3gPFdTo9uzZ\nI1JTU0WPHj308xITE8WIESNEZWWlEEKIoqIic5VnkYxlPmTIEBEfHy+EECIuLk4MHTrUXOVZpPz8\nfHH48GEhhBCXL18W9913nzh58qR45ZVXRGRkpBBCiCVLloh58+aZs0yLYirzn376Seh0OiGEEPPm\nzWPmjchU5kIIkZ2dLUaNGiW8vb1FSUmJOcu0KKYy5/to0zGVOd9Hm9bVq1eFEEJUVVWJfv36ib17\n9zb4PZRX5JvAoEGD4OLiYjDvk08+weuvvw4bGxsAQIcOHcxRmsUylrmbm5v+yuTFixeNPgWJ7lyn\nTp0QHBwMAHBwcEBAQADy8vIMPtxt8uTJ2Lp1qznLtCjGMj9//jxGjhwJjebPH+f9+vVDbi4f79lY\nTGUOAHPmzMHSpUvNWZ5FMvWzJSYmhu+jTcRU5nwfbVr29vYAgMrKSuh0Ori4uDT4PZSNvCTp6enY\ns2cP7r//fgwdOhQHDx40d0kWb8mSJZg7dy68vLzwyiuvYPHixeYuyWJlZWXh8OHD6Nevn8EnMnfs\n2BGFhYVmrs4y3Zj5jdasWYMxY8aYqSrLdmPm27Ztg1arRc+ePc1dlkW7MfMzZ87wfVSC2szvv/9+\nvo82sZqaGgQHB6Njx476oU0NfQ9lIy9JdXU1Lly4gOTkZLz//vv429/+Zu6SLN7UqVMRHR2N7Oxs\nLF++HM8995y5S7JIV65cwYQJExAVFQVHR0eDZYqi1PsD4aj+rly5gokTJyIqKgoODg76+QsXLkSr\nVq0QFhZmxuos042ZazQaLFq0CPPnz9cvF3xuRKO7MXNHR0e+j0pw888Wvo82LY1GgyNHjiA3Nxd7\n9uzBzz//bLC8Pu+hbOQl0Wq1GD9+PACgb9++0Gg0KCkpMXNVli0lJQWPPfYYAGDixIlISUkxc0WW\np6qqChMmTMDTTz+NRx99FMCfVxAKCgoAAPn5+XB1dTVniRanNvOnnnpKnzkArFu3DnFxcfj666/N\nWJ1lujnzjIwMZGVlISgoCD4+PsjNzUXv3r1RVNSwT0Im04yd53wfbVrGMuf7qBxOTk54+OGHcejQ\noQa/h7KRl+TRRx9FYmIiAODMmTOorKxE+/btzVyVZfPz88Pu3bsBAImJibjvvvvMXJFlEUJg6tSp\n6NatG2bPnq2fP3bsWHzxxRcAgC+++MKg2aS7Yyrz+Ph4vP/++9i2bRtat25txgotj7HMAwMDUVhY\niMzMTGRmZkKr1SI1NZW/tDYSU+c530ebjqnM+T7adIqLi/VPpLl27Rr++9//olevXg1/D23Cm3Fb\nrEmTJgk3NzfRqlUrodVqxZo1a0RlZaV46qmnRI8ePURISIj4+eefzV2mRanN3MbGRp/5gQMHRGho\nqAgKChL333+/SE1NNXeZFmXv3r1CURQRFBQkgoODRXBwsPjhhx9ESUmJGD58uPD39xcjR44UFy5c\nMHepFsNY5nFxccLPz094eXnp502fPt3cpVoMU5nfyMfHh0+taUSmfrbwfbTpmDrP+T7adI4dOyZ6\n9eolgoKCRGBgoFi6dKkQQjT4PZQfCEVEREREpEIcWkNEREREpEJs5ImIiIiIVIiNPBERERGRCrGR\nJyIiIiJSITbyREREREQqxEaeiIiIiEiF2MgTEREREakQG3kiIroj3t7eSEhIMHcZREQtFht5IiK6\nI4qiQFEUc5dBRNRisZEnIlK56OhovPHGG+Yug4iIJGMjT0Skci+88AI2btyIwsLCBm0XGRmJv/71\nrwbzZs2ahVmzZgEAlixZAj8/P7Rt2xbdu3fH1q1bTe5Lo9Hg999/108/++yzeOutt/TT58+fx4QJ\nE+Dq6gpfX1+sWLGiQbUSEVFdbOSJiFROURSEhYXhq6++atB2TzzxBOLi4nDlyhUAgE6nw//+7//i\nySefBAD4+fkhKSkJly5dwjvvvIOnnnoKBQUF9a6pdthNTU0NHnnkEfTq1Qvnz59HQkICPvroI/z0\n008NqpeIiAyxkScisgDPPvss1q1b16BtvLy8EBISgm+//RYAkJiYCHt7e4SGhgIAJk6ciE6dOgEA\n/va3v8Hf3x8pKSn13r8QAgBw4MABFBcX45///Cesra3h4+OD8PBwfPPNNw2ql4iIDLGRJyKyAH/8\n8QfKy8sb1GgDQFhYGGJjYwEA69ev11+NB4Avv/wSvXr1gouLC1xcXHD8+HGUlJTUe9+1V+TPnTuH\n8+fP6/fj4uKCxYsXo6ioqEG1EhGRIWmN/HPPPYeOHTsiMDDQ5Dovvvgi/P39ERQUhMOHD8sqjYhI\n1eLj45GSkoJ//vOfWLt2LcrKyrBlyxYsXrz4tttOnDgRu3btQl5eHrZu3YqwsDAAfzbfERER+Pjj\nj1FaWooLFy6gR48e+qvsN7O3t0d5ebl+Oj8/X/9vT09P+Pj44MKFC/qvS5cu4fvvv7/L75yIqGWT\n1shPmTIF8fHxJpfHxcXh7NmzSE9Px+rVqzF9+nRZpRERqdb69euRmJiIF154AX/961/x3XffwdbW\nFr1790ZlZeVtt+/QoQOGDh2KZ599Fr6+vujSpQsA4OrVq1AUBffccw9qamqwdu1aHD9+3OR+goOD\n8fXXX0On0yE+Ph579uzRLwsNDYWjoyOWLl2Ka9euQafT4fjx4zh48ODdB0BE1IJJa+QHDRoEFxcX\nk8u3b9+OyZMnAwD69euHixcvNvgJDERELUlycjJ27tyJpUuXAgAcHR3x6KOPNnjseVhYGBISEvRX\n4wGgW7dumDt3Lvr3749OnTrh+PHjGDhwoMl9REVF4bvvvoOLiwvWr1+Pxx57TL/MysoK33//PY4c\nOQJfX1906NABERERuHTpUgO/YyIiupEiTP2dtAlkZWXhkUceQVpaWp1ljzzyCF5//XUMGDAAADBi\nxAhERkaid+/essojIrIY586dw7p16/DOO++YuxQiImoizepm15t/p+AnBhIR3RmJ12iIiMhMrM1d\nQC0PDw/k5OTop3Nzc+Hh4VFnvW+//RZt27aVWRoRkSoNHDgQCQkJ5i6DiIjq4cqVKxg3blyDtmk2\njfzYsWOxcuVKTJo0CcnJyXB2dkbHjh3rrNe2bVuEhISYocK7s2TJErz22mvmLqNFYebyMXP5mLl8\nzFw+Zi4fM5cvNTW1wdtIa+SfeOIJ7N69G8XFxfD09MT8+fNRVVUFAJg2bRrGjBmDuLg4+Pn5oU2b\nNli7dq2s0oiIiIiIVEdaI1/7gSO3snLlSgmVmEd2dra5S2hxmLl8zFw+Zi4fM5ePmcvHzNWhWd3s\naslu9UFY1DSYuXzMXD5mLh8zl4+Zy8fM1UHq4ycbQ0JCgirHyBMRERERmZKamorhw4c3aJtmc7Pr\n3RJCoKioCDqdztylkBlYWVnB1dWVjywlIiKiFsNiGvmioiI4OjrC3t7e3KWQGZSXl6OoqMjgSUdJ\nSUm3/CRKanzMXD5mLh8zl4+Zy8fM1cFixsjrdDo28S2Yvb09/xpDRERELYrFjJE/f/483N3dzVAR\nNRc8B4iIiEit7mSMvMVckSciIiIiaknYyJPFSkpKMncJLQ4zl4+Zy8fM5WPm8jFzdWAj38INGDAA\n+/fvb/LjpKenY/DgwfDy8sKnn37a5McjIiIisnQcI69iQUFBWLFiBQYPHmzuUm7rhRdegJOTE/71\nr3812TFa4jlARERElqFFP0femIul5bh88XqT7d/RuTWc25nvSTmKouBOfw+rrq6GtfWdvfx3sm1u\nbi5CQ0Nvu96qVatQVFSEt956645qIyIiImopLHpozeWL1/HT1uNN9tWQXxKCgoLw0UcfoX///vD1\n9cXMmTNRUVEBAPjtt9/wyCOPwMfHBwMGDEB8fLx+u6ioKHTv3h1eXl7o168f9u7dCwD4+9//jtzc\nXISFhcHLywsrVqxAfn4+nnnmGdx3333o1asXVq9eXaeG6OhoDBw4EF5eXtDpdAgKCsLu3btvW8fN\n29bU1NT5Hk1tP27cOCQlJWHevHnw8vLC77//bjKniIgIbN26FUVFRfXO1hSO75OPmcvHzOVj5vIx\nc/mYuTpYdCPf3GzatAmbN29GamoqMjIy8MEHH6C6uhphYWEYPnw40tPTERkZiYiICJw9exbp6en4\n7LPPkJiYiOzsbGzevBmenp4AgJiYGGi1WsTGxiI7OxszZ85EWFgYevbsiZMnT2Lr1q2IiYlBYmKi\nQQ1btmzBxo0bkZmZCSsrKyiKAkVRUFVVZbSOjIwMo9tqNIanzq2237ZtG/r374+lS5ciOzsbvr6+\nJjNSFAUTJkzAhg0bGjF5IiIiIsvDRl4SRVEQHh4Od3d3ODs7Y86cOdiyZQsOHjyI8vJyzJ49G9bW\n1hg0aBBGjRqFzZs3w9raGpWVlTh9+jSqqqqg1Wrh7e1tdP+HDh1CSUkJXn75ZVhbW6Nz5854+umn\nsWXLFoMaIiIi4O7uDltbW4PtTdWxadOm225bn+0B1HsYUFhYGGJjY+u17q3wE+nkY+byMXP5mLl8\nzFw+Zq4ObOQl8vDw0P9bq9WioKAA+fn5BvMBwNPTE/n5+fDx8cGiRYsQGRmJLl26IDw8HAUFBUb3\nnZOTg4KCAvj4+Oi/li9fjuLiYpM13MhUHTcez9S29d1eURST29+ouLgY165dw6FDh+q1PhEREVFL\nxCwNkZgAACAASURBVEZeory8PP2/c3Nz0alTJ7i5uSEvL8/ganVOTo7+6SsTJkxAXFwcjh49CkVR\nMH/+fP16NzbGWq0WnTt3RmZmpv4rOzsb33zzjUENppppd3d3o3W4ubnddlsAJr+PG7evj507dyI1\nNRVz587F+vXrAQAZGRn4/vvvERkZiaNHj9Z7XxzfJx8zl4+Zy8fM5WPm8jFzdWAjL4kQAp9//jnO\nnz+PCxcu4MMPP8T48ePRu3dv2NnZITo6GlVVVUhKSsKPP/6I8ePH4+zZs9izZw8qKipga2sLW1tb\ng7HpHTp0QGZmJgAgJCQEDg4OiI6OxrVr16DT6XDy5EkcPny4XvXdqo766NOnz223v93Qmk2bNmHv\n3r2IiIjAuHHjEB8fj+vXr+PHH3+Em5sbZsyYgZUrV9arHiIiIiJLx0ZeEkVRMHHiREyYMAEhISHw\n9fXF3LlzYWNjg/Xr12Pnzp3w9/fHq6++ipiYGPj5+aGyshILFiyAv78/AgICUFpairffflu/z5de\negnLli2Dj48PYmJiEBsbi7S0NISEhMDf3x8vvfQSLl++XK/6blVHY21/qyv6Bw4cwK5du/R/cXB0\ndMTDDz+MLVu2YMaMGejduzfy8vLQuXPnetUDcHyfOTBz+Zi5fMxcPmYuHzNXB4v+QKic30vx09bj\nTVbLg4/2gKdvu3qtGxwcjOjoaFV8eFNztWzZMkyfPh329saf3c8PhCIiIiK14gdC3cTRuTUefLRH\nk+6f5Pjhhx8QERGB/Px83HvvvfXaJikpiVcUJGPm8jFz+Zi5fMxcPmauDhbdyDu3szfrJ69S4/j+\n+++xfPlyrF69GgMHDsTcuXPNXRIRERGR2Vn00BpqWXgOEBERkVrdydAa3uxKRERERKRCbOTJYvEZ\nuPIxc/mYuXzMXD5mLh8zVwdpjXx8fDy6du0Kf39/REZG1lleXFyMhx56CMHBwejRowfWrVsnqzQi\nIiIiItWRMkZep9OhS5cu2LlzJzw8PNC3b1/ExsYiICBAv867776LiooKLF68GMXFxejSpQsKCwth\nbW14Py7HyJMpPAeIiIhIrZrtGPmUlBT4+fnB29sbNjY2mDRpErZt22awjpubGy5dugQAuHTpEtq3\nb1+niSciIiIioj9JaeTz8vLg6empn9ZqtcjLyzNY5/nnn8eJEyfg7u6OoKAgREVFNegYVlZWKC8v\nb5R6SX3Ky8thZWVlMI/j++Rj5vIxc/mYuXzMXD5mrg5SLnkrinLbdRYtWoTg4GDs2rULGRkZGDly\nJI4ePQpHR8d6HcPV1RVFRUW4ePHi3ZbbJMrKyuDk5GTuMiyWlZUVXF1dzV0GERERkTRSGnkPDw/k\n5OTop3NycqDVag3W2b9/P958800AwL333gsfHx/89ttv6NOnT539zZgxA15eXgAAJycnBAYGYuDA\ngejYsaP+N8jaTyPjdMudHjhwYLOqpyVM185rLvW0lOlazaUeTnO6saf585w/zy1xOi0tDWVlZQCA\n7OxshIeHo6Gk3OxaXV2NLl26ICEhAe7u7ggNDa1zs+ucOXPg5OSEd955B4WFhejduzeOHTuGdu3a\nGezL1M2uRERERERq1WxvdrW2tsbKlSsxatQodOvWDY8//jgCAgKwatUqrFq1CgDwxhtv4ODBgwgK\nCsKIESOwdOnSOk28mt185YyaHjOXj5nLx8zlY+byMXP5mLk6WMs60OjRozF69GiDedOmTdP/+557\n7sF3330nqxwiIiIiIlWTMrSmMXFoDRERERFZmmY7tIaIiIiIiBoXG3lJONZMPmYuHzOXj5nLx8zl\nY+byMXN1YCNPRERERKRCHCNPRERERGRmHCNPRERERNRCsJGXhGPN5GPm8jFz+Zi5fMxcPmYuHzNX\nh//H3t2HRVXm/wN/Dw+WpKGmojAQGiigiBiCFrZWlumuVGpFpvYARbq2q5nL+t1s6WkRs63UTdk2\nrTRJt1rJ0rHQTOkXomlKaUomjYBiqOADKDCc3x9eTCKM3ujMfe4zvF/XxXV5z5yZ8/Yzw5mbM5+5\nhxN5IiIiIiIDYo88EREREZHO2CNPRERERNRKcCIvCXvN5GPN5WPN5WPN5WPN5WPN5WPNjYETeSIi\nIiIiA2KPPBERERGRztgjT0RERETUSnAiLwl7zeRjzeVjzeVjzeVjzeVjzeVjzY2BE3kiIiIiIgNi\njzwRERERkc7YI09ERERE1EpwIi8Je83kY83lY83lY83lY83lY83lY82NgRN5IiIiIiIDYo88ERER\nEZHO2CNPRERERNRKcCIvCXvN5GPN5WPN5WPN5WPN5WPN5WPNjYETeSIiIiIiA5LWI2+xWDB16lTY\nbDYkJycjNTW1yTYbN27EtGnTUFtbi86dO2Pjxo1NtmGPPBERERG5m8vpkfdyUZZGbDYbpkyZgpyc\nHAQEBGDgwIFISEhAeHi4fZuKigr88Y9/xLp162A2m1FeXi4jGhERERGRIUlprcnPz0dISAiCg4Ph\n7e2NxMREZGdnN9pm+fLlGDNmDMxmMwCgc+fOMqJJw14z+Vhz+Vhz+Vhz+Vhz+Vhz+VhzY5AykS8p\nKUFgYKB9bDabUVJS0mibwsJCHDt2DLfeeitiYmKwdOlSGdGIiIiIiAxJSmuNyWS65Da1tbXYvn07\n1q9fj6qqKgwePBiDBg1CaGhok20nT56MoKAgAICvry8iIyMRHx8P4Le/IDnmOD4+Xqk8rWHccJkq\neVrLuIEqeTjm2NljHs95PHfHcUFBASorKwEAVqsVycnJaCkpH3bNy8tDWloaLBYLACA9PR0eHh6N\nPvCakZGB6upqpKWlAQCSk5Nx1113YezYsY3uix92JSIiIiJ3o+wXQsXExKCwsBBFRUWoqanBihUr\nkJCQ0Gibu+++G7m5ubDZbKiqqsKWLVsQEREhI54UF545I9djzeVjzeVjzeVjzeVjzeVjzY3BS8pO\nvLywYMECDB8+HDabDUlJSQgPD0dmZiYAICUlBWFhYbjrrrvQr18/eHh44PHHH3eriTwRERERkTNJ\nW0feWdhaQ0RERETuRtnWGiIiIiIici5O5CVhr5l8rLl8rLl8rLl8rLl8rLl8rLkxcCJPRERERGRA\n7JEnIiIiItIZe+SJiIiIiFoJTuQlYa+ZfKy5fKy5fKy5fKy5fKy5fKy5MXAiT0RERERkQOyRJyIi\nIiLSGXvkiYiIiIhaCU7kJWGvmXysuXysuXysuXysuXysuXysuTFwIk9EREREZEDskSciIiIi0hl7\n5ImIiIiIWglO5CVhr5l8rLl8rLl8rLl8rLl8rLl8rLkxcCJPRERERGRA7JEnIiIiItLZ5fTIe7ko\nCxERGURtTR3OVNcKb39N+6vh4WFyYSIiIhLBibwkubm5iI+P1ztGq8Kay8eay+eMmp8+VYPsZduF\ntvXt5IPf3x8FjzaeV7RPI+PzXD7WXD7W3Bg4kSciItTV1QttZxPcjoiIXI898kRErVzFsSp89M42\noW07dPJBwrhoeLfiM/JERK7AdeSJiMjlTGyPJyJSAltrJGGvmXysuXysuXyya15ZUY11//tBePvY\nW4LRpdu1LkwkH5/n8rHm8rHmxsCJPBERCdPqNRwurmjB9i4MQ0TUyrFHnoiolWtJj3xLjUrsj67+\n7nVGnojIFZTukbdYLAgLC0NoaCgyMjIcbrd161Z4eXnh448/lhWNiIiIiMhwpEzkbTYbpkyZAovF\ngt27dyMrKwt79uxpdrvU1FTcddddMNgbBZeUm5urd4RWhzWXjzWXjzWXjzWXjzWXjzU3Bik98vn5\n+QgJCUFwcDAAIDExEdnZ2QgPD2+03fz58zF27Fhs3bpVRiwiIlKIra4etbU24e2vutoLJi6hQ0St\nmJSJfElJCQIDA+1js9mMLVu2NNkmOzsbGzZswNatW93u4MxPfsvHmsvHmsvnTjU/UVGNL7LFVsTx\n7dQWt4+KgJeX/PXs3anmRsGay8eaG4OUibzIpHzq1KmYPXs2TCYTNE27aGvN5MmTERQUBADw9fVF\nZGSk/QnX8FYQxxxzzDHHYuO+EecWENhfVAAAuCE40mnjLfnVuG3YUADAN9/8PwDA4ME3NTvO2/IN\nvtu5V+j+vb098fXXX8PT00P3+nHMMcccX864oKAAlZWVAACr1Yrk5GS0lJRVa/Ly8pCWlgaLxQIA\nSE9Ph4eHB1JTU+3b9OzZ0z55Ly8vh4+PD9566y0kJCQ0ui+jrlqTm8v1WGVjzeVjzeVzVPOzZ+tQ\nXye29uPZs3UuW7WmzVWe8PQU+zhWfb2Gs2fqhLbt1PkajBrXX5cz8nyey8eay8eay3c5q9Z4uShL\nIzExMSgsLERRURH8/f2xYsUKZGVlNdrm559/tv/70UcfxahRo5pM4omISMwhawW++fInoW3rba47\nn1Nz1gZAvO+diIjESZnIe3l5YcGCBRg+fDhsNhuSkpIQHh6OzMxMAEBKSoqMGLriX7Xysebyseau\nVV52ErYLzrKH9ohEWUllk21PVlaj6lSNrGitCp/n8rHm8rHmxsAvhCIiMogNn+7BgX2/6h1DCXq2\n1hARuYLSXwjV2jV8yIHkYc3lY83la/gAKMnD57l8rLl8rLkxcCJPRERERGRAnMhLwl4z+Vhz+Vhz\n+RqWZiR5+DyXjzWXjzU3Bk7kiYiIiIgMiBN5SdhrJh9rLh9rLh975OXj81w+1lw+1twYOJEnIiIi\nIjIgTuQlYa+ZfKy5fKy5fOyRl4/Pc/lYc/lYc2PgRJ6IiIiIyIA4kZeEvWbysebysebysUdePj7P\n5WPN5WPNjYETeSIiIiIiA+JEXhL2msnHmsvHmsvHHnn5+DyXjzWXjzU3Bk7kiYiIiIgMiBN5Sdhr\nJh9rLh9rLh975OXj81w+1lw+1twYOJEnIiIiIjIgTuQlYa+ZfKy5fKy5fOyRl4/Pc/lYc/lYc2Pg\nRJ6IiAzJpHcAIiKdeekdoLXIzc3lX7eSsebyseby7S8qaJVn5U9WnsG2r38RnsyH9vFDx87XOGXf\nfJ7Lx5rLx5obAyfyRERkOLW1Nnz/bbHw9j16dXZhGiIifbC1RhL+VSsfay4fay5fazwbrzc+z+Vj\nzeVjzY2BE3kiIiIiIgPiRF4SrscqH2suH2suH9eRF+Ph6byXOz7P5WPN5WPNjYE98kREOjl7pg6n\nT54R2tbDw4Sas3UuTuS+vv6iEG2uFnvJC4/qjutD2FNPROozaZqm6R2iJdavX48BAwboHYOI6IpV\nHq/Ch0u26R2DLnDzsFCE9euudwwiamW2b9+O22+/vUW3YWsNEREREZEBSZ3IWywWhIWFITQ0FBkZ\nGU2uf//99xEVFYV+/frh5ptvxq5du2TGcyn2msnHmsvHmsvHHnn5+DyXjzWXjzU3Bmk98jabDVOm\nTEFOTg4CAgIwcOBAJCQkIDw83L5Nz549sWnTJvj6+sJiseCJJ55AXl6erIhERERERIYh7Yx8fn4+\nQkJCEBwcDG9vbyQmJiI7O7vRNoMHD4avry8AIC4uDsXF4l/2oTquxyofay4fay4f15GXj89z+Vhz\n+VhzY5A2kS8pKUFgYKB9bDabUVJS4nD7t99+GyNHjpQRjYiIiIjIcKS11phMJuFtv/zySyxevBhf\nf/11s9dPnjwZQUFBAABfX19ERkba/3Js6OlSbdxwmSp5WsP4wtrrnac1jBcuXGiI30dVxnl5/w/7\ni/baz6o39Lu3ZFxy+ABuGZRw2bfnuOn4ZoQC4PFcpTGP5zyeu+O4oKAAlZWVAACr1Yrk5GS0lLTl\nJ/Py8pCWlgaLxQIASE9Ph4eHB1JTUxttt2vXLowePRoWiwUhISFN7seoy0/m5ubaHzySgzWXjzVv\nGWcsP7m/qIDtNU52qeUn+TyXjzWXjzWX73KWn5Q2ka+rq0Pv3r2xfv16+Pv7IzY2FllZWY0+7Gq1\nWnHbbbdh2bJlGDRoULP3Y9SJPBG1DhXHq1B9ulZoW61ew9oP3Wd1LnfBdeSJSA+XM5H3clGWpjvy\n8sKCBQswfPhw2Gw2JCUlITw8HJmZmQCAlJQUvPDCCzh+/DgmTZoEAPD29kZ+fr6siEREV+z4r6ex\n4dM9escgIqJWQOo68iNGjMDevXvx008/YebMmQDOTeBTUlIAAP/5z39w9OhR7NixAzt27HCrSfz5\n/X0kB2suH2suH9eRl4/Pc/lYc/lYc2PgN7sSERERERmQtNaa1o4fGJGPNZePNZePH3R1Pq1eQ/Xp\nGofX3xgd2+j6q328W7QyG7Ucjy3ysebGwIk8ERHRefI3/Yzv8q1C23bsfA3uvLsPTJ6cyBORfGyt\nkYS9ZvKx5vKx5vKxR9756urqUXWqxuFPwfff2v99pkpshSK6Mjy2yMeaGwMn8kREREREBsSJvCTs\nNZOPNZePNZePPfLyseby8dgiH2tuDJzIExEREREZECfykrDXTD7WXD7WXD72yMvHmsvHY4t8rLkx\ncCJPRERERGRAXH5SEvaayceay+euNa84ehr19ZrQtmfP1Lk4TWPs15aPNZfPXY8tKmPNjYETeSKi\nS9i5tRg/7S7TOwYREVEjbK2RhL1m8rHm8rHm8rFfW75GNdc0nDlTh9Onzgr91NbIfcfGXfDYIh9r\nbgw8I09ERHSZjv56Gv9771vh7YePjkRnv3YuTERErQkn8pKw10w+1lw+1lw+9mvLd2HNz1S35Ntd\nxT5rQY3x2CIfa24MnMgTUatTb6uHzSY2oTKZAGicfBERkXo4kZckNzeXf91KxprLZ5SanzpxFutX\n70a94AT9ZOUZFye6fPuLCnhWXrIrqXnN2TqUl50U2rZNGy9c27HtZe3H3Rjl2OJOWHNj4ESeiFql\n48eqoAkuKUnkLGs/FP9w8pA7enEiT0QXxVVrJOFftfKx5vKx5vLxbLx8rLl8PLbIx5obAyfyRERE\nREQGxIm8JFyPVT7WXD7WXD6uIy8fay4fjy3ysebGwB55InILVadrUFdrE9rWVl/v4jRERESuZ9I0\nY62rtn79egwYMEDvGESkmKKfyrHxsz1C22oA6gWXnyTSy5A7e6FX3256xyAiSbZv347bb7+9Rbfh\nGXkicg8ahNeGJzKCPTtL8ethsaUq2117NaJiA12ciIhUI61H3mKxICwsDKGhocjIyGh2mz/96U8I\nDQ1FVFQUduzYISuaFOw1k481l8/ZNbfV1Qv/eHianLpvo2C/tnyyal5edgo/7jok9GPdf1RKJr3w\neC4fa24MUs7I22w2TJkyBTk5OQgICMDAgQORkJCA8PBw+zZr1qzBTz/9hMLCQmzZsgWTJk1CXl6e\njHhSFBQUcCknyVhz+Zxd8535B2HdXy60bXV1rdP2ayQlhw9wOUTJVKz52TO1KCuthK1O7PMfvp18\ncE27q1ycynl4PJePNTcGKRP5/Px8hISEIDg4GACQmJiI7OzsRhP5Tz75BA8//DAAIC4uDhUVFSgr\nK4Ofn5+MiC5XWVmpd4RWhzWX71I1rz5dg9KDFeea1C/FBBwsOoajv552Tjg3deYs6yObijWvPF6N\nTz/YKbz9PeMHGGoiz+O5fKy5MUiZyJeUlCAw8LfePbPZjC1btlxym+LiYreZyBMRUF+vIffzfagT\nPGtIRK5Raq3AMcE/kjt2vgad/dq5OBERXQ4pE3mTSax39cIFdERvZwRWq1XvCK2OCjXX6jVoQqef\nzzGZTOK/Ly25bw2oqbE1+R1zlMHT00P4vm119Th08NyZmx++34ef9/560cy9IruJnZEnIZbNpxDR\n31/vGK2KO9T81IkzOHXijNC2Z8/U4vRJsW3b+rRBpy7XoL5e7Jfc08sDIoe8X375BTZbPTw9+fU3\nsqjwGkqXJmX5yby8PKSlpcFisQAA0tPT4eHhgdTUVPs2Tz75JIYOHYrExEQAQFhYGL766qsmZ+TX\nr1/v6rhERERERFKdOnUKd999d4tuI+WMfExMDAoLC1FUVAR/f3+sWLECWVlZjbZJSEjAggULkJiY\niLy8PHTo0KHZtpqWrq9JREREROSOpEzkvby8sGDBAgwfPhw2mw1JSUkIDw9HZmYmACAlJQUjR47E\nmjVrEBISgmuuuQZLliyREY2IiIiIyJAM982uREREREQk8QuhWpPHHnsMfn5+iIxsvM7w/PnzER4e\njr59+zb6fABdueZqnp+fj9jYWERHR2PgwIHYunWrjgndz8GDB3HrrbeiT58+6Nu3L+bNmwcAOHbs\nGO644w706tULd955JyoqKnRO6j4c1XzGjBkIDw9HVFQURo8ezWXjnMhRzRu8+uqr8PDwwLFjx3RK\n6H4uVnO+jrqGo5rzddR1zpw5g7i4OPTv3x8RERGYOXMmgMt4DdXI6TZt2qRt375d69u3r/2yDRs2\naMOGDdNqamo0TdO0I0eO6BXPLTVX89/97neaxWLRNE3T1qxZow0dOlSveG7p0KFD2o4dOzRN07ST\nJ09qvXr10nbv3q3NmDFDy8jI0DRN02bPnq2lpqbqGdOtOKr5559/rtlsNk3TNC01NZU1dyJHNdc0\nTbNardrw4cO14OBg7ejRo3rGdCuOas7XUddxVHO+jrrW6dOnNU3TtNraWi0uLk7bvHlzi19DeUbe\nBYYMGYKOHTs2umzhwoWYOXMmvL29AQBdunTRI5rbaq7m3bt3t5+ZrKioQEBAgB7R3Fa3bt3Qv39/\nAEC7du0QHh6OkpKSRl/u9vDDD2PVqlV6xnQrzdW8tLQUd9xxBzw8zh3O4+LiUFxcrGdMt+Ko5gDw\n9NNPY86cOXrGc0uOji2LFi3i66iLOKo5X0ddy8fHBwBQU1MDm82Gjh07tvg1lBN5SQoLC7Fp0yYM\nGjQIQ4cOxbZt2/SO5PZmz56N6dOnIygoCDNmzEB6errekdxWUVERduzYgbi4uEbfyOzn54eysjKd\n07mn82t+vsWLF2PkyJE6pXJv59c8OzsbZrMZ/fr10zuWWzu/5vv27ePrqAQNNR80aBBfR12svr4e\n/fv3h5+fn721qaWvoZzIS1JXV4fjx48jLy8Pr7zyCu6//369I7m9pKQkzJs3D1arFa+99hoee+wx\nvSO5pVOnTmHMmDF444030L59+0bXteQLrkjcqVOnMHbsWLzxxhto1+63b9x8+eWX0aZNG4wbN07H\ndO7p/Jp7eHjgH//4B55//nn79RrXjXC682vevn17vo5KcOGxha+jruXh4YHvvvsOxcXF2LRpE778\n8stG14u8hnIiL4nZbMbo0aMBAAMHDoSHhweOHj2qcyr3lp+fj3vvvRcAMHbsWOTn5+ucyP3U1tZi\nzJgxmDBhAu655x4A584gHD58GABw6NAhdO3aVc+Ibqeh5uPHj7fXHADeeecdrFmzBu+//76O6dzT\nhTXfv38/ioqKEBUVhR49eqC4uBg33ngjjhw5ondUt9Hc85yvo67VXM35OiqHr68vfv/73+Pbb79t\n8WsoJ/KS3HPPPdiwYQMAYN++faipqcF1112ncyr3FhISgq+++goAsGHDBvTq1UvnRO5F0zQkJSUh\nIiICU6dOtV+ekJCAd999FwDw7rvvNpps0pVxVHOLxYJXXnkF2dnZuPrqq3VM6H6aq3lkZCTKyspw\n4MABHDhwAGazGdu3b+cfrU7i6HnO11HXcVRzvo66Tnl5uX1FmurqanzxxReIjo5u+WuoCz+M22ol\nJiZq3bt319q0aaOZzWZt8eLFWk1NjTZ+/Hitb9++2oABA7Qvv/xS75hupaHm3t7e9ppv3bpVi42N\n1aKiorRBgwZp27dv1zumW9m8ebNmMpm0qKgorX///lr//v21tWvXakePHtVuv/12LTQ0VLvjjju0\n48eP6x3VbTRX8zVr1mghISFaUFCQ/bJJkybpHdVtOKr5+Xr06MFVa5zI0bGFr6Ou4+h5ztdR19m1\na5cWHR2tRUVFaZGRkdqcOXM0TdNa/BrKL4QiIiIiIjIgttYQERERERkQJ/JERERERAbEiTwRERER\nkQFxIk9EREREZECcyBMRERERGRAn8kREREREBsSJPBERERGRAXEiT0RERERkQJzIExHRZQkODsb6\n9ev1jkFE1GpxIk9ERJfFZDLBZDLpHYOIqNXiRJ6IyODmzZuH//u//9M7BhERScaJPBGRwT311FNY\nuXIlysrKWnS7jIwM3HfffY0u+/Of/4w///nPAIDZs2cjJCQE1157Lfr06YNVq1Y5vC8PDw/8/PPP\n9vEjjzyCWbNm2celpaUYM2YMunbtip49e2L+/PktykpERE1xIk9EZHAmkwnjxo3D0qVLW3S7Bx98\nEGvWrMGpU6cAADabDf/973/x0EMPAQBCQkKQm5uLEydO4O9//zvGjx+Pw4cPC2dqaLupr6/HqFGj\nEB0djdLSUqxfvx6vv/46Pv/88xblJSKixjiRJyJyA4888gjeeeedFt0mKCgIAwYMwP/+9z8AwIYN\nG+Dj44PY2FgAwNixY9GtWzcAwP3334/Q0FDk5+cL37+maQCArVu3ory8HM8++yy8vLzQo0cPJCcn\n44MPPmhRXiIiaowTeSIiN/Drr7+iqqqqRRNtABg3bhyysrIAAMuXL7efjQeA9957D9HR0ejYsSM6\nduyI77//HkePHhW+74Yz8r/88gtKS0vt99OxY0ekp6fjyJEjLcpKRESNeekdgIiIrozFYkFhYSGe\nffZZLFmyBJ06dUJBQQF27dqFUaNGYcCAAQ5vO3bsWEyfPh0lJSVYtWoV8vLyAJybfD/xxBPYsGED\nBg8eDJPJhOjoaPtZ9gv5+PigqqrKPj506BACAwMBAIGBgejRowf27dvnxP81ERHxjDwRkYEtX74c\nGzZswFNPPYX77rsPq1evxsqVKxEQEICnn34ac+fOvejtu3TpgqFDh+KRRx5Bz5490bt3bwDA6dOn\nYTKZ0LlzZ9TX12PJkiX4/vvvHd5P//798f7778Nms8FisWDTpk3262JjY9G+fXvMmTMH1dXV3B7M\nyQAAIABJREFUsNls+P7777Ft2zbnFIGIqJXiRJ6IyKDy8vKQk5ODOXPmAADat2+Pe+65BwEBAYiN\njcXBgwfRo0ePS97PuHHjsH79eowbN85+WUREBKZPn47BgwejW7du+P777xEfH+/wPt544w2sXr0a\nHTt2xPLly3Hvvffar/P09MSnn36K7777Dj179kSXLl3wxBNP4MSJE1fwvyciIpPm6H1SIiIytJdf\nfhnTpk2Dj4+P3lGIiMgFOJEnInJDn3zyCW699VYcPnwYoaGheschIiIXMNxE/vPPP4enp6feMYiI\niIiInOr2229v0faGW7XG09Pzoisw6GH27Nn461//qncMO9XyAMwkSrVMquUBmEmEankAZhKhWh6A\nmUSplkm1PAAzidi+fXuLb8MPuxIRERERGRAn8k5gtVr1jtCIankAZhKlWibV8gDMJEK1PAAziVAt\nD8BMolTLpFoegJlchRN5J4iMjNQ7QiOq5QGYSZRqmVTLAzCTCNXyAMwkQrU8ADOJUi2TankAZnIV\nw33Ydf369cr1yBMRERERXYnt27er+2FXi8WCqVOnwmazITk5GampqY2unzt3Lt5//30AQF1dHfbs\n2YPy8nJ06NBB6P41TcORI0dgs9mcnp3U4unpia5du8JkMukdhYiIiEg3Us7I22w29O7dGzk5OQgI\nCMDAgQORlZWF8PDwZrf/9NNP8frrryMnJ6fJdY7OyJeVlaF9+/b84pNWoKqqCidPnoSfn98V3U9u\nbu5Fv6lSD6plUi0PwEwiVMsDMJMI1fIAzCRKtUyq5QGYScTlnJGX0iOfn5+PkJAQBAcHw9vbG4mJ\nicjOzna4/fLly/Hggw+2aB82m42T+FbCx8eH77wQERFRqyfljPyHH36IdevW4a233gIALFu2DFu2\nbMH8+fObbFtVVYXAwEDs37+/2bYaR2fkS0tL4e/v7/zwpCQ+3kREROROlD0j35Je5tWrVyM+Pl64\nN56IiIiIqDWS8mHXgIAAHDx40D4+ePAgzGZzs9t+8MEHl2yrmTx5MoKCggAAvr6+iIyMRM+ePZ0X\nmAwjNzcXAOw9bi0ZN/z7cm/vivHChQsRGRnJPBcZFxQUYNKkScrkaXD+c4p5+PvmDnn4+2bc57dq\neQA+vx3tv7KyEsC5Ne2Tk5PRUlJaa+rq6tC7d2+sX78e/v7+iI2NbfbDrpWVlejZsyeKi4vRtm3b\nZu+LrTUEOOfxzs1V60MugHqZVMsDMJMI1fIAzCRCtTwAM4lSLZNqeQBmEnE5rTXS1pFfu3atffnJ\npKQkzJw5E5mZmQCAlJQUAMC7776LdevWYfny5Q7vhxN557rpppswd+5c3HTTTS7dT2FhIZKSklBU\nVIRZs2bh8ccfv6L74+NNRERE7kTpibyztGQiX1ZRjPITh12WpfO13eDXweyy+7+UqKgozJ8/H7fc\ncotuGUQ99dRT8PX1xUsvveSU++NEnoiIiNyJ0l8IpYfyE4fx4gcpLrv/WYmZuk7kTSYTLvfvsLq6\nOnh5Xd7Dfzm3LS4uRmxs7GXtz1VUe0sNUC+TankAZhKhWh6AmUSolgdgJlGqZVItD8BMriJl1Ro6\nd/b89ddfx+DBg9GzZ09MmTIFZ8+eBQDs3bsXo0aNQo8ePXDTTTfBYrHYb/fGG2+gT58+CAoKQlxc\nHDZv3gwAePLJJ1FcXIxx48YhKCgI8+fPx6FDhzBx4kT06tUL0dHR+Pe//90kw7x58xAfH4+goCDY\nbDZERUXhq6++umSOC29bX1/f5P/o6PZ33303cnNzkZqaiqCgIPz888/OLS4RERFRK+TWrTU/WLe5\n/Ix8n6AYoW2joqLQvn17rFy5Ej4+PnjwwQcRHx+P1NRUxMXFYcKECZgyZQq++eYbPPTQQ9iwYQM0\nTcPo0aORk5MDPz8/FBcXo66uDsHBwQCA/v37Y968ebjlllugaRpuu+02/P73v8fUqVNRUlKCe++9\nF3PnzsVtt91mz9CxY0csX74c1113Ha666ir7fQwePBiDBg1qkuPLL7/EDTfc0Oxtz1dbW3vR2yck\nJOD+++/H+PHjnVJ7ttYQERGRO1F2HXk61waTnJwMf39/dOjQAU8//TQ+/vhjbNu2DVVVVZg6dSq8\nvLwwZMgQDB8+HB999BG8vLxQU1ODH3/8EbW1tTCbzfZJ/IW+/fZbHD16FM888wy8vLxw/fXXY8KE\nCfj4448bZXjiiSfg7+/fZCLuKMeHH354yduK3B7ARduATpw4gT/+8Y8YN24cbr75Zjz44IOYOHEi\nqqurW1JmIiIiolaDE3mJAgIC7P82m804fPgwDh061OhyAAgMDMShQ4fQo0cP/OMf/0BGRgZ69+6N\n5ORkHD7c/Id3Dx48iMOHD6NHjx72n9deew3l5eUOM5zPUY7z9+fotqK3v9gXg+3cuRPz5s3DnDlz\n8NRTTyErKwvvvfeew2VIneH8dXZVoVom1fIAzCRCtTwAM4lQLQ/ATKJUy6RaHoCZXIUTeYlKSkrs\n/y4uLka3bt3QvXt3lJSUNDpbffDgQXvbyJgxY7BmzRrs3LkTJpMJzz//vH278yfGZrMZ119/PQ4c\nOGD/sVqt+OCDDxplcDSZ9vf3bzZH9+7dL3lbAA7/H+ff/mKGDBkCT09PZGdnIzo6Wug2RERERK0Z\nJ/KSaJqGt99+G6WlpTh+/Dj++c9/YvTo0bjxxhvRtm1bzJs3D7W1tcjNzcW6deswevRo/PTTT9i0\naRPOnj2Lq666CldddRU8PH57yLp06YIDBw4AAAYMGIB27dph3rx5qK6uhs1mw+7du7Fjxw6hfBfL\nISImJuaStxf5OMbGjRvRu3dvoX1eKRU/qa5aJtXyAMwkQrU8ADOJUC0PwEyiVMukWh6AmVzFrZef\n7HxtN8xKzHTp/YsymUwYO3YsxowZg8OHD2PkyJGYPn06vL29sXz5csyYMQOvvfYa/P39sWjRIoSE\nhGD37t144YUXsG/fPnh7eyMuLg6vvfaa/T6nTZuG1NRUpKWl4ZlnnkFWVhZmzZqFAQMG4OzZswgN\nDcXf/vY3oXwXy+Gs21/sjD4AnDx50qWtNERERETuxK1XrVHJ+SvM0JVzxuOt4vqxqmVSLQ/ATCJU\nywMwkwjV8gDMJEq1TKrlAZhJBFetISIiIiJqJXhGXhKekXcu1R9vIiIiopa4nDPybt0jr5LvvvtO\n7whERERE5EbYWkOtlorrx6qWSbU8ADOJUC0PwEwiVMsDMJMo1TKplgdgJleRNpG3WCwICwtDaGgo\nMjIymt1m48aNiI6ORt++fTF06FBZ0YiIiIiIDEdKj7zNZkPv3r2Rk5ODgIAADBw4EFlZWQgPD7dv\nU1FRgZtvvhnr1q2D2WxGeXk5Onfu3OS+jNojT87Fx5uIiIjcibKr1uTn5yMkJATBwcHw9vZGYmIi\nsrOzG22zfPlyjBkzBmazGQCancQTEREREdE5UibyJSUlCAwMtI/NZjNKSkoabVNYWIhjx47h1ltv\nRUxMDJYuXdqifXh6eqKqqsopeUltVVVV8PT0vOL7UbE3TrVMquUBmEmEankAZhKhWh6AmUSplkm1\nPAAzuYqUVWsu9Y2eAFBbW4vt27dj/fr1qKqqwuDBgzFo0CCEhoYK7aNr1644cuQIKioqrjRui1VW\nVsLX11f6fh1RLQ/g3Eyenp7o2rWrU+6LiIiIyKikTOQDAgJw8OBB+/jgwYP2FpoGgYGB6Ny5M9q2\nbYu2bdvilltuwc6dO5udyE+ePBlBQUEAAF9fX0RGRiI+Ph5+fn72v64avqlL1rih31+v/auex9lj\nPz+/K76/+Ph4Zf4/53+z3PnfNMc8zY/Pz6ZCHo75++aOefj7Ztznt2p5GvD53XhcUFCAyspKAIDV\nakVycjJaSsqHXevq6tC7d2+sX78e/v7+iI2NbfJh1x9//BFTpkzBunXrcPbsWcTFxWHFihWIiIho\ndF+OPuxKRERERGRUyn7Y1cvLCwsWLMDw4cMRERGBBx54AOHh4cjMzERmZiYAICwsDHfddRf69euH\nuLg4PP74400m8aq68K86vamWB2AmUaplUi0PwEwiVMsDMJMI1fIAzCRKtUyq5QGYyVW8ZO1oxIgR\nGDFiRKPLUlJSGo2feeYZPPPMM7IiEREREREZlpTWGmdiaw0RERERuRtlW2uIiIiIiMi5OJF3AtV6\nrFTLAzCTKNUyqZYHYCYRquUBmEmEankAZhKlWibV8gDM5CqcyBMRERERGRB75ImIiIiIdMYeeSIi\nIiKiVoITeSdQrcdKtTwAM4lSLZNqeQBmEqFaHoCZRKiWB2AmUaplUi0PwEyuwok8EREREZEBsUee\niIiIiEhn7JEnIiIiImolOJF3AtV6rFTLAzCTKNUyqZYHYCYRquUBmEmEankAZhKlWibV8gDM5Cqc\nyBMRERERGRB75ImIiIiIdKZ0j7zFYkFYWBhCQ0ORkZHR5PqNGzfC19cX0dHRiI6OxksvvSQrGhER\nERGR4UiZyNtsNkyZMgUWiwW7d+9GVlYW9uzZ02S73/3ud9ixYwd27NiBZ599VkY0p1Ctx0q1PAAz\niVItk2p5AGYSoVoegJlEqJYHYCZRqmVSLQ/ATK4iZSKfn5+PkJAQBAcHw9vbG4mJicjOzm6yncG6\nfIiIiIiIdCPUI9+/f388/PDDGDduHPz8/Fq8kw8//BDr1q3DW2+9BQBYtmwZtmzZgvnz59u3+eqr\nrzB69GiYzWYEBARg7ty5iIiIaHJf7JEnIiIiIndzOT3yXiIbPffcc1i6dCmeffZZ3HLLLZgwYQJG\njx6Nq6++WmgnJpPpktsMGDAABw8ehI+PD9auXYt77rkH+/bta3bbyZMnIygoCADg6+uLyMhIxMfH\nA/jtbRKOOeaYY4455phjjjlWdVxQUIDKykoAgNVqRXJyMlqqRavWHDt2DCtXrsSyZcvw/fff4957\n78WECRNw2223XfR2eXl5SEtLg8ViAQCkp6fDw8MDqampDm/To0cPfPvtt+jUqVOjy1U8I5+bm2t/\nYFSgWh6AmUSplkm1PAAziVAtD8BMIlTLAzCTKNUyqZYHYCYRLl+1plOnTpg4cSKefPJJBAYG4uOP\nP0ZKSgp69eqFL774wuHtYmJiUFhYiKKiItTU1GDFihVISEhotE1ZWZm9Rz4/Px+apjWZxBMRERER\n0TlCZ+Q1TcO6deuwbNkyrF69GoMGDcLEiRMxevRotG3bFh9//DEmT56Mw4cPO7yPtWvXYurUqbDZ\nbEhKSsLMmTORmZkJAEhJScG//vUvLFy4EF5eXvDx8cE///lPDBo0qMn9qHhGnoiIiIjoSlzOGXmh\nibyfnx86d+6MiRMn4qGHHoLZbG6yzdChQ7Fx48YW7fxycCJPRERERO7GZa01n332GX744QekpqY2\nO4kHIGUSr6qGDzCoQrU8ADOJUi2TankAZhKhR56yimL8YN3m8Ge15X/SM10KH7dLYyYxqmVSLQ/A\nTK7iJbLRnXfeiWPHjjW5vGvXrjhy5IjTQxERkbGUnziMFz9IcXj9H26YLDENEVHrINRa0759e5w8\nebLRZbW1tejWrRuOHj3qsnDNYWsNEZF6frBuu+hEflZiJvoExUhMRERkLE5fR37IkCEAgOrqavu/\nGxQXF2Pw4MEtjEhERERERM5w0R75pKQkJCUlwcvLC8nJyfZxcnIyFi5ciP/9T72eRz2o1mOlWh6A\nmUSplkm1PAAziVAtDwDs2LpT7whNqFYn1fIAzCRKtUyq5QGYyVUuekb+kUceAQAMGjQIYWFhMvIQ\nEREREZEAhz3yS5cuxYQJEwAAb7/9NkwmU7N38Nhjj7kuXTPYI09EpB72yBMRXRmn9shnZWXZJ/JL\nly5VZiJPREREREQX6ZFfs2aN/d8bN27El19+2ewPqddjpVoegJlEqZZJtTwAM4lQLQ/AHnkRquUB\nmEmUaplUywMwk6s4PCNfX18vdAceHkLfKUVERERERE7ksEdeZIJuMplgs9mcHupi2CNPRKQe9sgT\nEV0Zp/bI//zzz1cciIiIiIiIXMPhaffg4GChH1Kvx0q1PAAziVItk2p5AGYSoVoegD3yIlTLAzCT\nKNUyqZYHYCZXcXhG/vHHH8dbb70FAPbVay5kMpnw3nvvCe3IYrFg6tSpsNlsSE5ORmpqarPbbd26\nFYMHD8bKlSsxevRoofsmIiIiImptHPbIp6enY+bMmQCAtLQ0mEwmXLipyWTC3//+90vuxGazoXfv\n3sjJyUFAQAAGDhyIrKwshIeHN9nujjvugI+PDx599FGMGTOmyX2xR56ISD3skSciujJO7ZFvmMQD\n5ybyVyI/Px8hISH2VpzExERkZ2c3mcjPnz8fY8eOxdatW69of0RERERE7k547cj169cjOTkZI0eO\nxOOPP46cnBzhnZSUlCAwMNA+NpvNKCkpabJNdnY2Jk2aBAAOv4BKRar1WKmWB2AmUaplUi0PwEwi\nVMsDsEdehGp5AGYSpVom1fIAzOQqDs/In+/VV19FRkYGHn30UURHR8NqteKhhx7CjBkz8Mwzz1zy\n9iKT8qlTp2L27Nn2Fh4HHT8AgMmTJyMoKAgA4Ovri8jISMTHxwP47UGROS4oKNB1/6rnOZ8qeVQd\nFxQUMM8lxnx+q5vn2C/VAIBO17dtdqxKfVR9fquWh79vHDtzzOd38/uvrKwEAFitViQnJ6OlHPbI\nn8/f3x+ff/45+vbta7/shx9+wLBhw3Do0KFL7iQvLw9paWmwWCwAzvXfe3h4NPrAa8+ePe2T9/Ly\ncvj4+OCtt95CQkJCo/tijzwRkXrYI09EdGWc2iN/PpPJhBtuuKHRZT179hT+VteYmBgUFhaiqKgI\n/v7+WLFiBbKyshptc/669Y8++ihGjRrVZBJPRERERETnOJyJ19fX23/S0tKQnJyMffv2obq6Gnv3\n7sUTTzyB559/XmgnXl5eWLBgAYYPH46IiAg88MADCA8PR2ZmJjIzM532n9HLhW/36U21PAAziVIt\nk2p5AGYSoVoegD3yIlTLAzCTKNUyqZYHYCZXcXhG3sur6VUXnkVfvny5cD/PiBEjMGLEiEaXpaQ0\n/zbskiVLhO6TiIiIiKi1ctgjX1RUJHQHsr/dlT3yRETqYY88EdGVcWqPvOwJOhERERERiRNeRz47\nOxtPP/00Hn74YUyYMAETJ07ExIkTXZnNMFTrsVItD8BMolTLpFoegJkcKasoxg/WbfjBug3LPnrb\n/u+Gn7KKYl3zsUf+0lTLAzCTKNUyqZYHYCZXEVq15vnnn8fChQuRmJiIlStX4sknn8Ty5cvxwAMP\nuDofEREJKD9x2N7acuyXany6v22j62clZsKvg1mPaERE5CJC68gHBQXhs88+Q2RkJDp06ICKigrk\n5+fjxRdfxOrVq2XktGOPPBFRU3r3qOu9fyIio7ucHnmh1prKykpERkYCANq0aYOamhrExsbiq6++\nanlKIiIiIiK6YkIT+Z49e+KHH34AAPTp0wcLFy7Ee++9h06dOrk0nFGo1mOlWh6AmUSplkm1PAAz\niTj2S7XeEZpgj/ylqZYHYCZRqmVSLQ/ATK4i1CP/0ksvoby8HAAwe/ZsjBs3DqdOncKbb77p0nBE\nRERERNQ8oR55lbBHnoioKb171PXePxGR0Tl1HfkL7du3DytXrkRpaSkCAgJw3333oVevXi0OSURE\nREREV06oR3758uUYMGAACgoK0K5dO+zatQsDBgzA+++/7+p8hqBaj5VqeQBmEqVaJtXyAMwkgj3y\nYlR73FTLAzCTKNUyqZYHYCZXEToj/7e//Q1r1qzBLbfcYr9s8+bNmDBhAh566CGXhSMiIiIiouYJ\n9ch36dIFpaWl8Pb2tl9WW1sLf39//Prrry4NeCH2yBMRNaV3j7re+yciMjqXrSP/9NNPY+bMmaiu\nPvd2bVVVFf7v//4P06ZNE96RxWJBWFgYQkNDkZGR0eT67OxsREVFITo6GjfeeCM2bNggfN9ERERE\nRK2Nw4l8YGCg/efNN9/EG2+8gWuvvRZdu3aFr68vXn/9dSxatEhoJzabDVOmTIHFYsHu3buRlZWF\nPXv2NNpm2LBh2LlzJ3bs2IF33nkHTzzxxJX9zyRSrcdKtTwAM4lSLZNqeQBmEsEeeTGqPW6q5QGY\nSZRqmVTLAzCTqzjskV+6dOklb2wymYR2kp+fj5CQEAQHBwMAEhMTkZ2djfDwcPs211xzjf3fp06d\nQufOnYXum4iIiIioNXI4kR86dKjTdlJSUoLAwED72Gw2Y8uWLU22W7VqFWbOnIlDhw7h888/d9r+\nXS0+Pl7vCI2olgdgJlGqZVItD8BMIjpd31bvCE1ED4zSO0ITqj1uquUBmEmUaplUywMwk6sIrVpT\nU1ODl156CUuXLkVpaSn8/f0xYcIEPPvss2jTps0lby965v6ee+7BPffcY18RZ+/evc1uN3nyZAQF\nBQEAfH19ERkZaX8wGt4m4ZhjjjlubeOGlpqGifyFY3ffP8ccc8yxkcYFBQWorKwEAFitViQnJ6Ol\nhFatmTZtGvLz8/H3v/8dQUFBsFqteOGFFxATE4PXX3/9kjvJy8tDWloaLBYLACA9PR0eHh5ITU11\neJsbbrgB+fn5uO666xpdruKqNbm5ufYHRgWq5QGYSZRqmVTLAzCTI+evGnPsl+omZ+X1XrXmDzdM\nxvgxSS7b/+VQ4XE7n2p5AGYSpVom1fIAzCTCZd/sunLlSuzcudPetx4WFoYBAwagX79+QhP5mJgY\nFBYWoqioCP7+/lixYgWysrIabbN//3707NkTJpMJ27dvB4Amk3giIiIiIjpHaCJ/xTvx8sKCBQsw\nfPhw2Gw2JCUlITw8HJmZmQCAlJQUfPTRR3jvvffg7e2Ndu3a4YMPPpARzSlU+msOUC8PwEyiVMuk\nWh6AmUSwR16Mao+bankAZhKlWibV8gDM5CpCE/n77rsPCQkJeO6553D99dejqKgIL730Eu677z7h\nHY0YMQIjRoxodFlKym9vw/7lL3/BX/7yF+H7IyIiIiJqzYS+EGrOnDkYNmwYpkyZghtvvBFPPfUU\nbrvtNsyZM8fV+Qyh4QMMqlAtD8BMolTLpFoegJlEcB15Mao9bqrlAZhJlGqZVMsDMJOrXPKMfF1d\nHR5//HFkZmbihRdekJGJiIiIiIguQWjVmu7du8NqtcLb21tGpotScdUaIiK9XWrVGL1XrXH1/omI\njO5yVq0Raq2ZNm0annvuOdTU1FxWMCIiIiIici6hify8efMwd+5ctG/fHmazGYGBgQgMDLR/KVNr\np1qPlWp5AGYSpVom1fIAzCSCPfJiVHvcVMsDMJMo1TKplgdgJlcRWrVm2bJlzX47q0BXDhERERER\nuYBQj/zZs2fx0ksvISsrC6WlpfD390diYiKeffZZXH311TJy2rFHnoioKb171PXePxGR0bnsm10n\nTZqEffv2Yf78+QgKCoLVasXLL7+MkpISLFmy5LLCEhERERHR5RPqkV+1ahVWr16NESNGoE+fPhgx\nYgQ++eQTrFq1ytX5DEG1HivV8gDMJEq1TKrlAZhJBHvkxaj2uKmWB2AmUaplUi0PwEyuIjSR7969\nO6qqqhpdVl1dDX9/f5eEIiIiIiKiixPqkZ89ezaWL1+OKVOmIDAwEFarFW+++SbGjRuHgQMH2re7\n7bbbXBoWYI88EVFz9O5R13v/RERG57Ie+UWLFgEA0tPT7ZdpmoZFixbZrwOAAwcOtGjnRERERER0\neYRaa4qKilBUVIQDBw7Yfy4ct+ZJvGo9VqrlAZhJlGqZVMsDMJMI9siLUe1xUy0PwEyiVMukWh6A\nmVxFaCLvLBaLBWFhYQgNDUVGRkaT699//31ERUWhX79+uPnmm7Fr1y6Z8YiIiIiIDEOoR94ZbDYb\nevfujZycHAQEBGDgwIHIyspCeHi4fZtvvvkGERER8PX1hcViQVpaGvLy8hrdD3vkiYia0rtHXe/9\nExEZ3eX0yEs7I5+fn4+QkBAEBwfD29sbiYmJyM7ObrTN4MGD4evrCwCIi4tDcXGxrHhERERERIYi\nbSJfUlKCwMBA+9hsNqOkpMTh9m+//TZGjhwpI9oVU63HSrU8ADOJUi2TankAZhLBHnkxqj1uquUB\nmEmUaplUywMwk6sIrVrjDCaTSXjbL7/8EosXL8bXX3/d7PWTJ09GUFAQAMDX1xeRkZGIj48H8NuD\nInNcUFCg6/5Vz3M+VfKoOi4oKGCeS4z5/HY8vnAC3zDudH1bqftv2J/s/Rv9+a1aHv6+cezMMZ/f\nze+/srISAGC1WpGcnIyWktYjn5eXh7S0NFgsFgDnlrL08PBAampqo+127dqF0aNHw2KxICQkpMn9\nsEeeiKgpvXvU9d4/EZHRKd0jHxMTg8LCQhQVFaGmpgYrVqxAQkJCo22sVitGjx6NZcuWNTuJJyIi\nIiKic6RN5L28vLBgwQIMHz4cEREReOCBBxAeHo7MzExkZmYCAF544QUcP34ckyZNQnR0NGJjY2XF\nuyIXvt2nN9XyAMwkSrVMquUBmEkEe+TFqPa4qZYHYCZRqmVSLQ/ATK7iJXNnI0aMwIgRIxpdlpLy\n21ux//nPf/Cf//xHZiQiIiIiIkOS1iPvLOyRJyJqSu8edb33T0RkdEr3yBMRERERkfNwIu8EqvVY\nqZYHYCZRqmVSLQ/ATCLYIy9GtcdNtTwAM4lSLZNqeQBmchVO5ImIiIiIDIg98kREbkDvHnW9909E\nZHTskSciIiIiaiU4kXcC1XqsVMsDMJMo1TKplgdgJhHskRej2uOmWh6AmUSplkm1PAAzuQon8kRE\nREREBsQeeSIiN6B3j7re+yciMjr2yBMRERERtRKcyDuBaj1WquUBmEmUaplUywMwkwj2yItR7XFT\nLQ/ATKJUy6RaHoCZXIUTeSIiIiIiA2KPPBGRG9C7R13v/RMRGZ3yPfIWiwVhYWEIDQ0WNmk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+ "text": [ + "" + ] + } + ], + "prompt_number": 22 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Interpretation\n", + "\n", + "Recall that Bayesian methodology returns a *distribution*. Hence we now have distributions to describe the unknown $\\lambda$s and $\\tau$. What have we gained? Immediately, we can see the uncertainty in our estimates: the wider the distribution, the less certain our posterior belief should be. We can also see what the plausible values for the parameters are: $\\lambda_1$ is around 18 and $\\lambda_2$ is around 23. The posterior distributions of the two $\\lambda$s are clearly distinct, indicating that it is indeed likely that there was a change in the user's text-message behaviour.\n", + "\n", + "What other observations can you make? If you look at the original data again, do these results seem reasonable? \n", + "\n", + "Notice also that the posterior distributions for the $\\lambda$s do not look like exponential distributions, even though our priors for these variables were exponential. In fact, the posterior distributions are not really of any form that we recognize from the original model. But that's OK! This is one of the benefits of taking a computational point of view. If we had instead done this analysis using mathematical approaches, we would have been stuck with an analytically intractable (and messy) distribution. Our use of a computational approach makes us indifferent to mathematical tractability.\n", + "\n", + "Our analysis also returned a distribution for $\\tau$. Its posterior distribution looks a little different from the other two because it is a discrete random variable, so it doesn't assign probabilities to intervals. We can see that near day 45, there was a 50% chance that the user's behaviour changed. Had no change occurred, or had the change been gradual over time, the posterior distribution of $\\tau$ would have been more spread out, reflecting that many days were plausible candidates for $\\tau$. By contrast, in the actual results we see that only three or four days make any sense as potential transition points. " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "###Why would I want samples from the posterior, anyways?\n", + "\n", + "\n", + "We will deal with this question for the remainder of the book, and it is an understatement to say that it will lead us to some amazing results. For now, let's end this chapter with one more example.\n", + "\n", + "We'll use the posterior samples to answer the following question: what is the expected number of texts at day $t, \\; 0 \\le t \\le 70$ ? Recall that the expected value of a Poisson variable is equal to its parameter $\\lambda$. Therefore, the question is equivalent to *what is the expected value of $\\lambda$ at time $t$*?\n", + "\n", + "In the code below, let $i$ index samples from the posterior distributions. Given a day $t$, we average over all possible $\\lambda_i$ for that day $t$, using $\\lambda_i = \\lambda_{1,i}$ if $t \\lt \\tau_i$ (that is, if the behaviour change has not yet occurred), else we use $\\lambda_i = \\lambda_{2,i}$. " + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "figsize(12.5, 5)\n", + "# tau_samples, lambda_1_samples, lambda_2_samples contain\n", + "# N samples from the corresponding posterior distribution\n", + "N = tau_samples.shape[0]\n", + "expected_texts_per_day = np.zeros(n_count_data)\n", + "for day in range(0, n_count_data):\n", + " # ix is a bool index of all tau samples corresponding to\n", + " # the switchpoint occurring prior to value of 'day'\n", + " ix = day < tau_samples\n", + " # Each posterior sample corresponds to a value for tau.\n", + " # for each day, that value of tau indicates whether we're \"before\"\n", + " # (in the lambda1 \"regime\") or\n", + " # \"after\" (in the lambda2 \"regime\") the switchpoint.\n", + " # by taking the posterior sample of lambda1/2 accordingly, we can average\n", + " # over all samples to get an expected value for lambda on that day.\n", + " # As explained, the \"message count\" random variable is Poisson distributed,\n", + " # and therefore lambda (the poisson parameter) is the expected value of\n", + " # \"message count\".\n", + " expected_texts_per_day[day] = (lambda_1_samples[ix].sum()\n", + " + lambda_2_samples[~ix].sum()) / N\n", + "\n", + "\n", + "plt.plot(range(n_count_data), expected_texts_per_day, lw=4, color=\"#E24A33\",\n", + " label=\"expected number of text-messages received\")\n", + "plt.xlim(0, n_count_data)\n", + "plt.xlabel(\"Day\")\n", + "plt.ylabel(\"Expected # text-messages\")\n", + "plt.title(\"Expected number of text-messages received\")\n", + "plt.ylim(0, 60)\n", + "plt.bar(np.arange(len(count_data)), count_data, color=\"#348ABD\", alpha=0.65,\n", + " label=\"observed texts per day\")\n", + "\n", + "plt.legend(loc=\"upper left\");" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "display_data", + "png": 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h+P3334X1JyQkID09Hb169aryPTpnzhxoaWkhISEB69atw+7du2vFMDJCCCG1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\nvIeuDOYuh9nL0PvMllpVCcfB3ajfXwjH/kKox0vdvjZw4P+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+ "text": [ + "" + ] + } + ], + "prompt_number": 24 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Our analysis shows strong support for believing the user's behavior did change ($\\lambda_1$ would have been close in value to $\\lambda_2$ had this not been true), and that the change was sudden rather than gradual (as demonstrated by $\\tau$'s strongly peaked posterior distribution). We can speculate what might have caused this: a cheaper text-message rate, a recent weather-to-text subscription, or perhaps a new relationship. (In fact, the 45th day corresponds to Christmas, and I moved away to Toronto the next month, leaving a girlfriend behind.)\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "##### Exercises\n", + "\n", + "1\\. Using `lambda_1_samples` and `lambda_2_samples`, what is the mean of the posterior distributions of $\\lambda_1$ and $\\lambda_2$?" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# type your code here." + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 25 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "2\\. What is the expected percentage increase in text-message rates? `hint:` compute the mean of `lambda_1_samples/lambda_2_samples`. Note that this quantity is very different from `lambda_1_samples.mean()/lambda_2_samples.mean()`." + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# type your code here." + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 26 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "3\\. What is the mean of $\\lambda_1$ **given** that we know $\\tau$ is less than 45. That is, suppose we have been given new information that the change in behaviour occurred prior to day 45. What is the expected value of $\\lambda_1$ now? (You do not need to redo the PyMC part. Just consider all instances where `tau_samples < 45`.)" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# type your code here." + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 17 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### References\n", + "\n", + "\n", + "- [1] Gelman, Andrew. N.p.. Web. 22 Jan 2013. [N is never large enough](http://andrewgelman.com/2005/07/31/n_is_never_larg/).\n", + "- [2] Norvig, Peter. 2009. [The Unreasonable Effectiveness of Data](http://static.googleusercontent.com/media/research.google.com/en//pubs/archive/35179.pdf).\n", + "- [3] Patil, A., D. Huard and C.J. Fonnesbeck. 2010. \n", + "PyMC: Bayesian Stochastic Modelling in Python. Journal of Statistical \n", + "Software, 35(4), pp. 1-81. \n", + "- [4] Jimmy Lin and Alek Kolcz. Large-Scale Machine Learning at Twitter. Proceedings of the 2012 ACM SIGMOD International Conference on Management of Data (SIGMOD 2012), pages 793-804, May 2012, Scottsdale, Arizona.\n", + "- [5] Cronin, Beau. \"Why Probabilistic Programming Matters.\" 24 Mar 2013. Google, Online Posting to Google . Web. 24 Mar. 2013. ." + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from IPython.core.display import HTML\n", + "\n", + "\n", + "def css_styling():\n", + " styles = open(\"../styles/custom.css\", \"r\").read()\n", + " return HTML(styles)\n", + "css_styling()" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "html": [ + "\n", + "\n" + ], + "metadata": {}, + "output_type": "pyout", + "prompt_number": 1, + "text": [ + "" + ] + } + ], + "prompt_number": 1 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [], + "language": "python", + "metadata": {}, + "outputs": [] + } + ], + "metadata": {} + } + ] +} diff --git a/Chapter1_Introduction/README.md b/Chapter1_Introduction/README.md index 4aa18c55..86c73888 100644 --- a/Chapter1_Introduction/README.md +++ b/Chapter1_Introduction/README.md @@ -1,4 +1,4 @@ -Chapter 1: Introduction to Bayesian Methods -=========== - -### [Read it online here](http://nbviewer.ipython.org/urls/raw.github.com/CamDavidsonPilon/Probabilistic-Programming-and-Bayesian-Methods-for-Hackers/master/Chapter1_Introduction/Chapter1_Introduction.ipynb) +Chapter 1: Introduction to Bayesian Methods +=========== + +### [Read it online here](http://nbviewer.ipython.org/urls/raw.github.com/CamDavidsonPilon/Probabilistic-Programming-and-Bayesian-Methods-for-Hackers/master/Chapter1_Introduction/Chapter1_Introduction.ipynb) diff --git a/Chapter1_Introduction/data/txtdata.csv b/Chapter1_Introduction/data/txtdata.csv index 6e657538..2411f62d 100644 --- a/Chapter1_Introduction/data/txtdata.csv +++ b/Chapter1_Introduction/data/txtdata.csv @@ -1,74 +1,74 @@ -1.300000000000000000e+01 -2.400000000000000000e+01 -8.000000000000000000e+00 -2.400000000000000000e+01 -7.000000000000000000e+00 -3.500000000000000000e+01 -1.400000000000000000e+01 -1.100000000000000000e+01 -1.500000000000000000e+01 -1.100000000000000000e+01 -2.200000000000000000e+01 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+3.100000000000000000e+01 +1.900000000000000000e+01 +1.100000000000000000e+01 +1.800000000000000000e+01 +2.000000000000000000e+01 +1.200000000000000000e+01 +3.500000000000000000e+01 +1.700000000000000000e+01 +2.300000000000000000e+01 +1.700000000000000000e+01 +4.000000000000000000e+00 +2.000000000000000000e+00 +3.100000000000000000e+01 +3.000000000000000000e+01 +1.300000000000000000e+01 +2.700000000000000000e+01 +0.000000000000000000e+00 +3.900000000000000000e+01 +3.700000000000000000e+01 +5.000000000000000000e+00 +1.400000000000000000e+01 +1.300000000000000000e+01 +2.200000000000000000e+01 diff --git a/Chapter2_MorePyMC/MorePyMC.ipynb b/Chapter2_MorePyMC/MorePyMC.ipynb index 2b5ef50b..2673dd42 100644 --- a/Chapter2_MorePyMC/MorePyMC.ipynb +++ b/Chapter2_MorePyMC/MorePyMC.ipynb @@ -1,2616 +1,2616 @@ -{ - "metadata": { - "name": "" - }, - "nbformat": 3, - "nbformat_minor": 0, - "worksheets": [ - { - "cells": [ - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Chapter 2\n", - "======\n", - "______\n", - "\n", - "This chapter introduces more PyMC syntax and design patterns, and ways to think about how to model a system from a Bayesian perspective. It also contains tips and data visualization techniques for assessing goodness-of-fit for your Bayesian model." - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## A little more on PyMC\n", - "\n", - "### Parent and Child relationships\n", - "\n", - "To assist with describing Bayesian relationships, and to be consistent with PyMC's documentation, we introduce *parent and child* variables. \n", - "\n", - "* *parent variables* are variables that influence another variable. \n", - "\n", - "* *child variable* are variables that are affected by other variables, i.e. are the subject of parent variables. \n", - "\n", - "A variable can be both a parent and child. For example, consider the PyMC code below." - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "import pymc as pm\n", - "\n", - "\n", - "parameter = pm.Exponential(\"poisson_param\", 1)\n", - "data_generator = pm.Poisson(\"data_generator\", parameter)\n", - "data_plus_one = data_generator + 1" - ], - "language": "python", - "metadata": {}, - "outputs": [], - "prompt_number": 1 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "`parameter` controls the parameter of `data_generator`, hence influences its values. The former is a parent of the latter. By symmetry, `data_generator` is a child of `parameter`.\n", - "\n", - "Likewise, `data_generator` is a parent to the variable `data_plus_one` (hence making `data_generator` both a parent and child variable). Although it does not look like one, `data_plus_one` should be treated as a PyMC variable as it is a *function* of another PyMC variable, hence is a child variable to `data_generator`.\n", - "\n", - "This nomenclature is introduced to help us describe relationships in PyMC modeling. You can access a variables children and parent variables using the `children` and `parents` attributes attached to variables." - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "print \"Children of `parameter`: \"\n", - "print parameter.children\n", - "print \"\\nParents of `data_generator`: \"\n", - "print data_generator.parents\n", - "print \"\\nChildren of `data_generator`: \"\n", - "print data_generator.children" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "Children of `parameter`: \n", - "set([])\n", - "\n", - "Parents of `data_generator`: \n", - "{'mu': }\n", - "\n", - "Children of `data_generator`: \n", - "set([])\n" - ] - } - ], - "prompt_number": 2 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Of course a child can have more than one parent, and a parent can have many children." - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### PyMC Variables\n", - "\n", - "All PyMC variables also expose a `value` attribute. This method produces the *current* (possibly random) internal value of the variable. If the variable is a child variable, its value changes given the variable's parents' values. Using the same variables from before:" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "print \"parameter.value =\", parameter.value\n", - "print \"data_generator.value =\", data_generator.value\n", - "print \"data_plus_one.value =\", data_plus_one.value" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "parameter.value = 0.0281609254306\n", - "data_generator.value = 0\n", - "data_plus_one.value = 1\n" - ] - } - ], - "prompt_number": 3 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "PyMC is concerned with two types of programming variables: `stochastic` and `deterministic`.\n", - "\n", - "* *stochastic variables* are variables that are not deterministic, i.e., even if you knew all the values of the variables' parents (if it even has any parents), it would still be random. Included in this category are instances of classes `Poisson`, `DiscreteUniform`, and `Exponential`.\n", - "\n", - "* *deterministic variables* are variables that are not random if the variables' parents were known. This might be confusing at first: a quick mental check is *if I knew all of variable `foo`'s parent variables, I could determine what `foo`'s value is.* \n", - "\n", - "We will detail each below.\n", - "\n", - "#### Initializing Stochastic variables\n", - "\n", - "Initializing a stochastic variable requires a `name` argument, plus additional parameters that are class specific. For example:\n", - "\n", - "`some_variable = pm.DiscreteUniform(\"discrete_uni_var\", 0, 4)`\n", - "\n", - "where 0, 4 are the `DiscreteUniform`-specific lower and upper bound on the random variable. The [PyMC docs](http://pymc-devs.github.com/pymc/distributions.html) contain the specific parameters for stochastic variables. (Or use `object??`, for example `pm.DiscreteUniform??` if you are using IPython!)\n", - "\n", - "The `name` attribute is used to retrieve the posterior distribution later in the analysis, so it is best to use a descriptive name. Typically, I use the Python variable's name as the `name`.\n", - "\n", - "For multivariable problems, rather than creating a Python array of stochastic variables, addressing the `size` keyword in the call to a `Stochastic` variable creates multivariate array of (independent) stochastic variables. The array behaves like a Numpy array when used like one, and references to its `value` attribute return Numpy arrays. \n", - "\n", - "The `size` argument also solves the annoying case where you may have many variables $\\beta_i, \\; i = 1,...,N$ you wish to model. Instead of creating arbitrary names and variables for each one, like:\n", - "\n", - " beta_1 = pm.Uniform(\"beta_1\", 0, 1)\n", - " beta_2 = pm.Uniform(\"beta_2\", 0, 1)\n", - " ...\n", - "\n", - "we can instead wrap them into a single variable:\n", - "\n", - " betas = pm.Uniform(\"betas\", 0, 1, size=N)\n", - "\n", - "#### Calling `random()`\n", - "We can also call on a stochastic variable's `random()` method, which (given the parent values) will generate a new, random value. Below we demonstrate this using the texting example from the previous chapter." - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "lambda_1 = pm.Exponential(\"lambda_1\", 1) # prior on first behaviour\n", - "lambda_2 = pm.Exponential(\"lambda_2\", 1) # prior on second behaviour\n", - "tau = pm.DiscreteUniform(\"tau\", lower=0, upper=10) # prior on behaviour change\n", - "\n", - "print \"lambda_1.value = %.3f\" % lambda_1.value\n", - "print \"lambda_2.value = %.3f\" % lambda_2.value\n", - "print \"tau.value = %.3f\" % tau.value\n", - "print\n", - "\n", - "lambda_1.random(), lambda_2.random(), tau.random()\n", - "\n", - "print \"After calling random() on the variables...\"\n", - "print \"lambda_1.value = %.3f\" % lambda_1.value\n", - "print \"lambda_2.value = %.3f\" % lambda_2.value\n", - "print \"tau.value = %.3f\" % tau.value" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "lambda_1.value = 0.539\n", - "lambda_2.value = 1.858\n", - "tau.value = 1.000\n", - "\n", - "After calling random() on the variables...\n", - "lambda_1.value = 0.343\n", - "lambda_2.value = 0.316\n", - "tau.value = 6.000\n" - ] - } - ], - "prompt_number": 4 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "The call to `random` stores a new value into the variable's `value` attribute. In fact, this new value is stored in the computer's cache for faster recall and efficiency." - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### **Warning**: *Don't update stochastic variables' values in-place.*\n", - "\n", - "\n", - "Straight from the PyMC docs, we quote [4]:\n", - "\n", - "> `Stochastic` objects' values should not be updated in-place. This confuses PyMC's caching scheme... The only way a stochastic variable's value should be updated is using statements of the following form:\n", - "\n", - " A.value = new_value\n", - "\n", - "> The following are in-place updates and should **never** be used:\n", - "\n", - " \n", - " A.value += 3\n", - " A.value[2,1] = 5\n", - " A.value.attribute = new_attribute_value\n", - " " - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "#### Deterministic variables\n", - "\n", - "Since most variables you will be modeling are stochastic, we distinguish deterministic variables with a `pymc.deterministic` wrapper. (If you are unfamiliar with Python wrappers (also called decorators), that's no problem. Just prepend the `pymc.deterministic` decorator before the variable declaration and you're good to go. No need to know more. ) The declaration of a deterministic variable uses a Python function:\n", - "\n", - " @pm.deterministic\n", - " def some_deterministic_var(v1=v1,):\n", - " #jelly goes here.\n", - "\n", - "For all purposes, we can treat the object `some_deterministic_var` as a variable and not a Python function. \n", - "\n", - "Prepending with the wrapper is the easiest way, but not the only way, to create deterministic variables: elementary operations, like addition, exponentials etc. implicitly create deterministic variables. For example, the following returns a deterministic variable:" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "type(lambda_1 + lambda_2)" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "metadata": {}, - "output_type": "pyout", - "prompt_number": 5, - "text": [ - "pymc.PyMCObjects.Deterministic" - ] - } - ], - "prompt_number": 5 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "The use of the `deterministic` wrapper was seen in the previous chapter's text-message example. Recall the model for $\\lambda$ looked like: \n", - "\n", - "$$\n", - "\\lambda = \n", - "\\cases{\n", - "\\lambda_1 & \\text{if } t \\lt \\tau \\cr\n", - "\\lambda_2 & \\text{if } t \\ge \\tau\n", - "}\n", - "$$\n", - "\n", - "And in PyMC code:" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "import numpy as np\n", - "n_data_points = 5 # in CH1 we had ~70 data points\n", - "\n", - "\n", - "@pm.deterministic\n", - "def lambda_(tau=tau, lambda_1=lambda_1, lambda_2=lambda_2):\n", - " out = np.zeros(n_data_points)\n", - " out[:tau] = lambda_1 # lambda before tau is lambda1\n", - " out[tau:] = lambda_2 # lambda after tau is lambda2\n", - " return out" - ], - "language": "python", - "metadata": {}, - "outputs": [], - "prompt_number": 7 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Clearly, if $\\tau, \\lambda_1$ and $\\lambda_2$ are known, then $\\lambda$ is known completely, hence it is a deterministic variable. \n", - "\n", - "Inside the deterministic decorator, the `Stochastic` variables passed in behave like scalars or Numpy arrays (if multivariable), and *not* like `Stochastic` variables. For example, running the following:\n", - "\n", - " @pm.deterministic\n", - " def some_deterministic(stoch=some_stochastic_var):\n", - " return stoch.value**2\n", - "\n", - "\n", - "will return an `AttributeError` detailing that `stoch` does not have a `value` attribute. It simply needs to be `stoch**2`. During the learning phase, it's the variable's `value` that is repeatedly passed in, not the actual variable. \n", - "\n", - "Notice in the creation of the deterministic function we added defaults to each variable used in the function. This is a necessary step, and all variables *must* have default values. " - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### Including observations in the Model\n", - "\n", - "At this point, it may not look like it, but we have fully specified our priors. For example, we can ask and answer questions like \"What does my prior distribution of $\\lambda_1$ look like?\" " - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "%matplotlib inline\n", - "from IPython.core.pylabtools import figsize\n", - "from matplotlib import pyplot as plt\n", - "figsize(12.5, 4)\n", - "\n", - "\n", - "samples = [lambda_1.random() for i in range(20000)]\n", - "plt.hist(samples, bins=70, normed=True, histtype=\"stepfilled\")\n", - "plt.title(\"Prior distribution for $\\lambda_1$\")\n", - "plt.xlim(0, 8);" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "metadata": {}, - "output_type": "display_data", - "png": 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- "text": [ - "" - ] - } - ], - "prompt_number": 10 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "To frame this in the notation of the first chapter, though this is a slight abuse of notation, we have specified $P(A)$. Our next goal is to include data/evidence/observations $X$ into our model. \n", - "\n", - "PyMC stochastic variables have a keyword argument `observed` which accepts a boolean (`False` by default). The keyword `observed` has a very simple role: fix the variable's current value, i.e. make `value` immutable. We have to specify an initial `value` in the variable's creation, equal to the observations we wish to include, typically an array (and it should be an Numpy array for speed). For example:" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "data = np.array([10, 5])\n", - "fixed_variable = pm.Poisson(\"fxd\", 1, value=data, observed=True)\n", - "print \"value: \", fixed_variable.value\n", - "print \"calling .random()\"\n", - "fixed_variable.random()\n", - "print \"value: \", fixed_variable.value" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "value: [10 5]\n", - "calling .random()\n", - "value: [10 5]\n" - ] - } - ], - "prompt_number": 11 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "This is how we include data into our models: initializing a stochastic variable to have a *fixed value*. \n", - "\n", - "To complete our text message example, we fix the PyMC variable `observations` to the observed dataset. " - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "# We're using some fake data here\n", - "data = np.array([10, 25, 15, 20, 35])\n", - "obs = pm.Poisson(\"obs\", lambda_, value=data, observed=True)\n", - "print obs.value" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "[10 25 15 20 35]\n" - ] - } - ], - "prompt_number": 12 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### Finally...\n", - "\n", - "We wrap all the created variables into a `pm.Model` class. With this `Model` class, we can analyze the variables as a single unit. This is an optional step, as the fitting algorithms can be sent an array of the variables rather than a `Model` class. I may or may not use this class in future examples ;)" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "model = pm.Model([obs, lambda_, lambda_1, lambda_2, tau])" - ], - "language": "python", - "metadata": {}, - "outputs": [], - "prompt_number": 13 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Modeling approaches\n", - "\n", - "A good starting thought to Bayesian modeling is to think about *how your data might have been generated*. Position yourself in an omniscient position, and try to imagine how *you* would recreate the dataset. \n", - "\n", - "In the last chapter we investigated text message data. We begin by asking how our observations may have been generated:\n", - "\n", - "1. We started by thinking \"what is the best random variable to describe this count data?\" A Poisson random variable is a good candidate because it can represent count data. So we model the number of sms's received as sampled from a Poisson distribution.\n", - "\n", - "2. Next, we think, \"Ok, assuming sms's are Poisson-distributed, what do I need for the Poisson distribution?\" Well, the Poisson distribution has a parameter $\\lambda$. \n", - "\n", - "3. Do we know $\\lambda$? No. In fact, we have a suspicion that there are *two* $\\lambda$ values, one for the earlier behaviour and one for the latter behaviour. We don't know when the behaviour switches though, but call the switchpoint $\\tau$.\n", - "\n", - "4. What is a good distribution for the two $\\lambda$s? The exponential is good, as it assigns probabilities to positive real numbers. Well the exponential distribution has a parameter too, call it $\\alpha$.\n", - "\n", - "5. Do we know what the parameter $\\alpha$ might be? No. At this point, we could continue and assign a distribution to $\\alpha$, but it's better to stop once we reach a set level of ignorance: whereas we have a prior belief about $\\lambda$, (\"it probably changes over time\", \"it's likely between 10 and 30\", etc.), we don't really have any strong beliefs about $\\alpha$. So it's best to stop here. \n", - "\n", - " What is a good value for $\\alpha$ then? We think that the $\\lambda$s are between 10-30, so if we set $\\alpha$ really low (which corresponds to larger probability on high values) we are not reflecting our prior well. Similar, a too-high alpha misses our prior belief as well. A good idea for $\\alpha$ as to reflect our belief is to set the value so that the mean of $\\lambda$, given $\\alpha$, is equal to our observed mean. This was shown in the last chapter.\n", - "\n", - "6. We have no expert opinion of when $\\tau$ might have occurred. So we will suppose $\\tau$ is from a discrete uniform distribution over the entire timespan.\n", - "\n", - "\n", - "Below we give a graphical visualization of this, where arrows denote `parent-child` relationships. (provided by the [Daft Python library](http://daft-pgm.org/) )\n", - "\n", - "\n", - "\n", - "\n", - "PyMC, and other probabilistic programming languages, have been designed to tell these data-generation *stories*. More generally, B. Cronin writes [5]:\n", - "\n", - "> Probabilistic programming will unlock narrative explanations of data, one of the holy grails of business analytics and the unsung hero of scientific persuasion. People think in terms of stories - thus the unreasonable power of the anecdote to drive decision-making, well-founded or not. But existing analytics largely fails to provide this kind of story; instead, numbers seemingly appear out of thin air, with little of the causal context that humans prefer when weighing their options." - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### Same story; different ending.\n", - "\n", - "Interestingly, we can create *new datasets* by retelling the story.\n", - "For example, if we reverse the above steps, we can simulate a possible realization of the dataset.\n", - "\n", - "1\\. Specify when the user's behaviour switches by sampling from $\\text{DiscreteUniform}(0, 80)$:" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "tau = pm.rdiscrete_uniform(0, 80)\n", - "print tau" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "37\n" - ] - } - ], - "prompt_number": 14 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "2\\. Draw $\\lambda_1$ and $\\lambda_2$ from an $\\text{Exp}(\\alpha)$ distribution:" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "alpha = 1. / 20.\n", - "lambda_1, lambda_2 = pm.rexponential(alpha, 2)\n", - "print lambda_1, lambda_2" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "29.0394614963 13.5921161471\n" - ] - } - ], - "prompt_number": 15 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "3\\. For days before $\\tau$, represent the user's received SMS count by sampling from $\\text{Poi}(\\lambda_1)$, and sample from $\\text{Poi}(\\lambda_2)$ for days after $\\tau$. For example:" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "data = np.r_[pm.rpoisson(lambda_1, tau), pm.rpoisson(lambda_2, 80 - tau)]" - ], - "language": "python", - "metadata": {}, - "outputs": [], - "prompt_number": 16 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "4\\. Plot the artificial dataset:" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "plt.bar(np.arange(80), data, color=\"#348ABD\")\n", - "plt.bar(tau - 1, data[tau - 1], color=\"r\", label=\"user behaviour changed\")\n", - "plt.xlabel(\"Time (days)\")\n", - "plt.ylabel(\"count of text-msgs received\")\n", - "plt.title(\"Artificial dataset\")\n", - "plt.xlim(0, 80)\n", - "plt.legend();" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "metadata": {}, - "output_type": "display_data", - "png": 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wevVqzJ07F+fOndO+d8uWLYiIiMDly5fh4eGBd999V7use/fu+N///ofLly8jODgYU6dO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\nukYiIiIyUnxqJpF+ybrP+/Tp0+Ht7Y0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- "text": [ - "" - ] - } - ], - "prompt_number": 17 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "It is okay that our fictional dataset does not look like our observed dataset: the probability is incredibly small it indeed would. PyMC's engine is designed to find good parameters, $\\lambda_i, \\tau$, that maximize this probability. \n", - "\n", - "\n", - "The ability to generate artificial datasets is an interesting side effect of our modeling, and we will see that this ability is a very important method of Bayesian inference. We produce a few more datasets below:" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "def plot_artificial_sms_dataset():\n", - " tau = pm.rdiscrete_uniform(0, 80)\n", - " alpha = 1. / 20.\n", - " lambda_1, lambda_2 = pm.rexponential(alpha, 2)\n", - " data = np.r_[pm.rpoisson(lambda_1, tau), pm.rpoisson(lambda_2, 80 - tau)]\n", - " plt.bar(np.arange(80), data, color=\"#348ABD\")\n", - " plt.bar(tau - 1, data[tau - 1], color=\"r\", label=\"user behaviour changed\")\n", - " plt.xlim(0, 80)\n", - "\n", - "figsize(12.5, 5)\n", - "plt.title(\"More example of artificial datasets\")\n", - "for i in range(4):\n", - " plt.subplot(4, 1, i)\n", - " plot_artificial_sms_dataset()" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "metadata": {}, - "output_type": "display_data", - "png": 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nve13xNcEeZzZvcThjpQfffQR1q1bh/379yMiIgKHDh1ii1EiIiIioi70sncD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\ncinFEJF43t5sgIjcg68tRI5xevcSci/LIn8Sj9n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- "text": [ - "" - ] - } - ], - "prompt_number": 18 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Later we will see how we use this to make predictions and test the appropriateness of our models." - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "#####Example: Bayesian A/B testing\n", - "\n", - "A/B testing is a statistical design pattern for determining the difference of effectiveness between two different treatments. For example, a pharmaceutical company is interested in the effectiveness of drug A vs drug B. The company will test drug A on some fraction of their trials, and drug B on the other fraction (this fraction is often 1/2, but we will relax this assumption). After performing enough trials, the in-house statisticians sift through the data to determine which drug yielded better results. \n", - "\n", - "Similarly, front-end web developers are interested in which design of their website yields more sales or some other metric of interest. They will route some fraction of visitors to site A, and the other fraction to site B, and record if the visit yielded a sale or not. The data is recorded (in real-time), and analyzed afterwards. \n", - "\n", - "Often, the post-experiment analysis is done using something called a hypothesis test like *difference of means test* or *difference of proportions test*. This involves often misunderstood quantities like a \"Z-score\" and even more confusing \"p-values\" (please don't ask). If you have taken a statistics course, you have probably been taught this technique (though not necessarily *learned* this technique). And if you were like me, you may have felt uncomfortable with their derivation -- good: the Bayesian approach to this problem is much more natural. \n", - "\n", - "### A Simple Case\n", - "\n", - "As this is a hacker book, we'll continue with the web-dev example. For the moment, we will focus on the analysis of site A only. Assume that there is some true $0 \\lt p_A \\lt 1$ probability that users who, upon shown site A, eventually purchase from the site. This is the true effectiveness of site A. Currently, this quantity is unknown to us. \n", - "\n", - "Suppose site A was shown to $N$ people, and $n$ people purchased from the site. One might conclude hastily that $p_A = \\frac{n}{N}$. Unfortunately, the *observed frequency* $\\frac{n}{N}$ does not necessarily equal $p_A$ -- there is a difference between the *observed frequency* and the *true frequency* of an event. The true frequency can be interpreted as the probability of an event occurring. For example, the true frequency of rolling a 1 on a 6-sided die is $\\frac{1}{6}$. Knowing the true frequency of events like:\n", - "\n", - "- fraction of users who make purchases, \n", - "- frequency of social attributes, \n", - "- percent of internet users with cats etc. \n", - "\n", - "are common requests we ask of Nature. Unfortunately, often Nature hides the true frequency from us and we must *infer* it from observed data.\n", - "\n", - "The *observed frequency* is then the frequency we observe: say rolling the die 100 times you may observe 20 rolls of 1. The observed frequency, 0.2, differs from the true frequency, $\\frac{1}{6}$. We can use Bayesian statistics to infer probable values of the true frequency using an appropriate prior and observed data.\n", - "\n", - "\n", - "With respect to our A/B example, we are interested in using what we know, $N$ (the total trials administered) and $n$ (the number of conversions), to estimate what $p_A$, the true frequency of buyers, might be. \n", - "\n", - "To set up a Bayesian model, we need to assign prior distributions to our unknown quantities. *A priori*, what do we think $p_A$ might be? For this example, we have no strong conviction about $p_A$, so for now, let's assume $p_A$ is uniform over [0,1]:" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "import pymc as pm\n", - "\n", - "# The parameters are the bounds of the Uniform.\n", - "p = pm.Uniform('p', lower=0, upper=1)" - ], - "language": "python", - "metadata": {}, - "outputs": [], - "prompt_number": 19 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Had we had stronger beliefs, we could have expressed them in the prior above.\n", - "\n", - "For this example, consider $p_A = 0.05$, and $N = 1500$ users shown site A, and we will simulate whether the user made a purchase or not. To simulate this from $N$ trials, we will use a *Bernoulli* distribution: if $ X\\ \\sim \\text{Ber}(p)$, then $X$ is 1 with probability $p$ and 0 with probability $1 - p$. Of course, in practice we do not know $p_A$, but we will use it here to simulate the data." - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "# set constants\n", - "p_true = 0.05 # remember, this is unknown.\n", - "N = 1500\n", - "\n", - "# sample N Bernoulli random variables from Ber(0.05).\n", - "# each random variable has a 0.05 chance of being a 1.\n", - "# this is the data-generation step\n", - "occurrences = pm.rbernoulli(p_true, N)\n", - "\n", - "print occurrences # Remember: Python treats True == 1, and False == 0\n", - "print occurrences.sum()" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "[False False False ..., False False True]\n", - "87\n" - ] - } - ], - "prompt_number": 20 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "The observed frequency is:" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "# Occurrences.mean is equal to n/N.\n", - "print \"What is the observed frequency in Group A? %.4f\" % occurrences.mean()\n", - "print \"Does this equal the true frequency? %s\" % (occurrences.mean() == p_true)" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "What is the observed frequency in Group A? 0.0580\n", - "Does this equal the true frequency? False\n" - ] - } - ], - "prompt_number": 21 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "We combine the observations into the PyMC `observed` variable, and run our inference algorithm:" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "# include the observations, which are Bernoulli\n", - "obs = pm.Bernoulli(\"obs\", p, value=occurrences, observed=True)\n", - "\n", - "# To be explained in chapter 3\n", - "mcmc = pm.MCMC([p, obs])\n", - "mcmc.sample(18000, 1000)" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "output_type": "stream", - "stream": "stdout", - "text": [ - " \r", - "[****************100%******************] 18000 of 18000 complete" - ] - }, - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "\n" - ] - } - ], - "prompt_number": 22 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "We plot the posterior distribution of the unknown $p_A$ below:" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "figsize(12.5, 4)\n", - "plt.title(\"Posterior distribution of $p_A$, the true effectiveness of site A\")\n", - "plt.vlines(p_true, 0, 90, linestyle=\"--\", label=\"true $p_A$ (unknown)\")\n", - "plt.hist(mcmc.trace(\"p\")[:], bins=25, histtype=\"stepfilled\", normed=True)\n", - "plt.legend()" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "metadata": {}, - "output_type": "pyout", - "prompt_number": 23, - "text": [ - "" - ] - }, - { - "metadata": {}, - "output_type": "display_data", - "png": 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Ntn3bSUlJ2Lt3L958800888wzDo+HbbbZZptttp25nZOTg9LSUgBAfn4+EhMT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\nl19+GQBQXFyM2NhYhISEIC4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- "text": [ - "" - ] - } - ], - "prompt_number": 23 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Our posterior distribution puts most weight near the true value of $p_A$, but also some weights in the tails. This is a measure of how uncertain we should be, given our observations. Try changing the number of observations, `N`, and observe how the posterior distribution changes.\n", - "\n", - "### *A* and *B* Together\n", - "\n", - "A similar anaylsis can be done for site B's response data to determine the analogous $p_B$. But what we are really interested in is the *difference* between $p_A$ and $p_B$. Let's infer $p_A$, $p_B$, *and* $\\text{delta} = p_A - p_B$, all at once. We can do this using PyMC's deterministic variables. (We'll assume for this exercise that $p_B = 0.04$, so $\\text{delta} = 0.01$, $N_B = 750$ (signifcantly less than $N_A$) and we will simulate site B's data like we did for site A's data )" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "import pymc as pm\n", - "figsize(12, 4)\n", - "\n", - "# these two quantities are unknown to us.\n", - "true_p_A = 0.05\n", - "true_p_B = 0.04\n", - "\n", - "# notice the unequal sample sizes -- no problem in Bayesian analysis.\n", - "N_A = 1500\n", - "N_B = 750\n", - "\n", - "# generate some observations\n", - "observations_A = pm.rbernoulli(true_p_A, N_A)\n", - "observations_B = pm.rbernoulli(true_p_B, N_B)\n", - "print \"Obs from Site A: \", observations_A[:30].astype(int), \"...\"\n", - "print \"Obs from Site B: \", observations_B[:30].astype(int), \"...\"" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "Obs from Site A: [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0] ...\n", - "Obs from Site B: [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0] ...\n" - ] - } - ], - "prompt_number": 24 - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "print observations_A.mean()\n", - "print observations_B.mean()" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "0.056\n", - "0.0306666666667\n" - ] - } - ], - "prompt_number": 25 - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "# Set up the pymc model. Again assume Uniform priors for p_A and p_B.\n", - "p_A = pm.Uniform(\"p_A\", 0, 1)\n", - "p_B = pm.Uniform(\"p_B\", 0, 1)\n", - "\n", - "\n", - "# Define the deterministic delta function. This is our unknown of interest.\n", - "@pm.deterministic\n", - "def delta(p_A=p_A, p_B=p_B):\n", - " return p_A - p_B\n", - "\n", - "# Set of observations, in this case we have two observation datasets.\n", - "obs_A = pm.Bernoulli(\"obs_A\", p_A, value=observations_A, observed=True)\n", - "obs_B = pm.Bernoulli(\"obs_B\", p_B, value=observations_B, observed=True)\n", - "\n", - "# To be explained in chapter 3.\n", - "mcmc = pm.MCMC([p_A, p_B, delta, obs_A, obs_B])\n", - "mcmc.sample(20000, 1000)" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "output_type": "stream", - "stream": "stdout", - "text": [ - " \r", - "[****************100%******************] 20000 of 20000 complete" - ] - }, - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "\n" - ] - } - ], - "prompt_number": 26 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Below we plot the posterior distributions for the three unknowns: " - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "p_A_samples = mcmc.trace(\"p_A\")[:]\n", - "p_B_samples = mcmc.trace(\"p_B\")[:]\n", - "delta_samples = mcmc.trace(\"delta\")[:]" - ], - "language": "python", - "metadata": {}, - "outputs": [], - "prompt_number": 27 - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "figsize(12.5, 10)\n", - "\n", - "# histogram of posteriors\n", - "\n", - "ax = plt.subplot(311)\n", - "\n", - "plt.xlim(0, .1)\n", - "plt.hist(p_A_samples, histtype='stepfilled', bins=25, alpha=0.85,\n", - " label=\"posterior of $p_A$\", color=\"#A60628\", normed=True)\n", - "plt.vlines(true_p_A, 0, 80, linestyle=\"--\", label=\"true $p_A$ (unknown)\")\n", - "plt.legend(loc=\"upper right\")\n", - "plt.title(\"Posterior distributions of $p_A$, $p_B$, and delta unknowns\")\n", - "\n", - "ax = plt.subplot(312)\n", - "\n", - "plt.xlim(0, .1)\n", - "plt.hist(p_B_samples, histtype='stepfilled', bins=25, alpha=0.85,\n", - " label=\"posterior of $p_B$\", color=\"#467821\", normed=True)\n", - "plt.vlines(true_p_B, 0, 80, linestyle=\"--\", label=\"true $p_B$ (unknown)\")\n", - "plt.legend(loc=\"upper right\")\n", - "\n", - "ax = plt.subplot(313)\n", - "plt.hist(delta_samples, histtype='stepfilled', bins=30, alpha=0.85,\n", - " label=\"posterior of delta\", color=\"#7A68A6\", normed=True)\n", - "plt.vlines(true_p_A - true_p_B, 0, 60, linestyle=\"--\",\n", - " label=\"true delta (unknown)\")\n", - "plt.vlines(0, 0, 60, color=\"black\", alpha=0.2)\n", - "plt.legend(loc=\"upper right\");" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "metadata": {}, - "output_type": "display_data", - "png": 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xmCskt61bt8LFxQV79uxBdnY2XnvtNQDAgQMHEBUVhczMTBgaGjbbt3HaRkND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fddvPnmm3jmmWdw9OhRxMfH48SJE0bUStO4XC7eCVcgJSUFEgAiIzTP1KJZtHU0cwUPhZivNu5r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\nRK5CYII=\n", - "text": [ - "" - ] - } - ], - "prompt_number": 29 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Notice that as a result of `N_B < N_A`, i.e. we have less data from site B, our posterior distribution of $p_B$ is fatter, implying we are less certain about the true value of $p_B$ than we are of $p_A$. \n", - "\n", - "With respect to the posterior distribution of $\\text{delta}$, we can see that the majority of the distribution is above $\\text{delta}=0$, implying there site A's response is likely better than site B's response. The probability this inference is incorrect is easily computable:" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "# Count the number of samples less than 0, i.e. the area under the curve\n", - "# before 0, represent the probability that site A is worse than site B.\n", - "print \"Probability site A is WORSE than site B: %.3f\" % \\\n", - " (delta_samples < 0).mean()\n", - "\n", - "print \"Probability site A is BETTER than site B: %.3f\" % \\\n", - " (delta_samples > 0).mean()" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "Probability site A is WORSE than site B: 0.003\n", - "Probability site A is BETTER than site B: 0.997\n" - ] - } - ], - "prompt_number": 30 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "If this probability is too high for comfortable decision-making, we can perform more trials on site B (as site B has less samples to begin with, each additional data point for site B contributes more inferential \"power\" than each additional data point for site A). \n", - "\n", - "Try playing with the parameters `true_p_A`, `true_p_B`, `N_A`, and `N_B`, to see what the posterior of $\\text{delta}$ looks like. Notice in all this, the difference in sample sizes between site A and site B was never mentioned: it naturally fits into Bayesian analysis.\n", - "\n", - "I hope the readers feel this style of A/B testing is more natural than hypothesis testing, which has probably confused more than helped practitioners. Later in this book, we will see two extensions of this model: the first to help dynamically adjust for bad sites, and the second will improve the speed of this computation by reducing the analysis to a single equation. " - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## An algorithm for human deceit\n", - "\n", - "Social data has an additional layer of interest as people are not always honest with responses, which adds a further complication into inference. For example, simply asking individuals \"Have you ever cheated on a test?\" will surely contain some rate of dishonesty. What you can say for certain is that the true rate is less than your observed rate (assuming individuals lie *only* about *not cheating*; I cannot imagine one who would admit \"Yes\" to cheating when in fact they hadn't cheated). \n", - "\n", - "To present an elegant solution to circumventing this dishonesty problem, and to demonstrate Bayesian modeling, we first need to introduce the binomial distribution.\n", - "\n", - "### The Binomial Distribution\n", - "\n", - "The binomial distribution is one of the most popular distributions, mostly because of its simplicity and usefulness. Unlike the other distributions we have encountered thus far in the book, the binomial distribution has 2 parameters: $N$, a positive integer representing $N$ trials or number of instances of potential events, and $p$, the probability of an event occurring in a single trial. Like the Poisson distribution, it is a discrete distribution, but unlike the Poisson distribution, it only weighs integers from $0$ to $N$. The mass distribution looks like:\n", - "\n", - "$$P( X = k ) = {{N}\\choose{k}} p^k(1-p)^{N-k}$$\n", - "\n", - "If $X$ is a binomial random variable with parameters $p$ and $N$, denoted $X \\sim \\text{Bin}(N,p)$, then $X$ is the number of events that occurred in the $N$ trials (obviously $0 \\le X \\le N$), and $p$ is the probability of a single event. The larger $p$ is (while still remaining between 0 and 1), the more events are likely to occur. The expected value of a binomial is equal to $Np$. Below we plot the mass probability distribution for varying parameters. " - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "figsize(12.5, 4)\n", - "\n", - "import scipy.stats as stats\n", - "binomial = stats.binom\n", - "\n", - "parameters = [(10, .4), (10, .9)]\n", - "colors = [\"#348ABD\", \"#A60628\"]\n", - "\n", - "for i in range(2):\n", - " N, p = parameters[i]\n", - " _x = np.arange(N + 1)\n", - " plt.bar(_x - 0.5, binomial.pmf(_x, N, p), color=colors[i],\n", - " edgecolor=colors[i],\n", - " alpha=0.6,\n", - " label=\"$N$: %d, $p$: %.1f\" % (N, p),\n", - " linewidth=3)\n", - "\n", - "plt.legend(loc=\"upper left\")\n", - "plt.xlim(0, 10.5)\n", - "plt.xlabel(\"$k$\")\n", - "plt.ylabel(\"$P(X = k)$\")\n", - "plt.title(\"Probability mass distributions of binomial random variables\");" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "metadata": {}, - "output_type": "display_data", - "png": 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KSmBubo6FCxdi0aJFTdr35cuXIZfL4ebmplzm4+Nz33fuFy1aVGefGnvMwsJC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\ngg==\n", - "text": [ - "" - ] - } - ], - "prompt_number": 32 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "The special case when $N = 1$ corresponds to the Bernoulli distribution. There is another connection between Bernoulli and Binomial random variables. If we have $X_1, X_2, ... , X_N$ Bernoulli random variables with the same $p$, then $Z = X_1 + X_2 + ... + X_N \\sim \\text{Binomial}(N, p )$.\n", - "\n", - "The expected value of a Bernoulli random variable is $p$. This can be seen by noting the more general Binomial random variable has expected value $Np$ and setting $N=1$." - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "##### Example: Cheating among students\n", - "\n", - "We will use the binomial distribution to determine the frequency of students cheating during an exam. If we let $N$ be the total number of students who took the exam, and assuming each student is interviewed post-exam (answering without consequence), we will receive integer $X$ \"Yes I did cheat\" answers. We then find the posterior distribution of $p$, given $N$, some specified prior on $p$, and observed data $X$. \n", - "\n", - "This is a completely absurd model. No student, even with a free-pass against punishment, would admit to cheating. What we need is a better *algorithm* to ask students if they had cheated. Ideally the algorithm should encourage individuals to be honest while preserving privacy. The following proposed algorithm is a solution I greatly admire for its ingenuity and effectiveness:\n", - "\n", - "> In the interview process for each student, the student flips a coin, hidden from the interviewer. The student agrees to answer honestly if the coin comes up heads. Otherwise, if the coin comes up tails, the student (secretly) flips the coin again, and answers \"Yes, I did cheat\" if the coin flip lands heads, and \"No, I did not cheat\", if the coin flip lands tails. This way, the interviewer does not know if a \"Yes\" was the result of a guilty plea, or a Heads on a second coin toss. Thus privacy is preserved and the researchers receive honest answers. \n", - "\n", - "I call this the Privacy Algorithm. One could of course argue that the interviewers are still receiving false data since some *Yes*'s are not confessions but instead randomness, but an alternative perspective is that the researchers are discarding approximately half of their original dataset since half of the responses will be noise. But they have gained a systematic data generation process that can be modeled. Furthermore, they do not have to incorporate (perhaps somewhat naively) the possibility of deceitful answers. We can use PyMC to dig through this noisy model, and find a posterior distribution for the true frequency of liars. " - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Suppose 100 students are being surveyed for cheating, and we wish to find $p$, the proportion of cheaters. There are a few ways we can model this in PyMC. I'll demonstrate the most explicit way, and later show a simplified version. Both versions arrive at the same inference. In our data-generation model, we sample $p$, the true proportion of cheaters, from a prior. Since we are quite ignorant about $p$, we will assign it a $\\text{Uniform}(0,1)$ prior." - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "import pymc as pm\n", - "\n", - "N = 100\n", - "p = pm.Uniform(\"freq_cheating\", 0, 1)" - ], - "language": "python", - "metadata": {}, - "outputs": [], - "prompt_number": 33 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Again, thinking of our data-generation model, we assign Bernoulli random variables to the 100 students: 1 implies they cheated and 0 implies they did not. " - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "true_answers = pm.Bernoulli(\"truths\", p, size=N)" - ], - "language": "python", - "metadata": {}, - "outputs": [], - "prompt_number": 34 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "If we carry out the algorithm, the next step that occurs is the first coin-flip each student makes. This can be modeled again by sampling 100 Bernoulli random variables with $p=1/2$: denote a 1 as a *Heads* and 0 a *Tails*." - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "first_coin_flips = pm.Bernoulli(\"first_flips\", 0.5, size=N)\n", - "print first_coin_flips.value" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "[False True True True True False False True False False False False\n", - " False True True False True True False False True True False False\n", - " False False False True False False True False True True True True\n", - " True False True False True True True True True False False False\n", - " True True True True True True False True False False False True\n", - " True True False False False False True False True False False True\n", - " True False False False False True True False False True False True\n", - " False False True False False False True True True True True False\n", - " False False False False]\n" - ] - } - ], - "prompt_number": 35 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Although *not everyone* flips a second time, we can still model the possible realization of second coin-flips:" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "second_coin_flips = pm.Bernoulli(\"second_flips\", 0.5, size=N)" - ], - "language": "python", - "metadata": {}, - "outputs": [], - "prompt_number": 36 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Using these variables, we can return a possible realization of the *observed proportion* of \"Yes\" responses. We do this using a PyMC `deterministic` variable:" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "@pm.deterministic\n", - "def observed_proportion(t_a=true_answers,\n", - " fc=first_coin_flips,\n", - " sc=second_coin_flips):\n", - "\n", - " observed = fc * t_a + (1 - fc) * sc\n", - " return observed.sum() / float(N)" - ], - "language": "python", - "metadata": {}, - "outputs": [], - "prompt_number": 37 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "The line `fc*t_a + (1-fc)*sc` contains the heart of the Privacy algorithm. Elements in this array are 1 *if and only if* i) the first toss is heads and the student cheated or ii) the first toss is tails, and the second is heads, and are 0 else. Finally, the last line sums this vector and divides by `float(N)`, produces a proportion. " - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "observed_proportion.value" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "metadata": {}, - "output_type": "pyout", - "prompt_number": 38, - "text": [ - "0.42999999999999999" - ] - } - ], - "prompt_number": 38 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Next we need a dataset. After performing our coin-flipped interviews the researchers received 35 \"Yes\" responses. To put this into a relative perspective, if there truly were no cheaters, we should expect to see on average 1/4 of all responses being a \"Yes\" (half chance of having first coin land Tails, and another half chance of having second coin land Heads), so about 25 responses in a cheat-free world. On the other hand, if *all students cheated*, we should expect to see approximately 3/4 of all responses be \"Yes\". \n", - "\n", - "The researchers observe a Binomial random variable, with `N = 100` and `p = observed_proportion` with `value = 35`: " - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "X = 35\n", - "\n", - "observations = pm.Binomial(\"obs\", N, observed_proportion, observed=True,\n", - " value=X)" - ], - "language": "python", - "metadata": {}, - "outputs": [], - "prompt_number": 39 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Below we add all the variables of interest to a `Model` container and run our black-box algorithm over the model. " - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "model = pm.Model([p, true_answers, first_coin_flips,\n", - " second_coin_flips, observed_proportion, observations])\n", - "\n", - "# To be explained in Chapter 3!\n", - "mcmc = pm.MCMC(model)\n", - "mcmc.sample(40000, 15000)" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "output_type": "stream", - "stream": "stdout", - "text": [ - " \r", - "[****************100%******************] 40000 of 40000 complete" - ] - }, - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "\n" - ] - } - ], - "prompt_number": 40 - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "figsize(12.5, 3)\n", - "p_trace = mcmc.trace(\"freq_cheating\")[:]\n", - "plt.hist(p_trace, histtype=\"stepfilled\", normed=True, alpha=0.85, bins=30,\n", - " label=\"posterior distribution\", color=\"#348ABD\")\n", - "plt.vlines([.05, .35], [0, 0], [5, 5], alpha=0.3)\n", - "plt.xlim(0, 1)\n", - "plt.legend();" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "metadata": {}, - "output_type": "display_data", - "png": 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- "text": [ - "" - ] - } - ], - "prompt_number": 42 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "With regards to the above plot, we are still pretty uncertain about what the true frequency of cheaters might be, but we have narrowed it down to a range between 0.05 to 0.35 (marked by the solid lines). This is pretty good, as *a priori* we had no idea how many students might have cheated (hence the uniform distribution for our prior). On the other hand, it is also pretty bad since there is a .3 length window the true value most likely lives in. Have we even gained anything, or are we still too uncertain about the true frequency? \n", - "\n", - "I would argue, yes, we have discovered something. It is implausible, according to our posterior, that there are *no cheaters*, i.e. the posterior assigns low probability to $p=0$. Since we started with a uniform prior, treating all values of $p$ as equally plausible, but the data ruled out $p=0$ as a possibility, we can be confident that there were cheaters. \n", - "\n", - "This kind of algorithm can be used to gather private information from users and be *reasonably* confident that the data, though noisy, is truthful. \n", - "\n" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### Alternative PyMC Model\n", - "\n", - "Given a value for $p$ (which from our god-like position we know), we can find the probability the student will answer yes: \n", - "\n", - "\\begin{align}\n", - "P(\\text{\"Yes\"}) = & P( \\text{Heads on first coin} )P( \\text{cheater} ) + P( \\text{Tails on first coin} )P( \\text{Heads on second coin} ) \\\\\\\\\n", - "& = \\frac{1}{2}p + \\frac{1}{2}\\frac{1}{2}\\\\\\\\\n", - "& = \\frac{p}{2} + \\frac{1}{4}\n", - "\\end{align}\n", - "\n", - "Thus, knowing $p$ we know the probability a student will respond \"Yes\". In PyMC, we can create a deterministic function to evaluate the probability of responding \"Yes\", given $p$:" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "p = pm.Uniform(\"freq_cheating\", 0, 1)\n", - "\n", - "\n", - "@pm.deterministic\n", - "def p_skewed(p=p):\n", - " return 0.5 * p + 0.25" - ], - "language": "python", - "metadata": {}, - "outputs": [], - "prompt_number": 43 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "I could have typed `p_skewed = 0.5*p + 0.25` instead for a one-liner, as the elementary operations of addition and scalar multiplication will implicitly create a `deterministic` variable, but I wanted to make the deterministic boilerplate explicit for clarity's sake. \n", - "\n", - "If we know the probability of respondents saying \"Yes\", which is `p_skewed`, and we have $N=100$ students, the number of \"Yes\" responses is a binomial random variable with parameters `N` and `p_skewed`.\n", - "\n", - "This is where we include our observed 35 \"Yes\" responses. In the declaration of the `pm.Binomial`, we include `value = 35` and `observed = True`." - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "yes_responses = pm.Binomial(\"number_cheaters\", 100, p_skewed,\n", - " value=35, observed=True)" - ], - "language": "python", - "metadata": {}, - "outputs": [], - "prompt_number": 44 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Below we add all the variables of interest to a `Model` container and run our black-box algorithm over the model. " - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "model = pm.Model([yes_responses, p_skewed, p])\n", - "\n", - "# To Be Explained in Chapter 3!\n", - "mcmc = pm.MCMC(model)\n", - "mcmc.sample(25000, 2500)" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "output_type": "stream", - "stream": "stdout", - "text": [ - " \r", - "[****************100%******************] 25000 of 25000 complete" - ] - }, - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "\n" - ] - } - ], - "prompt_number": 45 - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "figsize(12.5, 3)\n", - "p_trace = mcmc.trace(\"freq_cheating\")[:]\n", - "plt.hist(p_trace, histtype=\"stepfilled\", normed=True, alpha=0.85, bins=30,\n", - " label=\"posterior distribution\", color=\"#348ABD\")\n", - "plt.vlines([.05, .35], [0, 0], [5, 5], alpha=0.2)\n", - "plt.xlim(0, 1)\n", - "plt.legend();" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "metadata": {}, - "output_type": "display_data", - "png": 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- "text": [ - "" - ] - } - ], - "prompt_number": 47 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### More PyMC Tricks\n", - "\n", - "#### Protip: *Lighter* deterministic variables with `Lambda` class\n", - "\n", - "Sometimes writing a deterministic function using the `@pm.deterministic` decorator can seem like a chore, especially for a small function. I have already mentioned that elementary math operations *can* produce deterministic variables implicitly, but what about operations like indexing or slicing? Built-in `Lambda` functions can handle this with the elegance and simplicity required. For example, \n", - "\n", - " beta = pm.Normal(\"coefficients\", 0, size=(N, 1))\n", - " x = np.random.randn((N, 1))\n", - " linear_combination = pm.Lambda(lambda x=x, beta=beta: np.dot(x.T, beta))\n", - "\n", - "\n", - "#### Protip: Arrays of PyMC variables\n", - "There is no reason why we cannot store multiple heterogeneous PyMC variables in a Numpy array. Just remember to set the `dtype` of the array to `object` upon initialization. For example:\n", - "\n", - "\n" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "N = 10\n", - "x = np.empty(N, dtype=object)\n", - "for i in range(0, N):\n", - " x[i] = pm.Exponential('x_%i' % i, (i + 1) ** 2)" - ], - "language": "python", - "metadata": {}, - "outputs": [], - "prompt_number": 48 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "The remainder of this chapter examines some practical examples of PyMC and PyMC modeling:" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "\n", - "##### Example: Challenger Space Shuttle Disaster \n", - "\n", - "On January 28, 1986, the twenty-fifth flight of the U.S. space shuttle program ended in disaster when one of the rocket boosters of the Shuttle Challenger exploded shortly after lift-off, killing all seven crew members. The presidential commission on the accident concluded that it was caused by the failure of an O-ring in a field joint on the rocket booster, and that this failure was due to a faulty design that made the O-ring unacceptably sensitive to a number of factors including outside temperature. Of the previous 24 flights, data were available on failures of O-rings on 23, (one was lost at sea), and these data were discussed on the evening preceding the Challenger launch, but unfortunately only the data corresponding to the 7 flights on which there was a damage incident were considered important and these were thought to show no obvious trend. The data are shown below (see [1]):\n", - "\n", - "\n", - "\n" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "figsize(12.5, 3.5)\n", - "np.set_printoptions(precision=3, suppress=True)\n", - "challenger_data = np.genfromtxt(\"data/challenger_data.csv\", skip_header=1,\n", - " usecols=[1, 2], missing_values=\"NA\",\n", - " delimiter=\",\")\n", - "# drop the NA values\n", - "challenger_data = challenger_data[~np.isnan(challenger_data[:, 1])]\n", - "\n", - "# plot it, as a function of tempature (the first column)\n", - "print \"Temp (F), O-Ring failure?\"\n", - "print challenger_data\n", - "\n", - "plt.scatter(challenger_data[:, 0], challenger_data[:, 1], s=75, color=\"k\",\n", - " alpha=0.5)\n", - "plt.yticks([0, 1])\n", - "plt.ylabel(\"Damage Incident?\")\n", - "plt.xlabel(\"Outside temperature (Fahrenheit)\")\n", - "plt.title(\"Defects of the Space Shuttle O-Rings vs temperature\")" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "Temp (F), O-Ring failure?\n", - "[[ 66. 0.]\n", - " [ 70. 1.]\n", - " [ 69. 0.]\n", - " [ 68. 0.]\n", - " [ 67. 0.]\n", - " [ 72. 0.]\n", - " [ 73. 0.]\n", - " [ 70. 0.]\n", - " [ 57. 1.]\n", - " [ 63. 1.]\n", - " [ 70. 1.]\n", - " [ 78. 0.]\n", - " [ 67. 0.]\n", - " [ 53. 1.]\n", - " [ 67. 0.]\n", - " [ 75. 0.]\n", - " [ 70. 0.]\n", - " [ 81. 0.]\n", - " [ 76. 0.]\n", - " [ 79. 0.]\n", - " [ 75. 1.]\n", - " [ 76. 0.]\n", - " [ 58. 1.]]\n" - ] - }, - { - "metadata": {}, - "output_type": "pyout", - "prompt_number": 49, - "text": [ - "" - ] - }, - { - "metadata": {}, - "output_type": "display_data", - "png": 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AUaNG6e9z7/aTJMngZDuFQlEuZ9V5YpwQAuPGjcOsWbPKzbv7w93dyp7bJ0+eNCgQy5R9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\nNSem76FIJEJDQwN8fHwwPT0NnU4HLy8vAEBwcDA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- "text": [ - "" - ] - } - ], - "prompt_number": 49 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "It looks clear that *the probability* of damage incidents occurring increases as the outside temperature decreases. We are interested in modeling the probability here because it does not look like there is a strict cutoff point between temperature and a damage incident occurring. The best we can do is ask \"At temperature $t$, what is the probability of a damage incident?\". The goal of this example is to answer that question.\n", - "\n", - "We need a function of temperature, call it $p(t)$, that is bounded between 0 and 1 (so as to model a probability) and changes from 1 to 0 as we increase temperature. There are actually many such functions, but the most popular choice is the *logistic function.*\n", - "\n", - "$$p(t) = \\frac{1}{ 1 + e^{ \\;\\beta t } } $$\n", - "\n", - "In this model, $\\beta$ is the variable we are uncertain about. Below is the function plotted for $\\beta = 1, 3, -5$." - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "figsize(12, 3)\n", - "\n", - "\n", - "def logistic(x, beta):\n", - " return 1.0 / (1.0 + np.exp(beta * x))\n", - "\n", - "x = np.linspace(-4, 4, 100)\n", - "plt.plot(x, logistic(x, 1), label=r\"$\\beta = 1$\")\n", - "plt.plot(x, logistic(x, 3), label=r\"$\\beta = 3$\")\n", - "plt.plot(x, logistic(x, -5), label=r\"$\\beta = -5$\")\n", - "plt.legend();" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "metadata": {}, - "output_type": "display_data", - "png": 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P9afNZCG7qIFv8uvYVdbMusIG1hU2EOCh5tLEQKYmBzM06MxF4UDIpy40iHGr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\nDSy4t2TIC+BEzKdi0FO08idMf/OfUMxGGlavZ/u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- "text": [ - "" - ] - } - ], - "prompt_number": 54 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "But something is missing. In the plot of the logistic function, the probability changes only near zero, but in our data above the probability changes around 65 to 70. We need to add a *bias* term to our logistic function:\n", - "\n", - "$$p(t) = \\frac{1}{ 1 + e^{ \\;\\beta t + \\alpha } } $$\n", - "\n", - "Some plots are below, with differing $\\alpha$." - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "def logistic(x, beta, alpha=0):\n", - " return 1.0 / (1.0 + np.exp(np.dot(beta, x) + alpha))\n", - "\n", - "x = np.linspace(-4, 4, 100)\n", - "\n", - "plt.plot(x, logistic(x, 1), label=r\"$\\beta = 1$\", ls=\"--\", lw=1)\n", - "plt.plot(x, logistic(x, 3), label=r\"$\\beta = 3$\", ls=\"--\", lw=1)\n", - "plt.plot(x, logistic(x, -5), label=r\"$\\beta = -5$\", ls=\"--\", lw=1)\n", - "\n", - "plt.plot(x, logistic(x, 1, 1), label=r\"$\\beta = 1, \\alpha = 1$\",\n", - " color=\"#348ABD\")\n", - "plt.plot(x, logistic(x, 3, -2), label=r\"$\\beta = 3, \\alpha = -2$\",\n", - " color=\"#A60628\")\n", - "plt.plot(x, logistic(x, -5, 7), label=r\"$\\beta = -5, \\alpha = 7$\",\n", - " color=\"#7A68A6\")\n", - "\n", - "plt.legend(loc=\"lower left\");" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "metadata": {}, - "output_type": "display_data", - "png": 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vTWfk+FhiBga6KVrBlUxNVtZ/nwnAhVcMFTPCCcI5nLUcYunSpaxdu5YPPvgA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\nXWniubW5PNLFZFhoX3WTjXe2FVHZZG3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HxYfqOX9WMpkXik4eQfCWM54sY9KkSRQUFFBS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- "text": [ - "" - ] - } - ], - "prompt_number": 55 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Adding a constant term $\\alpha$ amounts to shifting the curve left or right (hence why it is called a *bias*).\n", - "\n", - "Let's start modeling this in PyMC. The $\\beta, \\alpha$ parameters have no reason to be positive, bounded or relatively large, so they are best modeled by a *Normal random variable*, introduced next." - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### Normal distributions\n", - "\n", - "A Normal random variable, denoted $X \\sim N(\\mu, 1/\\tau)$, has a distribution with two parameters: the mean, $\\mu$, and the *precision*, $\\tau$. Those familiar with the Normal distribution already have probably seen $\\sigma^2$ instead of $\\tau^{-1}$. They are in fact reciprocals of each other. The change was motivated by simpler mathematical analysis and is an artifact of older Bayesian methods. Just remember: the smaller $\\tau$, the larger the spread of the distribution (i.e. we are more uncertain); the larger $\\tau$, the tighter the distribution (i.e. we are more certain). Regardless, $\\tau$ is always positive. \n", - "\n", - "The probability density function of a $N( \\mu, 1/\\tau)$ random variable is:\n", - "\n", - "$$ f(x | \\mu, \\tau) = \\sqrt{\\frac{\\tau}{2\\pi}} \\exp\\left( -\\frac{\\tau}{2} (x-\\mu)^2 \\right) $$\n", - "\n", - "We plot some different density functions below. " - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "import scipy.stats as stats\n", - "\n", - "nor = stats.norm\n", - "x = np.linspace(-8, 7, 150)\n", - "mu = (-2, 0, 3)\n", - "tau = (.7, 1, 2.8)\n", - "colors = [\"#348ABD\", \"#A60628\", \"#7A68A6\"]\n", - "parameters = zip(mu, tau, colors)\n", - "\n", - "for _mu, _tau, _color in parameters:\n", - " plt.plot(x, nor.pdf(x, _mu, scale=1. / _tau),\n", - " label=\"$\\mu = %d,\\;\\\\tau = %.1f$\" % (_mu, _tau), color=_color)\n", - " plt.fill_between(x, nor.pdf(x, _mu, scale=1. / _tau), color=_color,\n", - " alpha=.33)\n", - "\n", - "plt.legend(loc=\"upper right\")\n", - "plt.xlabel(\"$x$\")\n", - "plt.ylabel(\"density function at $x$\")\n", - "plt.title(\"Probability distribution of three different Normal random \\\n", - "variables\");" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "metadata": {}, - "output_type": "display_data", - "png": 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MV0MfAgCcO7cBJ+EAAC1amaJLT1sAwMN76VqLjzRd0dHR8Pf3BwC0atUKzs7O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\nlxDvONzLb3+xFrNF5YYFxVE5aHjPtoNU7mxmxmV5XP03RWe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- "text": [ - "" - ] - } - ], - "prompt_number": 57 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "A Normal random variable can be take on any real number, but the variable is very likely to be relatively close to $\\mu$. In fact, the expected value of a Normal is equal to its $\\mu$ parameter:\n", - "\n", - "$$ E[ X | \\mu, \\tau] = \\mu$$\n", - "\n", - "and its variance is equal to the inverse of $\\tau$:\n", - "\n", - "$$Var( X | \\mu, \\tau ) = \\frac{1}{\\tau}$$\n", - "\n", - "\n", - "\n", - "Below we continue our modeling of the Challenger space craft:" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "import pymc as pm\n", - "\n", - "temperature = challenger_data[:, 0]\n", - "D = challenger_data[:, 1] # defect or not?\n", - "\n", - "# notice the`value` here. We explain why below.\n", - "beta = pm.Normal(\"beta\", 0, 0.001, value=0)\n", - "alpha = pm.Normal(\"alpha\", 0, 0.001, value=0)\n", - "\n", - "\n", - "@pm.deterministic\n", - "def p(t=temperature, alpha=alpha, beta=beta):\n", - " return 1.0 / (1. + np.exp(beta * t + alpha))" - ], - "language": "python", - "metadata": {}, - "outputs": [], - "prompt_number": 58 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "We have our probabilities, but how do we connect them to our observed data? A *Bernoulli* random variable with parameter $p$, denoted $\\text{Ber}(p)$, is a random variable that takes value 1 with probability $p$, and 0 else. Thus, our model can look like:\n", - "\n", - "$$ \\text{Defect Incident, $D_i$} \\sim \\text{Ber}( \\;p(t_i)\\; ), \\;\\; i=1..N$$\n", - "\n", - "where $p(t)$ is our logistic function and $t_i$ are the temperatures we have observations about. Notice in the above code we had to set the values of `beta` and `alpha` to 0. The reason for this is that if `beta` and `alpha` are very large, they make `p` equal to 1 or 0. Unfortunately, `pm.Bernoulli` does not like probabilities of exactly 0 or 1, though they are mathematically well-defined probabilities. So by setting the coefficient values to `0`, we set the variable `p` to be a reasonable starting value. This has no effect on our results, nor does it mean we are including any additional information in our prior. It is simply a computational caveat in PyMC. " - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "p.value" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "metadata": {}, - "output_type": "pyout", - "prompt_number": 59, - "text": [ - "array([ 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5,\n", - " 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5,\n", - " 0.5])" - ] - } - ], - "prompt_number": 59 - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "# connect the probabilities in `p` with our observations through a\n", - "# Bernoulli random variable.\n", - "observed = pm.Bernoulli(\"bernoulli_obs\", p, value=D, observed=True)\n", - "\n", - "model = pm.Model([observed, beta, alpha])\n", - "\n", - "# Mysterious code to be explained in Chapter 3\n", - "map_ = pm.MAP(model)\n", - "map_.fit()\n", - "mcmc = pm.MCMC(model)\n", - "mcmc.sample(120000, 100000, 2)" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "output_type": "stream", - "stream": "stdout", - "text": [ - " \r", - "[****************100%******************] 120000 of 120000 complete" - ] - }, - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "\n" - ] - } - ], - "prompt_number": 60 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "We have trained our model on the observed data, now we can sample values from the posterior. Let's look at the posterior distributions for $\\alpha$ and $\\beta$:" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "alpha_samples = mcmc.trace('alpha')[:, None] # best to make them 1d\n", - "beta_samples = mcmc.trace('beta')[:, None]\n", - "\n", - "figsize(12.5, 6)\n", - "\n", - "# histogram of the samples:\n", - "plt.subplot(211)\n", - "plt.title(r\"Posterior distributions of the variables $\\alpha, \\beta$\")\n", - "plt.hist(beta_samples, histtype='stepfilled', bins=35, alpha=0.85,\n", - " label=r\"posterior of $\\beta$\", color=\"#7A68A6\", normed=True)\n", - "plt.legend()\n", - "\n", - "plt.subplot(212)\n", - "plt.hist(alpha_samples, histtype='stepfilled', bins=35, alpha=0.85,\n", - " label=r\"posterior of $\\alpha$\", color=\"#A60628\", normed=True)\n", - "plt.legend();" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "metadata": {}, - "output_type": "display_data", - "png": 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h4SgoKMDChQsRFBSk935JSQm8vb11bS8vLxQXF7NA70IcVyaO0sdJ195swDdf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\ne3p6QqPR6NoajQZeXl7tLlNcXAxPT08AvzwNq1+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- "text": [ - "" - ] - } - ], - "prompt_number": 61 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "All samples of $\\beta$ are greater than 0. If instead the posterior was centered around 0, we may suspect that $\\beta = 0$, implying that temperature has no effect on the probability of defect. \n", - "\n", - "Similarly, all $\\alpha$ posterior values are negative and far away from 0, implying that it is correct to believe that $\\alpha$ is significantly less than 0. \n", - "\n", - "Regarding the spread of the data, we are very uncertain about what the true parameters might be (though considering the low sample size and the large overlap of defects-to-nondefects this behaviour is perhaps expected). \n", - "\n", - "Next, let's look at the *expected probability* for a specific value of the temperature. That is, we average over all samples from the posterior to get a likely value for $p(t_i)$." - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "t = np.linspace(temperature.min() - 5, temperature.max() + 5, 50)[:, None]\n", - "p_t = logistic(t.T, beta_samples, alpha_samples)\n", - "\n", - "mean_prob_t = p_t.mean(axis=0)" - ], - "language": "python", - "metadata": {}, - "outputs": [], - "prompt_number": 62 - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "figsize(12.5, 4)\n", - "\n", - "plt.plot(t, mean_prob_t, lw=3, label=\"average posterior \\nprobability \\\n", - "of defect\")\n", - "plt.plot(t, p_t[0, :], ls=\"--\", label=\"realization from posterior\")\n", - "plt.plot(t, p_t[-2, :], ls=\"--\", label=\"realization from posterior\")\n", - "plt.scatter(temperature, D, color=\"k\", s=50, alpha=0.5)\n", - "plt.title(\"Posterior expected value of probability of defect; \\\n", - "plus realizations\")\n", - "plt.legend(loc=\"lower left\")\n", - "plt.ylim(-0.1, 1.1)\n", - "plt.xlim(t.min(), t.max())\n", - "plt.ylabel(\"probability\")\n", - "plt.xlabel(\"temperature\");" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "metadata": {}, - "output_type": "display_data", - "png": 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IIW2MatgJIYQQQgjpoARL2OfOnQsvLy9ER0c32eb5559HWFgYevfujTNnzgjV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\nDKx0LFRmZ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- "text": [ - "" - ] - } - ], - "prompt_number": 64 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Above we also plotted two possible realizations of what the actual underlying system might be. Both are equally likely as any other draw. The blue line is what occurs when we average all the 20000 possible dotted lines together.\n", - "\n", - "\n", - "An interesting question to ask is for what temperatures are we most uncertain about the defect-probability? Below we plot the expected value line **and** the associated 95% intervals for each temperature. " - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "from scipy.stats.mstats import mquantiles\n", - "\n", - "# vectorized bottom and top 2.5% quantiles for \"confidence interval\"\n", - "qs = mquantiles(p_t, [0.025, 0.975], axis=0)\n", - "plt.fill_between(t[:, 0], *qs, alpha=0.7,\n", - " color=\"#7A68A6\")\n", - "\n", - "plt.plot(t[:, 0], qs[0], label=\"95% CI\", color=\"#7A68A6\", alpha=0.7)\n", - "\n", - "plt.plot(t, mean_prob_t, lw=1, ls=\"--\", color=\"k\",\n", - " label=\"average posterior \\nprobability of defect\")\n", - "\n", - "plt.xlim(t.min(), t.max())\n", - "plt.ylim(-0.02, 1.02)\n", - "plt.legend(loc=\"lower left\")\n", - "plt.scatter(temperature, D, color=\"k\", s=50, alpha=0.5)\n", - "plt.xlabel(\"temp, $t$\")\n", - "\n", - "plt.ylabel(\"probability estimate\")\n", - "plt.title(\"Posterior probability estimates given temp. $t$\");" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "metadata": {}, - "output_type": "display_data", - "png": 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5DbEJdJdfQgghfUclMYR0w+6woaziDIrOHkFURCwmXDHb1yERP3fxtJozJB5D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- "text": [ - "" - ] - } - ], - "prompt_number": 66 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "The *95% credible interval*, or 95% CI, painted in purple, represents the interval, for each temperature, that contains 95% of the distribution. For example, at 65 degrees, we can be 95% sure that the probability of defect lies between 0.25 and 0.75.\n", - "\n", - "More generally, we can see that as the temperature nears 60 degrees, the CI's spread out over [0,1] quickly. As we pass 70 degrees, the CI's tighten again. This can give us insight about how to proceed next: we should probably test more O-rings around 60-65 temperature to get a better estimate of probabilities in that range. Similarly, when reporting to scientists your estimates, you should be very cautious about simply telling them the expected probability, as we can see this does not reflect how *wide* the posterior distribution is." - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### What about the day of the Challenger disaster?\n", - "\n", - "On the day of the Challenger disaster, the outside temperature was 31 degrees Fahrenheit. What is the posterior distribution of a defect occurring, given this temperature? The distribution is plotted below. It looks almost guaranteed that the Challenger was going to be subject to defective O-rings." - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "figsize(12.5, 2.5)\n", - "\n", - "prob_31 = logistic(31, beta_samples, alpha_samples)\n", - "\n", - "plt.xlim(0.995, 1)\n", - "plt.hist(prob_31, bins=1000, normed=True, histtype='stepfilled')\n", - "plt.title(\"Posterior distribution of probability of defect, given $t = 31$\")\n", - "plt.xlabel(\"probability of defect occurring in O-ring\");" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "metadata": {}, - "output_type": "display_data", - "png": 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4Mlmch0hyMF9IKuYKycF8IWNhEU9EREREZGJYxJPJ4jxEkoP5QlIxV0gO5gsZ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\nLS0NpaWlOj/cVSqVmDdvHhYuXIi7d+8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- "text": [ - "" - ] - } - ], - "prompt_number": 68 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### Is our model appropriate?\n", - "\n", - "The skeptical reader will say \"You deliberately chose the logistic function for $p(t)$ and the specific priors. Perhaps other functions or priors will give different results. How do I know I have chosen a good model?\" This is absolutely true. To consider an extreme situation, what if I had chosen the function $p(t) = 1,\\; \\forall t$, which guarantees a defect always occurring: I would have again predicted disaster on January 28th. Yet this is clearly a poorly chosen model. On the other hand, if I did choose the logistic function for $p(t)$, but specified all my priors to be very tight around 0, likely we would have very different posterior distributions. How do we know our model is an expression of the data? This encourages us to measure the model's **goodness of fit**.\n", - "\n", - "We can think: *how can we test whether our model is a bad fit?* An idea is to compare observed data (which if we recall is a *fixed* stochastic variable) with an artificial dataset which we can simulate. The rationale is that if the simulated dataset does not appear similar, statistically, to the observed dataset, then likely our model is not accurately represented the observed data. \n", - "\n", - "Previously in this Chapter, we simulated artificial datasets for the SMS example. To do this, we sampled values from the priors. We saw how varied the resulting datasets looked like, and rarely did they mimic our observed dataset. In the current example, we should sample from the *posterior* distributions to create *very plausible datasets*. Luckily, our Bayesian framework makes this very easy. We only need to create a new `Stochastic` variable, that is exactly the same as our variable that stored the observations, but minus the observations themselves. If you recall, our `Stochastic` variable that stored our observed data was:\n", - "\n", - " observed = pm.Bernoulli( \"bernoulli_obs\", p, value=D, observed=True)\n", - "\n", - "Hence we create:\n", - " \n", - " simulated_data = pm.Bernoulli(\"simulation_data\", p)\n", - "\n", - "Let's simulate 10 000:" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "simulated = pm.Bernoulli(\"bernoulli_sim\", p)\n", - "N = 10000\n", - "\n", - "mcmc = pm.MCMC([simulated, alpha, beta, observed])\n", - "mcmc.sample(N)" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "output_type": "stream", - "stream": "stdout", - "text": [ - " \r", - "[****************100%******************] 10000 of 10000 complete" - ] - }, - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "\n" - ] - } - ], - "prompt_number": 69 - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "figsize(12.5, 5)\n", - "\n", - "simulations = mcmc.trace(\"bernoulli_sim\")[:]\n", - "print simulations.shape\n", - "\n", - "plt.title(\"Simulated dataset using posterior parameters\")\n", - "figsize(12.5, 6)\n", - "for i in range(4):\n", - " ax = plt.subplot(4, 1, i + 1)\n", - " plt.scatter(temperature, simulations[1000 * i, :], color=\"k\",\n", - " s=50, alpha=0.6)" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "(10000, 23)\n" - ] - }, - { - "metadata": {}, - "output_type": "display_data", - "png": 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LHMdh7NixiIiIwM6dOwGYv6gRsRxTeQDAli1bEBYWhkWLFtHXYW3g/v37cHd3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- "text": [ - "" - ] - } - ], - "prompt_number": 71 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Note that the above plots are different (if you can think of a cleaner way to present this, please send a pull request and answer [here](http://stats.stackexchange.com/questions/53078/how-to-visualize-bayesian-goodness-of-fit-for-logistic-regression)!).\n", - "\n", - "We wish to assess how good our model is. \"Good\" is a subjective term of course, so results must be relative to other models. \n", - "\n", - "We will be doing this graphically as well, which may seem like an even less objective method. The alternative is to use *Bayesian p-values*. These are still subjective, as the proper cutoff between good and bad is arbitrary. Gelman emphasises that the graphical tests are more illuminating [7] than p-value tests. We agree.\n", - "\n", - "The following graphical test is a novel data-viz approach to logistic regression. The plots are called *separation plots*[8]. For a suite of models we wish to compare, each model is plotted on an individual separation plot. I leave most of the technical details about separation plots to the very accessible [original paper](http://mdwardlab.com/sites/default/files/GreenhillWardSacks.pdf), but I'll summarize their use here.\n", - "\n", - "For each model, we calculate the proportion of times the posterior simulation proposed a value of 1 for a particular temperature, i.e. compute $P( \\;\\text{Defect} = 1 | t, \\alpha, \\beta )$ by averaging. This gives us the posterior probability of a defect at each data point in our dataset. For example, for the model we used above:" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "posterior_probability = simulations.mean(axis=0)\n", - "print \"posterior prob of defect | realized defect \"\n", - "for i in range(len(D)):\n", - " print \"%.2f | %d\" % (posterior_probability[i], D[i])" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "posterior prob of defect | realized defect \n", - "0.47 | 0\n", - "0.20 | 1\n", - "0.25 | 0\n", - "0.32 | 0\n", - "0.39 | 0\n", - "0.11 | 0\n", - "0.08 | 0\n", - "0.19 | 0\n", - "0.94 | 1\n", - "0.71 | 1\n", - "0.20 | 1\n", - "0.02 | 0\n", - "0.39 | 0\n", - "0.98 | 1\n", - "0.40 | 0\n", - "0.05 | 0\n", - "0.20 | 0\n", - "0.01 | 0\n", - "0.03 | 0\n", - "0.01 | 0\n", - "0.05 | 1\n", - "0.04 | 0\n", - "0.92 | 1\n" - ] - } - ], - "prompt_number": 72 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Next we sort each column by the posterior probabilities:" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "ix = np.argsort(posterior_probability)\n", - "print \"probb | defect \"\n", - "for i in range(len(D)):\n", - " print \"%.2f | %d\" % (posterior_probability[ix[i]], D[ix[i]])" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "probb | defect \n", - "0.01 | 0\n", - "0.01 | 0\n", - "0.02 | 0\n", - "0.03 | 0\n", - "0.04 | 0\n", - "0.05 | 0\n", - "0.05 | 1\n", - "0.08 | 0\n", - "0.11 | 0\n", - "0.19 | 0\n", - "0.20 | 0\n", - "0.20 | 1\n", - "0.20 | 1\n", - "0.25 | 0\n", - "0.32 | 0\n", - "0.39 | 0\n", - "0.39 | 0\n", - "0.40 | 0\n", - "0.47 | 0\n", - "0.71 | 1\n", - "0.92 | 1\n", - "0.94 | 1\n", - "0.98 | 1\n" - ] - } - ], - "prompt_number": 73 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "We can present the above data better in a figure: I've wrapped this up into a `separation_plot` function." - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "from separation_plot import separation_plot\n", - "\n", - "\n", - "figsize(11., 1.5)\n", - "separation_plot(posterior_probability, D)" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "metadata": {}, - "output_type": "display_data", - "png": 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- "text": [ - "" - ] - } - ], - "prompt_number": 74 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "The snaking-line is the sorted probabilities, blue bars denote defects, and empty space (or grey bars for the optimistic readers) denote non-defects. As the probability rises, we see more and more defects occur. On the right hand side, the plot suggests that as the posterior probability is large (line close to 1), then more defects are realized. This is good behaviour. Ideally, all the blue bars *should* be close to the right-hand side, and deviations from this reflect missed predictions. \n", - "\n", - "The black vertical line is the expected number of defects we should observe, given this model. This allows the user to see how the total number of events predicted by the model compares to the actual number of events in the data.\n", - "\n", - "It is much more informative to compare this to separation plots for other models. Below we compare our model (top) versus three others:\n", - "\n", - "1. the perfect model, which predicts the posterior probability to be equal to 1 if a defect did occur.\n", - "2. a completely random model, which predicts random probabilities regardless of temperature.\n", - "3. a constant model: where $P(D = 1 \\; | \\; t) = c, \\;\\; \\forall t$. The best choice for $c$ is the observed frequency of defects, in this case 7/23. \n" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "figsize(11., 1.25)\n", - "\n", - "# Our temperature-dependent model\n", - "separation_plot(posterior_probability, D)\n", - "plt.title(\"Temperature-dependent model\")\n", - "\n", - "# Perfect model\n", - "# i.e. the probability of defect is equal to if a defect occurred or not.\n", - "p = D\n", - "separation_plot(p, D)\n", - "plt.title(\"Perfect model\")\n", - "\n", - "# random predictions\n", - "p = np.random.rand(23)\n", - "separation_plot(p, D)\n", - "plt.title(\"Random model\")\n", - "\n", - "# constant model\n", - "constant_prob = 7. / 23 * np.ones(23)\n", - "separation_plot(constant_prob, D)\n", - "plt.title(\"Constant-prediction model\")" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "metadata": {}, - "output_type": "pyout", - "prompt_number": 75, - "text": [ - "" - ] - }, - { - "metadata": {}, - "output_type": "display_data", - "png": 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- "text": [ - "" - ] - } - ], - "prompt_number": 75 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "In the random model, we can see that as the probability increases there is no clustering of defects to the right-hand side. Similarly for the constant model.\n", - "\n", - "The perfect model, the probability line is not well shown, as it is stuck to the bottom and top of the figure. Of course the perfect model is only for demonstration, and we cannot infer any scientific inference from it." - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "##### Exercises\n", - "\n", - "1\\. Try putting in extreme values for our observations in the cheating example. What happens if we observe 25 affirmative responses? 10? 50? " - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "2\\. Try plotting $\\alpha$ samples versus $\\beta$ samples. Why might the resulting plot look like this?" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "# type your code here.\n", - "figsize(12.5, 4)\n", - "\n", - "plt.scatter(alpha_samples, beta_samples, alpha=0.1)\n", - "plt.title(\"Why does the plot look like this?\")\n", - "plt.xlabel(r\"$\\alpha$\")\n", - "plt.ylabel(r\"$\\beta$\")" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "metadata": {}, - "output_type": "pyout", - "prompt_number": 76, - "text": [ - "" - ] - }, - { - "metadata": {}, - "output_type": "display_data", - "png": 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SSnkUFUFVlSGTkbrv0ahHNmvw+SAY9MhkLF1dBmN8hMMetbWWSy+Vkf5duyTQ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- "text": [ - "" - ] - } - ], - "prompt_number": 76 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### References\n", - "\n", - "- [1] Dalal, Fowlkes and Hoadley (1989),JASA, 84, 945-957.\n", - "- [2] German Rodriguez. Datasets. In WWS509. Retrieved 30/01/2013, from .\n", - "- [3] McLeish, Don, and Cyntha Struthers. STATISTICS 450/850 Estimation and Hypothesis Testing. Winter 2012. Waterloo, Ontario: 2012. Print.\n", - "- [4] Fonnesbeck, Christopher. \"Building Models.\" PyMC-Devs. N.p., n.d. Web. 26 Feb 2013. .\n", - "- [5] Cronin, Beau. \"Why Probabilistic Programming Matters.\" 24 Mar 2013. Google, Online Posting to Google . Web. 24 Mar. 2013. .\n", - "- [6] S.P. Brooks, E.A. Catchpole, and B.J.T. Morgan. Bayesian animal survival estimation. Statistical Science, 15: 357\u2013376, 2000\n", - "- [7] Gelman, Andrew. \"Philosophy and the practice of Bayesian statistics.\" British Journal of Mathematical and Statistical Psychology. (2012): n. page. Web. 2 Apr. 2013.\n", - "- [8] Greenhill, Brian, Michael D. Ward, and Audrey Sacks. \"The Separation Plot: A New Visual Method for Evaluating the Fit of Binary Models.\" American Journal of Political Science. 55.No.4 (2011): n. page. Web. 2 Apr. 2013." - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "from IPython.core.display import HTML\n", - "\n", - "\n", - "def css_styling():\n", - " styles = open(\"../styles/custom.css\", \"r\").read()\n", - " return HTML(styles)\n", - "css_styling()" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "html": [ - "\n", - "\n" - ], - "metadata": {}, - "output_type": "pyout", - "prompt_number": 1, - "text": [ - "" - ] - } - ], - "prompt_number": 1 - }, - { - "cell_type": "code", - "collapsed": false, - "input": [], - "language": "python", - "metadata": {}, - "outputs": [], - "prompt_number": 105 - } - ], - "metadata": {} - } - ] -} +{ + "metadata": { + "name": "" + }, + "nbformat": 3, + "nbformat_minor": 0, + "worksheets": [ + { + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Chapter 2\n", + "======\n", + "______\n", + "\n", + "This chapter introduces more PyMC syntax and design patterns, and ways to think about how to model a system from a Bayesian perspective. It also contains tips and data visualization techniques for assessing goodness-of-fit for your Bayesian model." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## A little more on PyMC\n", + "\n", + "### Parent and Child relationships\n", + "\n", + "To assist with describing Bayesian relationships, and to be consistent with PyMC's documentation, we introduce *parent and child* variables. \n", + "\n", + "* *parent variables* are variables that influence another variable. \n", + "\n", + "* *child variable* are variables that are affected by other variables, i.e. are the subject of parent variables. \n", + "\n", + "A variable can be both a parent and child. For example, consider the PyMC code below." + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import pymc as pm\n", + "\n", + "\n", + "parameter = pm.Exponential(\"poisson_param\", 1)\n", + "data_generator = pm.Poisson(\"data_generator\", parameter)\n", + "data_plus_one = data_generator + 1" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 1 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "`parameter` controls the parameter of `data_generator`, hence influences its values. The former is a parent of the latter. By symmetry, `data_generator` is a child of `parameter`.\n", + "\n", + "Likewise, `data_generator` is a parent to the variable `data_plus_one` (hence making `data_generator` both a parent and child variable). Although it does not look like one, `data_plus_one` should be treated as a PyMC variable as it is a *function* of another PyMC variable, hence is a child variable to `data_generator`.\n", + "\n", + "This nomenclature is introduced to help us describe relationships in PyMC modeling. You can access a variables children and parent variables using the `children` and `parents` attributes attached to variables." + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "print \"Children of `parameter`: \"\n", + "print parameter.children\n", + "print \"\\nParents of `data_generator`: \"\n", + "print data_generator.parents\n", + "print \"\\nChildren of `data_generator`: \"\n", + "print data_generator.children" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Children of `parameter`: \n", + "set([])\n", + "\n", + "Parents of `data_generator`: \n", + "{'mu': }\n", + "\n", + "Children of `data_generator`: \n", + "set([])\n" + ] + } + ], + "prompt_number": 2 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Of course a child can have more than one parent, and a parent can have many children." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### PyMC Variables\n", + "\n", + "All PyMC variables also expose a `value` attribute. This method produces the *current* (possibly random) internal value of the variable. If the variable is a child variable, its value changes given the variable's parents' values. Using the same variables from before:" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "print \"parameter.value =\", parameter.value\n", + "print \"data_generator.value =\", data_generator.value\n", + "print \"data_plus_one.value =\", data_plus_one.value" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "parameter.value = 0.0281609254306\n", + "data_generator.value = 0\n", + "data_plus_one.value = 1\n" + ] + } + ], + "prompt_number": 3 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "PyMC is concerned with two types of programming variables: `stochastic` and `deterministic`.\n", + "\n", + "* *stochastic variables* are variables that are not deterministic, i.e., even if you knew all the values of the variables' parents (if it even has any parents), it would still be random. Included in this category are instances of classes `Poisson`, `DiscreteUniform`, and `Exponential`.\n", + "\n", + "* *deterministic variables* are variables that are not random if the variables' parents were known. This might be confusing at first: a quick mental check is *if I knew all of variable `foo`'s parent variables, I could determine what `foo`'s value is.* \n", + "\n", + "We will detail each below.\n", + "\n", + "#### Initializing Stochastic variables\n", + "\n", + "Initializing a stochastic variable requires a `name` argument, plus additional parameters that are class specific. For example:\n", + "\n", + "`some_variable = pm.DiscreteUniform(\"discrete_uni_var\", 0, 4)`\n", + "\n", + "where 0, 4 are the `DiscreteUniform`-specific lower and upper bound on the random variable. The [PyMC docs](http://pymc-devs.github.com/pymc/distributions.html) contain the specific parameters for stochastic variables. (Or use `object??`, for example `pm.DiscreteUniform??` if you are using IPython!)\n", + "\n", + "The `name` attribute is used to retrieve the posterior distribution later in the analysis, so it is best to use a descriptive name. Typically, I use the Python variable's name as the `name`.\n", + "\n", + "For multivariable problems, rather than creating a Python array of stochastic variables, addressing the `size` keyword in the call to a `Stochastic` variable creates multivariate array of (independent) stochastic variables. The array behaves like a Numpy array when used like one, and references to its `value` attribute return Numpy arrays. \n", + "\n", + "The `size` argument also solves the annoying case where you may have many variables $\\beta_i, \\; i = 1,...,N$ you wish to model. Instead of creating arbitrary names and variables for each one, like:\n", + "\n", + " beta_1 = pm.Uniform(\"beta_1\", 0, 1)\n", + " beta_2 = pm.Uniform(\"beta_2\", 0, 1)\n", + " ...\n", + "\n", + "we can instead wrap them into a single variable:\n", + "\n", + " betas = pm.Uniform(\"betas\", 0, 1, size=N)\n", + "\n", + "#### Calling `random()`\n", + "We can also call on a stochastic variable's `random()` method, which (given the parent values) will generate a new, random value. Below we demonstrate this using the texting example from the previous chapter." + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "lambda_1 = pm.Exponential(\"lambda_1\", 1) # prior on first behaviour\n", + "lambda_2 = pm.Exponential(\"lambda_2\", 1) # prior on second behaviour\n", + "tau = pm.DiscreteUniform(\"tau\", lower=0, upper=10) # prior on behaviour change\n", + "\n", + "print \"lambda_1.value = %.3f\" % lambda_1.value\n", + "print \"lambda_2.value = %.3f\" % lambda_2.value\n", + "print \"tau.value = %.3f\" % tau.value\n", + "print\n", + "\n", + "lambda_1.random(), lambda_2.random(), tau.random()\n", + "\n", + "print \"After calling random() on the variables...\"\n", + "print \"lambda_1.value = %.3f\" % lambda_1.value\n", + "print \"lambda_2.value = %.3f\" % lambda_2.value\n", + "print \"tau.value = %.3f\" % tau.value" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "lambda_1.value = 0.539\n", + "lambda_2.value = 1.858\n", + "tau.value = 1.000\n", + "\n", + "After calling random() on the variables...\n", + "lambda_1.value = 0.343\n", + "lambda_2.value = 0.316\n", + "tau.value = 6.000\n" + ] + } + ], + "prompt_number": 4 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The call to `random` stores a new value into the variable's `value` attribute. In fact, this new value is stored in the computer's cache for faster recall and efficiency." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### **Warning**: *Don't update stochastic variables' values in-place.*\n", + "\n", + "\n", + "Straight from the PyMC docs, we quote [4]:\n", + "\n", + "> `Stochastic` objects' values should not be updated in-place. This confuses PyMC's caching scheme... The only way a stochastic variable's value should be updated is using statements of the following form:\n", + "\n", + " A.value = new_value\n", + "\n", + "> The following are in-place updates and should **never** be used:\n", + "\n", + " \n", + " A.value += 3\n", + " A.value[2,1] = 5\n", + " A.value.attribute = new_attribute_value\n", + " " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "#### Deterministic variables\n", + "\n", + "Since most variables you will be modeling are stochastic, we distinguish deterministic variables with a `pymc.deterministic` wrapper. (If you are unfamiliar with Python wrappers (also called decorators), that's no problem. Just prepend the `pymc.deterministic` decorator before the variable declaration and you're good to go. No need to know more. ) The declaration of a deterministic variable uses a Python function:\n", + "\n", + " @pm.deterministic\n", + " def some_deterministic_var(v1=v1,):\n", + " #jelly goes here.\n", + "\n", + "For all purposes, we can treat the object `some_deterministic_var` as a variable and not a Python function. \n", + "\n", + "Prepending with the wrapper is the easiest way, but not the only way, to create deterministic variables: elementary operations, like addition, exponentials etc. implicitly create deterministic variables. For example, the following returns a deterministic variable:" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "type(lambda_1 + lambda_2)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "pyout", + "prompt_number": 5, + "text": [ + "pymc.PyMCObjects.Deterministic" + ] + } + ], + "prompt_number": 5 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The use of the `deterministic` wrapper was seen in the previous chapter's text-message example. Recall the model for $\\lambda$ looked like: \n", + "\n", + "$$\n", + "\\lambda = \n", + "\\cases{\n", + "\\lambda_1 & \\text{if } t \\lt \\tau \\cr\n", + "\\lambda_2 & \\text{if } t \\ge \\tau\n", + "}\n", + "$$\n", + "\n", + "And in PyMC code:" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import numpy as np\n", + "n_data_points = 5 # in CH1 we had ~70 data points\n", + "\n", + "\n", + "@pm.deterministic\n", + "def lambda_(tau=tau, lambda_1=lambda_1, lambda_2=lambda_2):\n", + " out = np.zeros(n_data_points)\n", + " out[:tau] = lambda_1 # lambda before tau is lambda1\n", + " out[tau:] = lambda_2 # lambda after tau is lambda2\n", + " return out" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 7 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Clearly, if $\\tau, \\lambda_1$ and $\\lambda_2$ are known, then $\\lambda$ is known completely, hence it is a deterministic variable. \n", + "\n", + "Inside the deterministic decorator, the `Stochastic` variables passed in behave like scalars or Numpy arrays (if multivariable), and *not* like `Stochastic` variables. For example, running the following:\n", + "\n", + " @pm.deterministic\n", + " def some_deterministic(stoch=some_stochastic_var):\n", + " return stoch.value**2\n", + "\n", + "\n", + "will return an `AttributeError` detailing that `stoch` does not have a `value` attribute. It simply needs to be `stoch**2`. During the learning phase, it's the variable's `value` that is repeatedly passed in, not the actual variable. \n", + "\n", + "Notice in the creation of the deterministic function we added defaults to each variable used in the function. This is a necessary step, and all variables *must* have default values. " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Including observations in the Model\n", + "\n", + "At this point, it may not look like it, but we have fully specified our priors. For example, we can ask and answer questions like \"What does my prior distribution of $\\lambda_1$ look like?\" " + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "%matplotlib inline\n", + "from IPython.core.pylabtools import figsize\n", + "from matplotlib import pyplot as plt\n", + "figsize(12.5, 4)\n", + "\n", + "\n", + "samples = [lambda_1.random() for i in range(20000)]\n", + "plt.hist(samples, bins=70, normed=True, histtype=\"stepfilled\")\n", + "plt.title(\"Prior distribution for $\\lambda_1$\")\n", + "plt.xlim(0, 8);" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "display_data", + "png": 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uVHV1tZYtW6a8vLwGazIzM7VmzRpJ0meffaZ//OMf6tu371mUjpY69aoWQodsbZGvHbK1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\nO0EFAADQaiGb6Qb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+ "text": [ + "" + ] + } + ], + "prompt_number": 10 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "To frame this in the notation of the first chapter, though this is a slight abuse of notation, we have specified $P(A)$. Our next goal is to include data/evidence/observations $X$ into our model. \n", + "\n", + "PyMC stochastic variables have a keyword argument `observed` which accepts a boolean (`False` by default). The keyword `observed` has a very simple role: fix the variable's current value, i.e. make `value` immutable. We have to specify an initial `value` in the variable's creation, equal to the observations we wish to include, typically an array (and it should be an Numpy array for speed). For example:" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "data = np.array([10, 5])\n", + "fixed_variable = pm.Poisson(\"fxd\", 1, value=data, observed=True)\n", + "print \"value: \", fixed_variable.value\n", + "print \"calling .random()\"\n", + "fixed_variable.random()\n", + "print \"value: \", fixed_variable.value" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "value: [10 5]\n", + "calling .random()\n", + "value: [10 5]\n" + ] + } + ], + "prompt_number": 11 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "This is how we include data into our models: initializing a stochastic variable to have a *fixed value*. \n", + "\n", + "To complete our text message example, we fix the PyMC variable `observations` to the observed dataset. " + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# We're using some fake data here\n", + "data = np.array([10, 25, 15, 20, 35])\n", + "obs = pm.Poisson(\"obs\", lambda_, value=data, observed=True)\n", + "print obs.value" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "[10 25 15 20 35]\n" + ] + } + ], + "prompt_number": 12 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Finally...\n", + "\n", + "We wrap all the created variables into a `pm.Model` class. With this `Model` class, we can analyze the variables as a single unit. This is an optional step, as the fitting algorithms can be sent an array of the variables rather than a `Model` class. I may or may not use this class in future examples ;)" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "model = pm.Model([obs, lambda_, lambda_1, lambda_2, tau])" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 13 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Modeling approaches\n", + "\n", + "A good starting thought to Bayesian modeling is to think about *how your data might have been generated*. Position yourself in an omniscient position, and try to imagine how *you* would recreate the dataset. \n", + "\n", + "In the last chapter we investigated text message data. We begin by asking how our observations may have been generated:\n", + "\n", + "1. We started by thinking \"what is the best random variable to describe this count data?\" A Poisson random variable is a good candidate because it can represent count data. So we model the number of sms's received as sampled from a Poisson distribution.\n", + "\n", + "2. Next, we think, \"Ok, assuming sms's are Poisson-distributed, what do I need for the Poisson distribution?\" Well, the Poisson distribution has a parameter $\\lambda$. \n", + "\n", + "3. Do we know $\\lambda$? No. In fact, we have a suspicion that there are *two* $\\lambda$ values, one for the earlier behaviour and one for the latter behaviour. We don't know when the behaviour switches though, but call the switchpoint $\\tau$.\n", + "\n", + "4. What is a good distribution for the two $\\lambda$s? The exponential is good, as it assigns probabilities to positive real numbers. Well the exponential distribution has a parameter too, call it $\\alpha$.\n", + "\n", + "5. Do we know what the parameter $\\alpha$ might be? No. At this point, we could continue and assign a distribution to $\\alpha$, but it's better to stop once we reach a set level of ignorance: whereas we have a prior belief about $\\lambda$, (\"it probably changes over time\", \"it's likely between 10 and 30\", etc.), we don't really have any strong beliefs about $\\alpha$. So it's best to stop here. \n", + "\n", + " What is a good value for $\\alpha$ then? We think that the $\\lambda$s are between 10-30, so if we set $\\alpha$ really low (which corresponds to larger probability on high values) we are not reflecting our prior well. Similar, a too-high alpha misses our prior belief as well. A good idea for $\\alpha$ as to reflect our belief is to set the value so that the mean of $\\lambda$, given $\\alpha$, is equal to our observed mean. This was shown in the last chapter.\n", + "\n", + "6. We have no expert opinion of when $\\tau$ might have occurred. So we will suppose $\\tau$ is from a discrete uniform distribution over the entire timespan.\n", + "\n", + "\n", + "Below we give a graphical visualization of this, where arrows denote `parent-child` relationships. (provided by the [Daft Python library](http://daft-pgm.org/) )\n", + "\n", + "\n", + "\n", + "\n", + "PyMC, and other probabilistic programming languages, have been designed to tell these data-generation *stories*. More generally, B. Cronin writes [5]:\n", + "\n", + "> Probabilistic programming will unlock narrative explanations of data, one of the holy grails of business analytics and the unsung hero of scientific persuasion. People think in terms of stories - thus the unreasonable power of the anecdote to drive decision-making, well-founded or not. But existing analytics largely fails to provide this kind of story; instead, numbers seemingly appear out of thin air, with little of the causal context that humans prefer when weighing their options." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Same story; different ending.\n", + "\n", + "Interestingly, we can create *new datasets* by retelling the story.\n", + "For example, if we reverse the above steps, we can simulate a possible realization of the dataset.\n", + "\n", + "1\\. Specify when the user's behaviour switches by sampling from $\\text{DiscreteUniform}(0, 80)$:" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "tau = pm.rdiscrete_uniform(0, 80)\n", + "print tau" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "37\n" + ] + } + ], + "prompt_number": 14 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "2\\. Draw $\\lambda_1$ and $\\lambda_2$ from an $\\text{Exp}(\\alpha)$ distribution:" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "alpha = 1. / 20.\n", + "lambda_1, lambda_2 = pm.rexponential(alpha, 2)\n", + "print lambda_1, lambda_2" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "29.0394614963 13.5921161471\n" + ] + } + ], + "prompt_number": 15 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "3\\. For days before $\\tau$, represent the user's received SMS count by sampling from $\\text{Poi}(\\lambda_1)$, and sample from $\\text{Poi}(\\lambda_2)$ for days after $\\tau$. For example:" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "data = np.r_[pm.rpoisson(lambda_1, tau), pm.rpoisson(lambda_2, 80 - tau)]" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 16 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "4\\. Plot the artificial dataset:" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "plt.bar(np.arange(80), data, color=\"#348ABD\")\n", + "plt.bar(tau - 1, data[tau - 1], color=\"r\", label=\"user behaviour changed\")\n", + "plt.xlabel(\"Time (days)\")\n", + "plt.ylabel(\"count of text-msgs received\")\n", + "plt.title(\"Artificial dataset\")\n", + "plt.xlim(0, 80)\n", + "plt.legend();" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "display_data", + "png": 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wevVqzJ07F+fOndO+d8uWLYiIiMDly5fh4eGBd999V7use/fu+N///ofLly8jODgYU6dO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\nukYiIiIyUnxqJpF+ybrP+/Tp0+Ht7Y0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+ "text": [ + "" + ] + } + ], + "prompt_number": 17 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "It is okay that our fictional dataset does not look like our observed dataset: the probability is incredibly small it indeed would. PyMC's engine is designed to find good parameters, $\\lambda_i, \\tau$, that maximize this probability. \n", + "\n", + "\n", + "The ability to generate artificial datasets is an interesting side effect of our modeling, and we will see that this ability is a very important method of Bayesian inference. We produce a few more datasets below:" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "def plot_artificial_sms_dataset():\n", + " tau = pm.rdiscrete_uniform(0, 80)\n", + " alpha = 1. / 20.\n", + " lambda_1, lambda_2 = pm.rexponential(alpha, 2)\n", + " data = np.r_[pm.rpoisson(lambda_1, tau), pm.rpoisson(lambda_2, 80 - tau)]\n", + " plt.bar(np.arange(80), data, color=\"#348ABD\")\n", + " plt.bar(tau - 1, data[tau - 1], color=\"r\", label=\"user behaviour changed\")\n", + " plt.xlim(0, 80)\n", + "\n", + "figsize(12.5, 5)\n", + "plt.title(\"More example of artificial datasets\")\n", + "for i in range(4):\n", + " plt.subplot(4, 1, i)\n", + " plot_artificial_sms_dataset()" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "display_data", + "png": 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nve13xNcEeZzZvcThjpQfffQR1q1bh/379yMiIgKHDh1ii1EiIiIioi70sncD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\n4v3m3FbxAAAAAElFTkSuQmCC\n", + "text": [ + "" + ] + } + ], + "prompt_number": 18 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Later we will see how we use this to make predictions and test the appropriateness of our models." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "#####Example: Bayesian A/B testing\n", + "\n", + "A/B testing is a statistical design pattern for determining the difference of effectiveness between two different treatments. For example, a pharmaceutical company is interested in the effectiveness of drug A vs drug B. The company will test drug A on some fraction of their trials, and drug B on the other fraction (this fraction is often 1/2, but we will relax this assumption). After performing enough trials, the in-house statisticians sift through the data to determine which drug yielded better results. \n", + "\n", + "Similarly, front-end web developers are interested in which design of their website yields more sales or some other metric of interest. They will route some fraction of visitors to site A, and the other fraction to site B, and record if the visit yielded a sale or not. The data is recorded (in real-time), and analyzed afterwards. \n", + "\n", + "Often, the post-experiment analysis is done using something called a hypothesis test like *difference of means test* or *difference of proportions test*. This involves often misunderstood quantities like a \"Z-score\" and even more confusing \"p-values\" (please don't ask). If you have taken a statistics course, you have probably been taught this technique (though not necessarily *learned* this technique). And if you were like me, you may have felt uncomfortable with their derivation -- good: the Bayesian approach to this problem is much more natural. \n", + "\n", + "### A Simple Case\n", + "\n", + "As this is a hacker book, we'll continue with the web-dev example. For the moment, we will focus on the analysis of site A only. Assume that there is some true $0 \\lt p_A \\lt 1$ probability that users who, upon shown site A, eventually purchase from the site. This is the true effectiveness of site A. Currently, this quantity is unknown to us. \n", + "\n", + "Suppose site A was shown to $N$ people, and $n$ people purchased from the site. One might conclude hastily that $p_A = \\frac{n}{N}$. Unfortunately, the *observed frequency* $\\frac{n}{N}$ does not necessarily equal $p_A$ -- there is a difference between the *observed frequency* and the *true frequency* of an event. The true frequency can be interpreted as the probability of an event occurring. For example, the true frequency of rolling a 1 on a 6-sided die is $\\frac{1}{6}$. Knowing the true frequency of events like:\n", + "\n", + "- fraction of users who make purchases, \n", + "- frequency of social attributes, \n", + "- percent of internet users with cats etc. \n", + "\n", + "are common requests we ask of Nature. Unfortunately, often Nature hides the true frequency from us and we must *infer* it from observed data.\n", + "\n", + "The *observed frequency* is then the frequency we observe: say rolling the die 100 times you may observe 20 rolls of 1. The observed frequency, 0.2, differs from the true frequency, $\\frac{1}{6}$. We can use Bayesian statistics to infer probable values of the true frequency using an appropriate prior and observed data.\n", + "\n", + "\n", + "With respect to our A/B example, we are interested in using what we know, $N$ (the total trials administered) and $n$ (the number of conversions), to estimate what $p_A$, the true frequency of buyers, might be. \n", + "\n", + "To set up a Bayesian model, we need to assign prior distributions to our unknown quantities. *A priori*, what do we think $p_A$ might be? For this example, we have no strong conviction about $p_A$, so for now, let's assume $p_A$ is uniform over [0,1]:" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import pymc as pm\n", + "\n", + "# The parameters are the bounds of the Uniform.\n", + "p = pm.Uniform('p', lower=0, upper=1)" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 19 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Had we had stronger beliefs, we could have expressed them in the prior above.\n", + "\n", + "For this example, consider $p_A = 0.05$, and $N = 1500$ users shown site A, and we will simulate whether the user made a purchase or not. To simulate this from $N$ trials, we will use a *Bernoulli* distribution: if $ X\\ \\sim \\text{Ber}(p)$, then $X$ is 1 with probability $p$ and 0 with probability $1 - p$. Of course, in practice we do not know $p_A$, but we will use it here to simulate the data." + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# set constants\n", + "p_true = 0.05 # remember, this is unknown.\n", + "N = 1500\n", + "\n", + "# sample N Bernoulli random variables from Ber(0.05).\n", + "# each random variable has a 0.05 chance of being a 1.\n", + "# this is the data-generation step\n", + "occurrences = pm.rbernoulli(p_true, N)\n", + "\n", + "print occurrences # Remember: Python treats True == 1, and False == 0\n", + "print occurrences.sum()" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "[False False False ..., False False True]\n", + "87\n" + ] + } + ], + "prompt_number": 20 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The observed frequency is:" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# Occurrences.mean is equal to n/N.\n", + "print \"What is the observed frequency in Group A? %.4f\" % occurrences.mean()\n", + "print \"Does this equal the true frequency? %s\" % (occurrences.mean() == p_true)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "What is the observed frequency in Group A? 0.0580\n", + "Does this equal the true frequency? False\n" + ] + } + ], + "prompt_number": 21 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We combine the observations into the PyMC `observed` variable, and run our inference algorithm:" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# include the observations, which are Bernoulli\n", + "obs = pm.Bernoulli(\"obs\", p, value=occurrences, observed=True)\n", + "\n", + "# To be explained in chapter 3\n", + "mcmc = pm.MCMC([p, obs])\n", + "mcmc.sample(18000, 1000)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + " \r", + "[****************100%******************] 18000 of 18000 complete" + ] + }, + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "\n" + ] + } + ], + "prompt_number": 22 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We plot the posterior distribution of the unknown $p_A$ below:" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "figsize(12.5, 4)\n", + "plt.title(\"Posterior distribution of $p_A$, the true effectiveness of site A\")\n", + "plt.vlines(p_true, 0, 90, linestyle=\"--\", label=\"true $p_A$ (unknown)\")\n", + "plt.hist(mcmc.trace(\"p\")[:], bins=25, histtype=\"stepfilled\", normed=True)\n", + "plt.legend()" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "pyout", + "prompt_number": 23, + "text": [ + "" + ] + }, + { + "metadata": {}, + "output_type": "display_data", + "png": 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Ntn3bSUlJ2Lt3L958800888wzDo+HbbbZZptttp25nZOTg9LSUgBAfn4+EhMT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\nl19+GQBQXFyM2NhYhISEIC4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+ "text": [ + "" + ] + } + ], + "prompt_number": 23 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Our posterior distribution puts most weight near the true value of $p_A$, but also some weights in the tails. This is a measure of how uncertain we should be, given our observations. Try changing the number of observations, `N`, and observe how the posterior distribution changes.\n", + "\n", + "### *A* and *B* Together\n", + "\n", + "A similar anaylsis can be done for site B's response data to determine the analogous $p_B$. But what we are really interested in is the *difference* between $p_A$ and $p_B$. Let's infer $p_A$, $p_B$, *and* $\\text{delta} = p_A - p_B$, all at once. We can do this using PyMC's deterministic variables. (We'll assume for this exercise that $p_B = 0.04$, so $\\text{delta} = 0.01$, $N_B = 750$ (signifcantly less than $N_A$) and we will simulate site B's data like we did for site A's data )" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import pymc as pm\n", + "figsize(12, 4)\n", + "\n", + "# these two quantities are unknown to us.\n", + "true_p_A = 0.05\n", + "true_p_B = 0.04\n", + "\n", + "# notice the unequal sample sizes -- no problem in Bayesian analysis.\n", + "N_A = 1500\n", + "N_B = 750\n", + "\n", + "# generate some observations\n", + "observations_A = pm.rbernoulli(true_p_A, N_A)\n", + "observations_B = pm.rbernoulli(true_p_B, N_B)\n", + "print \"Obs from Site A: \", observations_A[:30].astype(int), \"...\"\n", + "print \"Obs from Site B: \", observations_B[:30].astype(int), \"...\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Obs from Site A: [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0] ...\n", + "Obs from Site B: [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0] ...\n" + ] + } + ], + "prompt_number": 24 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "print observations_A.mean()\n", + "print observations_B.mean()" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "0.056\n", + "0.0306666666667\n" + ] + } + ], + "prompt_number": 25 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# Set up the pymc model. Again assume Uniform priors for p_A and p_B.\n", + "p_A = pm.Uniform(\"p_A\", 0, 1)\n", + "p_B = pm.Uniform(\"p_B\", 0, 1)\n", + "\n", + "\n", + "# Define the deterministic delta function. This is our unknown of interest.\n", + "@pm.deterministic\n", + "def delta(p_A=p_A, p_B=p_B):\n", + " return p_A - p_B\n", + "\n", + "# Set of observations, in this case we have two observation datasets.\n", + "obs_A = pm.Bernoulli(\"obs_A\", p_A, value=observations_A, observed=True)\n", + "obs_B = pm.Bernoulli(\"obs_B\", p_B, value=observations_B, observed=True)\n", + "\n", + "# To be explained in chapter 3.\n", + "mcmc = pm.MCMC([p_A, p_B, delta, obs_A, obs_B])\n", + "mcmc.sample(20000, 1000)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + " \r", + "[****************100%******************] 20000 of 20000 complete" + ] + }, + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "\n" + ] + } + ], + "prompt_number": 26 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Below we plot the posterior distributions for the three unknowns: " + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "p_A_samples = mcmc.trace(\"p_A\")[:]\n", + "p_B_samples = mcmc.trace(\"p_B\")[:]\n", + "delta_samples = mcmc.trace(\"delta\")[:]" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 27 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "figsize(12.5, 10)\n", + "\n", + "# histogram of posteriors\n", + "\n", + "ax = plt.subplot(311)\n", + "\n", + "plt.xlim(0, .1)\n", + "plt.hist(p_A_samples, histtype='stepfilled', bins=25, alpha=0.85,\n", + " label=\"posterior of $p_A$\", color=\"#A60628\", normed=True)\n", + "plt.vlines(true_p_A, 0, 80, linestyle=\"--\", label=\"true $p_A$ (unknown)\")\n", + "plt.legend(loc=\"upper right\")\n", + "plt.title(\"Posterior distributions of $p_A$, $p_B$, and delta unknowns\")\n", + "\n", + "ax = plt.subplot(312)\n", + "\n", + "plt.xlim(0, .1)\n", + "plt.hist(p_B_samples, histtype='stepfilled', bins=25, alpha=0.85,\n", + " label=\"posterior of $p_B$\", color=\"#467821\", normed=True)\n", + "plt.vlines(true_p_B, 0, 80, linestyle=\"--\", label=\"true $p_B$ (unknown)\")\n", + "plt.legend(loc=\"upper right\")\n", + "\n", + "ax = plt.subplot(313)\n", + "plt.hist(delta_samples, histtype='stepfilled', bins=30, alpha=0.85,\n", + " label=\"posterior of delta\", color=\"#7A68A6\", normed=True)\n", + "plt.vlines(true_p_A - true_p_B, 0, 60, linestyle=\"--\",\n", + " label=\"true delta (unknown)\")\n", + "plt.vlines(0, 0, 60, color=\"black\", alpha=0.2)\n", + "plt.legend(loc=\"upper right\");" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "display_data", + "png": 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xmCskt61bt8LFxQV79uxBdnY2XnvtNQDAgQMHEBUVhczMTBgaGjbbt3HaRkND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fddvPnmm3jmmWdw9OhRxMfH48SJE0bUStO4XC7eCVcgJSUFEgAiIzTP1KJZtHU0cwUPhZivNu5r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\nRK5CYII=\n", + "text": [ + "" + ] + } + ], + "prompt_number": 29 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Notice that as a result of `N_B < N_A`, i.e. we have less data from site B, our posterior distribution of $p_B$ is fatter, implying we are less certain about the true value of $p_B$ than we are of $p_A$. \n", + "\n", + "With respect to the posterior distribution of $\\text{delta}$, we can see that the majority of the distribution is above $\\text{delta}=0$, implying there site A's response is likely better than site B's response. The probability this inference is incorrect is easily computable:" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# Count the number of samples less than 0, i.e. the area under the curve\n", + "# before 0, represent the probability that site A is worse than site B.\n", + "print \"Probability site A is WORSE than site B: %.3f\" % \\\n", + " (delta_samples < 0).mean()\n", + "\n", + "print \"Probability site A is BETTER than site B: %.3f\" % \\\n", + " (delta_samples > 0).mean()" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Probability site A is WORSE than site B: 0.003\n", + "Probability site A is BETTER than site B: 0.997\n" + ] + } + ], + "prompt_number": 30 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "If this probability is too high for comfortable decision-making, we can perform more trials on site B (as site B has less samples to begin with, each additional data point for site B contributes more inferential \"power\" than each additional data point for site A). \n", + "\n", + "Try playing with the parameters `true_p_A`, `true_p_B`, `N_A`, and `N_B`, to see what the posterior of $\\text{delta}$ looks like. Notice in all this, the difference in sample sizes between site A and site B was never mentioned: it naturally fits into Bayesian analysis.\n", + "\n", + "I hope the readers feel this style of A/B testing is more natural than hypothesis testing, which has probably confused more than helped practitioners. Later in this book, we will see two extensions of this model: the first to help dynamically adjust for bad sites, and the second will improve the speed of this computation by reducing the analysis to a single equation. " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## An algorithm for human deceit\n", + "\n", + "Social data has an additional layer of interest as people are not always honest with responses, which adds a further complication into inference. For example, simply asking individuals \"Have you ever cheated on a test?\" will surely contain some rate of dishonesty. What you can say for certain is that the true rate is less than your observed rate (assuming individuals lie *only* about *not cheating*; I cannot imagine one who would admit \"Yes\" to cheating when in fact they hadn't cheated). \n", + "\n", + "To present an elegant solution to circumventing this dishonesty problem, and to demonstrate Bayesian modeling, we first need to introduce the binomial distribution.\n", + "\n", + "### The Binomial Distribution\n", + "\n", + "The binomial distribution is one of the most popular distributions, mostly because of its simplicity and usefulness. Unlike the other distributions we have encountered thus far in the book, the binomial distribution has 2 parameters: $N$, a positive integer representing $N$ trials or number of instances of potential events, and $p$, the probability of an event occurring in a single trial. Like the Poisson distribution, it is a discrete distribution, but unlike the Poisson distribution, it only weighs integers from $0$ to $N$. The mass distribution looks like:\n", + "\n", + "$$P( X = k ) = {{N}\\choose{k}} p^k(1-p)^{N-k}$$\n", + "\n", + "If $X$ is a binomial random variable with parameters $p$ and $N$, denoted $X \\sim \\text{Bin}(N,p)$, then $X$ is the number of events that occurred in the $N$ trials (obviously $0 \\le X \\le N$), and $p$ is the probability of a single event. The larger $p$ is (while still remaining between 0 and 1), the more events are likely to occur. The expected value of a binomial is equal to $Np$. Below we plot the mass probability distribution for varying parameters. " + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "figsize(12.5, 4)\n", + "\n", + "import scipy.stats as stats\n", + "binomial = stats.binom\n", + "\n", + "parameters = [(10, .4), (10, .9)]\n", + "colors = [\"#348ABD\", \"#A60628\"]\n", + "\n", + "for i in range(2):\n", + " N, p = parameters[i]\n", + " _x = np.arange(N + 1)\n", + " plt.bar(_x - 0.5, binomial.pmf(_x, N, p), color=colors[i],\n", + " edgecolor=colors[i],\n", + " alpha=0.6,\n", + " label=\"$N$: %d, $p$: %.1f\" % (N, p),\n", + " linewidth=3)\n", + "\n", + "plt.legend(loc=\"upper left\")\n", + "plt.xlim(0, 10.5)\n", + "plt.xlabel(\"$k$\")\n", + "plt.ylabel(\"$P(X = k)$\")\n", + "plt.title(\"Probability mass distributions of binomial random variables\");" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "display_data", + "png": 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KSmBubo6FCxdi0aJFTdr35cuXIZfL4ebmplzm4+Nz33fuFy1aVGefGnvMwsJC\nrFq1Cm+99RaEEPfVr2qGXidHuseYICnGBEkxJkiVoccD79wbsDNnzqBv377w8vLCkiVLcObMGfj7\n+ytff+edd5q87+LiYlhZWakts7S0RFFRw58y/P777zh9+jT++OMPBAcHIy8vD+3atcOUKVOwevVq\nrR3z7bffxrRp0+Do6MhvEiYiIiLSAO/cG7Bz587Bx8cHRkZGmDVrFtatW4e0tDT06tXrvvdtYWGB\nO3fuqC0rLCyEpWXDZUk3btyAu7s7MjIyMHbsWDz++ONYs2aNVo+ZkpKCw4cPY86cOQCgtTv3hl4n\nR7rHmCApxgRJMSZIlaHHA+/cG7DKyn8ewH3mmWfQr18/eHh4aGXWmJ49e6KiogJXrlxRlsmcO3cO\nXl5eDW770EMPYcWKFXj44YcBVCXitra2Wj3mkSNHkJmZCT8/PwBVd/0VCgUuXbqEX3/9VePzJCIi\nImpLmNxLNPXhV227d+8eTE1NlW0bGxtMmDAB8fHxeOmllzTah0KhwL1796BQKFBZWYmysjLI5XIY\nGxvDwsIC48aNw4oVK/DBBx/g7NmziIuLw88//wwAyqkzP/7441r3fejQIUyfPh0AEBMTg/nz5zfY\nn4aOqWrGjBl47LHHAFTdtV+7di0yMjLw7rvvanTudTH0OjnSPcYESTEmSIoxQaoMPR6Y3KPqC6Ys\n2xkDMG1w3aaybGcMU2PNqqCSkpLw/vvvw9zcHEOHDkXXrl0BALNnz8aePXuU6y1YsAAA6iyJWb16\ntVoN/Pbt2xEZGYnXXnsNQFXN/osvvggPDw/Y2tpizZo18PDwAABcu3YNkydPrnW/hYWFKCgowG+/\n/Yby8nL069cP48eP16hP9R3zySefxIMPPoiIiAiYm5urzQZkYWEBc3NzjT4hICIiImqrZEJbxcwG\naP/+/QgICKix/Nq1a8qEGeA31EqVl5dj2LBhiI+Ph7GxcY3Xd+7ciZMnT2L58uW671w9pO9rbeLj\n4w3+L27SLcYESTEmSErfMfH7olW4m5WD0qwcdBzQR2/90KaChNMwd3KAmZMDHlgdqe/uNIq+46Fa\nUlISRo4cWWO5Xu/cx8XFISIiAgqFAmFhYYiMVH9zY2NjsWzZMhgZGcHIyAirV6/GQw89BABwdXWF\ntbU1jI2NYWJi0uAXOtWnn1PLSLp1xdTUFMeOHav1tUuXLuGTTz5Bjx49UFhYCGtrjhsRERGRodBb\ncq9QKDB8ijY8AAAgAElEQVR//nzs27cP3bp1Q1BQECZMmKD2cOWoUaPw6KOPAqh6aHPSpEn4448/\nAAAymQwHDx5kmYaO9e7dG7t379Z3N5rMEP7SJsPCmCApxgRJMSZIlaHHg96mwkxMTIS7uztcXV1h\nYmKCKVOmIDY2Vm0dCwsL5c9FRUXo3Lmz2uutuKKIiIiIiKjR9JbcZ2dnw9nZWdl2cnJCdnZ2jfV+\n+OEHeHl5ITQ0FB9++KFyuUwmw6hRoxAYGIjPP/9cJ32mls/Q56Yl3WNMkBRjgqQYE6TK0ONBb2U5\nmn7j6MSJEzFx4kT89ttvmD59Oi5evAigah50R0dH5OXlYfTo0fD09MSQIUOas8tEREREpCd/HUpE\n3t4jUJSV67UfV69noEPsEa3tz7idKexGD0LnYcFa2Z/ekvtu3bohMzNT2c7MzISTk1Od6w8ZMgQV\nFRW4efMmOnXqBEdHRwCAnZ0dJk2ahMTExFqT+7lz58LFxQVA1Vzxvr6+yi9Qotbl9u3buHLlirIW\nrvova2m7Wl2vs8022227PXjwYIPqD9v6b1cv09fxk69noDw/H73/7kvy9QwAQF9HlxbbvlOcj2A4\nNGo8Ou09gbK8fJxKr3r+0t+2avsz+Tk6bZfn5+N4Xr7W9vf73dswyU7H038n9/XlL/Hx8cjIqBrP\nsLAw1EZvU2FWVFTAw8MD+/fvR9euXREcHIyYmBi1B2ovX74MNzc3yGQyJCUl4YknnsDly5dRUlIC\nhUIBKysrFBcXY8yYMXjjjTcwZswYtWNoOhUmtQ58X4mIqDXiVJhVVMehNWnqlKAGNxWmXC7H2rVr\nERISAoVCgeeeew5eXl6Ijo4GAISHh+Pbb7/FV199BRMTE1haWuKbb74BAOTk5Ci/YKmiogJPP/10\njcSeqDaGMjctGQ7GBEkxJkiKMWF49PlHTvL1DOWnEPerIOG0VvajSq/z3IeGhiI0NFRtWXh4uPLn\n1157Tfltqqrc3Nxw+rT2B4OIiIiIqCXT22w5RPrAOy8kxZggKcYESTEmSJW27to3F73euTcUunj6\nWttPQhMRERERSfHOPYC8vUdQlpePu1k5zfavLC8feXu1N22SJj7//HM89NBDcHR0xLx582q8XlBQ\ngOnTp8PZ2Rn+/v749ttvm71PjTnmxYsX8eijj8LV1RWBgYHYtWvXfR/f0OemJd1jTJAUY4KkGBOk\nqnr2H0PFO/cAFGXlqCgsatanr82dHCC3tmzUNidPnsQHH3yApKQknDlzBnK5HDdu3MC///1vFBcX\n49VXX0VwcN2fBDg6OmLhwoX49ddfUVpaWuP1RYsWoV27drh48SLOnj2LKVOmwMfHB56eno0+P01p\nesyKigpMmzYNs2bNwg8//ID4+HhMnToVBw8eRM+ePZutf0REREQtGZN7ieZ4+rqpT0IHBgZi5MiR\nKCwsxI8//ojJkyfD3t4eISEhGD9+PMzNzevdfty4cQCA5OTkGsl9cXExdu7ciaNHj6J9+/YYMGAA\nxo4di+3bt2PZsmVN6m9DGnPMS5cuITc3F3PmzAFQ9T0HwcHB2LZtG15//fUm94F1kyTFmCApxgRJ\nMSZIlaHX3LMsx4BVVlZCLpdj9uzZWLdunXJ5SUkJzM3NsXDhQixatKhJ+758+TLkcrnaF3r5+Pgg\nNTX1vvq8aNGiOvt0v8esrKy87/4RERERtWZM7g3YmTNn0LdvX4SGhiI3NxdnzpxRe/2dd97B6tWr\nm7Tv4uJiWFlZqS2ztLREUVFRg9v+/vvv2LJlC5YvX47du3dj06ZNyu8gWL16dZ19aswxe/Xqhc6d\nO+PDDz/EvXv38Ouvv+LYsWO1lhc1BusmSYoxQVKMCZJiTJAqQ6+5Z3JvwM6dOwcfHx8YGRlh1qxZ\nWLduHdLS0tCrV6/73reFhQXu3LmjtqywsBCWlg0/F3Djxg24u7sjIyMDY8eOxeOPP441a9Zo9Zgm\nJibYsmUL9u7dCy8vL3z66aeYOHEiv4GWiIiIqB5M7g1YZWWl8udnnnkGP//8M/bs2YOgoKD73nfP\nnj1RUVGBK1euKJedO3cOXl5eDW770EMP4cCBA3j44YcBACkpKbC1tdX6Mb29vfHTTz/hjz/+wI4d\nO3D16lUEBAQ0eJz6sG6SpBgTJMWYICnGBKky9Jp7PlAr0RxfA9wU9+7dg6mpqbJtY2ODCRMmID4+\nHi+99JJG+1AoFLh37x4UCgUqKytRVlYGuVwOY2NjWFhYYNy4cVixYgU++OADnD17FnFxcfj5558B\nQDl15scff1zrvg8dOoTp06cDAGJiYjB//vwG+9PQMaXOnz8PNzc3VFZWYsOGDcjLy8PUqVM1Onci\nIiKitojJPaq+YEpubQlzJ4dmO4bc2hLG7UwbXhFAUlIS3n//fZibm2Po0KHKUpTZs2djz549yvUW\nLFgAAHWWxEjr37dv347IyEi89tprAKpq9l988UV4eHjA1tYWa9asgYeHBwDg2rVrmDx5cq37LSws\nREFBAX777TeUl5ejX79+GD9+vEZ9qu+YTz75JB588EFEREQAALZt24bNmzejoqICAwcOxHfffQcT\nExMNRrBu8fHxvANDahgTJMWYICnGBKlKvp5h0HfvmdwDsBs9CHl7jzR6HvrGqP6GWk0EBATgq6++\nqrHc09NTbT74hurcFy9ejMWLF9f5eocOHbB58+Yay8vLy5GTk1PnXfLDhw8jNDQU//rXv2q81lCf\n6jomUPXHh6qoqChERUXVuz8iIiIi+geTewCdhwWj87C6vwyqrTE1NcWxY8dqfe3SpUv45JNP0KNH\nDxQWFsLa2lrHvbs/vPNCUowJkmJMkBRjglQZ8l17gMk9NVLv3r2xe/dufXeDiIiIiGrB2XKoTeFc\nxSTFmCApxgRJMSZIFee5JyIiIiIinWByT20K6yZJijFBUowJkmJMkCpDr7lnck9ERERE1Eq0yeS+\nXbt2uHnzJoQQ+u4KaUlJSQmMjY0bXI91kyTFmCApxgRJMSZIlaHX3Ot1tpy4uDhERERAoVAgLCwM\nkZGRaq/HxsZi2bJlMDIygpGREVavXo2HHnpIo23r06lTJxQVFeHatWuQyWRaPSfSD2NjY9jb2+u7\nG0RERER6pbfkXqFQYP78+di3bx+6deuGoKAgTJgwAV5eXsp1Ro0ahUcffRQAkJKSgkmTJuGPP/7Q\naNuGWFpawtKy+b60igwT6yZJijFBUowJkmJMkCrW3NchMTER7u7ucHV1hYmJCaZMmYLY2Fi1dSws\nLJQ/FxUVoXPnzhpvS0RERETU1ugtuc/Ozoazs7Oy7eTkhOzs7Brr/fDDD/Dy8kJoaCg+/PDDRm1L\nJMW6SZJiTJAUY4KkGBOkijX3ddC01n3ixImYOHEifvvtN0yfPh2pqamNOs7cuXPh4lL18YmNjQ18\nfX2VH69V/7Ky3XbaKSkpBtUftvXfrmYo/WGbbbYNr52SkqLX4ydfz0B5fj56A8o28E95SEts3ynO\nRzAcGjUeHf4+/5TifFhdz9Bb/9Nu5mp1f2fyc2BqXI4H/j6/+v6/io+PR0ZG1fZhYWGojUzoacqY\nhIQELF++HHFxcQCAFStWwMjIqN4HY3v27InExESkpaVptO3+/fsREBDQfCdBRERE1Mx+X7QKd7Ny\nUJqVg44D+ui7O1pRkHAa5k4OMHNywAOrNZsUheOgLikpCSNHjqyxXG9lOYGBgUhLS0N6ejrKy8ux\nbds2TJgwQW2dy5cvK6erTEpKAlA1040m2xIRERERtTV6S+7lcjnWrl2LkJAQeHt746mnnoKXlxei\no6MRHR0NAPj222/h6+uLvn374uWXX8Y333xT77ZEDZGWYhAxJkiKMUFSjAlSxZr7eoSGhiI0NFRt\nWXh4uPLn1157Da+99prG2xIRERERtWVt8htqqe2qfjiFqBpjgqQYEyTFmCBVnOeeiIiIiIh0gsk9\ntSmsmyQpxgRJMSZIijFBqgy95p7JPRERERFRK8HkntoU1k2SFGOCpBgTJMWYIFWsuSciIiIiIp1g\nck9tCusmSYoxQVKMCZJiTJAq1twTEREREZFOMLmnNoV1kyTFmCApxgRJMSZIFWvuiYiIiIhIJ5jc\nU5vCukmSYkyQFGOCpBgTpIo190REREREpBNM7qlNYd0kSTEmSIoxQVKMCVLFmnsiIiIiItIJJvfU\nprBukqQYEyTFmCApxgSpYs09ERERERHpBJN7alNYN0lSjAmSYkyQFGOCVLHmnoiIiIiIdILJPbUp\nrJskKcYESTEmSIoxQapYc1+PuLg4eHp6olevXli1alWN17du3Qp/f3/4+flh0KBBOHv2rPI1V1dX\n+Pn5oW/fvggODtZlt4mIiIiIDJJcXwdWKBSYP38+9u3bh27duiEoKAgTJkyAl5eXch03NzccPnwY\nNjY2iIuLw+zZs5GQkAAAkMlkOHjwIGxtbfV1CtQCsW6SpBgTJMWYICnGBKlizX0dEhMT4e7uDldX\nV5iYmGDKlCmIjY1VW2fgwIGwsbEBAPTv3x9ZWVlqrwshdNZfIiIiIiJDp7c799nZ2XB2dla2nZyc\ncPz48TrX37BhA8aOHatsy2QyjBo1CsbGxggPD8fzzz/frP2l1iE+Pp53YAzEqaxCHM8sRLmiUq/9\nSE85AVffIK3tz9TYCP2drdHPyVpr+yTd4nWCpBgTpCr5eoZB373XW3Ivk8k0XvfAgQPYuHEjjhw5\nolx25MgRODo6Ii8vD6NHj4anpyeGDBlSY9u5c+fCxaXqDbCxsYGvr6/yF7T6ARm22047JSXFoPrT\nltsxu/ajqKwCHXv1BQBcO38KANDVu59O2wBgfqdca/vr3TcYxzMLUZp+Vq/jyzbbbGuvnZKSotfj\nJ1/PQHl+PnoDyjbwT3lIS2zfKc5HMBwaNR4d/j7/lOJ8WKkk2Lruf9rNXK3u70x+DkyNy/HA3+dX\n1/lX/5yRUbV9WFgYaiMTeqptSUhIwPLlyxEXFwcAWLFiBYyMjBAZGam23tmzZzF58mTExcXB3d29\n1n1FRUXB0tISCxYsUFu+f/9+BAQENM8JENF9eT8+A7l3ynGjuFzfXdEqewtTdLEyRcRgw72rQ0Qt\ny++LVuFuVg5Ks3LQcUAffXdHKwoSTsPcyQFmTg54YHVkwxuA4yCVlJSEkSNH1lgu11bnGiswMBBp\naWlIT09H165dsW3bNsTExKitk5GRgcmTJ2PLli1qiX1JSQkUCgWsrKxQXFyMX375BW+88YauT4GI\ntMTXwVLfXdCKlJwifXeBiIjaOL09UCuXy7F27VqEhITA29sbTz31FLy8vBAdHY3o6GgAwJtvvomC\nggLMmTNHbcrLnJwcDBkyBH369EH//v0xbtw4jBkzRl+nQi2I6kdbREBVzT2RKl4nSIoxQaoMfZ57\nvd25B4DQ0FCEhoaqLQsPD1f+vH79eqxfv77Gdm5ubjh9+nSz94+IiIiIqCXhN9RSm1L9cApRNW3O\nlEOtA68TJMWYIFWGPFMOwOSeiIiIiKjVYHJPbQrrJkmKNfckxesESTEmSFWrq7n/448/cOrUKWRl\nZaG8vBy2trZwd3fHoEGDYGZm1hx9JCIiIiIiDWic3H/11VfYt28f7Ozs4O/vj969e8Pc3By3b9/G\nhQsXEBMTA2tra4SHh8PDw6M5+0zUZKybJCnW3JMUrxMkxZggVYZec99gcl9SUoL//e9/eOSRR/DM\nM8/Uu+7du3fxzTffIDU1FY8++qjWOklERERERA1rsOb+9u3bWLJkCYKC1O9u1fbFtmZmZpg5cya/\nFZYMFusmSYo19yTF6wRJMSZIlaHX3DeY3Ds6OkIur3mDv3v37igtLQUAfP311zh69KjyNWdnZy12\nkYiIiIiINNHk2XLee+89mJubIysrC926dcPJkye12S+iZsG6SZJizT1J8TpBUowJUmXoNfeNSu43\nb96M3NxcAIC/vz/OnTuHqVOn4v/+7/9ga2vbLB0kIiIiIiLNNGoqzOjoaGzcuBFFRUUYOnQo7ty5\ng0mTJuGVV15prv4RaVV8fDzvwJCa9JQTvHtPanidICnGBKlKvp5h0HfvG3XnfsOGDThw4AAOHTqE\nkJAQ2NraYvv27QgODsabb77ZXH0kIiIiIiINNOrOffX89e3bt8eYMWMwZswYAFUz6iQnJ2u/d0Ra\nxjsvJMW79iTF6wRJMSZIlSHftQfu44FaVTY2Nhg+fLg2dkVERERERE3UqDv31WJjY5VfUqX6M5Gh\n03fd5KmsQhzPLES5olJvfWgOpsZG6O9sjX5O1vruSqOx5p6k9H2dIMPDmCBVhl5z36TkPiEhQZnQ\nq/5MRPU7nlmIgtJ7KCpT6LsrWmXZzhjHMwtbZHJPRETUmjQpuSdqqfR956VcUYmiMgVuFJfrtR/a\nZwoLU2N9d6JJeNeepPR9nSDDw5ggVYZ81x5gck+kN74Olvruglak5BTpuwtERET0N608UEvUUsTH\nx+u7C2Rg0lNO6LsLZGB4nSApxgSpSr6eoe8u1EuvyX1cXBw8PT3Rq1cvrFq1qsbrW7duhb+/P/z8\n/DBo0CCcPXtW422JiIiIiNoavSX3CoUC8+fPR1xcHM6fP4+YmBhcuHBBbR03NzccPnwYZ8+exdKl\nSzF79myNtyWqDesmSYo19yTF6wRJMSZIlaHX3OstuU9MTIS7uztcXV1hYmKCKVOmIDY2Vm2dgQMH\nwsbGBgDQv39/ZGVlabwtEREREVFb06QHap9//vlaf26M7OxsODs7K9tOTk44fvx4netv2LABY8eO\nbdK2RNU4VzFJ6Xuee373geHhdYKkGBOkqlXOc+/m5lbrz40hk8k0XvfAgQPYuHEjjhw50uht586d\nCxeXqjfAxsYGvr6+yl/Q6gdk2G477ZSUFL0ePz0lF+au/gD+eZCzOrFsqW3YeSnb8cjQeDzSU06g\noKQC8u6++u3/37Sxv7z8UtgHDNDo/KvbZ41dUVB6D5eSEwEAXb37AQCunT/VotsFacm4claOfuGT\nGjUebLNtiO2UlBS9Hj/5egbK8/PRG1C2gX/KQ1pi+05xPoLh0Kjx6PD3+acU58NKJcHWdf/TbuZq\ndX9n8nNgalyOB/4+v7rOv/rnjIyq7cPCwlAbmRBC1PpKLQoKCtCxY0dNV69XQkICli9fjri4OADA\nihUrYGRkhMjISLX1zp49i8mTJyMuLg7u7u6N2nb//v0ICAjQSn+JtOH9+Azk3inHjeLyVjUVpr2F\nKbpYmSJisOZ3MjgWVVTHoTVpSkwQUe1+X7QKd7NyUJqVg44D+ui7O1pRkHAa5k4OMHNywAOrIxve\nABwHqaSkJIwcObLG8kbduf/www/xxhtvNOrAdQkMDERaWhrS09PRtWtXbNu2DTExMWrrZGRkYPLk\nydiyZYsysdd0WyKilqY1/ZFDRET60ajkft26dXjxxRdha2tb47Vdu3bhkUce0fzAcjnWrl2LkJAQ\nKBQKPPfcc/Dy8kJ0dDQAIDw8HG+++SYKCgowZ84cAICJiQkSExPr3JaoIaybJCl919yT4eF1wjD8\ndSgReXuPQFGm/0+1tF1jbdzOFHajB6HzsGCt7ZN0p1XV3K9evRqbN2/G1KlTYWdnp1x+8OBBREVF\nNSq5B4DQ0FCEhoaqLQsPD1f+vH79eqxfv17jbYmIiKh1yNt7BGV5+ago1P8nQeX5+birMNXa/uTW\nlsjbe4TJPTWLRiX3U6dOhRACH3/8McaMGYODBw9i7dq1uHnzZq1384kMDe/GkRTv2pMUrxOGQVFW\njorCIpRm5ei7K+gNoLREe/0wd3KA3Lp1lOG1RYZ81x5oZHK/a9cu+Pr6IjMzEz4+PvDy8sLrr7+O\nxx57TO3bY4mIiIi0pbU8PAlUPUBJ1Jwa9SVW06dPh7e3N27cuIFjx45h8eLF8PX1hYmJCfr169dc\nfSTSGtXppIiAmlNiEvE6QVLVUxcSAYYfD426cz9ixAisW7cOnTp1AlA1a813332Hu3fvomfPnujQ\noUMDeyAiIiIioubSqDv3ixcvVib21SZPnoyMjAyMGDFCqx0jag6spSUp1tyTFK8TJGXoNdakW4Ye\nD41K7oOCav9PcNKkSfD09NRKh4iIiIiIqGkaldzXZ9asWdraFVGzYS0tSbHmnqR4nSApQ6+xJt0y\n9HjQWnI/evRobe2KiIiIiIiaoMHk/urVq4iJidF4h3/99Rc+//zz++oUUXNhLS1JseaepHidIClD\nr7Em3TL0eGhwtpwePXpACIHIyEg4OztjxIgR8Pb2hkwmU65TVFSExMRE/Prrr+jcuTNefvnlZu00\nERERERHVpFFZjpubG1atWgWFQgE/Pz8YGxujXbt2GDlyJEJCQjBv3jykp6dj4cKFiIiIUEv8iQwJ\na2lJijX3JMXrBEkZeo016Zahx0Oj5rm/ePEizp49iytXriA6Ohpr166Fq6trM3WNiIiIiIgao1EP\n1Pr7+8PHxwfjx4/Hjh07sGfPnubqF1GzYC0tSbHmnqR4nSApQ6+xJt0y9HhoVHIvl/9zo9/c3BxW\nVlZa7xARERERETVNo5L7TZs2YfPmzbhy5QoAwMTEpFk6RdRcWEtLUqy5JyleJ0jK0GusSbcMPR4a\nVXNvaWmJ2NhYvPrqq5DL5XBxccHNmzfx8MMP4+DBg/wiKyIiIiIiPWpUcv/mm28iMDAQQgicPXsW\nBw4cwM8//4wlS5agrKyMyT0ZPNbSkhRr7kmK1wmSMvQaa9ItQ4+HRiX3gYGBAACZTAZ/f3/4+/sj\nIiIClZWV+Pe//90sHSQiIiIiIs00qua+zp0YGWHq1Kna2BVRs2ItLUmx5p6keJ0gKUOvsSbdMvR4\n0EpyD1RNk9lYcXFx8PT0RK9evbBq1aoar6empmLgwIEwMzPDmjVr1F5zdXWFn58f+vbti+Dg4Cb3\nm4iIiIiotWhUWY42KRQKzJ8/H/v27UO3bt0QFBSECRMmwMvLS7lOp06d8NFHH+GHH36osb1MJsPB\ngwdha2ury25TC8daWpJizT1J8TpBUoZeY026ZejxoLU7942VmJgId3d3uLq6wsTEBFOmTEFsbKza\nOnZ2dggMDKxzyk0hhC66SkRERETUIugtuc/Ozoazs7Oy7eTkhOzsbI23l8lkGDVqFAIDA/H55583\nRxepFWItLUmx5p6keJ0gKUOvsSbdMvR40FtZjkwmu6/tjxw5AkdHR+Tl5WH06NHw9PTEkCFDaqw3\nd+5cuLhUfXxiY2MDX19f5Ueu1RdwtttOOyUlRa/HT0/Jhblr1fMp1UlldVlIS23DzkvZjkeGxuOR\nnnICBSUVkHf31W///6aN/eXll8I+YIBG5/9PAll1fcq7mIT0PHO9v5/aal87fwql7eXAYJdGjQfb\nbFe3r17PgBdMAfyTTFWXQ+i6nXYzV6v7O5OfA1PjcjwAaDQeydczUJ6fj95/r6/v8dBG+05xPoLh\noNH5V7c7/H3+KcX5sLqe0ebiofrnjIyq7cPCwlAbmdBTbUtCQgKWL1+OuLg4AMCKFStgZGSEyMjI\nGutGRUXB0tISCxYsqHVfdb2+f/9+BAQEaL/zRE30fnwGcu+U40ZxOXwdLPXdHa1IySmCvYUpuliZ\nImKw5nWIHIsqHAei2v2+aBXuZuWgNCsHHQf00Xd3tKYg4TTMnRxg5uSAB1bXzHlq0xrHguNQpSnj\nUC0pKQkjR46ssVxvZTmBgYFIS0tDeno6ysvLsW3bNkyYMKHWdaV/f5SUlODOnTsAgOLiYvzyyy/w\n9fVt9j4TERERERkyvSX3crkca9euRUhICLy9vfHUU0/By8sL0dHRiI6OBgDk5OTA2dkZ7733Hv77\n3//CxcUFRUVFyMnJwZAhQ9CnTx/0798f48aNw5gxY/R1KtSCsJaWpFhzT1K8TpCUoddYk24Zejzo\nreYeAEJDQxEaGqq2LDw8XPmzg4MDMjMza2xnaWmJ06dPN3v/iIiIiIhaEr3duSfSB85fTVKc556k\neJ0gKUOf15x0y9Djgck9EREREVErweSe2hTW0pIUa+5JitcJkjL0GmvSLUOPByb3REREREStBJN7\nalNYS0tSrLknKV4nSMrQa6xJtww9HpjcExERERG1EkzuqU1hLS1JseaepHidIClDr7Em3TL0eGBy\nT0RERETUSjC5pzaFtbQkxZp7kuJ1gqQMvcaadMvQ44HJPRERERFRKyHXdweobTiVVYjjmYUoV1Tq\ntR/pKSe0eqfW1NgI/Z2t0c/JWmv7JN3SdkxQyxcfH8+796Qm+XqGwd+tJd0x9Hhgck86cTyzEAWl\n91BUptBrPwpKKmB+p1xr+7NsZ4zjmYVM7omIiMggMLknnShXVKKoTIEbxdpLrJtC3t1Xy30whYWp\nsRb3R7rGu/Ykxbv2JGXId2lJ9ww9Hpjck875OljquwtakZJTpO8uEBEREanhA7XUpnBOc5JiTJAU\n57knKUOf15x0y9Djgck9EREREVErwbIcalNYX01SjAnDYSizagEuOBmvvTtznFWr5TP0GmvSLUOP\nByb3RERkEAxlVi1t46xaRKRLTO6pTeGc5iTFmDAchjKrVt7FJNh5BGhxj5xVq6Uz9HnNSbcMPR70\nmtzHxcUhIiICCoUCYWFhiIyMVHs9NTUVzz77LJKTk/HWW29hwYIFGm9LREQtlz5n1UrPM4erlo7P\nWbWISNf09kCtQqHA/PnzERcXh/PnzyMmJgYXLlxQW6dTp0746KOPsHDhwkZvS1Qb3qElKcYESTEm\nSMqQ79KS7hl6POgtuU9MTIS7uztcXV1hYmKCKVOmIDY2Vm0dOzs7BAYGwsTEpNHbEhERERG1NXpL\n7rOzs+Hs7KxsOzk5ITs7u9m3pbaNc5qTFGOCpBgTJGXo85qTbhl6POit5l4mk+lk27lz58LFperj\nExsbG/j6+iq/Wrz6i0rY1k372vlTKLh7D3AYCuCf/0CrPwLXRTvnykWt7S/vYhIqzEzQpf9Ajccj\nPZpL2XIAABImSURBVCUX5q7+ejv/5mjDzkvZjkeGxvGQnnICBSUVkHf31W///6aN/eXll8I+YIBG\n5//PFyVVXZ/yLiZV1Xob2Pvb1Pa186dQ2l4ODHbReDz4+8G2avvq9Qx4wRTAP8lUdTmErttpN3O1\nur8z+TkwNS7HA4BG45F8PQPl+fno/ff6+h4PbbTvFOcjGA4anX91u8Pf559SnA8rlYda20o8VP+c\nkVG1fVhYGGojE0KIWl9pZgkJCVi+fDni4uIAACtWrICRkVGtD8ZGRUXB0tJS+UCtptvu378fAQHa\nnPGAmur9+Azk3inHjeJyvT4op00pOUWwtzBFFytTRAzWrP6O4/APjkUVjsM/OBak6vdFq3A3Kwel\nWTnoOKCPvrujNQUJp2Hu5AAzJwc8sFqzyUBa41hwHKo0ZRyqJSUlYeTIkTWW660sJzAwEGlpaUhP\nT0d5eTm2bduGCRMm1Lqu9O+PxmxLRERERNRW6C25l8vlWLt2LUJCQuDt7Y2nnnoKXl5eiI6ORnR0\nNAAgJycHzs7OeO+99/Df//4XLi4uKCoqqnNbooawlpakGBMkxZggKUOvsSbdMvR40Os896GhoQgN\nDVVbFh4ervzZwcEBmZmZGm9LRERERNSW6e3OPZE+cP5qkmJMkBRjgqQMfV5z0i1Djwcm90RERERE\nrQSTe2pTWEtLUowJkmJMkJSh11iTbhl6PDC5JyIiIiJqJZjcU5vCWlqSYkyQFGOCpAy9xpp0y9Dj\ngck9EREREVErweSe2hTW0pIUY4KkGBMkZeg11qRbhh4PTO6JiIiIiFoJJvfUprCWlqQYEyTFmCAp\nQ6+xJt0y9Hhgck9ERERE1Eowuac2hbW0JMWYICnGBEkZeo016ZahxwOTeyIiIiKiVoLJPbUprKUl\nKcYESTEmSMrQa6xJtww9HpjcExERERG1EkzuqU1hLS1JMSZIijFBUoZeY026ZejxwOSeiIiIiKiV\nYHJPbQpraUmKMUFSjAmSMvQaa9ItQ48HJvdERERERK2EXJ8Hj4uLQ0REBBQKBcLCwhAZGVljnZde\negl79uxB+/bt8eWXX6Jv374AAFdXV1hbW8PY2BgmJiZITEzUdfepBUpPOcG7cqSGMUFS+o6Jvw4l\nIm/vESjKyvXWh+Zg3M4UdqMHofOwYH13pdGSr2cY/N1a0h1Djwe9JfcKhQLz58/Hvn370K1bNwQF\nBWHChAnw8vJSrrN792788ccfSEtLw/HjxzFnzhwkJCQAAGQyGQ4ePAhbW1t9nQIREZHW5e09grK8\nfFQUFum7K1olt7ZE3t4jLTK5J2pJ9JbcJyYmwt3dHa6urgCAKVOmIDY2Vi25//HHHzFjxgwAQP/+\n/XHr1i3k5uaiS5cuAAAhhM77TS0b79CSFGOCpPQdE4qyclQUFqE0K0ev/dA2cycHyK0t9d2NJjHk\nu7Ske4YeD3pL7rOzs+Hs7KxsOzk54fjx4w2uk52djS5dukAmk2HUqFEwNjZGeHg4nn/+eZ31nYiI\nSBc6Duij7y5oRUHCaX13gajN0NsDtTKZTKP16ro7Hx8fj+TkZOzZswcff/wxfvvtN212j1opzl9N\nUowJkmJMkJShz2tOumXo8aC3O/fdunVDZmamsp2ZmQknJ6d618nKykK3bt0AAF27dgUA2NnZYdKk\nSUhMTMSQIUNqHGfu3Llwcan6+MTGxga+vr4YPHgwgKo/EACwraP2tfOnUHD3HuAwFMA//4FWfwSu\ni3bOlYta21/exSRUmJmgS/+BGo9HekouzF399Xb+zdGGnZeyHY8MjeMhPeUECkoqIO/uq9/+/00b\n+8vLL4V9wACNzr+6DVRdn/IuJiE9z1zv76e22tfOn0Jpezkw2EXj8eDvxz/tM/k5KCvOR9XV8p9k\norocoKW1U4rz0S4f6O/koNH5x8fH4+r1DHjB1CD6n3YzV6v7O5OfA1PjcjwAaDQeydczUJ6fj95/\nr6/v8dBG+05xPoKheTwAQIe/zz+lOB9WKg+1tpV4qP45I6Nq+7CwMNRGJvRUuF5RUQEPDw/s378f\nXbt2RXBwMGJiYmo8ULt27Vrs3r0bCQkJiIiIQEJCAkpKSqBQKGBlZYXi4mKMGTMGb7zxBsaMGaN2\njP379yMgIEDXp0a1eD8+A7l3ynGjuBy+Di2z5lIqJacI9ham6GJliojBmtXfcRz+wbGownH4B8ei\nyu+LVuFuVg5Ks3JaVVmOuZMDzJwc8MDqmjPj1aY1jgPAsajGcajSlHGolpSUhJEjR9ZYrrc793K5\nHGvXrkVISAgUCgWee+45eHl5ITo6GgAQHh6OsWPHYvfu3XB3d4eFhQW++OIL4P+3d6+xUdV5GMef\naTtlabtYSmQa2rLlovYiYrGkWYNGRVAIVgONKWIgXBQxRiG+0JfGF4LxBaB1E2OM4g0wMRFial80\nbBqRnbrQcllgodQ2TiktwbZAO71MZ86+YGnaQeXSw/xPz3w/79rMOX2Y/NI+nPmf85fU1tampUuX\nSrryn4QVK1ZcU+wBAACAeGP0OfeLFi3SokWLRnxv/fr1I76uqKi45rjp06fr8GFuzsHNM/38ajgP\nM4FopmfiQveAOjr7lBgMqaXNHY/DTAmGFO7sU0b62Hx2v9Ofa47Ycvo8GC33bneo5ZJqA5c0EI6Y\njmK75MQEleRM0APZE0xHAQBXOd8TkhWxZEWk3gF3/P1IjkiDEUvne0KmowCuR7m/jWoDl9TZG1J3\nf9h0FNuljUtUbeDSmCv3XKFFNGYC0UzPRNiyZEUsKRJR76A7/n6kRiIKRyx5xuj+NE6+SovYc/o8\nUO5vo4FwRN39YZ3vGZsfQ/65ZKUmJ5oOAQCulpHiNR0BwBhDuY8Rtzz5Qbry9IexyvRaWjgPM4Fo\nzASiOX2NNWLL6fNgbBMrAAAAAPai3COucDUO0ZgJRGMmEM3JV2kRe06fB8o9AAAA4BKUe8SVoS3h\ngf9jJhCNmUC0+nO/mo4AB3H6PFDuAQAAAJeg3COusJYW0ZgJRGMmEM3pa6wRW06fB8o9AAAA4BKU\ne8QV1tIiGjOBaMwEojl9jTViy+nzQLkHAAAAXIJyj7jCWlpEYyYQjZlANKevsUZsOX0eKPcAAACA\nS1DuEVdYS4tozASiMROI5vQ11ogtp88D5R4AAABwiSTTAYBYYi0tojETzpFy5Khm/Ougsnv7lJHi\nNZbDJ0kHDttyLm8wpHHj/6LI34ulec5ep+s0F7oH1NHZp8RgSC1t3UazJHkydMymDCnBkMKdfcpI\nH7DlfIg9p6+5p9wDABwh7VCdBi91KfFyj7w9iabj2CKlP6zEv6Yq6VCdpCWm44wp53tCsiKWrIjU\nOxAxHcc2yRFpMGLpfE/IdBS4lNFyX1VVpY0bNyocDmvdunV64403rnnNq6++qh9++EEpKSn67LPP\nVFRUdMPHStK2/fati0pOTFBJzgQ9kD3BtnMitpqP/ZsrtRiBmXAOTyikpGCvxnX8Jm+SuVWj/+3t\nVN74ibacK2UwonBigjwhitzNCluWrIglRSLqHQwbzdLU2appE6fYcq7USEThiCWPZdlyPsRe/blf\nHX313li5D4fDeuWVV1RdXa2srCzNnTtXpaWlys/PH3pNZWWlzpw5o4aGBtXW1mrDhg3y+/03dOxV\n7Zft+9grbVyiagOXKPdjWNsvpyhyGIGZcKZgwbW/z2PlzC+HNXW6PT8/4ehxW84T70wu05Kkw22d\nykj5m9EMcI6G39op97/n559/1syZM5WbmytJKi8v1549e0YU9L1792rVqlWSpJKSEnV1damtrU1N\nTU3XPfaq8z12rmlLVmqyOz4qjld9PZdNR4DDMBOI1jvIWmiMxExguO6BftMR/pSxcn/27Fnl5OQM\nfZ2dna3a2trrvubs2bNqbW297rFXzcpMsyWvXTfSAMBwTrmJ1E7cRArYy0k3F9uFG4tvH2Pl3uPx\n3NDrrFGuSfNu/ceojr9qjqTe4gekh0pu6rhJh+uVffCQLRmcYiy/F5dO/FPednvWOY7l98FOt/o+\nSM54L0zPxPCbSPs6bIlhXIo06ptITS5n6fjtVyX0pRr7+cOxrOcK0++D6ZkYfnNx8n9OGsthp0Hd\n2o3FXb0h9QRD6thnbj+KhvONauwaZ9v5UntDyrTtbJLHGm17vkV+v19vvfWWqqqqJEmbN29WQkLC\niBtjX3rpJT3yyCMqLy+XJOXl5ammpkZNTU3XPVaS9uzZo7Q0e67cAwAAAE4yf/78a75n7Mp9cXGx\nGhoa1NzcrClTpmj37t3auXPniNeUlpaqoqJC5eXl8vv9Sk9Pl8/n06RJk657rCQ9/fTTsfrnAAAA\nAMYZK/dJSUmqqKjQE088oXA4rLVr1yo/P18fffSRJGn9+vVavHixKisrNXPmTKWmpurTTz/902MB\nAACAeGZsWQ4AAAAAe5nbJeQ2q6qqUl5enu666y69++67puPAsEAgoEcffVSFhYW699579f7775uO\nBAcIh8MqKirSU089ZToKHKCrq0tlZWXKz89XQUGB/H6/6UgwbPPmzSosLNSsWbP03HPPqb/f2Y9A\nhP3WrFkjn8+nWbNmDX2vo6NDCxYs0N13362FCxeqq6vLYMJrubLcX93kqqqqSidOnNDOnTt18qQ7\n7i7HrfF6vdq6dauOHz8uv9+vDz/8kJmAtm/froKCght+ehfc7bXXXtPixYt18uRJHT16lOWeca65\nuVkff/yx6urqdOzYMYXDYe3atct0LMTY6tWrhx7gctWWLVu0YMECnT59WvPnz9eWLVsMpft9riz3\nwzfI8nq9Q5tcIX5lZmbq/vvvlySlpaUpPz9fra2thlPBpJaWFlVWVmrdunWjfuQuxr6LFy/qxx9/\n1Jo1ayRdubfrjjvuMJwKJk2YMEFer1fBYFCDg4MKBoPKysoyHQsx9tBDD2nixIkjvjd8k9VVq1bp\nu+++MxHtD7my3P/R5leAdOVqTH19vUpKbv657HCPTZs26b333lNCgit/DeImNTU16c4779Tq1as1\nZ84cvfDCCwoGg6ZjwaCMjAy9/vrrmjp1qqZMmaL09HQ9/vjjpmPBAdrb2+Xz+SRJPp9P7e3thhON\n5Mq/anzEjj/S3d2tsrIybd++nT0Q4tj333+vyZMnq6ioiKv2kCQNDg6qrq5OL7/8surq6pSamuq4\nj9oRW42Njdq2bZuam5vV2tqq7u5uffXVV6ZjwWE8Ho/jeqcry31WVpYCgcDQ14FAQNnZ2QYTwQlC\noZCWLVum559/Xs8884zpODDowIED2rt3r6ZNm6bly5dr3759WrlypelYMCg7O1vZ2dmaO3euJKms\nrEx1dXWGU8GkgwcP6sEHH9SkSZOUlJSkpUuX6sCBA6ZjwQF8Pp/a2tokSefOndPkyZMNJxrJleV+\n+AZZAwMD2r17t0pLS03HgkGWZWnt2rUqKCjQxo0bTceBYe+8844CgYCampq0a9cuPfbYY/r8889N\nx4JBmZmZysnJ0enTpyVJ1dXVKiwsNJwKJuXl5cnv96u3t1eWZam6uloFBQWmY8EBSktLtWPHDknS\njh07HHfB0NgmVrcTm1wh2k8//aQvv/xS9913n4qKiiRdecTZk08+aTgZnMBpH6nCjA8++EArVqzQ\nwMCAZsyYMbRxIuLT7NmztXLlShUXFyshIUFz5szRiy++aDoWYmz58uWqqanRhQsXlJOTo7fffltv\nvvmmnn32WX3yySfKzc3VN998YzrmCGxiBQAAALiEK5flAAAAAPGIcg8AAAC4BOUeAAAAcAnKPQAA\nAOASlHsAAADAJSj3AAAAgEtQ7gEAAACXoNwDAAAALkG5BwCMyqlTpzRv3jx98cUXpqMAQNyj3AMA\nRuWee+6R1+vVwoULTUcBgLhHuQcAjEowGFR3d7d8Pp/pKAAQ9yj3AIBR2b9/vx5++GGdOXNG3377\nraZOnSrLskzHAoC4RLkHAIzKvn37dPnyZfX392vZsmU6deqUPB6P6VgAEJco9wCAUampqVF+fr42\nbNiglpYWjR8/3nQkAIhblHsAwC27ePGiwuGwNm3apNmzZ6uxsVFff/216VgAELco9wCAW1ZfX68l\nS5ZIkkpKSnTkyBHl5uaaDQUAccxjcdcTAAAA4ApcuQcAAABcgnIPAAAAuATlHgAAAHAJyj0AAADg\nEpR7AAAAwCUo9wAAAIBLUO4BAAAAl6DcAwAAAC5BuQcAAABc4n9dXs8u8rofIwAAAABJRU5ErkJg\ngg==\n", + "text": [ + "" + ] + } + ], + "prompt_number": 32 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The special case when $N = 1$ corresponds to the Bernoulli distribution. There is another connection between Bernoulli and Binomial random variables. If we have $X_1, X_2, ... , X_N$ Bernoulli random variables with the same $p$, then $Z = X_1 + X_2 + ... + X_N \\sim \\text{Binomial}(N, p )$.\n", + "\n", + "The expected value of a Bernoulli random variable is $p$. This can be seen by noting the more general Binomial random variable has expected value $Np$ and setting $N=1$." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "##### Example: Cheating among students\n", + "\n", + "We will use the binomial distribution to determine the frequency of students cheating during an exam. If we let $N$ be the total number of students who took the exam, and assuming each student is interviewed post-exam (answering without consequence), we will receive integer $X$ \"Yes I did cheat\" answers. We then find the posterior distribution of $p$, given $N$, some specified prior on $p$, and observed data $X$. \n", + "\n", + "This is a completely absurd model. No student, even with a free-pass against punishment, would admit to cheating. What we need is a better *algorithm* to ask students if they had cheated. Ideally the algorithm should encourage individuals to be honest while preserving privacy. The following proposed algorithm is a solution I greatly admire for its ingenuity and effectiveness:\n", + "\n", + "> In the interview process for each student, the student flips a coin, hidden from the interviewer. The student agrees to answer honestly if the coin comes up heads. Otherwise, if the coin comes up tails, the student (secretly) flips the coin again, and answers \"Yes, I did cheat\" if the coin flip lands heads, and \"No, I did not cheat\", if the coin flip lands tails. This way, the interviewer does not know if a \"Yes\" was the result of a guilty plea, or a Heads on a second coin toss. Thus privacy is preserved and the researchers receive honest answers. \n", + "\n", + "I call this the Privacy Algorithm. One could of course argue that the interviewers are still receiving false data since some *Yes*'s are not confessions but instead randomness, but an alternative perspective is that the researchers are discarding approximately half of their original dataset since half of the responses will be noise. But they have gained a systematic data generation process that can be modeled. Furthermore, they do not have to incorporate (perhaps somewhat naively) the possibility of deceitful answers. We can use PyMC to dig through this noisy model, and find a posterior distribution for the true frequency of liars. " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Suppose 100 students are being surveyed for cheating, and we wish to find $p$, the proportion of cheaters. There are a few ways we can model this in PyMC. I'll demonstrate the most explicit way, and later show a simplified version. Both versions arrive at the same inference. In our data-generation model, we sample $p$, the true proportion of cheaters, from a prior. Since we are quite ignorant about $p$, we will assign it a $\\text{Uniform}(0,1)$ prior." + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import pymc as pm\n", + "\n", + "N = 100\n", + "p = pm.Uniform(\"freq_cheating\", 0, 1)" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 33 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Again, thinking of our data-generation model, we assign Bernoulli random variables to the 100 students: 1 implies they cheated and 0 implies they did not. " + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "true_answers = pm.Bernoulli(\"truths\", p, size=N)" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 34 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "If we carry out the algorithm, the next step that occurs is the first coin-flip each student makes. This can be modeled again by sampling 100 Bernoulli random variables with $p=1/2$: denote a 1 as a *Heads* and 0 a *Tails*." + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "first_coin_flips = pm.Bernoulli(\"first_flips\", 0.5, size=N)\n", + "print first_coin_flips.value" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "[False True True True True False False True False False False False\n", + " False True True False True True False False True True False False\n", + " False False False True False False True False True True True True\n", + " True False True False True True True True True False False False\n", + " True True True True True True False True False False False True\n", + " True True False False False False True False True False False True\n", + " True False False False False True True False False True False True\n", + " False False True False False False True True True True True False\n", + " False False False False]\n" + ] + } + ], + "prompt_number": 35 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Although *not everyone* flips a second time, we can still model the possible realization of second coin-flips:" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "second_coin_flips = pm.Bernoulli(\"second_flips\", 0.5, size=N)" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 36 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Using these variables, we can return a possible realization of the *observed proportion* of \"Yes\" responses. We do this using a PyMC `deterministic` variable:" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "@pm.deterministic\n", + "def observed_proportion(t_a=true_answers,\n", + " fc=first_coin_flips,\n", + " sc=second_coin_flips):\n", + "\n", + " observed = fc * t_a + (1 - fc) * sc\n", + " return observed.sum() / float(N)" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 37 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The line `fc*t_a + (1-fc)*sc` contains the heart of the Privacy algorithm. Elements in this array are 1 *if and only if* i) the first toss is heads and the student cheated or ii) the first toss is tails, and the second is heads, and are 0 else. Finally, the last line sums this vector and divides by `float(N)`, produces a proportion. " + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "observed_proportion.value" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "pyout", + "prompt_number": 38, + "text": [ + "0.42999999999999999" + ] + } + ], + "prompt_number": 38 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Next we need a dataset. After performing our coin-flipped interviews the researchers received 35 \"Yes\" responses. To put this into a relative perspective, if there truly were no cheaters, we should expect to see on average 1/4 of all responses being a \"Yes\" (half chance of having first coin land Tails, and another half chance of having second coin land Heads), so about 25 responses in a cheat-free world. On the other hand, if *all students cheated*, we should expect to see approximately 3/4 of all responses be \"Yes\". \n", + "\n", + "The researchers observe a Binomial random variable, with `N = 100` and `p = observed_proportion` with `value = 35`: " + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "X = 35\n", + "\n", + "observations = pm.Binomial(\"obs\", N, observed_proportion, observed=True,\n", + " value=X)" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 39 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Below we add all the variables of interest to a `Model` container and run our black-box algorithm over the model. " + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "model = pm.Model([p, true_answers, first_coin_flips,\n", + " second_coin_flips, observed_proportion, observations])\n", + "\n", + "# To be explained in Chapter 3!\n", + "mcmc = pm.MCMC(model)\n", + "mcmc.sample(40000, 15000)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + " \r", + "[****************100%******************] 40000 of 40000 complete" + ] + }, + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "\n" + ] + } + ], + "prompt_number": 40 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "figsize(12.5, 3)\n", + "p_trace = mcmc.trace(\"freq_cheating\")[:]\n", + "plt.hist(p_trace, histtype=\"stepfilled\", normed=True, alpha=0.85, bins=30,\n", + " label=\"posterior distribution\", color=\"#348ABD\")\n", + "plt.vlines([.05, .35], [0, 0], [5, 5], alpha=0.3)\n", + "plt.xlim(0, 1)\n", + "plt.legend();" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "display_data", + "png": 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+ "text": [ + "" + ] + } + ], + "prompt_number": 42 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "With regards to the above plot, we are still pretty uncertain about what the true frequency of cheaters might be, but we have narrowed it down to a range between 0.05 to 0.35 (marked by the solid lines). This is pretty good, as *a priori* we had no idea how many students might have cheated (hence the uniform distribution for our prior). On the other hand, it is also pretty bad since there is a .3 length window the true value most likely lives in. Have we even gained anything, or are we still too uncertain about the true frequency? \n", + "\n", + "I would argue, yes, we have discovered something. It is implausible, according to our posterior, that there are *no cheaters*, i.e. the posterior assigns low probability to $p=0$. Since we started with a uniform prior, treating all values of $p$ as equally plausible, but the data ruled out $p=0$ as a possibility, we can be confident that there were cheaters. \n", + "\n", + "This kind of algorithm can be used to gather private information from users and be *reasonably* confident that the data, though noisy, is truthful. \n", + "\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Alternative PyMC Model\n", + "\n", + "Given a value for $p$ (which from our god-like position we know), we can find the probability the student will answer yes: \n", + "\n", + "\\begin{align}\n", + "P(\\text{\"Yes\"}) = & P( \\text{Heads on first coin} )P( \\text{cheater} ) + P( \\text{Tails on first coin} )P( \\text{Heads on second coin} ) \\\\\\\\\n", + "& = \\frac{1}{2}p + \\frac{1}{2}\\frac{1}{2}\\\\\\\\\n", + "& = \\frac{p}{2} + \\frac{1}{4}\n", + "\\end{align}\n", + "\n", + "Thus, knowing $p$ we know the probability a student will respond \"Yes\". In PyMC, we can create a deterministic function to evaluate the probability of responding \"Yes\", given $p$:" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "p = pm.Uniform(\"freq_cheating\", 0, 1)\n", + "\n", + "\n", + "@pm.deterministic\n", + "def p_skewed(p=p):\n", + " return 0.5 * p + 0.25" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 43 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "I could have typed `p_skewed = 0.5*p + 0.25` instead for a one-liner, as the elementary operations of addition and scalar multiplication will implicitly create a `deterministic` variable, but I wanted to make the deterministic boilerplate explicit for clarity's sake. \n", + "\n", + "If we know the probability of respondents saying \"Yes\", which is `p_skewed`, and we have $N=100$ students, the number of \"Yes\" responses is a binomial random variable with parameters `N` and `p_skewed`.\n", + "\n", + "This is where we include our observed 35 \"Yes\" responses. In the declaration of the `pm.Binomial`, we include `value = 35` and `observed = True`." + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "yes_responses = pm.Binomial(\"number_cheaters\", 100, p_skewed,\n", + " value=35, observed=True)" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 44 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Below we add all the variables of interest to a `Model` container and run our black-box algorithm over the model. " + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "model = pm.Model([yes_responses, p_skewed, p])\n", + "\n", + "# To Be Explained in Chapter 3!\n", + "mcmc = pm.MCMC(model)\n", + "mcmc.sample(25000, 2500)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + " \r", + "[****************100%******************] 25000 of 25000 complete" + ] + }, + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "\n" + ] + } + ], + "prompt_number": 45 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "figsize(12.5, 3)\n", + "p_trace = mcmc.trace(\"freq_cheating\")[:]\n", + "plt.hist(p_trace, histtype=\"stepfilled\", normed=True, alpha=0.85, bins=30,\n", + " label=\"posterior distribution\", color=\"#348ABD\")\n", + "plt.vlines([.05, .35], [0, 0], [5, 5], alpha=0.2)\n", + "plt.xlim(0, 1)\n", + "plt.legend();" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "display_data", + "png": 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+ "text": [ + "" + ] + } + ], + "prompt_number": 47 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### More PyMC Tricks\n", + "\n", + "#### Protip: *Lighter* deterministic variables with `Lambda` class\n", + "\n", + "Sometimes writing a deterministic function using the `@pm.deterministic` decorator can seem like a chore, especially for a small function. I have already mentioned that elementary math operations *can* produce deterministic variables implicitly, but what about operations like indexing or slicing? Built-in `Lambda` functions can handle this with the elegance and simplicity required. For example, \n", + "\n", + " beta = pm.Normal(\"coefficients\", 0, size=(N, 1))\n", + " x = np.random.randn((N, 1))\n", + " linear_combination = pm.Lambda(lambda x=x, beta=beta: np.dot(x.T, beta))\n", + "\n", + "\n", + "#### Protip: Arrays of PyMC variables\n", + "There is no reason why we cannot store multiple heterogeneous PyMC variables in a Numpy array. Just remember to set the `dtype` of the array to `object` upon initialization. For example:\n", + "\n", + "\n" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "N = 10\n", + "x = np.empty(N, dtype=object)\n", + "for i in range(0, N):\n", + " x[i] = pm.Exponential('x_%i' % i, (i + 1) ** 2)" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 48 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The remainder of this chapter examines some practical examples of PyMC and PyMC modeling:" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "##### Example: Challenger Space Shuttle Disaster \n", + "\n", + "On January 28, 1986, the twenty-fifth flight of the U.S. space shuttle program ended in disaster when one of the rocket boosters of the Shuttle Challenger exploded shortly after lift-off, killing all seven crew members. The presidential commission on the accident concluded that it was caused by the failure of an O-ring in a field joint on the rocket booster, and that this failure was due to a faulty design that made the O-ring unacceptably sensitive to a number of factors including outside temperature. Of the previous 24 flights, data were available on failures of O-rings on 23, (one was lost at sea), and these data were discussed on the evening preceding the Challenger launch, but unfortunately only the data corresponding to the 7 flights on which there was a damage incident were considered important and these were thought to show no obvious trend. The data are shown below (see [1]):\n", + "\n", + "\n", + "\n" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "figsize(12.5, 3.5)\n", + "np.set_printoptions(precision=3, suppress=True)\n", + "challenger_data = np.genfromtxt(\"data/challenger_data.csv\", skip_header=1,\n", + " usecols=[1, 2], missing_values=\"NA\",\n", + " delimiter=\",\")\n", + "# drop the NA values\n", + "challenger_data = challenger_data[~np.isnan(challenger_data[:, 1])]\n", + "\n", + "# plot it, as a function of tempature (the first column)\n", + "print \"Temp (F), O-Ring failure?\"\n", + "print challenger_data\n", + "\n", + "plt.scatter(challenger_data[:, 0], challenger_data[:, 1], s=75, color=\"k\",\n", + " alpha=0.5)\n", + "plt.yticks([0, 1])\n", + "plt.ylabel(\"Damage Incident?\")\n", + "plt.xlabel(\"Outside temperature (Fahrenheit)\")\n", + "plt.title(\"Defects of the Space Shuttle O-Rings vs temperature\")" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Temp (F), O-Ring failure?\n", + "[[ 66. 0.]\n", + " [ 70. 1.]\n", + " [ 69. 0.]\n", + " [ 68. 0.]\n", + " [ 67. 0.]\n", + " [ 72. 0.]\n", + " [ 73. 0.]\n", + " [ 70. 0.]\n", + " [ 57. 1.]\n", + " [ 63. 1.]\n", + " [ 70. 1.]\n", + " [ 78. 0.]\n", + " [ 67. 0.]\n", + " [ 53. 1.]\n", + " [ 67. 0.]\n", + " [ 75. 0.]\n", + " [ 70. 0.]\n", + " [ 81. 0.]\n", + " [ 76. 0.]\n", + " [ 79. 0.]\n", + " [ 75. 1.]\n", + " [ 76. 0.]\n", + " [ 58. 1.]]\n" + ] + }, + { + "metadata": {}, + "output_type": "pyout", + "prompt_number": 49, + "text": [ + "" + ] + }, + { + "metadata": {}, + "output_type": "display_data", + "png": 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AUaNG6e9z7/aTJMngZDuFQlEuZ9V5YpwQAuPGjcOsWbPKzbv7w93dyp7bJ0+eNCgQy5R9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\nNSem76FIJEJDQwN8fHwwPT0NnU4HLy8vAEBwcDA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+ "text": [ + "" + ] + } + ], + "prompt_number": 49 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "It looks clear that *the probability* of damage incidents occurring increases as the outside temperature decreases. We are interested in modeling the probability here because it does not look like there is a strict cutoff point between temperature and a damage incident occurring. The best we can do is ask \"At temperature $t$, what is the probability of a damage incident?\". The goal of this example is to answer that question.\n", + "\n", + "We need a function of temperature, call it $p(t)$, that is bounded between 0 and 1 (so as to model a probability) and changes from 1 to 0 as we increase temperature. There are actually many such functions, but the most popular choice is the *logistic function.*\n", + "\n", + "$$p(t) = \\frac{1}{ 1 + e^{ \\;\\beta t } } $$\n", + "\n", + "In this model, $\\beta$ is the variable we are uncertain about. Below is the function plotted for $\\beta = 1, 3, -5$." + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "figsize(12, 3)\n", + "\n", + "\n", + "def logistic(x, beta):\n", + " return 1.0 / (1.0 + np.exp(beta * x))\n", + "\n", + "x = np.linspace(-4, 4, 100)\n", + "plt.plot(x, logistic(x, 1), label=r\"$\\beta = 1$\")\n", + "plt.plot(x, logistic(x, 3), label=r\"$\\beta = 3$\")\n", + "plt.plot(x, logistic(x, -5), label=r\"$\\beta = -5$\")\n", + "plt.legend();" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "display_data", + "png": 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P9afNZCG7qIFv8uvYVdbMusIG1hU2EOCh5tLEQKYmBzM06MxF4UDIpy40iHGr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\nDSy4t2TIC+BEzKdi0FO08idMf/OfUMxGGlavZ/u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+ "text": [ + "" + ] + } + ], + "prompt_number": 54 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "But something is missing. In the plot of the logistic function, the probability changes only near zero, but in our data above the probability changes around 65 to 70. We need to add a *bias* term to our logistic function:\n", + "\n", + "$$p(t) = \\frac{1}{ 1 + e^{ \\;\\beta t + \\alpha } } $$\n", + "\n", + "Some plots are below, with differing $\\alpha$." + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "def logistic(x, beta, alpha=0):\n", + " return 1.0 / (1.0 + np.exp(np.dot(beta, x) + alpha))\n", + "\n", + "x = np.linspace(-4, 4, 100)\n", + "\n", + "plt.plot(x, logistic(x, 1), label=r\"$\\beta = 1$\", ls=\"--\", lw=1)\n", + "plt.plot(x, logistic(x, 3), label=r\"$\\beta = 3$\", ls=\"--\", lw=1)\n", + "plt.plot(x, logistic(x, -5), label=r\"$\\beta = -5$\", ls=\"--\", lw=1)\n", + "\n", + "plt.plot(x, logistic(x, 1, 1), label=r\"$\\beta = 1, \\alpha = 1$\",\n", + " color=\"#348ABD\")\n", + "plt.plot(x, logistic(x, 3, -2), label=r\"$\\beta = 3, \\alpha = -2$\",\n", + " color=\"#A60628\")\n", + "plt.plot(x, logistic(x, -5, 7), label=r\"$\\beta = -5, \\alpha = 7$\",\n", + " color=\"#7A68A6\")\n", + "\n", + "plt.legend(loc=\"lower left\");" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "display_data", + "png": 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vTWfk+FhiBga6KVrBlUxNVtZ/nwnAhVcMFTPCCcI5nLUcYunSpaxdu5YPPvgA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\nXWniubW5PNLFZFhoX3WTjXe2FVHZZG3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HxYfqOX9WMpkXik4eQfCWM54sY9KkSRQUFFBS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+ "text": [ + "" + ] + } + ], + "prompt_number": 55 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Adding a constant term $\\alpha$ amounts to shifting the curve left or right (hence why it is called a *bias*).\n", + "\n", + "Let's start modeling this in PyMC. The $\\beta, \\alpha$ parameters have no reason to be positive, bounded or relatively large, so they are best modeled by a *Normal random variable*, introduced next." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Normal distributions\n", + "\n", + "A Normal random variable, denoted $X \\sim N(\\mu, 1/\\tau)$, has a distribution with two parameters: the mean, $\\mu$, and the *precision*, $\\tau$. Those familiar with the Normal distribution already have probably seen $\\sigma^2$ instead of $\\tau^{-1}$. They are in fact reciprocals of each other. The change was motivated by simpler mathematical analysis and is an artifact of older Bayesian methods. Just remember: the smaller $\\tau$, the larger the spread of the distribution (i.e. we are more uncertain); the larger $\\tau$, the tighter the distribution (i.e. we are more certain). Regardless, $\\tau$ is always positive. \n", + "\n", + "The probability density function of a $N( \\mu, 1/\\tau)$ random variable is:\n", + "\n", + "$$ f(x | \\mu, \\tau) = \\sqrt{\\frac{\\tau}{2\\pi}} \\exp\\left( -\\frac{\\tau}{2} (x-\\mu)^2 \\right) $$\n", + "\n", + "We plot some different density functions below. " + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import scipy.stats as stats\n", + "\n", + "nor = stats.norm\n", + "x = np.linspace(-8, 7, 150)\n", + "mu = (-2, 0, 3)\n", + "tau = (.7, 1, 2.8)\n", + "colors = [\"#348ABD\", \"#A60628\", \"#7A68A6\"]\n", + "parameters = zip(mu, tau, colors)\n", + "\n", + "for _mu, _tau, _color in parameters:\n", + " plt.plot(x, nor.pdf(x, _mu, scale=1. / _tau),\n", + " label=\"$\\mu = %d,\\;\\\\tau = %.1f$\" % (_mu, _tau), color=_color)\n", + " plt.fill_between(x, nor.pdf(x, _mu, scale=1. / _tau), color=_color,\n", + " alpha=.33)\n", + "\n", + "plt.legend(loc=\"upper right\")\n", + "plt.xlabel(\"$x$\")\n", + "plt.ylabel(\"density function at $x$\")\n", + "plt.title(\"Probability distribution of three different Normal random \\\n", + "variables\");" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "display_data", + "png": 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MV0MfAgCcO7cBJ+EAAC1amaJLT1sAwMN76VqLjzRd0dHR8Pf3BwC0atUKzs7O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\nnr3//jx7H/8VxrVz2Tl6NqBw0SV5klifwoQpGTQd6KS5qZs3f7eRBXd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+ "text": [ + "" + ] + } + ], + "prompt_number": 57 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "A Normal random variable can be take on any real number, but the variable is very likely to be relatively close to $\\mu$. In fact, the expected value of a Normal is equal to its $\\mu$ parameter:\n", + "\n", + "$$ E[ X | \\mu, \\tau] = \\mu$$\n", + "\n", + "and its variance is equal to the inverse of $\\tau$:\n", + "\n", + "$$Var( X | \\mu, \\tau ) = \\frac{1}{\\tau}$$\n", + "\n", + "\n", + "\n", + "Below we continue our modeling of the Challenger space craft:" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import pymc as pm\n", + "\n", + "temperature = challenger_data[:, 0]\n", + "D = challenger_data[:, 1] # defect or not?\n", + "\n", + "# notice the`value` here. We explain why below.\n", + "beta = pm.Normal(\"beta\", 0, 0.001, value=0)\n", + "alpha = pm.Normal(\"alpha\", 0, 0.001, value=0)\n", + "\n", + "\n", + "@pm.deterministic\n", + "def p(t=temperature, alpha=alpha, beta=beta):\n", + " return 1.0 / (1. + np.exp(beta * t + alpha))" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 58 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We have our probabilities, but how do we connect them to our observed data? A *Bernoulli* random variable with parameter $p$, denoted $\\text{Ber}(p)$, is a random variable that takes value 1 with probability $p$, and 0 else. Thus, our model can look like:\n", + "\n", + "$$ \\text{Defect Incident, $D_i$} \\sim \\text{Ber}( \\;p(t_i)\\; ), \\;\\; i=1..N$$\n", + "\n", + "where $p(t)$ is our logistic function and $t_i$ are the temperatures we have observations about. Notice in the above code we had to set the values of `beta` and `alpha` to 0. The reason for this is that if `beta` and `alpha` are very large, they make `p` equal to 1 or 0. Unfortunately, `pm.Bernoulli` does not like probabilities of exactly 0 or 1, though they are mathematically well-defined probabilities. So by setting the coefficient values to `0`, we set the variable `p` to be a reasonable starting value. This has no effect on our results, nor does it mean we are including any additional information in our prior. It is simply a computational caveat in PyMC. " + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "p.value" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "pyout", + "prompt_number": 59, + "text": [ + "array([ 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5,\n", + " 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5,\n", + " 0.5])" + ] + } + ], + "prompt_number": 59 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# connect the probabilities in `p` with our observations through a\n", + "# Bernoulli random variable.\n", + "observed = pm.Bernoulli(\"bernoulli_obs\", p, value=D, observed=True)\n", + "\n", + "model = pm.Model([observed, beta, alpha])\n", + "\n", + "# Mysterious code to be explained in Chapter 3\n", + "map_ = pm.MAP(model)\n", + "map_.fit()\n", + "mcmc = pm.MCMC(model)\n", + "mcmc.sample(120000, 100000, 2)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + " \r", + "[****************100%******************] 120000 of 120000 complete" + ] + }, + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "\n" + ] + } + ], + "prompt_number": 60 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We have trained our model on the observed data, now we can sample values from the posterior. Let's look at the posterior distributions for $\\alpha$ and $\\beta$:" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "alpha_samples = mcmc.trace('alpha')[:, None] # best to make them 1d\n", + "beta_samples = mcmc.trace('beta')[:, None]\n", + "\n", + "figsize(12.5, 6)\n", + "\n", + "# histogram of the samples:\n", + "plt.subplot(211)\n", + "plt.title(r\"Posterior distributions of the variables $\\alpha, \\beta$\")\n", + "plt.hist(beta_samples, histtype='stepfilled', bins=35, alpha=0.85,\n", + " label=r\"posterior of $\\beta$\", color=\"#7A68A6\", normed=True)\n", + "plt.legend()\n", + "\n", + "plt.subplot(212)\n", + "plt.hist(alpha_samples, histtype='stepfilled', bins=35, alpha=0.85,\n", + " label=r\"posterior of $\\alpha$\", color=\"#A60628\", normed=True)\n", + "plt.legend();" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "display_data", + "png": 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h4SgoKMDChQsRFBSk935JSQm8vb11bS8vLxQXF7NA70IcVyaO0sdJ195swDdf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\ne3p6QqPR6NoajQZeXl7tLlNcXAxPT08AvzwNq1+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+ "text": [ + "" + ] + } + ], + "prompt_number": 61 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "All samples of $\\beta$ are greater than 0. If instead the posterior was centered around 0, we may suspect that $\\beta = 0$, implying that temperature has no effect on the probability of defect. \n", + "\n", + "Similarly, all $\\alpha$ posterior values are negative and far away from 0, implying that it is correct to believe that $\\alpha$ is significantly less than 0. \n", + "\n", + "Regarding the spread of the data, we are very uncertain about what the true parameters might be (though considering the low sample size and the large overlap of defects-to-nondefects this behaviour is perhaps expected). \n", + "\n", + "Next, let's look at the *expected probability* for a specific value of the temperature. That is, we average over all samples from the posterior to get a likely value for $p(t_i)$." + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "t = np.linspace(temperature.min() - 5, temperature.max() + 5, 50)[:, None]\n", + "p_t = logistic(t.T, beta_samples, alpha_samples)\n", + "\n", + "mean_prob_t = p_t.mean(axis=0)" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 62 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "figsize(12.5, 4)\n", + "\n", + "plt.plot(t, mean_prob_t, lw=3, label=\"average posterior \\nprobability \\\n", + "of defect\")\n", + "plt.plot(t, p_t[0, :], ls=\"--\", label=\"realization from posterior\")\n", + "plt.plot(t, p_t[-2, :], ls=\"--\", label=\"realization from posterior\")\n", + "plt.scatter(temperature, D, color=\"k\", s=50, alpha=0.5)\n", + "plt.title(\"Posterior expected value of probability of defect; \\\n", + "plus realizations\")\n", + "plt.legend(loc=\"lower left\")\n", + "plt.ylim(-0.1, 1.1)\n", + "plt.xlim(t.min(), t.max())\n", + "plt.ylabel(\"probability\")\n", + "plt.xlabel(\"temperature\");" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "display_data", + "png": 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IIW2MatgJIYQQQgjpoARL2OfOnQsvLy9ER0c32eb5559HWFgYevfujTNnzgjV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\nDKx0LFRmZ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+ "text": [ + "" + ] + } + ], + "prompt_number": 64 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Above we also plotted two possible realizations of what the actual underlying system might be. Both are equally likely as any other draw. The blue line is what occurs when we average all the 20000 possible dotted lines together.\n", + "\n", + "\n", + "An interesting question to ask is for what temperatures are we most uncertain about the defect-probability? Below we plot the expected value line **and** the associated 95% intervals for each temperature. " + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from scipy.stats.mstats import mquantiles\n", + "\n", + "# vectorized bottom and top 2.5% quantiles for \"confidence interval\"\n", + "qs = mquantiles(p_t, [0.025, 0.975], axis=0)\n", + "plt.fill_between(t[:, 0], *qs, alpha=0.7,\n", + " color=\"#7A68A6\")\n", + "\n", + "plt.plot(t[:, 0], qs[0], label=\"95% CI\", color=\"#7A68A6\", alpha=0.7)\n", + "\n", + "plt.plot(t, mean_prob_t, lw=1, ls=\"--\", color=\"k\",\n", + " label=\"average posterior \\nprobability of defect\")\n", + "\n", + "plt.xlim(t.min(), t.max())\n", + "plt.ylim(-0.02, 1.02)\n", + "plt.legend(loc=\"lower left\")\n", + "plt.scatter(temperature, D, color=\"k\", s=50, alpha=0.5)\n", + "plt.xlabel(\"temp, $t$\")\n", + "\n", + "plt.ylabel(\"probability estimate\")\n", + "plt.title(\"Posterior probability estimates given temp. $t$\");" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "display_data", + "png": 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5DbEJdJdfQgghfUclMYR0w+6woaziDIrOHkFURCwmXDHb1yERP3fxtJozJB5D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+ "text": [ + "" + ] + } + ], + "prompt_number": 66 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The *95% credible interval*, or 95% CI, painted in purple, represents the interval, for each temperature, that contains 95% of the distribution. For example, at 65 degrees, we can be 95% sure that the probability of defect lies between 0.25 and 0.75.\n", + "\n", + "More generally, we can see that as the temperature nears 60 degrees, the CI's spread out over [0,1] quickly. As we pass 70 degrees, the CI's tighten again. This can give us insight about how to proceed next: we should probably test more O-rings around 60-65 temperature to get a better estimate of probabilities in that range. Similarly, when reporting to scientists your estimates, you should be very cautious about simply telling them the expected probability, as we can see this does not reflect how *wide* the posterior distribution is." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### What about the day of the Challenger disaster?\n", + "\n", + "On the day of the Challenger disaster, the outside temperature was 31 degrees Fahrenheit. What is the posterior distribution of a defect occurring, given this temperature? The distribution is plotted below. It looks almost guaranteed that the Challenger was going to be subject to defective O-rings." + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "figsize(12.5, 2.5)\n", + "\n", + "prob_31 = logistic(31, beta_samples, alpha_samples)\n", + "\n", + "plt.xlim(0.995, 1)\n", + "plt.hist(prob_31, bins=1000, normed=True, histtype='stepfilled')\n", + "plt.title(\"Posterior distribution of probability of defect, given $t = 31$\")\n", + "plt.xlabel(\"probability of defect occurring in O-ring\");" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "display_data", + "png": 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JWbNmNRlb7eVNxShlnDWio6NRXl6OGTNmAACmTJmCN954A7t27aq3r7Zt2zY6/vqOQWJi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\nLS0NpaWlOj/cVSqVmDdvHhYuXIi7d+8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+ "text": [ + "" + ] + } + ], + "prompt_number": 68 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Is our model appropriate?\n", + "\n", + "The skeptical reader will say \"You deliberately chose the logistic function for $p(t)$ and the specific priors. Perhaps other functions or priors will give different results. How do I know I have chosen a good model?\" This is absolutely true. To consider an extreme situation, what if I had chosen the function $p(t) = 1,\\; \\forall t$, which guarantees a defect always occurring: I would have again predicted disaster on January 28th. Yet this is clearly a poorly chosen model. On the other hand, if I did choose the logistic function for $p(t)$, but specified all my priors to be very tight around 0, likely we would have very different posterior distributions. How do we know our model is an expression of the data? This encourages us to measure the model's **goodness of fit**.\n", + "\n", + "We can think: *how can we test whether our model is a bad fit?* An idea is to compare observed data (which if we recall is a *fixed* stochastic variable) with an artificial dataset which we can simulate. The rationale is that if the simulated dataset does not appear similar, statistically, to the observed dataset, then likely our model is not accurately represented the observed data. \n", + "\n", + "Previously in this Chapter, we simulated artificial datasets for the SMS example. To do this, we sampled values from the priors. We saw how varied the resulting datasets looked like, and rarely did they mimic our observed dataset. In the current example, we should sample from the *posterior* distributions to create *very plausible datasets*. Luckily, our Bayesian framework makes this very easy. We only need to create a new `Stochastic` variable, that is exactly the same as our variable that stored the observations, but minus the observations themselves. If you recall, our `Stochastic` variable that stored our observed data was:\n", + "\n", + " observed = pm.Bernoulli( \"bernoulli_obs\", p, value=D, observed=True)\n", + "\n", + "Hence we create:\n", + " \n", + " simulated_data = pm.Bernoulli(\"simulation_data\", p)\n", + "\n", + "Let's simulate 10 000:" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "simulated = pm.Bernoulli(\"bernoulli_sim\", p)\n", + "N = 10000\n", + "\n", + "mcmc = pm.MCMC([simulated, alpha, beta, observed])\n", + "mcmc.sample(N)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + " \r", + "[****************100%******************] 10000 of 10000 complete" + ] + }, + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "\n" + ] + } + ], + "prompt_number": 69 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "figsize(12.5, 5)\n", + "\n", + "simulations = mcmc.trace(\"bernoulli_sim\")[:]\n", + "print simulations.shape\n", + "\n", + "plt.title(\"Simulated dataset using posterior parameters\")\n", + "figsize(12.5, 6)\n", + "for i in range(4):\n", + " ax = plt.subplot(4, 1, i + 1)\n", + " plt.scatter(temperature, simulations[1000 * i, :], color=\"k\",\n", + " s=50, alpha=0.6)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "(10000, 23)\n" + ] + }, + { + "metadata": {}, + "output_type": "display_data", + "png": 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LHMdh7NixiIiIwM6dOwGYv6gRsRxTeQDAli1bEBYWhkWLFtHXYW3g/v37cHd3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+ "text": [ + "" + ] + } + ], + "prompt_number": 71 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Note that the above plots are different (if you can think of a cleaner way to present this, please send a pull request and answer [here](http://stats.stackexchange.com/questions/53078/how-to-visualize-bayesian-goodness-of-fit-for-logistic-regression)!).\n", + "\n", + "We wish to assess how good our model is. \"Good\" is a subjective term of course, so results must be relative to other models. \n", + "\n", + "We will be doing this graphically as well, which may seem like an even less objective method. The alternative is to use *Bayesian p-values*. These are still subjective, as the proper cutoff between good and bad is arbitrary. Gelman emphasises that the graphical tests are more illuminating [7] than p-value tests. We agree.\n", + "\n", + "The following graphical test is a novel data-viz approach to logistic regression. The plots are called *separation plots*[8]. For a suite of models we wish to compare, each model is plotted on an individual separation plot. I leave most of the technical details about separation plots to the very accessible [original paper](http://mdwardlab.com/sites/default/files/GreenhillWardSacks.pdf), but I'll summarize their use here.\n", + "\n", + "For each model, we calculate the proportion of times the posterior simulation proposed a value of 1 for a particular temperature, i.e. compute $P( \\;\\text{Defect} = 1 | t, \\alpha, \\beta )$ by averaging. This gives us the posterior probability of a defect at each data point in our dataset. For example, for the model we used above:" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "posterior_probability = simulations.mean(axis=0)\n", + "print \"posterior prob of defect | realized defect \"\n", + "for i in range(len(D)):\n", + " print \"%.2f | %d\" % (posterior_probability[i], D[i])" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "posterior prob of defect | realized defect \n", + "0.47 | 0\n", + "0.20 | 1\n", + "0.25 | 0\n", + "0.32 | 0\n", + "0.39 | 0\n", + "0.11 | 0\n", + "0.08 | 0\n", + "0.19 | 0\n", + "0.94 | 1\n", + "0.71 | 1\n", + "0.20 | 1\n", + "0.02 | 0\n", + "0.39 | 0\n", + "0.98 | 1\n", + "0.40 | 0\n", + "0.05 | 0\n", + "0.20 | 0\n", + "0.01 | 0\n", + "0.03 | 0\n", + "0.01 | 0\n", + "0.05 | 1\n", + "0.04 | 0\n", + "0.92 | 1\n" + ] + } + ], + "prompt_number": 72 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Next we sort each column by the posterior probabilities:" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "ix = np.argsort(posterior_probability)\n", + "print \"probb | defect \"\n", + "for i in range(len(D)):\n", + " print \"%.2f | %d\" % (posterior_probability[ix[i]], D[ix[i]])" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "probb | defect \n", + "0.01 | 0\n", + "0.01 | 0\n", + "0.02 | 0\n", + "0.03 | 0\n", + "0.04 | 0\n", + "0.05 | 0\n", + "0.05 | 1\n", + "0.08 | 0\n", + "0.11 | 0\n", + "0.19 | 0\n", + "0.20 | 0\n", + "0.20 | 1\n", + "0.20 | 1\n", + "0.25 | 0\n", + "0.32 | 0\n", + "0.39 | 0\n", + "0.39 | 0\n", + "0.40 | 0\n", + "0.47 | 0\n", + "0.71 | 1\n", + "0.92 | 1\n", + "0.94 | 1\n", + "0.98 | 1\n" + ] + } + ], + "prompt_number": 73 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We can present the above data better in a figure: I've wrapped this up into a `separation_plot` function." + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from separation_plot import separation_plot\n", + "\n", + "\n", + "figsize(11., 1.5)\n", + "separation_plot(posterior_probability, D)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "display_data", + "png": 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+ "text": [ + "" + ] + } + ], + "prompt_number": 74 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The snaking-line is the sorted probabilities, blue bars denote defects, and empty space (or grey bars for the optimistic readers) denote non-defects. As the probability rises, we see more and more defects occur. On the right hand side, the plot suggests that as the posterior probability is large (line close to 1), then more defects are realized. This is good behaviour. Ideally, all the blue bars *should* be close to the right-hand side, and deviations from this reflect missed predictions. \n", + "\n", + "The black vertical line is the expected number of defects we should observe, given this model. This allows the user to see how the total number of events predicted by the model compares to the actual number of events in the data.\n", + "\n", + "It is much more informative to compare this to separation plots for other models. Below we compare our model (top) versus three others:\n", + "\n", + "1. the perfect model, which predicts the posterior probability to be equal to 1 if a defect did occur.\n", + "2. a completely random model, which predicts random probabilities regardless of temperature.\n", + "3. a constant model: where $P(D = 1 \\; | \\; t) = c, \\;\\; \\forall t$. The best choice for $c$ is the observed frequency of defects, in this case 7/23. \n" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "figsize(11., 1.25)\n", + "\n", + "# Our temperature-dependent model\n", + "separation_plot(posterior_probability, D)\n", + "plt.title(\"Temperature-dependent model\")\n", + "\n", + "# Perfect model\n", + "# i.e. the probability of defect is equal to if a defect occurred or not.\n", + "p = D\n", + "separation_plot(p, D)\n", + "plt.title(\"Perfect model\")\n", + "\n", + "# random predictions\n", + "p = np.random.rand(23)\n", + "separation_plot(p, D)\n", + "plt.title(\"Random model\")\n", + "\n", + "# constant model\n", + "constant_prob = 7. / 23 * np.ones(23)\n", + "separation_plot(constant_prob, D)\n", + "plt.title(\"Constant-prediction model\")" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "pyout", + "prompt_number": 75, + "text": [ + "" + ] + }, + { + "metadata": {}, + "output_type": "display_data", + "png": 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+ "text": [ + "" + ] + } + ], + "prompt_number": 75 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "In the random model, we can see that as the probability increases there is no clustering of defects to the right-hand side. Similarly for the constant model.\n", + "\n", + "The perfect model, the probability line is not well shown, as it is stuck to the bottom and top of the figure. Of course the perfect model is only for demonstration, and we cannot infer any scientific inference from it." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "##### Exercises\n", + "\n", + "1\\. Try putting in extreme values for our observations in the cheating example. What happens if we observe 25 affirmative responses? 10? 50? " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "2\\. Try plotting $\\alpha$ samples versus $\\beta$ samples. Why might the resulting plot look like this?" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# type your code here.\n", + "figsize(12.5, 4)\n", + "\n", + "plt.scatter(alpha_samples, beta_samples, alpha=0.1)\n", + "plt.title(\"Why does the plot look like this?\")\n", + "plt.xlabel(r\"$\\alpha$\")\n", + "plt.ylabel(r\"$\\beta$\")" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "pyout", + "prompt_number": 76, + "text": [ + "" + ] + }, + { + "metadata": {}, + "output_type": "display_data", + "png": 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SSnkUFUFVlSGTkbrv0ahHNmvw+SAY9MhkLF1dBmN8hMMetbWWSy+Vkf5duyTQ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+ "text": [ + "" + ] + } + ], + "prompt_number": 76 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### References\n", + "\n", + "- [1] Dalal, Fowlkes and Hoadley (1989),JASA, 84, 945-957.\n", + "- [2] German Rodriguez. Datasets. In WWS509. Retrieved 30/01/2013, from .\n", + "- [3] McLeish, Don, and Cyntha Struthers. STATISTICS 450/850 Estimation and Hypothesis Testing. Winter 2012. Waterloo, Ontario: 2012. Print.\n", + "- [4] Fonnesbeck, Christopher. \"Building Models.\" PyMC-Devs. N.p., n.d. Web. 26 Feb 2013. .\n", + "- [5] Cronin, Beau. \"Why Probabilistic Programming Matters.\" 24 Mar 2013. Google, Online Posting to Google . Web. 24 Mar. 2013. .\n", + "- [6] S.P. Brooks, E.A. Catchpole, and B.J.T. Morgan. Bayesian animal survival estimation. Statistical Science, 15: 357\u2013376, 2000\n", + "- [7] Gelman, Andrew. \"Philosophy and the practice of Bayesian statistics.\" British Journal of Mathematical and Statistical Psychology. (2012): n. page. Web. 2 Apr. 2013.\n", + "- [8] Greenhill, Brian, Michael D. Ward, and Audrey Sacks. \"The Separation Plot: A New Visual Method for Evaluating the Fit of Binary Models.\" American Journal of Political Science. 55.No.4 (2011): n. page. Web. 2 Apr. 2013." + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from IPython.core.display import HTML\n", + "\n", + "\n", + "def css_styling():\n", + " styles = open(\"../styles/custom.css\", \"r\").read()\n", + " return HTML(styles)\n", + "css_styling()" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "html": [ + "\n", + "\n" + ], + "metadata": {}, + "output_type": "pyout", + "prompt_number": 1, + "text": [ + "" + ] + } + ], + "prompt_number": 1 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 105 + } + ], + "metadata": {} + } + ] +} diff --git a/Chapter2_MorePyMC/README.md b/Chapter2_MorePyMC/README.md index 37910b9f..d7aa095c 100644 --- a/Chapter2_MorePyMC/README.md +++ b/Chapter2_MorePyMC/README.md @@ -1,4 +1,4 @@ -Chapter 2: A little more on PyMC -================================= - -### [Read it online here](http://nbviewer.ipython.org/urls/raw.github.com/CamDavidsonPilon/Probabilistic-Programming-and-Bayesian-Methods-for-Hackers/master/Chapter2_MorePyMC/MorePyMC.ipynb) +Chapter 2: A little more on PyMC +================================= + +### [Read it online here](http://nbviewer.ipython.org/urls/raw.github.com/CamDavidsonPilon/Probabilistic-Programming-and-Bayesian-Methods-for-Hackers/master/Chapter2_MorePyMC/MorePyMC.ipynb) diff --git a/Chapter2_MorePyMC/daft_plot.py b/Chapter2_MorePyMC/daft_plot.py index 5f68e901..1eab338e 100644 --- a/Chapter2_MorePyMC/daft_plot.py +++ b/Chapter2_MorePyMC/daft_plot.py @@ -1,31 +1,31 @@ -#daft drawing for SMS example -import matplotlib.pyplot as plt - - - -try: - import daft -except ImportError: - print "python library Daft required." - - -pgm = daft.PGM([9, 4], origin=[.5,.5]) -pgm.add_node(daft.Node("tau", r"$\tau$", 4.0, 3.5)) -pgm.add_node(daft.Node("alpha", r"$\alpha$", 6, 4.0)) -pgm.add_node(daft.Node("lambda1", r"$\lambda_1$", 5.5, 3.2,)) -pgm.add_node(daft.Node("lambda2", r"$\lambda_2$", 6.5, 3.2)) -pgm.add_node(daft.Node("lambda", r"$\lambda$", 5.0, 2.0)) -pgm.add_node(daft.Node("obs", "obs", 5.0, 1.0, 1.2, observed=True)) - - - -pgm.add_edge("tau", "lambda") -pgm.add_edge("alpha", "lambda1") -pgm.add_edge("alpha", "lambda2") -pgm.add_edge("lambda1", "lambda") -pgm.add_edge("lambda2", "lambda") - -pgm.add_edge("lambda", "obs") -pgm.render() -plt.figure( figsize=(12,5) ) +#daft drawing for SMS example +import matplotlib.pyplot as plt + + + +try: + import daft +except ImportError: + print "python library Daft required." + + +pgm = daft.PGM([9, 4], origin=[.5,.5]) +pgm.add_node(daft.Node("tau", r"$\tau$", 4.0, 3.5)) +pgm.add_node(daft.Node("alpha", r"$\alpha$", 6, 4.0)) +pgm.add_node(daft.Node("lambda1", r"$\lambda_1$", 5.5, 3.2,)) +pgm.add_node(daft.Node("lambda2", r"$\lambda_2$", 6.5, 3.2)) +pgm.add_node(daft.Node("lambda", r"$\lambda$", 5.0, 2.0)) +pgm.add_node(daft.Node("obs", "obs", 5.0, 1.0, 1.2, observed=True)) + + + +pgm.add_edge("tau", "lambda") +pgm.add_edge("alpha", "lambda1") +pgm.add_edge("alpha", "lambda2") +pgm.add_edge("lambda1", "lambda") +pgm.add_edge("lambda2", "lambda") + +pgm.add_edge("lambda", "obs") +pgm.render() +plt.figure( figsize=(12,5) ) plt.show() \ No newline at end of file diff --git a/Chapter2_MorePyMC/data/challenger_data.csv b/Chapter2_MorePyMC/data/challenger_data.csv index 49ae6b84..c604a5e9 100644 --- a/Chapter2_MorePyMC/data/challenger_data.csv +++ b/Chapter2_MorePyMC/data/challenger_data.csv @@ -1,26 +1,26 @@ -Date,Temperature,Damage Incident -04/12/1981,66,0 -11/12/1981,70,1 -3/22/82,69,0 -6/27/82,80,NA -01/11/1982,68,0 -04/04/1983,67,0 -6/18/83,72,0 -8/30/83,73,0 -11/28/83,70,0 -02/03/1984,57,1 -04/06/1984,63,1 -8/30/84,70,1 -10/05/1984,78,0 -11/08/1984,67,0 -1/24/85,53,1 -04/12/1985,67,0 -4/29/85,75,0 -6/17/85,70,0 -7/29/85,81,0 -8/27/85,76,0 -10/03/1985,79,0 -10/30/85,75,1 -11/26/85,76,0 -01/12/1986,58,1 -1/28/86,31,Challenger Accident +Date,Temperature,Damage Incident +04/12/1981,66,0 +11/12/1981,70,1 +3/22/82,69,0 +6/27/82,80,NA +01/11/1982,68,0 +04/04/1983,67,0 +6/18/83,72,0 +8/30/83,73,0 +11/28/83,70,0 +02/03/1984,57,1 +04/06/1984,63,1 +8/30/84,70,1 +10/05/1984,78,0 +11/08/1984,67,0 +1/24/85,53,1 +04/12/1985,67,0 +4/29/85,75,0 +6/17/85,70,0 +7/29/85,81,0 +8/27/85,76,0 +10/03/1985,79,0 +10/30/85,75,1 +11/26/85,76,0 +01/12/1986,58,1 +1/28/86,31,Challenger Accident diff --git a/Chapter2_MorePyMC/separation_plot.py b/Chapter2_MorePyMC/separation_plot.py index cbb68ed5..d8ca5e23 100644 --- a/Chapter2_MorePyMC/separation_plot.py +++ b/Chapter2_MorePyMC/separation_plot.py @@ -1,55 +1,55 @@ -# separation plot -# Author: Cameron Davidson-Pilon,2013 -# see http://mdwardlab.com/sites/default/files/GreenhillWardSacks.pdf - - -import matplotlib.pyplot as plt -import numpy as np - - - -def separation_plot( p, y, **kwargs ): - """ - This function creates a separation plot for logistic and probit classification. - See http://mdwardlab.com/sites/default/files/GreenhillWardSacks.pdf - - p: The proportions/probabilities, can be a nxM matrix which represents M models. - y: the 0-1 response variables. - - """ - assert p.shape[0] == y.shape[0], "p.shape[0] != y.shape[0]" - n = p.shape[0] - - try: - M = p.shape[1] - except: - p = p.reshape( n, 1 ) - M = p.shape[1] - - #colors = np.array( ["#fdf2db", "#e44a32"] ) - colors_bmh = np.array( ["#eeeeee", "#348ABD"] ) - - - fig = plt.figure( )#figsize = (8, 1.3*M) ) - - for i in range(M): - ax = fig.add_subplot(M, 1, i+1) - ix = np.argsort( p[:,i] ) - #plot the different bars - bars = ax.bar( np.arange(n), np.ones(n), width=1., - color = colors_bmh[ y[ix].astype(int) ], - edgecolor = 'none') - ax.plot( np.arange(n+1), np.append(p[ix,i], p[ix,i][-1]), "k", - linewidth = 1.,drawstyle="steps-post" ) - #create expected value bar. - ax.vlines( [(1-p[ix,i]).sum()], [0], [1] ) - #ax.grid(False) - #ax.axis('off') - plt.xlim( 0, n) - - plt.tight_layout() - - return - - - +# separation plot +# Author: Cameron Davidson-Pilon,2013 +# see http://mdwardlab.com/sites/default/files/GreenhillWardSacks.pdf + + +import matplotlib.pyplot as plt +import numpy as np + + + +def separation_plot( p, y, **kwargs ): + """ + This function creates a separation plot for logistic and probit classification. + See http://mdwardlab.com/sites/default/files/GreenhillWardSacks.pdf + + p: The proportions/probabilities, can be a nxM matrix which represents M models. + y: the 0-1 response variables. + + """ + assert p.shape[0] == y.shape[0], "p.shape[0] != y.shape[0]" + n = p.shape[0] + + try: + M = p.shape[1] + except: + p = p.reshape( n, 1 ) + M = p.shape[1] + + #colors = np.array( ["#fdf2db", "#e44a32"] ) + colors_bmh = np.array( ["#eeeeee", "#348ABD"] ) + + + fig = plt.figure( )#figsize = (8, 1.3*M) ) + + for i in range(M): + ax = fig.add_subplot(M, 1, i+1) + ix = np.argsort( p[:,i] ) + #plot the different bars + bars = ax.bar( np.arange(n), np.ones(n), width=1., + color = colors_bmh[ y[ix].astype(int) ], + edgecolor = 'none') + ax.plot( np.arange(n+1), np.append(p[ix,i], p[ix,i][-1]), "k", + linewidth = 1.,drawstyle="steps-post" ) + #create expected value bar. + ax.vlines( [(1-p[ix,i]).sum()], [0], [1] ) + #ax.grid(False) + #ax.axis('off') + plt.xlim( 0, n) + + plt.tight_layout() + + return + + + diff --git a/Chapter3_MCMC/IntroMCMC.ipynb b/Chapter3_MCMC/IntroMCMC.ipynb index d4e77ff7..99dee201 100644 --- a/Chapter3_MCMC/IntroMCMC.ipynb +++ b/Chapter3_MCMC/IntroMCMC.ipynb @@ -1,1428 +1,1428 @@ -{ - "metadata": { - "name": "" - }, - "nbformat": 3, - "nbformat_minor": 0, - "worksheets": [ - { - "cells": [ - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "# Chapter 3\n", - "\n", - "\n", - "_______\n", - "\n", - "## Opening the black box of MCMC" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "The previous two chapters hid the inner-mechanics of PyMC, and more generally Markov Chain Monte Carlo (MCMC), from the reader. The reason for including this chapter is three-fold. The first is that any book on Bayesian inference must discuss MCMC. I cannot fight this. Blame the statisticians. Secondly, knowing the process of MCMC gives you insight into whether your algorithm has converged. (Converged to what? We will get to that) Thirdly, we'll understand *why* we are returned thousands of samples from the posterior as a solution, which at first thought can be odd. " - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### The Bayesian landscape\n", - "\n", - "When we setup a Bayesian inference problem with $N$ unknowns, we are implicitly creating an $N$ dimensional space for the prior distributions to exist in. Associated with the space is an additional dimension, which we can describe as the *surface*, or *curve*, that sits on top of the space, that reflects the *prior probability* of a particular point. The surface on the space is defined by our prior distributions. For example, if we have two unknowns $p_1$ and $p_2$, and priors for both are $\\text{Uniform}(0,5)$, the space created is a square of length 5 and the surface is a flat plane that sits on top of the square (representing that every point is equally likely). " - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "%matplotlib inline\n", - "import scipy.stats as stats\n", - "from IPython.core.pylabtools import figsize\n", - "import numpy as np\n", - "figsize(12.5, 4)\n", - "\n", - "import matplotlib.pyplot as plt\n", - "from mpl_toolkits.mplot3d import Axes3D\n", - "\n", - "jet = plt.cm.jet\n", - "fig = plt.figure()\n", - "x = y = np.linspace(0, 5, 100)\n", - "X, Y = np.meshgrid(x, y)\n", - "\n", - "plt.subplot(121)\n", - "uni_x = stats.uniform.pdf(x, loc=0, scale=5)\n", - "uni_y = stats.uniform.pdf(y, loc=0, scale=5)\n", - "M = np.dot(uni_x[:, None], uni_y[None, :])\n", - "im = plt.imshow(M, interpolation='none', origin='lower',\n", - " cmap=jet, vmax=1, vmin=-.15, extent=(0, 5, 0, 5))\n", - "\n", - "plt.xlim(0, 5)\n", - "plt.ylim(0, 5)\n", - "plt.title(\"Landscape formed by Uniform priors.\")\n", - "\n", - "ax = fig.add_subplot(122, projection='3d')\n", - "ax.plot_surface(X, Y, M, cmap=plt.cm.jet, vmax=1, vmin=-.15)\n", - "ax.view_init(azim=390)\n", - "plt.title(\"Uniform prior landscape; alternate view\");" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "metadata": {}, - "output_type": "display_data", - "png": 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fpG3btgwfPhzQSki9//77rF27lkGDBtGvXz+efvrpgM00wn3nijvXunVr5s+f\nz3//+1+uvfZaXn/9dZ577rm42RWOoUOHsnfvXqpWrRoQbx5qLu3atWPlypX88MMP/PGPf+TKK69k\nypQpVKlSJaC2co8ePfB4PAEi9YorrihyLlGIsi5KvGrVKtnv3pIHrisUiti4vpeTcTdn07dvX7WF\njsk4ceKEqh5fStLT03nxxRf9nj6zEypGuKLx1ltvMW7cOI4ePRpTP+vWrWPo0KFs2rSpSBKX4tym\nevXqYb/kyuMaDWaMZTSbzWazF8xps0KhMCVerxe32w1onjIpJR6P55zeEWvFihXcf//9SrQqAlBV\nBRQKhUKhqKDoglVPqpNSYrFY/HGrycnJRTywFUHMxsMrPGvWrDhYojjXUMI1GswYy2g2m81mL5jT\nZoXiPOP48ePlbUKp8Hq9AS8dj8cTkHVeWFiIxWIJeIUTjWUlaIcNG8awYcPKZCzF+YcSrgqFQqFQ\nVBCMYjVUBntSUhIQWDIpWNwC/mxvo5gNJWgrgndWoSgJKsY1GswYy2g2m81mL5jTZoVCUSHRQwJ0\nj6ouXIOxWq0kJydjsWiPb5vNht1ux2q1kpSU5Benegysy+WisLCQgoIC8vPzKSwsxOVy+cfQBW3w\nS6GoqCiPq0KhUCgU5YTRuxpKrOqJWPrfwVgsFr8XVsfYV3C4QSTvrNFLGypuVn/polmhKA+UcI0G\nM8Yyms1ms9kL5rRZoVBUCKIRrPornPcVQi/1CyFCiln9FSocwRh6oGMUs0II//azwVvvqnADRVmi\nhKtCoVAoFGVEKOFoJNrl+pIu5xv7NIraSGJW98wGi9rghLDyTgZTnF8of380mDGW0Ww2m81eMKfN\nCoWiXNC9mm6321/eyijsIi3TJxJ9XKvVit1ux+FwkJKSQkpKCsnJydhsNqxWa4BNejyu0+n0x84W\nFBTgdDoD5qZiZxWJQHlcFQqFQqFIEKG8q8GCtSKKOj3cQPfOSinJz88HwG63B3hpjeEGwd5Zoxg3\n/h3sjVXeWUW0KOEaDWaMZTSbzWazF8xps0KhKBN0YedyuUK+X1EFazRYrYHSIVS4QazJYDrGz5rx\nWinijxKuCoVCoVDEiWBPZDBmFqzh0OcTXG0glJiNlAwWXHvWYrFQWFgIgMPhCCj1pTh/UTGu0WDG\nWEaz2Ww2e8GcNisUioRgjGHVa6QGexrjEcNqJtGmhxvYbDaSk5P9sbMOhyOq2rN6aAJQpPascVOF\nc+2HgCJPeW13AAAgAElEQVQyyuOqUCgUCkUpCRXrGUpcxiJY9ZhQKSVOpzMg/MCYCGUGovHOGv/W\nCY6fDQ4zUNUNzh+UcI0GM8Yyms1ms9kL5rRZoVDEhWgEq8ViKeJ1Le04wed09CoF+njRbPNaEQlO\nBoPAhDCr1RpQ87YkyWAWi0Ulg51DKOGqUCgUCkWURCtYYxWM4frWl9ddLpd/2VxvEykRyvjSz1d0\njDbabLaAkIJItWdDXYPg66C8s+ZFCddoOLPGfN41s9lsNnvBnDYrFIpSYfTyRRKsEJsojBRuoI+R\nlJTkj/e0Wq1FvJElKVNlVu9sNMlgwR7a4kS9cacyl8uFEAK73e7vW1ExUMJVoVAoFIoIhPLsGYkk\nWI3xqZGEYXFiWBddkSoVhBNywYLOOKfgfkIJufIStCUVi+HCDULFz0YS9fo900WsCjeoWCjhGg1m\n9KqZzWaz2QvmtFmhUERNcYI1HsIuGu9taQWSLuRCjVdS76xxjuWRDBZLYltJRb1xowi9HFdJas8q\nQZtYlHBVKBQKhcKAvlQcToDES7DqYxlJdAxqab2zRvLz8yucd7akRBL1esJbcExtqNqzoRLBlHc2\nsSjhGg1mjGU0m81msxfMabNCoQhLqO1ZjcRLnIWLtyxP4Vecd9br9fqrF+jvneuxsxaLheTk5GKT\nwYCor4MStLGjhKtCoVAozmtCxT8aqciCNZHCxyjkdE8kQEpKiqljZ0tKaWrPluQ6GPvTBXDwjwjF\nWZRwjQYzetXMZrPZ7AVz2qxQKPwUJ1h1ggVLaQiOY41VvJWn6IvknQ3nmTSTdzbaHwPFJYOVtMKD\nEMK/uYTNZlPe2TAo4apQKBSK84poPKz6uXgkXgX3XVEEWjwxzilYyJXWO1ve16g040fyzgZfg0jX\nIT8/P2QymAo3UMI1OswYy2g2m81mL5jTZoXiPKYkIQGRPLDFkciNCTweT0yVBsqaeHlnCwoKot7i\ntSISTbiBXptXPx8qGSxUItj5Vt1ACVeFQqFQnNMEC1YIfKjHM4Y13OYB8Ypj9Xq9OJ1O/7Hb7UZK\nGZWQqShE8s6WxCtp9thZCAw3SEpKoqCgAACHw1Gi2rPB1+Fcrm6QEOEqhEgCtgI/SSkHJmKMMsWM\nXjWz2Ww2e8GcNisU5xH6Q768BKsuHOLpudVFiVG4BAuZ4OXlihQ/Golgr6TX6/ULueTk5FLFzpbG\nOxuPMJHSoI8bvD2v8f3SJoMVdx3MJGgT5XG9H9gNVElQ/wqFQqFQhCRSUXkoG8FqrAEar34BrFYr\nNpsNl8uFy+XybwFr5mSo4iguCao0sbNmmr9OpOtQmqQ44zXRPflJSUkVfpvbuAtXIcSFwLXAY8D4\nePdfLpgxltFsNpvNXjCnzQrFOYxea1R/aAfHgpalYI2l71CiK1LFA5vNVsS20i63myHUAELHjMZa\n2SBUDGpZUhpPb0nCLoLPhUKPta3Ioj4RHtc5wINAWgL6VigUCoUigFAeVv28TkkFmS4WjX1EEqz6\nZ0pLOMEaznMb6Xy8BV15irmSEK/YWR1dwJnVO1tcMlhw3Lf+vtPpRAhBcnJyWZsdFXEVrkKI64Gj\nUsqvhBC9wjb8eQTYGml/W6qBo/1Zz9WZNdp/K9qxTkWxRx2X/3GlXhXLnlDHx5+Dwq/B1ojvtnjg\nZt95heIcIFSdzGDi5QWFolufxsODGy6ONZJoLSnxKlWlo4conKveWZ3gRLhYY2eLoyxia8OFGzid\nTjwejynuqYhnDIMQ4nFgOOAGHGhe1yVSytv0NqtWrZL97u0btzEVCkV0XN/Lybibs+nbt2/F/r+S\noggnTpyomMFm5UQowRrK8xiLpzCUB9TYd7SC1dhPuNjE4vo19mGz2bDZbLjdbn9MYjw9Y8Fizihu\nQ2EUcPGOndWTs4QQpKSkxNxfNEgpKSwsxOv1BiSJhSOesbN63LLVavXHmZYVTqcTt9vt/37FklQY\nD6pXrx72AsbV4yqlnARMAhBC9AT+ZhStpsWMsYxms9ls9oI5bVYoTEw0glUnXl7W4D7LwsNanoRb\nYjZm+CclJQUI2lD1RhPtnUwUxvtgtVqxWq0BHveyqmxQ1pRXJYXSkOg6rspLoFAoFIqYiEawRuMd\ni3asRAnLUJ7L0pZqKmuMNuoe3ngkggX3baS8y1LpGMMsElnZwEzisTxJmHCVUq4F1iaq/zLFjF41\ns9lsNnvBnDYrFCaiJII1UZUCjGOUtt9Qf5fWA1eRShRFmwBk1jJdxdkQ7/mHKt1WVphJNKudsxQK\nhUJRoYg2hjVRpa3ikRSlfzYeQtvYtrxjD6MhXnVXjfdBSmkKUQWxz9/tdvsTpcxcdzZRKOEaDWaM\nZTSbzWazF8xps0JRgTF6pcpLsOqvWARiuMSueMQ5er1e8vPz/f3odTcregxlpMz+4MoGwfdGSumf\nc6ISwRJNNN5ZvQaxfj7azQPiMX/lcVUoFAqFogSEWlY1Eq1gNYrOUG0jhRzEQwxH2jygtKEBoQS0\nUeAUFhb6+w+15F5RxUhxYs7j8eB2uwPOR0oEi5eYK0sRZ/TO6nO22WwBu6HFGjt7rqGEazSY0atm\nNpvNZi+Y02aFooLh9XpxuVwRqwMkysMK8ROs4by3+vvxtDc5ORm3243L5fKPZcYY0nDoYg60ZXN9\nzsFL7cHL78F9mEnEw9nvSbiNH0obOxuNoFceV4VCoVAoIlDcxgFlIVj1caLpI1rvbbDdpRWtxdWQ\n1e23WCw4HI4Sx5Amask5UZzriWDREK/Y4eD7HoqKHEethGs0mDGW0Ww2m81eMKfNCkU5U1xh+3gL\n1lCCTR8nEpHej0awltbmcElKxZX5Ki6GNPiaR1uuqjxFXTRewHiKOf1VXqKtNF7P0gr6cOge7pLa\nUZYo4apQKBSKhBPNTkyhHsCxjmnsOx7CMhHhBokSwvH2Uho/X1FFDZQuESzUvJ1O5znvnQ3+3unh\nJ3a7vcLOVQnXaDCjV81sNpvNXjCnzQpFGRMsWIEiAi1e8XWJqkJgNsFaHLF6KfPz8023M1Q0Ij7Y\nE13WIRaJ9vSGuwYej8ef4KfvilaR76USrgqFQqGIO9EIVv0VaekyGhJZfkrvP7hfKL3QLi/BGolo\nQg2MGf5mCDWIhlAiPi8vDwCbzRbgpY0mxCIeWf3ldc30JDiIfQe6RKKEazSYMZbRbDabzV4wp80K\nRYIpiWA1notUwioc4TyhxnFKSyISxhLhuU2kl84oZqWUfuGakpISdaiBsQ8zLLkbr6fVag2wM5GJ\nYBUpGaoi2RIKJVwVCoVCETP6w7skgjWWscJ5LIGwMbTR9h0uQSpW20ubKBaK8hR+4UINgpfbgz2V\nRsyQ3R9sTyISwUL9aCnr62CmUlighGt0mNGrZjabzWYvmNNmhSLOBD+09XNG4rlkn4jyU+H6Dh4j\nXpR3WEAi0EWdkUjJQBU5u78kRAqxCDf3cF5pHa/Xe859P+KJEq4KhUKhKDHlLVjj1X8kMRxLnF+i\n4lg9Hg8FBQUBQr2iJtPEq6qBx+MJyPCv6KLOaF8or3S4ygY6BQUFAAExs4mMGVYe13MRM8Yyms1m\ns9kL5rRZoYgRvVyOLi6MVQF0zC5YE1GBwNh/afo0Eiyo9Sz/shA58SBSqEG4OrPGxDBIXKhBIkVc\npFADj8dTZCc0ff7B3tl4b++qhKtCoVAozlluuukm3nnnHf/D1yiqzCpY49F3Ijy34fq02+14PJ4i\nWf4QXuSYUcw6nU5/QXyLxRKX+NGKhlF0ulwuhBCkpKQkNBHM7CjhGg1m9KqZzWaz2QvmtFmhiAGX\ny0XlypXp2rUrr7/+Oq1atQJiLw+lEymRJ9b+SyNYo6l2kKhKAeG8thaLhaSkJIQQuN1uhBA4HI4S\nZfnH22OXKHSbLBYLdrsdOPtD6Vybb7DXs6wSwUKNXdFRwlWhUCgUEfF4PLz33ns8/fTTHDx4EIB3\n3nmHGTNmxN2rFe/driB0pYB41GKF+FYKiNSnMY44lEApSZa/mT12xtjRcKEGxnmbfb5G4pEIBkXn\nboYkOCNKuEaDGWMZzWaz2ewFc9qsUJSCb775hnvuuQeASpUq8dRTT3HDDTcAFXe3K73vRJS2SkS/\nJe2zuCoK0Wb5R7NLlFmW3OPhoTTOsyyT3krr9SwuESxUEmWouYMWRyylrPD3WwlXhUKhUESkbdu2\n3HnnnbRr147MzEx69uxZJFO8pIQSahC/OFmIv/c2EQldiUoSC0Ukj10oT2U4gVNYWGgKUVvcfENl\n9uv3QUpJfn5+yIQ3s3hni/vhYrwOcFbQWq1WrNaKKw9j+z/P+YIZvWpms9ls9oI5bVacM2zcuJFe\nvXrRo0cPXnrppZBtZsyYQY8ePbjqqqv4/vvvA97zeDz07NmToUOH+s898sgjXHbZZfTq1YuHH36Y\nU6dOAZCTk8OiRYtYsGABGzZs4JFHHim13ZEEEcQnjjW4v1gFVvDDPh79JqLP0qCPabVasdvtJCcn\nk5KSQkpKCsnJydhsNn9MrY6eAV9YWEh+fj75+fkUFhbicrn8m1BUVIzztdlsReYbSuwZ51tQUEB+\nfj4FBQX+5LFYNrwoS8Ldax2r1UpSUlLMP0oTTcW2TqFQKBRF8Hg8jB07lkWLFvHFF1/w5ptv8t13\n3wW0ycrKYteuXaxfv54nnniCMWPGBLy/YMECWrRoESBIevfuzaZNm1i9ejV5eXnMmTPH/17jxo1Z\nu3YtQ4cO5c477yyxzcUJtVgI1bex/1jjWI1/nyuCtTh0j50u7hwOh/+9YDEbLO50MRuruCvLpKHg\nUAOLxUJKSgoOhwO73Y7Vag34nnq9XtxuN06ns4iYLY2AL88EKX1Mq9UaUrxXNJRwjYYza8rbgpJj\nNpvNZi+Y02bFOcG2bdto3LgxDRo0wGazcdNNN5GZmRnQJjMzkyFDhgDQqVMnTp06xdGjRwE4fPgw\nK1euZPjw4QEP1969e/sFVJ8+ffj555+LjJ2Wlub3xELxO1UlUqiFE6w68Yw3BeLmuQ0uIRZNn8XF\ntJYlwZ7KUOJOn2s4cVfRPZXGMAPdQ+lwOIrM1yjg9fmazRutqgooFAqFIqEcOXKEevXq+Y8zMjLY\ntm1bsW2OHDlCrVq1mDx5Mo8++iinT58OO8aiRYsYPny4/zgnJ4fu3btTUFCAlJIrrrgioo2ljd2M\nJiGmuBJUwVnU0RIuqx+IixcqWLCCecRCOKKJm40mCSxULGlFJNR8oeS7gQVn9uvXpKznHUpIV0Rx\nbUR5XKPBjLGMZrPZbPaCOW1WnBNE+3ALfgBJKfn888+pWbMmbdu2DfuAmj17NpUrV/ZXDqhTpw47\nd+5kw4YNDBgwgLlz55Kbmxt2zFBe0EiCpCTzicVrWVzf4WJv410pIJbyS1JKXC5XkZ2kKhKRPJWh\n4ma9Xm/IUANd7FVkz6xOcGhFJG80FA010OeqbyxRHt7ZivpjIRjlcVUoFAqTUbduXQ4fPuw/Pnz4\nMBkZGRHb/Pzzz9StW5dly5aRmZlJVlYWhYWFnD59mtGjR/PCCy8A8NZbb5GVlcWHH37o/6zdbvcX\ngO/WrRtLly5l//79tG3b1t+mOC9orCSytFU4z3Co+ZS2T53SxPMG9xXswdO3fK3IHsviyjaF8lTq\neDyeIhn+sf4ACEc8l82j9UYb5+v1enE6nQF9JPLemi1MAJTHNTrMGMtoNpvNZi+Y02bFOUGHDh3Y\nv38/OTk5OJ1Oli5dSv/+/QPaDBgwgMWLFwOwZcsW0tLSqF27NlOnTmXXrl18/fXXLFy4kCuuuMIv\nWleuXMncuXN56623ApJxjh8/7hdKx44d4/jx4zRs2BAonYe1JOhLrcGlrcxUKcBod2n7NGK1Wilw\n2opNjjLGVlZUr2U4T2VycnKRcArjPM0YNwvhvdH6XPUEsUQnvpkZ5XFVKBQKk2G1Wpk7dy7Dhw/H\n7XZz22230aJFC1577TUARowYwVVXXcXGjRvp3r07qampzJs3L2RfRjE1ceJEnE4nN954IwCdO3fm\nmWeeYcOGDTz55JNYrVZq1KhBv379qFq1KlA0HCHe27/Gu75pSfqN1usaLjZWF8ClzagPNfbx321s\n+q+Df/7bwaWt3HRt6yKjpqRWDS/Vq3qoXsXjX2Y2645RupjVBbdeV7SkcbMVfZ5GjN5ovYaqMSwm\nlIc2HnMO/oFlBgEsytrIVatWyX739i3TMRUKBVzfy8m4m7Pp27dvxf2/tyIkJ06cqDBPk4MHDzJ7\n9mxSUlJ49NFH/Q+8WEWlLrBCPUBL2rf+cDcu05YmlMEoDsIlZ4UTEMa5hLInHOGEdW6ehV37kpn8\nj0rs3h/K5ySpX8dLt3ZurrzUTUYtL7VqeKiR5qV6mhspwyesRSN4pNQK8gOkpqZGnEO8KCwsxOPx\n+GNEgwledg8V/2wkmmV3l8uFy+Xye0TLioKCArxeb7HlqIoLNQimuDl7PB7/hhIOh6PU4THxpnr1\n6mH/sSuPq0KhUCiiYvv27UyfPp3169cD0LdvX/8uWvHyZiXCwwrhvaGx9BtPj3C4/jxeC98ftDNn\nUQrL1iZH6EHw4y9J/PhLEu9+frZdnQu8XNbGzZWdXFze3oXXC2mVvKRXc4M8m/xUnPeuIhKPDP9g\nYVde2f3REs85V9Q5FocSrtFgxj3pzWaz2ewFc9qsUJSSV155hQcffBDQkrUeeOABOnXqFLel+2Di\nFR8b3HesYjgRIQzhvLYHf7bz7ufJ/OPfKXg8pev7l2MWco5YaNbAy78+cLDwg2Sqp0k6tXLTt6uL\nRhleaqZ7SU/zckE1NxaLJ2KFBdD2tK/I4kcPNYg2CSxUSIXb7UZKWWahBrEmSRU35+C/g+fr9Xop\nKCjwx99WZCq2dQqFQqGoEFx99dXMmjWLESNGsHHjRsaNGxfTkmKkzPtYa6aG6tNMgvXob1bO5FtZ\nt81K9nYbHo8ESj5G9TQvz08+Q84vFoY+VJkz+Vofv/0uWLHJzopNZ5fCq1SSdLzYRZ/L3DRr4KFW\nupf0qppn1pYUWJqpLLPe40U4YRcublZKWaTkmBnjZoubs7HsVrgfKhUNJVyjwYxeNbPZbDZ7wZw2\nK84pNm7cyKRJk/wJWqG2Yp0xYwYrVqwgJSWF559/nubNm/vf83g89OnTh4yMDN5++20AHnnkET7/\n/HNSUlLo1q0bDz/8MGlpadSvX5/x48ezePFiDh06xJdffkmXLl1KbHNxD8l4e2/jEW4A8Q01CCeC\nT+dZ+fo7O39/NpWf/pdEq6ZuenVyM+qmQqpUltit8P1BC5+tt7N+exLhCwN5efqBPOrUhInPpZBz\npPhH/ekzgrVb7azdelbMpjokbZq7eGZCPsdOWnDYPVxQzUPNGpJkmzvq5feKLGaDl931uFo9sz/a\nJLB4VLooC4LnrFcm0HcBqwjxrcWhhKtCoVCYEI/Hw9ixY1m6dCl169b1x5u2aNHC3yYrK4tdu3ax\nfv16tm7dypgxY8jKyvK/v2DBAlq0aBGwmUDv3r2ZPn06AA888ABz5sxh2rRp7Nmzh/fee48vvviC\nAQMGMG7cONavX18i72goD2OsNVP1fiOFHJSWSP3FUtoqWLC63Bb2HEzmyYUprP7PWeG44zsbO76z\n+Y+tSZIWjT1ceamLP19fSJVKXpJtcOAnTcyu3Wrlj1c7GTLAyT/eTOGLLTZi4borC/nz9U4emZfq\n78tuk7Rq6qZPFzdtm2ue2ZrVvaRXdZOSbH4xqxOc3R8uKSqUmC3NXGMNFYgV3TtbUZKzIqGEazSY\nMZbRbDabzV4wp82Kc4Zt27bRuHFjGjRoAMBNN91EZmZmgHDNzMxkyJAhAHTq1IlTp05x9OhRatWq\nxeHDh1m5ciXjx49n/vz5/s/07t3b/3efPn347LPP/H0NHjwYm82Gw+GgUaNGfPXVV1x66aXF2hpJ\nsMZShieSYNXHKA2JSLwK9bcQFvYftrPoYwcvve9Aysh9uz2Cb36w8s0PZx/dFoukeUMvwwcW8uiY\nfI4eF3glDOpTiCNZkrXZittdMvHetL6bZ/6Wx9qtNm4cVwWv96xdTpfg6z02vt5zVhQnJUmaN/DS\nu4uLS1u7qV3DS80aXtKreqic6g6IqwwWs8EiryIuvxttKm3cbLBHtqLMtbwFc2lQwlWhUChMyJEj\nR6hXr57/OCMjg23bthXb5siRI9SqVYvJkyfz6KOPcvr06bBjLFq0iOHDhwPwyy+/0KlTJwBSUlJI\nT0/nl19+iWhjIuJC9X4hvnVTw9lr7DsWW4P7OnLMxucbk5nxQip5BaW/FqkOyeQ78zj6m4XrRqdx\nOk8ghKRpfS/dO7h47qE8qqVJUpIlP/9qYcVGG59vtOF0Fp2P3e7l+cl5FDphxJTK/H46ujl7PIJv\nDyTx7YGzos5q9fLqrDw87mQKnFD3Ai+1anipluahRtrZWrOR6pEa400rIpESokJ5ZyPV1TV+3kwi\nsjyIu3AVQjiAtUAyUAAsllLOifc4ZYoZvWpms9ls9oI5bVacM0T7cAt+6Esp+fzzz6lZsyZt27b1\nl7YKZvbs2VSuXJkbbrihyHtpaWk4nc6I9U8TIVj1vovz3pY09CCcvfp7pbUzlA2nztjYm2MHqYnO\nXp1drPzSGlJIRsbLzHvzaXKhl6nzUtj/09nHuZSCH3KS+CEnidc/8p+lUT0vl7dz88yEfKqneank\nkBw9YSFrk42Gdd1c3t7LjAUp/Pf72KTBkP4FDBng5Ol/pbBxhzFcQas12729mysudZNR00vNELVm\ng5ff9d2/ysIzG6/s/uA+wyWBBc9Vz+wvKy+08rgCUsoCIURvKWWeECIZ2CaEWCal/CHeYykUCsX5\nSt26dTl8+LD/+PDhw2RkZERs8/PPP1O3bl2WLVtGZmYmWVlZFBYWcvr0aUaPHu3f+vWtt94iKyuL\nDz/8MGRfVatWZffu3dSpUydgvFgEa3FiMxrBWlKK89wa7YnWExZOsBY6LXx70MGj81P5cqcNISSN\nMrx07+jyC8lUh+TIMQufbwjvFQW4oXchI24sZMG7DqbOi7ZIvuDg4SQOHk7irc/0Oq+SQb2djP1T\nId8ftJBXANNG53Pid8Gq/1j5dK2dU2eiF9SN67l59qE8vviPFmJQNPRBqzX7zvIk3ll+1oa6F0gu\na6vVmq1f26tVNEjzUKOqEzh7j8y6O1aoJLBgMWusYBCvuNlzlYSECkgp83x/VvaNUZiIccoMM8Yy\nms1ms9kL5rRZcc7QoUMH9u/fT05ODnXq1GHp0qW8/PLLAW0GDBjAyy+/zODBg9myZQtpaWnUrl2b\nqVOnMnXqVAA2bNjAvHnz/KJ15cqVzJ07l08//RSHw+Hvq3///tx5553cc889eL1ecnJy6NChA1C6\nXamiJZHhBsXteFWS/sN7bQV7c+y8/H4Kb3ySjF7WSkrBgcNJHDicxJvL/L3QqJ6XHu1d/N+EfGpU\n8ZKaIvnlmIXPN9rY96OFmffmk73dxuAHqpS6titopbJemHqG/T9aGDimCvmFel+SjJqakJw2Op8L\naniplAK5uYIvtlr5+As7J04Filmr1cu8h/OQwO1TKnMyyhAD31XiyDHBh6vtfLjaDnh5ZHQ+zRta\nWLy8Mt3bO2lUT1I73Ut6NS/paZFrzZpF4BnFrC5chRA4HI5Sb55Qmrkqj6sPIYQF+ApoDYyTUv6Y\niHEUCoXifMVqtTJ37lyGDx/uL4fVokULXnvtNQBGjBjBVVddxcaNG+nevTupqanMmzcvZF/Gh9bE\niRNxOp3ceOONAHTu3JlnnnmGli1bMmzYMHr37s1vv/3GnXfe6f9cvHelgrIVrImqx/rTUTufrLXz\nxMJUCp3R9H3WK/rmp/7eadnYwwtTz/DT/yycyRf0aO+ieUMvn2+0sjzbRkGJwgy8PH5fPvXrenlw\ndio//hJcFULw86+CpavsLF111ptbq4aXLpe4mDgyn9rpmpjNL4RTuYJG9bxMez6Fbbtjq2LQvb2T\nv48s4OUlycx4QfPILltz1oa0yl46tHTT9zI3FzX0UKuGVmv2gmpurEmehAq8sqK4jQSiEbNmSHiL\nBZHIoGchRCPgM+BPUsqvAFatWiX73ds3YWMqFIrQXN/Lybibs+nbt++583+w84QTJ05UqOyUl19+\nmTNnztCkSROuvvpq//lYM++N223G4r019qULgNIKYV0UhBo/nAj+7ZSNTTvsTJxTiWMnY9ku1cuk\nvxbQtrmH6fNT2HNA9zWdjRXt2s5FejWpxav+piVfLd9gI6+g6LiDehdyx42FzHvbQdamaEMMQtOy\nsVZ5IHubjapVvGTUlKSmSJwu2Pi15pn96X/RlUpLq+Tz/h5OYtaLKVGKfA2t1qybfl3dtGjkoc4F\nbuqkS6pW9mD31ZoNRTgxm5+fj5QSh8NRZlvdejweCgsLsVgsAasckYgUNxuKcGEVeXnaAnlKSoo/\nsbEiUL169bBfgoQKVwAhxDPAT1LK58AnXG96A2yNtAaWauBof3bJ9cwa7b/qWB2r49iPjz8HhV+D\nrRHNGnl44aleSriakIokXHfs2MF9993Hzp07qVu3LuvXryc1NTVmr064SgClXf7UH8AWiyUmz20o\n4RpOBOcXJrF7fzL5hQIBfHfQwsdf2PlyZ6TNAkIzoHshd99ayKsfJvPh6uTiP4CkXm1J9w4uLm/n\npkZVzSt67KTgq91JXNPDyYav7Mx5wxFTiIHd7uWFKXnk5gmmzE3l9JnAvqpW8dLxYq3O64W1vVRK\nkbg98OVOKx+usnEoaDOEv9+RR/uWHh7+RwoHD8e2CHx1t0Lu/VMh/3jTwfGTgr6XabVma9bwUqu6\nlgBWKcUTcfML/Z7abDb/JgSJ9laWRriGoqRi1jjf5ORk/7+VikCZClchxAWAW0p5UgiRDqwD7pNS\nrgKTelzNGMtoNpvNZi+YzmblcTUvFUW4PvTQQyxcuBCAypUrM3bsWEaNGkWlSpUSHm8aa3/GfkvS\np+qgO44AACAASURBVFG46n0HC1avtPD9ITv//HeKb3ld+DcL6N3ZxSXNPKRV9mK3Cfbst7BsTXgx\n27CuluC05Rsrz7yagjsGkWm1enl91hnyCwSnzgguqK6J2d9+F2RtsvJZtp3cvOgF9T1D8unTxcWj\nL6Syc2/0IrNKqqR9Sze9u7homOGlSqokOdlL3Zpe3vnMwbOLUkozPT/VKnt5cdoZvtmXxOMvh75m\n1iRJ80YeenV2c2mr0LVmw5HoJDC3243T6YxZuIbC+CMrONQgFHa7vcw8zZGIJFwTEeNaF3hdCJEE\n/AI8q4tWhUKhUJiXxo0bk5yczHXXXccFF1zA2LFjY+ovnMCMV51XI7EIYb3PUOELh47YWZKVzLOL\nAgVTqM0CrEmSlk089Oni4o4bC6lS2YvdKti938Jn66zccWMhHo+Fv06vzG+/xyYe7r61gKu6upj1\nkoOvvg0sSZVRU9KtnZuZ9+aTXk0TsydOCVb6xGxwJYF2zd08em8eS1fauXl8FfQEs2g5nSfI3m4j\ne7uNVIcmMvcftvL0v+z07OTmlUdzqZwqERbYsSeJj76ws+uH6OTJxJF5tG3h4W8h43XP4vYIdu+z\nsnvf2X71erdXXurisrZuWjb24LB7SavkpkZV6f/RUlYVDRLh2Y20eYLb7cblcvnbmaWGbMJDBYIx\npcdVoTgHUB5X8xLJ47px40YmTZrkT9C68847i7SZMWMGK1asICUlheeff57mzZv73/N4PPTp04eM\njAzefvttAD788EOeeuop9u7dy6pVq2jXrh0AP/zwA1dccQUNGjTg+PHjDBw4kCeeeKLEXsxwS+36\ncWmTZxKReBVcMF6379cTVtZtS2bSP1OjLtQfCptV8n/jz9DoQi+//mahSiUvSUmCb/Za+HhNMtu/\ntVCSMIOOF7uYNrqApatsvPbR2SoGkdFKUnVt56Z7Bxc1a3ip5IDfc6FeLS8/5CTx9zmVOJMf2/86\n7h+ez+Xt3EyZm8LeQ0WFqcMuuaS5mz6d3TRr6KFyqherRfDNvqLXol1zNzPuzefNT+y8tyKaUIrw\nOOxeXn5US36bPj+V2uleLm/v5oqOWq3ZWukeqqd5qZHmxust+n3QKa2Y1T2uSUlJJCfHNpeS4PV6\nKSgoQAhBSkpKiWofJ5qy9rgqFAqFogzweDyMHTuWpUuXUrduXfr27UvPnj0Dtn3Nyspi165drF+/\nnq1btzJmzBiysrL87y9YsIAWLVqQm5vrP9eqVSveeOMNxo8fHzCe3W6nSZMmLF68mBkzZvDkk0/6\nH3alrXFqFJahRGI0hCvHZey/tH0G95Wbn8R/v09m4pxU9ubE9gi98lInE/5SwL8/S2bc01qIAWhi\ntlVTN326uLj7j5qAs1kFu36w8OGqZHZ8X1TMplXysuCRM/z4i4WhD1Uu4W5cWkkqYyWBCX/J57K2\nbl7/2EGnVm7mT82lkkNyKlew+j82Pllj52RudIJaE5l5vPu5nVv/VplwYrrAKdi6y8bWXWc9xHab\npHVTN706a9eiehUvtS/wkmwXPPxcKqv/E10CWDhGDCpgYC8Xk/95Nvkt50gSOUeSeCfzbK3ZjJqS\nLm20WrMN6nipVcNDjaqS9KpuIHx5rmAhGy7JD8q+JJUZS2GBEq7RYbJYRsB8NpvNXjCnzYpzim3b\nttG4cWMaNGgAwE033URmZmaAcM3MzGTIkCEAdOrUiVOnTnH06FFq1arF4cOHWblyJePHj2f+/Pn+\nzxg9sqFIS0vj999/j9rORNV5jSSES5sdHc5Wt8fCd4ccHDthwW6TPHBbAcs32FixoaTlqCCjppd/\nTjzDf/cmccuEKjhdgdfA5Rbs+M7Gju+KCrh+3VyMGeohrbIkySL57/cWalWX1KgmmfzPVA7EmODU\n+RIXU+7K561Pk5k9QROZb3921gtYq4aXy9q6mXxXPjVreKmcooUCrNlStMarw+7lhal5/HZKMOzv\nVUrlsXW6BF/tsfHVHht/+UMBg/q4uO/JSrg9gt6dXdw6oJAqlSTJNskPORY+y7aTvd2K1xv5nmTU\n9PL8lFyyNtoY/EB4Ma2hlQg7W2tWI72al86t3fS5zEnvLm7O5AtqpHlJr+bGIqKvNVtRvJxmQQlX\nhUKhMClHjhyhXr16/uOMjAy2bdtWbJsjR45Qq1YtJk+ezKOPPsrp06ejHjMnJ4cBAwZw+PBhvvzy\nS7p06RK2bXE7U5WWRAjhSF7bAz87ePszB/MXO/B6BcZyVE+Nz9cy+B2Sn45ayMy2k7XZittdVDhZ\nrV7+MTEPuxXueawSR3+LXvAaBZzOoN6F3P3HQr7cacXh8PDEuHySLLDjuyQ+XB19nCj4SlI9coac\nIxZunVCFgjAlqY7+piWXGeurajVe3UwclU+ddC+VUyE1xUuNql7GP5XKhq9jW/6uX9fD3IlnWLFJ\nE5n6jly7DAliSUmS5g28XNnJxa3986hWReJIlhw8bGH5ejurt+j3xMsT4/KpnS4ZNa0yx2MoV3b8\npIVfTwpaNvEyZW4qn2+wk1ZZq6rQ9zI3FzXwULO6lwuqaWI2Uq1Z0FZQXC5XmdWaVR7XcxkzetXM\nZrPZ7AVz2qw4pyhJXdPg488//5yaNWvStm1b1q9fH1U/derUYefOnVSrVo3u3btz++238+WXX1Kl\nSpWQY8azUkBx/Saiz1+O21i52c70+ZXIzTP2H3rr0sb1NOH03EN5VK0iSXVIDv1s4ZN1dlo2ctG3\nq4cnF6aw5ZvYCvVfWNvDPybmsWVnEgPvrRKQFJZs1+qaDrjCyf1/zqdKJUiywPZvk/hotZ3d+4s+\n9qfcmUerizxM/kdKqTy2R3/T5vjJOjstG7t56oF8lmQl8/OvFv7Q28WdtziplCLJK4C1W+18/IWN\nX09Es8Tv5dkH86icCrdPrVxkxy4jHo/g2wNJfHvgbL8Wi6TphV6uuNTFP/6eR9MGHio54ORpwQuL\nHZzOC9tdsVitXhZMyeNkruCP488K/VO5FtZssbNmy1lhXylF0ra5JmZbNPZQO91DejUvF1QNrDUr\npfQnS4G5Nk4oS5RwVSgUCpNSt25dDh8+7D8+fPgwGRkZEdv8/PPP1K1bl2XLlpGZmUlWVhaFhYWc\nPn2a0aNH+7d+DYXdbsdu1x7I1atXJykpif379/uTtyAxCVKJ6jdcn7+fsbJ9dzJ/nxM5Uz2Qs1u4\nvv6R3pfklqsLmfzXfPb/lESBEyaOymffj4UsW5NM9vaS1Xe1Wr384+952Kxw56OVQnoLC0PEiepJ\nT3/o7WTCX/KplAoWAUeOQasmHp5/J4VZL6VGbUc4216Ymkd+geDPEytz2if0P1tXdGl9wl8KqFNT\n2zQhvxCyt9n4cLWdX0+cnc/V3QoZM6yQZ193sHZr6TZL8HoFe3OS+PEXQc9OLr7eY+XR+anUreml\newcXs/+WR/U07QfGkWNJZG2KbieyP/g2cpjxQgrbvy3+R8iZfMGmHTY27TjbNtmuhX707+FiUG8n\nx09CzRqSC6p5SEn2+EtWJXJnLOVxPZcxYyyj2Ww2m71gTpsV5xQdOnRg//795OTkUKdOHZYuXcrL\nL78c0GbAgAG8/PLLDB48mC1btpCWlkbt2rWZOnUqU6dOBWDDhg3MmzcvpGg1emuPHz9OtWrVSEpK\nIjc3l0OHDtGwYUN/u3ht0WpM9krE1q/h+ix0WdhzIJmZC1LZ8HVsXtH0al6en5zL3kNWrrsnze+R\ns1gkLRp66dnZybDrCkmrLEm2w3cHIm9WcMeN+Vzf08UTL5fcYxuc9FQ9zctL03LJPZPEqi+TuL6n\nkyEDChFCsH13EktX2fk+RNZ/OEYMKuAPvV3MWJDC13vCf+74SQvLN9hZvuGsEK1R1Uvn/2fvvMOj\nKNA//pnZ2dmSSkhCEjoqHaQX8USayqkoIIJ4KHqWE1Sq0kSEOxUVFaQq5+mpZ0OBAzVAAtISQbqg\nVOkh9JJk++zM74/JbnZDQjYJ+mO9/TyPj2R3M/tms3nmu++87/fbVGHkww5SEzXiolUSq6g4XCKP\nTowKOX2rNP5yt5PeXd1MnGn1d5sPHjdw8LiBj5f6HqVRK1XlphsVpo6wkxCn6eENFwQyN0ikr9f9\nbmOjVOa/ZGP7Xok+w2MKx0Yqhsst0LCul9aNvfxlXDT7j0h+r9ku7RRaNVKoVlUlOUElIc5LtEUJ\ninq9GvZcEeEaIUKECBF+VyRJYubMmQwaNMhvh9WgQQM+/PBDAAYPHkyPHj3Izs6mU6dOWK1WZs2a\nVeKxAk9e33zzDWPHjuX8+fMMGDCAZs2asWDBArKyspg6dSqSJJGbm8s///lP4uLirpqwDLTE+j0F\nKwgcOGbi1DkRQYB7u7oQRcrdEQUQRZU3R9uJj4WRr0dz4kzw96uq75J2kem+z9+1S1sPj/ZxERtV\n6CKwX2TnAZGH7nazdI2JPsPL76EajMrLzzqoUU1j+OtR5BQThRaTxo0NFO67zU29Gg5irBoaAlt+\nNrBwpcyvx4Ilw3U1Fd58zs7yLDlo9rQ8nL8ksjxLZnmWrHuy1td4cko0NZJVnurvJC1ZXwBzeSBr\nq8TiVSZyz5b9O0lN1JevVm00ct/ImDJqE4qcBAJGP6ona3RorjBlqIO2TTx4NYHT50SOnhSItWpc\nLKjY70L/4GAje7vEfSOLXreSvGYDxx06NFdISdSDExJivcTHeH93r9lrgYiPa4QI/yNEfFzDl2sl\nOSuQgQMH0rFjR3r27EmNGjX8t1dmDu9KiT6VTbzyHb/4MXPOyHy3Vubl96w43QKiqFG/tkrnNm5a\nNtS392Uj7DkksmiViS0/l+6r+vA9Tu7t6mbaB5ZKd2wT4lQ+fqWA46d1MR0bpSIK8NM+A4tXmcq1\neAVweycXQwa4mPu5OajjWRZWsy5mu7bzUK+Gl2irhqZBbDTk2QSenBJVKR9b0O2y/v6MnY+Xmkr1\nZI2PUWnTROHWtgrVC6NkPQpkbZNYvNIU8AFBF+fVkzWee9MaNH5QEWpU8zJrvI2la2TeX2giJVGj\nbVOFW1p7SE7QwxsK7AJrN0ssXSOX+XzPPODg5lYKo960cjzkMZTiaNROU7mto5u/9nFz8pxIUpUi\nr1lNu/Lfke8/RdG7uLIsI0lS2Pi4RoRrhAj/I0SEa/hyLQlXTdNYsmQJY8eO5dSpU/Tr148ZM2Zc\nlcWR0sz+K3LcskTw+UsSG3fJjH07ilPnriw2JINGo3peunfw0Kiel5hoFYMA2/dILFwpYzLC5KF2\nvltnZP7X5gp1HgMqZ+KTDhpdpzJxpiWoy+lbvOraTqF+bV1ECoLG1l8kFmbKJfrKVquqMnuCja27\nJV7/l7lSEbIAA+5w0r+nm0+Wmmh8nZc61b3EWDVUTWDjTxILM40cyQ1NVMuyyryJdi7kCUycaS2n\n9yzExegb/F3bKdSoppKa6CU+VmP3QYmJsy2VEIYAKi8/4yA1SWP0m9YrJpklxqu0babQubWHaoka\n0RZ9dnf9ViNLV8vknhVJTVSZO7HAL4Ar1zmHR3o7+fOfPIyeZuHICYnAEInObTzUqKZSraru7JAQ\nW+Q1WxK+mVmDwXBNxL1CRLhWnnCcZQy3msOtXgi7miPCNXy5VoRrfn4+ffv2ZfPmzYAeAfvCCy/Q\ns2fPoDjJ8vJ7JV4JgoDTZeDnX01MnG0pFoVaPkyyxs0t3fz9aSeHT4gYJQ2vKvDjTn1GtCLb+d3a\nu3n2QSf/XGhi6erQLKR8HdFuHTzUq64SE6XhVWHjTwZuqKVgNouMm24tU5yXRc1UL++MsfH9j0Zm\nfna5OI+2arRoqNCtnYdaabqo9noFNu7Uxf2x3OD3h8+TddJsCzv3V25qUZZV3pto5/QFgWkfWmh8\nnUKXdgq1UvTOrKLCxp8kFq8MTVS3bOhh8lAH7y4w8e3aill5VYlVad1Y7xB3aefB4YRLBSLf/yjx\n39WXvx6hEh+t8s8pNtZslpj5qZmyBHBivN6p7tbBQ61UfWa2apxuzyWgBD1WkiQk6dqYII0kZ0WI\nECFChEoTExNDTEwMycnJNG3alCFDhnDTTTdV+HhX8k6taOentMQrTRPYe8TE7M8sLFhRlFJVMVQm\nD7GTlgwDno/iaKEYirJotGyk8PA9bmql6jOiLrfAum1GFq+USxWPqYkq74y3sX2PgftGxuBRQq/N\n7rx8Y31ATyeD7nazY4+BVIvGzHE2PF7I3iaxKOiyetmIosrbz9uxmOCvk6JL7TwW2AXWbzWyfmtR\nHTFW/fV4tLeLWim6mBUFPUZ2ebaxwnOxgTzQ00m/2z28OMviH584fT7YjiomSqNVIw+P9HZTK8Wp\ni3svuqgO6BCLosrcF2zYHCL9R8fgcFW8tgt5IkdOiDSv72X6x2YWrDD56/hrbxe1UlWiLRqqBj/u\nNPDf7y+fIS7O432ddO/oYdhr1svmk0vjbLGFOEHQePkZB/d0Fakap8/FGo3Gwp//2ui2lkWk4xoh\nwv8IkY5r+FJWxzU7O5vx48f7F7SeeOKJyx4zZcoUVqxYgcViYfbs2UHpWF6vl65du5KWlsZnn30G\nwOLFi3nttdfYv38/K1eu9FteHT9+nIULFzJnzhwsFgvTp0+nffv25bqkX9qSVOCWc3lPolcSwcdP\nm8krEDl2UmR5lpFv1upb4hXh/tucDLzTzcxPzazcWPasaFyMbgHVpZ2H6skq0VYNmwNWbpT5do2R\nSUMcWM0wfoa1XIEEJVGjmpd3xtnI2mZk+idmvAFjAbHReuetSzuFmoUzok43rN18uRWVj97dXQzu\n5eL1DyxkbavczK7fkzUKvlgmc0trhZop+piBWxH4YbvE4lVyyC4C1aqqzHnBxtotEu/8p/zjGTFW\njRsbKnRr76F2qkrNFH2eedMuiTf/ba5kApnKG6PsxEbDc29aybtCNG60Ve+Yd2nroW4NXcwiwLbd\nBpZ8r/vuVo1Xmf9SAZk/GJnzRdld1tKoV0Nh9gQHrRp7MckCDocDTdMwm83+BK9wmHGNdFwjRIgQ\nIYzxer0888wzLFq0iNTUVLp160bnzp2DYl8zMjLYtWsX69evZ/PmzQwdOpSMjAz//fPmzaNBgwYU\nFBT4b2vcuDEff/wxI0eODHq+goICvvrqK0aPHo3T6WTEiBGsX78+JKFZVuKVb2SgvCfPkkYNAM5d\nNJK1w8S46VFcyBNJSVS5qYWHvz/tILGKnnZ14qzIt2tKT7vy0biewivD7GRuMNJnROhWSJfyRTI3\nyGRuKBK5SVVUJj1lZ0BPN+cvCZhljX88YyPjByPfrpWxO8vvZDBjrB2zDI+/VHIaVF6ByKqNMqsC\nxHaVWD3xauTDDtKSNKwWDZtdYPPPIt06eMjaJtO7krZPoHuyPj3QxZv/trBmsy6AVwa8HrHRKq0b\nKTzZz0X1al5irOBWYP2Wkl0EJg+1USdN46m/ly99LJD8wg7x9j0G/jnZxpotRmZ+aqbp9V4evMtN\nnepOYqwaaLD5Zz2JrKQZ4uL4xgxmfWZmRXbZH2wK7AJZ24xBHwwsJn2WuVdXD+++aMPh1u2zqsZr\ntGzoZdue0hcES0IQNEY97OShXm5qpmhh7ywQEa6hEGazjED41Rxu9UJ41hzhD8eWLVuoW7cutWrV\nAqBPnz6kp6cHCdf09HQGDBgAQJs2bcjLy+P06dMkJyeTk5NDZmYmI0eOZM6cOf7vCezIBpKenk7f\nvn1JSEjg7Nmz1KlTh23bttG2bdsr1vlbJV6V1Lm1OQ38tE9m3PQo9h4uOs2dPCuyMNPEwswiy6M6\n1VVuae1h+hg7VQpjQn89JrJktYn1Ww1EW2HOCwWcuWBg0PgY8m2VO+k3rqfwynA7y9YbeebVqMJO\noW69dFMLD68Mc1A1XsVq1jhxRo+QXfFD6aL6gZ5O7r/DzWv/srBhR/m6ohfyRJZnyyz3CyyVuS/Y\nadNEZf8Rieb1Fb6cVsDFfIHMH6Ryd6rjo1XenWRj1wEDfYbHlLoYllcg8v0mme8DLu/Hxai0aaww\n5AEnNZK9RFt1a6ia1bzM/dLCpNnmcv2sJfF4Xye33eTh+beKEsOytolBIjLKondE+/d0U7e6k+hC\nMbul0O/WJ2ZFUWX2eDsuj1DpMQOHS+DQcQPtH3Pw0VIT8782YZKhyXUKXTt4GDLAS0yUhmSAn38V\n+WaNzKZdJVu31U7Tu6xtmngxm3TrNx/FfVyvlW5rWUSEa4QIESKEMbm5uVSvXt3/dVpaGlu2bCnz\nMbm5uSQnJzNhwgQmT55Mfn5+SM938uRJ2rRpQ1xcHAcPHiQ1NZWTJ0+W+vjfKvGqJMHqVUX2HpKZ\n9qGV9PWhWD4JHM4xcDjHwEdL9FsMBt0Oq2t7F9NG2zl/SUBTYf8RqJ3qLbcNlQ+rWd8qP3/JwKCx\nMf5kKV8dOacFFqwItIMqEtVvP28nIVbDYtI4mCOydLVMzmmBN0Y5WLXBSJ/hZfmUlk3PTi7+NsDF\njI8trPoxWACnJKp0vFFh8hAHVauoxFh1c/7lWUaWZRlL7BCPf9xO0+u9jH6zPOljRVzKF1m5UWbl\nRhlJUnn3RRvnLxmY94WZW9t5+PAf+YXjDgLrthj57/elzxAXJy1J93hdtl6m36hornTp3eYQyN5u\nJDvA3sy3ENfvdjf1ajipkeIlPlpj534DM/5jrpRoBRj2Fwftmin8bUq0/2dyuWHrbmNQUpdR0mh8\nnULnNgqP9XERE6Vbt+07KvLdWpk2jT0M7u2hdurlXdZwEaklERGuoRCOXbVwqznc6oXwrDnCH47y\nzJUW/3r58uUkJSXRvHlz1q9fX67njYmJIS8vr9Qafs8AAUEQOHRC5ot0EzM/swTNdpYXr1egfm2F\n2zoqTJ5rJn2dCZOs0fR6hTtvcTNikJNoq4qm6RvzX2WWvSE+9q92WjZSmDjTWo5EqstFtShqNKrj\nZfZEGyfPirjcAp3bKqQk2Vm8qvSu25VIqqLPim7bI9G3lK7oybMii1bKLFrp+zCgUb2a3iF+dZgu\nZq0mjdxzBnYdEOh5s4ePl5h5ZX7lYmQB+t/upH9PD5PnWtixV3/tMjYEjzu0baow7C8O0pL02V2H\nSygxRhb0MYPaqRqPT4rmbAkjFaHgW4jbstvAey/a2fqzxNR/WWhY10vvbh7q1XQSa9UQRH1W9b+r\nZH9q15VITVSZM7GAJd/LPDjmyoIawKMI7NhrZMfeIjErGTS6tvcwb6KNhHgNq1ks8zjhNjoQEa4R\nIkSIEMakpqaSk5Pj/zonJ4e0tLQrPubEiROkpqaydOlS0tPTycjIwOVykZ+fz1NPPVVi9GvxYzVr\n1oy8vDxyc3NJSUnx3/9bCFbfcUsaNTh93ojLLfLGBxYWrzJWah7zupoKb4yyk7VNn2P1CWCXW2DL\nL0a2/BJ8CblVI4W/9nZRO81b6N0psHazkUWrZM5dFLmltZvRg538e4mJqe9bqKx358P3OLn7Fg+j\nXreypbDz5kvd6tbew+N99QhZg6gHFSxaKV+hQ6zy8jAHNZJVnnk1ipMhpFEVIZBzSmDBchMLlusd\nYpOs8smrNppeJ3A4R+KernqM7PFTIt+tk1m58cozxMVJqqIy70Ub67Yarug+cCFPZEW2HDRPGhwj\nq4tZQdComaIy5/OrM2bQq4uLR3u7mTizyM7rx50iP+4MnlVteoNCry4eRjzkJDZKQxRhx14D/10t\ns3Nf0e9m1EN2WjTy8sRL0ZUITdB4sp+Lx+5zUb0aCELpxwnXuFeICNfQCMdZxnCrOdzqhfCsOcIf\njpYtW3Lw4EGOHj1KSkoKixYtYv78+UGP6dmzJ/Pnz6dv375s2rSJ2NhYqlWrxsSJE5k4cSIAWVlZ\nzJo1q0TRGihC77jjDp544gl69+5Nbm4uhw4domXLlqiqGuQM4ONqzLGWNGqQb5fYtltmzHQrAgKd\n23qYOd5OfIyGyQh7D4ssXHnlpCsfZlnvOtocAo9OjOZiCElQNofAuq1G1gXYPyXEqbRrpvD3p23c\n2EDF6YLDJ0REQcNq1sptsO+jYV2FqSPsfLtGF9SBAljxCuzaL7Frf3BQQdMbFO7q7GH4oMIlI2DT\nLgNfZ8rUqa4yYpCTOV+YWRbSSMWVGXyPk15dLvdkFQSNutX1uNIZY/TfjdmkcShH5Nu1Mms2S6jq\n5a/1i0/ZuL6WytCXyyuodQJjZEVRZdZ4G26PgX8tMnJLaw//fjnfv4i2erOR/66SuZAX2vNEW1Xm\nv2Tjp30SfYZHX/GDksMlsGmXkU27it4jZlmjaX2Fnjd7GPagk8RCX9XzeQIvvBNVYdGakqgy54V8\nWjV0YTZpeDzli3oNp9GBiHCNECFChDBGkiRmzpzJoEGD/HZYDRo04MMPPwRg8ODB9OjRg+zsbDp1\n6oTVamXWrFklHivw5PbNN98wduxYzp8/z4ABA2jWrBkLFiygYcOGDBw4kAEDBpCTk8PHH39c4nLH\nb7V45VFE9hwy8fJ8C2s2F4muQzkGPlys/9tQmHTVrb2HJ+/TbY4EQWPTTomvM4PDAcY/bqd5fS9T\n5lpCupx7Jc5fgts6urGYBO4bEUPuWYG0JI1OLT28MsxOQrxGlFkj57Qu3DJ+KFm4+ZBl3Vc03yYy\naFzoi2Eut8CWn41s+Tm4Q9y5jZv/vGbjcI4+ZvDQ3S7q1fCyKPPyzf1QqJnqZeZYGytK8WTVNIGD\nxw0cPG7g3//VbxNFjetrqnRu46Hf7XbiozVMssaBoyK7Dhjod7ubDxaZmTK3Ysb/gXTv4OaZB528\nMt/Cxp/01+K7dUXvmcR4/YPG2L86SCnszBbYBVb9qCdeFRezD/fSBfpzb1o4eLxi7xWnW2DzLiOb\ndxkZ+5gdowRD/x5NSpKX227y8MxAvTMrGWDXAZH/rjKV4SKg8cR9Lh6/z0H1JCcAqlpyvHHgf777\nw7HjGvFxjRDhf4SIj2v4cq0kZwWiaRoDBw4kKSmJl19+2W9i/lslXoHAweMyH/7Xwj8Xmsq9wCwk\nUgAAIABJREFUjORbqOnR0UOdNC/Vq6nExWjs2ifx3FvWkDtupTHgDicDerp589+WoC7s5WjUq6EL\ntzZNFOJi9KWrfUdE/vu9iQ079DnVoQ84uLWth8lzrBVeCAvkxadsNKitMma61R+FGuwxqxFl0bA7\n4ftNZXUh9VCCKCuMuQqvnUlW+fS1As5eFNE0iIvWMEqw+6DIktXln921mlX+OdnG3sMGXn7PUq6Y\n26QqKu2be7iltUK1qrqYtTmgbnWV79bJV2Xko2aql1njbHy+zMRn35Us0GWjprsItFNoWK/IRWDX\nft3xYutukeQEmDvRRocbvURZBP8HPVVVg/4rC1mWKz3Kc7WJRL5GiBAhIlzDmGtNuObm5vLqq6/y\n6aefoqoqU6dO5aGHHqpUl9V3LiqpU3TijG7ZNGWutdIb2zVTvbz9vJ0tPxt4f6GZ1k0Ubm3jISVR\nDwc4e0EgPUtm2TojTnfZYql+bYXXR+r+rnO+MFdoxtZg0GhQx0vXdh5u7+TxJ0ytyDayaGVoiz2l\n0amFmzGPOfnnVyaWhBAjmxiv0r65wq1tPaRUVbFa4EKewPIsiW/Xytzc0sPQB1y89ZE5qONdUfp2\ndzKol4eX5ljYvqfo5wyc3W16vZfoKA2jAXbuN7B4pcyOfSV3IR/p7eTOP3kYN8PC/pAX4Upn2F8c\ndGimsCBDpmNzheRCMXupQCRzg8S3a2TybKGL6hf/ZqNuDY2Rr5df8MtG3UWgS1uFgXe6kY1QqwTH\ngEBCFbOCIGAyVb7LfbWICNfKEo6zjOFWc7jVC2FXc0S4hi/XknDNysqif//+2O12BEHgkUceYcSI\nESQmJlYqprWkOdYCu8S2PUaGTY2p0KXsQGRZZeY4G5oqMGGmtUSTft+2/J9aeujU0kNCXNFM5tLV\n+kymTyz55mILHAIvzLxyOlIoWM0q704q4OQ5Ay/NtqJ4oVl9he4dPFxfUyXGqqJq8MN2I19llB3b\nGhulMm+SjUPHRabMs+JyV/TPXiMtSeP2Ti6e7Ofm2CkBgwAnzhhIX28kY4OEOwSBX5ykKipzJ9r4\nYYfE2x+HJvhlo+7u0KW9QqO6euqWKMLW3QbWbTUw6iEXGRuMzPm84ulSPmpU8zJ7go2vM2U+WmK6\n7HgpiSodmnv4UytFD7OwaFzMF0v1u62dqvDOOAefLJVZkFFxgVg1Xh8f6djCS0xUxT8kKoqCx+MJ\nukLiu2pyLRARrpUlzAQKEH41h1u9EHY1R4Rr+HItCVebzUa7du1o3bo1x48fJz09HU3TrmpMq9Ml\nsvuwmf98a6JFAy/VEvUozNPnRJauubIhf0kM/4uDm1t5+Pu7Vr+lUqgIgu7r2qWtmxYNvcTGqFRL\n0McMXn7PwqKVld9Qf/4RO62beHlh5pW7hDFWjdZNPHRtp1AzVXcysDthzSaZRQGX9p9/xE7LRl7G\nz7BUMrpUZ+xf9Tng59/2jRlo1E5T+VMrDx2aK8THaljMGkdy9N9PaUtXPsY/bqdxPS/PvRlV6Q8k\nZllj9gsFxERBvk3wBwRs2mVg0SqZX4+V/+d/6SkbtatrjHrDyvlLodankZqo0eFGD51aKiRVUYmy\naly4JCLLGoIGz0yN4lIIi3+l8Ze7XAz7i5Pra1U+/crj8eDxeJAkCVmWr6m4V4gI1wgRIhARruFM\nWcI1Ozub8ePH+5eznnjiicseM2XKFFasWIHFYmH27NlByVher5euXbuSlpbGZ599BuC3xjp8+DB1\n69Zl7ty5REdHc/ToUdq3b0/9+vU5ePAgffv2ZerUqQAYDKEZzZe2eKVpAvuPyry7wMKn3xXvcmnU\nStUN+TveqIsls6yx55ChVPeAW1q7GfWws3CWUKayXbiOLdyMfdTJZ+km9h0W6dHRww21fd1Qgaxt\nEgszy+6G+mjb1MMLTzj4z7cmvlxesfqqxqt0bO6hcxuFpjcoWC3gdsPcL8x8F+K4Q2m0bKgweaid\nj5cGBiOUjCAULl219dCqsUJ8tG6Gv/+IyOJVMht3GmhWX+XlZ+z8e4mJryvRdfTRuJ7C1BEO/r1E\nDjqeL+2qewcPddL0ERCvCj/skFiYKXP8VMnv04Z19bGPDxabWLSy8vXdUEthxlg7GT8YqZWqUjVe\n/wB25qLemQ013rdKrMqcF+x0auklNrrSZQHgdrtRFAWj0YjRaAwr4RpxFYgQIUKEMMbr9fLMM8+w\naNEiUlNT6datG507dw6KfM3IyGDXrl2sX7+ezZs3M3ToUDIyMvz3z5s3jwYNGlBQUOC/bdq0abRr\n145PPvmEGTNm8OabbzJp0iQA6tWrx5o1a3jwwQcZN25cyLWW1mEVRZFjp2SWrtb9Tt2eks5ZAkdz\nDXzyjYFPvtFv8bkH9Ojg4W/9vMRGqSDAzr0GWjfxsH2PzP2jYypxmVynarzK7AkF7DssBR0vMMUo\nxqrRpomHp/o7qZniJcqikW8XWLlRX3QKvHQcG6VfJj9yQqT/6Biclajv3EWRVT8a6d/TzU/7JF6a\nYyUhXuPmlh5eG+UgMU7FYtY4dlIfd1j145W7oaCPVbz7op4aNuC5mJBsvPQPHQb2HzXA1/ptBoNG\nw7peenR08844G2cviLg9Ak3qedl7vVKJpTOVWRMc+oLgmGgK7MH1lZR2FWPVaNXYw2N9XdRO1cWs\n2wPrt0osXiXz/KMOzDI8OKZ4qlnFeHmYjaR4jf7PFXeDKAxvuNHDy8/q8b5RFo0zFwQyfpBJXxec\nRHb/7S5GP+LkhqvQZf2jEBGuoRBml4SB8Ks53OqF8Kw5wh+OLVu2ULduXWrVqgVAnz59SE9PDxKu\n6enpDBgwAIA2bdqQl5fH6dOnSU5OJicnh8zMTEaOHMmcOXP837Ns2TKWLl0KwIABA+jVq5dfuPqI\ni4sjLy+PuLi4MussLUDg/CWJrO0yY6dHlTJ3WjreYh6mkqTnxderqfHTfpk6Nbz8Z2o+BTaBjBIE\nZNmovDHKTnKCxqhpUeSU0qkDyLcLfL9J5vtNRQtLSVVUOrX0MHmoQ790bFExGSEmGv460cqBY5Wf\nKRz2oIObWipBYwY5pwS+WGbii2V611AQdCeDW9t6mDXeTpVYDdmod6uLJ26V5slaEbxegfp1vNza\nVmHIP6LY8ovRP6f651sKPWaj9A8xm3cZWLiy7Ev7Xdu5GTbIyevvW8jaHvrrl28XWLNZDlooi4tR\nebiXk0+m2jh+WsBq0pj9Qj5rNsssLgyRKC8N6+ohFu8uMPHNmpK6toXhDcXifWtUU7mphcIrwxwk\nFHZmjRI0u0ElPlZ31biaRAIIIkSIECHC/wu5ublUr17d/3VaWhpbtmwp8zG5ubkkJyczYcIEJk+e\nTH5+ftD3+IQtQHJyMqdPn/bfd/ToUTp16sTFixdp166dXxSXRGmLV3angZ0HTEyYYeXnXyt/Knqy\nn4PbO3mY+k8LP+4KFjQ+ATllqMO/SHP8pD6PWVoHsm93J4PudvPOf8ys+rFi2/NnLogsXmVi8SqT\nP0Xr429MmE0aIx5yER/rxCxr7DtkYGE5I1ub1Vf4x9N2vloh03/0leNBNU3g12MGfj1m4P2F+m2S\nQaNBXS/dO+iJWymJXhLiIN8Gw1+LYu/hyv1OqsarzJtoY9PPEn2Gx/iXr9wega27jUHdaqtZo2VD\nhQf+7KZedSfRVg2PF7K3SSxaqY9emGWV+ZP1ZbP7RsTgUSonuERR5Y2RdvLtAncOKep6+1K3nn/E\nQbWqKtFWXfSu3CDxzWqZi6Uu4ekfcqKtMPD58nZtBY6fMvDlcgNfLjfRu5uL0YPt1E3TfVmdzmAP\n1mvNuur3JiJcQyEcu2rhVnO41QvhWXOEPxyhnsCKX57XNI3ly5eTlJRE8+bNWb9+/RWfw/c8KSkp\n7Ny5k/j4eB577DFefPFF7rrrLqKjg4fvSptj9aoi+w7LnL1owCBqPNTLyaJVRf6l5cU3J7popUyf\n4cGpUj4CBWRhdf4O5OwJdr9v6M8HRDbsNPBkPzdrN+spVZWJkIWiMYPdByXuGxnjH4PwGfL7L6d3\n8EW2qogCbP5FYsFy+bLlKllWeXeijQt5Ig+OjbnsMnmoKF6Bnw9I/HxA5O3n7Zw8Z+DJyVZqpnrp\n28PN9TWdREdpKApkby/f7K5vmWv4a1ZyTpc992x3CmRtNwZ1UGOiikYv/tTag6pCnk3gcI6BaKvG\nhbyK/166tnMzfJCLv79rDkq1guDULR/JCbpF2At/c5CUoBJlhot5Ait+kPhunUydNJVXh9uZ9Zk5\n6PvKS0yUxsxxNv7UykW01YuqCkFWVoEUDxQor5iNdFwjRIgQIcL/C6mpqeTk5Pi/zsnJIS0t7YqP\nOXHiBKmpqSxdupT09HQyMjJwuVz+hay5c+eSnJzMqVOnqFatGidPniQpKQnQzcplWT85t2jRgs2b\nN3Pw4EGaN2/uPxmWJFgFQeBwrsxXK0y8/bEFr1dAFDUa1Fbp3tHNo/e69IQrNDb8ZGTBitKXaEDv\nos4cX8CBoxIDnospp79rUaLTvxbpt0RbVD55rYA6NTTOXRTp0NxD26YKWdskvsowcepceUW1yj+e\ncVAr9cpjBl6/gCw6HVtM+nLRoLvd1Elz6POYikCBHVKTVMZPj7oqXerbO7kYMsDFW/8u8mTNPSvy\n487LBeSQAU6qV9OdDGwOkVU/SixZFdyBbFxP4dXhDv7zrczU962Vqi3fpo+BPP2Ak4WZMjM/NZMQ\np+lJV485SKmqEmWBS/kCy7N1AVnWGIgsq/zzJRuHcgz0GR4dcjDB6fP6fPDS1UWiNDVR5aYWHjLn\n55F7VsTrhd7d3ESZtQotxd3V2cWEJ1w0rKsiCBI+eVaSB+tvJWbDhYhwDYVwnGUMt5rDrV4Iz5oj\n/OFo2bIlBw8e5OjRo6SkpLBo0SLmz58f9JiePXsyf/58+vbty6ZNm4iNjaVatWpMnDiRiRMnAro/\n66xZs5g7dy4Ad9xxB59//jnDhg3j888/589//jMA586dIz4+HoPB4J+VrV27NnC5YAX9ZHrmvJHV\nW2QmvBPsd6qqArsPGdh9yOK/zWrWaN1Y4fH7XNQqtHzKtwksyzLyzRoZpxumjbKTEKcx6o1ock5X\nzk4J4JmBDjq38fDiLCs/7Ss6LcZEabRt4uHZBx3UqKaPGFzI02v5do1cqjjp2cnF3/q7mPO5meXZ\n5e/AOVwCG34ysqEwprR+bYU3n7OzY6+Ri/kqzz/qIMqicT5PZNk6Y7mFUpVYlXkv2ti530Df4TFX\nFHD5NoHvf5T5/sfgqNQONypM+JuD5AR9HjMuWgVE7h8dxflLoblLXIlxhZZZQ/4R7f/QcO6iQPo6\nmfR1xQWkwpShei0Wsy40v1snsTzb6PeY7dvdyV/udvPCO1dnNCU5QWXwvS5emBlF5gYjvjnVm1sq\nvDbSQZU4lSizRu5ZkfR1cql+t9FWjbefL6BLOw+JVQwUv2IgCAIGgyHIseNqiNlIxzVChAgRIvy/\nIEkSM2fOZNCgQX47rAYNGvDhhx8CMHjwYHr06EF2djadOnXCarUya9asEo8VeBIbPXo0Tz31FDff\nfLPfDgt0661XX30VSZIwm8088MAD/jGBQNEqiiL5NgPb98qMnW4N2U/T7hRYt9UYFJuaUtjd+mZW\nPm5FQBA0du43ULeGl5zTUJERAygaM/hyuYn7Rl4+ZpBvE1j1oxw045qaqHJzKw9TR9hJjNcwmzUO\n5+iZ8geOirwz3s62Xwz0HXFlQRgKkqQyZ4INp1tg4JgSttOTNW5upbsHJMTqQunQCZEl3weHJQQy\n/jE7ja/3MmpaUfRreTl7UeSbNTLfrJG5u7OLv/Z18er7VpITNF4a4iQhTsVi0jiaq0e2luXrGohu\nSeXgk29kXp1fdtc296zI15kyX2f6fkdFtmnTRjlIreolJUl/X/59noXdhyr7QUflnXEOQKP/6EDH\nBX1O9fNlBj5fVjSSUqe6ys0tPbw12k58rIbVrL8u362VMUgaEx53UK+6w38VIxSuhpgNTKoLFLLh\nQMTHNUKE/xEiPq7hy7UUQBDIkiVL+PLLL/F6vXzwwQeAflL1eEX2HDLx2vsWVm6sfCzojfUVJj9t\nJ32dkfe+0g3/69dW6dbBTYsGXmKjNURBY9Muia8yLp8LLY7ui6kv+vz93crFyAqCHtc6+wUb5y+K\naGgIwLbdei37Khg7+lAvB/d29TBlnjUoCrWsWm6opXJrOw+tGirExeizuz/tF9m138Dge9x8tMTE\nV1fBQ7VKrMq7Lxaw9ReJN/6tj34Ur+X6mvoccavGei0mI+w+KLJoVUm+uyozxtoxGmDM21FXxZLq\nr72d3H6zhzFvWTAYBL2WRgrxMRomWWPfEZGlq01kbw9tvrpVIw8vDXHw1kcWVm+qmCOEIGg0vd7L\nB/+wUTVewyK7UFUVWZaRpKvbSyxNzJaELMsVTr77LYj4uEaIECFChKuG0+lk7ty5TJs2DYfDgSRJ\nHDx4kOuuu07vtOZJ2J1wT1c3URaNrO3GClkLxUerzJ5oI+eUyINjYrA5is5lew8b2Hu4aMTAYtJo\n1UjhoV5Fc6E2h0DGhkAbLJWXhzmoWU3l+besHKtgxzGQe7u5GdzLxZS5VtZs1sWMSdZoXl/hvtvc\n1KvhIDZKw+0RWLPZyMKVV7ZZuq6mwrTRdpZnGek7IgZNK8/CjcC+Iwb2HSn6uaItKp+9XkDtVI3T\n50X63eaibw83G36SWLA89IWrQEYPttOqkZcRb5Q+u1uSr6tU6LvbvdB3NyZKj2w9eQYa1fMyZV5U\nUKe9oiRV0eNzM38wcv+oIseFA0eLajUY9A8cXdt5GHyPi5hoDUmEnQdE/rvSxI59gcJaZfYEOy63\nwP2jKue726WtwpSnHVxXU/dlderGAb/JJfvSOrNerxe32+1/jC/5LlyIdFxDIRxnGcOt5nCrF8Ku\n5kjHNXy51jquY8eO5b333gOgfv36zJ8/nxtuuME/QxeIpgmcuSBy5oKBk2dF9hySSF9vZMdeqZSg\nAQCVqcPtVK+m8cJMC0dOVKzH4rPB6txa4caGCkZJ4/wlkbc+Mpd6KT1UaqZ6mTHGRtZWI29/Yi7T\nfSA+Rt9M79beQ0qiitWscfaCwLfrZJZnG1EUmDnOjgCMf8fKxUpEg/oYfI+Tu291M2m2Ncjs3xcd\n26294g9L8In8pd/L5NlKfu6GdRVeG2Hn83SZz9IrH3VrllXen1LAsVMGCuwC9Wro87IeL2Rtk1iU\naSp3JOzowXZaNPQy6o2oci/UyUaNJtcpdO+gUL+Ol9goDatZJS1Z5a2PrPzn24p3qi0mjWmj7dze\nyUPV+CKh6nQ6UVUVk8kUcvJcZdE0DYfDAYDVar3mUrMg0nGNECFChAhXkaeffpotW7bw9NNPs3Dh\nQurXr+8/+RUXroKgkZzgJTnBS5ProFt7eKyPyOkLBk6fEzhxxsCGnyRWbpA5lCPSr4eLB+9yM+sz\nM5kbKjdmcOaCyLbdBh7q5eK7dTIzPjFTJ02la3s3A//sJjZaRTLAlt269VQoc7iiqF/SNhnh8Zei\nQ+4kX8wvbrOkL/Pc2tbDd7PzUVXQgK27DTSo42XjTqiosK6dqjB9rJ0V2UbuG3l51zbfLrB6k8zq\nYmEJN7XwMOmpQssni75Y9N1amcyNBt5+zoGqwV/GXp1kqQd6Oul3u74s9cvB4Nc9NlqlbROFpwc6\nqJ6se6kW2AUyN0gsKUVY105VeGecnQUrTPxlbMUcDdwegW17jGzbY0QUVeZNtHPslMSr78t0be/h\nX1MKiLZqKF49PvbrjNA61n9q5eYfz9ppVFfBYAgekfj/WJIq/pyRGdcyCMuOa4QIfwAiHdfwJZSO\na3Z2NuPHj/cvaD3xxBOXPWbKlCmsWLECi8XC7NmzqV+/vv8+r9dL165dSUtL47PPPgPw22MdPnzY\nv6DlW8R69913+eijjzh27BiffPIJ7dq1QxCEkObkinu8CoLApQIDlwokzCaBVRsllmXJbPhJ4lIF\nO4+SpDJrvA1NE5jwjpXzl0o+jlnWaNFQoUdHD3Wr65evHS7I3CCzeGWwSHqgp5P773Dz2r8sbNhR\n+UvaNVO9zHjexurNRmZ+akYU9dndHh3dNL1en90VBNi008CCFTJHcssS1ipvP28nygpj3rJyIa8y\nXVt9sWj0w3aur6VxKR8kCfYd1hOuyhOWEEjVeJV3X7SxfpvEjE/MIY9CJCeodLzRwy2tlUJhXeQe\n0KG5m9REgZFvXJ1OdacWbsY85uSV9yx+Z4dAYqI0Wjf20K2DQs1CtwmHC9ZsNgYlbplkjddH2Oje\n0UGVGCXoGL6/Fa/Xqz/2d+y4qqqK0+lEEAQsFkvYdVyvunAVBKEm8BGQDJwBPtQ07UPf/RHhGiHC\n/w8R4Rq+lCVcvV4v7dq1Y9GiRaSmptKtWzfmz58fFPuakZHB/Pnz+fLLL9m8eTPjxo0jIyPDf//s\n2bPZsWMHBQUFfPrppwBMmjSJqlWr8uyzzzJjxgwuXrzIpEmT2LNnD0888QQrV67kjjvu4MKFC6xf\nvx6DwXBF4VpaKEGg36R/oUQTOH9J5swFkZNnRXbtl0jPMrJrv1Tmtv6T/RzcdpOHf7xnYdvu8gvM\nqvG6SLq1rUJygkqVWJWq8Rq79ksMedmKolR+M/3tMXaiLDD27dJFNRTN7va4yUPtVC/RVrA7IeMH\nY1D30efJ+uaHFtZuqbyojo9WefclGz/tNTD1X/rylW8utFt7D81u8C3FweZfDHydUXbH+rlH9Mv4\no9+IKvcIwOVo9OjoYexfHew/YiA2WsNs0jh0XHcyWLc1dCcDH6Koi+qzF0UmzbZeYZTlchLi9FGQ\nzm08pCaqJCVoxEVrNKqnb/QXX5IqCZ+YLW5fdbXxer24XC5EUcRsNoedcP0tRgU8wAhN07YLgpAI\n7BIEYaOmabt/g+f6fQizWUYg/GoOt3ohPGuO8Idky5Yt1K1bl1q1agHQp08f0tPTg4Rrenq6P5q1\nTZs2fg/W5ORkcnJyyMzMZOTIkcyZM8f/PcuWLWPp0qUADBgwgF69ejFp0iTS09Pp27cvRqMRs9lM\nnTp12LZtG23atCmxvpIEK3DFE7MoaFSrqlCtKjS9Hrp3gCf7iZy5aODUWZGcMyLrthhZvcnI8VMi\nINCqkcKkp+wsWinTd0TJKVqhcO6iyDdrTCzLMjJ7go38XANjp5vp0NzDzHF24mM0JANs22PgqxXl\ncw64p6uLR+918cYHZtZvK3sUwuG6PFWqarzuXTrpKQc1U72kJmqIosYr8y2s31b5rt2oh+20aeJl\n9LTgBTavV+CXXyV++bVYWEJhXGudNKe+iKbA2s1GFq3UP3hcV1PhrefsfLHMxBsfVC6YQEcf1zCI\ncM+zsf70MFEsdFVo6+GBPwckov0qsniliW17ijsZFNG5jZtRDzuZMs/C5p/LL/zPX9L9WlduMPLq\nMDsdb1RIStAQBLGwtuDxAN8HNN+SlO92r9fr78LC7ydmw4mrLlw1TTsJnCz891lBEDYBaUD4CtcI\nESJEuIbJzc2levXq/q/T0tLYsmVLmY/Jzc0lOTmZCRMmMHnyZPLz84O+xydsAZKTkzl9+jQAJ0+e\n9ItUQRBIS0vj5MmTJdbmO0EHUtGTr8WsUrOalxrJGq00jV6dBS7kGTh3UcLuEqiVCqOn+bb7K3dy\nf7S3k7s6u/n7u0Vd258PSLy/UL/fJGs0q69wXw8319VyEGPVcHkEvt9oZNEq+bLL9KmJKjPH29j4\nk4E+I2Ius48qD+cu6klOzW5QSEkUGDgmCoMBurT1MGu8vdDuCXbtF1mYaWLHvtBO9fVr644GXywz\n8cDzFkJ5DR0ugQ07jEGjE75FtFEP27m1rYLDKXD0pIjLo2GW1XKnSgXSvpmbF550Mu1Di9/FwYeq\nCoVuE0Vi2yhpNL5OoXt7D0Mf8BJjLRy/2GXgqwyZY6dE5r9kJ/e0QN8RMXiUiv9e2jbx8MZoB83r\nq4iiQGmvX/GrDABms7nwZ9A7sl6v1y9wSxOzvisc/0txr/AbL2cJgnA90ATY8Fs+z29OOHbVwq3m\ncKsXwrPmCH9IQj0BFe94aprG8uXLSUpKonnz5qxfv/6Kz1HS85R2EgxlLCCUegNHCErq2ibEqVSN\n9/i/fm+ShzMXDJw+r48YbN+jz8vuOWQoc/Mf9NjSV4bb+XaNkT7DS+/autwCm3cZ2RyQdV8lVqXj\njQrjHnNQLVHfkM89KxAXpaF4BYb8I4rT5ys/g9myoYfJQx18tMTEKwEm/R/kGPhgsf5vyaDR9AaF\n7jd5eOZBJzFWFQ2B7O0SX60IXioSRZV3Ch0NHhxbPOig/FzMF8mzQZPrVcbPiGLVjxJpSRqdWnp4\nbaSDqvF6QMGREyJL14QWUCBJKvMm2jh/SeS+kTG4QrSk8igCO/Ya2bG36PdkNWu0aKDw8rMOqsZr\nOF1glAQe7e1iYabeJS4PkkHjlWF2enVRqFa1YtZSvo5s8c5sST6sJYnZ8sS9XmtjAeXlNxOugiBE\nA5+jjw3YfqvniRAhQoT/dVJTU8nJyfF/nZOTQ1pa2hUfc+LECVJTU1m6dCnp6elkZGTgcrn8C1lz\n584lOTmZU6dOUa1aNU6ePElSUtJlx5JlmZycHFJSUoLEZUUFa0kCGAi5aysZNFITFVITodn1Kt3b\nawwZYODcRSOnzokcO2lg9SY9metkwJylWVaZO9HGpQKRQRXcnL+QJ/LdOpnvCiNJ7+jk4umBLlZt\nlLiulsrbY2zIEuw6ILJguemybfqykGWVdyfqM5gDngtMbbocxSuwfY+R7XuKBFu0VY+wHTLASfVq\nXmIsuo9qWrKXCTOjWFlJFwdfje+9aOPEmWCBeeKMwIIVJhas0C2lfAEFXdp5uP92vUtslPQu8dcr\nTewM6BLf3snFkP4upsy1sKUCM8vFcSsaT97vYP8RiYfGW1C8AnExupPBiIccpCVrRFuLqw7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+0kJcAjE6O5kFey4LM59A18n7csQEqiys0tPbw6zEHVKvp86q/HRJZ8b+SR3k5OnZPoO+Lq+NtW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\nW4Au0KOrpjfNetML+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- "text": [ - "" - ] - } - ], - "prompt_number": 3 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Alternatively, if the two priors are $\\text{Exp}(3)$ and $\\text{Exp}(10)$, then the space is all positive numbers on the 2-D plane, and the surface induced by the priors looks like a water fall that starts at the point (0,0) and flows over the positive numbers. \n", - "\n", - "The plots below visualize this. The more dark red the color, the more prior probability is assigned to that location. Conversely, areas with darker blue represent that our priors assign very low probability to that location. " - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "figsize(12.5, 5)\n", - "fig = plt.figure()\n", - "plt.subplot(121)\n", - "\n", - "exp_x = stats.expon.pdf(x, scale=3)\n", - "exp_y = stats.expon.pdf(x, scale=10)\n", - "M = np.dot(exp_x[:, None], exp_y[None, :])\n", - "CS = plt.contour(X, Y, M)\n", - "im = plt.imshow(M, interpolation='none', origin='lower',\n", - " cmap=jet, extent=(0, 5, 0, 5))\n", - "#plt.xlabel(\"prior on $p_1$\")\n", - "#plt.ylabel(\"prior on $p_2$\")\n", - "plt.title(\"$Exp(3), Exp(10)$ prior landscape\")\n", - "\n", - "ax = fig.add_subplot(122, projection='3d')\n", - "ax.plot_surface(X, Y, M, cmap=jet)\n", - "ax.view_init(azim=390)\n", - "plt.title(\"$Exp(3), Exp(10)$ prior landscape; \\nalternate view\")\n" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "metadata": {}, - "output_type": "pyout", - "prompt_number": 4, - "text": [ - "" - ] - }, - { - "metadata": {}, - "output_type": "display_data", - "png": 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iZux8GzfZsc3OEat9pJQII4mmRJhVMjBz//kx37RpR9KrV6/Mqd83YXbu3Nm4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\nWbdQKCqNri2H5ieCkRvmEmm1HLlhrilbLTcH4hJfTdPcwO8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urpznaRN3/JjK7vyvMoeP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- "text": [ - "" - ] - } - ], - "prompt_number": 4 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "These are simple examples in 2D space, where our brains can understand surfaces well. In practice, spaces and surfaces generated by our priors can be much higher dimensional. \n", - "\n", - "If these surfaces describe our *prior distributions* on the unknowns, what happens to our space after we incorporate our observed data $X$? The data $X$ does not change the space, but it changes the surface of the space by *pulling and stretching the fabric of the prior surface* to reflect where the true parameters likely live. More data means more pulling and stretching, and our original shape becomes mangled or insignificant compared to the newly formed shape. Less data, and our original shape is more present. Regardless, the resulting surface describes the *posterior distribution*. \n", - "\n", - "Again I must stress that it is, unfortunately, impossible to visualize this in large dimensions. For two dimensions, the data essentially *pushes up* the original surface to make *tall mountains*. The tendency of the observed data to *push up* the posterior probability in certain areas is checked by the prior probability distribution, so that lower prior probability means more resistance. Thus in the double-exponential prior case above, a mountain (or multiple mountains) that might erupt near the (0,0) corner would be much higher than mountains that erupt closer to (5,5), since there is more resistance (low prior probability) near (5,5). The peak reflects the posterior probability of where the true parameters are likely to be found. Importantly, if the prior has assigned a probability of 0, then no posterior probability will be assigned there. \n", - "\n", - "Suppose the priors mentioned above represent different parameters $\\lambda$ of two Poisson distributions. We observe a few data points and visualize the new landscape: " - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "# create the observed data\n", - "\n", - "# sample size of data we observe, trying varying this (keep it less than 100 ;)\n", - "N = 1\n", - "\n", - "# the true parameters, but of course we do not see these values...\n", - "lambda_1_true = 1\n", - "lambda_2_true = 3\n", - "\n", - "#...we see the data generated, dependent on the above two values.\n", - "data = np.concatenate([\n", - " stats.poisson.rvs(lambda_1_true, size=(N, 1)),\n", - " stats.poisson.rvs(lambda_2_true, size=(N, 1))\n", - "], axis=1)\n", - "print \"observed (2-dimensional,sample size = %d):\" % N, data\n", - "\n", - "# plotting details.\n", - "x = y = np.linspace(.01, 5, 100)\n", - "likelihood_x = np.array([stats.poisson.pmf(data[:, 0], _x)\n", - " for _x in x]).prod(axis=1)\n", - "likelihood_y = np.array([stats.poisson.pmf(data[:, 1], _y)\n", - " for _y in y]).prod(axis=1)\n", - "L = np.dot(likelihood_x[:, None], likelihood_y[None, :])\n" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "observed (2-dimensional,sample size = 1): [[2 2]]\n" - ] - } - ], - "prompt_number": 24 - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "figsize(12.5, 12)\n", - "# matplotlib heavy lifting below, beware!\n", - "plt.subplot(221)\n", - "uni_x = stats.uniform.pdf(x, loc=0, scale=5)\n", - "uni_y = stats.uniform.pdf(x, loc=0, scale=5)\n", - "M = np.dot(uni_x[:, None], uni_y[None, :])\n", - "im = plt.imshow(M, interpolation='none', origin='lower',\n", - " cmap=jet, vmax=1, vmin=-.15, extent=(0, 5, 0, 5))\n", - "plt.scatter(lambda_2_true, lambda_1_true, c=\"k\", s=50, edgecolor=\"none\")\n", - "plt.xlim(0, 5)\n", - "plt.ylim(0, 5)\n", - "plt.title(\"Landscape formed by Uniform priors on $p_1, p_2$.\")\n", - "\n", - "plt.subplot(223)\n", - "plt.contour(x, y, M * L)\n", - "im = plt.imshow(M * L, interpolation='none', origin='lower',\n", - " cmap=jet, extent=(0, 5, 0, 5))\n", - "plt.title(\"Landscape warped by %d data observation;\\n Uniform priors on $p_1, p_2$.\" % N)\n", - "plt.scatter(lambda_2_true, lambda_1_true, c=\"k\", s=50, edgecolor=\"none\")\n", - "plt.xlim(0, 5)\n", - "plt.ylim(0, 5)\n", - "\n", - "plt.subplot(222)\n", - "exp_x = stats.expon.pdf(x, loc=0, scale=3)\n", - "exp_y = stats.expon.pdf(x, loc=0, scale=10)\n", - "M = np.dot(exp_x[:, None], exp_y[None, :])\n", - "\n", - "plt.contour(x, y, M)\n", - "im = plt.imshow(M, interpolation='none', origin='lower',\n", - " cmap=jet, extent=(0, 5, 0, 5))\n", - "plt.scatter(lambda_2_true, lambda_1_true, c=\"k\", s=50, edgecolor=\"none\")\n", - "plt.xlim(0, 5)\n", - "plt.ylim(0, 5)\n", - "plt.title(\"Landscape formed by Exponential priors on $p_1, p_2$.\")\n", - "\n", - "plt.subplot(224)\n", - "# This is the likelihood times prior, that results in the posterior.\n", - "plt.contour(x, y, M * L)\n", - "im = plt.imshow(M * L, interpolation='none', origin='lower',\n", - " cmap=jet, extent=(0, 5, 0, 5))\n", - "\n", - "plt.scatter(lambda_2_true, lambda_1_true, c=\"k\", s=50, edgecolor=\"none\")\n", - "plt.title(\"Landscape warped by %d data observation;\\n Exponential priors on \\\n", - "$p_1, p_2$.\" % N)\n", - "plt.xlim(0, 5)\n", - "plt.ylim(0, 5)\n" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "metadata": {}, - "output_type": "display_data", - "png": 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EEuLQv6gpHu6Ee2VIlW/HkD7LgYw+E/f4fRfxS9bipzym5JyK8HbDo5BxZQ2A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QQZsL2CJFMECRt8DLlZIyYheNC4w+goFhgPgnoX1A8ZSiUFxIaPs5f9JRLvOYQmUGyI540m\nK2snuXL9Ady1M0yrnRv4Xc8LkWnYpE0Wlyx1StSYoMYEJj5TbHGMJWbYSPVKjxEb3HkaFKlTpEaJ\nVifffQILnxxN8rQw8TsJdNocnaHdC893WKqeZHXzONXGFPH/YFkek1PrTE+vkss1j1yJZSCsIFr9\nPyTxys0hnO+zDJxMa4y7FfOIEb7Ejka4EVW9iniMdzDCCxNVbKeN386wvHWC41M3d/h+gwm2WGeW\nJgXWmGF2Ny1EAMOgOWmhqgGZVmSNxvKFe7XLC0h/dQ/JoKOODGSDaN07aWzSXx5Wl1Tsl31Zv+aY\nFh1L1i6zsyfdRozrQrTk6Ta2D1NeLs4/YYrYAAjtpFUyCJ3oHz+gbDQK2IyyJMdOnhxNTIJDc6Ip\nBesb89y6dZogtDGMkLkTN7Cm3dFJwnMT4X9vIffqWZKk6J9AHKARrtNLBhn96cOf3rTZ2mfqMeBd\nCN+FlmaE61MguuSr7u3OIfJQt5Cg/TeAh0idOmzZiad9Rasyf2KV6cwSGzePsfTIf0njygaLpy7S\ntvsn39EDNvX9egBmvot2IiQJHwuFSYDNOrOsM4uMqlvkaDFBjQwuBul0FN1gz/ZOqfYp60jbf7KM\nFtqUIJ2asjsFRaevpNXvpaMEmLTJ0KCAR4Y2Dh4Zto+sFBZ+lJzDxyLAJ4MXLWkBnzpFJFs+14m7\nup1gz932x+fxA4u1reNsbU1Tr08m/4sRki/VKExXyZXqtI0sNYrUKKYGVkLPFKP+WWuARAvnysmD\nfzvTgiHyoLyFBN7EOIXIDcbjijX2Ri8ZpE6vd6XfZ2P++T4iLflaGgVxARmhLe1OfYoZgx8g3rOu\ntj9pzDfnp3Gmm/jLGS4tP4gz2cIw0gPfpS0NUVhc5gwtsmSia9TbwrNl6UIAgjigfFpxT/MWpU0x\ndtQcBBnJbeDodAk9MFOnROr/g07X1f//OAO0WHviFa9F9WMaSCwDu48ozyKGfY5uI7uETEbHDDbd\nmkhL1pNGNRmWmqKVvbzkxjD9pOVXBjTyGRqFDIFjDUQj0dvyxXK+c493qx8b3zqtUehNPiEmNc0I\n2UuSnd3quK0cN2+cod2MRB+KLQoLG4QOtBra9+pURD0A89GfTWyn/aKg6OUQsbneRn60KeDzCE34\nAIIuB6YmHjHuME84SN7aLHAD/BWwt2er3BEFpOF+G3gZaftP7HhEX5RmN7GzbdavLlCrTfPBxcex\nTp1nprQ/gZUGCgefAo3I2MwigoMZXPK45NlkBpOALC4F6h2G82GK/h80FESEnQx1irQ7hnM2lXdu\n4WPj4+BFQxi/Qy8ZRbheluXqAlvVGWr1SRLXkSJfrFGa2qQ4sTX62t4xthDD+0ckjauDqF48QGJE\njVhjOMZRInZp39qxFiCddwYxGHbJseNMNHHXi7TbOTY255mZXtn5AC2JwSrHOM6twWYeDYNWwcHL\nWEyst3D8EMs9oARjBmIAx7ZdPHhUJMZ4HBTpkSRgixOuqZ5zxcnV9CUOBnWQPjNuenqboBHQcNYz\nhga2QTtv4mUNGs7BUj9UNOtap9Tpi0wCcjTxcA6tD/Z9i/WVBTbW5gED0/KZPrGMKoaj4/1eReyt\nWCnoUcQBOgI5QY4ad0ivrsNG3Ghvgfsm2D87/CnuRTwJlxBaylm4HRZCrtjk5OU/YPWBX6XZLPHu\n5Z/gxPRVzi68v68Pl0VIPkoGE2DikqNFDpcsPg5NCl2jZKFatKKQw2YUBiKcNGsf3CTfr2zxZHmA\n5Ba7QLo7izYOLfIdY9sl1ym3+3q2BQYhGdqRwR37wduRN1yQ5p0fFtcqH+yYHXUYKAVbzWmWaydY\nr87RcHUOqqJY3GJicp2JiQ0C+whf0bcq8NnyYHV9RMP7HbqnSaYQCbmHGCfZGWMHxPPRN+QF2cl6\nMBGv8AdI9skvpFc1DMjO1mguTXPr1iKTE+s7ts3yrSEOHm2yLHOcY10ag/D9SpUny/1544FtsjGf\nZ3alLt7ZAOlbYi71QUJXU4G9JV/RfqPKZSjft4dz7RdiqolNV5eggNCWpTm5P+3l+co6T6TIwsQB\nlxtMoaIfSpxhzU48kX8Io5MwNFlePcHS6j2EoQUoijMbTB1fxbRCGsGQNMXXK/BMeX8v0kMCL88j\nN6qAZMA8yfaU9p9QHFIPnzY1mTZN2dta6cS3SSTC8i1ovgXhT4Nhp6uj6J4SfcrrSWR0tgr8W+Dn\n6WPrJTtafqJ7e8tPfraCM0Hx7Brmqk99eZKbG4ssVU+wePwj5qZvYRjpFJQ0DXBd/7t7urSbOFug\ngYOLwsQgJIwoGgE2dUqdlLg6zE6NmNARYuNFVI1kMVCRB1lhRK6TeH2DJaY4jop+HxXV8rGjspwh\nPluA3SkL+9okjNbdqiT9oDpnQju7Hz26PjYtsujzk3vRGU+jo6zSwIgMhWGPbVDA8xxq9Uk2azM0\n6hOEmni6YYRkSg1yEw2ypQa+4dDGZpV52nWNyqJreA9CM4G9RZevIfy93v3x66mAKwi16wMSj5yJ\n8FjvRxycAeKh61VOOAiqSdr+MR1lRJDW5k8i73AdGmtgRdlg0tr1ReSZex9pw+PXXGvvN1ciFRQF\nmXyTdjPP5aX7mDiZtME6jU9vX49zC4MQH4cbnIqS+opVu8o6N5AZ2L5tgQGNYxvYvs/MVp2C2wYb\nlIMMHiypY+jqKPUBymnPtpuyf5+McEJkAhq2Wwy682pYOspuNBUFvi0DGSPo7p5D06CVtWnlHDay\nE51BW5oq1bDUj1Xq3IimyOM6HjZVJqO+p0N8wSCkGUUY7XbevdBO4j5FKYOl9ZNsrswTRLaIU2xS\nWtjAC2y2WuIg6+ovatqsQC1FAWuT/vTDYakiNZK+4TskAfgPIM4YhyTYeJjz7hcFZcQCP+9ATzgI\nqfQkcEO44dZnhj9FBhmRfR1pzL+NKKYMe5qyHFSY32KmtMLKzZO0GkUu33iQlfUTnDr+MaVi7cCm\nhWQ2Mex0JpJ9PiTA6gSHiLltdfaFqUKEgyFbvp+P9nzlMeSKjIj9bnbKYniHGEl0exdv/HAxX350\nqPp+YFNtTLFVn2ajPovrdnslHMclN1EnX6qRKzRpm1rDOCpxt3EWtF6sI4b3hagcYxZpaEdDRn2M\nOwoGYllfAO9qYoSnYRbhklYRb/hDO5965uQSty6eob4+zdbkFJPFzR0OkKux8fBxUJgss8A8Szj4\nPFYejALp2zbLs1PMN9fINkLstqQGVwEyUDXZd/72QaD82O519g3xbxJRZmzN7xSa4GVN/KxBNVfU\nZkv2v3ONM1yGGJFkQg6/41hRWHiE0ffqfw8SYWiwuTHH6uoCnicGdibXJL+wRaYo/b9X34NJ92R5\nH64Scd58jyR51QziN51lPBPaB3eoEW4ATwN/Bv6rYH6a23oJJpGpzFcQ7XAT+IXbv6pMzuXkvZeo\nb02yfus4jdYEH1x+nFv5Rc4e+4CZ4sqBv6sSEK8w8QG/y7tjRoEiYeSKCaKyispK84XH3u14ATrr\n5LsSD3nvovvC5ZrEJ45Wjg1ug3TvtbpDSGNtP8NK4xhbjRk2GzPUWxPoN9swAorFKvlSnUJxi0y2\nPVJKLLtCN7yXtf15Eg+HPvEybmzHGBqxEf4x5HZxrBjIYO8HSNu9kxEOOLk2E/NrVFfm+PDap3j8\nvu/h2L0CANu/IjbEA2yWOMEMa3RHV+6OIGPSyJiYnqK46YtsXog4gmIda4ftegR3O2Ill1hiMean\na5z10BRefWhBc8JODO8DJDsLtV643g0KXcGWMfXRRHV5rw8SfmCxunaC5bUTBIE4a5yMy/TxZfIT\ntb0lZNtPbCLv4nvRtgM8gcyIHqZCzh2GIzbCB4mgB2j0Kd8PTIBaAvc9qD2cVBmEjhL/5xnEA/4a\n4g0HidjthXZ5XivhQy9rqb2b0/nOuWceuE5jbZL66jTV5jTnL3+OTLbJ8dkbzEytYJrhnuko2ZSp\nVN3PnaaUkq6I0t9HbhN0jO6PKpc5V5ZQfX8AI3kQ5ZP9Uk3p/UynhaQlBHK7OOT9U96vVN5lovyk\n1FdZ2u0cjUaJanOSZqOI1+5N8aXIFJpkCw3Moo+TdzFMaLsZ2syAC65GKWlrU4dDJ8/ZKfJ7L1N+\nr1VAlUXLVbc7HIRucgaRGYwbWD3mbb9oJHuhnew0BdnvmDEd5YCQZl32tvmnpdj+qH8Cpd52fQZp\nx68hQcAn6X4GS8k7uVKaQ2XAyHh47Sw/vvZpTpz5GMtI2kFbaxO7Y0kU86ygMFljnh9WVnmiPI1B\nOqVAV8HYsCJajAUTuSpWEDDRbDLZqGMHSv6HSVH0CGywFJ13ytCfybRy2vO/l+lOzTKofB/KT2/f\nD6Snrdf2qyydgNDAFGqJGWz3RynAcyyamQytjIObcXBNneKRlNtdVJP+iWuGoaMoJF18rJh1qXKZ\nezve8JgIaVPXaI9pyXN6r2OQJDv9rrXtZlhZO0ljYxKl5IGwcy6F+S0CE5pGlmYjm554LY12kkYv\neaMCT5R3rtOvXEc83x+QSF2eQwbGim61n2EpJQdBTRwxB9Ed6gmHRGDyr4Fvgnro9kfH8fR5bIiH\n7BjsMwhMU1Ga36Qwu0W4lmV97RhtN8/VG/dxY+k0M1MrnJy6SjFXHZ0I5jG2QSnxctcaE1SXztBo\nTlBvThCE3a+OYYRk8w1yhQb5QgOj4GOaMmjpHSSMLELEoPkIMbyvkvAzHcRGuhcxvONOdsT4dWPc\nyTgB5EBtQLgO5i7J2GzEeX4J+D67ag0bBmRma3jLEzTrJdZuLbCwcGuA9tfAiEwxhYlLlnVmu+J7\nhkFgWWyUSgRFheWHZFs++YaHGYLunB+d9GxDovf3bCe79FYzNEXNJHAM6rk8nmOBYRyailWsvNWK\nZAy61bZiWdvg0NLLg/Q3tdokm+tzNGqJsy9brJObr+EURAJTl6U9MlSRQPwLyGyOAdyH+Efjn2zE\nDN5RxB1shINk+vgmcA3aP4LscLzdLuiG+OsIr+lX2V01ZZcMU6apmJpfZnpuherWFNXVORqtEitr\nJ1lZO0k+U2ducolTk5cpZu8Mgzz2gt9tUAoa7QJ1d4Jaa5Kt5jT1VgkvyMLZ57q8bLbdppCvkSk0\nyecbZPNNQqO/B36k0UAa0YuIMaM3mrNlUQ46CxwjMbzHDesYBwITGeVdAP99yDyz+yGnkcHiFWQA\neXbn6oalWFi8yo2P72VzbZ5r1lkWj13a9WtiQh4EnCsv4ke5GwJM5lnp8qIPDMMQDWvHgkyAESgs\nD0n6E2d61PuDHInEYMydDqM6B6APHqP8NEnSnzgm0dQWPSlQH3QYJib4DihT6CXtQuKp9Q5JfjWI\ndLvrFGhQ7MqcbBBGKlttHiifwjjE4BzXzbG2eYy1jWP4vvQdhhFSmKpSmtvAybYP3pkTe8F3wwoy\n6H2fZKR4GvgMooY1Vj0ZCkdghA9CQelNA+anfDYH/BTw51D7G2g/JEopOgXFTin3Qx4J1vw2MrXy\n+4hqyiTp0zm1ZA6uNq2XtenIUkIpmbhvjUyzirtZxN0s0GwXubpyjqsr53Acl+LEFjPFVUrFLUwz\nTKWcyPbuCXp0eomdQkcZNllPGgaRA9wvCkpafeg2gPvRVpQC18/hujlaboGGW8Rt5Wi7OVQfYV/D\nDLDzHnbOxcm3MTIBph1gGNBqZWipDDSmu6LRAz85z0D0kv2K/O41kHvrhYgU80eI8bLcU79EkjZ7\ngoRqogdgjgLVZC/1045pMMaBIy1ZT9yuR0Z4+wK0n0mnFurlh4F3ER3iB0meWY0e0col6lbVxYDs\nfBV3ZYIry/dRNwtMz3XzvHsNHt07O89KJ8x9i2m2mMLGZ5PJTmZEPUFbmiJWV7K2bLI/O9UGpcgE\nPpPtKhnfJ+P5OJ6kb4uys6VCGclCvIaOkdwrE97ZGZ06rmCEYKhU23obQsPAt0x828K1HDzbwrNt\n6naR0JSbkkYjTEtolkbZGCRhmvC5RUGrTilS5rL0/zr6t40o03Kx89le6C5ST1dpyfTdXwtKNKoT\n1DamcBvJftPxyUw2cCaaeJ7DZmsCWtDSE+voili1lMRrt6NqklZHIYGW5+mW8l9EYoKyyOu8ssP5\n4WAUTsZ0lKPGU8Abwg0PXgV7Z8/0rjgF/AwSrLkK/BHwAhLd2681erMCT5WH+gon7+HkNzi2cJ1W\nvUhja4JmtYjnZdlYO8bG2jEZBeerTBU2KBU2KeW3yIxIjOLNygVOlB/eveIRIwhNGu0irXaeVjtP\n3S3htvO4bn4bnSSGZXtkci2yuRZmzieTa2E5PrWX3uwo4QTBiNyIQaCQ5/gKYnhfoztFvIkkrFpE\neN667XGhAveWD+UyxxhDcB/S0F5CesveWIs+eBB5tuMkUU/tfohTdEGBuzrJ2q0ToAyOzw1CTYEr\nlUucLp8jRJGjFalNOSyxQJFal6F92zAM2rZD3c51VApt5WOGCjsIyPptrCDEDBR2EGKGCiNQYjRH\ny37hG6/BT34JlGkQWCbKNAijsm9ZBJYpZTNpU3XDMzzEqDwFeDi0yFGnRJtMjwxuInlrENIiR9Kx\nJzf/euV9TpUfZL8Rhgb12iRbWzNUq9MdrrdhhGQn6xSmq/iWmTyHhxmse6ECD5e797lIvMUFJPAS\nxGo8h4yXY7riiBm2dxLuAiPcBL4C/D/gvwzmw4hVsQdMIob495G+4D8Dl4Gfozt17h5hGJAv1cmX\n6jjKpdUs0qhN0KwVabaK1BtT1BtJbuNcps5EbotivkoxW2U6u0bGdu8ICstBIFQGrpej4U3Q8nK0\nvDytdkEMby+P56dP31mmTzbbJJttYuc8Mtkm2WwL7OTHvGMoJTp0o/tytPTaBFOIwX0PwqPVn59x\nYzrGkSKP9O6XkDT2A1jUFvBpZAbzm4iBsAudHMApuUw411m5eYq1pQU+cEPuP3kB0xyM16EwyOIS\nYOLjEGJRY5IaE7TIMcM6+W2zunuAYRBaBm3LhExiZXfNdvq+GOAh2H4g3u24auzh7vof6NoZe88D\n2xJvugnVWYPNhVbwqV0AACAASURBVFjutttk2K9kaLeLAJMG+SgtnSxhzzV158bwu5K5HYa0YBCa\nbNVm2NiaZ7M2GyXWEWQLDUpTm1iTLUxL7kbgHrHaiQJuAD9GaIrx41VAvN73M068to8YISN80GQ9\nejm2Lk4APwF8D9r/Hqq/JbQUGI6O0vvVn0YMlndIHsgngWdIpjyPl2VaH7qnSDVqSqukl5PewdRo\nKplcRC3JQnaqhh3UCVoZlGfhNbL4rQytdpFWu8jyVhKBZJo+TrZNLtMkk3FxMi45p4XjuNi2h23s\nTk3RMRAFpXw/H+5SJa1xTlNT0Rt3X1kEgY3vO7h+Ft938H2Htp/B9xwC38HzMlGigp0aUYWV8aPF\nw3CCzrbn2RgGeBg0/Tz4efDpJD+AnoQ4587Cx1FZp5QcRJKZYY4NEO/2rWi5yXaVjxySNGcW4XYX\ntONXd/i+Yrl/8ob9UinZC6Vkr3SUeDvcAP/HoC7wwzfvh3/AGPuCQW5EWrv+acQIfxtqmhGeRk1Z\nQWZwjiNpsf8M+Duktv01jiUbi8vkjm3SWplkZfMkW+40x05fw3W6B+A63WCmPNFJCpvQThQzrEcJ\n0IhoKtOAirIWu1gEQ6tg6fv1tlmnInbRDG2t/dZ8EIO062lt9vGy1VGd622/06iDw6pSpSU6c3vq\nixlt45LtJHzr7QNiiokXJYlTHarJzt+r3+Og/ABXOvvT6S799gNU/Qma1RKNaolmvSijmQhW1sMp\ntgidAMMOqZOldVMbNaYlX9tPekm/cr4MLyF2jq5oMoeMixeQWdStPscOSo8cNSrjCGCEjPC94meR\np2cJWn8L+dtIZ98LAwn0OY5wDq8jGaA+QLjj9+79K9JgWgqz6JLJSoOsFJgtkbLzosV3M4Shjdu0\ncZv9Rs8Kx27j2B623cax29iWh235ZKw2luVhWwGm6WOZAaYZ4hhtTDPENMKhPexKgVImoTLxQodQ\nmYShRRiaBKFFGFq0wwxBKEZ2ENgEoY0fGdx+4OBH+wfzUCgs28N2PCxH1nbGQ2UUluNjOT6hoXUS\nGo3EGLEXcWDUEEP7erReYntynzwyLl1APIKxZPnYcwEqhPAqeO9D+J7Q2CJ8/HHAgb7UYwyIR4G/\nBC5DsAbW7G4HCB5A3o8VhJYyYPy4XWiTP7FOe2WCdivPjYvnyJzwmZ5cGaINNKLsDCax4R3zj5sU\naFLAwsclQy4yysdIR4CJR4YGeXwcvGjpL2wYm92qq06v1/4goRS0mgVq9UnqtUmazYRfDgon3yI3\nUYdciOlIg61L1B4Z2ohz6UOkT4mnRnJIU3iWu8pKHEXcRT9vBvgl4P8C9zWwFiGzB7UUHQWEnnIF\neAPxHv4pYuScrcBXygefhMeATN4lk08ab0e1CQIbz82g2hbtdhavncHzZAkCB8/P7kjL2BkKwwgx\njCgJTxS1E37nJczPl8XojiJ/QhWHyO8HlAwQbF+MbNvHtjxMx5ey42HYoayN7R6cA5G4eu0l+OIL\n+3/endBEZllukhje/SLPp5BncQGYJzG6YW+G9/UKnCrv4QQjgnALvA8h+AD8i3T/KBkwHgDjYX76\ny/cC3z2iixwjQRYxxN+G5utQ+rnBDnOALyFZkH+EKDY8OdihVibg5LlLrF4/SbNW4qNrjzC1tcrp\nExfJON0G83LlRxwrf2qHsxnYBCgCFAYWIW0yBNgRXWWS2FDP0yBPkwzu7SmsHALerNR4qlzaveKQ\nEP52BpcsDYq0ydCOtnspJTGEVuIjEoJhJCGoB0XuT0e8WnmHufLj6deuwG3nqNYnqdWnqNanCPU4\nIyMkX6yTn6hhTbidGYrmUVNNQAzvS4gz8TKJE6dZEU74fYjzJu7O70bnjWpDcH33eoeAQzLC0+YC\n0igovTy6tGlLvZxHosu+DHwdGv8BGhN0EkAMekk7TdtkEP3wW0hWqFuI8/094BGkwY+ZCmlJgkpJ\nIxHmkimyVkkr6/VzWoSN3e2+NXOaIoodyN20wbJdHFxsBRYKFZio0AQFKjRRgVYOTVRgJJ8rAxUm\nofVKWajeIJ/QIQwc+kNhmEJENIyobEZlS7iWhhlimLJtmArDDMWYN0MMKyQIk8CUEGkz2jgEEWVE\naCOa+ojf02Dr03m+1ijvhdpwzYYPnJ3r3C7tQiHqI6vRshKt+xncDjCNNJIzCMVEp7Bu0T2VuBcq\nyBr9G+KDoIjs5zlVG9THEF5EXDy9EjCzSDTfg8BZScmnIOuMvZMHgzRFFP3GNXrq/ATwNrTeBO8F\nMPLdGVlzKeVFxH5/F/ib6FQ7eMRrrYSa0jhRkIQ+RReaDpvVOTZrMxTmqpycu4xpxS/aR9QiLcQ0\nFZQJ7eUVSonCwadAo0NZiT3kANc4HWl0hDh4UZ2APK2OWalTSnRP+iBKVzr0OoNwui+xQi6Ks+qt\nn6ZSJQGRoDBpd2ghJj52JzOz6qTI3I7Yt+13TG2TFvlOkOWwVJZh1VfWqVKN7rFLFqXA9xw2G9O0\n63na9Tyh320+GXaAlWtj59u4gY1rGLjtCcJrc0mlQZKvDUsjGaS8iTh0riLOHL3PmEUEKVokE4Fr\nQ55/0CRph5mUbVu/EEm8BG8iHGMfyTVztLiLPOExvog8QW8CX4Pgn4A1v3+nt5BMUPchEfnvl8WA\neg3JGvUo8ClAn406IhgGmHYIjrxxOl+wizuowbKS/UoBykiM8Fjr6qEHgKudiB/DoLtMuoJI0Gsw\n99kfjmKWis+W9+c8PnQyXy+RGN394rcsxOCeRQzuKRIv92FILs2XD+jE+wzlCcUkvATBJaSn0XuZ\nDDKvej/CWRiQ3jDGEeIE0sheBPU6GEPMQi0i78SHiGzhT0enGwCGAeR8pk+tUL81jbtVpLEyxaX1\nR5iZX2JqZo2p8oDu9e4zdygVQplQ5LUX14gSAUkyoKRbrjHZMcht/I40YoAZlYNI7ePgGs1HymKA\nS7xnrC1iEmBFvGsxlCU41Yyuqj9feztkllVXUGl3PFndiXvUvs207o7CC5+j2czTbBapNSZpNYoE\nfrfjybACnIKLXXDBCjGdpM1p147YtFKII/Aq4u2+Sbc25TwSmD9PMohtlQ/xAg8RagPCdyD8Ad0O\nmcWjuqIu3IVGuAH8ApLO6X2o/QGU/qv9NcRBfrkHSWKILiD3961omQceQzzko3Gvh0ZsXHerqo4x\nENoknu0lxNBeQRrGfj9jBrEN50g83FN0ywneqTz2/YZqg39VDO7gshjgXR5AA3npziGG9yIM4PEb\nY9TwReAihK+B8TmGkqa6H7nl7wEvIu9XOrtgGywnYHJxFa9RpXZrBr+ZZeXWPawtL3Bs9gbHZm6Q\ncdq7nygV3cZpjmZHPE+MUjG9VUfXw8bbIVlLYhrHfmPVMc6NaKHje06MRdUx341OzTDit6uesw5m\nVG+/Lv0sQMcP7mF3ztaty3643iulwPVybDRnaTaLNJolGq1SRz4whmn6OEWXTKFJptgitI2O06k9\nKvzuj0hUsfQZUQMZiJ5GYtw6hvdhXuAhItwC/4cQvAvqqvZBEXgCoS0cRxqHo8URG+Fp1JRecUzd\nTag/Wfrl66PUCUTm4N+CugTVfwX8Q7qs4UGmNmopZX1adKMCi2Uxxn3k4b+GGFwvRcsUMiW6iEz3\nxPZA2pRqV1lrkOzukXiYS7Z1Opo3iCLMsKoxOl6vwDPlweunGY+D7B+2vNfj08rvVhIN1fgZCRGj\neguZ7tPLdfrDQJ6fyWg9EZX1mKNWdI7NAa9tp+m/vUzhrVVgsrxznYOmoPiAqoK6AuFlJDDjBttH\nMieQlysWsO3Vl+6t36/tGU1O7p0Dvd1OS6udlpStXxs/jVjTH0LwDdj4e0mVtPZSb8vOkvBf/xx5\ndB6n+9Zr7XpYS4z85Q3N4FdgTTUIGxlCz+bWX3zIrWdewCm2mJ5dJV+qYRjpSXnyKSooaYoo3UnY\n3MgcD3HwOwatFZnKiYEdC/HtPz6uXOLe8llAD4E0Is+41THcY+93iIkXecWJKCUxeikryf7hkvik\nKbHsdqxkRS7itbK0W1ncVgG/6aDCnkH66xWMZ5/HcHwRNrEDlKVw3QxuLQO1qXRqSe/2IPSSQSmx\nejkkkaO9GZX1CUAHcQbOI46dflRZ/ZzXKrBQvr3r3CsdZT/6EbUJwY8QadMrWgUHoS88gcyExoOr\n0XAq3oWe8BgZJO/8v0Pyq/4BtH8ZMjsF1OwR09HyOPKgX0bshU0k09R55Bc/hUwFxbI/d/FduOPR\nRu7fdcSw3kLoJFvIZEuapLBJYmAXo/UkYjDE7f0IyyYdGZQP4U0Ir0UUkyskWSJiGIjAeRy+f4Z0\no2+MOxcGkgPi94E3IXgarCFyQBhINs0cIjH7A4Q6+F8wUA4g/TxmzsfM+YRtC/IuAeDV8yzXFzEt\nn8JkFWPCoFisYuxnphyMyBNOV7Bit9ysH19mxPdWnW2B6nihd4Lu6db/AxeHRvSD+dt0wvtLFKYF\nVh4WlAI/sHHdHK6bp9Eq0nZztFu5bR5uEGqJlfU6izdbxVqQdqetxRgdqdkWG903SAL29TGtgRjb\nx6MlT/IQ3I39i1KibhW+B+GPkU46hoVQFR5DDHB9pmI0jO8Yd7n5Fxvifw68CY0/guBZyP00+zY9\nvVjevs8kSf0dIsZb7CFfJ5kuei26jOMkiVMWovIo35lhvOCjjPjerCEGda83exNtVF7uf44CMtMx\nSWJ0TyIN4G5BjaOO2At+UFAhhKsQXAPvuqzDm2wf2WTBWAS1SDKlNALTv2McAo4h6YrfgMafQum/\nBmPItvtepI19DXGQ/QFi258d/mrMTMDEVx8n9G/ibhXwNnP47Sy19Rlq6zOYZkCxuMVccZnJ0jpZ\np3UI7IrEcNaDHfump98BaYbzYvmBPV3dQSJUBs22JGlruXnq7Qla7i5ZkR0PJ+vi5FyMfIida2Pa\nAV5by/L5wpcO619IRxt5Xq9Hyw22kwQmkGc7VsfSm85hqSaxF3yUodpCQ/Teg+B9upkRDmJ4fypa\n364q3OFihEy9ndRRdBqGfslVdscEwhGfBV4E91VwP4TmL4N5XKroD2sppZxGR8kNsD+HcH3nkNZw\nFTH2NqJ/4Ua0xDARQ24quuzpaHuG7ucqjVIySJkB9u8X9kJHSdu/kxe5jdzThrZuIAZ3s6e826DY\nRAztfLQuIPcz3taPbyGJcpYHvNaDVg05jO8emFISAisQxA97vPTLyzyPGNr3ICTGY1GyC/3H3om+\n1u8ieuv0e8gOL/Dr7scgyleDlD3geeA9eXY2K8CXh0+8No/QQH+M9Nv/Dnm0vkRCNe9NAKRfxfRk\np7ymlZnywPQgMCGEMLCoVmeoViX5imEFZItNnHwLJ+9SzNUwTXmO0+goupc727W/vwrKIEnY9oI0\nOkkvgq56Or1Ep53095yn0VECLMLAxG87NL0CQdvG9xw8V6hBoSda7H1hKLBCWQzAUmCGBO0sgWfT\n8oqwrB27X1SR2zlXE7EFVhDVtTXECdTbP+VJcj9MI31RfM6l27ju/VIiGeTY2znGVyQydB/QrakI\n8vI+iEx53U93wzCIKtPRY4SM8IOEgUjRnAb+BLgF7f8T7DJYX2BPP8NKZTgViSyJlzyHGIwbJB7Z\nDcTgj430j/scP0HCKy6S0B1iI7HEwXpf3q3AY+UD/AINAfKy6kZ1XG727G9qnw+KLN1Gdo7kd8xG\niwFcrMCZshzzSaGRtCqQKw9/nGpBeEsWdROCtKxCICPNU8g00GK0HoYrMMbdjxzwi8C/AV5BZkMe\nHP40eeCzSDsb00b/GPgMMms9KN6owNNlKQsHBKwQp9QUuVfXxggNgmYGFVi0tkq0tsRDs4bCybpk\nci6FbI1stkUm08LOeJj7SmPZP6xXzjNTfmLfz6sUhKGJ52doezm8KDOy6+XxPUeMba8PX7v7LJi2\nj+kEmBmfEDCcANMOaLczidRtiipXKt6swFPl2/vHdoNCDO7riNG9HK1743wNpHmcQ5xxRQ42oHKj\nAtPlAzjxkFAbEsunLiLGd2+A1T0It/shpL/QjZ3RfId2wifECI9xBvht4K+BN8F/UTQj3b8DmUcY\nOkXkfiBDd7QyyHO0iXhs6lq5inhaXbZ5arpgIB1OTltno3I2+s4MMsHgRPsijXGsaG32LIZ27jpo\n2ZplCkxBRFyUJYgWP7reuOxpixut2z1LK1q73L6RG//v8dLrwY5/D4vBvLljbIfyIViBYBmCW+Av\nQbgkATJ9MYM0miei9UmGUrwY4xOMMwgl7BvAH4P36+DcM/xpYp74IhKjcw2Rln0HeBqRJ9/DGNCw\nFEbBo1BqiJHpWZg+eM0sXlOyHHtuDs/NUWdKO1KRcVwyjks20yTjuDh2m4JdJ+O0caw2Wbs1soY6\niFEtGZAd3CCLHzh4gUPLz0k2ZN+hHWQlO7Lv4PkOSu1uHBtGiJ1pYzoBVsbHcjyULQo2puMTaka6\nnoXyKLrzbQhIjOxlEqWsfikJ8ojBrcvS6rgblUyUArUO/scQfiz5HdRGT6UJxMt9PyJbOgIJj/YR\nR2CE69MCg/ImGjt8Nsz3xcFbX0YEvf8K1ApU/wjxkj8P1QeSt3cg2klZgiR66wwSvT9InYloATEY\nPRLaQ1tb62WfhIJxIChLVunDgIH8Ho622D37LK0cDy76BaTEA4Je434g+ktZZsP6nfOwyqnXtkP9\nPX13WdaqDazIu6JWQC0jPcoa/T0PNsLljYmKJ6J1r3UTj8pgsOnCYeuk0VR6j4/r3V2N++gg7b6l\nKaX08jxjPIdYMOdh898Av4k8Zymn303p6gTiAPkw+spXgG8j9v5jdMvJT2vlUlmMdoBScn2eVt4s\naZQV/bGPmRYKsALJvRAaoKDt5Wh7OWoN3TjvhhElNDOsEDMqm1aYJEDTEqWZpi9J0qJMx4nDUJjj\nXeGbUaI2kHWobGGQKQP12AuoWwYokyAwITSiRG8GYSBrFcr+4adgJZlb51JMBaFJh9oeiFyi5+e6\n7+FeKBKD7C+Uhbo0aP0mSeD+JhL7tYk4zvo1kQ5iR8QKWbFjKD5vPVoO4v9MrVOWYM+B6w9ZBvAD\nhF4SK11dZntWuhxJ0P19CJdMT44Re/H6fcmwfcTR4xPmCddxP+IV/x5QQR6IP4T2AthfAvNTjNzP\nY5B4sSF93GIixriHjMR177NP4rGOywHbvdi6h7uTrKfP9cTrOGt9vNYXS1t3pm/p9rzHxrZuYNvR\nd/Zr18ce6/2FCkFtQbAaGdqrEEbrLqNIh4G4bo7RbXTP0s2vHl3v3Rh3EgxE2qSFKF7938A/Rizp\n20TscYwTmywhM+AXkUf6PsQemE47wZDQ28xsEkVnZNtixAYmlhWgfMlmbISGZDzWjF0VmuCNqKCm\nEcpsgKllQ46M6yQzsgwWfM/WnCWaR9zX2o7dRV0OFz7SHG4g48E4mH+T9BtSQAztKWTibwKxM3Vv\n+N3ah6kqqGui1a2uIlNPvf9sAXnJzpBIxo2WjOBBYsSszMOGBTyDkAK/B7wG6hZ4/x4ogPkk5J4C\na4cMe9UKTJQP4VqHgIm85DkOJhjzU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- "text": [ - "" - ] - } - ], - "prompt_number": 25 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "The plot on the left is the deformed landscape with the $\\text{Uniform}(0,5)$ priors, and the plot on the right is the deformed landscape with the exponential priors. Notice that the posterior landscapes look different from one another, though the data observed is identical in both cases. The reason is as follows. Notice the exponential-prior landscape, bottom right figure, puts very little *posterior* weight on values in the upper right corner of the figure: this is because *the prior does not put much weight there*. On the other hand, the uniform-prior landscape is happy to put posterior weight in the upper-right corner, as the prior puts more weight there. \n", - "\n", - "Notice also the highest-point, corresponding to the darkest red, is biased towards (0,0) in the exponential case, which is the result from the exponential prior putting more prior weight in the (0,0) corner.\n", - "\n", - "The black dot represents the true parameters. Even with 1 sample point, the mountains attempts to contain the true parameter. Of course, inference with a sample size of 1 is incredibly naive, and choosing such a small sample size was only illustrative. \n", - "\n", - "It's a great exercise to try changing the sample size to other values (try 2,5,10,100?...) and observing how our \"mountain\" posterior changes. " - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### Exploring the landscape using the MCMC\n", - "\n", - "We should explore the deformed posterior space generated by our prior surface and observed data to find the posterior mountain. However, we cannot naively search the space: any computer scientist will tell you that traversing $N$-dimensional space is exponentially difficult in $N$: the size of the space quickly blows-up as we increase $N$ (see [the curse of dimensionality](http://en.wikipedia.org/wiki/Curse_of_dimensionality)). What hope do we have to find these hidden mountains? The idea behind MCMC is to perform an intelligent search of the space. To say \"search\" implies we are looking for a particular point, which is perhaps not an accurate as we are really looking for a broad mountain. \n", - "\n", - "Recall that MCMC returns *samples* from the posterior distribution, not the distribution itself. Stretching our mountainous analogy to its limit, MCMC performs a task similar to repeatedly asking \"How likely is this pebble I found to be from the mountain I am searching for?\", and completes its task by returning thousands of accepted pebbles in hopes of reconstructing the original mountain. In MCMC and PyMC lingo, the returned sequence of \"pebbles\" are the samples, cumulatively called the *traces*. \n", - "\n", - "When I say MCMC intelligently searches, I really am saying MCMC will *hopefully* converge towards the areas of high posterior probability. MCMC does this by exploring nearby positions and moving into areas with higher probability. Again, perhaps \"converge\" is not an accurate term to describe MCMC's progression. Converging usually implies moving towards a point in space, but MCMC moves towards a *broader area* in the space and randomly walks in that area, picking up samples from that area.\n", - "\n", - "####Why Thousands of Samples?\n", - "\n", - "At first, returning thousands of samples to the user might sound like being an inefficient way to describe the posterior distributions. I would argue that this is extremely efficient. Consider the alternative possibilities:\n", - "\n", - "1. Returning a mathematical formula for the \"mountain ranges\" would involve describing a N-dimensional surface with arbitrary peaks and valleys.\n", - "2. Returning the \"peak\" of the landscape, while mathematically possible and a sensible thing to do as the highest point corresponds to most probable estimate of the unknowns, ignores the shape of the landscape, which we have previously argued is very important in determining posterior confidence in unknowns. \n", - "\n", - "Besides computational reasons, likely the strongest reason for returning samples is that we can easily use *The Law of Large Numbers* to solve otherwise intractable problems. I postpone this discussion for the next chapter. With the thousands of samples, we can reconstruct the posterior surface by organizing them in a histogram. \n", - "\n", - "\n", - "### Algorithms to perform MCMC\n", - "\n", - "There is a large family of algorithms that perform MCMC. Most of these algorithms can be expressed at a high level as follows: (Mathematical details can be found in the appendix.)\n", - "\n", - "1. Start at current position.\n", - "2. Propose moving to a new position (investigate a pebble near you).\n", - "3. Accept/Reject the new position based on the position's adherence to the data and prior distributions (ask if the pebble likely came from the mountain).\n", - "4. 1. If you accept: Move to the new position. Return to Step 1.\n", - " 2. Else: Do not move to new position. Return to Step 1. \n", - "5. After a large number of iterations, return all accepted positions.\n", - "\n", - "This way we move in the general direction towards the regions where the posterior distributions exist, and collect samples sparingly on the journey. Once we reach the posterior distribution, we can easily collect samples as they likely all belong to the posterior distribution. \n", - "\n", - "If the current position of the MCMC algorithm is in an area of extremely low probability, which is often the case when the algorithm begins (typically at a random location in the space), the algorithm will move in positions *that are likely not from the posterior* but better than everything else nearby. Thus the first moves of the algorithm are not reflective of the posterior.\n", - "\n", - "In the above algorithm's pseudocode, notice that only the current position matters (new positions are investigated only near the current position). We can describe this property as *memorylessness*, i.e. the algorithm does not care *how* it arrived at its current position, only that it is there. \n", - "\n", - "### Other approximation solutions to the posterior\n", - "Besides MCMC, there are other procedures available for determining the posterior distributions. A Laplace approximation is an approximation of the posterior using simple functions. A more advanced method is [Variational Bayes](http://en.wikipedia.org/wiki/Variational_Bayesian_methods). All three methods, Laplace Approximations, Variational Bayes, and classical MCMC have their pros and cons. We will only focus on MCMC in this book. That being said, my friend Imri Sofar likes to classify MCMC algorithms as either \"they suck\", or \"they really suck\". He classifies the particular flavour of MCMC used by PyMC as just *sucks* ;)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "##### Example: Unsupervised Clustering using a Mixture Model\n", - "\n", - "\n", - "Suppose we are given the following dataset:\n" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "figsize(12.5, 4)\n", - "data = np.loadtxt(\"data/mixture_data.csv\", delimiter=\",\")\n", - "\n", - "plt.hist(data, bins=20, color=\"k\", histtype=\"stepfilled\", alpha=0.8)\n", - "plt.title(\"Histogram of the dataset\")\n", - "plt.ylim([0, None])\n", - "print data[:10], \"...\"\n" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "[ 115.85679142 152.26153716 178.87449059 162.93500815 107.02820697\n", - " 105.19141146 118.38288501 125.3769803 102.88054011 206.71326136] ...\n" - ] - }, - { - "metadata": {}, - "output_type": "display_data", - "png": 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- "text": [ - "" - ] - } - ], - "prompt_number": 37 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "What does the data suggest? It appears the data has a bimodal form, that is, it appears to have two peaks, one near 120 and the other near 200. Perhaps there are *two clusters* within this dataset. \n", - "\n", - "This dataset is a good example of the data-generation modeling technique from last chapter. We can propose *how* the data might have been created. I suggest the following data generation algorithm: \n", - "\n", - "1. For each data point, choose cluster 1 with probability $p$, else choose cluster 2. \n", - "2. Draw a random variate from a Normal distribution with parameters $\\mu_i$ and $\\sigma_i$ where $i$ was chosen in step 1.\n", - "3. Repeat.\n", - "\n", - "This algorithm would create a similar effect as the observed dataset, so we choose this as our model. Of course, we do not know $p$ or the parameters of the Normal distributions. Hence we must infer, or *learn*, these unknowns.\n", - "\n", - "Denote the Normal distributions $\\text{Nor}_0$ and $\\text{Nor}_1$ (having variables' index start at 0 is just Pythonic). Both currently have unknown mean and standard deviation, denoted $\\mu_i$ and $\\sigma_i, \\; i =0,1$ respectively. A specific data point can be from either $\\text{Nor}_0$ or $\\text{Nor}_1$, and we assume that the data point is assigned to $\\text{Nor}_0$ with probability $p$.\n", - "\n", - "\n", - "An appropriate way to assign data points to clusters is to use a PyMC `Categorical` stochastic variable. Its parameter is a $k$-length array of probabilities that must sum to one and its `value` attribute is a integer between 0 and $k-1$ randomly chosen according to the crafted array of probabilities. (In our case $k=2$) *A priori*, we do not know what the probability of assignment to cluster 1 is, so we create a uniform variable over 0,1 to model this. Call this `p`. Thus the probability array we enter into the `Categorical` variable is `[p, 1-p]`." - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "import pymc as pm\n", - "\n", - "p = pm.Uniform(\"p\", 0, 1)\n", - "\n", - "assignment = pm.Categorical(\"assignment\", [p, 1 - p], size=data.shape[0])\n", - "print \"prior assignment, with p = %.2f:\" % p.value\n", - "print assignment.value[:10], \"...\"\n" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "prior assignment, with p = 0.31:\n", - "[1 1 0 0 0 0 1 1 1 1] ...\n" - ] - } - ], - "prompt_number": 38 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Looking at the above dataset, I would guess that the standard deviations of the two Normals are different. To maintain ignorance of what the standard deviations might be, we will initially model them as uniform on 0 to 100. Really we are talking about $\\tau$, the *precision* of the Normal distribution, but it is easier to think in terms of standard deviation. Our PyMC code will need to transform our standard deviation into precision by the relation:\n", - "\n", - "$$ \\tau = \\frac{1}{\\sigma^2} $$\n", - "\n", - "In PyMC, we can do this in one step by writing:\n", - "\n", - " taus = 1.0/pm.Uniform( \"stds\", 0, 100, size= 2)**2 \n", - "\n", - "Notice that we specified `size=2`: we are modeling both $\\tau$s as a single PyMC variable. Note that this does not induce a necessary relationship between the two $\\tau$s, it is simply for succinctness.\n", - "\n", - "We also need to specify priors on the centers of the clusters. The centers are really the $\\mu$ parameters in this Normal distributions. Their priors can be modeled by a Normal distribution. Looking at the data, I have an idea where the two centers might be — I would guess somewhere around 120 and 190 respectively, though I am not very confident in these eyeballed estimates. Hence I will set $\\mu_0 = 120, \\mu_1 = 190$ and $\\sigma_{0,1} = 10$ (recall we enter the $\\tau$ parameter, so enter $1/\\sigma^2 = 0.01$ in the PyMC variable.)" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "taus = 1.0 / pm.Uniform(\"stds\", 0, 100, size=2) ** 2\n", - "centers = pm.Normal(\"centers\", [120, 190], [0.01, 0.01], size=2)\n", - "\n", - "\"\"\"\n", - "The below deterministic functions map an assignment, in this case 0 or 1,\n", - "to a set of parameters, located in the (1,2) arrays `taus` and `centers`.\n", - "\"\"\"\n", - "\n", - "@pm.deterministic\n", - "def center_i(assignment=assignment, centers=centers):\n", - " return centers[assignment]\n", - "\n", - "@pm.deterministic\n", - "def tau_i(assignment=assignment, taus=taus):\n", - " return taus[assignment]\n", - "\n", - "print \"Random assignments: \", assignment.value[:4], \"...\"\n", - "print \"Assigned center: \", center_i.value[:4], \"...\"\n", - "print \"Assigned precision: \", tau_i.value[:4], \"...\"\n" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "Random assignments: [1 1 0 0] ...\n", - "Assigned center: [ 174.74278858 174.74278858 126.25164007 126.25164007] ...\n", - "Assigned precision: [ 0.00034557 0.00034557 0.00012237 0.00012237] ...\n" - ] - } - ], - "prompt_number": 40 - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "# and to combine it with the observations:\n", - "observations = pm.Normal(\"obs\", center_i, tau_i, value=data, observed=True)\n", - "\n", - "# below we create a model class\n", - "model = pm.Model([p, assignment, observations, taus, centers])\n" - ], - "language": "python", - "metadata": {}, - "outputs": [], - "prompt_number": 41 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "PyMC has an MCMC class, `MCMC` in the main namespace of PyMC, that implements the MCMC exploring algorithm. We initialize it by passing in a `Model` instance:\n", - "\n", - " mcmc = pm.MCMC( model )\n", - "\n", - "The method for asking the `MCMC` to explore the space is `sample( iterations )`, where `iterations` is the number of steps you wish the algorithm to perform. We try 50000 steps below:" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "mcmc = pm.MCMC(model)\n", - "mcmc.sample(50000)\n" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "output_type": "stream", - "stream": "stdout", - "text": [ - " \r", - "[****************100%******************] 50000 of 50000 complete" - ] - }, - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "\n" - ] - } - ], - "prompt_number": 42 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Below I plot the paths, or \"traces\", the unknown parameters (centers, precisions, and $p$) have taken thus far. The traces can be retrieved using the `trace` method in the `MCMC` object created, which accepts the assigned PyMC variable `name`. For example, `mcmc.trace(\"centers\")` will retrieve a `Trace` object that can be indexed (using `[:]` or `.gettrace()` to retrieve all traces, or fancy-indexing like `[1000:]`)." - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "figsize(12.5, 9)\n", - "plt.subplot(311)\n", - "lw = 1\n", - "center_trace = mcmc.trace(\"centers\")[:]\n", - "\n", - "# for pretty colors later in the book.\n", - "colors = [\"#348ABD\", \"#A60628\"] \\\n", - "if center_trace[-1, 0] > center_trace[-1, 1] \\\n", - " else [\"#A60628\", \"#348ABD\"]\n", - "\n", - "plt.plot(center_trace[:, 0], label=\"trace of center 0\", c=colors[0], lw=lw)\n", - "plt.plot(center_trace[:, 1], label=\"trace of center 1\", c=colors[1], lw=lw)\n", - "plt.title(\"Traces of unknown parameters\")\n", - "leg = plt.legend(loc=\"upper right\")\n", - "leg.get_frame().set_alpha(0.7)\n", - "\n", - "plt.subplot(312)\n", - "std_trace = mcmc.trace(\"stds\")[:]\n", - "plt.plot(std_trace[:, 0], label=\"trace of standard deviation of cluster 0\",\n", - " c=colors[0], lw=lw)\n", - "plt.plot(std_trace[:, 1], label=\"trace of standard deviation of cluster 1\",\n", - " c=colors[1], lw=lw)\n", - "plt.legend(loc=\"upper left\")\n", - "\n", - "plt.subplot(313)\n", - "p_trace = mcmc.trace(\"p\")[:]\n", - "plt.plot(p_trace, label=\"$p$: frequency of assignment to cluster 0\",\n", - " color=\"#467821\", lw=lw)\n", - "plt.xlabel(\"Steps\")\n", - "plt.ylim(0, 1)\n", - "plt.legend()\n" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "metadata": {}, - "output_type": "display_data", - "png": 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L9npkcgJjE1M0NOh+RrXNEly43Tr60pWTuWmmUwrlESW5tBEDHc3a3UZOCCQy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\neX1Wr16N4OBgjBkzBgEBAfjoo4+gVCrh6emJn3/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okvP159dtXeDp14X1hDuV3lVdTreH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Sz/2RwJJvnnswBavDs+hyehnJRacUeCoaWmnu++XsKq2O9V10vtI2ytinQBAEWiRSVDe2olUi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- "text": [ - "" - ] - } - ], - "prompt_number": 47 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Notice the following characteristics:\n", - "\n", - "1. The traces converges, not to a single point, but to a *distribution* of possible points. This is *convergence* in an MCMC algorithm.\n", - "2. Inference using the first few thousand points is a bad idea, as they are unrelated to the final distribution we are interested in. Thus is it a good idea to discard those samples before using the samples for inference. We call this period before converge the *burn-in period*.\n", - "3. The traces appear as a random \"walk\" around the space, that is, the paths exhibit correlation with previous positions. This is both good and bad. We will always have correlation between current positions and the previous positions, but too much of it means we are not exploring the space well. This will be detailed in the Diagnostics section later in this chapter.\n", - "\n", - "\n", - "To achieve further convergence, we will perform more MCMC steps. Starting the MCMC again after it has already been called does not mean starting the entire algorithm over. In the pseudo-code algorithm of MCMC above, the only position that matters is the current position (new positions are investigated near the current position), implicitly stored in PyMC variables' `value` attribute. Thus it is fine to halt an MCMC algorithm and inspect its progress, with the intention of starting it up again later. The `value` attributes are not overwritten. \n", - "\n", - "We will sample the MCMC one hundred thousand more times and visualize the progress below:" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "mcmc.sample(100000)\n" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "output_type": "stream", - "stream": "stdout", - "text": [ - " \r", - "[****************100%******************] 100000 of 100000 complete" - ] - }, - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "\n" - ] - } - ], - "prompt_number": 48 - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "figsize(12.5, 4)\n", - "center_trace = mcmc.trace(\"centers\", chain=1)[:]\n", - "prev_center_trace = mcmc.trace(\"centers\", chain=0)[:]\n", - "\n", - "x = np.arange(50000)\n", - "plt.plot(x, prev_center_trace[:, 0], label=\"previous trace of center 0\",\n", - " lw=lw, alpha=0.4, c=colors[1])\n", - "plt.plot(x, prev_center_trace[:, 1], label=\"previous trace of center 1\",\n", - " lw=lw, alpha=0.4, c=colors[0])\n", - "\n", - "x = np.arange(50000, 150000)\n", - "plt.plot(x, center_trace[:, 0], label=\"new trace of center 0\", lw=lw, c=\"#348ABD\")\n", - "plt.plot(x, center_trace[:, 1], label=\"new trace of center 1\", lw=lw, c=\"#A60628\")\n", - "\n", - "plt.title(\"Traces of unknown center parameters\")\n", - "leg = plt.legend(loc=\"upper right\")\n", - "leg.get_frame().set_alpha(0.8)\n", - "plt.xlabel(\"Steps\")\n" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "metadata": {}, - "output_type": "display_data", - "png": 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SzpURFxdH8+bNy6SnpKSQl5fHgAEDpDQhhJ50x8rKSu9amZqaVuhMR0dHk5CQ\ngLOzs5Sm0Wjo1auXtF30kVcR5ubmepKtrKwszM3NKz3m30Z23h8zfHx8HoueoLjfj0q/s66HSL+V\nCckUxCeTE3KHeu1bYlBi4lFuWBTmLR1rrU6Pi20fRmTb1i6yfWsP2ba1R3Z2drV732NjY6XfMTEx\n2NnZSdulJSwODg5s2LCBp59+utyy3Nzc+PLLL3nmmWdQKpX06dOnTB5ra2uMjY2JioqSesBjYmIk\nx9DMzIy8vDwpf2Jiot7xAwcOZODAgSiVSj799FPmzJkj6epLUtJpLUnJNimVSqZNm8aWLVsYMWIE\nhoaGTJkyBSEE+bGJ2NvYcDswCFX/dAAK4pNQ1TWmadOm1K1bl9u3b5eZtAkgtAKtUomhqa532s7O\nrkx7S9q5Mpo2bUpAQECZdGtra0xNTfH19a12WRXZAXTX1snJCT8/vwrzVzW5t127dly/fp2uXbsC\ncOPGDb0PnIcBWfMu81ChyVdSmFPx8FTK6b+ggtn1aRcCEBVMtJGRkZGReTwRQvDDDz8QFxdHeno6\nX331lSTPKI9p06bx6aefEhMTA+h6f48eLe4wcnV1JTo6Gg8PjwonXxoaGvLCCy+wYsUKcnJyiI6O\nZvPmzYwbNw6ATp064evrS0xMDFlZWaxdu1aqa4SvP3/u3Udubi7GxsaYmZmV6zwD2NjYEBUVVUaW\nUnJbpVKhUqmwtrbGwMCAEydO4O3tjValRpWSxvgRo/jd8wgXAvzRarXEJyQQGnwTOzs7end7kg/m\nziPW928KC5TcDrkl6dfV6Znk3AqXzjNmzBhWr15NamoqqamprFy5kvHjx1do55KMHTuW06dPs3//\nfgoLC0lLS+PGjRsYGBgwZcoUFi1aREqKTnoVFxenp1GvDBsbGyIjI6Xt7t27U69ePdavX09+fj4a\njYagoCAuX75cxm4V8fLLL7Np0ybi4+OJi4tj06ZNTJgwoVr1+beQnffHjKIeIE2BkphfD923clPO\n+pFzO7LqjDWkMCdXbxJq3N5jxO87UaMy1Fk5xRu1uGyB3LtWe8i2rV1k+9Yesm1rj5po3seOHYub\nmxvdunWjRYsWvPfee3r7SzJjxgyGDRuGm5sbjo6ODB06VK9XuE6dOjz33HOcPXu2zITGkmV98cUX\nmJmZ0a1bN0aMGMG4ceOkiCf9+/fnxRdfpE+fPgwaNIihQ4eiUCjIC4+hsCCfTRs24uLiQsuWLfH1\n9eWLT1eiWQUUAAAgAElEQVQAoFUXSp1QWnUho0aMBKBly5aSZrt0PSwsLPDw8ODVV1+lRYsW7N27\nl+HDh6NOzwSgc7v2rHx/EZ98vZ7Oo4Yy4d1ZpCYnoUxOY/UHSynIzGLItMm0atOaV6ZOJTExEaHR\nSvXQKFUIIZg3bx5dunShT58+9OnThy5dukja8vLsXBIHBwd2797N119/TcuWLenXrx+BgYGALqZ6\nixYtGDJkCE5OTowZM4awsLBqlTt58mRCQkJwdnZm6tSpGBgY8Ouvv3L9+nW6detG69ateffddyUZ\nTHV63qdNm8awYcPo3bs3ffr0YdiwYQ9VmEiQF2l6bFGlpJN49AzNprxwX8qL/nk/APU7t8ey071p\nzbVKFaqMLNIvXsV+9CCpXFPHJjTq97TeeaqD/YuuKJPSSDvvj+2I/iQeOU3TCc/pSWnKIz86HpMm\nNigq6OmQKZ/C3DyST5zH/gXXqjPLyMg8NjzsizR16dKF9evX07dv3wddFQl1Vg6FWTmYOuhLQTKv\nBku/6z/RBk1eAQojQ3JuhVOvjbPU012nYQNUaRlSvqL3lTo7FyNzMxQGOge0MK8AZUIy5i2aUZqS\n56oJlp3bk3k1GGMrS+kDwLRZE+o0tLyn8mqKVqNBqNSSXOdh5UEu0iT3vD+iCK0WZXJamfTSMYfV\nmWXj5KqzcihIvLfIAFlXg0k67kP0z/spzM2jMDev6oOA/JgEYncfQZmQQmGWfp3yo+LQFhbWuC7x\n+06Qdt4foLj3XqOt8gMg5fRf5EXG1fh8//V4zgkHvLg6o+wqc/eD/7ptaxvZvrWHbNvao7px3h9G\nVKkZqFLT0ap17zah1aLO1peEZt24Re6dYkmMMiW9+Pi7jjtAXlTxJNi8O1F671B1eiaF2Tlo8gvQ\nFCirXb98UbHEtMjpL3LcAbRqNaDTy2cHh+mPeN9FaLXkxxZr+wsSU/RG1nPDYyhIqNr3UMYl6cl1\nZMoiO++PKHkRsSR5nq1wf9HDIOGgFwAFcUnSvjQff5KPl33hVFcvrrzr+MfvPU783uM66UslAzgF\ncUmkeF/US8uPSdBzsmN/PfSPZDm5YVG6cnYfAZAemPmxiRTEJ1OYm0fSsXP3XH5lZF4JRqvSPdiS\nvXxJ/+sq6ows6eEmNJpq6ezuJ6k+fxO940CNjjk/2J0038tlyvG061XBEeA3bja3Pn+4l+2WkSlN\nblgUBQnJD7oaMo8hRRKTIglndlAoAPlR8eTdiSr/mBxdJ5i6hMNekiIHuOgdXfJtokrRdeLl3Aon\nNzQSrbpQL8jD/UKo1GiUKpRJqWhVKvLCo8vkKdLYa/J1HxHKhGSybtyS3oWFWdnSB0HunWg0ShV5\nUXHkhIRTmFeAtlCDKi1Ten/LVIzsvD9iZAQEke53HVHBze0UnkJBYgp54TFSWrrfdZK9LqAq+qqv\nQO4V88tB8iJ0xwkhyI/Wfe2X94VdkryIWGJKOYrawkJUabo/0mSvC1J6UR2KnO2SpJdyHGtCbinH\nX5mUitBoSDnlS/LJ8ySf9EWZlEruHd0DJzswtEYLPmnyCujaxAnQtaGkk5t1PYTYXbooAQVxieTc\nCifhz1MkHDgJQMzOP8m6Uv7wpTozm8LcfDQFyvu6ANWN9zwInPdFlflUqRnS6Ez2jVBSz/qRFxXP\ncaf+XJu1nKyrlb8EUs/9zZ112ynMzef0kxVPEKsKWTdcuzxI+0Z8t0uv57A2iNvjWaOP/3PPvszf\nL825L+eW793ao7qa9ytXrtxXyYzQavWex9rCss9mrboQrUqNMjlNr8c752YYuaGRFGbrvzfVmVkV\nnq8gPqnCfQCisJDMq8HFTrlGi1atpjAvv1S9NWQHhSK02iolM6aKmrl/qrQMcm6G6aVlXg1GnZmt\n19sOkHs7Qq9uhTl50jtfq1Lp0rJzKMzORZ2RjaaggNzQcLIDb5EfHSfZrjA7l8yrweTHVW6f/yJy\nqMhHjJybdxCaYsddlZ5FHav6FCQkk+Gvm/xRule96A8u8egZzFs5SenRP+/H/kVXjOoVxy8tvDus\np0xI0UV2Aahickfm5SAAsoPDMGvuQHZQKKrUTJSJyVj3eVIvb0Gc7o9cVWJ4sDZIOeVLnUZW0nbR\nMGPWNd3DT52RRV5ELAojI+o0aoCRuVmFZWVevUnWNd3qauYtmpEfm0ju7Uga9uxapdynqAci68Yt\nVKkZGNYzQ5OTR+PBvShITCH5uA/GDeqjztA92O91joImT7eUtKGZCSmn/yK/mrKgMz3GYubUlGe9\ntgG63pCzT7sBELfnGE3GF88LKBo9+Hvie7T/dA5mzsWxgFWpGRTEJJB5LeSe50TcL4RWS9qFAKx7\nP1l1Zpn7SnZwGBbtW+ql3Vy6DmVCCm2Xvi2lhXz8NVk3bvHU7rLxs++Fa7M+xu75QXT59pNqH1Oy\nU6IwN5+TLQfhNP0l2i//H6DrAJDWl5D5zyC0WslJtuzcnsKcXHLDorDs3B6NUoXCyBADQ0OpR72I\nem1bYGhSFwBNvr5Tfa/a8yK0SpXedn5M7X4M14SiDj/TprbSe0hoteSGRkh5VMmpescUOfvaAiVU\nIt/JvTtSoUpOxbRJ+YtY/VeRe94fMUo67gCJh07pnMAT51GnZeAXWvkSvrm3IxElehHi950g3e86\n2cFhd8vXUpibpy+hqabkI+Pv68TtOUp20G2Uiboh6dRzf5ebV1Oqx6A2KO8DoWRvSNqFAFLPXiJ+\n73HyImPR5CtJPqUv78m5HSk57uXZVplY/FAq/YAFiNtTHH6sID6J3NAIXYzd1AzpI6vIcS86XxGa\nAmWFUp/sm3ekkRFVWiZxf3iScMgbrVIlpQN42vWiMLfY1qnn/taT8Ghy8iiITyLzqq5tCQe89Ot/\nV4ZUMkRnyilfzvV6ieBFX0n5ihx+3yGvVDlSUx73UzecERCI39jZ9628x4Ha1mUXZueSERDE+QFT\npHkwqvSs4pe5Rv8FnXDYm9Sz5cdhrm2KQtEq45M54ayL3lF0nyceOg1ATmgE3p1GAbrRsaK/0fzY\nRL2/V7g/ti1vFU2ZB6N5F9ri6yCEkHqMM68Gk3MzjOwbt8o9Li8ittz0h5XKNO/3gjozm/zo6nUa\nFUl9VKm124n3OCM77w8R0T/vR5WuezHk3olGqy4k8eiZ4h7wCsi4dK1G5yn98sm5GUbG39cBnQQk\nfu9xUk751qjMR53Us37E7TlKQWyCzgGOTUSVlllGyhP9837JEVFnZOnZqUhvXx0Sj5wuNz3d9zJC\nqyXx6Bnifj+KMim1zJAkQIbfNTL8bwC6IUkArVJZbh2KPiryYxLwGzebqJ/26u1XKBT4Dn210vr+\n/fK7JB4+o5cW9dMf5ea9MWcFyuQ0sq6HSI6SKiWdlLN+nB/sXul57gva8p0grVJV7gRumXsnJzSC\nnNuRnGztysURrwOQ/tc1Us76car9MP6e8C5Q8XwaTYHug7nkCNadDT9ze9UPgE5+V/rYwuxcAtwX\nVKt+eZFxXP/fp+SERpD+11VSz/3NyVbF0ZI0+QWk+vxN0AerASiITST9r6sok9LuHh/L+UHuXHB9\nBYAz3V/Eq92wMudJ97te5rlaE2J2/skx+2fv+fhHmbyImErX9vg30KoLUSalos7KQZS4F4s6bkqj\nLKdjSKusfI2Sx52iHniZfwdZNvOQUDRBozArmzpW9Uk7749Vz65S73FBfDIKo/JDG5Z8aTzVul3t\nV/YxJ/V8AAWxZZd8LrJtdqCu5yXhz+otIlFTYn45qLedcsqXZlNeQJ2ZTcJBL0laU5idq7svKlc1\nocnLJ/6sH1dnfAhA8KLVZAfeosXsqTWqV+lJxxWhTEnnzFNj0BaosBs9iHYfvcPpbsVyoPAtv+I8\nQ3/Bi39DNxz4/kpifzvMsIQLVWd+zPin9vW060Xvczup17q5XrpPn4llQq76T5wr/U7/6yoAkd/u\nIvX0JTpuWIpl53YUxOtG5k401y2J3n3nVzQe+AwAt1ZsBqB+p7ZcnbkMTU4ezxz5jvpPtAGFgkTP\nsyQd80GdkYVxg/rSqGHCQS/yP5qFaVNbQNdrGr3jALG7jhC7q+IP69KjNH+Nfkv6fbbHOOl3XmT5\nPau9e/fG064Xzaa+gMuX1fuoKE1mgE7y6D91Ac2nv4z1s/+dUMrqzGwURkZ68s0izE1M0ShVGNat\nU/3ysnIQGi11rOpX+5js4Ns1WiOkvPcDlD+X62Glppp3mYcL2Xl/SIj9rZwFlUoMNSefPP8v1ua/\nTUUP5geJJq8ATb5OgqBKLY5IUJ374kw5E0ljfvmTmF/+LFPe/aDkSFDCAa8yUpyQZRtwnjGBvKh4\nIr/9jVbzXkNoBcZW9atcPOOfUDTfQUYfVUo64Vt+pe2SmZXmSzrmU8Z5B6o90TrnVji+Q1/lWe+f\nEXejM5Uuo2QPfMDUYkf44og3ALBwaU12oL7W+PyAKcVtSUrFpIkNWqWKtPMBhG/4uVp1qw4lHfmb\nyzbQav7rGJmbcvm1Rbq6321T0eTFIv1zdSj6W0w+7oNpE5v/lPNeRHbQbeo2saFOg/qoUjPIj4nH\n0NwMTW4elp2rvzR9URQUY0sL1JlZKBQGGDconviqVatRGBqiMNA5r0IrauS4yzwYhBC1+n541JA/\nvR5i0i9drfExVWneZe6dB2nb+P0nyLkVAVQsuXmUUKVlcvZpNyK//x2vdsPY2K4v0dv3c2fjDiK+\n3fXPCi/nAX/m6bFkB93WS8spMaHqcUaVlsnJ3Xsr3H/qiZGEb9xRJv3m8o2c61M8QnLr002kXbhM\n6MrvAYgv9VFWXRIPny6bqNUSvGQNN5dWPoG1pOOefuk6AdPe19uvKVAS++shTjQfgP+k90offt+I\n2PKrNELg/acu0lRhdi7eXUdzovkAaUQBKHc9jiKEVltmrkx1Q/Y+7NREx69VqdGq1ajvykaLPoDy\n1DrbZF4NJvNaSLFEsFAjTQKt6Dx5d6LJj4ojLzIGTX6BbsVQIcgOuk3W9RCpjPyomq358cSIwcQk\nPDwTRmuKgbExcP817wA7DuzjyTHP0XGkK5nZ9y4jKw91WmbVmf5DyD3vD5Bk74sUZuVKq40CZPgH\n6k2YkZEBXc9kfgXD9o8iRfrokgS9v1L67TDxuTLD6FfeWILLygUYNyh/OLwgPpm6do2I+/2olL/J\n2KEEfbBab52DmF8PYWxpweVXP/hPSGiuvLmEa2fPMnh8zUJ5pp7zIzc0Uk8ucmmMLmKM02vjuDp9\n6T3Vp0jPXhKtupDI73+vUTkBU+eXSbv04tvl5KwdEg56EfXjHmm7vI8SrboQ747P6d1nWqUKTYGS\nhEPeJBz0IvWM/sTdkmF+S6LJV2JoWv3e/NqmMCcPg7rGkjNYmoK4JERhIaaOTarsMZVCA5ZawE+r\nVEGRvENoyQ2LxKBuXcyaNwUgJzQSTV4eJk1sqdu4oZ7mvDC3+LcyMUUnzzEolngVyR8rC+FYHjeO\nnKxR/n/K2q0/EBkXy5pFH96X8uraNcbIwoz8wPIn3t4r6sJCVmzewP7N39PWucV9Lbsy3n77bZo0\nacLixYvvW5nnzp1j5cqVXLt2jQYNGnDlypX7Vvb9otKe9+joaAYMGICLiwtPPPEE69evByAtLQ1X\nV1fatGnDkCFDyMgoHnb//PPPad26Ne3ateP48eO1W/uHmIpWQC1JQUwChVnZxO8/IaVpcvNI8yk/\nQkt1eJw077bD+0m/zcsZrv+3eZxs+6ApHZmhg4G+o36ylSvhm3bqSTIS/jxFdlBxnOHcu05O0nEf\nPO16cbrraKK37SN6+34p/5U3l+o57gA33v2My69+AOi03Lc+30LU1r2V6qL/CTm3Ix9oJBFNbr6e\nfZXJaZLmvCTZwWF42vXiuLOu1zj7hq6Xu6RcpIiSUpX7wZXX79+L99+iaD5S6Xu3JDeXri2TFrhw\nFV5thxL4nkcZxx3Kj9Dl9/IcTjgP4NbnWyR5Tk24/Nqie14EL+3iFXLLiaSSGxZJfnRZiWHRyIE6\nPQt1RhZZ125Kq3Oqs3PIj0sk82pwhXKrzKvBaO+G2C1Pl61VKiVtuSZP1xOvyVfqonlVoDkvmqgu\ntBoKNY/XAkA1GeEwtrLE2Ko+oLjvmvfktFSUKhWtHJ2qzvwQoSnnPjQ3N2fKlCksX778AdSoelR6\n9YyNjVmzZg2BgYFcvHiRr7/+muDgYDw8PHB1deXWrVsMGjQIDw8PAIKCgti1axdBQUF4enoyc+ZM\ntI/JEGBNyb0TLa2Aqs7KIdn7ou6PTKulMDdfLwRgYfZ/d4Z6ZdRpZIWZswP2L7rS8JkuD7o6Mv8y\nIR9v5Nps/bjdRS+pi6Omc67neK7PWUH4pp3S/qCFq/Tylxe+szR31m0naOEqrv/vUyktbN22SleW\nrYqiVXXzYxPx6T2B2F/LmdNSDS64TiPyR11UH61SdU+rgioMix/zQgguDJ7GmafG4GnXi9QSHQU5\nIbrlyLX5yirbXrTKskzFZF4LIWqrTq4U+f3v5EfH6yZNV+NeOO48gLA1PwG66556+hKgu1e92g+v\n8vjoXw4S8c1vpF24jCotk8TDp0k5VfGEc3VmdoXXPGjhKjL8dNHIhBBS+M/y0OQXkHU95K5zXuwk\nZwfdJvdONHl3olHd7dTKunFLmsdTmpK95uUhSq2v0WPoINauXcuQaZPo8vwwFnzxGcq7iwFdvBJA\nz3EvsOXXX3ja7Xne//JzhBBs3vkz/SeNp9voEcxavlSSeUx7/z2279OPpDX8NXeO++je5y0G9iYq\nTvcxk5WTw9zPPuHJF0fS+2U3Nu7YJj2j1m79gXc/+1gqIyYhnhYDe0s+0R7Pw/SbNI6OI13pO3Ec\nB06W7ew8c+kim3f+zGFvL54YMZiRb0wD4OU5s1j1w7eMnTWDDsMHERUXy+9HD+M6bRIdR7rSb9I4\ndv6pv3DicZ9zDH15HM2bN+epHk9z5tJfUhsWfvUlPcaNpue4F1j947cV+m1KlYqPN67lmXGjeWbc\naD75eh0qtZo70VG4uk8CoPOooUx+73/lHu93/Spus6bTedQwnn1pDH94HpHKXbF5I8++PIanxoxi\nyZqVKFVK/ev34/e0bduWDh06sHOn7pm/detW9uzZw4YNG3B0dGTSJF0d4uPjmTp1Km3atKFr1658\n++23Uh08PDxwd3dnxowZODk58euvv5apZ7du3Rg3bhxOTg/vh0ilzrudnR1duuicpnr16tG+fXti\nY2M5ePAg7u66kG/u7u7s36/r6Tpw4AATJkzA2NiY5s2b06pVKy5dulTLTXh4KOoRyQ4OQ1vioZR4\nyJuCmASESk1GQCDxe4+hTEqtqJh/xOOmebfu/aQknzA0M32gdXncbPswEaQt/2Ud/4f+C61oeL3I\nmYj97TDpF+/fkKanXS887XoR+vk3AAS8srDKY3LDY9Cq1ORFxqFKy+TqzGUca9qHY/bPSusAxP7u\niSolvdxly4UQFX5kZF2/RfJJneTi1uffcLrL6ErrkhUYKsX197TrRcIhbzAwkOybeuYSysQUaa0H\n/UgrslzvXqjo3vUd8or0O3jJGs485Ub0tn3VKlObryT0i+9QJqdx3Km/3j5Nbh6edr2ke0lbWKi3\npkWa72UC3/Pg5kfruTTmbU510Dn7RT3i8ftPcuvzLVL+yB//wKvt0IorU0Lyos7IIic0XG935tVg\nadVMUc5KpEWUXnEUkDTuFVETXfYBrxNsX7mWM7/sJjwmmo07tkr7UtLTyMrJ4vyuvXz23gK2/vE7\nJy/4sGvd1/z1x0EsLSz4cK1u3YrnB7ny56liaUxoRDhxSYkMeKbsx82y9WvIzc/j7M49/Lb2a/Ye\nP8rvR3VzICqTCuXl5/PxxnVs/eIrrh8+wR8bv6FDq9Zl8vV7+hlmTprKcwMGc+PISQ5/V9ym/SeO\n4TF/IYFHTtLUzo5GVlb8+PlKrh8+wZcLFvPppvUEhuqkMTczUpjn8SnLPlhEZGQkBw8cpLGtLirT\n++tWYdaoIQEBlzn03U+c8/Pjt8N/llvvr3ds4+rNYI58v40j32/janAwG3/eSotmjhz7STdv5tqh\n4+xYXXbuSkxCAq8unMcrY8YRsP8wh7/bSvu7bf7yu81ExsZw9PttnP5lFwkpyazf9pPe9cvOziEo\nKIh169axYMECsrKymDZtGmPHjmX27NlERUXxyy+/oNVqmThxIp06dSIoKIj9+/ezZcsWTp0qjg7n\n6enJ6NGjiYyMZOzYsRVep4eZamveIyIiuHz5Mj169CAxMRHbuxfe1taWxERdHOq4uDieeeYZ6RgH\nBwdiYx8fnW5lCCGI3XWY+h3bknU9BGNLnS43ZuchaXhQlZFFTnBYZcXI3MVmWNmlro3qmaHJy8d2\n5AASD3sDUK+NM5ZdOxC76/C/XUWZfwkhBBHf/AbA5WlVO9P3k6SjZwlZsRl1eibpF6/Qx+e3MnnO\n9RxfcQFFzofQcuO9z0k65oN136do8FRHGvbqhvWz3Uj805srby6pWH9/t4zSH/w5tyNJ8b5I6tm/\nabP4LcydHbgwyB3TZvb089P1HJaWo+THVBxJSZOnrHCfzIPBu+NzFe674PoKwxIucGfddm6v/J66\nNta0/WgW194uf6g/ZNkG0ApCPt4IQKt5r6MwMiR40Wopz5UZH2Lu3IzW7+ui+6izcsgJDsMCKMzL\nr/AjU6NUE/PrYbQFSlRp9x69ynZEv6ozlYNCoWDqC27YNW4MwNuTp7Js/Rree/VNAAwMDJgz7XWM\njYwAI3YeOsDy2XOxbaTL/z/3V+n9shtrtB8ypHcflq5ZRVxSIk1sbNl/8jjD+va7e2yJNms0HD7t\nxZHvt2FmaoqZqSmvj5vAvhOejB/xXJVSFgMjI0LuhGHf2AZbW1saN2xYbj4hBKLUh7VCAWOHjaCV\nU3NdWRjofVz06NyFPk8+zaVrV+ncrRu/bf2W8SOeo29fnX2bNG2CYWomyWlpeJ89S3hEOHWNjbFu\nYMWrY8fz25FDTBw1GiOLenofXQe9TrD8f3NpaNkAgNnur7D4q5XMffUNqvr4P+h1nN7dn+K5gYMB\naFC/Pg3q10cIwW+H/uToD9uoX08XFWjmxKnMWbGc+W/MAMDIyIj33pmNoaEhrq6umJubExoaSvfu\n3SUbFREQEEBqairz5s0DwMnJiSlTprB3714GDtQtyvb0008zfLjuo9bExKTSej+sVMt5z8nJwc3N\njXXr1mFhYaG3T6FQVPqF+V8J7VMUhq50z1rJocOiFTVrk0ddl93gyY4oDA2p27jsg8ykqS1Cq8XI\nvLgHvn7HthjUMZaOLVpsqjZ41G37MFOZbvh019EoEx6cTCN8w88YW9VHnZ5FdtBtLDq0IickHBMH\nO717sTwujtQ5D+kXiyNHpZ71I/WsH2Grf8S8tRO5oTotcm54DJn+N7AZ2gcji2J7SC+mUs6AT+/i\nSDDJJ4pDhuZHx3Oh1KJbHQzM8bTrRdOXRlRY1xtzP6u0LTLlU9m9W9uUlLook1IrdNyLKHLcAY43\nK9tBkrBf1+OccTmQp35bS8TmYklByeXupXkkd+/JvDtRWHa5/8/Hmuiym9jYlPhtS2Jq8TOjoWUD\n6pSYWBuTEM+MDz9AUaJ8Q0NDUtLTsLFuxIBnenLQ6yQzJkzikPdJPOaV7TRIy8xEXVhIU1s7Ka2p\nrS0JKZU/q0wd7DHOzOaHH35g48aNOslKjx588skn2OQV+wtG5uaVyofsG9vobZ/+y5d1234kIjYG\nrVZQoCzgic6dMW/RjLi4OFwHD8bYsh4ACgMD7Lq48PfFv1AXqmnfXheKU2i0CAQODg5SeE5NXgGq\ntAxUqekkpqaUaq8dSanVezbHJyfTrEmTMumpGRnkKwsYNf01KU2n4y8edbGqb0lda6tiG5qakluB\nbaKjo0lISMDZ2VlK02g09OpV/LfSpJx6PGpU6byr1Wrc3NyYMmUKL7ygW2jF1taWhIQE7OzsiI+P\nx+buH03Tpk2Jjo6Wjo2JiaFp06blljtz5kwcHR0BsLS0pGPHjtJCIkXLTT8q2+fOniX55AXJufML\nvYlRPTO62jtK24De/trerv9Ea9oqDf+V813Pz6AgJqHK/KMXziHuD0/8Qm9Sp1FDOlvZlMlv0b6l\nzr5JMeXau/4TbXTbzo3o0akLhmYm+Pj4IJpb06d9SzT5Sk7tP/iv2/th247Q5kpORdGw/qO6fTku\n8sHXJ1Vnz/MDp5Lh1oe43z3pYGDOoJBj/6j83NDIYtnF3R78ou0hk18G4Nwpb5I3/0CTu47SVzad\nqy7/sn+5+2N3HXng11PefgS2T3nTJSOLsDU/EaTNxYxipzJfaMlPSsZUYUBhTq4kbSlytB/EtgDi\n7ioA8oWW8MQEbK0bAaAUQk/6ky+02NvYsur9xXRzeaLc8oYOHMSW7Vt5ulNnCpQqunTpSkkKhKCp\npSXGRkbcjo+lpVNzTBUGxCYmYtuoMflCi6mJCQUFBVL5yWm6kTNlHUMMbBsysJUTAwcOJCUlhZUr\nVzJnzhx+3/QdWenpKAwNsG3lSHbIHTQK0JT4cM8XWrQUd4zmCy0qlYq3PlrMmkUf0rvXsxgaGjLn\nw8UIBWRnZ2NjY0N4RASg2wawsLDAobkTderU4cqVK1haWurtLyJPowZLc0hNx9a6EWHxcTg0b46J\ngNjEBBpbN9KTN+ULLQai2J4KR3vyImNpYmPD1ZtBZextWt8Ck7p1ObF1BzZ3yzJpYoMiPkW6fgJQ\nGCik+pXU5BcWFqJSFY8INWzYkGbNmuHv71+mvaDzaQtLzJkovb/0tlarJTs7u8L9Pj4+XL9+ncxM\nXSjLqKgoXn+9bDS1+41CVDK2I4TA3d0da2tr1qxZI6UvWLAAa2tr3n//fTw8PMjIyMDDw4OgoCAm\nTpzIpUuXiI2NZfDgwdy+fbtM77uXlxfduj2ci1DkhkWhycsHAwPqu5TVoJVH0onzKO9hIllt4Bd6\nk0C3A+YAACAASURBVKdat8P+BVe9KDa1if2YoWQH3SbnZsWSoMaDn8XEvjFpFy6TGxZJsykvEP3z\nfuraNdazXdHqof+ErMBQMgMCcZj0vLRaqc2wvtIE4nulyLaPAoHzv3zQVagRQSU+Nh4lnjnynbSA\n0MPMo2rfR4H/gm3tP5pJ817d//Xz5gtttXrfe7/shoV5PX7yWIVJ3bq8sfh9enTpyrzX3uTilQDm\nfvYJF3YXzzf4cc8uTpw/x6qFS2hqa0dqRjoBgTdwfbYPACq1mqfdRtGxbTvaOrdkycx3pGNbDOzN\n6R27cGzSlHc/+xilRsPKee+TnpnFtPfn8uZLExk/4jl8/P343yfLOPrLLhrY2fC/JR9w7NgxkpOT\nSU1Nxc/Pj379+mFqasoXX3yBr68vBw8eJOd2JAbGRpg5NUVotGz57Av2nTzG7nWbJF9qwruzeGHw\nUF4aOQqz5g4kBYXQZdRwfvlqPU936syZSxeZuWwJM15/g6UfLycgIAA3Nze2bdtG7969SUhIICkp\niS5dujB58mSaNWvGokWLMDc3JzIykvj4eL2eatDNbVj947f4BgTw674/yA4KZfqSD+jZtRtzX32D\nmIR4+k4cx+2TZzEwKL5mlp3bkx+TQETwTYa+MhmP+R8wtE9fsnNyiU9OokOr1ny8cS1Jqaks/99c\nrBtYkdPAnIATp+j7VA/p+gWGFM8569KlC+vXr6dv3758/PHHxMTESJNStVotgwYN4sUXX+SNN96g\nTp06hISEoFQq6dq1Kx4eHkRERLBlyxYqQgiBUqnk3LlzzJs3j0uXLqFQKKhTR3+l35SUFBo1alTm\n+ICAAAYNGlQm/X5S6V/F+fPn2bFjB97e3nTt2pWuXbvi6enJwoULOXHiBG3atOHUqVMsXKgbUurQ\noQPjx4+nQ4cODB8+nE2bNj1yspm0CwFkXgkmMyCQ6J/3o86oOgbsg3DcGw/pjVkLxzLp5i0dadD9\nCWmo3W704PtzwrvXsdmUF/Qc7CZjh2NkborVUx1r7Hg3GTscG9dnaTblBSy7udyfegL1XVrTbMoL\n0gp6gBQf2XZ4Pxo+W/svIaunO1eZx7zlwzuTve3SquNlt/1wFgBWPapu6+PKxeemP+gqyMj851Eo\nFIwe7MrU+XPoN2k8zR0ceGeKu97+krziNp7BvXozdf67dBzpitvb07l6M1jaX8fYmKF9+nEhwJ/R\ng1zLnKuI5bPnYtGoIf2nvMxL/5vJ6MFDGDd8JAC9uz/FmHFjGTJpPCNeGsuwYcOkY7VaLZs3b8bF\nxYWWLVty8eJFVq3SRcqq18oJMyedYkFhaMDLs3S6766jh/P89FfL1MPY0gLbzi589M4cZi1fSpfn\nh3PQ6ySuvfpIktJu3bqxceNGFi9eTPPmzXn++eeJi9MtTrVp0ybUajU9e/akRYsWvPLKK9I8xtLM\nmfkOnZ54gr59+zL8tal0bN+eWVOmVWjnIumNib0Nji1a8KPHKr7f/SvdRo/guTdf4eYdXYff0g8W\n49TUgTGzptPpuSG4vTSemOxMKUR0ZX7k5MmTCQkJ+T975x4XZZ32/8+cGBjOZ5CDgKCogIomImqm\nZpilVuamu1qaZdlTW/4qy3affWrbp9Nu+VRbdlorXQ9lW7Z5XjINz8dEkAABBxBQzjDAMIf798cw\nN3M+wNzMgev9vJ7Xch/mvr/zaZy57uv7+V4XEhMTsWLFCvD5fGzfvh0FBQXIzMxESkoKnnnmGTZj\nbs3qDWhi35iYGDzwwAOoqanBsGHDcP/9xiVznYnFzDtXODvz3nK+CAIfMfxHjzA6VrXlO6N92qC0\n+/oNiKPCwOPzoVYo0X65BP7pI/tdBq6/hM+dBu/IMJPjjVl6F/hCIRi1Gu2FpQhIH4Xr/zoIcUSI\n2eYfthD72wVQtnWwDXKqtnwHv9EjEDwpXe88RqVC9ba+leoxS+9CzfYfEDnvVniFBUNWUY22S7/q\nNaYCNOXQar7a65DMuy5VW75DQNpIBE4YA6WsE0JfCeQ3mwachTfEf2wK/EYmoPbbQ4haOAeiAD+0\nXvoVYBi0XTJdpSbolgy0nLlktD8gI9Xsa2xloJn33LrjqP3uEOQ3m5DwyG9wKHGWUVm3KXs+xsn5\njyLzy7dMNszRJXL+TNOdNQnCBRBHh0NuUPte4CfBnJKDODBsmpNG5To4K/NuK9OXLsYbz72IqZmD\nO0bfpHi99SmtvxQDYCDwlYDvJYIk3jHeam03Wd+UBL21B16hwfCJ1XjQFe0d6CyvgldYCATeXuiq\nrmODZ0egVijBEwrYwLf1lyvgi0RsDX/Dxa0CiQ/8DPqzaN+HMMAfXsEBEPj7gi8QsMeEAf5QtrXr\njZtRqwGGAU8ggKvhspl3T6W9sARtl+3vLnYz7zjblKJmxw9ou1yCxqP9b6jUX7SBux58/f+UPD4f\nAemjAADR99yO0GmT+nUvbZaax+cbdbb0H51sdD5PIEDMA3chZKrm4YwvFGLYfbnwCtMsNvFNjDUK\n3AEAAm4+isMWz0PAOI3VRegr0Tum+6VrDzG/mc/+HTYzC8HZE+A3KglCP1/ELV8EUYBmUVBgxigE\njjO22fiNTIT/2JGQDI9ByNRMBKSPQvjcvgDBNymuX+MyRc7hLXa/5tZzmunl6EW3I+GR3wAA/FI1\nHfP8xyRj4va3IQoJhCRRM87w26ci++BmjHn9WbPXHP2XZ4w+owRhK9NPfMXJdVNffRoZ7/83Mj9/\ng90Xfd9cpP/fH3B72X/A4/NtmoUiPA+BT99idP+xKQhIG6V33H9MitFviHd0OIT+fvBNindY4K6F\nLxJBKPGBd0zfglFt4A70/b55hQbBKzTYoYG75v5CvYy174jhEPQu2A/ISDX63TIM3AHAe1gkJIlx\n8E2MhSgogA3cAcBneAy8I8MgkOj/TvP4fJcM3J3NkP011X4Im88UoPVCkcVzO6W1rA2FUSqhVvQt\nduiuMV96zVFEzr8N4shwi+fE/XYBACD/2DGjY9r3Gn3P7UbH9OgNrkKmTULknTMh8PGGJDFWr9Op\n3uleptti80VC8HTKagkk1ksx8YVCDFtsvfmIvQh8xHr2GV205SiDs/QbQEXfa7rmcVmYD6LvuV3v\nffvERcMvebjFqiPR994BnkAIcWQ44pYvQnDWOARljoHARwzfEfEIHD8a4ohQAIAkMQ5Cf18ETUyz\n631qCZuZhYjcGfAbqVlp7z96BIav+Y3F1wh8Jcje/xky/v4nJD7xW/jERBqdM/IPawFoSrmF3zYF\ns4v2wSskELl1x8Hj8RCYMQrxD91r8vq3FfwA76hwTNzyltkxmKuVTTgGrvXNrTuOqYc2W/+O6Se+\nibEY/eozmF283+jYnKvW29VH3nmrXinOjA/+B9OP7UDC6iUYtjgXgeNSMWXvpwCA4EnpelV5wm7L\n0ruW4eecPrvcYU+dd0fhHaX5rfUbmYCA9FHwH50MvlCoaXbW67/ni8Xgi4zrfYgjQuGbFMcurnQU\n/mNT4DdKk0DxCg2Cd3SE0Tk8Ph8BaSMh8BbbdE3Dhan2IvSTwHtYJHyTh/dZeII0i17NxSvi8BA2\nuWWIV1AABBJv+KW4rp3UlRiywbuWjuKraL9SDkATpJui8cgpKHvbKzcdP4+aHYNrk+GLRYiYm4OI\n3BnwiYvWOxZ51yybg16hn6+mtvT0SZAkxLL7Y5beBb9RSQjq9Z2LI0LhFRqEYYs1Hj1t1lyXuOWL\nTH55DQStL51rRAF+8I6OYL9w/EYmsOsHwudOYwPxyDtnIvZ3CxHQm8EQ+fuyDaNiltyJYffbqLuv\nD4bdn4uwWVlmz9GOxStUUz/Xf4zxrIYuup8DgZ9Eb784PAS+Ol+Ao1823e1Oy5ySAwgcPxrD7rvD\nbJbRJ1YT0Cf9/kGTx3XRZum1sE22enU1F+QT7k1A+iiM+/BlhEzN1MuUTdnzMTv7BQCB4zX/noKz\nxiFw/GjcXnHY5PVu2fUufFMSMPO8xho4fPX9EAUFYOK2txFxh2amKmX9I0YzaibH1nvP2b8egFd4\nCKIXzYHvCP01Q0GZYzDz/HeIW6Fv3fNNSWC9t/5pKUYzTD7DTVdUIwaPn7fvcphlRhwZBt9kzfcn\nj8/XS9YEpGmKWJj6TeQS9uEBmt8Kr/AQszPfgzoukVDv359A4g0ejw/vKBPuAMKhDPngHdDUYmcY\nBo1HTpk9p/HnwbfHAJpsufYfhzg8BGEz9QNAr+AAvaB3Wk6Oxev5joiHJCEWodM1Nhq+WAy+UIjg\nyRnsGgBHLDL2HhaBIAM/vKvAF3shfM5U8MVeiF12NwAgeFIaIuffpmdJ4vVOE0oSYuCXOoItXam9\nhq0ZDkDzJccXWn7YiVu+SG8dRkDaSABAYOZYiHuzQdqMvMBXgrjlizDs/nmIXjDbaPo24+9/wuyS\nvu6k2mA+++Bm5Py0Fbdd6luXYMsXvmR4DO6oPWbTA1vk/Jns3zk/bWU/n75JcRCFBCJqgbFtauGL\nT4Pv7WW0n3AMA6mGMvZvlhtjeQ/TzwJmfvkGbiv4ATG/uROpf/49giamYeKWtxC1YDZy646z2fms\n3R8ie/9nEPiIEX3fXPb1YbdNAV/shdBpkzD9521G1w+fNQWZX7yJmb98j8T/Wq55f28+j8Dxo9kg\nW8vMC7uRW3ccI55aAUCzuG9WwQ9mZ+O8h0UY/Xvgi4SY8oOm4+6IZzRdUwMnjoUoSFMqLsOfAhVH\nI0mMg098jF113h1BQIZpi6UWHp+PwHGjIR7k4N1oHDye2ZlvWzHs2eMIxOEhCMgYZf1EYsA4NnXq\nThgEqNp26+awpeqMI/GJi4b/mGQ2a2kLksRYu5+8vaONp7d4DvCf80VCkwuCXQ2tXnyxF7zEfcFj\nxB3T2ek9UYAfgm8Z/AcRv9EjIAoJgmT4MASMTYFaqQRfKIRXWDC7/kD7ABE4fjTk9X0dOAXeYr2H\ni2k/bYWsohp+yX0Z+fT/+wNu5p2weTw2P9TpLIH3G5nA/i2OCMXson0ANDaLw+MXQF7XgPDZ2Rjx\nzEqMeGalXtMZwjXQVr6YceprHM3qq7gQMjUTPQ3NSHh8qd752u+s9P/7A7tPHBGK8R//GQDgM9zY\nC5zy/COo/UbzsDnhH6+xi+AsofugHb9iEeJ7M+a6nyFT32/9QRToD55AAP/eWaXsPZ8AAI7NfhCh\n0ychMHMMqrd+3+/rp778FLqqauGXmoTCZ9+w/gIPgycUglEqAR4f4shQCH0lRl1F2XP5fM0iRhsQ\n+vlC2WHd1uQVEgRRSKDbVccjhi5DLvOuaNOshlZ1dunvbx2Y/2sgGHquAY13WeuDtpXQaZNwzITn\n3Rz+Y0caWRxiHrgLfDFlQE1pr20WNVgIvMWQ6AQ62sy9OCLUKOsiSYi1WLKRJxDoBe4AEPObO9mA\nylGEzcpGxO2a4Cnn8BazGU7NoDQ/lBP/+TfOtc2tO47cuuOYXbwfCY8v4/RershAfNmh0ybi9srD\nkAyPQdrGlxB66y3wCg/BuE0vY9rRfyJ26V12XS8ydwbmVutXe5IMj0Ha2xsAaOxz5nyxtnDL1+8C\nAG4v/7Hf1zDFHTU/G1ltcvK+QMOcCUj76wuY/O3fkfryU4hftRiTv/vArmsnrHkAo199BnG/W+jI\nIbsdfJEQ3pFh4An44AsE4CfFwn+s1qoSAu+oCJOWFZ+4YfAeFsn+HZA+Cr4jhhv999Ki9bX3vT7a\nJvuVJzFQzzvhXDw+865WKsEoVOzUfd3uvsVNsvIqcy8bNPxGj4DfyAQ0n7rI7tNaWrgmKHOM0T5H\n+9iJocWkbX9j/xYFWp6W5SLLNafsEP6T3Ldo0js2Clk6gZQoKACpf/ovVH64jd3nN3oEOq6YbzA2\nFAnOGofmU7+w29pZnNgH5iP2gfnmXmYzpixkAeNGQeKASkuh0yfpLU4dLEKyJyAke4LV85KeWoHG\nY+fQeq4QAJD29osmz5tbfRQHY2c4dIyuhjgiDPIbDeB7eUEyMgGA8XcCXyg0qpwi9PNFd+1NqLo0\nSTivEM1CSUVzGwS+PuDx+RD2rgWSJMVBJeuGvL6vFKgoNFiTpOLz0Vnh/DiAIOzF4zPvzScu4vou\nzVS9YU30pmPn2L+d1iHVxMyg7mJSe9H1ZROOhbS1nfGf/gViK5aF6PvuQESupqOhVlvdhbbhs7Mx\nbtMrdt1Xa9nI/FJT2YYvFOiVUzPFtMNbkPH+fyPt7RchGRGPKXs+tuue7oCh5113zYOhjSXjw/9x\nSmm2gLEpmHF856Dfd6CY+17QeuIBzSyAdjt22V0ImaKZbZ24/W123Y2WcR9pZsP4QqHJh5DJ3/7d\n5rEZVsrhEoG36apiPnF9ny9tNRK/UUmQJMXDOzoc/mNHwjcpFnyRyCh5ZM6XLfT31bPkafEbmQCB\nwcyxyN8P3lFhbLUWQPO9IAoKgCjAz+ElFd0FLjzvxODh8cG7qksOAOgoqXTuQGwkZsmd1k8iCBcn\n6q7brGbWR730uF59bQDI+XELwmdnAwAyt/5Vb/GrPYiCAxCSk4nIO02/Pjh7AuIfXoycn7YCAIYt\nzkXssrsx49gOvTKd2Qf+YfM9xRGhCMlxXvM5Q7xNPLRoqxSJI0KR9vYG+I0ewXbKBYCphzZj2D1z\njV5H2M/wRx9g/+YJ+Eh84ncANMkZQa9FI/y2KUavM1epQ9sLIiR7AvtwamqmInhKn31u0vZ3+jl6\n+zFecM6DV2gwmxUXh4dCMnwY/MemQOAthqh3kT1fKBjQw6IoMMD6SdDMHvHFg1PRzJUoLS3FjBkz\nEB8fj08++cTZwyEchMcH79pZOGd62i2hndoL7C3TOFC/+WD7socSpC13aLXli4QYdn8uQqZN1FRU\n6M3Ehd9uXEXJKzQI0098hZkXd2NW0T62pCAAgAdM/uZ9jPpv06Uvs779O8b8ZR27ANGQGSe/Qm7d\ncZNNtkzBEwlx26V/I2HNUusnDwI+w4dh7Bt9XW+1nnfdhX6xy+7CtMNbII7sW9+hbeymzWoaetMJ\nY8x9LwRPzgAAZH7xBvhiL8Q/dC+G9SZnEtcuYx8cDTFcjKnN2I9963lM2PwaACBibg6ydn+ICJ1/\nF1pvOHh8ZH75JlJffdqu92GtH4Q5tBl3UUgQfHtL7gaOG43AcansrFfguNFs1SBrVbd0scWX7YgC\nC/YilUoRGhoKtY0LZ53Ju+++ixkzZkAqleKRRx5h93Ppec/Pz0daWv96lVjiyJEjyMrKQmxsLBYu\nXIjq6v53jXd3PD54t7hgjkPEprqg6uCbkoDQ6ZPcoiILQQwm0Ytux+Rd77HbU/Z+auQLDhiXiuDs\nCfBNjIV3VDi8QgLZ4CD1ld8jMH1g5crsta5NPbgZgCaoyq07rlfXHAB4OguMM794A6KQoAGNTxev\nsGDcoqPXsCV34tZTuxA+Oxu5dccRMq2v/nVAWgoEEv2GYsGT0nF7+Y96CzxTX30at1cctivQIgzR\neCIj7tBYw4T+vsh4V1OBR+AtNvvg6DsiXs9yNuvKfkzL3w7vyDC9hnmGC9Rz8r4AX+yFgIyRiJg7\nDQmrlwDQWMh0s/GGpfy0C0DjH7qP3adbZlaLKXuJ74jh8EnQVCPiCfgQ+Engm5xg8n1xhh1rZ7xC\nAo06hQ8EbfNGU6hUKofdZyBUV1dj1Cj3Kt+oVCqN9jU2NuLBBx/ESy+9hPLycowfPx6rVq1ywuhc\nA48P3tHb6Uwt7+H8Vtq63EBfeTVddGtxB6Sl6AUIPnHRkCT23+uuhXzZ3EHacoclbYMyx0AcHqK3\nb+qBf2DCp38xeX7Co79xaMWkGae/0YwxfzumHtps8hzDh/CpB/6BpKc1Da1CcjKR9ORyDF+tKbMY\nccd0uxtVZep0pxX46HuLo+6ehdBpE3FbwQ+Ye+0npG/coHd84pdv4b+uHAGgWZx7e3me0fUFEm+9\nTsh8oXDQmqa5O+Y+u0ET0zH61Wfsvp44IhS3XdjNbvN4PKNKUVpily8EX+e/05yy/yD1T0/qnRMx\nNweT/6XxyWdueQtBOmVvb/nmfUTeqXkg8O39/QnISDVrYxH691UBCkgfBaGfBAKxF3giEQTeYvB4\nPIvdpu3FFl8231uMcePG4f3338f06dORkJCAhx9+GHK5nD3nwIEDmDFjBlKzJuHeNQ+jqEjTVf2f\n//wnli3rqz41adIkrFy5kt1OS0tDYWGh0T3nz9cs2k5MTER8fDzOnDmDbdu2ITc3Fy+99BKSk5Px\nxhtvoLKyEgsXLkRycjJSUlKwZs0atLX1lZ2urq7GihUrMHLkSCQnJ2P9+vXssa1bt2LKlClISkrC\n4sWLLWaZ9+3bh+zsbCQmJmLBggUoKSkBACxcuBD5+flYv3494uPjUV5ebqRtc3MznnjiCYwdOxZJ\nSUlYvny5kW6JiYnIzc1ldQNgVnOZTIYlS5agrq4O8fHxiI+PR319PRiGwcaNGzFx4kQkJydj1apV\naGlpAdA3k7F161ZkZGTgnnvuMXqP//73vzF69GgsWLAAXl5eWL9+PQoLC1FWVmZWF0/G44P3npvN\nAMD5ivLQW7PAE/Z94Qn9fRGRq6kUELVwDoA+S0zssruN6reLAvwQOm1wqswQhDsyq3Avcn78EnOl\nRwb1vpJ4jU/cOzqCtZXYQtCEMeCLvTD5m/eR8txqva65geNHA7qzgr1/T/t5m+FlwBd76fmg41f1\nZUhn/vI9Rv1J41kXh4eAL/Yymm0USLzhFRoEgY83gjIdP5VNmEbgI2Yf2LjCL3k4Zl36ge2MzBcJ\nTc8292anw+dMRerLT2FMr6UqNCcTo/70JGac2gUASFz7WySuXQqhrw+y939m5GP37fXYe4UE6WW8\nA8YkO2WWW9swicfjYffu3di1axcuXryIwsJCbN++HQBw6dIlPPXUU9i4cSPKy8vx0EMPYdmyZVAo\nFMjJycGJE5peF7W1tVAoFDh7VtOQsbKyEp2dnRg7dqzRfffu3cueI5VKccsttwAAzp8/j8TERJSU\nlGDdunVgGAbr1q3DlStXcPLkSdTU1OD1118HoMnML126FPHx8fjll19QWFjIBq179+7Fxo0bsWXL\nFpSVlSE7OxurV682qUFZWRkeffRRvP766ygrK8OcOXOwbNkyKJVK7N69G9nZ2XjzzTchlUqRlGQ8\n2/PYY49BLpfjxIkTKCkpwdq1a63qBsCs5r6+vvj6668RFRUFqVQKqVSKyMhIfPTRR9i3bx9++OEH\nXLlyBUFBQXjuuef0xnLixAmcOnUKu3btMhpncXGxnhVHIpEgMTERV65cMamLp+Pxc6K2NPtwBEYz\ndzwexOEhiLp7FtA7tRY0KR039h/ltJJDfn4+ZYg5grTlDlu09QoNgleo4+wm9jD71wN6GcXYZXej\n6dQv6Lwqxe0Vh02+JuKO6Zh77Se918T01kSPmJuD3Ov5qPxoB9qvXEXNV5qKWH4pCZhx6msI/Xwh\n9PfFsdkPQujrg4D0UZhzNQ+MUglRoD9kZdfgPSxSr1GRJfLz83F7hWPrnhManP29IPT3ReITv7V4\nDo/Hw/RjO8Dj8cATChG79C7WtiP09WE/27prRALHj0ZI9gQ0HDbuPO7VGzDrMvfTCwN9Kzi4Wr/U\nZnt7u81VUdasWYPISE2t99zcXBQUaBovfvHFF3jwwQeRmalZTP7AAw/gnXfewdmzZ5GdnQ0/Pz9c\nunQJpaWlmDVrFi5fvozS0lKcPn0aU6eabhpnzi4TFRXFBtne3t5ITExEYmIiACA0NBSPP/443npL\nM4t27tw51NfX45VXXgG/98FnyhTNAubNmzfj6aefRkqKZh3DM888g3feeQfV1dWIjdWfof/2228x\nd+5c3HqrZgblySefxEcffaQ3flPjbW9vh0wmQ15eHsrLyxEQoLETZWdn26SbJc1N3e/zzz/Hm2++\niehoTTLk+eefx7hx4/DRRx+x56xfvx4+PqZnbjo7OxEWpv995+/vD5ms/z0s3BmPD94xSAtKvEKD\n2S6sPvHD2BX2oqAAdv9AGo8QBOE8dGvWT9q5EUETx6KnsQXy+ka77CWGAU/CGk1FEq/wEDBKjUdW\n13I39eBmdtG97sND5hdv2v0eiKGNbsMivpfIYlM3LRO3vY0uaS1alX2204CMVJOVpAwD78EmIiKC\n/dvb2xt1dXUAgKqqKuzcuVOv0opSqURtbS0AICcnB/n5+aioqEBOTg4CAwNx7NgxnDlzxmzwbo6Y\nGH277I0bN/Diiy/i5MmT6OjoAMMwCArSJCBqamoQFxfHBu66VFVVYcOGDfjjH/+ot7+2ttYoeK+v\nr9fbx+PxEBMTw74/7T5T1NTUIDg4mA3cDcdgSTfAvOamqKqqwvLly/Xer1AoxI0bN9htQ/108fX1\nNVpk29bWBj+/oRlXeX7wPkgIJN7g93pRw26drHeMJxKZegknUGaYO0hb7nAnbbX/voV+vibXtvSH\nUS89bnK/o3zn7qSvu+HJ2vJ4PEiGD0NnQ4PevsFiILXIteOMjY3FunXrsG7dOpPnTZ06Ffv374dU\nKsW6desQGBiIr776CmfPnsWjjz5q8drW9v/5z3+GQCDA8ePHERgYiD179rC+9piYGFRXV0OlUkFg\nMBsfGxuL5557Dvfddx+sERUVpedFZxgGNTU1bIbbHP7+/oiJiUFzczPa2tqMAnhrulnClD6xsbF4\n7733MHnyZKNjUqnU7Ou0pKamYseOHey2TCZDZWUlUlNtqwjmabit551Rq1G9ra/RiLpHwTZh0nZO\n7Si7Nqhj8h0Rj2H3zzPaL/T1QezvFoIv9jJbd5ogCIIgCMegtW6sWLECmzdvxrlz58AwDGQyGQ4e\nPIiOjg4AfZl3uVyO6OhoZGVlIS8vD83NzcjIyDB57dDQUPD5fFRUVFgcg0wmg0Qigb+/P65fv473\n3uurCjVx4kRERkbi5ZdfRmdnJ7q7u3HqlMaitHLlSrz99tsoLi4GoMkwf/fddybvsWjRIhw6kV2p\nqQAAIABJREFUdAhHjx6FQqHA+++/D29vb70g2ZLNZ86cOXj22WfR2toKhUKB48eP26SbJcLDw9mH\nAi0PPfQQXn31VXbhbUNDA/bt22f1WlruuusuXLlyBf/+97/R3d2NN998E2lpaUhOTrb+Yg/EfYN3\npQqMTikmXW9707FzULR1QNHcZuqlnMHj8dg24qaOAeDcs0u1yLmDtOUO0pZbSF/uIG25o7+1yHk8\nHvubO378eGzcuBHr169HUlISbrnlFr0M7ogRI+Dn58f6zQMCApCYmIisrCyzmWCJRIJ169Zh3rx5\nSEpKwtmzZ/XuqeX555/HpUuXkJCQgGXLluHuu+9mzxEIBNi2bRsqKiqQkZGB9PR0NkCfP38+fv/7\n32P16tUYPnw4cnJy8OOPptesJCcnY9OmTVi/fj1SUlJw6NAhbNu2DUKdMq+m3odW202bNkEkEiEr\nKwujRo1iPejmdLM066A9NnLkSNx7773IzMxEUlIS6uvr8dhjjyE3Nxf33Xcf4uPjcccdd+D8+fMW\nx6hLaGgovvjiC7z66qsYMWIELl68iM8++8ziazwZHmOpUClH5OXlsYsg+ou6R4GanXsQt3wRAEAp\n60Ltvw4gbvkiNgM/WASOH21XFQoucfbiKU+GtOUO0pZbSF/uGAraNjQ0GC0WHAzsWbBK2AdpO3DM\n/bs4f/48Zs+ezem93Tbzbg51j4Ory5h5GvRNHo7Y3y3UnDKInnZrePqPiDMhbbmDtOUW0pc7SFvu\noOCSO0hb98btg3e1QglVl5ydcqnd/R+HXDdkqvHMgG5nNnFkGHtPZ3VxJQiCIAiCIIYWTos6Fa39\n87IZ0nj0DK7v2sdmyNXdciuv6CPq7lkm90sSY/XKamkJSO/roKpX9nHwFt9bhfyX3EHacgdpyy2k\nL3eQttzRX887YR3S1r1xWqnIlvOFCL9tyoCv0329HgCgaLP/g6ibSdcSs+ROvU6pWgR+EoCnedbR\n+uy1CH0ldt+bIAiCIAiCIOzFeXXeHbxMtrvafHMAe+CLvYz2hc6YDK+wIPQ0NBsdi112N6cdU+2F\n/JfcQdpyB2nLLaQvd5C23EG+bO4gbd2bIWfW9h0xHAAg9Pdjt7V/m0MyfJgmu26iMI8rBe4EQRAE\nQRCEZ+P04L27vgHd9Q3WT7QCo1LbdJ5A22K81yMfMnUCohfNAQCII8NNXLgvYLcW5LsC5L/kDtKW\nO0hbbiF9uYO05Q7yZXMHaeveOD14v/mf47h50PYvP0alMlnHvePXcrvuGzxlnF3nA5oGS4Z+d4Ig\nCIIgCIIYLJwavDMMw2a2be0VpVYoB3RPgY83AECozcDrwPc29ru7G+S/5A7SljtIW24hfbmDtOUO\n8mUPnNLSUsyYMQPx8fH45JNP2P2krXvjvOCdYcCoVODxBWYbIenSWVkNAFB1aUpBKttldt8y8q5Z\n8E0ZbvJY9L1zEZI9QW9fRO4MROTOsPs+BEEQBEF4JlKpFKGhoVCrbbPrOpN3330XM2bMgFQqxSOP\nPDIo98zPz0daWppDr6lQKPDggw9i/PjxCA0NxbFjxxx6fXfDavC+atUqREZGIj09nd13+vRpTJ48\nGRMmTMAtt9yCM2fOsMdee+01pKSkIDU1FQcPHjR7XUalhqz0GngC688P6h4FGn8+i+7rN9g4v37v\nT1ZfZ4hA7MU2VjJ8YBD6SsAX6RffEYeHQBweYvd9nAn5L7mDtOUO0pZbSF/uIG25w9V92ZYcAyqV\nahBHYp7q6mqMGjXKaL8ra6tUmnZYTJ06FZs2bUJkZGRfLDdEsRo5r1y5Evv379fb9/zzz+PPf/4z\nLly4gFdeeQXPP/88AKCoqAg7d+5EUVER9u/fj7Vr15p9MlW0tqGtoAT+Y5M1gbQNtplO6XWbsvS6\n6NVy1y5SnTYJAomxbYYgCIIgCPdi3LhxeP/99zF9+nQkJCTg4Ycfhlze17DxwIEDmDFjBhITE5Gb\nm4uioiIAwD//+U8sW7aMPW/SpElYuXIlu52WlobCwkKj+82fPx8AkJiYiPj4eJw5cwbbtm1Dbm4u\nXnrpJSQnJ+ONN95AZWUlFi5ciOTkZKSkpGDNmjVoa2tjr1NdXY0VK1Zg5MiRSE5Oxvr169ljW7du\nxZQpU5CUlITFixejurra7Pvft28fsrOzkZiYiAULFqCkpAQAsHDhQuTn52P9+vWIj49Hebnx2sDm\n5mY88cQTGDt2LJKSkrB8+XKrulnSXCaTYcmSJairq0N8fDzi4+NRX18PhmGwceNGTJw4EcnJyVi1\nahVaWloA9M1kbN26FRkZGbjnnnuMxikSibBmzRpMmTIFfOpqbz14nz59OoKDg/X2RUdHo7W1FQDQ\n0tKCmJgYAMDu3buxdOlSiEQiJCQkIDk5GadPnzZ7bYGvDwLSeruW2uJ5t9EXr0vQ5AzELrtbb59v\nYqzHPrWR/5I7SFvuIG25hfTlDtKWO2z1ZfN4POzevRu7du3CxYsXUVhYiO3btwMALl26hKeeegob\nN25EeXk5HnroISxbtgwKhQI5OTk4ceIEAKC2thYKhQJnz54FAFRWVqKzsxNjx441ut/evXvZc6RS\nKW655RYAwPnz55GYmIiSkhKsW7cODMNg3bp1uHLlCk6ePImamhq8/vrrADSZ+aVLlyI+Ph6//PIL\nCgsL2aB179692LhxI7Zs2YKysjJkZ2dj9erVJt97WVkZHn30Ubz++usoKyvDnDlzsGzZMiiVSuze\nvRvZ2dl48803IZVKkZSUZKTtY489BrlcjhMnTqCkpARr1661qpslzX19ffH1118jKioKUqkUUqkU\nkZGR+Oijj7Bv3z788MMPuHLlCoKCgvDcc8/pvZcTJ07g1KlT2LVrl03/3Ycy/WrS9Prrr2PatGl4\n9tlnoVar2Q//9evXMWVKX9fU2NhY1NTUmL6Ig5s0mUMcFky12AmCIAiCQ/ZHTR3wNXLrjvf7tWvW\nrEFkZKTmOrm5KCgoAAB88cUXePDBB5GZmQkAeOCBB/DOO+/g7NmzyM7Ohp+fHy5duoTS0lLMmjUL\nly9fRmlpKU6fPo2pU02/J3N2maioKDbI9vb2RmJiIhITEwEAoaGhePzxx/HWW28BAM6dO4f6+nq8\n8sorbCZZGz9t3rwZTz/9NFJSUgAAzzzzDN555x1UV1cjNjZW757ffvst5s6di1tvvRUA8OSTT+Kj\njz7SG7+58dbV1SEvLw/l5eUICNC4FLKzs23SzZLmpu73+eef480330R0dDQAjYNj3Lhx+Oijj9hz\n1q9fDx8fckXYQr+C94cffhjvvvsu7rnnHnz99ddYtWoVDh06ZPJccxnulz7fhNjoaPgVnARTVoVp\ncUGYPkOzOFTrIdRmNPKPHUNDaTFmJmsWm54pLQYA3JKSanWbJxAgPz8fHYp2xPZWkzG6vgdt6/ov\nXWE8nrSt3ecq4/Gk7YKCAjz++OMuMx5P2yZ9udv+8MMPkZ6e7jLj4WI7ODgYYWFhAPq80trMrXZb\nG3ibO96fbV1ftqXz1Wo1IiIi2G0+nw+ZTFPUoqKiAjt27GArrTAMA6VSidraWgDA5MmTkZeXh+vX\nryMnJwc+Pj748ccfcenSJUydOtXk/To6Othx6Y4xJiZG7/wbN27gueeew5kzZyCTycAwDAIDA9He\n3o6amhrExcWx49S9/rVr17Bhwwb88Y9/1AuEa2trERgYqHd+VVUV+94BoKOjA1FRUez7UyqVehYi\n3fHW1NQgKChIL07THq+qqsLOnTvx8ccfA9DEckqlEhUVFexi1IiICPZ8b29v1NXVob29HZ2dnSav\nt3z5cvZePB4PQqEQ5eXl6OnpMamfuf/eupo48vPWn23t96vWjSKVSs3OkjgSHmNDjcbKykrcfffd\n7FNVQEAA69tiGAZBQUFobW1lp4NeeOEFAJonsZdffhlZWVl618vLy0NkaR0EfhJEzZ+J6m3/xrAl\n88AX9j1LMCoV5Deb4B0VDnWPAjU79wAA/FJHoKP4qs1vcKjVZc/Pz6dpXI4gbbmDtOUW0pc7hoK2\nDQ0NbPA+mLS3t9tknRk/fjxbVQXQuAOuXbuGDz/8EOvWrUNsbCzWrVtn8rVffvkl9u/fD6lUiq+/\n/hqXL1/GV199hbNnz+Lzzz/HuHHGPWGqqqowfvx43Lx5k82ab9u2DVu3bmUtNYAmCy6Xy/HWW28h\nMDAQe/bswfr163H58mWcPn0ay5cvR1FREQQG7oDFixdj6dKluO+++6y+97/+9a8oKirCP/7xDwCa\nmCwtLQ2ffPIJpk6digULFmDJkiX43e9+p/e69vZ2yGQypKWl6WXetVjTzZTmlZWV2LRpE44dO4Y1\na9bg8uXL7PlZWVl47733MHnyZKNrSaVSTJgwQU9PS6SlpeHjjz82OzMyWJj7d3H+/HnMnj2b03v3\ny/WfnJyMI0eOAAB+/PFHjByp8a0vWLAAO3bsQE9PDyoqKlBaWmryP5SWvqc94+y8rKIaNw8ZlwKy\nJ3Afinj6j4gzIW25g7TlFtKXO0hb7hhILXJtXnLFihXYvHkzzp07B4ZhIJPJcPDgQTZ7npOTg/z8\nfMjlckRHRyMrKwt5eXlobm5GRkaGyWuHhoaCz+ejoqLC4hhkMhkkEgn8/f1x/fp1vPfee+yxiRMn\nIjIyEi+//DI6OzvR3d2NU6dOAdAUCnn77bdRXKxxEbS1teG774ybUwLAokWLcOjQIRw9ehQKhQLv\nv/8+vL299WIvUzlaf39/REVFYc6cOXj22WfR2toKhUKB48eP26SbJcLDw9Hc3Ky3OPehhx7Cq6++\nyi68bWhowL59+6xeSxe5XI7u7m6jv4ciVm0zS5cuxZEjR9DQ0IC4uDi88sor+Pjjj/HEE09ALpfD\nx8eHnVYZM2YMlixZgjFjxkAoFOKDDz4wa5sx+jAZfrZ0j/djoSqgqetOEARBEMTQgcfjsbHH+PHj\nsXHjRqxfvx5Xr16Fj48PpkyZwmZtR4wYAT8/P9ZvHhAQgMTERISFhZmNXyQSCdatW4d58+ZBqVTi\nq6++0runlueffx5r165FQkICkpKScP/992PTpk0AAIFAgG3btuHFF19ERkYGeDweFi9ejKysLMyf\nPx8ymQyrV69GVVUVAgICcNttt2HRImMnQXJyMjZt2oT169ejtrYWGRkZ2LZtG4Q6TgZLBTo2bdqE\nl156CVlZWejp6cH06dMxdepUs7rl5ORY1XzkyJG49957kZmZya6LfOyxx8AwDO677z7U1tYiPDwc\n9957L+bNm2d1jFomT56M6upqVisej4eLFy8arQMYCthkm3E0eXl5iCiphSjAD5F33orq7T9g2OJc\nvTrrHaWVaD55EXHLF0Et70HNV3stXNE0scvuHnKLVYfCFK6zIG25g7TlFtKXO4aCtq5umyHsh7Qd\nOG5nm3EIDGPKLcMi8BZrTlOrLTZCMIckKX7IBe4EQRAEQRCEZ+Male5NNGni9wbvYBh0SWvtvqT3\nsAjrJ3kgnp4BciakLXeQttxC+nIHacsdlBnmDtLWvelXqUiHYCWZ3lmpqQ/PMAxazhbYdenwOTkQ\nRw3+FB9BEARBEARBcIlrZN4BqFRqvW1tVZnu6jowKpVd1/KODvfYDqrW0K1JTjgW0pY7SFtuIX25\ng7TlDt2a5IRjIW3dGycG74zGLgPNKuODpU2QNhuX/WkrKBnsgREEQRAE0YsT6loQhMvjzH8XLpN5\nBwC5QfYdAIImpdt1jfA5pssYDRXIf8kdpC13kLbcQvpyx1DQViQSoaWlZdCDFfJlcwdpOzC6u7uN\nmmsNJk7zvOt9CZhYsMrCt8/+4h0dPoBREQRBEAShS1BQEDo7O9HQ0ADAtprcBOGpMAwDgUCA4OBg\np43BeQtWYdsXAM9aq1w+H1CrLT8ADCGGQs1hZ0Hacgdpyy2kL3cMFW0lEgkkEsmg3nOoaOsMSFv3\nxrl13nVRq6Fu6wCj1rfOWAvwYx+Yj9jfLgBf7OXoERIEQRAEQRCES+EanncegPJKdBz4CbLSa/a9\nls+3np0fQtCTNHeQttxB2nIL6csdpC13kLbcQdq6N66TeVcqNbt7y0JKEuMsvlzg4623TR48giAI\ngiAIwtNxbsq6N+BWd8sBlQo8aBYCqOU96KyosvhSrzD9hQJ8L7LNAFRzmEtIW+4gbbmF9OUO0pY7\nSFvuIG3dG6cuWNWFV1MLBPkADIOeljar5wdNSkNXVS27HX57Dhi1fc2cCIIgCIIgCMKdcFrwXtve\nA1/fHkTo7BMEBgAMA0apQo+SAXjmi+ALJD4A+uwyAh8x10N2C8jHxh2kLXeQttxC+nIHacsdpC13\nkLbujdNsMw2yHjR2KfX2CUKCwKgZKNs6UNLQibKGToiCAiCOotrtBEEQBEEQBOFUz7uAx0Ntuxyt\nvUE8T8BnF7IyYKAaMwp8kZAWo9oB+di4g7TlDtKWW0hf7iBtuYO05Q7S1r1xuuf9Yk07mNZuzQZf\nE7wb1no3CTVkIgiCIAiCIIYYTg3eGfRm2UNDwGtsQqtCjdZ6mSYDDwB+fprjFKjbDPnYuIO05Q7S\nlltIX+4gbbmDtOUO0ta9cW7mncfrDd81tph2NR++ZVfB5/PAjE0FLyJMc542dufzAVuy8gRBEARB\nEAThgbhEa1Jed69tJiEeoYtuR9ii24HE4TCXb/eJix60sbkb5GPjDtKWO0hbbiF9uYO05Q7SljtI\nW/fG6Z53BgBPJtP8zQB8sRf4PB7AUxqcBdbnHjYzCwzDsOUiCYIgCIIgCGIo4OQOqzp/C0VgGAY8\n8GC2uIyO953H42HYfXdwOjx3hHxs3EHacgdpyy2kL3eQttxB2nIHaeveODd41/XF8Hv97zxoMu86\n+MRFQxwZNpgjIwiCIAiCIAiXw6nBu56nvXfxqqmku//oEYiYOw3iiFCII0IHZ3BuCvnYuIO05Q7S\nlltIX+4gbbmDtOUO0ta9cbrnnQeAGZUCiL3Ybb4Z20z4XJrmIQiCIAiCIIYuPMYJRdTz8vJQl1cE\nv9goyCaMhxqAv1iAdrkKqeESiPh8FNR3AADmp2rsMrIeFXy9BIM9VIIgCIIgCIKwifPnz2P27Nmc\n3sMlSkUa4iU0Tr3/VN6MGx096FFRnXeCIAiCIAhiaOIy1WZ4vRu83v8zxc2OHhwqbRqMkbkt5GPj\nDtKWO0hbbiF9uYO05Q7SljtIW/fGavC+atUqREZGIj09XW//e++9h9GjRyMtLQ3r169n97/22mtI\nSUlBamoqDh48aPHaDANo60Jqw3WzZSIB9Kg0Dp+2biVKGjqtDZ0gCIIgCIIgPAqrC1ZXrlyJJ598\nEitWrGD3HT58GN9//z0uXboEkUiEmzdvAgCKioqwc+dOFBUVoaamBnPmzEFJSQn4fNPPCLpme1+x\nAGowJn3tpQaBevFNGW7KFBgZJrHlPQ4pqHYrd5C23EHacgvpyx2kLXeQttxB2ro3VjPv06dPR3Bw\nsN6+Dz/8EC+++CJEIhEAIDw8HACwe/duLF26FCKRCAkJCUhOTsbp06dNXpcHAExfxj3K3wszEoMR\n4eeld97Vxk42y369XQ4AuClT2Pr+CIIgCIIgCMJj6JfnvbS0FEePHsWUKVMwc+ZMnD17FgBw/fp1\nxMbGsufFxsaipqbGzFV40M2967pldK0zLV3K/gxxyEI+Nu4gbbmDtOUW0pc7SFvuIG25g7R1b/pV\n512pVKK5uRknT57EmTNnsGTJEpSXl5s8l2fGxL7p31sQHRcP5YV8+Pj6QzV1IhbMvQ0AcPrEMVy5\n0YnRmVlICPHBmZPH0dGjwujMLADAlfOnAADzU+cD6PsQaqeBaJu2udjW4irj8aTtgoIClxqPp22T\nvtxtFxQUuNR4aJu2bdnW4irjceftgoICtLa2AgCkUilWr14NrrGpzntlZSXuvvtu9ktq3rx5eOGF\nF3DrrbcCAJKTk3Hy5El8+umnAIAXXngBAJCbm4uXX34ZWVlZetfLy8vDjR+vwDszDfLYWCjVDCbG\n+CPKXwwAaJQpcLJKI8SU+ECclLaaHJe2BjxBEARBEARBOBuXrfO+aNEi/PjjjwCAkpIS9PT0ICws\nDAsWLMCOHTvQ09ODiooKlJaWYvLkySavYaGojEEJSYIgCIIgCIIgABuC96VLl2Lq1KkoKSlBXFwc\nNm/ejFWrVqG8vBzp6elYunQpvvzySwDAmDFjsGTJEowZMwbz5s3DBx98YNY2AwAMj28yOLc1YN9T\n3AAAOHy1GV0KlY2v8mwMp8QIx0Hacgdpyy2kL3eQttxB2nIHaeveCK2dsH37dpP7t2zZYnL/hg0b\nsGHDBptuzpgJ0+3NtncqVOjoUcFHZFxmkiAIgiAIgiA8Bed1WOUBjJkoXSjg6Z5mE82dyoGPyQPQ\nLqIgHA9pyx2kLbeQvtxB2nIHacsdpK1747TgnQceeDzTt/cX608IBPtYnSCAtKXbIeMiCIIgCIIg\nCFfFeZn33rtrLfE8Czn2MF8vs8cIfcjHxh2kLXeQttxC+nIHacsdpC13kLbujdOC92h/LzAC6xl1\n8IDYALHZwwqV2mhffXsP1NYrYBIEQRAEQRCEW+G04D1u2V1AhPU67b5eAlgoWIM2uabKDNPbrbW0\noRNna9rQIFM4ZJzuBvnYuIO05Q7SlltIX+4gbbmDtOUO0ta9cVrwLhQJIVeqIbAQmUtEAngJLA+x\nvr0HANCjYtClUOFaM3nfCYIgCIIgCM/EacG7n1iIOSkhmJEUbPL4lLhATIzxt3qdiuYu9u8uhbGF\nZqhBPjbuIG25g7TlFtKXO0hb7iBtuYO0dW9sMJ1zh6WseqiviP3bUqMnXU5IWwc8JoIgCIIgCIJw\nVXgMM/grO/Py8pCZmclu7yluwKSYAET6m64q061UI6+sye77zE+17qknCIIgCIIgCEdw/vx5zJ49\nm9N7OLdUpI3Y23GVIAiCIAiCIDwRtwjeB4JKzUCltj65wDAMlDac5+qQj407SFvuIG25hfTlDtKW\nO0hb7iBt3Ru3CN4Hknk/dq0F+0sarZ5X2tCFAzacRxAEQRAEQRDOwi2C94HQ3lsHvkOutHieTKEa\njOFwDtVu5Q7SljtIW24hfbmDtOUO0pY7SFv3xmWCd4sFZRxgej9S0WLZFuP+jhmCIAiCIAjCw3GZ\n4H0wcEJhnUGHfGzcQdpyB2nLLaQvd5C23EHacgdp6964RfDe38R7u4FVhsfjobCuQy+Ib+tW4soN\n2QBGRxAEQRAEQRCDg1ObNNmKrU2aDDklbTPaV9nSDYWawbAAMSL8vFDdKkdFcxfCdZpCuTPkY+MO\n0pY7SFtuIX25g7TlDtKWO0hb98YtMu/9Ra5Sm9xf0yaHtKVbb99NmcLovOauvn0Nsh6PKCVJEARB\nEARBuC8uEbx7CXjwEXE/lNNVrWaPCXqz+1cbOwFo6sMfv9Z3/qmqNlQ2dXE7QAdAPjbuIG25g7Tl\nFtKXO0hb7iBtuYO0dW9cIni/PSUU/mLuHTzNXebLRap6ffDFNzv19t+U9Vhs8rTv10a0dlsuQ0kQ\nBEEQBEEQjsAlgndbifTzcti1tAG5rjXG8BgAnK5qw6+9AX1Lt9KoYo2aYVwqeHeGj62grgNlDRqN\nCus60KNSQ6lm2FkMLaerWqEwY2VyB8gjyB2kLbeQvtxB2nIHaTswatvl+PR0jcljpK174xbBu3a5\nqq+XwGHX1Gbau5XGweThq8162xXNGrtMfUcPGjqNg/2hXiNe2tKNa71rCCpbutHUqUCDrMfELIYC\nsh7PaIZFEARBEK7MT1eb8dWlG84eBsEBbhG8C/gO6NJkAK/3kcBU8G5uoSsASJu7jfYV1Hc4bmAD\nxJk+tk4bAnN3fs4hjyB3kLbcQvpyB2nLHaTtwNAaBe749AK6DLrIk7bujVsE71pcocdSXUcPmjsV\nFn3wnkxFUxcKTTysqNQMDpf3zVgMTXUIgiAIwjVgdP5X1qPC3E8voL69x5lDIhyEWwXvg4nKwpPC\ncWkrqlqNM/CuANc+ttKGTlQ2d6PG4P2be5hpMVhTcPF6u833unJD5lI2G/IIcgdpyy2kL3eQttxB\n2g4M3V9l7U/01SaNndWStjt+qcNJqfnqfITzoeDdDIdKmyweN6wT32PCfuOJKHq/AeRKg2DdsJFW\n7+Fj1/S/ADoVtunU0qVAeVMXatvk/RonQRAEQQxlrumUt/7djkIAwP8cqrD6un+cqcVrhytR1eKa\nSUrCDYP32ACxQ67T1KUwyh7bQ7tcPyNc1+EaU1GD5WNjLBhjiuplOK+TYd9T3ICShk6z5xvS1Kkw\nCvpdAfIIcgdpyy2kL3eQttxB2g6MIxUtZo9Z07ZLocbDu644ekiEg3C74D0j2s9h17pY67iFpgzD\nGHVgVakZ1LYbd3MdLG7KHPtAYarD7J7iBqN9XSZmIUrtCN7JL08QBEEMVaTN3WatqK3dSr3fYoVK\njcpm128gSTgWq8H7qlWrEBkZifT0dKNjf/vb38Dn89HU1Gcxee2115CSkoLU1FQcPHjQsaMFwOPx\nMMxE9l3EQUUae2iQKXCgpFFv3+W6DpyvaUdBXd9DwoWadqNa8Y5E62OTK9U4XdXm0GsX35DpbZ+t\n7t/13dUKQ/5L7iBtuYX05Q7SljuGqrarv7mCfb9q4okrN2Q4VtmXQb9/awFeO1zJbn9XeBOPflNs\n1/V7lGpMmzYNfzxwFV/9Uu+QMRODi9XgfeXKldi/f7/R/qqqKhw6dAjDhw9n9xUVFWHnzp0oKirC\n/v37sXbtWqjVjvOCW7JqZMb4O+w+tnJN52nXVMnJHpXxeK+3y+GqhWq6FCq0mWg41aVQYU9xA1vL\nHQCaOpWo17EK2fPodN5g0WpVS7deoyvda/3a0Ik9xQ0ms/4EQRAE4YloSzu+deQaXv5PBZ7+voQ9\n9nNFC/ubqBt7/Ke0CW8flbLbt40INnntd/KluNHRg1NVbXpV4gDzxScI18Jq8D59+nQ9tmV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FeXbmDx1gKs+Vdf9ryssQsnpZp1Aw0yBVbsLMLlOs1n85FdV/DxqRr8pbdLXkuvlWbupxfQ0qXA\nvl8bMffTC/jb0b5s1XvHq/GBzsOEreg+ONW0dts09Uo4F1MPitZwROMyhoHVh+AferPzN2U9+Lmi\nBXUmHoqJocEHJ6rx16NSqNQMmnvXKWk/hvd8ecmJIxsY2tnOpeOjBuV+te2eXdXO2Xhc8B4XZHvg\nLeDzECIRgc/Tn8TnuZeNTQ9ned61dfX9xZZtShI3tjEZasulJeaX2g6TfvlupRpXex8GTIU1hmVA\nz1a3syUxG0wEuGd1Vvtrz7M1XjJ8sLjW0o1dBTdwpHcB7q6CG+yxdrkKn5zSNOX4xSDLyYPG29oh\nV/YrWFv59RW8sM96o53iG7J+BZCegCt4h/92VIov7FikXNHUhdzPBp4dPH6tFYu+vARZjwr/74dS\nvc+8Ib/dXog/51VgxU7bu2K6graeijO01VaU+X8/lOI3/9RYOtz9W2NGYhBuT9FYZqYnBGHZ+EjO\nPe+OZqh+d5vD44J3LY6Ov904nuechGBv1ksXIhFhigWLkdDNFvg4E+2PSFmvt17bYVfbglr7XcYw\nDCqaunBFZ6FpUX0HXuwNaH+62oxCM4v2fipvQcnNTnxxrhav/EeTMdddSKrljyamQP+jk8E3xJp1\nxxT3binA3mL96epX/lPOziT0qNRsec9ugwcnw21TPPV9idGDAzF4HCxtwteXbK973WymGtT9Wwvw\n01X9B0elmjHbaEn72Thf046Cug5s2G/bdP6/Lt+wfhLhcZQ3aWb1dPuqOGIGyFm8Pm8E/jA7EUvG\nRQLQlMV+aNIw7H4wgz1HItIPBRenRwzqGG3hp3LjzudDGY8N3s2hfcP2dmB1l3+6g+l55/N4uC0p\nGKnhvuyqex6AUIkI4Sbq5vv3NriI8LVsnbljZKjDx+oIBns9gTaz/2tDJwrrOnCuWt8io9vBtayx\nk+3yBwDfFNzAuV5LTbdSbeQR13o6T1xrxVtHruGfF+osVuUwVb7UEnf+wzhjaraKDq/P29pg4J/P\nr2xFfm8mf29xI57+dwkATfa+XaepmjnfvSH9eajwBLj0Djd3KfD5WdvWIPSoGJNVjkzBM5Myae1W\norC+77Na3dqN1buK8NT3JQb30g/m/9xr57KVTSdrUNLQiQ4rzfvI884drqLtURcKHH83wTG2l3On\nTrD/wgK99ZtPuWJlPioXqY/HBu+GVhgt8zj6UIb4OL+G+WCQOzIU80aFQiISIFQihMRLwAbu/l4C\n1hYzPtofYyM1tfPnp4ZhfmoYAnq/ILQLZsxhT3be3ocwd6WqVW7UAViu1ASiDIwDnZ8r+xbl7vyl\nHpcN1kx8qrN6/9og1Co2tbBWi/r/t3fegVGV2ft/7rT0Mull0nsPvRiQltClg0QBQVzLur91dVnd\npl8rsK66RV0LIqg0O65CFhcEzEoRKQKB0AKEhJYOBFLf3x8zczN35k5Lpobz+Qfmzp2Ze0/uzD3v\n+z7nOToJtanUWn/2a8aHh/kf9Ns0J3cJDl+6jrUHjc+o1za34Y0fuvycjdXvtHcy4QqRia/24Us3\nsPqni1iw4SgWfXIM1U2tOF17U7C0/vx/rUvWxWb6H/2yHO+S00Wv5dK1FoPiVH0e+PQY/rLjnIOO\nyDzz+0WKbl9yZ6zodmODYKDr9/bBwdGC7dEBjm+oaA53s+W0N70yeZ+YHtKjP7QqwAPxSuuKVvur\n/Lr9ebbEnpp3T5kEUgkHCcfhzsRADFD5C54fnqiEQqq+pBQyCeKVXhhnZhY9wFNmsGRnjIJ40422\n7I0zPfQ79BLX41duoEIz8765vBYtRiQDgLikpEHEl92e/Ok/Z4w+V3ezHYq4HJOvP1N7U/QWpD+T\nfqHxFq/dF8ONV797hD21w6aSAwCYu/YINpZ12TVqf5r//J/T2FvZNcjceqoOv/n6JACgo5Phjzry\nloabbShacQBFKw4AAM7U3cSaA5cMiuLWa9rRP/ffM1avFmn1zfpoi6OPXbkhalFKmnf7Ye/Yfnzo\nCv6607TdoyMmN/T58+gEk8//a1oaAOH4tjDFuhXrgoICSDi1UcfQOMN7a8n9+bgzwbn3XF2klLsL\n6JXJe09ResmRFe4r2MZB6KSiP9Mul/buUI5PCxZ4xEo4DpwFlb1igyjdbVlhPugX7W+wDwAMilFv\nTwzywshEpWiKYGyFpbej3wzK3TGV3Fc1teChL47jX7urDJ7TnWmtqLuJRZ8cwwsi8ghtN9frrR0C\nuRHRc6z9Bv5Y2YTGW+3YU9kkkCNoC7T3XWjC+JUH+YGZ2pbUsgTq/X3qv3Pp2e7ZwYqhvcJ+/dUJ\n/O+s68gniJ5jrK7C2QR5m16dTgoWt1zesriPVZ/z3swMvD09nX+cG+GLlyckA1DfW58aGW/UhMJT\n5tic53a91xujd2ecNkBXlpEU7AUAiPRTQO6iw0B76bJt+cWJU3oiMUgdS6W3HG0is1kT00MQotHG\nK6ScUZea1FDH+ca7soe+uyPmOVzbrL6xXmg0Lrn55Zfl/P+/OHIVgFoPX9V4C0UrDvBFjNrmUku/\nO4tffHYcN9us008+9Pkx7BSx7bzQeMuke4mrYE/tsO5PQ9GKA2YbaP3vXCM+PmRcZiNWUHrwonjj\nMEdwqqaZPyexmglLY3vlutqGkrAce2ve/3dOPcg7U+s6A/r+Kj9khfvii/m5eHdGV2K9eVG+QXLO\nAPxlQjLGplrffKm0tBTRAZ6I0kxKPjUiDr8bEYe8qC4VgVTCodiIteQCI/Ide+GqOZezoOTdQjiu\nq+ASsG7UqZXgmLNR7C729qUfbuOlMwnHCVYuTFlAhfkoEKpX4DpUx80mNtATEb4KJCi9bHqMhHPY\nfLwWm8trseVELeauNd9576qO/WW7znW08BN1A5X2ToYr11tRqTcAmLL6Z4s7AAJqB4ofRZL0V3ee\nt9i9pDei7Qkg2AZ1El9+9QZKysX1xJ9obESvt3ag4WYbDlabTs7XmdDU67Pkm5MW72sJLR0M4zUF\n2GLjkm2n6wSDwU7G+IGnLh/uvygomt1b2cjLgAjn8tAXx426FTka7USZj0IKX0VXzmFMCpwf5Ycn\nhscZf0MLc95RyUEIE+nDojs415XKKhycTOvnAbc7lLxbQEF8IAJ1kk2FVIKMMB+EW9hwSPtlzAr3\nRaodOoxmhHnD30OGftF+Al12XKCnTQo6dQcttiLcT4ExFrRqHhDjzxe6alF6ywWONf1U/kgIsn9j\nLWdq3ns7Ws/hhlvteO3782Z1qGKIWVd+/PMVLPxY3LO72crZd3fGXtrh7ysa8PdSdTHqV2VXBc9V\nNrQIGoaJ8cO5RsxecwS/22Tep99SHG0HWtoWI3Bq+s+JOtGB541WYXJ4vt7xWmp3ozvX7b4LTXhn\nj6HETp9d54TSqv1V1zBv/VGrP89aFvaP5CWhgHqmfdn4JP6xIEfQ3L6/vi/P4H3uygzBlExDA47l\nGtmLOSyNre5E5aDYruN2VVe424XbMnkP8pIj2NtydxhdG6VRSUpkhKmtERVW6tzt5YwilXAYlhCI\nCD9hhXiYrwKBZpxdnImH5kfBFk4hXnIpJqaHwMvBOjzCtVlz4JKoLAsAHv6iHB9b4TsuRm+tfz1R\n04wTNeY7A+vOur/+g7pT7hVNo7C/7DhnVWdoY7P0rkRbRyee3nIarZoi8G2n1ANG7aLPv3ZdMLA7\nBdTFrqVG9PLrDxn2VbideOjz4wYDP0C9elPZoJa/tVjREO+LI1cFDeIYY4IVjpb2TnR0MjzzrbDO\n5s9bzuDydcd0BdX+JN3bJwIvjUtGX03d17sz0jGvr6FMRSFyX3t0aAx+OTTGYHufKKF5RqRfz2as\nx6YG475+kfjlEBUmpofg9yPj8Y+7UkWPiXAct2X0+6v8BLoua/CSd1kjesiEyfjAGPHCSwAoTA4y\nmEG2BT5yqUCPrtVlj00NRpivAtl6hbfWkq2xe7QnWmtIa6RIzEjaZM2gzFpI824/xDTvjmDF3mpc\nvNaC+pttqG1uQ9nlG90uYquou2kyyXCm5tla7fCjX5bjUZ16AjH+e7IO1SLSo5U/ds9a0ZLBgrO5\neqMNu883YdKqQ3h5xzks234OTacP4s9b1IngF0evisZE1AFJ87u98kfLu84C6mR0sxsMdCzlTN1N\nfuCnz3+37wQAgSyJMYaaG60GPv5a9Muz9mn6Y9TeaMPfSs/jrlWH8OYu8c9zBKOSguClcViLCRRO\nuDFAYATh5yFFYg9Wlbcs7mMwqafF0t8EqYRDcZ8ITMkKhVTCYWSSEulh6rxA3x/enkT6k2xGF9ed\nlrUjljrD+HlITSaUKSHeCPVRwFejZTelyTI3Sh2XGowSM0vMAOAlk/DNewAgUyS59pZL+YTYy0Ib\nRn3yI/2gkHEIsWMyrCXIW46ilCDU3GizqFMmQdiSBRuEspr+Kj+8NC4Z31c0ICXES/Tm19HJ0HSr\nHeVXuxLOBz8/juL8cNzXP0r0cz746SK2nKyz2hHCVTHmfb2zFxdl6q40fKsn01qtcTTSb6a2/XS9\nuEuNTo3G0cvXDRzO9Hn/x2qE+ykwPCEQr31/HuPTXFO2oB3EahM8S3no82NYPiFFkBCuP3QZiA4V\nTFDNXXcEdc3tmJ0bhsUDow3eRzd3v3qjFX/UdIf+qaqJ7+Bsyb3W1kg49Yx7uJ8CjxXEYEG/SKj0\n/NT1V/MVUgnemp7hyMO0iglpwVhnovjclihvk146lnJbzrxbSkG8oZe5LhKOQ5C33Kx8RuusAlhv\nq6aPftGK/mx+/oAh8O9GYayYr32oj8IiO0hbIJdKEOnvgYQg44WnXnIJ/DSuMykh3sgUuTkE2FEm\nRJp3+6HVvLsCWlvC57dWYP6GMr7Dqy4bDl3GnLVHDNxHxAafN9s6UFF3k18rmvHhzz0+xl9tLMc/\nSitRZqEsxdaad1NF5r2Zr4/VGGzTXrtrDqjlL/oFvC/vPIcdZgY0v/n3SRy/0vW3rGpsMbiW1h26\njDd3XcBL353tzqGbpdVGEye/23TKoNutlu/0int1OVN3C7M+Ooxb7Z38sbDobME+jDHUNavjW3+z\nHUUrDmD3eaF2XZvo76yoxz3rujTsukXEWltSR6B1qRuiY7Tg6yFDTKCn4P66Zm4W7/ziCKg/gXtj\nNnlftGgRwsPDkZPT1URlyZIlyMjIQF5eHqZPn47Gxq4vz9KlS5GSkoL09HRs2bLFPkftICz1Mtcl\nI9THIOH3sKE2TF8Won90I5OU6BNtKAky5xiTFe7Lt0TOifBFRA91cvZALpVgeKISgHoULpboxyu9\nkGaHomDi9kHfKeQ5Ed94fWmNNokXk9d/uP8SHvz8OP/4Wov5QtmOTmbSiaT8ajN+qmrCY/8+gb2V\njWjr6MTvNp3ERwcM9dNHL10320XSGEUrDuDFbRXYXF6LG60dfGz+d852Puq9la/KruK/J+sMEsXS\nigZ1Aqt3b6m/2ZX0L/ykDO/vM5QftXYwXgZijt9vPoViTeHshcZbJlc1Lza1YNKqQxa9r6U0iMjP\nln53Du/u6TqvCpF+FYs/LcOjG8UlW3U6MdJGtaS8Fs2aTssl5bXYpUnmX9h6VvBabQ8AR6HtMP7G\n1DTc0ycCCwdEYc3cLKP7u6ObityGuY2piVLCELORX7hwIUpKSgTbioqKcPToURw6dAipqalYunQp\nAKCsrAwbNmxAWVkZSkpK8Mgjj6Cz8/aSQSQGe1lkCalbWBnqI4eltaz6S0f63qe7fvifYImR4zjI\nJJxJxxiZ3odH+3tQK2IRSPNuP5yleTfGir2GbhU3Wjvx2eErqG1uM6i4mKCxEtx+2tALXkwH/9r3\n53G+4Rb+uuOcqMa+04KZbe0ef/rPGZSU1+Jg9XVRecYbuy7g6fe/QtGKA7gqUkxZfvUGilYcwMeH\nLosey44zDXjt+/OY9sHPvIvKc/81HNDcrhi7dl//4YKotOi5rRX4687zoo4ouh752oTUFDdaO3DI\niM3mT1XXUKMZbC365BjfqEyfx746YbQWo/FWO39M/yittMiNRXvnmL3mCG7onFHKLokAACAASURB\nVMPPGq/+r493rV6cEUner1xvw1mNE482ttpbmtiKzw/nGjH1A/Vq1qvfW+9SZS+0xyzhOCzoF4nY\nQE+XStBt4aE/KycMb0xNM/r8b4fHWvxeL4xNFDx+f5bryoVcAbPJ+7Bhw6BUKgXbCgsLIZGoXzpo\n0CBcuKAu/ti4cSPmzp0LuVyO+Ph4JCcnY+/evXY4bNdGIZWY9UCN1/ElHxgTAI7joLRA8qHNqbUJ\ntyXNk7SWTqONWDOOTOz6+05MD+n1iXuoj7h2LtBTxstytAMw/U66xO3Bxz9fMdi2t7IRb++pwty1\nR0RtKQG1ZGLz8Rr++a/KruLfIlKLzeW1WPzpMWw5WYejlwylL6Zyd+1g4NK1rkRcrHmQGI06M5f1\nzW1outXOF1iu+LHaooJaV+1K6U6IxfmZb89g/MqDqNX0LjBX/8MYw/qDl7Bk0ykcuSS0x9RNmrXF\nsjeMDAbKrtzAT1XijcZmfXQYs9ccBgAcuXzdIjcW3VvStA+6JGK//abLDrSqsQW1N9qwfLt43YQ+\nMz5UH4PuVW7sO+gsJqULbRvvzgvHwv6ObWSkZUZ2qEM+x0MmQYqJle6C+EB8MCdT1EFHH12VwyuT\nUhCt079m0yLXkVW6Cj1e81i5ciUmTJgAAKiuroZKpeKfU6lUqKoy77fa25BKOBSmBEMqkljHKT3R\nL9oPicFe6Ksnbxmso4kDAH+x2XIzebUpHZunTAIvmQQxAZ7w1elY2tssn0ylMQoph37RhstzE9ND\ncEd8IAbE+CMj1IcvVM6L7Cois4fm3Vtun8Zd7oYrad6NoZtQN7cZT6xeK63EX3acQ11zGz4/omNZ\nZ2R/a/3mJ4vIG4zJ+y5fa8Wp2pt8fHWP4d71R/Hbb07im2PWSWrmrDHfPOt2wtbXrjaR3nGmAXUi\nzZ60FK87ig2aQebjXwsbU+kmzbM+0iS+Jn4YTU3Y6Mu8DphpqCX2TpevCZP+hZ+U4Z715q8j3dh+\n+vNlkw5Ip5zsVjRAx21u8YAoDIwJwFwj3UntzYODVWYL422teS/ODzfYJpFwiPDzQF6kOtfprzLv\n8hfoKUNOhPq+q/W3v11rbEzRo6ztxRdfhEKhQHFxsdF9HFXw6C7IpRLevULfyUZ3Fr1/tD+GiejU\nRRN6KxiZpEROhA/u1My2j0pSmnmF+xHuq+C9bfUHUOG+aklQf5EEHlBbgSYGe/HLm94K+yTXfgqp\nZnZf/aNESbzrY+3tQy1hMf/7d+ma4WymmNxi55l6ozp4sU+Z9dFhzNsglDn88styXGi8hYvXWtDW\nyXC2/hZ+1pm1XSOimScci26DsrvXHjGawOvXZjS3dqD8qvEC5jqRFZMvjhiuMBlDe41VaboV60p8\nZnz4M1b+WI3W9k6BLh1QF2zrX4eA9f093tlbLagL0OcRM9amjuL/ChMwzkWdgOwJY8DauVlYNKBr\ntUErQNCuZM/MCRN97bpidWHy5kX5+PjervpKhUyCEYmBvV4N0B26nQmuWrUKmzZtwtatW/lt0dHR\nqKys5B9fuHAB0dGGVk4A8MgjjyA2Vq2HCggIQE5ODj8S1Gqx3P1xakY/dDBm9PmsfoNEX39s/x50\nnvfG5KKR/GMAyO0/GD4KKY7t3wMfuRSxOf0NXq+rYxM7Po7juvYJSYdU57Gz42Wrxz/v282fn278\n5t9VCH9PGUpLS9Uj+dAM/vmAmgDB+zHGMGLQUACArPoorrd0oKL+JjL6DuLfTzsT353Hwd5yLJxa\nhLP1N/Hp5m3wkksQnzOg2++n/7izsgaSmFwAXbpR7SyWJY/9PaSAKqfbr7f2cXP1KUQMm+mwz3PE\n439C3SCF10SnjBLd/81PS5B4MwUFBQW4dK0F/9m2E1/vvgD/pHy1NOKbrQj0lOG1swFGP+/Vcz/D\nI07999Z+Hxpv+YjGd+aydZBwgG+i4fHX32zHHX9YhQ7GnB4/ez/e9Od7cffaIz1+v0vffwrvqGS7\nHe+E5z9CoKcM0DivGNt/X1U8Xth6Fn9Ku46m06cMnj+q6AdA+Hv5r91VaDp9ENtOd72f9nnt70nT\n6YOY+lIZmsMy1e/z024c28/h25tR2LK4D0pLS1FVdhLrW/JxvaXD4Pg+/mYrmk5Xdev8desJnH29\nGHs80fei2i6xUK3Z7qw8gp8rXed+aOyxdpst3q/p9El05BYhxEcB1bVTaDp9Ev5J+ZBLJfz+n80b\njPKrzWg6fRDR/h64FpoBX4UU1cd+wrH9N1BQUACpxDAfGa6owg//q3J6vEw9Pnz4MG/ccv78eSxe\nvBj2hmMWrEecPXsWkydPxuHD6uW3kpISPPHEE9ixYwdCQrp0XmVlZSguLsbevXtRVVWFMWPG4NSp\nUwaz71u3bkXfvn1tfCruR31zG34438i7vADAN5pinmHxgfD3lPGPAXWH1qLUYHxzvAYpId5IDvYy\n0LyXlpZavBz2zfEaFKUEWex77258c7wGUo5DUrAXTtQ0C+IMqG3LtPIH/efE+Pv6TUjOH2hynyh/\nD1Q3tcBLJsGQuABcutaKsiuGs2FpId5I1mgFT9Q0I9xXYbQDY3d4/8dqNFngamKMuzJD8FWZoVbb\nXjSdPugW0hlrCfCU8ZrjnAhfHNbTJmuZmx+O4vwIA0lMbKAnzjfcsuozV8zMwNm6m3hh21l+W2+N\nb0/YuCAXU1b33LbTVWLrIeXQ0sHwwZxMzNfrXaBFV0ohtooT5C3DxPQQzOsbiXnrj4pq3B8eHI1P\nfr6CmuY2/v1MOSP9aqgK/zTShMkcrhJbUywfn4wnN5/Cs4WJeObbM27Tx8GaXMEcRSsOYGZOGH4x\nSD1Zu7eyER8fuoK/TkoR7PdjZRP++J/TSAv1RvnVZvxmWCxe+/6828TMUvbv34/Ro0fb9TPMzrzP\nnTsXO3bsQE1NDWJiYvDss89i6dKlaG1tRWFhIQBgyJAhePPNN5GZmYnZs2cjMzMTMpkMb775Jslm\nTOBpooGSuW6s3nKJaLGqNV/GlBBvA6eZ3sTQuABIOM5ogd2gmAB8d8bQHcQYD88ch29P1SHYWw4P\nmUTQSdHfQ4amlnb0ifITtKf20chuJAC0KukJacGC70WqJomfmB6Cm20daO9kTm90Mz4t2KHJu6vf\noLuLbmdNY4k7AKw7eFm0X4S1iTsALP70mMG23hpfe6BtpmMprhLbFo0l5ckaQwcXLVeut+L/vj2D\n5ROSRZ+va27Hh/svYV7fSFxrEZeoNNxq5yVkp2ubkRRs2pq3u4k74DqxNUV+lC/en5WB8w2GnXVd\nGVtr3rU6dUBtwjEwJsBgH21n9Dm54ThR0wwPM8YehHHMJu/r1q0z2LZo0SKj+//hD3/AH/7wh54d\n1W2Cl1xqdsZ3RKISp2ubUdnY9cMwNjXYJkl3ai/3Q9faavoqpKJtnLV69gSl8cZQuihkEvSP9oe/\np5TXfY5IVOJ8wy1E+3vwibouYb4KjE4OQkXdTZypu4mhcQEmB7ReNtK+q1dTuj/zzpnQauvOJmsp\niA/AkjvjMGX1z8iN8BXoqAnLcHbB3e1Af5WfWZ/07HD3vn6fF+lLoOXxr0/gyvU2fCLipqSLqZn0\ndQe7Omo+/EU5JmWYX7XsbTw+LBYrf6xGw612cByH6ABPt0vebYmlM+cqjYNMQUIgChICse2UazkG\nuRO9Uy/Ri/BRSA1m2E0l7rbwbu1tSCWcTVorl5aWItxPAS+5FEnBXhiXGgwfhRQZYT7w95QZLarx\nlEl4pwdHtXjWTuKKHZHWxjROr6tuhJ8CH92dhd+PjOO3ad120kO7Bnob7snGXyemYPGAKH7b02MS\n+YGHv6f5AcijQ1WCx67m8+4M7Nn4iOKr5vmiJORH+Rp9fkZ2KJ4pTLDqPd0ptleuq1chjVlDdgex\nrrO2wtViq01SOxnDa5NT8K9pXR7n7iYycEauEOXv0eskMs6Cknc3wEsjr0kP9XHykfROuvOjy3Gc\nVRXwMhdaHozUtOD+8yhhksKYeqVgZFIQH5MHNBrGv92Vyu8n4TjkRvoiUNOXwFgzjekmvIZDjHjt\nE72fcF/nNaqRSjh0aPRrjAH+HlKsmNl1/SqkEpMN7XoLpqQ1hGkW9IvEkLgARAd4CiRDA1T+eHFs\nkhOPzP2wl5vb7QAl7y6GWAOhxCAvjE0NRqzeTKkYttaxEV30JLZJQV4YkWidLaeY1McUKk1SDgD/\n744YPD5MvLvduNRgrJubLbielo1PwtNjupJ5/QGNWH3FkLgAPDAwStBMQ8vyCckmJWH6ZfLuoG11\nZ5wd37GpXQ3iEoMtk6lZSm6EL4K8zX9Xvl6o9ozWWhwyAJ/Oy0VsoPjv6rhUy+z+nB3b3oyzYqud\nlxmfFsyvEj48WD2RcU+fCNEVVKmEE3i9uzqukCsMivHH6tmZzj4Mt6T3TzG4GWrpgbDAkuM4yFxn\n4pboBlIJJ6qJN8bE9BDU3GjFnkrh8rZCyqG1w7CabkSiEl5yCRpvtSMvyo9P/EvKa9HeyXBCR0/N\ncUCw3iCxr57vvfZy0+8UrCs58POQYVauYWMOxoA+UX5osEMnzmfGJODZ/xrX9BKuya8LYqH0kuO7\n0/VY2D8Su7ohEbojLkBUWqSQqWVxdc3GPcBTQ7z5gmBtN9pOnRHkjOxQHLp4HSM0fS+0S/tXbrRi\nf5VpjTzR+0gL9cb4tBDcER8APw8ZXv/hQq82d3AWHMfxK8GEddDMu4vR00ZipHm3Hkt/kh0dW+3y\nfWJQ10zlHXGB/Ax+/2h/eMkkSAry4msjhicqBTP2f52UIpC8AMJrbGCMPwbHGs4WRfh5YFSSEvFK\nL4GswBoC9WanknVmXLWH8Pk8oZe8LvodiMVQBRj+8BelBInseXvjTO3wylkZkEk4LBoQhQ/vzoJc\n0r3bjlY+mBHmLejUOCkjRHTF0hjtnWrdjK5F7oODVXhzWjoSgoSrAk+PNq9/dzVddm/CmbEdlxYs\nkFCF+zlP7mUPKFdwbyh5dzGSg72QG2G8oIqwLXfEBfB+666Gh0yCiekhggTVWyHlZ/B9PaQYlRyE\n9DDjtRAyCQeZhMM3C/Owbq66yYvu+PCFsUl4rshQp+khk+CpkfEAIJAV6HestYTscB+8PysDuZE6\n17XmIHw9ZEYLmHSLZAHgjalpBlr5lbMy8fKEZEHnvjviA60+RqL7LBuvvn5GJ4vLwlQisqruIOE4\nSDggN9KPt3IsiA9AZpiPwaRHYpDxz8wM80Wkn8Kgw7UYpMklAOCbhXmi1ocE4SwoeXcxvBVSxBjR\nYFqCK+jY3IlAL7nFy6GuFNtQH7lFyYcWuVSCYB85EoO8hEm0Fbw+JQ1L7owzu59uHvXKpBQ8NTIe\n0QGemJbVlWDrJ+H+Sfl4Y2qaYJtUwuGFsYn845QQb6SF+mDzIqEONi/Kj28OAgBKL+NqwDG36ay8\nPbXDfaP9kR7qjUExAbw7kRZ9RyMAkIsUbwd5y4zKyrTt1qUSDl8vzMfC/pG85OXpMYkI9JLjRqva\nFvV+jQOS/oB2fr8I/v//ryAGq+dkWXp6ZiHNu/1wdGyfHp2Ae/tE4O68CMH23tjI0JXuZ4T1kOad\nIFwcX4UU4b4KQbfD7s4CvTU9vdvHkRpq2QqFrsxHt3FHuJ8CWxb3QUcng1TCGSThYXouJGNSghDp\n54HVczLR2t7Jbzfm8hPkJeP1zIA6ia+/KdRBB4sk9jIJJ3gdYT3/mKIeeG07LfRtFkt5wnwVeHt6\nOkrPNuDD/Zfw+bwcMAC7zjXis8NXsGhAFP685QxGJSkxOjkI/VR+WPnjRcQpPfmBdpiP8Frx0Axk\ntddGZpgPNh2vBQC8NzOjRxMiA1T+aO3oxKGLQu/3opQgPDE8Fs1tnZj2gbpT628KYvBaaWW3P4tw\nDtreFelh3ihIoJU7wvWh5L2XYcuWx4QQZ8WW4zjEBnqKtip3NTYvyoe5hQxtgqWbhDedPggplyPY\nL9LPQ/CvLo8Pi8XHP18WbPvXtHQwqLtIAsDqOVk4VdOMx78+CUDtNlJRdxMb9BrUfDYvB1NW/2z+\n5NwYe7WZ/9PoeMFjbXOvt6alY9f5RgyJFR9kJgR54XSt2q7QV6MrLkoNRpHG4UVfSrVpUT50J+z/\nX0EMHhzctdqiP/QqSg3G4NgAqwvFxXhxnFoWNHX1ITS3dWJGdig+O3IVvh5ScByHA3t3AVDP9OdG\nmq/TICzHXtftv+/Lw7LvzvIF0O/NzMAP5xoR4tO7dO2moFzBvel9a0EEQTgNqYQz2UHWGM+MSYCv\nh8xs4q9lXFowVs4SWowpveUI8pbzNpeeMglCNTfjFTMyoJBKkCbSK8FWXW2ttfbsDcTpzWhrY58Y\n7IV7+kTYzBZSpndd6fuxazXvupePv6dxKU530LrVzMxROyyJ2af6KCTUhMYF0S9+95BJBHJJf08Z\nxqVZZg1KEK4AJe+9DBpJ2w+Krf0YP3oEAODePhGmd7QA3eLFTs2crH6PhCg72JP5ebhucaO9tMOc\nnldTcZ8Ig+65xrClVIlp/s72bP71zJgEvDA2EcE+csQpPfmEUPd3Qeuw9Hc9hydL+LMFzja3CwM1\nfum2um79Xfi76SzofubeUPJOEG5AiI8cfaJ6/5L8vX0jbfp+3kZn1RmmZoUiI0xcxz8nN0x0u7sy\nNK77ThnJRmbPAzxlBs2RUkO8cVem8c66uhTEB+DXBTHdPi5dxqUGY1SSEsMTAvHF/FybvKc+WRG+\nfK3JuzMy0F8ltFjNDu9a1TEWM1Po2l/ejug28lo8MAp/vyvVaAMtY9ypp1cfornutbU38/tFYvFA\ndVGzdtz52uSUbh4xQTgPSt57GeTdaj+cGVsJx9lltthV0I1tkg07cAZ4iltRBnrK8cgQFf5+V5fD\nja5kR0wSYQ5LO3I6mocHR2OEx4Vuv95TLsFX9+UZFBh/cm8Or1fvDr4eMpNdeK1hVHIQnhoZD47r\nucbdWkpLSzEkNoC3VgW6507iJZei5P7by7nmgzmZiNdbFft8Xg7ilV7ICPPBfRG1oq9720jh/Y6K\nBgBdjkbhmiL4SRnq6yzMR47Zeo3lssJvT2tmyhXcG0reCYJwKYpSghBkwu7RHOby7g3F2XwRohjz\n+0WafQ8xxCwQXYFxacGQdbMxEgAMiQ2Ap0wCqYTDcM3Mpr6t5+3Os0WJBm5J+izsb35VqTuDRneG\nA4el45KxYmYGBsT4IzHIy2BA+Na0dEHs/mNigDM9W73q8/k89eoLXwvBcQjyliHFRXt6EIS1UPLe\nyyAdm/2g2NoP3dhOyw7D+ntyTOzdM5TecpOzs93Nwa31kHfULCvHcaLX7tcis+laFvSL5AtwZ+nM\nVGpV6pQEdWHqd+GdGemYpWkgNjMnDOmh3lBIOaMzx5bw9JgE0c7C7oJ+XUKwjxyxgZ4YnqA0sLIt\nKChAYrAX5uSpr8HxacFGC+K/mJ+LBf3USb6HTFs43FVXsb44R9BBV99u9HaD7mfuDSXvBEEQGu7O\nC8eIJCWfIPxlQjJenpAsui+vndXgZ6WEpKezrO/MMJ4APleUyD8v1+iB9OUJCs1sui6vTlLrf+/p\nE4EHBkYZWD3qdzIljLOwfyRiAjyRHKJOGOVSCZaOT8YaTadjcxTndw2awn0VeHqMuqC1ID4Q+TqW\nlB+KNJzSzkC7Ij4KKV8fYOlqlXavx0zUSPgopPCSS7GhuCu+WeG+RotVFw6Iwqf32m+SgCDsCSXv\nvQzSsdkPiq39cJXYLhoQhUg/D3jJ1T+N+VF+yBMpFA7xFmpn35+V0a3P++cU611JtMQrjdcGDI4N\nQLzSC1sW94FUwqG0tJSfSZfrJey6NQG6zxSlBuPZokTBvoyydwOMXbtz8yMglXCCPgU+CikCPGXw\nlBu/9Y5JCcKjQ1W4r38U3tTIkxb2j0SWTkFsh87fQeltOGgsTAmCt4nP0MUeTiwvjE3kr7ffDo/F\nxgW5/Iy7h1QCVYB6IBnkbdodSBtbjuOwclaGway7l8g5KnXec0SSEp/OEy9glkk4+N+G9q5aXOU3\nl+gelLwTBNGriPb3EDh/WEKc0lOQDE/LCsWKGYYJ+WuamWmZ3oxhdIC4K0aqiLzkj6Pi+YRZzHce\nAO4w4w4TrSleTgv1RkyAh0USnGfGJGDtXMNZWgFmJkKVXvazYuytpIf5GBRNR/p5GP1b/O7OON6x\nR9sZdlRyEJRecv59OnWSd2N/Mkv7Lay1cCXAHIlBXd+BgTEB/ECvKDVY3UuB15+rm2xtXGCdK5BK\n5zumPbXi/AhsWdwH64ttcw4E4S5Q8t7LIB2b/aDY2g9bxtbXQ4ZXJ1s3o/3PKWn4m443t1wqMfCG\n/2J+LrI0lnPGJqB1Z7Vfn5rGa3C1fHpvDl/0qUVfd35HXICggYw+MQEevPXdXyem4M1p6ZBwHGJM\n6KALCgrg6yFDiI8C3gqpwew7j5mJ9QcHR2OdjZK93kJ3r90QHwWeNuPt3qXdFqK1yH99Spqos02Y\nrwKqAA8EecmwYmYG5uaH4x963vODNF7qcqn1Dj1i++uvUOlfSlOzuqQ8MglnUXM0Y7HVWsBqtfDm\nZvAJQ+h+5t7cvmtGBEEQGjxlp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TqFqqoqPPfcc/z7Xb58GbW1taiursbq1avxi1/8AidP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\ngiAIN4GSd4IgCIIgCIJwE/4/A0GofKoLPsoAAAAASUVORK5CYII=\n", - "text": [ - "" - ] - } - ], - "prompt_number": 50 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "The `trace` method in the `MCMC` instance has a keyword argument `chain`, that indexes which call to `sample` you would like to be returned. (Often we need to call `sample` multiple times, and the ability to retrieve past samples is a useful procedure). The default for `chain` is -1, which will return the samples from the lastest call to `sample`.\n", - "\n", - "#### Cluster Investigation\n", - "\n", - "We have not forgotten our main challenge: identify the clusters. We have determined posterior distributions for our unknowns. We plot the posterior distributions of the center and standard deviation variables below:" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "figsize(11.0, 4)\n", - "std_trace = mcmc.trace(\"stds\")[:]\n", - "\n", - "_i = [1, 2, 3, 0]\n", - "for i in range(2):\n", - " plt.subplot(2, 2, _i[2 * i])\n", - " plt.title(\"Posterior of center of cluster %d\" % i)\n", - " plt.hist(center_trace[:, i], color=colors[i], bins=30,\n", - " histtype=\"stepfilled\")\n", - "\n", - " plt.subplot(2, 2, _i[2 * i + 1])\n", - " plt.title(\"Posterior of standard deviation of cluster %d\" % i)\n", - " plt.hist(std_trace[:, i], color=colors[i], bins=30,\n", - " histtype=\"stepfilled\")\n", - " # plt.autoscale(tight=True)\n", - "\n", - "plt.tight_layout()\n" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "metadata": {}, - "output_type": "display_data", - "png": 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cRzscuyCgLPMy7uVc1UxA7STl3AMcvy5JOXZ18OCAac1vf/4n0Mo86L2iXobP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- "text": [ - "" - ] - } - ], - "prompt_number": 51 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "The MCMC algorithm has proposed that the most likely centers of the two clusters are near 120 and 200 respectively. Similar inference can be applied to the standard deviation. \n", - "\n", - "We are also given the posterior distributions for the labels of the data point, which is present in `mcmc.trace(\"assignment\")`. Below is a visualization of this. The y-axis represents a subsample of the posterior labels for each data point. The x-axis are the sorted values of the data points. A red square is an assignment to cluster 1, and a blue square is an assignment to cluster 0. " - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "import matplotlib as mpl\n", - "figsize(12.5, 4.5)\n", - "plt.cmap = mpl.colors.ListedColormap(colors)\n", - "plt.imshow(mcmc.trace(\"assignment\")[::400, np.argsort(data)],\n", - " cmap=plt.cmap, aspect=.4, alpha=.9)\n", - "plt.xticks(np.arange(0, data.shape[0], 40),\n", - " [\"%.2f\" % s for s in np.sort(data)[::40]])\n", - "plt.ylabel(\"posterior sample\")\n", - "plt.xlabel(\"value of $i$th data point\")\n", - "plt.title(\"Posterior labels of data points\")\n" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "metadata": {}, - "output_type": "display_data", - "png": 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+sZtpGUudn6W0u43c0UEGquvpr64nrE1EFbvSM2m58z4cjScIGE23neN9M1BG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- "text": [ - "" - ] - } - ], - "prompt_number": 58 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Looking at the above plot, it appears that the most uncertainty is between 150 and 170. The above plot slightly misrepresents things, as the x-axis is not a true scale (it displays the value of the $i$th sorted data point.) A more clear diagram is below, where we have estimated the *frequency* of each data point belonging to the labels 0 and 1. " - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "cmap = mpl.colors.LinearSegmentedColormap.from_list(\"BMH\", colors)\n", - "assign_trace = mcmc.trace(\"assignment\")[:]\n", - "plt.scatter(data, 1 - assign_trace.mean(axis=0), cmap=cmap,\n", - " c=assign_trace.mean(axis=0), s=50)\n", - "plt.ylim(-0.05, 1.05)\n", - "plt.xlim(35, 300)\n", - "plt.title(\"Probability of data point belonging to cluster 0\")\n", - "plt.ylabel(\"probability\")\n", - "plt.xlabel(\"value of data point\")\n" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "metadata": {}, - "output_type": "pyout", - "prompt_number": 60, - "text": [ - "" - ] - }, - { - "metadata": {}, - "output_type": "display_data", - "png": 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qiipceHExyv+6AJ+pTyD3hwOovZxuWK/Kyoe+QQ3bsADwJWJcWfUNMr7YgcJ9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- "text": [ - "" - ] - } - ], - "prompt_number": 60 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Even though we modeled the clusters using Normal distributions, we didn't get just a single Normal distribution that *best* fits the data (whatever our definition of best is), but a distribution of values for the Normal's parameters. How can we choose just a single pair of values for the mean and variance and determine a *sorta-best-fit* gaussian? \n", - "\n", - "One quick and dirty way (which has nice theoretical properties we will see in Chapter 5), is to use the *mean* of the posterior distributions. Below we overlay the Normal density functions, using the mean of the posterior distributions as the chosen parameters, with our observed data:" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "norm = stats.norm\n", - "x = np.linspace(20, 300, 500)\n", - "posterior_center_means = center_trace.mean(axis=0)\n", - "posterior_std_means = std_trace.mean(axis=0)\n", - "posterior_p_mean = mcmc.trace(\"p\")[:].mean()\n", - "\n", - "plt.hist(data, bins=20, histtype=\"step\", normed=True, color=\"k\",\n", - " lw=2, label=\"histogram of data\")\n", - "y = posterior_p_mean * norm.pdf(x, loc=posterior_center_means[0],\n", - " scale=posterior_std_means[0])\n", - "plt.plot(x, y, label=\"Cluster 0 (using posterior-mean parameters)\", lw=3)\n", - "plt.fill_between(x, y, color=colors[1], alpha=0.3)\n", - "\n", - "y = (1 - posterior_p_mean) * norm.pdf(x, loc=posterior_center_means[1],\n", - " scale=posterior_std_means[1])\n", - "plt.plot(x, y, label=\"Cluster 1 (using posterior-mean parameters)\", lw=3)\n", - "plt.fill_between(x, y, color=colors[0], alpha=0.3)\n", - "\n", - "plt.legend(loc=\"upper left\")\n", - "plt.title(\"Visualizing Clusters using posterior-mean parameters\")\n" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "metadata": {}, - "output_type": "pyout", - "prompt_number": 61, - "text": [ - "" - ] - }, - { - "metadata": {}, - "output_type": "display_data", - "png": 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Eh4d/cDmUD4OOUYo0dBvJT4y/vz+mT5/e3GI0CefOncPEiRM/uByBQPCfOqAi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\nykGtbdJB7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- "text": [ - "" - ] - } - ], - "prompt_number": 61 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### Important: Don't mix posterior samples\n", - "\n", - "In the above example, a possible (though less likely) scenario is that cluster 0 has a very large standard deviation, and cluster 1 has a small standard deviation. This would still satisfy the evidence, albeit less so than our original inference. Alternatively, it would be incredibly unlikely for *both* distributions to have a small standard deviation, as the data does not support this hypothesis at all. Thus the two standard deviations are *dependent* on each other: if one is small, the other must be large. In fact, *all* the unknowns are related in a similar manner. For example, if a standard deviation is large, the mean has a wider possible space of realizations. Conversely, a small standard deviation restricts the mean to a small area. \n", - "\n", - "During MCMC, we are returned vectors representing samples from the unknown posteriors. Elements of different vectors cannot be used together, as this would break the above logic: perhaps a sample has returned that cluster 1 has a small standard deviation, hence all the other variables in that sample would incorporate that and be adjusted accordingly. It is easy to avoid this problem though, just make sure you are indexing traces correctly. \n", - "\n", - "Another small example to illustrate the point. Suppose two variables, $x$ and $y$, are related by $x+y=10$. We model $x$ as a Normal random variable with mean 4 and explore 500 samples. " - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "import pymc as pm\n", - "\n", - "x = pm.Normal(\"x\", 4, 10)\n", - "y = pm.Lambda(\"y\", lambda x=x: 10 - x, trace=True)\n", - "\n", - "ex_mcmc = pm.MCMC(pm.Model([x, y]))\n", - "ex_mcmc.sample(500)\n", - "\n", - "plt.plot(ex_mcmc.trace(\"x\")[:])\n", - "plt.plot(ex_mcmc.trace(\"y\")[:])\n", - "plt.title(\"Displaying (extreme) case of dependence between unknowns\")\n" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "output_type": "stream", - "stream": "stdout", - "text": [ - " \r", - "[****************100%******************] 500 of 500 complete" - ] - }, - { - "metadata": {}, - "output_type": "pyout", - "prompt_number": 62, - "text": [ - "" - ] - }, - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "\n" - ] - }, - { - "metadata": {}, - "output_type": "display_data", - "png": 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AIBAIBDWMkIsIBAKBQCAQCAQqCLmIQCAQCAQCgUBwCSGMbEGdIrRwAn8RdUUQ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TRBggfJbqN97sTfXwUATY08EC/DSBZkC0ZDnFxAq92wwTxx5hgsWBJDkCTYFSvP9rfeB6JROCaN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\nyC7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- "text": [ - "" - ] - } - ], - "prompt_number": 62 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "As you can see, the two variables are not unrelated, and it would be wrong to add the $i$th sample of $x$ to the $j$th sample of $y$, unless $i = j$." - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "#### Returning to Clustering: Prediction\n", - "The above clustering can be generalized to $k$ clusters. Choosing $k=2$ allowed us to visualize the MCMC better, and examine some very interesting plots. \n", - "\n", - "What about prediction? Suppose we observe a new data point, say $x = 175$, and we wish to label it to a cluster. It is foolish to simply assign it to the *closer* cluster center, as this ignores the standard deviation of the clusters, and we have seen from the plots above that this consideration is very important. More formally: we are interested in the *probability* (as we cannot be certain about labels) of assigning $x=175$ to cluster 1. Denote the assignment of $x$ as $L_x$, which is equal to 0 or 1, and we are interested in $P(L_x = 1 \\;|\\; x = 175 )$. \n", - "\n", - "A naive method to compute this is to re-run the above MCMC with the additional data point appended. The disadvantage with this method is that it will be slow to infer for each novel data point. Alternatively, we can try a *less precise*, but much quicker method. \n", - "\n", - "We will use Bayes Theorem for this. If you recall, Bayes Theorem looks like:\n", - "\n", - "$$ P( A | X ) = \\frac{ P( X | A )P(A) }{P(X) }$$\n", - "\n", - "In our case, $A$ represents $L_x = 1$ and $X$ is the evidence we have: we observe that $x = 175$. For a particular sample set of parameters for our posterior distribution, $( \\mu_0, \\sigma_0, \\mu_1, \\sigma_1, p)$, we are interested in asking \"Is the probability that $x$ is in cluster 1 *greater* than the probability it is in cluster 0?\", where the probability is dependent on the chosen parameters.\n", - "\n", - "\\begin{align}\n", - "& P(L_x = 1| x = 175 ) \\gt P(L_x = 0| x = 175 ) \\\\\\\\[5pt]\n", - "& \\frac{ P( x=175 | L_x = 1 )P( L_x = 1 ) }{P(x = 175) } \\gt \\frac{ P( x=175 | L_x = 0 )P( L_x = 0 )}{P(x = 175) }\n", - "\\end{align}\n", - "\n", - "As the denominators are equal, they can be ignored (and good riddance, because computing the quantity $P(x = 175)$ can be difficult). \n", - "\n", - "$$ P( x=175 | L_x = 1 )P( L_x = 1 ) \\gt P( x=175 | L_x = 0 )P( L_x = 0 ) $$\n", - "\n", - "\n", - "\n", - "\n", - "\n" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "norm_pdf = stats.norm.pdf\n", - "p_trace = mcmc.trace(\"p\")[:]\n", - "x = 175\n", - "\n", - "v = p_trace * norm_pdf(x, loc=center_trace[:, 0], scale=std_trace[:, 0]) > \\\n", - " (1 - p_trace) * norm_pdf(x, loc=center_trace[:, 1], scale=std_trace[:, 1])\n", - "\n", - "print \"Probability of belonging to cluster 1:\", v.mean()\n" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "Probability of belonging to cluster 1: 0.025\n" - ] - } - ], - "prompt_number": 63 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Giving us a probability instead of a label is a very useful thing. Instead of the naive \n", - "\n", - " L = 1 if prob > 0.5 else 0\n", - "\n", - "we can optimize our guesses using a *loss function*, which the entire fifth chapter is devoted to. \n", - "\n", - "\n", - "### Using `MAP` to improve convergence\n", - "\n", - "If you ran the above example yourself, you may have noticed that our results were not consistent: perhaps your cluster division was more scattered, or perhaps less scattered. The problem is that our traces are a function of the *starting values* of the MCMC algorithm. \n", - "\n", - "It can be mathematically shown that letting the MCMC run long enough, by performing many steps, the algorithm *should forget its initial position*. In fact, this is what it means to say the MCMC converged (in practice though we can never achieve total convergence). Hence if we observe different posterior analysis, it is likely because our MCMC has not fully converged yet, and we should not use samples from it yet (we should use a larger burn-in period ).\n", - "\n", - "In fact, poor starting values can prevent any convergence, or significantly slow it down. Ideally, we would like to have the chain start at the *peak* of our landscape, as this is exactly where the posterior distributions exist. Hence, if we started at the \"peak\", we could avoid a lengthy burn-in period and incorrect inference. Generally, we call this \"peak\" the *maximum a posterior* or, more simply, the *MAP*.\n", - "\n", - "Of course, we do not know where the MAP is. PyMC provides an object that will approximate, if not find, the MAP location. In the PyMC main namespace is the `MAP` object that accepts a PyMC `Model` instance. Calling `.fit()` from the `MAP` instance sets the variables in the model to their MAP values.\n", - "\n", - " map_ = pm.MAP( model )\n", - " map_.fit()\n", - "\n", - "The `MAP.fit()` methods has the flexibility of allowing the user to choose which optimization algorithm to use (after all, this is a optimization problem: we are looking for the values that maximize our landscape), as not all optimization algorithms are created equal. The default optimization algorithm in the call to `fit` is scipy's `fmin` algorithm (which attempts to minimize the *negative of the landscape*). An alternative algorithm that is available is Powell's Method, a favourite of PyMC blogger [Abraham Flaxman](http://healthyalgorithms.com/) [1], by calling `fit(method='fmin_powell')`. From my experience, I use the default, but if my convergence is slow or not guaranteed, I experiment with Powell's method. \n", - "\n", - "The MAP can also be used as a solution to the inference problem, as mathematically it is the *most likely* value for the unknowns. But as mentioned earlier in this chapter, this location ignores the uncertainty and doesn't return a distribution.\n", - "\n", - "Most often it is a good idea, and rarely a bad idea, to prepend your call to `mcmc` with a call to `MAP(model).fit()`. The intermediate call to `fit` is hardly computationally intensive, and will save you time later due to a shorter burn-in period. \n", - "\n", - "#### Speaking of the burn-in period\n", - "\n", - "It is still a good idea to provide a burn-in period, even if we are using `MAP` prior to calling `MCMC.sample`, just to be safe. We can have PyMC automatically discard the first $n$ samples by specifying the `burn` parameter in the call to `sample`. As one does not know when the chain has fully converged, I like to assign the first *half* of my samples to be discarded, sometimes up to 90% of my samples for longer runs. To continue the clustering example from above, my new code would look something like:\n", - "\n", - " model = pm.Model( [p, assignment, taus, centers ] )\n", - "\n", - " map_ = pm.MAP( model )\n", - " map_.fit() #stores the fitted variables' values in foo.value\n", - "\n", - " mcmc = pm.MCMC( model )\n", - " mcmc.sample( 100000, 50000 )\n" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Diagnosing Convergence\n", - "\n", - "### Autocorrelation\n", - "\n", - "Autocorrelation is a measure of how related a series of numbers is with itself. A measurement of 1.0 is perfect positive autocorrelation, 0 no autocorrelation, and -1 is perfect negative correlation. If you are familiar with standard *correlation*, then autocorrelation is just how correlated a series, $x_\\tau$, at time $t$ is with the series at time $t-k$:\n", - "\n", - "$$R(k) = Corr( x_t, x_{t-k} ) $$\n", - "\n", - "For example, consider the two series:\n", - "\n", - "$$x_t \\sim \\text{Normal}(0,1), \\;\\; x_0 = 0$$\n", - "$$y_t \\sim \\text{Normal}(y_{t-1}, 1 ), \\;\\; y_0 = 0$$\n", - "\n", - "which have example paths like:" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "figsize(12.5, 4)\n", - "\n", - "import pymc as pm\n", - "x_t = pm.rnormal(0, 1, 200)\n", - "x_t[0] = 0\n", - "y_t = np.zeros(200)\n", - "for i in range(1, 200):\n", - " y_t[i] = pm.rnormal(y_t[i - 1], 1)\n", - "\n", - "plt.plot(y_t, label=\"$y_t$\", lw=3)\n", - "plt.plot(x_t, label=\"$x_t$\", lw=3)\n", - "plt.xlabel(\"time, $t$\")\n", - "plt.legend()\n" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "metadata": {}, - "output_type": "display_data", - "png": 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p5KEeHgmSNsFy9eL1Bx+Pv3x946AOFpsdMiktiEwIIeGMztKE+OCadDJdLMviO+9dwdPH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\nZk8ftxzHKSZSgilHsTFuDAJKY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- "text": [ - "" - ] - } - ], - "prompt_number": 65 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "One way to think of autocorrelation is \"If I know the position of the series at time $s$, can it help me know where I am at time $t$?\" In the series $x_t$, the answer is No. By construction, $x_t$ are random variables. If I told you that $x_2 = 0.5$, could you give me a better guess about $x_3$? No.\n", - "\n", - "On the other hand, $y_t$ is autocorrelated. By construction, if I knew that $y_2 = 10$, I can be very confident that $y_3$ will not be very far from 10. Similarly, I can even make a (less confident guess) about $y_4$: it will probably not be near 0 or 20, but a value of 5 is not too unlikely. I can make a similar argument about $y_5$, but again, I am less confident. Taking this to it's logical conclusion, we must concede that as $k$, the lag between time points, increases the autocorrelation decreases. We can visualize this:\n" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "def autocorr(x):\n", - " # from http://tinyurl.com/afz57c4\n", - " result = np.correlate(x, x, mode='full')\n", - " result = result / np.max(result)\n", - " return result[result.size / 2:]\n", - "\n", - "colors = [\"#348ABD\", \"#A60628\", \"#7A68A6\"]\n", - "\n", - "x = np.arange(1, 200)\n", - "plt.bar(x, autocorr(y_t)[1:], width=1, label=\"$y_t$\",\n", - " edgecolor=colors[0], color=colors[0])\n", - "plt.bar(x, autocorr(x_t)[1:], width=1, label=\"$x_t$\",\n", - " color=colors[1], edgecolor=colors[1])\n", - "\n", - "plt.legend(title=\"Autocorrelation\")\n", - "plt.ylabel(\"measured correlation \\nbetween $y_t$ and $y_{t-k}$.\")\n", - "plt.xlabel(\"k (lag)\")\n", - "plt.title(\"Autocorrelation plot of $y_t$ and $x_t$ for differing $k$ lags.\")\n" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "metadata": {}, - "output_type": "display_data", - "png": 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jsXXr1lLjKcrLV+p3Q0XlqlWrFi5fvoygoCDcvn0b9erVw/Dhw/Hf//5XnUZWVhbHPZBN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\naWruK5afblT6KDkVBZl3S6WvT7mlniPdz4nlJ7a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- "text": [ - "" - ] - } - ], - "prompt_number": 66 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Notice that as $k$ increases, the autocorrelation of $y_t$ decreases from a very high point. Compare with the autocorrelation of $x_t$ which looks like noise (which it really is), hence we can conclude no autocorrelation exists in this series. \n", - "\n", - "\n", - "####How does this relate to MCMC convergence?\n", - "\n", - "By the nature of the MCMC algorithm, we will always be returned samples that exhibit autocorrelation (this is because of the step `from your current position, move to a position near you`).\n", - "\n", - "A chain that is [Isn't meandering exploring?] exploring the space well will exhibit very high autocorrelation. Visually, if the trace seems to meander like a river, and not settle down, the chain will have high autocorrelation.\n", - "\n", - "This does not imply that a converged MCMC has low autocorrelation. Hence low autocorrelation is not necessary for convergence, but it is sufficient. PyMC has a built-in autocorrelation plotting function in the `Matplot` module. " - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "###Thinning\n", - "\n", - "Another issue can arise if there is high-autocorrelation between posterior samples. Many post-processing algorithms require samples to be *independent* of each other. This can be solved, or at least reduced, by only returning to the user every $n$th sample, thus removing some autocorrelation. Below we perform an autocorrelation plot for $y_t$ with differing levels of thinning:" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "max_x = 200 / 3 + 1\n", - "x = np.arange(1, max_x)\n", - "\n", - "plt.bar(x, autocorr(y_t)[1:max_x], edgecolor=colors[0],\n", - " label=\"no thinning\", color=colors[0], width=1)\n", - "plt.bar(x, autocorr(y_t[::2])[1:max_x], edgecolor=colors[1],\n", - " label=\"keeping every 2nd sample\", color=colors[1], width=1)\n", - "plt.bar(x, autocorr(y_t[::3])[1:max_x], width=1, edgecolor=colors[2],\n", - " label=\"keeping every 3rd sample\", color=colors[2])\n", - "\n", - "plt.autoscale(tight=True)\n", - "plt.legend(title=\"Autocorrelation plot for $y_t$\", loc=\"lower left\")\n", - "plt.ylabel(\"measured correlation \\nbetween $y_t$ and $y_{t-k}$.\")\n", - "plt.xlabel(\"k (lag)\")\n", - "plt.title(\"Autocorrelation of $y_t$ (no thinning vs. thinning) \\\n", - "at differing $k$ lags.\")\n" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "metadata": {}, - "output_type": "display_data", - "png": 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v3+aN9Swd612lgXmyfMyRNDBPhtM48S8ru1EqjXdTqISEBJw4cQIJCQkYMmQI\n7t27h0mTJmHUqFFGG8Oaib3RFyCdm32R8Yn9dsAlt6AKoiEiIqKqpLNYf9OmTdi7dy/u3r2LkpIS\n1VKeq1ev1mugGjVqIDg4GMHBwZgxYwZiY2ORlpaG1atXqy0hStWbr50LTpg7CNLJNaCDuUMgEXjm\nSxqYJ8vHHEkD82Q4rRP/jz76CIsXL0ZUVBTWrVuHsWPHYs2aNXj11Vf1HmjIkCHIzMzEsGHDEBoa\nitzcXHz44YdYtWpVpYMnItPgfQSIiIiqH63LeS5btgx//fUX/vOf/6B27dpYuHAhtmzZgmvXruk9\n0ODBg7FmzRrcunUL06ZNQ4MGDTB9+nTV9QNkHa48vmPuEEiErKRTOHszV9S/jId55g7Xah04cMDc\nIZAIzJPlY46kgXkynNYz/g8fPkSbNm0AALVq1UJBQQGCgoKwd+9evQcKDg5GUlISPvjgA9W+hIQE\nuLi46N0XSVfdB/dFrf4DcAUgqRD77QC/GSAiIjIvrRP/pk2b4vz582jVqhVatWqFxYsXw8nJCfXr\n19d7IDc3N7i5uant69mzp979kLS1gg1qi1j9BwCu//d6Eqp6+txvgcuJmg/rXaWBebJ8zJE0ME+G\n0zrx//TTT3HnTmlpxrx58zB06FDk5OTg22+/rZLgiKj64HUDRERE5qV14t+vXz/Vz8HBwUhJSTF5\nQGR6Ytf8N8V6/0lFj9AONY3aJxnfgyuJqOXd1qh98psB4+Oa1tLAPFk+5kgamCfDlZv4l928S5em\nTZsaPRiqGmLX/Df3ev9i7wYM8HqA6obXDRARERlfuYm/r6+vzifJZDIUFxebJCBd4uPj8e6776K4\nuBjR0dGYOnVquTZ79uzB5MmTUVhYCBcXF+zZs6fqAyWNWijsgWJxq8CIvRswwOsBjE2fGn9TEPvt\ngLWXD/HMlzQwT5aPOZIG5slw5Sb+JSWG/2c/a9YsyGQy1VKdZTf9EgRB9TMAfPzxx3r1W1xcjPHj\nx2Pnzp1wd3dHp06dMGDAAAQEBKjaPHjwAO+88w527NgBDw8P1TUKpD+xJUGAacqCiHRh+RAREZF4\nOu/cCwDp6enIzMxESEiIqE7T09NVE/y8vDz89ttv6NSpE7y9vZGWlobjx49j4MCBegd77Ngx+Pr6\nwsfHBwAQFRWFTZs2qU3816xZg4EDB8LDwwMAuFyoAcSWBAHiy4JMVeMvtiyIJUHimKLGn4yP9a7S\nwDxZPubimcFAAAAgAElEQVRIGpgnw2md+CuVSgwZMgSJiYkAgNzcXPz666/YsWMHfvjhhwqft3Ll\nStXPUVFRiIuLU5vo//7771i3bp3ewWZmZsLT01O17eHhgaNHj6q1SU5ORmFhIXr06IFHjx5h0qRJ\nGD58uN5jkbSILQtiSZD1svayICIiIq0T/7feegvPP/889u/fD2dnZwDAc889hylTpogeYNu2bfj5\n55/V9vXv3x+jRo3SO1iZiElbYWEhTp06hYSEBDx+/BidO3dGSEgI/Pz89B6PjE+fGn8yH3PX+JtC\ndSwL4pkvaWCeLB9zJA3Mk+G0TvyPHTuGbdu2QS6Xq/Y5ODjg4cOHogfw9fVFbGwsJk2apNq3ePFi\nURcRP8vd3R3p6emq7fT0dFVJTxlPT0+4uLjA1tYWtra2CAsLw+nTp8tN/LfsWgwH+wYAAJtadmjk\n4gNv95YAgLTMCwCg17asqABe3oHi2t9IgqCoZdB4VTG+T4OmosevdT8LZRm9UFI6uWopr2PQdjPY\niG5fWFSoKiHS1j7HvxNcj+4HALh7tAIAZGac17jdwLcdzjjXQ3ZK6Tde9ZqVHt9ntx9cSUReUUmF\nj1dmu0AhV5XaVJfx7Vr8n0nGF7utz/hnMmqg7PTGjYsnAQCuAR3KbXs42KCTrLTMrew/pLJbynOb\n29zmNre5XRXbZT8rlaX/H0VHR6MiMqHsClwNWrZsiQ0bNsDf3x9OTk64f/8+Lly4gKioKJw5c6bC\nTp/2999/48UXX0RRURHc3d2RmZkJhUKB33//HR06dBDVR5mioiL4+/sjISEBbm5uCAoKQlxcnFqN\nf1JSEsaPH48dO3YgPz8fwcHB+OWXX9CyZUtVm4SEBOxaf0vUmLKCPAi1bIzWzlRtzd2n/PEj2Dy8\nq7NdWvoZ9DiXKKrP/No2qJ0v7tsBsW0vvjQGxU6NRPX50LYmjrrqvku1XU256LPjYtuaok992hak\nnRFd42/O12Tu49SmcR18FdlcVJ+mwHpXaWCeLB9zJA3MkzinTp1Cz549NT6m9Yz/+++/j8jISEyf\nPh1FRUWIi4vD3LlzNS6hWZH27dsjOTkZR44cwY0bN+Dq6orOnTujZk39L/BUKBSIjY1Fnz59UFxc\njNGjRyMgIADfffcdAGDMmDFo0aIF+vbti7Zt20Iul+PNN99Um/STaYi9ELjo7jWTjJ8V9ByK6jrq\nbCfY1BHdp8OdW4CIiT9ZL143QEREUqL1jD8AbNq0CUuWLEFaWhq8vLwwduxYvPjii6IHyM/Px8qV\nK5GYmIicnJz/DSyTYfXq1ZWP3AA842++Pm2ylPD9Y6WoPvU543+l3yjkNdI9qdLnNdW4n4XtHXSf\n9a6OZ7KtuU9TjW/ubweIiMg6VOqMf1FREXr16oX4+Hi88MILlR585MiROHPmDPr374/GjRsDKL+e\nPxFRdce7ERMRkblVOPFXKBS4du0adHwhoFN8fDyuXbsGJycng/qh6uHa7RTVRcC6iC3fAYACe+OX\n5CgKC6323gBcx9/4TLGqEOtdpYF5snzMkTQwT4bTWuP/4YcfYty4cZgzZw48PT3VztI/vdKPNt7e\n3sjPzzcsSrJKBfXqiyrfAUpLeIxNJpTw3gBU5fS5bqBImQX+H0hERGJpnfiXLQf0bC2+TCZDcXGx\nqAFGjBiBF198ERMnTlSV+pQJDw/XJ1aqBpo0aAZgv7nDEKXA3glXI0bobCd//EjUNwMAUDf3EXLq\n2ButnanaPmrYCPE8428W+nwz4OTQ3OjlQwv3K5HxUNwf0vefFMHJVvcN4MW2k1Kf+hxTnqG0fMyR\nNDBPhtP6CZecnIwaNWoYNEBMTAxkMhlmzpxZ7rFr10yzwgtZLrGT6dK25l1RR+xKRTZZSviI+GYA\nKL1g2el2ltHamaotv8WQBrF/JOjzLULGw3zcf1Ikqq1dTTkyHur+RldsOyn1yRWdiEiKtF7c27p1\nazx48AC1a9eu9ACpqamVfi5VP6m3U1Q3GtPFFOU7JM7N68miv8Wojtc4SIXYazH0+RbBrqa4Mk5r\np88xvXHxJMCJv0Vj7bg0ME+G03pxr5+fH+7cuQN3d/eqjImIzKxGUaGo6xsAfjtApMvt3EKu6ERE\nFkFrqc+wYcPQv39/TJw4sdzFvfrU59+8eRPHjh3D3bt31VYJeuONNyoRMkmZt2sLGLZOFFWFFgp7\noJjfuFg6R99A0fcRIPOp06Sd0Vd0IuPiWWRpYJ4Mp3Xi/+233wIAPvroo3KPia3P37hxI4YNGwY/\nPz+cO3cOrVu3xrlz5/CPf/yDE38iIiIioiqideJvjPr8mTNnYvny5Rg8eDCcnJzw999/Y8WKFTh3\n7pzBfZP0pN1IEl3jT+aTVPQI7VDT3GGQDrzfgjSIzRMvGDYf1o5LA/NkOJ3rlhUVFeHQoUPIzMyE\nu7s7unTpAoVC3HJnAJCeno7BgwertgVBwIgRI9C4cWN89dVXlYuaiCyGw+0sq73RGZExmeImb0RE\nT9M6g09KSkL//v3x5MkTeHp6Ij09HTY2NtiyZQsCAgJEDdCwYUPcvHkTjRs3ho+PDw4fPgwXFxeU\nlLAu1RpVxxp/fZYoVeQ8gNf+zSaOyHD61PgrCgt4ozMzYY2/NJgiT2K/HeA3A+LwLLI0ME+G0zrx\nHzduHN566y28//77kMlkEAQBX331Fd5++23s3r1b1ADR0dE4cOAABg0ahMmTJyM8PBwymQxTpkwx\nygsgMjex6/0DpWv+ExEZit8OEFFlaF2wOTExEe+9955qNR+ZTIZJkybh77//Fj3AtGnTMGjQIACl\nd/G9dOkSTp48iU8//dSAsEmq0m4kmTsEEiGp6JG5QyARHlxJNHcIJALzZPkOHDhg7hBIBObJcFrP\n+Lu5uWHPnj3o2bOnat/+/fsNWtff29u70s8lIiIi8XjBMBE9TevE//PPP8cLL7yAyMhIeHl5IS0t\nDX/88Qd++umnqoqPqpnqWONfHXEdf2lgjb80mDNPLAkSh7Xj0sA8GU5rqc+AAQNw6tQptGrVCjk5\nOWjTpg1OnTqFF198sariIyIiIiIiI9B6xj8vLw8+Pj6YNWuWal9BQQHy8vJgY2Nj8uCo+uE6/tLA\ndfylgev4SwPzZPm4Prw0ME+G0zrx7927N/79738jJCREte/kyZOYPn069uzZY+rYiKgaEbveP8A1\n/4nMgUuEElV/Wif+Z8+eRVBQkNq+oKAgJCZWfoWCsjX9jxw5gpCQECiVSpSUlMDHx6fSfZJ0sMZf\nGkxR4y92vX+Aa/6LxRp/aZBKnqz5egCeRZYG5slwWif+jo6OyMrKgqurq2rfrVu3ULdu3UoPGBcX\nh8uXLyM1NRXdu3dHaGgobty4wYk/ERGRBHClICLp0jrxHzhwIF577TV8/fXXaNasGa5cuYL33nsP\nr7zySqUHnDx5MoDSZUG9vLxw8OBB2NnZVbo/khbW+EsDa/ylgbXj0lDd8lQdvxlg7bg0ME+G0zrx\n//TTT/H+++8jODhYdUHvG2+8gc8//1zvgbp37w4vLy/06dMHvXv3RteuXQFwXX8iIiIioqqgdTlP\nW1tbLFq0CDk5Obh58yZycnIQGxtbqRV9EhIS8M477yAtLQ1DhgxB+/btsXLlysrGTRLl7drC3CGQ\nCC0U9uYOgURw9OW3Z1LAPFk+nkWWBubJcFrP+JeRy+Vo2LChQQPVqFEDwcHBCA4OxowZMxAbG4u0\ntDSsXr0aI0aMMKhvIqkosHfC1Qjdv++KnAfw2r+5CiKyTGJXAOLqP0SWjSsFEVkWURN/YxgyZAgy\nMzMxbNgwhIaGIjc3Fx9++CFWrVpVVSGQBbD2Gn9BUROPXX10trPJUpo+GC3MXeMvdgUga1/9p7rV\njldX1pwnqVwPwNpxaWCeDKe11MeYBg8ejDVr1uDWrVuYNm0aGjRogOnTp0MQuLgjEREREZGpVdkZ\n/+DgYCQlJeGDDz5Q7UtISICLi0tVhUAWgOv4S4Mp1vEn45PK+vDWjnnSzdxLhPIssjQwT4YrN/FP\nSEiATMTX5+Hh4XoN5ObmBjc3N7V9PXv21KsPIiIiqn6kUhJEJHXlJv6jR49Wm/hnZGRALpfD2dkZ\nd+/eRUlJCTw9PXH16tUqDZSqB2uv8ZcKc9f4kzjWXDsuJcyT5WPtuDQwT4YrN/FPTU1V/Tx37lzc\nvXsXn3zyCezs7PD48WPMnj0b9evXr8oYiYiIiIjIQFpr/BcsWIDr16+jVq1aAAA7OzvMnTsXbm5u\nmDFjRpUESNULa/ylgTX+0sDacWlgniwfzyJLA/NkOK0T/zp16uDYsWNqB/r48eOoU6eO6AHy8/Ox\ncuVKJCYmIicnR7VfJpNh9erVlQiZiIiIrJW5LwQmkjKtE/9PP/0UERER6N+/Pzw8PJCeno6tW7di\n0aJFogcYOXIkzpw5g/79+6NRo0aQyWQQBEHUBcRU/bDGXxqkUuMv9kZfQPW82Rdrx6WBeTIuU1wI\nzNpxaWCeDKd14j98+HB06NAB69evx40bNxAQEIBZs2ahZcuWogeIj4/HtWvX4OTkZHCwRERPE3uj\nL4A3+yIiItK5jn/Lli0xc+ZMZGVllVuOUwxvb2/k5+dXKjiqfljjLw2s8ZcG1o5LA/Nk+XgWWRqY\nJ8Npnfjfv38f77zzDtavXw+FQoHHjx9j8+bNOHbsGD799FNRA4wYMQIvvvgiJk6ciMaNG6s9pu+9\nAIiIiIiIqHLk2h4cO3Ys6tWrh7S0NNSuXRsA0LlzZ6xdu1b0ADExMcjKysLMmTMxevRotX+VER8f\njxYtWsDPzw/z58+vsN3x48ehUCjw+++/V2ocMo20G0nmDoFESCp6ZO4QSIQHVxLNHQKJwDxZvgMH\nDpg7BBKBeTKc1jP+CQkJuHHjBmrW/N9Ffg0aNMCtW7dED/D0fQEMVVxcjPHjx2Pnzp1wd3dHp06d\nMGDAAAQEBJRrN3XqVPTt2xeCwMISkp4CeydcjRghqq0i5wG89m82cURERNIjdgWgImUWWEVC1kDr\nxN/R0RG3b99Wq+1XKpWVqvU3hmPHjsHX1xc+Pj4AgKioKGzatKncxD8mJgaDBg3C8ePHzRAlacMa\nf3EERU08dvUR1dYmS2n08VnjLw2sHZcG5sl8xK4A1MarTRVEQ4Zijb/htJb6REdHY9CgQdi1axdK\nSkpw+PBhjBw5EmPGjNFrkD///BNvvPEGIiMjAQAnTpzArl279A42MzMTnp6eqm0PDw9kZmaWa7Np\n0yaMGzcOALhsKBERERERdJzxnzp1KmxtbTF+/HgUFhbi9ddfx9ixYzFp0iTRA8TExOA///kPoqOj\nsX79egCAjY0NJk6ciEOHDukVrJhJ/Lvvvot58+ap7hdQUanPll2L4WDfoDSeWnZo5OIDb/fSZUrT\nMi8AgF7bsqIC1fr0OtvfSIKgqGXQeFUxvk+DpkYfv2xsMa/PFOPrsy16fDPn89rtFBSU5KKlvPTG\nehdKSs9uGbKdkp+N/qgnqn1S0SPULCnQ2X8z2Igev7CoUHUfAWO8HgBwRKnslNJ663rNAivcLlDI\nVeuui2kvZtuuxf+Jav/gSiLyikpE9V/W1pivR5/xTXE8xY4v9niaO5/ZKYm4l3UV9bu8bJbxrT2f\nYse/cd8GiGyuqiEvO7PMbcvaXrx4Mdq0aWMx8VjKdtnPSmVpBUB0dDQqIhMqmBkXFRVh9OjR+O67\n72BjY1NhB7o0bdoUCQkJaNKkCZycnHD//n0UFxejQYMGuHfvnl59HTlyBHPmzEF8fDwA4PPPP4dc\nLsfUqVPVxit7SXfu3IGdnR2WLl2KAQMGqNokJCRg13px1ynICvIg1NL9+sW2M1VbqfSpTEsUfQMv\nqbwmc/dpk6WE7x8rRbXNr22D2vm6S3hO1yhEu2JxN/AS26fYdqbqM7duPdxzaSiqrdibfdnVlIsu\n4RDbVp8+C9LOiLoxlCni1KetNfcJmDdP1tynPm1d7idhzT+HiOqTzIc38BLn1KlT6Nmzp8bHKjzj\nr1Ao8Oeff6JGjRoGDZ6Tk6NWngMABQUFqlWC9NGxY0ckJycjNTUVbm5u+OWXXxAXF6fW5urVq6qf\nX3/9dfTv319t0k/mxRp/aaiONf7V8WZfrB2XBubJ8hW7tRZ1ETAAeDjYYHJXLxNHRJpw0m84raU+\nkydPxuzZs/HRRx+hVq1alRqga9eumDdvHj744APVvpiYGPTo0UPvvhQKBWJjY9GnTx8UFxdj9OjR\nCAgIwHfffQcAel97QERERCT2ImAiqdM68f/mm2+QlZWFBQsWoEGDBqoae5lMpqoj0iUmJgb9+/fH\n0qVLkZOTg+bNm8Pe3h5bt26tVMARERGIiIhQ21fRhH/FihWVGoNMJ+1GkuhSHzKfpKJHqhp7slwP\nriSKKiEh82KeLB9zJA0s9TGc1on/Tz/9ZPAAbm5uOH78OI4fPw6lUglPT08EBQVBLte6oBARERER\nERmR1ol/9+7djTLIzp07sXbtWty6dQtbt27FiRMnkJ2djfDwcKP0b0zOjWvDt7UTatVSQCYDIJQA\nMhF/pIhtZ6q2kunTjcfJyH3KCxrA5nl3UW1LZHLIBd21xm4VtBOKS/DkciruLVoL8OZ4ZsfacWlg\nniyfPjkSe1MwXgtgfDzbbzitE/9Zs2aplsUE1JfT/Pjjj0UNYMzlPE3Nt40DOnTxhoeXK9f/J6pA\nzoOHuADgXmyczrZERNUNrwcgKdN6SjE9PR3p6enIyMhARkYGjh07hi+//BIpKSmiB1i4cCF27tyJ\n6dOnq1YICggIQFJSkmGRm0Bjj7rw9HbjpJ9Ii7qODrBt7mPuMAildclk+Zgny8ccScPT69ZT5Wg9\n479y5cpy++Lj47FmzRrRAxhzOU9Tk8s54ScSQ1aD1+gQERFJjd7/e/fu3RsbN24U3b5sOc+nVXY5\nTyIi+h9HX66QJQXMk+VjjqSBNf6G03rG/+mbYQHA48eP8fPPP8PLS/zFKsZezpOIyNQcbmfhlR8W\n6mwn9g6/RGR9xF4EDPBCYKo6Wif+vr6+att2dnYIDAzEqlWrRA/w9HKeaWlp8PLy4nKeRGTRxN7l\n19x3+OXa49LAPFk+U+SIFwEbH9fxN5zW2XdJSYnav5ycHBw4cAAdOnQQPcCZM2cgl8sRHByMwYMH\nIyQkhJP+Svrjjz/g7OyM5ORknW2zs7OxfPnyKohKvGev9XiWppj79u1rypAqFdPTvvvuO4SEhGDs\n2LHGDo2IiIjIqPSage/evRt79+7Va4B+/fqhfv36ePHFF7Fw4UKcOnVKtTwo6ee3335Dnz598Ntv\nv+ls++DBAyxbtsxksQiCoJbHZ7c10bVakqaY4+PjKx+kCJWJ6WnLly/Hhg0bsGTJElHjiTlORGKx\nLlkamCfLxxxJA8/2G07rxD8sLAwHDx4EAMyfPx9RUVEYMmQIPvvsM9EDpKen48SJE3jhhRdw5swZ\nDBo0CE5OTujXr59hkVuZnJwcnDx5El988QU2bNgAAFAqlQgNDVW1iYmJwfz58wEAH330EVJTU9Gt\nWzfMmTMHALBo0SKEhoYiNDRUbaK6du1adO3aFWFhYXj77bcrbKtUKhEUFIS3334boaGhOHz4sNp2\nZmYmAGDdunXo1asXunXrhvfeew8lJeo3RRk2bBjCw8PRpUsXtbIxTTGXnZGvKJ7g4GC8++676NKl\nCwYOHIi8vLxyx66s3ZgxYxASEoJRo0bhyZMn5dppGkNTTGXee+89pKWl4ZVXXsHixYtFH7ey40RE\nRAT873oAXf8W7leaO1SSOK01/ufPn0dISAgA4Pvvv8euXbtQr149dOnSBTNnzhQ9SNOmTVFYWIjC\nwkLk5+cjPj4et27dMixyK7N9+3b07NkTHh4ecHFxwenTp+Hk5KTW5umz13PmzEFSUpLqG5rExETE\nxcVh586dKCkpQe/evREaGgqFQoEFCxZgx44dcHJywoMHDyps6+DggKtXr2Lx4sXo0KEDlEql2jYA\nXLp0CRs3bsSOHTtQo0YNvP/++/j111/x6quvqmKLjY2Fo6Mjnjx5gl69emHAgAFwcnIqF3PZazp9\n+nSF8Vy7dg3Lly/Hf/7zH7zxxhvYsmULXnnllXLH78qVK4iJiUFQUBAmTJiAZcuWYfz48arHK3rN\nmmIqs2DBAuzatQtbtmyBk5OT6OP2tAsXLmDbtm3o1q0bOnXqhHfeeQeLFi3S51eDrBhrx6WBebJ8\n5s4RrwcQhzX+htNZ4w9AdcOuVq1awcPDA/fv3xc9wODBg+Hl5YWRI0ciJSUFw4YNQ2pqKo4fP25A\n2Nbnt99+wwsvvAAAeOGFF/Dbb79pLVN5tpzkyJEjiIyMhK2tLerUqYPIyEgcPnwYBw4cwAsvvKD6\nI8LR0bHCtjKZDJ6enmqT12e39+3bh9OnTyM8PBzdunXD/v37kZaWphbLkiVLEBYWhj59+iAzM1P1\n+1VRCYy2eLy9vdGqVSsAQGBgIJRKzWdD3N3dERQUBKD0d/Lo0aOixtCHPsetzJMnT1CzZk0IgoBL\nly7B2dlZrzGJiIiIxNJ6xj80NBTjx4/HjRs38NJLLwEo/SOgQYMGogf4+++/IZfL0a5dO7Rr1w6B\ngYGoV6+eYVFbmfv37+PAgQO4ePEiZDIZiouLIZfLMWbMGLUyGk1lLmVkMlm5mnx92pb9kWFnZ6fW\n9tltAIiKisKsWbM09n3w4EHs27cPf/75J2xsbDBgwAAUFBRUGIumeJ+Op1atWqr9crkcRUVFFb4m\nTc9/+vGKxhBLn+NWpkOHDli0aBEmTZqEn3/+GcHBwQCAkydP6nURPVknR99APC4s0d2QzIp5snzM\nkTTwbL/htJ7xX7lyJRwdHdGuXTtVfXNSUhImTZokeoDk5GQcOnQIPXr0wMGDB9G3b180b94co0eP\nNihwa7Jp0ya8+uqrOH36NBITE3H27Fl4eXkhNTUVd+7cwf3795Gfn48dO3aonlO3bl3k5OSotjt3\n7oxt27bhyZMnyM3NxbZt29ClSxd07doVmzZtUn2Lc//+fY1tO3fuLOqi1LCwMGzevBl37txR9ZeR\nkaF6PDs7G46OjrCxscHly5dx4sSJCmPWFrvYeMpkZGSovmVav369qoStTEhIiMYx6tSpozEmTSob\np62tLQDgxIkT6NSpEwDgr7/+Ev3ayHzK1vsX8y/st5/MHS4REVk5rWf8XVxc8Pnnn6vti4yM1HsQ\nNzc3+Pv748aNG0hPT8fu3buxfft2vfuxVhs2bCj3x1b//v2xYcMG/POf/0SvXr3g6uoKf39/1Rnm\n+vXrIzg4GKGhoejduzfmzJmDIUOGoFevXgCAESNGoHXr1gBKL1KNjIxEjRo10LZtW8TGxmpsq1Qq\nNZ4pf5q/vz9mzJiBgQMHoqSkBDVr1sS///1veHh4AAB69uyJFStWICQkBH5+fqqJbkUxA0Dbtm0r\nHU8ZX19fLFu2DBMmTECLFi3wxhtvqD3erl27Co+Pppg0jadPnE/z8PDAxo0bcfr0aTRs2FA16c/O\nzua3YxZO7Hr/gGnW/Dd3XTKJwzxZPqnkyNpvCsYaf8PJBB2nIxMTE7Fv3z7cvXtX7czlxx9/LGqA\nAQMGYP/+/bC3t0e3bt1U//z8/AyL3AAJCQnYtb78xcVh/TwQFNraDBGRKSmVSgwZMkS1QpUlWb16\nNZo0aQJXV1ds27YNEydOxC+//ILOnTvDzc0NCoXWv83N5txvfyDjndLVvfJr26B2fsVlZmXEtjN3\nn6Ya/3oTP6wd/a7OdnY15aJLDgrSzoiarOjTpynaWnOfgHnzZM196tNWbI706dPcx6lN4zr4KrK5\nqLZSwYm/OKdOnULPnj01Pqa11Of7779HaGgodu/ejXnz5uHs2bP46quvcOWKuDNcQGk91qlTp6BU\nKvHjjz8iOjoafn5+WLBggX6vgsgA+tbrVxV3d3fk5ubi0KFDmDBhAoDSazWuX79ebhlUomdx7XFp\nYJ4sH3MkDZz0G07rxH/+/PnYvn07NmzYADs7O2zYsAHr16/X6yzkJ598giZNmmjcT1QVvLy8cODA\nAXOHoVHPnj3Rt29fjBgxQvXHyciRIxESEqJ24TIRERGRobTO4G/fvo2wsDAApSumFBcXo2/fvhg6\ndKjOjnft2gVBEFBcXIxdu3apPZaSksLaZSIiA0mlLtnaMU+WrzrmqDpeD8BSH8Npnfh7eHjg2rVr\naNKkCfz8/LBp0ya4uLigdu3aOjt+4403IJPJkJ+fr7aCj0wmQ6NGjRATE2N49ERERERUDm8KRppo\nnfj/85//xMWLF9GkSRN8+OGHGDhwIAoKCvDNN9/o7Dg1NRUAMHz4cPz4449GCZaISKrKlv7U5VHD\nRogfoPtbVYBrj0sF82T5mCNp4Nl+w2md+L/++uuqnyMiInD//n0UFBTA3t5e9ACc9BMRiV/60xTL\nfhIRaSO2LEgqJUFUMZ1X6d69exd//PEHbt68iX/961+4c+cOHj58qFqXXYw///wTa9euxa1bt7B1\n61acOHEC2dnZCA8PNyh4IiJrVh3rkqsj5snyWXuOpFIWxBp/w2ld1Wfv3r3w9/fHmjVrVKvwJCcn\nY9y4caIHiImJwbhx4+Dn54d9+/YBAGxsbPDBBx8YEDYREREREelD6xn/SZMmYe3atejVqxecnJwA\nACEhITh69KjoARYuXIiEhAQ0adIEX3zxBQAgICAASUlJBoRNRESsS5YG5snyMUfimHulIJ7tN5zW\niX9aWhp69eqltq9mzZooLi4WPUBOTg48PT3V9hUUFIhaGYiIiIiILINUSoKoYlpLfQICAhAfH6+2\nLyEhAW3atBE9QNeuXTFv3jy1fTExMejRo4ceYZKprVmzBs8//3yFjw8ePBi//PKLweNkZGTAy8sL\ngiAY3BeZT179xrgaMQJXI0YgK+g5c4djtR5cSTR3CCQC82T5mCNpsNSbcUqJ1jP+CxYsQGRkJJ5/\n/nPUKVsAACAASURBVHnk5eXhrbfewpYtW7Bp0ybRA8TExKB///5YunQpcnJy0Lx5c9jb22Pr1q0G\nB18VFu5XIuNhnsn6N8cV8kqlEu3bt8ft27chl2v9209l3bp1Rhnbw8MDSqXSKH2R+ZTUqo3Hrj4A\nAJss5pOIiNRxpSDLpHXiHxISgtOnT+Onn35C3bp14eXlhePHj+u1oo+bmxtOnDiB48ePIy0tDZ6e\nnggKChI94TS3jId51fZrLZ51J7I8Ytf7B/675r8Vr0QiFawft3zMkfGZoiyINf6G0zn7dnd3x9Sp\nU/Htt99i2rRpek36ASA/Px+zZ8/G0KFDMXLkSAwbNgyzZ89GXp7pzqJXV+3atUNsbCy6du0KHx8f\njB49Gvn5+arHV61ahY4dO6JZs2Z47bXXcPPmTY399OvXDwDQpEkT1R9zsv+uHT579mw0bdoU7du3\nx86dO1XP6d+/v+qeDGvWrEFERITWtnPnzkVERAS8vLwwcOBA3Lt3D0Dptw3Ozs4oKSnR2RYA1q5d\ni7Zt28LX1xdffvkl2rVrh7179xrjcBJZpLL1/sX8c7x9y9zhEhGRhGid+D948AAff/wxXnrpJfTu\n3Vv177nnxNf0jhs3Drt370ZMTAyOHz+OmJgY7NmzR68lQamUTCbDpk2bsH79eiQmJuL8+fOIi4sD\nAOzbtw+ffvopVqxYgYsXL8LT0xPR0dEa+9m2bRuA0rsrK5VKdOrUCYIg4OTJk/Dz80NKSgomTpyI\nSZMmqY0te+rGQqdOnaqwLQD8/vvvWLRoES5fvozCwkLExsZW+LoqapuUlIR//etfWLp0KS5evIjs\n7GzcvHlTLQ4ia3bl8R1zh0AisH7c8jFH0sAaf8NpLfV55ZVXUFJSgpdeegk2Njaq/fpMvDZu3IiU\nlBTVcqCtWrVCcHAwmjVrhhUrVlQybOs1ZswYNGrUCADQt29fnD17FgDw66+/YtiwYaoLr2fNmoWm\nTZsiIyOj3Lc0FZX4eHp6Yvjw4QCAV199Fe+//z5u376NBg0a6NVWJpNh6NChaNq0KQDgxRdfxPbt\n2zWOqa3t5s2b0bdvXwQHBwMApk+fju+//17kkSIiIiJLp88SoUXKLLDaxzBaJ/7Hjh3DrVu3DFp6\n09XVFY8fP1ZN/AHgyZMncHNzq3Sf1qxhw4aqn21sbJCVlQUAyMrKQvv27VWP1alTB/Xr18f169dF\nl2c93bednR0AIDc3V+PEX1fbZ+PMza24zq+itjdv3lT7PbG1tUX9+vVFvRYia+Br54IT5g6CdGL9\nuOVjjsxHn2sB2niJX1WSNNM68e/SpQuSkpLQrl07vTpNSEhQfSswfPhwREREYPz48fD09IRSqcSi\nRYswYsSIykdN5TRu3FhttZzc3Fzcu3dP4x9YUimVady4Ma5cuaLafvLkiVr9PxERERGJp3Xiv3Ll\nSkRERKBz585o1KiRqkREJpNh9uzZFT5v9OjRapNLQRDw+eefq20vWbIEU6dONTR+q1eWk4EDB+LN\nN9/EoEGD4Ofnh08++QQdO3bUeLbf2dkZcrkc165dQ7NmzUwalyFt+/fvjz59+uDYsWMIDAzE/Pnz\nuRKRBSqwd8LVCN1/yCtyHsBr/+YqiMh6sMZfGh5cSUQtrr5k0ZgjaThz4gimiGjHJUIrpnXiP2PG\nDGRmZiIrKwvZ2dmiO01NTTU0rgrFx8fj3XffRXFxMaKjo8v98fDzzz/jiy++gCAIsLe3x+LFi9G2\nbeXfzB4ONrobGcCQ/p++4LZbt26YMWMGRo4ciQcPHiA4OBg//PCDxufZ2dnhvffeQ0REBIqKirBu\n3bpyF++W9a9r3IraPr39bHuxbQMCAjB//nxER0fj8ePHGDt2LFxcXFCrVi2NcZF5CIqaqjX9teF6\n/0REZIjCYqHaLrFeVWSCllOo9vb2uHTpksXU4xcXF8Pf3x87d+6Eu7s7OnXqhLi4OAQEBKjaHD58\nGC1btoSDgwPi4+MxZ84cHDlyRK2fhIQE7Fpffhm8sH4eCAptbfLXQZWTk5ODpk2b4uTJk/D09DR3\nOFbt2MFz2PdHBgBAVpAHoZbuP2BtspTw/WOlqP7za9ugdr7uJX/FtjNVW3P3mVu3Hu65NNTZ7lHD\nRogfMFRUn3Y15aJrncW2teY+zT2+Nfdp7vGl0qe5xzdFn20a18FXkc1F9VkdnTp1Cj179tT4mNYz\n/k2aNEHNmjVNElRlHDt2DL6+vvDx8QEAREVFYdOmTWoT/86dO6t+Dg4ORkZGRlWHSUYUHx+PsLAw\nCIKA2bNno1WrVpz0E/1X2Zr/ulyXyHU9RETGoM9KQdZWFqR14j9ixAi88MILmDBhgmoJyTLh4eEm\nDUyTzMxMtUmfh4cHjh49WmH7ZcuW4fnnn6+K0MhEtm/fjnHjxkEQBLRv377C8iUia5RU9AjtYDkn\nZ0gz1o9bPuZIGsTmyRR3Da4utE78Y2NjIZPJMGPGjHKPXbt2zWRBVUSf1Wh2796N5cuX4+DBgyaM\niEzt66+/xtdff23uMIgMlhX0HIrqOupsx4ugiYiqjrV9O6B14m/Ki3Qrw93dHenp6art9PR0javW\nnDlzBm+++Sbi4+PV7h/wtC27FsPBvnTNeZtadmjk4gNA3Hr3RNYuL/+x6ue0G0kQFLXg7d6ydDvz\nAgCU2/ZX1AUAXCgpPQvTUl6nwu3CokLVmWwx7cVsN4ONWcevVa8+8hp5VXh8yraVV0/gcqd/oKlL\n6U3trt65CgAat51yHuDC3jid4995avWf7JTSO5TWaxaocfvBlUTkFZVU+HhltgsUctVZOmONb9fi\n/0wyvthtfca3UchRpqrHt/Z8ih2/cYv/w+PCEov/fTJFPs09vj7Hs2yfsX+f7osc/8bFkzggU+If\n/72LWNmdhM29XfZz2bLu0dHRqIjWi3stTVFREfz9/ZGQkAA3NzcEBQWVu7hXqVQiPDwcP/30E0JC\nQjT2w4t7iQzDi3v17/NKv1HIa6T7TJHY4wmIP6ZiLwIGTHMhsFQuCOSFk9WrT3OPL5U+zT2+VPoE\nACdbBTwcdN/U1tzfDFT64l5Lo1AoEBsbiz59+qC4uBijR49GQEAAvvvuOwDAmDFj8PHHH+P+/fsY\nN24cAKBmzZo4duyYOcMmIohf7x9guYtY126nwFdEO7EXAQO8ENgUWD9u+ZgjaTB3nqrDtQOSmvgD\nQEREBCIiItT2jRkzRvXzDz/8wAtAiSyQ2PX+Aems+S+2bh8ACuzrmzgaIiKyBJZ83YDkJv5ERJai\n4L91+2LICsSVBOnDvWlHXHVuorOdPt+gONzOwis/LBTVVp+yIGvm6BsoupSAzIM5kgap5MmSvxng\nxF9C2rVrh2+++QbdunWrsjG7dOmCL7/8El26dKmyMasTZ2dnnDx5UnXvCUszb948pKamYsmSJeYO\nhSrBFHdNZlkQEVH1xYm/DuemzEPuVdOVHdRp6oXWX00T1VYmk+m1pKkxHDp0qErHM7e4uDgsXboU\nKSkpsLe3x6BBgzBr1izUqFHD3KGZRFX/PpFxpd1Igpd3oO6GZFbmrksm3ZgjaaiOeRJbFmSskiBO\n/HXIvarE/cOJ5g6DKqm4uFivSXteXh7mzp2Ljh074vbt23jttdcQGxuLSZMmmTBK85HQol4G06ce\nv9CuLmo+ztHZjnX7RERkiKouC+LEX6IuXbqEqKgozJo1Cy+//DJ27NiBzz77DOnp6fD398eCBQvQ\nsmXpuuA3btzA1KlTceTIEdSpUwfjxo3DW2+9BaC01OPixYtQKBT466+/0KxZM8TGxqJVq1YASsuL\nYmJiEBYWhnnz5uHSpUuwtbXF1q1b4eHhgW+//RaBgaVnHE+fPo2JEyfi2rVr6NmzJ2QyGZo1a4aZ\nM2dqfA0//X979x9X4/0/fvxxahKlEEJHRcIyPwpJ3mOINb9CiGi982uWvWPebB+M9z5m1mzU26eZ\n2GaszSe/+ViYn7Mxk2VlY7QtFBWN/KipnM73j77OW6t0HTrOOc7zfru53Trnep3X9bqu1ynP67qe\nr9crIYG4uDiuXLmCj48PsbGxqNVq/vnPf2JnZ8fChQt1ZceNG0fPnj2JjIxUdDx16tRh165dREVF\nERMTw6lTp3RrOqSmpjJq1CjOnDlT4aIgIiJC93OzZs0YOXJkuXlyO3XqxOTJk0lMTCQzM5N+/fqx\nYsUKatcum95r+fLlrFy5EpVKxZw5cx7Yh1988QXvv/8+eXl5ODk5MW/ePEaOHElGRgYzZszg559/\nRqVS0bdvX9577z0cHBx0bZg0aRKJiYlcvHiRoKAg5s+fz7Rp0zh+/Dg+Pj58+umnODo6cvHiRby9\nvVm2bBlLlixBq9USGRnJK6+8UmmbkpOTeeONNzh37hwtWrTgnXfeoWfPng88DkNQOgOQPrnr+ubj\nlzg2UlTOmNyatcNyLt3MlzHzknttTqDelVxFZS15zIa55I5bOumnRyeBvxlKTU0lLCyMpUuX0r9/\nf9LS0oiKimL9+vV4e3uTmJhIaGgoycnJWFtbExoayqBBg/jkk0+4dOkSw4cPp3Xr1vTt2xeA3bt3\n89FHH7Fq1So+/PBDxo8fz4kTJ7C2tq6QCrJnzx7WrVvHBx98wKJFi3jttdf46quvKC4uJiwsjFde\neYWJEyeya9cuJk2aRFRUVKXHkJSURGxsLOvXr8fDw4OYmBgmTZrE7t27GTlyJFOmTNEF/vn5+Rw6\ndIhly5ZRWlqq6Hg+/fRTVq5cyZ07dzh+/Djbtm3TBfWJiYmMGDFC0ZOAo0ePllsnQqVSsX37djZt\n2kTt2rUJDAxk/fr1/P3vf2ffvn2sWLGCbdu24erq+sCnBAUFBcyZM4cDBw7g4eHBlStXuHbtmm77\nzJkz8ff35+bNm4SHhxMdHc3ixYt1bdi5cyfbtm2jpKSE5557jlOnThEXF4enpychISHEx8fz2muv\n6eo7cuQIJ06cICMjg2HDhtGhQ4cKY0UuX77M2LFjWblyJQEBARw6dIjw8HC+//57nJycqj1XNckQ\nueui5ikdCGzJAaWhKA3oG+Zdwe72TUV1FuRdYdQV6U8hTJE+MwWNa171Ngn8zcyRI0f4/PPPWbVq\nlW7A7dq1awkPD8fHp2ylujFjxhATE0NycjI2Njb88ccfzJo1CwA3NzfCwsLYsmWLLlDu3LkzQ4YM\nAWDatGmsWLGC5OTkShdA8/PzIyAgAIBRo0bpBoWeOHECjUaju/M+ePBgXXsqs2bNGmbMmIGnpycA\nr776KjExMWRlZeHn54dKpeK7776jR48ebN++HV9fX5ydnTlx4kS1x+Pr66ub8tXW1paQkBBWr15N\nREQEGo2GrVu38sUXX1R7rhMSEkhNTeV//ud/yr3/0ksv4ezsDEBgYCCnTp0CYNu2bYwbN4527doB\n8F//9V9s2bKlyvqtrKw4ffo0zZs3p0mTJjRpUrbAUsuWLWnZsmymFicnJ15++WXee++9cp+dMmUK\njRqV3ZH28/OjSZMmPPNM2eJzgwYN4vDhw+XKv/baa9SpUwcvLy9CQ0PZvHlzhcB/48aN9O/fX9e/\nzz33HJ07d2bv3r2MGTOm2vMlHj9j5/grHQhs6YOADZGXXP/qFZorOPdFtZUtBgeW3Z9PYu74k8iS\n+0mvlCAJ/J8MWq2WtWvX0rNnz3Kz7GRmZpKYmMjq1at17929e5ecnBxUKhU5OTm6QBLK8t7v/3zz\n5v/5hqhUKpo3b05OTk6lbbgXnALUrVuXO3fuUFpaSnZ2Ns2aNStX1sXFpcoc8szMTObOncv8+fPL\nvZ+dnY1arWbEiBFs3ryZHj16sHnzZkJCQnSf0+d4AAYOHMisWbO4ePEi586dw8HBAW9v70rbdc+X\nX37JokWL2Lp1qy5FqLJzYGtrS25u2V233Nzcchc7arW6yvrt7Oz4+OOPiYuLIyoqiu7du/PWW2/h\n6enJlStXmDNnDseOHeP27dtotVrq1y+fm964cWPdz3Xq1Cn3unbt2ty+XT4/3cXFpVy7Tp8+XaFN\nmZmZbN++nd27d+ve02g09OrVq8rjMDZ9FgWz5Hx8WTzNuDp+vZcOxfurLWdfcIvbdvUU1emYV3H1\neSGEqI4E/mZEpVKxbNkyYmNjmTdvHm+//TZQFsjNnDmTmTNnVvhMcnIybm5uJCcnV1nvpUuXdD+X\nlpZy+fJlmjZtqlfbmjZtSnZ2drn3srKyygXo91Or1cyePZvg4OBKtwcHBxMcHMz06dNJSUkhISFB\n97kHHU9lMx/Z2toSFBTEhg0bSE9P111EVGXfvn28+uqrJCYmlkvzqY6zszNZWVm61/f/XJm+ffvS\nt29fioqKWLRoETNmzODLL7/krbfewtramqNHj+Lo6MiXX37J66+//sC6qhukm5WVpXu6kpWVVeEi\nDcrO7ejRo4mNjX1gXaZEn0XBjJ2PbwhKc/yfxMXTzEnnEmuan0+vtlxRbVsaXFWWj6/PnXxRPckd\nNw/ST49OAn8zY29vz6ZNmxg2bBgLFy5kwYIFvPjii4SFhdG7d298fHwoLCzkyJEj+Pv706VLF+zt\n7Vm+fDmTJ0/GxsaGs2fPUlRUpLvrnZqays6dOwkMDCQ+Pp7atWvTrVs3vdrVrVs3rK2tdSk1X331\nFSdPnuTZZ5+ttHxERASLFy+mffv2tGvXjps3b3LgwAGGDRsGQIcOHWjYsCFRUVH07dtXN7C1uuOp\nKgAOCQkhMjKSvLy8Ck8Z7nf48GFeeuklPv/882qfCtxzb5/Dhg3jH//4ByEhIbRo0YIlS5ZU+Zmr\nV6+SnJxM7969qVOnDnXr1tWNOSgoKMDBwYF69epx+fLlCqlGD2Pp0qXExMRw/vx51q9fT3x8fIUy\no0aNIiAggAMHDtC7d29KSko4ceIErVq1qvAURYgnkT4DYS357rws8iaE+ZLAvxp2rQy7jPLD1O/g\n4MCWLVsYOnQotWrVYs6cOcTGxvL666/z22+/UadOHfz8/PD398fKyor169czf/58fHx8KCoqwtPT\nUzfTjkql4oUXXmDr1q1ERkbi4eHBunXrKh34Wtnd9HuvbWxsWLduHdOnT+ett96iX79+DBgwABsb\nm0qPYdCgQRQUFDBp0iQyMzNxcHCgT58+usAfYOTIkURHR/PJJ5/o3lNyPJXNTe/n54eVlRWdO3d+\nYArO0qVLuX37NqNHj9a916NHDxITEystf//+AgICmDp1KsOGDcPKyoq5c+eyefPmSj9XWlrKhx9+\nSGRkJCqVio4dO/L+++8DZfn4kZGRuLu706pVq3JjKapy/zFXdg78/f3p2rUrpaWlvPLKKzz33HMV\nyrq4uJCQkMCbb77J5MmTsba2pkuXLhXGFwjTYewcf6XMJVBUmjcP+t2dT7UuoRO1HqVpJuVJXOTN\nknPHzYn006NTaS1pIu//b//+/RzYVPEOTK9Banx7PmOEFhnPu+++S0ZGhkFWbg0ICGDixImMHTu2\nxut+GMOHDyc4OJjx48cbuymPzb3pPK9evYqVlVWN1Xv8yE8c/rIslUlVfAetTfVpB0rLGbtOY+9f\nnzovXvhRUeCvT51WhbewvfGHorJKxwMU1baldpGyVKsCeweuNWpSbTl9LhACd3xR4zPg6HNMqdYl\ndNJUH/jrU6fSssau0xD9WbeWleJ0D6Vliy+kKQ4oldZpiHYaok5j71+fOpX2k6Wfp2gfLf369at0\nm9zxt3A1ed139OhRPDw8cHJyYuPGjfzyyy9VfvEet5SUFFJTU3VjBYR4EhhiHn9jjwdQejdZ6dST\noDygN1TefLun6oHmyRtjooS5zBQkuePmQfrp0Ungb+GqSo15GOnp6UyYMIHCwkLc3d1Zs2ZNuRlw\njCUyMpKkpCSio6Oxs7MzdnMeu5rqXyFMiT7pJjIQ1vSZSzqYEOZOAn8LV91sMfoIDw8nPDy8xuqr\nKStWrDB2E4zG1dWVvLw8YzdDGIi55Phbul/u3nqicvwNwdjjBiR33DxIPz06CfyFEEIIYTbk6YAQ\nD08CfyGEMFOGyPHXh9KFwSx9UTBLzvE3BEM8HZDccfMg/fToJPAXQgjxUJQOBJZFwYQQwjRI4C+E\nEGZKcvzNg+T4G4/StKBTNqX88uI/H0OLxKOQHP9HJ4G/EEIIIZ5IStOCMpwbPIbWCGF8EvibkU6d\nOrF8+XJ69+792Pbp7+/P+++/j7+//2Pbp7kzRj/p44svviAhIYGkpCRjN0U8ImPn+CuldCwAPJnj\nASTH3/S1rtuIE8ZuhKiW5Pg/Ogn8q7Fn609cv1pgsPobNLbj+eHKVguuyTn3lTp69Ohj3Z+xbd68\nmSVLlpCTk0OtWrXw9/fn3XffpVmzZorrMEY/CWHKjL0omBBCiDIS+Ffj+tUCss5fN3YzxEPSaDRY\nW1srLt+9e3d27txJ48aNKSgoYObMmbzxxht8/PHHFcrevXuXp56SXyFhPJLjbx4kx9/05VxOlylC\nzYDk+D86K2M3QDycs2fP4u3tzZYtWwDYs2cPvXr1omXLlgQGBnL69Gld2ezsbF588UXatGmDt7c3\nq1at0m2Ljo4mPDyciRMn4urqSp8+ffj555912zt16sThw4d1ZSMiIoiMjMTV1RV/f39+/PFHXdnU\n1FR69+6Nq6srERERTJgwgbfffrvKY0hISMDPz49WrVoxcuRIsrKyAPjnP//JggULypUdN26cbiEu\nJcczdepU3NzciI2NRa1Wc/36fy7eUlNTadOmDRqNpkKb1Go1jRs3BkCr1WJtbY2zs3O587F8+XL+\n9re/4erqikajITExkY4dO9K6dWuWLVtW5fEC7N27lx49euDq6kr79u2Ji4sDID8/nzFjxtCmTRta\ntWrF2LFjuXz5su5zQ4YM4e233yYwMBBXV1dCQ0P5448/mDJlCm5ubgQEBJCZmakr7+TkxKpVq/Dx\n8cHT05N//etfaLWVJ4WcO3eO4cOH4+HhQffu3dm2bdsDj0EIIZ401ndLaHH+V0X/6l+9YuzmCvHQ\nJPA3Q6mpqYwaNYolS5YwYsQI0tLSiIqKIjY2lt9//52///3vhIaGUlJSQmlpKaGhoXTs2JHTp0+z\nbds2Vq5cyYEDB3T17d69m2HDhpGRkUFwcDDjx4/XBcV/TVnZs2cPI0aM4MKFC7zwwgu89tprABQX\nFxMWFsa4ceN09SQlJVWZ8pKUlERsbCyfffYZv/76Kz169GDSpEkAjBw5kq1bt+rK5ufnc+jQIYKD\ngxUfT1BQEBcuXGDatGn07NmzXDCbmJjIiBEjqnwScOzYMdzd3XFzcyMrK4s333yz3PYtW7awYcMG\nMjIySE9PZ/bs2axatYrTp09z7dq1cgH7X0VFRRETE8PFixf57rvv6NWrF1B2kTF+/HjS0tJIS0vD\n1ta2wqrK27ZtIz4+np9++omMjAyef/55xo8fz++//06bNm149913K5zjgwcPcvDgQXbt2kVCQkKF\n9hQUFDBixAhGjx5Neno6H330EbNnz+bs2bNVHoMwHW7N2hm7CUKBdk/VU1Qu13cAv7/woqJ/ub4D\nDNxqy6K0j4Rx1W8tTzgfleQpmJkjR47w+eefs2rVKt2A27Vr1xIeHo6Pjw8AY8aMISYmhuTkZGxs\nbPjjjz+YNWsWAG5uboSFhbFlyxb69u0LQOfOnRkyZAgA06ZNY8WKFSQnJ+Pn51dh/35+fgQEBAAw\natQoVq5cCcCJEyfQaDRMmTIFgMGDB+vaU5k1a9YwY8YMPD09AXj11VeJiYkhKysLPz8/VCoV3333\nHT169GD79u34+vri7OzMiRMnqj0eX19fXnjhBQBsbW0JCQlh9erVREREoNFo2Lp1K1988UWVbfPz\n8+P8+fNkZ2czbdo0FixYQHR0NFB2ITRlyhSaN28OwI4dO3j++ed152ru3Ll89NFHVdZdq1Ytfvnl\nF7y8vHBwcKBjx7JHlg0aNGDw4MG6cjNnziQoKEj3WqVSERoaipubGwABAQGcO3dOd+EQFBTE4sWL\ny+0rKioKR0dHHB0dmTp1Klu2bCEsLKxcmT179uDm5sbYsWMB6NChA4MHD2b79u26izohHidLXhSs\n2KEhd5xdFZVVOhYi13cAd+3rKyr7JJ5TQ1A6RaikBAlTJIG/GdFqtaxdu5aePXuWm2UnMzOTxMRE\nVq9erXvv7t275OTkoFKpyMnJoWXLlrptGo2m3OfvBbFQFmA2b96cnJycStvQpEkT3c9169blzp07\nlJaWkp2dXWEArIuLS5XpJZmZmcydO5f58+eXez87Oxu1Ws2IESPYvHkzPXr0YPPmzYSEhOg+p8/x\nAAwcOJBZs2Zx8eJFzp07h4ODA97e3pW2637NmjVj7ty5jBo1Shf43zuue3Jzc8vtr27dujRs2LDK\nOteuXcvSpUtZuHAh7du3Z8GCBXTr1o3CwkLmzZvHgQMHyM/PB8ruxmu1Wt1Tk3spSFB2QdOoUSPd\n69q1a1NQUH4Q+v3tVKvVZGdnV2hPVlYWP/zwQ4Xzee98C9P2JOb4P4mLghkix1/pBdIdx0aU1rVX\nVKc5ndOapk8fKZ0iVOmqwUI5yfF/dBL4mxGVSsWyZcuIjY1l3rx5uvx5tVrNzJkzmTlzZoXPJCcn\n4+bmRnJycpX1Xrp0SfdzaWkply9fpmnTpnq1rWnTphUCy6ysrHIB5f3UajWzZ88mODi40u3BwcEE\nBwczffp0UlJSdGkqarX6gcdT2Yw6tra2BAUFsWHDBtLT0/UKau/evUvdunUr7OMeZ2dnzp07p3td\nWFjItWvXqqzP29ubhIQENBoNq1atYsKECZw6dYoPPviA3377jX379tG4cWNOnTrFc889Vy7w11dW\nVhZt27bV/VzZzEQuLi74+/vrxooIIcyD0gskVbHyaUSVXkyU1LWnVuFtRXXKUwQhTIsE/mbG3t6e\nTZs2MWzYMBYuXMiCBQt48cUXCQsLo3fv3vj4+FBYWMiRI0fw9/enS5cu2Nvbs3z5ciZPnoyNJe+j\nWgAAERZJREFUjQ1nz56lqKhId9c7NTWVnTt3EhgYSHx8PLVr16Zbt256tatbt25YW1vrUmq++uor\nTp48ybPPPltp+YiICBYvXkz79u1p164dN2/e5MCBAwwbNgwoSzlp2LAhUVFR9O3bFwcHB4Bqj6eq\nJwwhISFERkaSl5dX4SnD/TZt2oSfnx9qtZrMzEwWLVqkS4OqzNChQxkwYADHjh3Dx8eHd955h9LS\nyucYLikpYdu2bTz//PM4ODhgb2+vG2dQUFCAra0tDg4OXL9+nSVLllT4fFXHVpW4uDi6du3KrVu3\niI+PZ9q0aRXKDBgwgIULF7JhwwaGDx8OwKlTp7C3t6dNmzZ67U88fuYyj78hmNPaAOYyj78+FxMl\njo2qLQfm8xTBEH2kNCUIJC1IKaXz+PfanEC9K7mK6tTn3Cut177gFrftlI0bedx9L4F/NRo0tjO5\n+h0cHNiyZQtDhw6lVq1azJkzh9jYWF5//XV+++036tSpg5+fH/7+/lhZWbF+/Xrmz5+Pj48PRUVF\neHp6Mm/ePKDs7vULL7zA1q1biYyMxMPDg3Xr1lU68LWyu+n3XtvY2LBu3TqmT5/OW2+9Rb9+/Rgw\nYAA2NjaVHsOgQYMoKChg0qRJZGZm4uDgQJ8+fXSBP5QN8o2OjuaTTz7RvafkeCq7Q+7n54eVlRWd\nO3dGrVZXeW7Pnj3Lm2++yY0bN3BycmL48OEVBtner127dixZsoQpU6ZQWFhIZGRkuRSbv9qwYQOv\nv/46Go0GT09P4uPjAZg6dSpTpkzB09OTZs2a8fLLL7Nr165yn63q3Ff1euDAgfTp04ebN28SGhqq\ny++//xzVq1ePzZs388Ybb/DGG29QWlpKhw4dWLRoUZXHIIQp0GdtAKvCW0YdN6A0z764XtVpgsL8\nKE0JAkkLqmn1r16hucJzX5B3hVFXlF2gNcy7gt3tm9WWK6ptS4Oryi48lO5fn4sJVsyocpNKq+9t\nxCfA/v37ObCp4nRcvQap8e2pbDGtJ8W7775LRkaGbpBuTQoICGDixIm6gaPGNnz4cN2sRU86Jycn\nfvjhB9zd3Q1S//EjP3H4y7LpV1XFd9Da2Fb7GaXljF2nsfevT50XL/yoKMff0s+T0rK2uRdp/eWn\niuosqm1L7SJld4j3+j5Ls2f6VFvOXM6TPnUqPaf6nE9DlE21LqGTRlm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- "text": [ - "" - ] - } - ], - "prompt_number": 67 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "With more thinning, the autocorrelation drops quicker. There is a tradeoff though: higher thinning requires more MCMC iterations to achieve the same number of returned samples. For example, 10 000 samples unthinned is 100 000 with a thinning of 10 (though the latter has less autocorrelation). \n", - "\n", - "What is a good amount of thinning? The returned samples will always exhibit some autocorrelation, regardless of how much thinning is done. So long as the autocorrelation tends to zero, you are probably ok. Typically thinning of more than 10 is not necessary.\n", - "\n", - "PyMC exposes a `thinning` parameter in the call to `sample`, for example: `sample( 10000, burn = 5000, thinning = 5)`. " - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### `pymc.Matplot.plot()`\n", - "\n", - "It seems silly to have to manually create histograms, autocorrelation plots and trace plots each time we perform MCMC. The authors of PyMC have included a visualization tool for just this purpose. \n", - "\n", - "As the title suggests, the `pymc.Matplot` module contains a poorly named function `plot`, which I prefer to import as `mcplot` so there is no conflict with other namespaces. `plot`, or `mcplot` as I suggest, accepts an `MCMC` object and will return posterior distributions, traces and auto-correlations for each variable (up to 10 variables). \n", - "\n", - "Below we use the tool to plot the centers of the clusters, after sampling 25 000 more times and `thinning = 10`." - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "from pymc.Matplot import plot as mcplot\n", - "\n", - "mcmc.sample(25000, 0, 10)\n", - "mcplot(mcmc.trace(\"centers\", 2), common_scale=False)\n" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "output_type": "stream", - "stream": "stdout", - "text": [ - " \r", - "[****************100%******************] 25000 of 25000 complete" - ] - }, - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "Plotting centers_0\n", - "Plotting" - ] - }, - { - "output_type": "stream", - "stream": "stdout", - "text": [ - " centers_1\n", - "\n" - ] - }, - { - "metadata": {}, - "output_type": "display_data", - "png": 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CUSalZwt3/e+tkdfgWhWioMYEVfXFy1tSAWjv40InP8MPu1sa7ZBiVp5k+cRg/m/vJQpL\n5SzYkyYCKxtn/vz56v8jIiJ4++23+eSTTwgPDycgIIDZs2cjk8mYNm0a4eHh6lIGS7Ny5UqCg4Nr\nFFiVl5djZ1d1CYRmjZWPjw/r1q1j3759ZGRkEB0dzaFDh7TkdEAp4Kzvt3dUVBRRUVFVnuvEiRMc\nP368zgMrWxl2shY/RI2VebCawOrGgS24tOxIUMQE1t3JfFzetpQ2j72HzNmNlO/fonGPYUgkEhyb\ntCBwSAyXt35HXsrfNOk7juKbGbR59B0UCgUX13xBhxlfgAQOL3uZVk/2BomEjp1DmD7nXfZvW8uD\nDz7IE088ofXQ0BxOKy+6Ra7cAYVCQUaxjKVbk7Br14/oLr4cPnyYSZMmsea6B57B95B39hj5+fls\n3rwZUAZezz77LDdu3OCJJ55g0KBBvPvuu7z//vuEhoaiUCjIyspi3bp1bNmyhYKCAiZNmqQTWGkO\nTlZ+uF3JLVb/n1VYxhvbzlaZMSorl+uVptBMhevjZkEpCWezqnzdkmQVaetsVfVhttNIHubc0Sir\nPGxqbYgHU92we/duAObMmcOcOXO0XjNHKQPAuXPneOmll7h58yZ2dnasWLGCgIAAFi5cyMaNGyku\nLmbUqFG89tprpKWlMXHiRPr27cvBgwdp1qwZcXFx/P777xw7dowZM2bg7OzMtm3bOH36NHPnzqWg\noABvb2+++eYb/Pz8GDNmDCEhIRw4cID77ruP5s2b8+mnn2JnZ4e7u7v6mQQVX5aJiYn89ttv3H//\n/djb29OqVSsCAwM5fPgwvXr10vFpyZIl/P7775SWlvL999/Trl07fv75Z44fP87HH3/M+vXr1ef0\n8PBg7dq1zJs3j+LiYvbv38+LL77I+PHja/3eCuoeoWFlHqwmsLp94xI+vUZorSvKOMfZH94GoOx2\nASU5yuJtF/+2ADh4NqGs6JbWPmUFOdy+cZl/v3sFAGnxLcoKlLpaa26488v6M3w4eBibf1jEjBkz\nGDx4MBMmPkBBSbmWXpadkxvzfj/F1RIZG49ewNG7GYv3XyG6i6/G2e601EFCt24VAcqqVatYvXo1\nRWUKzl1KJy3nNunp6YSGhiq3l0jYd+I0p5JPM3bsWABu3ryp512piIY0M1Yl5XKm/O9UdW+nFjm3\nywxvpIc5W1O4pBHA1TUFJeVcyy8hqLEz5XIF/1y9RUdfV5yMqLs7lp5P/ulMnTqvykHUqhPXzWpz\nQ0GhUPDL8WuENHWjS1M3S5tjs0yfPp3Zs2czcuRISkpKKC8vZ8eOHZw/f574+HjkcjmPPPII+/bt\no3nz5pw/f57ly5fz5Zdf8sQTT7Bp0yYmTpzIsmXL+OCDD+jatSulpaW8+uqrrFy5Em9vb9auXct/\n/vMf/u///g+JREJZWZm62H7AgAGsWbOGpk2bquvGKjNgwAA2bdpEz5491ev8/f3JyMjQu72Pjw8J\nCQksX76cr7/+mq+++gqoaEf22WefaZ3T3t6eN954g+PHj2tlDOsCW/kBYit+gG35YipWE1g5+bYi\n/9wJXFu0Ry6XI5VKcWnWhjaPvoOdkysKuRyJVEpu8n7tHRUKJFI7FArlgJfMxQMn35a0m/YJUjsZ\n7b0d+DdLOcSVd1uOM5B04zbvvfceAP369eOAS3eSrhVwX5eKuh231p3ISzlCnKcvealHaT2hov5g\nwIABHDx4EOTKcypQaKXQv/vuOxITExn85Q5uL36Bj3ZcwN/fnxMnThAaGkpBcRmfHy+h0L0FGzdu\nBFALFRaWlPPL8WsMaeuFZpLptzMVgVdRadWDe2dvFmJXSRysrFz/OGJ12SrA7EGVQqEg6VoBAZ5O\nuDvp3npP/O8U2UVlLBzbnsNX8vnhcAb3tHTng3vbGDz2xrymkHiJiCAvXB3sSL5egLujDGkD7NNt\nyoOpXK7Que6afP3XZTYla9fomQu5QsGb287S3MORZ/q1NOuxGxL5+flcvXqVkSNHAuDg4ABAQkIC\nCQkJDBw4EIDCwkLOnTtH8+bNCQgIoHPnzgB069ZNXTQLFVnqlJQUTp8+TXR0NKAc8tMcIlStB7jn\nnnuYNWsW48ePZ8yYMTWyv6ra0NGjRwMQGhrKpk2bdOzTd06FQmFU31WBwBaxmsCqSe9RnP/1Y05/\nO5uode788MuvNB8xldT/vgsKORKZPW0fe//O1hoPAIkEe/fGyEuLOfvjezQfMZVmQ2L49zulJMSN\nxj40mfC61m7/7N3BqPdXAzBkyBAO3JnxdiCt4heeT++RnF85j8xDv+HRqS8OHspMSEFJOc72Ulp1\n6cXVuLnknT2KV2ftL8I+ffoQFRXFVadW2Dm6kFdcxotz3uKtN5QFse06hSBrOwHvbpGMHj0aOzs7\nmge2593/fMiaf66z7uQNfjl+jTHB+mfZyasouLqUc5uZ63S1Wcot9JBTKBTsuZBD28Yu+Ls7cuhy\nHm/9fg5vFxm/PByis332HfG+/x7J4O/LSvXrmrbLKSmTc7tMzvMblb0Op/byr6UX1k9qZiGz1p/h\nsR7NiOmuvyZHFVTVBZdzijl8JZ/DV/Lv6sCqOl544QUef/xxrXVpaWnq4AuU7cLKyytqAjUDnY4d\nO/L777/rPbaLS4XG0ueff87hw4f5448/iIyMJCEhQV14rllj1axZM65cqZCWSU9P15qco4mjoyMA\ndnZ2WvZVd876wlaGza3FD1FjZR6sJrCS2jvQ5pG56uWXN6fg2qI9HaZ/qrWd/7DH1P/79qsYt2//\nZEXK2cmnOR7tlWnuYF8Xkq8XEvhARU1Ft4FRfDF7inpZNYPuSl5FhsbOwZm2k9+nMtH/PYFfzhlu\nN+1Mx5kL1Ovfn/q4+v/PP/+cvNtlTPjpHwAyC0p5c38pXaZ/xrtDgygoKWfyr6doHDaMzYvmkF1Y\nyoM/JxHzy0l6NG9U+ZQ6VFXI/uTqZL3rk68XMlSP9IShGqva8vflfP6z/QKgzJIcvaIMlrIKqx+a\nVAVVNUHly85z2QT7VhS1G6PsXx3/t/cSmQWlvDsssN7kGWr6YFKp4P/3cEaVgZWg7mnUqBH+/v5s\n3bqVkSNHUlxcjFwuZ/DgwXz00UdMnDgRV1dX0tPTtQIqTVQ/gNzc3NStddq2bcvNmzc5dOgQvXr1\norS0lLNnz9KxY0ed/c+fP0+PHj3o0aMH27dvJz09XR1YadZYRUVFMX36dGbNmkVGRgbnzp2jR48e\nJvmt75yNGjXi1q1bhncWWBWixso8GAysMjIyGDVqFMnJyRQUFHDx4kUmT56MRCKhRYsW/Pjjj0il\nUjp06IC/vzI7sGjRIoKDg2tlmDFNgI1BXzscuUb2pkyu4FriWnKSKnQsnJsF0WrcM1UeM+VmEY0b\nV93mYHNyJgv36kobJF0tIOaXk8Tep/1A3PZvxTCf5nd3VVkGfTpShqhu+LCuOJel3R6nusDkdpl5\n7EvPK9aaLSitZWSlugaZhaU0cdX/ZWhxLF2Lb+nzWxHffvsts2fPZt68edjb27NixQoiIyP5999/\nuffeewFl0BQbG4tEItH5TKiWJ02axEsvvaQuXl+xYgWvvfYaeXl5lJWVMXPmTL2B1TvvvMO5c+dQ\nKBQMHDhQPcyoiSpoHz9+PH379kUmk/Hpp5/q/XxqrtO0V/N/feds3rw5X331FQMHDqzT4nVbyYzY\nih9gW76YisHAytvbmx07dqjH8b28vNiyZQuNGjXirbfeYuvWrYwePRpfX996TQEbS2WFcICNpzJ5\nvKc/u85l8+GOC/gNuA+/AfcZfUz3Nt0orVS39M1fl3igqx9ztqRqZb4qc7tMrvP6939XFI0aM2Pt\n1d9SjbZVxdJD6TrrzJ2t+utiDttTs7m3vTe9W3rovF7Zs5JyOQUl5aCAB39O0tm+Jqh8UQC3iiuC\nXnPNADR0lBMZ+fxztYCHu/nVOLNVuT6qugfT35fzyL1dxhCNDGRdlpGlZd/mo4QLPNnLn14t9ct5\n1DYraEsEBQWxfv16nfUzZsxgxowZOus1hQmfeabix9yYMWO0aqS6dOmiNcNPhapGU8V///tfo22d\nPXs2s2fPrnabo0cr9PC6devGhg0bAGXgN2nSpCrP6enpqSMsbQ5uFJRQYsKPMDuphLLqNGsEAjNi\nMLBydHRUj7EDWqrEMpkMmUx5iKysLAYOHEhwcDBfffWV1j7Wxq07s88+3HHBbMfccCqTDaeMq2N5\nY9vZKl9LryYos3be/fM8oFSEX/lwF5ZVCuYqxxvT1ySTnlfCYz3013ZocinntjIIu8OW5EwGtNZV\nyJYr4M3fK95fc33pV9UIXIVKXyvQ24l+AcY1IQf4ZNdFdqRmsfLhLng52+u8vi7pOmdvFtHU3ZGJ\nIb7qe6eLnxsnr90irHkjnffVVBQKBf/75zodm7gQ2qyR2r5zWUW8+XvVch4irmoY2EKvwKSrBcxL\nuKBerutyhvrCWuqSRI2VeTC5xio9PZ34+Hjeflsph7B37148PT2ZN28eS5Ys4dlnnzWbkXXBo6tO\nIpVUL7xZFXX5Yb5cj/IGdenHJD0ZqMpfwOl5ytmaJ69WX4vx25mbOu12Dl+pqMN6P/6c2heFQqF1\nTQ1JNdwuk/PRjvMMCvKqtgWSscFLZg2HsOPvtBTacz6HsZ2aUC5XMPmLVURGhPNoWDN1JwCA3eey\n1f/PWJtMYamcAE8nvf0sVZTLFVwv0C/8quJ/J67hKJPSwsORpQeVwbAqiCoqrXrIG5SzWBPOZle7\njcBybN++nfff164V/f3339myZYuFLBJYM6LGyjyYFFgVFxfz+OOPs3TpUrXMgCqTFR0dzYIFC/Tu\nd27Vxzh6KYtr7ZxdcfFva3SvJltdTssOttj5C9NT6+18iYmJnD2dCQSol/POpuDephsSSfX7L9iT\npvf1xMQC/IN7kHghl8J0ZcaovP0Qrf2v38mGVXX8zcnN2Z+Wxx8Ju/lsVDut3lHKWjyl5tP+v/bi\n7iSrsteU6njyvi30vp6YmEhxmZwM93ZEBHmRlvQ3SpT1YMlHDuCd5Yl3u+6k3iwidd0fHNrvBi5t\n1cc/oWH/1dNHALjYphutvJzU5z94KYgufm4cObgPgB23/Um8kKvl/7yECwyQXUIikeAa2JXvDqaT\nd/YYk7r6Ac207FfgrfV+V/Z/V3Fzdp3PUR8/MbHALL22BOZhyJAhFm0pVNfUR7bq7M0ick3QAnR1\nsKOzn3GacbaU4bElX0zF6F6BkZGRxMfHY2dnx+TJk7nvvvsYN24coOwgL5fLcXR0ZOnSpWRnZ/PK\nK69o7W9sr8C7jQAvJy5m17wYvaGx/rFQfjp6ldX/KAU6Xwxvpc5C9W7pzsEayioAPNOvBXFHr6pl\nGkwhpntTfjqqnFVXeairqLSccT+cAGDlpC40dtUdqlOhmlk6s09ztYhsamYhW0/f5PGezXB3khG7\n/zJrkm4glcC2J7X7PT7TrwVjOzXh38xCnlmvK5lRHQMDPdl1Pkdr3ZC2XqRmFnGxiokOi8Z3oLBU\nzstbUtTrZvVtwaJ9ygbFqvdiyq+n1DWB+oYC7116VEtv7edJnbmQfRtHmZSQpm4W7xV48uRJpk+f\njp2dHZ07d2bx4sV4eHgQFhaGRCJh7dq1eHp6EhcXx6JFi9QtbRo10p6dW9+9AgX6STibrTUUaAo1\n7RVoKv0C3Hl3mGENPoH1Ume9AsvKyoiKiuL48eNERUUxd+5c1q1bR1paGl9++SUvvPACffv2ZcSI\nEbi5ueHt7c1PP/1kkhN3I3kmqqI3NMb/94TWsubQnqnh9td/Xa6FRUo0ewlWRjPAkWPcmLFcAUeu\n5LH+5A3239FFKymX80J4K9Yk3VBvUxnVz5uL2UW6LxpCzxu4PbX64blyhYJfjl/VWrfkQMWw4+bk\nTJKvF2jNoNWHVAKa8zgeXnlS/X99NOU2RIcOHdi7dy8ATzzxBEePHiU0NFRrok1paSmxsbHs2bOH\n1atXExsbq9OE2RawhRqryogaK/MiaqzMg8HASiaT6czu0Ncq4fDhw+azysox54e5NtmW2mLJh5KP\nq726Hskcxdem+rL+5A2ddeVyBb+duamlPG+svqpCoeC137QnJ1zNLzE4KUF1+HVJN2rsy65zOYY3\nqsSzG/7V7PIuAAAgAElEQVTVWac5a0qfXIgmCoWCc1lFVCHqbzWoJteAsoenh4cHycnJRERE0L9/\nf+bNm0dKSgohISFIpVKGDh3KtGnTLGhx3aGpYyUQ6EPUWJmHBtjwQ2AL3NbQ1aov4U1jmfvHWZ3A\nwlDmRoW+rSQSZbCmSUZ+MddvVRSVKxQK4lOySL1pQsbKAvxy/JpelX9rZOPGjYSEhODk5ERQUBCp\nqans3r2b7OxsNm3aRG5uLu7uSikJd3d3cnJqHqg2JGwpm2AL2SqwrWtiS76YitUorzckbOXDbEk/\nNIfgzBFWmdMXfcrv5Xqkc8rlCvZdzCVYQ5BU3zCfRAKllV6YvEq3ifYnuy4C1n9/Xb9VoqW9VhXG\nBqN1zdixYxk7dizPPfccf/75J8OGDQOUAplHjx5l3Lhx6ix8Xl6elqSMJrNmzaJVq1YAeHh4EBIS\nUuVkBrFcN8s0Uwqe1nYyjWpdXU7euXzLFe7UWFnL+yeWDdxfd/6v7eQbo4vXa4soXhdYO6qaIFVB\nuSYeTjL+F1PR31ChULApOVOnzsveTqIjHtvN341j6Q2/vUeAlxPTevuTmlnEisOGA6stU7ryz/Fj\nFi1eLykpUbePeeutt+jduzejR49GKpXy1ltv0bVrV6KjoxkyZAgJCQmsXr2atLQ0nRorWyhet4Ua\nq8rF66aUAFhj8bq11CWJGitt6qx4XaCLrRRM2oofUPe+qKZbl8sVTPzpH26VlNNZI1OlonJQBTXP\nyFnrdbmYfZu3fj/Ho2HG9SO0RBulymzbto0vvvgChUJBYGAg0dHR9OrVCzc3N4KCgvjggw+QSCRM\nmzaN8PBw9axAW8RaaqxKyuQUGtBHqwpryYLaKqLGyjzYRGD1wwOdWHoonT3nbbs2QmB51iVdVw9j\nnrym2y5JH9ZWQ1ZbjBXV/TMli8C6NcUgqmFATfRNtImJiSEmJqa+zLIols4mZBWV8vKWFKMnhGiS\nX6wdkFnjDxBTsPQ1MSe25IupNPjAyt5OQjN3R+YOCdQ7hFMX2MqH2Vb8APP4Ui5XVNsC50RGPksO\n6vZcNEROUc3U2K39usQdvWp4IyD2wBXmN+zRM0EdceNWqZECJgJBw8PgrMCMjAzCwsJwdnZGLpdz\n/vx5IiIiGDhwII888ghyuTLdHxcXR//+/RkzZgz5+brFv3VFFyOVbQUCQ9z/4wler6aPo6ofYE05\nl2X7ArAC62fhwoUsXLjQ4kOB5kRVNN7QsZZrorpHaoO1+GJJDAZW3t7e7Nixgz59+gDg5eXFli1b\n2LVrF4GBgWzdulVLYO/RRx8lNja2To32c3NQ//9wN786PZc+bOXDrOnHzD7NLWhJ7THHNSkslXPk\nSv39KKgKW7m/BNbFc889J2poBNUi7hHzYHAo0NHREUdHR/Wy5lRke3t7ZDIZqampJgnsdWziQu7t\nMjLyq28SW5mn+jSnf2tPCkvKcXGwq9G+toydhgp2SFM3/jHQ3FiT6C6+Wg1/BQKBbWJLNTDWPmxu\nLLZ0TWzJF1MxWSA0PT2dP//8k+HDh5OdnV0jgb3PRrVjRIfGzB/RlhUPdGJUx8ZVbntPS3eddY0c\nlcFUXQVVH97bBrdqjt0QPsxvDW7N9xODq91G5Ud4oDJYjpvUuc7tqisawjUxFlvyRSAQCO42TAqs\niouLefzxx1m6dClSqRRPT0+jBPZUhDZz48XwVrg42CGRSJjZpwVvDm5NRKDufiM7+uisc7GvPqDq\n2qx2dVetPJ2YP7JtrY5hCTRnn9lJJTT3cDJqP9VN4ONSdZNhgUDQsBE1VtaLtVwTUWNlHmo0K1Cl\nJTp9+nSefvppOnbsCEC7du1ISkpCLpcTHx9P37599e5/btXHjL2nE/Pn/66lXOwgk2KXfpI2RbfZ\njTJ7pfrASIcHEejlxPG/9wPKX/P2dhK9yqmP+d1G1qoLD4T68fPm7Xz91yWTlHMlEkg+coC8sxf0\nvq75YW4W3IOCkvI6Ue6t6bKdRIJrUFcADu77Cyd7KeCqd3uX66c4d+YUTcMnIJFofhj0b2/ty1f3\nrMbFv63V2FObZc37yxrsqckyQP7Z4xRn35k5GDYHgXVgLTpWAutF1FeZB4PK62VlZURFRXHkyBF6\n9OjB3LlzGT16ND169ADghRdeYNy4cfz0008sXrxYLbDXqFEjreMYq1z82KqTXNWouVoc3YFAb2e2\nnbnJl4nK/m0/PNCJZu6OVR0CUAaB9y4z7dfMz5M6U1Ku4PFfdduOgLaAYyNHOx1tFUsxuqMPm09n\nArBhcijO9nZVSlD8MbU7fV7/Hvc23Yhs48Xrka0B/arjDQFrFdU0hcq+TOnZjAkhvjy74UyDm2E4\nP0xhUeV1c2ELyuvWwtX8YiavOmUxuQVrVF4XWCd1prwuk8mIj4/XWqca9tPEXAJ7Hk4yrcCqTWMX\nQFmMrcLezrDgokQi4ZvxHXh6fc0bxUokEuSKqlWjrfUL/NEeTdWBlZ0RopQqP9wdTZMz83aWkVVU\nZtK+5sZar4kpVPYlqn1j7O2kvDqoNTPWnraQVQ2TkydPMn36dOzs7OjcuTOLFy/m008/ZePGjQQE\nBLBixQpkMhlxcXEsWrSoyh+GAoFAYCwmF6/XFVUJNEo1AgV7O+PMbufjwrvDaq79LMV4dWlr0tSW\nSbVrrAzx3rAgerVw12pR8t6wIKPP9/nodjUzUGASqlvfiEsqqESHDh3Yu3cvu3fvpri4mEOHDrFz\n50727NlDaGgo69evr3e5GEshaqysF2u5JqLGyjxYXWAV3dlX73rNWMq+Bt8wfVp5cH+XJjWyQSKp\nqCfTh+aH2ZralWhaUt1b9Fz/lgCUX/qHD6Pa4O5UkbHqG+Bh1Lm8nWU093BiYFDVExUmdTWvxpi3\nc9WZteoesMZkOK2Jyr6oflRIrCqMbxjIZBX3TFFREYcOHWLQoEEADB06lH379unIxezbt89C1tYt\nQqNIYAhxj5gHqwusBrXx4pWBrXTWa2esjP+CkUokzOjTQu9rbg52rH00hD+mdtfZp3JY9dmodnT3\nt16V97eGtNbKslUO+Nr5OKv/d3c0Xabiwa5+rHigE8sndgKott+Xay3OY04Wjm1vaRNqhepSNveo\nvq5QoJ+NGzcSEhKCo6MjXl5eOtIwOTk5NZKLaejYks6QrZQA2NI1sSVfTMXqAisw3KZGZqYxkdWP\nhuB2p77o4xEV8grKjJX2tq29nPh4ZDtl0Xff/jU6T3VZHQAf19rLHEQEeunt/P7xyLZ09nNVF6cD\n6tRWTT8AAZ5OPNnLH393R7WG2ANmykp9M75Dta/P7NO82uHN6h6wbRq70Laxc5WvWxuVfVH9qDBm\neFegy9ixY/nnn39wd3fH1dVVRxrGw8OjRnIxAoFAUB3W2YRZz/eHr5sDk7r60dTd0WzDb5pZsPZN\nXLTWVy7oNvWUcZM609jFnl3n9A9VTe7RDGd7Kd/eUT13tpfSrVkj9qXlmnbCSnT3b0R3/9oX4j7V\npzkDg7x01rf3cWHVw1148OekWh2/umB5zaMhNHKU0dnPjbl/nCXbyIL5Fh6ORHdWDgNHtvEi9WZR\nrWy0FDW99Wb2aV4jFX1HmZQpPZup78Ha0LSRg9bkE0tTUlKCg4OyBZYqG7Vr1y5eeeUVtTRM+/bt\njZKLmTVrFq1aKbPpmnIxgF75F2tbXrNmDYGBgVqzGy1lT97ZYygwj7yHpkSJsfur1tWl/MjlW65w\nZ1agofdj8eLFVnE/HTlyBEB9j5hyPM0aK0v7U9Nl1f9paWkATJ06FVMwKLdgLmoyXVmuUPDshjP4\nuTnw9lDji6mrY17CBRLOZmut0xwCLCgpJ/q/JwDY/HhXHGRSdp/P5j/bLwCw7rFQXO9kaR78eCXZ\njZUaXh5OMnJvK7/og7ydmNq7OW/caeQb1b4xsyOUD+Lpa5K5kK09VX51TAjuTjI2nLzBN/suA9Ch\niQs+LvbsvVh9YNXd341Ab2fWJt3Q8uWzXRdxd5Ix/R7d3n8qKYW5QwIJD/QkMTFRb9ZKtd2cgQFs\nT81iSk9/rcCzMoUl5Yy/895pMrW3P0sPplfrh4rY+zpWOeOt8lDtdweu8L9/rmut0ye3oLlf8vUC\nnt/4r1G2WJrKvqikMwB2n8vm2wNXyCworXL/1wYFMH/nRaPP18jRjjWPhppFauPr8R14aXMKxWXK\nWbWWllvYuHEjX3zxBQqFgsDAQJYtW8bnn3/Opk2btGYFmksupiFQ1ee+vjCn3IIpMivWKLdg6Wti\nTmzJlzqTW7AEUomEr8d1MGth+FP3NKdMrmDPef31E5p1Ww4y5Qhp/4CKIQFNS6p6IHx7n3YLmerM\n/2J0O3XReGsvbYV0zeNPv6c5Sw7oZhLspBKaNdKtuXl5YEDVJ1XZZXALJV2aujK0nbfB7aT1PEQ1\nuUczncBKxdRe/iw9pBvMBfu68p97g3jr93MA9G3lYbasYF2jmVmNCPLinlYejFlxvMrtI4K8ahRY\nmfPqtfdx4YcHOvFQLTOY5mLs2LGMHTtWa92cOXOYM0dbuNRccjENAVv50gNRY2WN2JIvpmKwxioj\nI4OwsDCcnZ2Ry+WUlpbSt29fGjVqxNmzZ9XbdejQgcjISCIjI0lOTq61YeaebeflYs/cIYFV1js5\n2En574OdWPlwF/U6zXhB0xy/jsZn3qqii4YuV9dqhuruq2JGo1QiMXl4UkVVH4DPRrXj9cgAmuoJ\n3PTbUvVrkW10hw+N5e2hgax7LFT3BT3nUz1gBwR6smFyKBsf76qzTccmrur/3xzS2mS76prKXxaV\nr7OhOLamNYjm/qyJUjCBQHA3YzCw8vb2ZseOHfTp0wcAe3t7NmzYwIQJE7S28/X1JSEhgYSEBIKD\nq2/+a0mqe+Y3beRIY41+eZpfOFV9+TjJqn4LNWfpGVs8rVBoZ6ykEglfjW1PeKAnczSyUV7OMtMz\nDQZ2DG3mRmQbw5kqFVV9kdek96Dm2zu1tz8vRbRiQGtP9fCrMefzdpHh7+6Is72d3uuiWfxtjICq\ntSCtZGvl5ZrSyddV6xYw9ztRW/sEdYPQsbJerOWaCB0r82AwsHJ0dNSZJePrq6s1lZWVxcCBA3nq\nqacoLi42n4VmpvOdGYfVaSLpQ7MUTXJZOczhaCdh7tBAWno4Mn9ExVj6Y2FNkUqU0gQqZvVtQT8j\nNKIUegYag31dmTskkKHtvBl8JwP0ZC9/hrT1pqWHIzHdm+rsYwzm+gBofpEuGN2Oab39eaR7UwYG\neeltrK0PzeRexyYu3Nu+cbXnW/lwF1ZpZBfzzh4jWCMjpQ/NwMrcWRVj9b8McW97b50vi8qmGmN7\ndUKvz/VvSez9HSuOb+b3QmSsrBOhUSQwhLhHzIPZ5Bb27t3Lrl27CAgIYMmSJeY6rNkZHezDq4MC\n+GZ8R8Mba6Cp9j6mkw8PhvqyKLoj7X1cWDaxE2HN3dWvx4Q1Y8uUbrTyrKidcnOU8VhYM+NOVk1V\n52uRrfljanc8ne1xcbBj2cROPNbDyOPWIe8OC+TZfi3o3NSNiaF+TO7RDDuphH4BHnwb3ZFNeobm\nNPF1c6jR+Rq72ONVKSNmKEDQvNklEolaKFUfnXyrD9Iq80RP81yDUR19mB2ureNW2S+JRMKi8R20\nJCpc7LU/yn0DPFj7aEiV2mutvZzV/lf3PpiCNYnmCnSxpRoYUWNlfdiSL6ZSq+J1zQeoKqsVHR3N\nggUL9G5vLdOVh7T1Nnr72Pt6UC5XsP+vverXh0UOJDExkYtJ52lZxf77NLZXva6cKdUIDyeZ3unH\nAIrGfVGg0MhadDeb/3lnU3Bv0w0Jutmq2h5ffikJZS6tic7rQY2dtc7ftZkbEfaX+TDhAu5tuvHD\ng504enCf+nWFoibTYysCoEsnD8OdWaT6tlfWvLmplz2B1yM709rLiUmf/gJUPKgz/z1C3s0io6dX\nnzp8gLyz52s9XVuuaM8DI4ew5YtVnLlRSKvOPZFKJDr+XD19RMv/3NRjFJXJ1cdTbX9flxCOpt/S\nOZ/K/81T+uFgJ9W6PrWxPzGxgIRdezi3805xfZh2kbhAIBDYOkbLLURGRhIfH4+dnbLmZcqUKbz1\n1lu0adOG0tJS5HI5jo6OLF26lOzsbF555RWt/W1punJtKCgpx95OgkOlfodzfz/LgUt5PNWnOcfS\n89mfphQsrCw1UBtU0+nfGRpI/9b1L4KoOn83fzfeGRqklrdQ+ah6/ZORbelmpPaWpkTAgNaevD20\n+t6Q2UWlSCUSPJy0f1NUlhro7u/G0fRbVR6nZ4tGPN23BX+kZNGmsTMRgV565Qqi2jdm2783jXEF\nUA6ldm7qRnGZnNSbhQT7ulZbs6Q6Z4cmLpy5UQho3zPH0/N5ZWuq1j6Lozuom5vrO1ZN+HhkW17V\nOP4fU7tryW9YWm7BXNjC80tVOxMWFibkFhByC/pQ3SO1GQ60Fl/MgalyCwaHAsvKyhg6dCjHjx8n\nKiqKgwcP8uCDD/LHH38wefJkNm3aRHZ2Nv369WPgwIFs2bKFWbNmmeREQ6E2tUmuDnY6QRUotaW+\nHNOe8Z2bVNsmxpxYqsjQWVZ9qxtT3M87e0xHtkIfXs72OkGVfiqCmeUTdSdjDGvXmOYeTkzp6U9E\nYNUzH8d3rlmfyvI72TpHmZTOfm4GC8EXR3fgoa5+vH+npqryEGZIMzeGtfPmmX762zrVlgCN4W7V\nhAFzdUaoiscee4zffvutTs9hi4j6GYEhxD1iHgx+w8hkMuLj47XWrVq1Sme7w4cPm8+quxAHmZRO\nfjWr6zEVS5XAPNWnOXFHrzLtHv/qN6xBZOXn5sC1WyV0a+amNVmgpnwb3ZElB69w5Eo+oJSJOJqu\n/L+Fh27Apu8tjJvUmUdWntRaF9TYmS/HtOeFTcaJk9ZUr7dNYxd19mnz412R2enOIHzlzmzSr/+6\nXKNjG8tz/Vty+noBL96pDXOQSZkzMAAHOwnknDf7+b777jtWrVrFgw8+SL9+/Zg6dSqurvXz2bEF\nbCWbAKLGyhqxJV9MxSoFQq0dW7lx6tuP+7r4Et25ibo2L7KNl1bR9T0t3fnn6i06+lat8l6Z7yYE\nk1VYir977YZMgxo7My+qDRtPZdK+iYvOzDZ/d0fS8ypmu+oLTpu4OvBwNz9+PnYNH1d7xndSZqs6\n+bkS2tSNE1d1hxY7+7ly8lqBelmB6dfFoRrpD1No5GiHvZ2EZ/q2pHdLdwpKyrVaF43u6IO3iz2j\ng30YHeyjta9KWPbIEfMHVjdv3uTcuXN4eHjg5+fHE088offHnkBgSRQKZVeKchOGIOylEpzsraOJ\nvaDmiMDKCqnrkUB9iu31heaEB63G0MD7w4OQK2rWbNhJJsXf3Tz+SCQSxmkM3b04oCWt7gwvPhDq\ny5eJlyq2reIYj/dUSk3YVxrulWosdvJ15dR1ZTD11uBA1p28TmZBKddvlRDStPoG5PVJsK8rHwwP\nUl8zB5mUDZNDSTibzYDWnurOAfXN559/zqxZs2jTRlm/0rJl1bMaDxw4wOzZs5FKpfTq1YsvvvgC\nDw8PwsLCkEgkrF27Fk9PT+Li4li0aFGVLW1sAWupsTInptRY1RcHL+XxzIYzRm1748wRmnSoqOGb\nHd5KS0S6vhA1VuZBBFYmUNc3TrCvKwcv5dHI0by/WL67vyPpeSUEeivFSq3tAyCRSLAzcZiyLnwZ\n0bEiCzOiQ2Pyi8tZpmqXU42dlYMqgGf6tWTu72d5vGczdp2raKvU2NWeqb21+zrW1XUZ3dGHizm3\n1dffEHYSiY50grO9HSM7+lSxR/0waNAgdVC1ZcsWRo0aVeW2rVu3JiEhAQcHB2JiYkhKSiI0NJSE\nhAT1NqWlpcTGxrJnzx5Wr15NbGwsL7/8cp37Ud+oviyFgGP9UK6Ay7nGaTrmFZRSrLFtmbyeCm0r\nIeqrzIN5xw4EZuGBUF+eH9CSxdE109oyRICXs9mELO82JBJJrWq4Wnk68cODnYls4212pXNjeW5A\nSz4f3c5oZfRBbep/5qgx7Nq1S/3/nj17qt3Wz88PBwelRpq9vT12dnYkJycTERHB66+/DkBKSgoh\nISFIpVKGDh3Kvn376s54K8CafkzVFmvNVtUUW/EDbOv+MhWRsTKBur5x7O2kjKqHrIAtfQDq2xd9\nMzuNxVBcY6nr8v7wIJYdSueVCGWxezsf4zJb9c2NGzfYvn07EomEa9euGbXPiRMnuHHjBsHBwaSm\npuLp6clTTz3Fpk2b8PHxwd1dKfDr7u5OTo7+Ru0CgUBgDCJjJRCYgLtjbX6TWKcyeZ9WHnx3fzDt\nm7jQvomL1SqoL1y4kH///ZfTp0/z5ZdfGtw+KyuLZ599luXLlwMVYsbjx48nKSkJDw8P8vKUunF5\neXk6LbxsBdEr0HqxFj9Er0DzYPDbISMjg1GjRpGcnExBQQHl5eVERESQlJTE8ePHCQpS6ufcDcWf\nKqytNslUbMUPqD9fZvVtwfmsIoJrMHOxMobiFVu6LnVBWloaubm5FBcX89VXX/H2229XuW1ZWRkx\nMTF89tln+Pr6UlhYiKOjI3Z2diQmJtK1a1fat29PUlIScrmc+Ph4+vbtq/dY1tI5wtRlVdF6YmKi\nxe3JO3sMBTVX9q+8rKKm+6vW1fb85louTE/VWj52cB+3fFzq/fpUrsOzpvu3PpZV/6elpQEwdepU\nTMGg8npxcTFFRUVER0ezfft2pFIp169f59VXX9VSXh8yZAg7d+5k9erVpKWl6RR/2oJysYrFixcz\nc+ZMS5tRa2zFD2hYvsTuv8yapBuAfmX9huSLIUxVLq6OKVOm8NJLL2Fvr+wV2aFDhyq3XblyJc8/\n/zydO3cGYN68eTz99NO4ubkRFBTE8uXLkUgk/PTTTyxevLjKH4a29PyyNOZUXjeF+lJerw016T4h\nqDtMfX4ZzFg5Ojri6Kg9nd3X11druXLx57Rp02psSEMiNzfX0iaYBVvxAxqWLzFhzSgslTO8vbfe\n1xuSL5agS5cudOnSxahtJ02axKRJk7TW6RMzjomJISYmxiz2CQSCuxuzFK/n5uaK4k+BwEhcHezU\nKuWCmpOQkMDOnTtxclJqjP3vf/+zsEUNA6FjZb1Yix9Cx8o81CqwUhW33i3FnypU468NHVvxA4Qv\ndxO//PILycnJ9OrVi8uX66ZNjy0idKwEhhA6VuahRoFV5XIs1XK7du0MFn/eunWLI0eO1MJU62Hq\n1Kk24Yut+AHCF2vl1i3dNj615cUXX8TBwYFevXrx0UcfsWjRIrOfw5axpWyCNWR5zIGt+AG2dX+Z\nisHAqqysjKioKI4fP05UVBQffvghn3/+OYmJiaSkpPDqq68yZswYpk2bRnh4uLr4szLjxo2rEwcE\nAsHdhZubG15eXgA4O1un1pZAILh7MRhYyWQy4uPjtdbpa3gqij8FAkF94OPjw549e3jppZeQSoUU\nn7GIGivrxVr8EDVW5kEorwsEggbFm2++yenTp5HL5XTq1MnS5jQYRI2VwBCixso81MvPvRdffJGI\niAheeOGF+jidWbhw4QJ+fn5ERkYSFRUFwKeffkp4eDgxMTGUlZUBSmHU/v37M2bMGPLz8y1pshYZ\nGRmEhYXh7OyMXC4HjLd/x44d9OvXj8GDB3PlyhWL+aBCny8eHh5ERkYyePBg9SxUa/flwIED9O/f\nn/DwcGbPng003Guiz5f6uiaTJk3ivffe44033mD8+PHmc+ouwVzZhAtZRfx9Oa/Gf2k5t82mYWUN\nWR5zYCt+gKixgnrIWB05coSCggJ2797NrFmz+Pvvv+nZs2ddn9YsDB8+nB9//BGA69evs3PnTvbs\n2cMnn3zC+vXrGTduHLGxsezZs4fVq1cTGxurI4xqKby9vdmxYwfR0dFAzez/z3/+w59//snJkyeZ\nN28eX3/9tVX5AhAaGkpCQoJ6ubS01Op9ad26NQkJCTg4OBATE8Pu3bsb7DWp7EtSUlK9XZOVK1cC\nyskzCxYsMKtfAuM5mp7P4v2WD/IFAmujzjNWBw4cYPjw4QANrnN8QkICERERfPnllxw+fJhBgwYB\nFX6kpqZqCaNak2+Ojo5q2QuFQsHff/9tlP1FRUU4Ozvj6upK7969OXnypAW9UKLpi4rk5GQiIiJ4\n/fXXAV2RWmv0xc/PDwcHBwDs7e05efJkg70mlX2xs7Ort2ty8uRJTp06xYkTJ6zivWgoiF6B1ou1\n+CF6BZqHOs9Y5eTkqPsJenh4NJgHob+/PykpKTg4ODBu3Djy8/PVivMqEdScnJwGI4yqT8RVn/2a\n6wDKy8stYq8hUlNT8fT05KmnnmLTpk34+Pg0GF9OnDjBjRs38PT0VBdfN9RrovIlODi43q7J6tWr\nAWXAbagm5MCBA8yePRupVEqvXr344osv+PTTT9m4cSMBAQGsWLECmUx2V/Q6FTVWAkOIGivzUOcZ\nK03x0Nzc3AYjHurg4ICzszN2dnaMHj2aNm3a6IigNhRhVIlEotdWQ+sA7OzsLGKzIVTv9fjx40lK\nSmowvmRlZfHss8+yfPnyBn9NNH2B+rsmPXv2pGfPnoSEhHD58mW2bNlS5baqIcs9e/Zw/fp1reHX\n0NBQ1q9frzVk+eijjxIbG1tjmxoStlQDYyu1SbbiB9jW/WUqdR5Y9e3bl+3blc0ut2/fXmXneGtD\nU9hw7969tG3bll27dgGoRVDbt29vUBjVGlAoFPTs2dMo+11cXCgqKqKgoICDBw+qm9daCwqFgsLC\nQnWmIzExkbZt2zYIX8rKyoiJieGzzz7D19e3QV+Tyr7U5zVZunQpycnJnD59mqVLl5KZmVnltqYO\nvwoEAoGp1PlQYPfu3XFyciIiIoLu3bs3mML1PXv2MHfuXBwdHYmIiKB3795EREQQHh5OQEAAs2fP\nRiaTGRRGtRT6hF2Ntf/NN99k2LBhODs788MPP1jYE/2+zJw5Ezc3N4KCgvjggw+QSCRW78v//vc/\n/rKQHksAACAASURBVP77b+bMmQPAvHnzGuw10efL008/XS/XpGPHjupJIjdu3GDy5MkG96np8Kst\nInSsrBdr8UPoWJkHiaJynxqBQCCwYl5//XWuX7+ORCLBz8+PDz/8sNrts7KyiI6OVgeDJ0+e5JVX\nXuHIkSPExcXx5JNP8s033/DNN9+QlZXFtGnTWLNmjdYxtm/fTlhYWF26VW+Y64tvXdJ1i88KNCUg\n+XvOEAB6frK9Lkwyicp+fDKyLd38G2adny0FVkeOHGHIkCE13k8IhAoEggbFhx9+yOXLl/H09MTR\n0bHabfUNvy5atIhXXnmlxkP6s2bNolWrVoCydjQkJET9BaIqCG8IywMGDDDL8U6fzwZaABWz2lTB\ngbUvq9ZZqz3HDu7jlo+LVdwvNV021/1liWXV/2lpaYCyb6spiIyVQCBoUDz33HMUFBSwbNkypk+f\nzpIlS6rcduXKlTz//PPqWq558+axe/duNm3apDUr8KeffmLx4sVVzgq0pYyVubCGjJUpWGPGqjIN\nOWNlS1h9xmrdunVa06wFAsHdgSkPpuqQSqUEBAQAGJyJO2nSJCZNmqS1rk+fPuraMBV3Q69TUWNl\nvViLH6LGyjzUW2Dl7u5+1/7imzVrFosWLbK0GRbjbvb/bvYdlL/4zI2joyOnTp3i//7v/8jOzjb7\n8W0VoWMlMITQsTIPBuUWnnjiCfz8/AgJCalym+eee4527drRtWtXjh49alYDbQFVXcbdyt3s/93s\ne12gUCiYMGECkydPpk2bNnz77beWNqnBYUvZBGvI8pgDW/EDbOv+MhWDgdWUKVPYtm1bla9v3bqV\n1NRUUlJSWLJkCTNnzjSrgQKBQKBCIpGQkJDAiBEjGDlypNWIpQoEAoEKg4FVeHg4Xl5eVb6+ceNG\ntY7MPffcQ05ODteuXTOfhTaAh4eHpU2wKHez/3ez73XBhg0b2LBhA0OGDGHixIlMnDjR0iY1GESv\nQOvFWvwQvQLNQ61rrK5cuULLli3Vyy1atODy5cv4+fnV9tA2Q3XDqHcDd7P/d7PvdcG2bdvYu3cv\nM2fOZPHixZY2p0EhaqwEhhA1VubBLMXrlRUbJBKJ3u1sRQempssNWdejNsvp6ens37+f1q1bo8Ka\n7BPL1qsDUxVpaWls2bKFtLQ0tm7dCsDIkSPNeg5bx5ZqYGylNslW/ADbur9MxSgdqwsXLjBmzBj+\n+ecfndeeeuopBg0axEMPPQQo203s2rVLJ2MldGDuPvbv38/IkSPp3bt3tXV6AtvFVB2YqlixYoXO\nDzdjWtrUFvH80kXoWNUdQsfKOrCYjtXYsWP5+uuveeihh9i/fz+enp5iGLASd7uuR15enqVNsBh3\n+7U3N48//rilTWiwCB0r68Va/BA6VubBYGA1adIkdu3aRWZmJi1btuS9996jtLQUgBkzZjBy5Ei2\nbt1K27ZtcXV15fvvv69zowUCgUBQM0SNlcAQosbKPBgMrFauXGnwIF9//bVZjLFV7vbo/W5W3L/b\nr72lycjIYNSoUSQnJ1NQUIBUKsXDw4OwsDAkEglr167F09OTuLg4Fi1aVGVLG1vClu5Ja8jymANb\n8QNs6/4yFYNyCwKBQNBQ8fb2ZseOHfTp00e9LjQ0lISEBHbs2IGnpyelpaXExsayZ88eHn30UWJj\nYy1osUAgaOiIwKoeuNtT73d7jZXAcjg6Our0E0xOTiYiIoLXX38dgJSUFEJCQpBKpQwdOpR9+/ZZ\nwtQ6R+hYWS/W4ofQsTIP9dYrUCAQCKyB1NRUPD09eeqpp9i0aRM+Pj7q4Wp3d3dycnIsbGHdIGqs\nBIYQNVbmwWBgtW3bNl544QXKy8uZOnUqr776qtbrmZmZxMTEcPXqVcrKynj55ZfFzJ1K3O1jzqLG\nSmBNqDJY48eP5+jRo4wbN06dVc3Ly9PJcKmwFR0+c+nqnT6fDbRQvm93Mi6qWiFrX1ats1Z7jh3c\nxy0fF6u4X2q63JB1G1X/11aHr1odq/Lycjp06EB8fDzNmzenV69erFy5kuDgYPU27777LsXFxcyb\nN4/MzEw6dOjAtWvXkMm0YzahA3P3IXSsBObWsTKVyMhI4uPjKS4uxtHRETs7O9566y26du1KdHQ0\nQ4YMISEhgdWrV5OWlsbLL7+stb94fukidKzqjs9GtSW0me1OoGgo1ImO1cGDB2nbtq1aOfuhhx5i\nw4YNWoFVs2bNOHHiBKD8tde4cWOdoOpu527X9bjba6zu5mtvacrKyoiKiuL48eNERUXx4YcfMnPm\nTNzc3AgKCuKDDz5AIpEwbdo0wsPD1bMCbRGhY2W9VPZjbdINDl/Jr/FxGrvYM7ydN072pjUnFzpW\n5qHaCEhfH8ADBw5obTNt2jQGDx6Mv78/+fn5/Prrr3VjaTXk5eWxY8cOxo8fb7ZjFhQUMHPmTDIz\nM4mKihJjzwJBA0QmkxEfH6+17vDhwzrbxcTEEBMTU19mWQRRY9Vw+OtiLn9dzK3xfkHezgxr523y\necX3nHmodlZgVT3/NPnoo4/o1q0b6enpHDt2jKeffpr8/JpH2rUhJyeH9evXG7WtER18APjxxx8Z\nPnw4W7duZc+ePWRkZJhsX1XRe2VbjLWtoSFqrAQC60HzniwqLSe7sLTmf0WllMkt/7yyhWwV2I4f\nIJ55YCBj1bx5cy5duqRevnTpEi1atNDa5q+//uLNN98EoE2bNgQGBnLmzBl69uypc7zqij+3b9/O\nwoULkcvlyGQyXnrpJVJSUli/fj1lZWV07NiR6OhoEhMTuXjxImfPnuX27dv88ccfLF++nF27djFw\n4ECWLFnCpUuXePfdd5HL5bz00kvcf//9TJgwAScnJwoLC3nzzTd59tlnsbe3p2fPnnz++ec6xWy/\n/fYbU6ZMAWDQoEH8+OOP9OvXT/36119/za+//oqDgwNjxoyhR48eFBcXs3LlSq5du8atW7f44IMP\nUCgUfPDBB+Tn5zNy5Ejmzp3L008/TW5uLunp6Tz//PP88ssv5Obm0rt3b959913Aeor5arN86tQp\n9bW3BnvEcsMp/hTUD9fyS3htW6pJ++bfLjezNQKBbVBt8XpZWRkdOnRg+/bt+Pv707t3b53i9dmz\nZ+Ph4cE777zDtWvX6NGjBydOnMDbWzsdaaj4MzY2lvLycmbNmqVeFx0dzQ8//IC7uzsPP/wwX331\nFcuXL8fOzo6XX36Z9957j3vuuYfOnTszd+5cVqxYgUKhYOTIkWzatAmJRMLo0aPZsmULzz77LP36\n9eORRx7hp59+oqSkhCeeeAKFQqE3M3f//ffz/fff4+7uzo8//ohcLtdq9lpUVISzszNyuZzhw4ez\nefNmfvjhBx0fhg8fzosvvsiwYcO499572bJlCy+99JLalsTERObPn8/mzZsNXKqGh6p4vWPHjvz1\n11+WNsci3O31BtZSvF5bbKF4XV+N1fmsImasPW1Js2qFKTVW1li8bq5asSBvZxaMaYezqLEyC3VS\nvC6Tyfj666+59957KS8v58knnyQ4OFitTDxjxgzeeOMNpkyZQteuXZHL5XzyySc6QZUxpKSk6NQ4\nnDp1Sr0uNzeXK1eUM1BCQ0MBZUatsuZMZmYmZ8+e5b777gOU9VeZmZkAdO/eHVBOs/7000+ZMWMG\ngwcP5sEHH9Sxx8PDg7y8PNzd3cnNzSUgIEDr9WPHjvHJJ59QVlbGpUuXyMzM1OuDXC6nUaNGyGQy\nAgMDuXr1qpYtEomEbt1sJw0sEAisE1FjJTCEqLEyDwan740YMYIRI0ZorZsxY4b6fx8fHzZt2lRr\nQ9q3b89ff/1Ft27dkMvlSKVSOnfuzIoVK3B3d1ev+/3337X2UygUyGQy5HI5AI0bN6Zdu3asWbMG\ne3t7ysrK1LMUVZkpmUzGe++9B//P3pnHRVX9///JsKMsIoqCiooLuYCau4KiaGju2sf8pKWmmaVW\ntti3zer3qUxL08rcMsst08otVzYBNRRz3wLBHURUdoEZuL8/xhkZGGAYBmYYzvPx6BH33HvPeb/v\nuc6855z3eR2gd+/eWgOr7t27c+jQIZ577jkiIyNZunSpxvlvv/2WJUuW0KxZMwIDA5EkScMH1UiY\nhYUF7dq1Qy6Xk5CQQKNGjTRskSQJmcy8BfBFjpVAYDqY0ztpLrlJ5uIHmNf7pS8mo4vw/PPP8+qr\nrzJ8+HCsrKz4888/mT9/Pi+88AKFhYXY2Niwfv16QDOp3sLCgkaNGvHw4UMmT57MRx99xJtvvsmY\nMWOQyWS4ubnx448/aty3d+9e1qxZA1DqMN+kSZN4+eWX2bhxI8HBwTRu3Fjj/PDhw5k4cSLt2rXD\n0dERCwsLrT58+OGHjB8/Xr2k287OTsMWVfAlEAgEAoGg5lNmjpUhMYccBX0xpznniiByrGpv36sQ\nOVamg8ixUiJyrEpH5FhpUiU5VrWFlStX8tdff6mP27Vrx4IFC4xokUAgEBgWkWMlKA+RY2UYKr1X\nIEBERARvvPEGcrkcNzc3IiIiqsLWKmPGjBkaeWOGxlyid30ROVYCgelgTu+kueQmmYsfYF7vl76U\nmTVdUFDArFmz2LdvHxcuXGDz5s1cvHhR45q0tDReffVVdu3axblz59i2bVuVGiwQCAS6kpSURJcu\nXdTSKACLFi3C39+fiRMnolAoANi4cSN9+vRh+PDh1S5wLBAIzIsyA6uiewVaW1ur9wosyqZNmxg7\ndqxaONTNza3qrK2h1Pah99q+V6DAeLi6uhIWFkbPnj0BSElJISIigqioKHx9fdm+fTtyuZyVK1cS\nFRXFpEmT1HIy5sayZctYtmyZWb2TGVdOGdsEg2AqfqjekcpgTu+XvpQZWGnbK1ClJaUiLi6O+/fv\nExgYSNeuXdUr9wQCgcDY2Nra4uLiAiilTWJjY+nfvz8AQUFBHD16lPj4eDp27IhMJlOXmSNz5swR\nOTSCMhHviGEoM8dKFxkAuVzOP//8Q2hoKDk5OfTq1YuePXvSunVrgxlZ06ntc84ix0pgKqSnp6vf\nRycnJ9LS0khLSytRZs6Y0ztpLrlJ5uIHmNf7pS+V3iuwadOmuLm5YW9vj729PQEBAZw+fVprYFXW\nXoGmsteZOBZ7BYpj89wr0MLCAmdnZ27evAkop6hdXFzUuywULdOGOX5+ebZ7Uun3o6ko1Re8uR+r\nykzFHkMd49oLMJ33q6Ydq/6u7OdXpfcKvHTpErNmzWL//v3k5eXRo0cPtmzZQrt27TTqMgcdGH0x\nJ12PiiB0rGpv36swFR2rwMBAQkJCuHfvHlOnTmX37t0sXLiQli1bMmrUKAYOHEh4eDjbtm3j+vXr\nvPXWWxr3m8Pnl9CxUiJ0rEpH6FhpYrS9An18fAgODsbX1xeZTMb06dNLBFUCgUBgDBQKBcHBwZw+\nfZrg4GA+++wzAgIC8Pf3x8vLi7lz52JlZcX06dPx9/fH1dWVTZs2GdvsKkHoWAnKQ+RXGQahvC6o\nMlQjVt27d2ffvn3GNkdgBExlxKqymOvnV00fsdIHUxyxMhT17K14K6AZBXp8q3s42dDMxd7wRtVg\nhPK6QCAQCAS1mAcPFby/P0Gvez8e1EIEVgaiTLkFgWGojUPvBw8eZMWKFYBSkuPdd98lPz/fyFZV\nP7Wx7wWmidCxMl1MxQ+hY2UYxIiVoEo4ceIEO3fuBODBgwesWrWK+fPnG9kqgaD2InKsBOUhcqwM\nQ7kjVvv27cPHx4fWrVvz5Zdflnrd8ePHsbKy4o8//jCogeaAuayQ0Bdd9NDMldre9wLTw5zeSXPR\nfzIXP8C83i99qfRegarr5s2bR3BwMNWUCy8QCAQCgUBgclR6r0CAb7/9lnHjxtGgQYMqM7QmU9uH\n3mtzsF3b+15gOogcK9PFVPwQOVaGocwcK217BcbExJS4ZseOHYSFhXH8+PFaPe0jEAgEporIsRKU\nh8ixMgxljljpEiS9/vrrLFiwAAsLCyRJqtWjE6VR2+eca3OwXdv7XmB6mNM7aS65SebiB5jX+6Uv\nld4r8MSJEzz77LMApKamsnfvXqytrRkxYkSJ+sxxry1xXPI4NDSUyMhIirNgwQKmT59OkyZNTMpe\ncWx6e20JBAJBTaXSewUWZcqUKQwfPpwxY8aUOGeuysW6YE57J5VFQUEBhw8f5t133+XSJe1qzu+9\n9x6jRo2iVatW1WydcagtfV8apqi8fvXqVXr06EG7du2wtbVl3759LFq0iJ07d+Ll5cW6deuwstL8\nzWkOn19ir0Alpqi8bqi9AivDx4NaELvjF0DsFajCaHsFCmofhYWFFBQUYGFhwZo1awgLC0MulzN5\n8mSmTJlS5tTf559/zt27d8nIyODixYv07duXcePG0b59ewCsra2ryw1BLWbw4MGsX78egJSUFCIi\nIoiKimLhwoVs376dcePGGdnCipGVr4BysjCmzngFgKNHDpOVpwDAWlZ7p+kFJRE5VoahXIHQIUOG\nMGTIEI2y0gKqn376yTBWmRmmHL3n5OTw9ttvExsbS1ZWFikpKbz++uvMmjWLNWvWcPbsWebOnYuv\nr6/6ns2bNzN79mzq1q2LQqEgNzcXgLS0NK1tqPLvVISHh5OUlER2djZnzpzh119/5f79+7i5ufHv\nv/9q3LtgwQIuXbrE3Llz8fDwoEePHqSnp+Pt7U3Tpk0ZO3YsEyZMqIInYxhMue9rM+Hh4QQEBDBm\nzBjatm1L//79AQgKCmLjxo01LrDafu4u4Vce6Hh1A37dqfx3lqsorDqjqgFjj/IYClPwQ2ZhQXZ+\ngV732lnJsHwUpIvPPKG8bhRSUlK4fPkyly5donXr1ty5c4fbt2/zzDPPlMhhK45CoSAvLw9LS0vs\n7OyQy+Xk5OSQkZHB6NGjycrK4r///S+TJk2iRYsW6vsePnxIQkICH330ER4eHnz77bfs27eP2bNn\nc+/ePWQyGYWFyg/Zr7/+mp9++gmZTEZqaio5OTk899xzjBw5ksuXLxMfHw9AVlYWlpaW6jZOnz6t\nk//x8fEaUy33798HQC6Xc/jwYfz8/HBwcOCtt95i3759JCcnEx8fz4ULF9R2xsXFERcXx5EjR/jx\nxx8JCQnh6NGjLFmyBF9fX15++WXc3Nw02t2wYQO7du3i8uXLjBs3jilTplC/fn1sbW2RJImHDx9i\nYWGBg4NDuT5s376dxMREAgMDOX/+PA8fPqRfv35qaRKB6eLh4UFcXBw2NjaMHDmSzMxMGjZsCICT\nk1OpPxBMmQcP5dxIzzO2GYIazNeR16lnX/GQwNHWivcGeFHfwaYKrKqZiMCqGoiOjqZz585s3bqV\nHTt2cPXqVa5duwaAo6MjhYWFZGdnc/ToUfr27UtQUBDt2rUjIyODe/fu4ejoiJubG7/99hu//vor\nERERtG/fngkTJpCUlMT333+v0d4333yDjY0NlpaWNGnShJCQEPbu3aseWXJ0dOT48eMkJSWRmZmp\n1WZVsAMQEhLC4cOHmTFjBgqFQh2A6YquK0WzsrIYPnw4lpaW2NrakpOToz534cIFrffk5uZy7tw5\nvLy8aNWqFSdPniQkJISlS5fi4ODAsmXLuHPnDunp6ezdu5dTp5R6MYsXL2bp0qUUFBSwfft2QkND\n+fbbb3F0dGT8+PG8+eabNGjQgGvXrmFhYUHz5s3JyMjg0qVLrFy5kuPHj3Pz5k3WrFlDUlISlpaW\nFBQU0KNHD7p06cJTTz1FQECAWeUbmAs2No+/AIYNG4aTkxO3bt0CICMjAxcXF633mfLim8Szx8m4\nlqEe+VDpIhU97pV7hhYtWrApyVHtU1nX14RjVVlF71eVGdt+1XFy1DYcPFoZ1Z4MwL+x8vtA9Y7o\ncr+LnRUxRw7jZGdN3759NRaymMq/j+pefFNm8rohqYnJnzk5OURFRWFnZ0e/fv0qfP+FCxdISUkh\nNjaW7Oxsli5dipWVFQqFQuO64lNl3bp1Y//+/axevZp58+bRtWtXOnfuzKVLl4iKilJfZ2dnh7u7\nuzpI00bRkSgV2mzQdl1xVMFDeWXF/dGGNhu01VWcqvCnbdu2XL58WaOuuXPnkpWVxapVq7C3t+fW\nrVscPXqUp59+Wqt/xW338/Nj2LBh1KlTh27dutGsWbMKC+gmJSVx5swZ3N3d6dTJ+FMF+mCKyetZ\nWVnUrVsXgEmTJjF79mw+/fRTdu/ezcKFC2nZsmWJqUBT//z69vB1dl28p9O1ppAobShE8rrxcbGz\n4ocxbdUjVub0Y7JKktdV7Nu3j9dff52CggKmTZvGvHnzNM5v3LiRhQsXIkkSjo6O/PDDDxo5OTWN\nVatWERERgaenJz/++CNNmjTh0KFDHD58mFdeeYUhQ4aoE/jPnTvHhx9+SGpqKt7e3kyfPh0bGxsm\nTpxIWloacrm8wu0nJyfz0ksvqackYmNjOXXqVIngQS6XlxlUmQq6BFrGRBVUFWXx4sXqvxUKBXPm\nzCE/P1/nOk+fPs25c+fUwVadOnV46qmnmDt3LqGhocTExHDt2jV69erFwoULAUhMTFRPJ+7du5fQ\n0FDmzJlDp06daNy4MXXr1uW9997Dy8urkh7XbqKiovjwww+xtbUlICCA7t27ExAQgL+/P15eXsyd\nO9fYJlYpNfULXBvm4ou5+AEixwp0GLFS/aIPCQnB09OTbt26lZBcOHr0KO3atcPZ2Zl9+/bx8ccf\n8/fff2vUY+hffAkJCZw8eZKUlBTatWtX5oiSJEnqoKS8/JevvvqKbdu2aSRRq0YxVKMSMpkMW1tb\nBg8ejI+PD19++aVG8PDaa6+xdOlSrSMwuoxY6ToqY6wRnvLKivujLbAyVX90qUuXESttZd26dSM/\nP18jF61t27YEBQVx7NgxTp48iUKhwNramoKCAo02VTY899xzTJgwgd69e5fqV9FVm8VlA4qSmppK\nVFQU165do3379gwcOBCZrNx92SuEKY5Y6YM5jVjVdkxxxKomU3zEypyoshGrovsFAur9AosGVr16\n9VL/3aNHD27evKm1rtzcXG7fvk1sbCyNGjWiadOmZGVl4eXlhZOTk8a1hYWF5OTkYGFhQZ06dQDl\nCM28efM4ePAgd+/eVY8gdO3aFVdXVw4ePMiRI0fIzc3l7NmzZGZm8umnn9K4cWOmT5+Oo6Mj3377\nLf369cPZ2RmAPXv2EB0dTXZ2Nm3atGHZsmVkZWVptV/1JVlYWEheXh47duzQunfi0qVLy3ustQpT\nHq2qTo4fP16iLC4ursSImSRJpQaFGzduxNbWll9//ZX09HT8/f0JDg5WL3qIjY1l8+bN/PTTTwwd\nOpSgoCB2795NWFiYOrBr0KABM2fORC6X8+KLL6oDRTs7O/r27cuECRMYPXo0oPw3l5eXh5WVFXZ2\ndiXsuXLlCjk5OTg7OxMbG6uuw9HRsVYr7psiw3KUaQSbkhzNZoSkJk+hFcVU/FC9I7sd/PWuw5ym\nAvWl3MBKl/0Ci/Ljjz8ydOhQrecmT57MgQMHAGUOip2dHTExMTRs2JDGjRvTpUsXXFxciIiI4MyZ\nMxQUFNCwYUOOHDlCnTp1yMnJYd26dSVGDFJTU5k1axZnz5597NijX+offfSRuiwnJ4fJkyfz5ptv\nsmzZMjp16lRiBKHoKjeBwBRZu3at+u9du3Zx7do1Vq9ejbe3Nx4eHoSGKn+J79mzh/3796t/EKgC\nO5lMRkhICM8884xGvbm5uYSEhNCsWTOCg4NRKBT89ttvvP3228hkMhwcHOjTpw/BwcFERUURGRlJ\ndnY2Dx8+5PXXX+ebb75Rj6zNnj0bKysrnn766Wp6KoLyePxlaRob/gpMj8oEVILHlBtYVeRXZ3h4\nOGvXruXw4cNaz6uCKoAzZ86og6OUlBRSUlI0clJU3L9/n1atWjFkyBD27t2rtd7r169XaKXa119/\nDWgfQRAYHlPPsarpqFaF/vvvv1y8eFHn+7Zu3aq1fO3atezevZtGjRpx5swZQDlK+/DhQ/bv38/+\n/fvV16o+H7755huNOr799lsAEViZIKYwMmIozMUXc/EDRI4V6BBY6bJfICgDpenTp7Nv3z7q1atX\nbsPavmjL+vItLagqDW2BliG/3IvXVVF/Kkp1+6PvNbpibv5Udf9Xtz+pqamkpKQY1QaBQCCoiZQb\nWHXt2pW4uDiuXr2Kh4cHW7ZsYfPmzRrXXL9+nTFjxrBhwwad94DTNophyJwMbcnLhqxflwTtmuxP\nadfog7Z6a7I/utZVG/0Ro5P68+ChnIfyiiuhW8osyNHhPpFjZbqYih8ix8owlBtY6bJf4KeffsqD\nBw+YOXMmoFx5d+zYsaq1XCAQCMyIpIw8Xt8VV2X1ixwrQXmIHCvDoJOOVXn7Ba5Zs4Y1a9YY1jKB\n2SBGMQQC08EURkYMhbn4Yi5+gMixAjCsaI1AIBAIBAJBLUbsFSiocsRolUBgfESOleliKn7ok2NV\nIEkUFkJKllJXMuboYXr06qPTvVYyC1wdzG/TehFYCQQCAfDGG29w4sQJunTpUkI+whxQfVnm3N5m\nEl/ihiDndrxZ+GIqfuiTY5WZV8DkrRdQLW25fSgUj5vlKwMAvBnQjEBv1wq3aeqUG1iVt08gwJw5\nc9i7dy8ODg6sW7eOzp07V4mxgpqJyLESmDr//PMP2dnZREZG8sorrxAbG0vXrl2NbVaVUPAw29gm\nGAxz8aWm+yEvePz5npeTRX6Bbp/3F1OycbHTb8TKq54tria6jU6ZgVVBQQGzZs3S2CdwxIgRGtvZ\n7Nmzh/j4eOLi4oiJiWHmzJkl9gkUCAQCUyYmJobBgwcDEBQUxNGjR/UOrFKzdd+suygysQWQoJax\n/Xwq28+n6nXvuv+0M7A1hqPMwEqXfQJ37tzJCy+8ACj3CUxLS+POnTu4u7tXndWCGoUYrRKYOmlp\nabRs2RIAZ2dnzp8/r3ddPx6/zcWUnArfJy8opK5N1W2p1T8tAoAf0u9UaTvVSWElfDGlZ1AZBlaY\n2wAAIABJREFUPwyJ6h2JcOmvdx2m4osxKTOw0mWfQG3X3Lx5UwRWAoGgxuDs7ExGRgYA6enpuLi4\naJzPysrin3/+0amuQU7K/0wP5TJ45XJ4hXFNMRRfvE1FffkgJOTRXyb0DPTwo2p49I5UxpZq8iU5\n/jzJVdxGVlaWXveVGVjpquSsu+L44+u0DWIU2yYQAIWW/il+r7ZtArXdp61+fW0o3qap+qNrXbps\ntaitPW1lugxQmao/huxrU/BHW5kh/Sn/3Q0teZMJ0qtXL1auXMkzzzxDaGgoU6ZM0Tg/cuRII1km\nEAhqGmUGVrrsE1j8mps3b+Lp6VlKjZOB5o/+dgE6Af0fHUc8+r84FsfiuOYeq/6++ujvSdQEOnfu\njJ2dHQEBAXTu3NlsE9cFAkHVYyGVkQCjUCho27YtoaGheHh40L17dzZv3lwief27775jz549/P33\n37z++utak9dDQ0Pp0qVL1Xhh4tT2vZNqs/+12XdQrrYbOHCgsc0QCASCaqNM5fWi+wS2a9eO8ePH\nq/cJVO0VOHToUFq2bEmrVq2YMWMGy5cvrxbDaxJnz541tglGpTb7X5t9r2kkJSXRpUsX7O3tKSws\nRC6X06tXLxwdHUlISFBft3HjRvr06cPw4cPJzMw0osWlU5YvV65cUV/Xtm1bAgMDCQwM5OLFi0a0\nuHSK+5KYmEhAQAD9+vXjueeeU2/mXhP7pTRfTL1fivuRmppKnz596N+/P+PGjUMulwM1s09K86Ui\nfVLuljZDhgzh8uXLxMfH83//93+Acp/AonsFfvfdd8THx3P69OlaOypVFunp6cY2wajUZv9rs+81\nDVdXV8LCwujZsyeg3Ex+x44djBs3Tp1HKpfLWblyJVFRUUyaNEn9A9PUKMuXojRs2JDw8HDCw8M1\nZiJMieK+1KtXj7/++otDhw7RokUL9uzZU2P7RZsvYPr9UtwPV1dXDh8+TEREBL6+vuzevbvG9ok2\nX6BifSL2ChQIBALA1ta2xGrAhg0bahzHxcXRsWNHZDKZWu/KFNHFF4D79+/Tr18/Xn75ZfLy8qrL\nvApR3BcXFxccHR0BZcBoZWVFfHx8jeyXor5YWVlhZaVMezb1finuh0z2OJTIysqifv36NbZPtPkC\nFesTEVhVA9evXze2CUalNvtfm303R9LT03FyUmopODk5kZaWZmSLKsfhw4c5dOgQXl5erFq1ytjm\nVIjbt29z8OBBBg8ezIMHD2p0v9y+fZuQkBC1SG1N7Jdjx47RrVs3Tp48SZ8+fWp0nxT3BSrWJ9W6\nV6CuOjDmxrRp02qt71C7/a/NvpsTKgmZonpXGRkZJUaFagJF5XBU9o8ePZolS5YYy6QKk5eXx+TJ\nk1mzZg0ymQwXF5ca2y/FfYGa2S/du3fn+PHjLF68mLVr19KnT58a2yfFfZk+fXqF+qTaAiuxMkgg\nENQUii+WVh23bt2ac+fOUVhYSEhICL169TKGeRWiNF/kcjmFhYXY2toSHR1Nq1atjGFehVDZ/tJL\nL/Hqq6/i4+MD1Ox+Ke5LTesXSZKQy+VYWyv3/HN0dCQ/P582bdrUyD7R5kuF+0QSCAQCgSSXy6WB\nAwdK9erVk4KCgqSYmBjpP//5j+Th4SH16dNH2rlzpyRJkrR+/Xqpd+/e0rBhw6SMjAwjW60dXXy5\nc+eO1KVLFykgIEAaNWqUlJWVZWyztVLcl0OHDkmOjo5S//79pf79+0vbt2+XJKlm9os2X2pCv2h7\nv/r16yf1799fGjlypNrmmtgn2nxJTk6uUJ+UqWMlEAgEAoFAINAdgyevb926lfbt22NpaVkit+SL\nL76gdevW+Pj4cODAAXX5iRMn6NixI61bt+a1114ztElG4+OPP6ZJkyZ07tyZzp07s3fvXvW50p6F\nObFv3z58fHxo3bo1X375pbHNqRaaN2+Or68vnTt3pnv37oByNcmgQYNo06YNgwcPrlFJnGUxdepU\n3N3d6dixo7qsLF9rwzsvEAgEBp8KvHjxonT58mWpf//+0okTJ9Tl58+fl/z8/KT8/HwpMTFR8vb2\nlgoLCyVJkqRu3bpJMTExkiRJ0pAhQ6S9e/ca2iyj8PHHH0tff/11iXJtz6KgoMAIFlYdCoVC8vb2\nlhITE6X8/HzJz89PunDhgrHNqnKaN28u3bt3T6Ps7bfflr788ktJkiRpwYIF0rx584xhmsGJjIyU\n/vnnH6lDhw7qstJ8rQ3vvEAgEEiSJBl8xMrHx4c2bdqUKN+xYwcTJkzA2tqa5s2b06pVK2JiYkhK\nSiIzM1P96/75559n+/bthjbLaEhaZlq1PYtjx44Zwbqq49ixY7Rq1YrmzZtjbW3Ns88+y44dO4xt\nVrVQvM937tzJCy+8AMALL7xgNu+3v78/9erV0ygrzdfa8M4LBAIBVKOO1e3btzU2cG7SpAm3bt0q\nUe7p6cmtW7eqy6wq59tvv8XPz48XX3xRPS1S2rMwJ27dukXTpk3Vx+boozYsLCwICgqia9eurF69\nGoA7d+7g7u4OgLu7O3fu3DGmiVVKab7WhndeIBAIQE+5hUGDBpGcnFyi/PPPP2f48OGVNqomUdqz\n+Oyzz5g5cyYfffQRAB9++CFvvvkmP/74o9Z6imrLmAPm5o+uHD58mMaNG3P37l0GDRqkXkKtwsLC\notY8m/J8rS3PQSAQ1C70CqwOHjxY4Xs8PT25ceOG+vjmzZs0adIET09Pbt68qVHu6empj1lGQddn\nMW3aNHXQqe1Z1CSfdaG4jzdu3NAYsTBXGjduDECDBg0YPXo0x44dw93dneTkZBo1akRSUpLWrUXM\nhdJ8rQ3vvEAgEIAOU4ExMTH06dMHf39/5s6di0Kh0HnH96K5JiNGjODXX38lPz+fxMRE4uLi6N69\nO40aNcLJyYmYmBgkSWL9+vWMGjWqClytfpKSktR///nnn+rVU6U9C3Oia9euxMXFcfXqVfLz89my\nZQsjRowwtllVSk5Ojvrdz87O5sCBA3Ts2JERI0bw888/A/Dzzz+bzfutjdJ8rQ3vvEAgEADlrwpM\nTk6W8vLyJEmSpOeee046e/asdOfOHWny5MlSfHy8JEmSlJ+fL/n7+0sFBQXSm2++KTk7O0t2dnaS\nu7u7FBwcrK7rs88+k7y9vaW2bdtK+/btU5fHxsZKHTp0kLy9vaXZs2cbMjnfqEyaNEnq2LGj5Ovr\nK40cOVJKTk5WnyvtWZgTe/bskdq0aSN5e3tLn3/+ubHNqXISEhIkPz8/yc/PT2rfvr3a53v37kkD\nBw6UWrduLQ0aNEh68OCBkS01DM8++6zUuHFjydraWmrSpIm0du3aMn2tDe+8QCAQVEggdMqUKcyb\nNw8fHx+mTJnCBx98gLe3NxcuXOD777/n+++/5/79+0yfPp3ff/+9KuNBgUAgEAgEApND51WBZ86c\n4e7duyWSccH8dnwXCAQCgUAg0Aedktfv37/P7Nmz2bp1q0a5Oe34LhAIBAKBQFBZyg2sFAoFEydO\n5KuvviqxmkmqwI7vmzZtUuvbCASC2kFWVhYjR440thkCgUBQbZQbWG3dupXY2FjeeecdQLnf15Il\nS4iOjiYuLo558+YxfPhwpk+fjr+/P66urmzatKlEPe7u7nTp0sXwHhiBBQsW8O677xrbjEpjLn6A\n8MVUKb5fqEAgEJg75QZWEyZMYMKECRplW7ZsKXHdxIkTmThxouEsEwgEAoFAIKhhVFjHCmDRokX4\n+/szceJEFAoFAB988AF9+/YlICCA+Pj4qrXayFy/ft3YJhgEc/EDhC+C0vnll18ICgpiwIAB3L59\nW+vnlzYdPoFAINCHcgOr5s2bEx4eTlRUFCkpKURGRhIREUFUVBS+vr5s376d9PR0/v77b6Kjo1mw\nYAHLly+vDtuNhkros6ZjLn6A8EWgnVu3bhEZGUlISAhhYWFYWVmV+PySy+WsXLmSqKgoJk2axMqV\nK41ttkAgqMGUG1i5u7tjY2MDgLW1NefPn6d///4ABAUFcfToUWxtbQEoLCzkwYMHuLm5GdxQSZKo\ngORWlTJz5kxjm2AQzMUPEL4ItLN//34KCgoICgpizpw5xMbGlvj8io+Pp2PHjshkMnWZQCAQ6IvO\newWqdKxcXFyQyZTxmEqzys7Ojt69e9O2bVsKCws5fPiwQY2UJInZO/5FZgHLRrY1aN0CgcB8uXPn\nDnK5nJCQEN59912tmntpaWlCh08gEBgMnQRCVTpWa9eu1apZdfXqVc6cOUNcXBy//fYb77//vkGN\nLJTg39QcLt3NMWi9+hIdHW1sEwyCufgBwheBdlxcXAgICABgwIABJCYmlvj8Ejp8AoHAkFRYx6pr\n164sX76ct99+W61ZlZmZqf7FV79+fdLT07XW9corr9CsWTNAKSrasWNH+vbtCzz+MintOOPKKQAk\nqRMWFhblXi+Oyz8+e/asSdlTmeOzZ8+alD219Vj1tyoBf9q0aRiT3r17s3r1agBOnjxJ06ZN2bJl\ni8bnV5s2bYQOn0AgKIG+Onzl7hW4efNmXnvtNdq3bw8odawiIyPZtWsXXl5erFu3DisrK2bMmMHF\nixdRKBQsW7aMrl27atQTGhqqt45VQaHEkLXKwGrfi52QPVJ8FwgEps0///zDwIEDjWrD22+/TWxs\nLA0aNGDjxo0sWbKkxOfXhg0b+OGHH9Q6fI6Ojhp1VObzSx+MoWVW3W0auz1XV1dAOSNTHe1VNeKd\nMTz6fn7ppWPVs2dPtWCoiupaSSNJgIirBAKBjixatEjj+J133inx+SV0+AQCgaHQeRNmY2IaawEf\nYy45MObiBwhfBOaFMbTMSmtz2bJlLFu2rNraqypqU3tV1WdltVkd1BSNv3JHrGJiYpg7dy4ymYxu\n3bqxePFiFi1axM6dOzWG0k+ePMm8efNQKBS89dZbDB06tEoMNrUgSyAQCAyNMbTMSmtzzpw51dpe\nVVGb2quqPiurTXNsT1/KzbG6c+cO9erVw8bGhokTJ/LSSy/x5Zdf8tdff7Fw4UJatmzJuHHjGDt2\nLBs2bMDe3l5rPaGhoRzLb8jtjDw+GdQSiwrkSckLCnn6p9MA/DXFD2vLGjHQJtCRM0lZfBV5jTf9\nm+Hn4Vj+DYIagynkWBmC6s6xElQ9VZ1jJaj56Pv5ZRCB0MTERHJzcxk3bhyjR48mJSVFa11/nLvL\n39czuJGWVyEjpWJ/Z+cXkJxZsToEpsv/7Y0nOTOfd/aY91ZIAoFAIDB/dB76KSoQWlxM786dO/z7\n77/8/vvvzJgxg88++6zMugoqo6Auwdj1Z3h+ywXuZcv1r6cSmEsOjKn4IS9Uvg+VmeY1FV8MgTn5\nItAPY7wDpbVZVfk61e1jbWqvunKszP2Z6otOyusqgdCtW7cSGxvLzZs3AU2BvW7dumFnZ0dgYCCL\nFy/WWk/Cli+xrdeIFTfcaN6ofrk6VlcfPOQfvHi5V5PHOlb4USgpda3+3J/CtDFPAbB48x4irtxn\n7Rv/wa2Ojdb6MnIV2Db3pX/Lehw9crjEeV2OfTp3p7BQ0jhfUCgRFR2FlUxW6v17QiJwsJHR/5FY\nYXXpCvXu04f/2xtP7tUzPOPrrj7/0/YDrNwdxffNfXmyiZPRdZBU/Qud9bpf6FiZxrHqb1PRsRJU\nnurK1xEYDtFnxqXcHCuFQsGIESP45JNP6NatGykpKUydOpXdu3erc6xGjRpFcHAwBw4c4Pjx4/z0\n00+sWLFCo57Q0FDe/UeZV/XD6LY0cbZj48lkfBo60NvrsdJxoSSx/OhNfBvV5X9hVwFwr2vDnax8\nAHZO9mPEOmW+1dv9mmEls8CvviWDP/oJV99+PNXGlTcDvLT68t9N50jNkfNSD0/GdWxY5oM5evQo\nc+fOJS0tjYsXLwLwz60M3t17hd5ezgxySKJRo0Z4e3vzwpbzpObI2fGCH1aykrlj19NymbbtIi1d\n7Vgx5oky2zU0t9JzmbJVaf+BaZ3V5YPXnFT/XbTcGJRlS/TVNO5k5jO2nP4SmCYix0pgqogcK0F5\nVJmOlWqUSqX78sUXXxAQEIC/vz9eXl7MnTsXKysrpk+fTv/+/bG0tGTdunVl1jn/YAIpWY+n8dY+\n8wTr/0lmgHc9CiXYeSGVnRdS1ecz8xTqv4vGgYsOKX8Vd3PO5cHpCFx9+6EoLD1OTM2RI0kSp25n\nlhtYtW/fnrCwMIYNG6Yu23f5HgBHrqVjlxpFly5d8Pb2JilTGfSlPZRT38G6RGL+8RvK7TIS7ueS\nnV9AHRvLMts2LGUvEtASB5oUn4YkAtCzmROeznZGtkYgEAgEgrIxmEDo+PHjGT9+vE6NFg2qAKZu\nvUihPI8fP32TRpbZ3MhU0Hb6IrJvXObmnlVQWIBzu9406vcfvl60kMSwUyhyMijIz6XNiwv4c/Mv\nZCac4fLKN3k4ag5PKuJZsmQJBQUFTJ8+nbFjx/Lqq69y7VoOeXdv0mzSLJ5a/Ap2dna0atWK6fM+\npY6NJU1dHn9xq/LItJF2+Ti/HvyV3bt3s337djKdu5Mc+Ruvhrky4ukh3L9/n4MHD5KZmcn8+fOh\nfjtyU29x7Y8ldPvJgnEDezP/40949fPlXDq0CztLeP/99/H399fp+VWEsgKnjCuncG1t3NGq4txK\nz8PT2bZEeba8sMz7oqOj1dNSNR1z8kWgH8Z4B0prU5WrY+jpper2sTa1V1V9Vlab1UFN+Ww0mI4V\nKIfNunbtikKhQCarmCTC3Zi/cGjqw/wP56pHom7uW4P3859gZV+XuJ8+oP6TgwALbBs0ocXAidzc\ns5qMuFga9BpJ3r0kvCfNR5Ikvv76fXbt2oWFhQXDhg1j9OjRANTxbIPXqDmk/hvG+PHjmTp1Khm5\ncsZtOAeUPyWmGomSWVkzYcIEunTpwkPPTvyzfjcFuTksX7OD+g7WPHz4kNmzZ3P37l2mTp3K5M9/\n5OaeVTR9egYOnq355MVObD0Wz76/dtLmxQX8PqENEyZMqJLAqjyVeksLSMnK58q9h/Rs5lQhGYyq\nYMrWC2pJjcLKLHLQQqEkkZotp2FdG4PWKxCYMyJfp+Yh+sy4lBv9NG/enPDwcKKiokhJSSEyMpKI\niAiioqLw9fVl+/bt6muXL1/Ok08+qZchuXdv4NjSl6v3c9VlD5MSuPLzR1xeMZf89Lvkp90FwMGj\nFQA2Lg1QPMzSqEeRncbZS/8yZswYRo8eTUZGBqmpymnFOk3bAtCs+0CuXbvGjBkz2LxlS4VtdfLu\nBMDV+zl8d+QmFlhQp0kbdQyzZcsWhg0bxosvvsiN28msjLlFfvpdHDxbA8oA7XJ8Arl3rnF5xVwm\nTJjAvXv3dG4/I1fBnkup5OQXlHutrEhkFRKnmUvg5N0JmcyCib+eZ/7BBI7fzNDZhqpEXqAMqA5f\n1b6ZtzZ0+RXz1aFrTPz1PJGJD/S2rTqoCb/IBFWLMd6B6m5TtFez2zNGmzXls7HcEauiO7pr07Ha\nuHEj48aN4/z58zRt2pQrV65QTj68VuwaNiMz4Qxbz7ZBKizEQibDobE33pPmY2lXR11GSqLmjZKE\nhcwSSVJOFVk5OCNzbcLvv/+OtbU1CoVCPaKmGr5JySngctNR2Da34NQPM3GethxQCpFefZDLkqjr\nvNu/Oc3q2ZGvKCRXUUhqdr6GX9bW1qTnKHOrJCSweBzCrF69mujoaO7evcuTAUE0BGycG5JzKw4H\nz9ZIkkS9xk2xb9SC1lM/Z+e0zigUj/PIyuPjkATOJWdzNjmLef2bl3lt0YHDhYeuEdTaVeO8ZZER\nqst3c+je1FlnO4rzUF7A39fT6dHUGYdK5JGpTEp7+HjK2BDjaCHxyoBq14VUAlrUM0CN1U9BocQ3\n0dfp1tSpxvogEAgE5oxBdKwAli5dyqxZswD0mk5q0P1psm9c5NKKufz74zwAPIdMI/6Xj7m88k3i\nfnqPQnk+F1Ky0fiatbDA2qk+hfI8rqz/hLz7STQeOJExY8YwcuRIpk57iYgrDzQ2b75yPJJLP7zO\n6e9eo0G7Huqq/jx3l1e3Xyb+3kOe+2E/g4aO4FJcPG37DObZpbuISFD6mnHlFP7+/uzY+CPXd36P\nRbGv/Z49exIcHMzSpUuxtHUAoMnTL3Fj9wour5jL/Pnz2ZmQh2unQC798AZP9n+KAZNmlxmQHr+R\nwaqYWxQUSpxLzlaXaWPbmTsMXnOS2Tsuc+Xew1LrzLhyiofyx6NekkSlpt+WRF3ni/BrfBVZuf2c\n9DGhIvomMiNPd5ZHWb6EX3nA/n/v87/Qq6TnKspcrFGUfEUhPx2/TXxqjqHMFFQhQsfK8NSm9oSO\nlXExiI5VfHw8Tk5O1K9fH6DUAEGlYwVgaV8HB49W6mm1rOsXaNBzuPpYpWvU9qVF6uOs6xeQdRiD\ny6NjO/fm6usb9X8WADs3T+zcPLlracX/BTbn++sufB5+lW5PDkIe/wB7d3D1649VXaXEQ36R9hZf\nOaWuT555nw5DnsdizCfq8xlFzodevsOzL73GjgylPxISfx89zJCB/fn666+Jjo4mKSOP823+Q468\nkPy0FBoHTcLJuxOvjG/Hgc83Ye3cAJ+ZS9T1/7EvjLFDlEs7i+sEzV7+OwBt3Eapr1dYywDfEtev\nOnabjCunOH4FLt/VfJ4qnaiMK6fIuR2v8bwvSPV4Pq4VbRvUIdD2FjfScrHx8mVMhwYcPly27te6\n7QfYGXMLJ+9ORF9N01vHysm7E9Kj85eupQMeAJyIOcIdZ7tK6VhlXInDybsTF1Ky+XnHAbzrO2i9\nPjNPwZ6QCDzLaM9YxxkubdTP66lPTtGxa09Wj32i3Ps/W7+b/f/eY7N3Jw5M62xw+0IjIjmTlEWH\nRnU4EXNU6FiZESJfp+Yh+sy4GETHytLSkm+++QYHBweOHTvG2LFjWbVqlUY9RXWsqouWrvYk3FeO\n2LR2sycuVfvozZ3oP0g79zgStm/ckmYjZ5Vb/5C29dl7+XFu1LN+7gxv50aDOjacT87ijd1xWu/r\n29yF6KtpJcpXjfUhM6+A/ZfvMbNXEw1ZBpXW06u9mvD90Zvq8h0v+GJvrTntVlQXqjjbJnbkj3Mp\nbDp1p0zfDkzrrK7nw4Et8G/hUuq1KVn5TPz1fIn7daW4vb9P6oijrRW7L6ay7PANAL4f1ZbWbg7c\ny5ZzNzufzLwC2jZwwMlOp98GWtvp39KFt/t5ldh7cswvZ8jKL+C7UW1p4+agc/2G5KG8gOM3MujW\n1Emjf7edTWFVzC2Na3V51l9GXCX00VRoVeiWLQi/StiVB3Rt4sjnwa3U5ULHSmCqCB0rQXkYXcdK\ntfJuwIABJcRBjYUqqAKILyWoAnDvOwb3vmMqXP/d7HyN419P3+HX03cY9oQbDtalz7KeScrUWp6v\nkHjzUTBWx9aSmT2blLim+CzWyJ/PMLVbY571a6STzd8duaGe0gSlHIO22aQD/z4OGJMz88jIVaiD\nmL2X73HkahofDmyBjZWMlKz8Evcn3HvIQ3kBjnZWNHW2rdD0sLZQ/9298fw+yZcJm8+pyxo52vDL\n+Pbq46sPHvJ15HWmdvOg86PNnPMVhfx1KZVeXiVzxyIS0ujs6cSQtvU1yrMeLQo4m5SlDqwKJYkP\n9l+heT17XurhqbMv+vLRgQROJykXZnwR7M2Gk8m80beZ3lO1Rfv4Xo5Sb82QHL6mXGgQe1P7uy2o\nGJs3byYwMJBGjXT7d11RHjx4wAsvvMCpU6eYMGECX375pdbr/Pz8iIiIoF49zXy+ffv2cfnyZV57\n7TWt9507d46kpCQGDRpkcNsFAlOn3ByrCRMmkJKSQnh4OOHh4WoNq6ioKDZs2FAkMVxJWFhYhaUW\nqgNDLtx/PK2mnd0XU/nrUumr/DLytK/mm7Xjsvrvu1m674O49niSztceK5KXlXHlVKn5RkXzpLac\nvsO4DWfZe0m5unJJ1HVibmSw/fxdHuTISwR7AC//eYk3dscxbdtF9lzWfcUjwC//KP3JL3isXZWZ\nV0Bcsfyg5EfCrLmKQj7+aSeztl/m8t0c5u2JJytPQVaegk2nkvnh71s8v+WC1rbu55T+nIsO5ibe\nf0jszUy2ndW+wbihkCSJJZv3qIMqgP/bd4Xzd7J56Y+LnE3KKnHPYS2jn9rqVTH/QIJhjAWy8hTK\nug0sjVHbWbFiBcnJyRW6p6Cg/FXCKmxtbXnvvff49NNP1WXa8lcsLCxYuXJliXyd4ODgUoMqUObk\nhoSElGmDuefniByrmt+evpQbAcXExNCnTx/8/f2ZO3cuAIsWLcLf35+JEyeiUCjIzMwkKCiIfv36\nMXz4cLKySn741zaydZBCKAttU4UA3x25qbX8g/1XGLzmJFfulZ2cnFNMaNNSB+l1VSC45vhtjfI1\nx28zftM5Pn+09VBpLI2+UWYAU5ydF1JJyswrMeX16vbLWq8fse40+/69R37B4y/3MevPMmb92TID\nXFCORCVl5mntr6JPqvgChari+M0MtpzRPk1bKEGMlgULn4QkaixC0EbRsOff1Bweygv45UQS1x/k\nlnpPeZxJymLM+rO8uO0ieQUisAJISEhg9OjRBAQEEBgYyLVr1wDlF11QUBD+/v4sWLAAgOvXr9Oj\nRw9ef/11evfuzdixY8nNzWXHjh3Ex8czY8YM+vfvT25uLqdOnWL48OEMGDCAcePGceeO8h0ZPnw4\n7733HgMHDmTFihVs376dPn36EBAQoLFrRHEcHBzo2bMnNja6abr9+eef9O3bl7g45Yj6pk2bmDdP\nucioaJvDhw9HLpfzxRdf8Oeff9KvXz8NSR5B9TBnzhyRZ2VEDKJjZWNjw8aNGzl06BAjR44sd0ub\nmo4q4Tvxvv5fSoZGNRI180/twYc2nLw74VaBKaHSBiXuZpcfNJ0uNv2Zkavg6LV0CkpZ1fbClgta\npyiLk56rlKlQ9Ulp50sjJSufF7Zc4JkNZ0ueLNK+ZTn/UlQBGihH2nZeuEvyo+OKcP3CHoA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9KfS0X4eFCLEmXaWq4qvSQ7K8NniZYXRJiT9pPKl/G+Denb3IXnOpdcjNHUxc7kcvYEhkPoWBme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\n/tRW7o3c3FwKCgqws7Ojfv361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- "text": [ - "" - ] - } - ], - "prompt_number": 68 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "There are really two figures here, one for each unknown in the `centers` variable. In each figure, the subfigure in the top left corner is the trace of the variable. This is useful for inspecting that possible \"meandering\" property that is a result of non-convergence." - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "The largest plot on the right-hand side is the histograms of the samples, plus a few extra features. The thickest vertical line represents the posterior mean, which is a good summary of posterior distribution. The interval between the two dashed vertical lines in each the posterior distributions represent the *95% credible interval*, not to be confused with a *95% confidence interval*. I won't get into the latter, but the former can be interpreted as \"there is a 95% chance the parameter of interest lies in this interval\". (Changing default parameters in the call to `mcplot` provides alternatives to 95%.) When communicating your results to others, it is incredibly important to state this interval. One of our purposes for studying Bayesian methods is to have a clear understanding of our uncertainty in unknowns. Combined with the posterior mean, the 95% credible interval provides a reliable interval to communicate the likely location of the unknown (provided by the mean) *and* the uncertainty (represented by the width of the interval)." - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "The plots titled `center_0_acorr` and `center_1_acorr` are the generated autocorrelation plots. They look different than the ones I have displayed above, but the only difference is that 0-lag is centered in the middle of the figure, whereas I have 0 centered to the left. \n", - "\n" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Useful tips for MCMC\n", - "\n", - "Bayesian inference would be the *de facto* method if it weren't for MCMC's computational difficulties. In fact, MCMC is what turns most users off practical Bayesian inference. Below I present some good heuristics to help convergence and speed up the MCMC engine:\n", - "\n", - "### Intelligent starting values\n", - "\n", - "It would be great to start the MCMC algorithm off near the posterior distribution, so that it will take little time to start sampling correctly. We can aid the algorithm by telling where we *think* the posterior distribution will be by specifying the `value` parameter in the `Stochastic` variable creation. In many cases we can produce a reasonable guess for the parameter. For example, if we have data from a Normal distribution, and we wish to estimate the $\\mu$ parameter, then a good starting value would be the *mean* of the data. \n", - "\n", - " mu = pm.Uniform( \"mu\", 0, 100, value = data.mean() )\n", - "\n", - "For most parameters in models, there is a frequentist estimate of it. These estimates are a good starting value for our MCMC algorithms. Of course, this is not always possible for some variables, but including as many appropriate initial values is always a good idea. Even if your guesses are wrong, the MCMC will still converge to the proper distribution, so there is little to lose.\n", - "\n", - "This is what using `MAP` tries to do, by giving good initial values to the MCMC. So why bother specifying user-defined values? Well, even giving `MAP` good values will help it find the maximum a-posterior. \n", - "\n", - "Also important, *bad initial values* are a source of major bugs in PyMC and can hurt convergence.\n", - "\n", - "#### Priors\n", - "\n", - "If the priors are poorly chosen, the MCMC algorithm may not converge, or at least have difficulty converging. Consider what may happen if the prior chosen does not even contain the true parameter: the prior assigns 0 probability to the unknown, hence the posterior will assign 0 probability as well. This can cause pathological results.\n", - "\n", - "For this reason, it is best to carefully choose the priors. Often, lack of covergence or evidence of samples crowding to boundaries implies something is wrong with the chosen priors (see *Folk Theorem of Statistical Computing* below). \n", - "\n", - "#### Covariance matrices and eliminating parameters\n", - "\n", - "### The Folk Theorem of Statistical Computing\n", - "\n", - "> *If you are having computational problems, probably your model is wrong.*\n" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Conclusion\n", - "\n", - "PyMC provides a very strong backend to performing Bayesian inference, mostly because it has abstracted the inner mechanics of MCMC from the user. Despite this, some care must be applied to ensure your inference is not being biased by the iterative nature of MCMC. " - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### References\n", - "\n", - "1. Flaxman, Abraham. \"Powell's Methods for Maximization in PyMC.\" Healthy Algorithms. N.p., 9 02 2012. Web. 28 Feb 2013. ." - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "from IPython.core.display import HTML\n", - "\n", - "\n", - "def css_styling():\n", - " styles = open(\"../styles/custom.css\", \"r\").read()\n", - " return HTML(styles)\n", - "css_styling()\n" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "html": [ - "\n", - "\n" - ], - "metadata": {}, - "output_type": "pyout", - "prompt_number": 1, - "text": [ - "" - ] - } - ], - "prompt_number": 1 - }, - { - "cell_type": "code", - "collapsed": false, - "input": [], - "language": "python", - "metadata": {}, - "outputs": [] - } - ], - "metadata": {} - } - ] +{ + "metadata": { + "name": "" + }, + "nbformat": 3, + "nbformat_minor": 0, + "worksheets": [ + { + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Chapter 3\n", + "\n", + "\n", + "_______\n", + "\n", + "## Opening the black box of MCMC" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The previous two chapters hid the inner-mechanics of PyMC, and more generally Markov Chain Monte Carlo (MCMC), from the reader. The reason for including this chapter is three-fold. The first is that any book on Bayesian inference must discuss MCMC. I cannot fight this. Blame the statisticians. Secondly, knowing the process of MCMC gives you insight into whether your algorithm has converged. (Converged to what? We will get to that) Thirdly, we'll understand *why* we are returned thousands of samples from the posterior as a solution, which at first thought can be odd. " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### The Bayesian landscape\n", + "\n", + "When we setup a Bayesian inference problem with $N$ unknowns, we are implicitly creating an $N$ dimensional space for the prior distributions to exist in. Associated with the space is an additional dimension, which we can describe as the *surface*, or *curve*, that sits on top of the space, that reflects the *prior probability* of a particular point. The surface on the space is defined by our prior distributions. For example, if we have two unknowns $p_1$ and $p_2$, and priors for both are $\\text{Uniform}(0,5)$, the space created is a square of length 5 and the surface is a flat plane that sits on top of the square (representing that every point is equally likely). " + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "%matplotlib inline\n", + "import scipy.stats as stats\n", + "from IPython.core.pylabtools import figsize\n", + "import numpy as np\n", + "figsize(12.5, 4)\n", + "\n", + "import matplotlib.pyplot as plt\n", + "from mpl_toolkits.mplot3d import Axes3D\n", + "\n", + "jet = plt.cm.jet\n", + "fig = plt.figure()\n", + "x = y = np.linspace(0, 5, 100)\n", + "X, Y = np.meshgrid(x, y)\n", + "\n", + "plt.subplot(121)\n", + "uni_x = stats.uniform.pdf(x, loc=0, scale=5)\n", + "uni_y = stats.uniform.pdf(y, loc=0, scale=5)\n", + "M = np.dot(uni_x[:, None], uni_y[None, :])\n", + "im = plt.imshow(M, interpolation='none', origin='lower',\n", + " cmap=jet, vmax=1, vmin=-.15, extent=(0, 5, 0, 5))\n", + "\n", + "plt.xlim(0, 5)\n", + "plt.ylim(0, 5)\n", + "plt.title(\"Landscape formed by Uniform priors.\")\n", + "\n", + "ax = fig.add_subplot(122, projection='3d')\n", + "ax.plot_surface(X, Y, M, cmap=plt.cm.jet, vmax=1, vmin=-.15)\n", + "ax.view_init(azim=390)\n", + "plt.title(\"Uniform prior landscape; alternate view\");" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "display_data", + "png": 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AyM/PZ/LkyXTs2JFGjRpx3XXXsWXLFn8furd3+fLl3H777bRs2ZLHH3/cv4S5atUq+vbt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+0kJcAjE6O5kFey4LM59A18n7csQEqiys0tPbw6zEHVKvp86q/HRJZ8b+SR3k5OnZPoO+Lq+NtW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\nW4Au0KOrpjfNetML+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+ "text": [ + "" + ] + } + ], + "prompt_number": 3 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Alternatively, if the two priors are $\\text{Exp}(3)$ and $\\text{Exp}(10)$, then the space is all positive numbers on the 2-D plane, and the surface induced by the priors looks like a water fall that starts at the point (0,0) and flows over the positive numbers. \n", + "\n", + "The plots below visualize this. The more dark red the color, the more prior probability is assigned to that location. Conversely, areas with darker blue represent that our priors assign very low probability to that location. " + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "figsize(12.5, 5)\n", + "fig = plt.figure()\n", + "plt.subplot(121)\n", + "\n", + "exp_x = stats.expon.pdf(x, scale=3)\n", + "exp_y = stats.expon.pdf(x, scale=10)\n", + "M = np.dot(exp_x[:, None], exp_y[None, :])\n", + "CS = plt.contour(X, Y, M)\n", + "im = plt.imshow(M, interpolation='none', origin='lower',\n", + " cmap=jet, extent=(0, 5, 0, 5))\n", + "#plt.xlabel(\"prior on $p_1$\")\n", + "#plt.ylabel(\"prior on $p_2$\")\n", + "plt.title(\"$Exp(3), Exp(10)$ prior landscape\")\n", + "\n", + "ax = fig.add_subplot(122, projection='3d')\n", + "ax.plot_surface(X, Y, M, cmap=jet)\n", + "ax.view_init(azim=390)\n", + "plt.title(\"$Exp(3), Exp(10)$ prior landscape; \\nalternate view\")\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "pyout", + "prompt_number": 4, + "text": [ + "" + ] + }, + { + "metadata": {}, + "output_type": "display_data", + "png": 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iZux8GzfZsc3OEat9pJQII4mmRJhVMjBz//kx37RpR9KrV6/Mqd83YXbu3Nm4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\nWbdQKCqNri2H5ieCkRvmEmm1HLlhrilbLTcH4hJfTdPcwO8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urpznaRN3/JjK7vyvMoeP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+ "text": [ + "" + ] + } + ], + "prompt_number": 4 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "These are simple examples in 2D space, where our brains can understand surfaces well. In practice, spaces and surfaces generated by our priors can be much higher dimensional. \n", + "\n", + "If these surfaces describe our *prior distributions* on the unknowns, what happens to our space after we incorporate our observed data $X$? The data $X$ does not change the space, but it changes the surface of the space by *pulling and stretching the fabric of the prior surface* to reflect where the true parameters likely live. More data means more pulling and stretching, and our original shape becomes mangled or insignificant compared to the newly formed shape. Less data, and our original shape is more present. Regardless, the resulting surface describes the *posterior distribution*. \n", + "\n", + "Again I must stress that it is, unfortunately, impossible to visualize this in large dimensions. For two dimensions, the data essentially *pushes up* the original surface to make *tall mountains*. The tendency of the observed data to *push up* the posterior probability in certain areas is checked by the prior probability distribution, so that lower prior probability means more resistance. Thus in the double-exponential prior case above, a mountain (or multiple mountains) that might erupt near the (0,0) corner would be much higher than mountains that erupt closer to (5,5), since there is more resistance (low prior probability) near (5,5). The peak reflects the posterior probability of where the true parameters are likely to be found. Importantly, if the prior has assigned a probability of 0, then no posterior probability will be assigned there. \n", + "\n", + "Suppose the priors mentioned above represent different parameters $\\lambda$ of two Poisson distributions. We observe a few data points and visualize the new landscape: " + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# create the observed data\n", + "\n", + "# sample size of data we observe, trying varying this (keep it less than 100 ;)\n", + "N = 1\n", + "\n", + "# the true parameters, but of course we do not see these values...\n", + "lambda_1_true = 1\n", + "lambda_2_true = 3\n", + "\n", + "#...we see the data generated, dependent on the above two values.\n", + "data = np.concatenate([\n", + " stats.poisson.rvs(lambda_1_true, size=(N, 1)),\n", + " stats.poisson.rvs(lambda_2_true, size=(N, 1))\n", + "], axis=1)\n", + "print \"observed (2-dimensional,sample size = %d):\" % N, data\n", + "\n", + "# plotting details.\n", + "x = y = np.linspace(.01, 5, 100)\n", + "likelihood_x = np.array([stats.poisson.pmf(data[:, 0], _x)\n", + " for _x in x]).prod(axis=1)\n", + "likelihood_y = np.array([stats.poisson.pmf(data[:, 1], _y)\n", + " for _y in y]).prod(axis=1)\n", + "L = np.dot(likelihood_x[:, None], likelihood_y[None, :])\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "observed (2-dimensional,sample size = 1): [[2 2]]\n" + ] + } + ], + "prompt_number": 24 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "figsize(12.5, 12)\n", + "# matplotlib heavy lifting below, beware!\n", + "plt.subplot(221)\n", + "uni_x = stats.uniform.pdf(x, loc=0, scale=5)\n", + "uni_y = stats.uniform.pdf(x, loc=0, scale=5)\n", + "M = np.dot(uni_x[:, None], uni_y[None, :])\n", + "im = plt.imshow(M, interpolation='none', origin='lower',\n", + " cmap=jet, vmax=1, vmin=-.15, extent=(0, 5, 0, 5))\n", + "plt.scatter(lambda_2_true, lambda_1_true, c=\"k\", s=50, edgecolor=\"none\")\n", + "plt.xlim(0, 5)\n", + "plt.ylim(0, 5)\n", + "plt.title(\"Landscape formed by Uniform priors on $p_1, p_2$.\")\n", + "\n", + "plt.subplot(223)\n", + "plt.contour(x, y, M * L)\n", + "im = plt.imshow(M * L, interpolation='none', origin='lower',\n", + " cmap=jet, extent=(0, 5, 0, 5))\n", + "plt.title(\"Landscape warped by %d data observation;\\n Uniform priors on $p_1, p_2$.\" % N)\n", + "plt.scatter(lambda_2_true, lambda_1_true, c=\"k\", s=50, edgecolor=\"none\")\n", + "plt.xlim(0, 5)\n", + "plt.ylim(0, 5)\n", + "\n", + "plt.subplot(222)\n", + "exp_x = stats.expon.pdf(x, loc=0, scale=3)\n", + "exp_y = stats.expon.pdf(x, loc=0, scale=10)\n", + "M = np.dot(exp_x[:, None], exp_y[None, :])\n", + "\n", + "plt.contour(x, y, M)\n", + "im = plt.imshow(M, interpolation='none', origin='lower',\n", + " cmap=jet, extent=(0, 5, 0, 5))\n", + "plt.scatter(lambda_2_true, lambda_1_true, c=\"k\", s=50, edgecolor=\"none\")\n", + "plt.xlim(0, 5)\n", + "plt.ylim(0, 5)\n", + "plt.title(\"Landscape formed by Exponential priors on $p_1, p_2$.\")\n", + "\n", + "plt.subplot(224)\n", + "# This is the likelihood times prior, that results in the posterior.\n", + "plt.contour(x, y, M * L)\n", + "im = plt.imshow(M * L, interpolation='none', origin='lower',\n", + " cmap=jet, extent=(0, 5, 0, 5))\n", + "\n", + "plt.scatter(lambda_2_true, lambda_1_true, c=\"k\", s=50, edgecolor=\"none\")\n", + "plt.title(\"Landscape warped by %d data observation;\\n Exponential priors on \\\n", + "$p_1, p_2$.\" % N)\n", + "plt.xlim(0, 5)\n", + "plt.ylim(0, 5)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "display_data", + "png": 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EEuLQv6gpHu6Ee2VIlW/HkD7LgYw+E/f4fRfxS9bipzym5JyK8HbDo5BxZQ2A\npQHPEUQhGi9Fgp4E8C6f7HCLKMnKcwAW+TC+V8IuFCQW7oQTQgghhBASMgzCvSLjTiF9lgMZfSak\nJopoA0Im6F3wKCJqF1wklXbBSdBQjkIIIaR+Kt1FGjFTSjUiUyioElGQrMhCGBlRGp2oZ42JFtwJ\n94qMuZTpsxzI6DMhtciroi0ImcdEGyCAP4g2QADPiDZASlwH4blcDosWLcJ73vOeIOwhhBASEbje\nE0JIcLj+bOTuu+/G3Llzcfjw4SDsaTxk1M3SZzmQ0WdSgqP1vtV4DEJ2EnYWFEcoXgfQiZxkxa5I\n0AqfbWkEws6NHoUiPlYdfNBFgsKYI+ysLvXhaid89+7deOihh3DllVdC06JQyYsQQkgQcL0nhJBg\ncRWEX3/99fiXf/kXxOOUkheQUTdLn+VARp9JAa73NuRU0RaEjCraAAE8IdoAATwt2gApcSxH+cUv\nfoHJkydj0aJFUFXVvuMbq4CWmfrv8V6gdWHxY23zpt5M7ZGN0bInjLZJVOxhO5j2yMZo2RPU32/+\nEABg7S+245KVq0BcrPcA8OYqIDVT/z3eC7QtBFoVvV3+nB8x2u1V2jkAbUZ72Djfpuh3K7PdYpwf\nMdrmfKNGO12lnQeQMtpjxvmUMb7ZjhvnM2XzZVQgsbE4nzl/0mhny+zJGv4kjLYZwCeM+cy2Zpw3\nv/Rpzm+OV5DAiGg/D2C5zfl1Dq7PAVhmtM0veZa3zzYe1xiPS2u0zf5rjcdzbdqmfUts2ub850CX\nLKw32omy9jnGoxmcn1Wjvdh4NL/geWaNttn/SePxXTXa7zQeNxiPZ9Rom/2fMh5Pt2mbgfhiB+0s\nil/mPM14rNU27VkE/Q/gOUsbFdrmfAuhvx4bLW04aD9vPJ5qPP5/ALYDmGK0V0E0Mc3h54yf+9zn\n8IMf/ADJZBIjIyMYGBjAX/3VX+H73/9+oc/DDz+MlX8no36MENLorHr/KC5ZuQ4rVnANc7LeA8aa\nf12F58tO7+xXej9R44c9X9RTN8JJ+ODECbcp5Pwa0+0T7NTOIPwJevygbQ5rDudz/f73ceHrvePP\nGe+66y7s2rULO3bswE9+8hOcd9554xZkQgghjQ/Xe0IICZ66M8fHYk6+bS0BQ6p8WSTosxzI6DOp\nSNX13s1dJOhMJmFkShlTi3KWoIlEkSAV9hlhmrVQ0DoUJStRIehsIk+hKEtpVNw+R7mgDHFMXX8d\ny5Ytw7I5d9rqAAAgAElEQVRly2p3JIQQ0tBwvSeEkGDg1969IuNOIX2WAxl9JqQWYe2CRwZFtAEC\niNoueBg0+i54Y9KInxMRQgiJCpWK9TS67KT8zhiZQkE+ELoNXgoFkWAJs0hQGHO4HV883An3ioy5\nlOmzHMjoMyG1MNMeSoMq2gABrK3dpenYULsL8R0G4YQQQgghhIQM5ShekVE3S5/lQEafiXtq3UUa\nRXZS7VprP7Mwj5/45adffUqOKzadgiIKGVeW1+7iGbeyCye4lWZYOad2l8AIUxZjHV98dhTuhBNC\nCCGEEBIyDMK9IqNulj7LgYw+E1ILs1S9NKiiDRDAGtEGCOBJ0QZICeUohBBC6idZ9gi4l0JEQXbi\ndPwEKt85GzFTih1WO8fgbLsuVH+Clqwk4Z9EpFGwe2MHna1EJKOiDeBOuGdk1M3SZzmQ0WdCatGm\niLYgXOKKYANEIGNxqjNFGyAlDMIJIYQQQggJmah/VhB9hlT5dgzpsxzI6DNxj9/FeqIsawH0POHm\n30WUpTN+SV9yKpBQPAzgkx2u8VIkSIV8lUKfAHBWiPOJyogSLbgTTgghhBBCSMgwCPeKjDuF9FkO\nZPSZkFrI9nfh1y54Q6GINkAAYe6CE5Po7tETQgiJPrWyowQtL6lll9drq10fBdmJF/y0IZBCQWES\nhSJBYRC1IkFyw51wr8iYS5k+y4GMPhNSi0FVtAXhklFFWyAAVbQBAlgv2gApYRBOCCGEEEJIyPBz\nA6/Ipg8E6LMsyOgzcY+b7ChBSFPCkLtY+yWVKh1dzO22j7DxFZcXeMStrYHIVxSb404kK0BjhlZR\nzI3enBlRrHAnnBBCCCGEkJBhEO4VGXWz9FkOZPSZuGcM+oaVhtJUy83KYVW0BeEypoq2QACqaAME\nsE60AVLSGPv1hBBCookGIGf8HkNxaydutMPMfBKGNCUF/wsUOUHU+DnLuTCyxgRB6DZ4KRQkiiT8\ny5YSZTK1u4QIg3CvyKibpc9yIKPPxD1p6IFaDnosYQ144pYfp3LaqNOjiLYgXNKKaAsEoIg2QADn\nijZAShiEE0IIqZ+k8aMByEMPxrOWdt7oF7N5JIQQSWEQ7pUhVb4dQ/osBzL6TNxjdxfJQw/Gx1Dc\nJYfxaAbg5i65KHmJk2vLzx1SgV7FZkAXc3u5NszxB1WgVXE5SQB2BN2n5LiKcHfDo1AoaA2ApQHP\nwUJB5TSexYQQQqJPHLp+Oo6ibtwqWzF3ys2+5g8hhEgCg3CvyLhTSJ/lQEafSTCYX9C0ylYyxmO5\nbMXsH1XZSq1d8GYjiF3wyKOINkAAQe+Ck0owCCeEEBIeMQAJlMpT8igNxK3pDq0BOSGENBEMwr0i\no26WPsuBjD4T97RWOFZvpUs72YqpI6+UbSXoqprl5/apQJ/ifdyoab/t+gyrQJsS7BxRwGrnmArE\nler9I5n20EtI9xiiWTWzuWEQTgghJBqUy1ZMyUol2YoZlFt3zAkhpIFgEO4VGXcK6bMcyOgziQ7W\nnW9gvGzFWiTI7B+GjtzcBZcFu13wZiauCDZABNwFFwGDcEIIIfXjpnqkX8eryVYAPXBvQVG24lel\nznpsjfK1TnB6bRSkM1GUvoRqRyNW6pQbJoTyypAq2oLwoc9yIKPPpDEwZStpAG3Q/xFoQTEGseYo\nH0Nx59yPmOOA6sMgDYSM60BOFW2BAFTRBkgJd8IJIYQ0Lma2lQSKGvFy2QrAbCuEkMjBINwrMupm\n6bMcyOgzcU+y7BEIV5pSyRazTy3Zihm4x1GqL69WMXOKEoytbq61I4hre5TKffycw20fLziyQXHQ\nx8E4TvsJk85Y/xtdbtOnGcLEICp1+kMzPLuEEELIeJqpSBAhpOmgJtwrMurl6LMcyOgzaV5M2UoS\nQMr4SaL0LlhJylKuI9+vBm1ptBhURVsQPhlVtAUCUEUbICXcCSeEEFI/IrKj2N25gigSBJTKVlLw\nx2c46BOFbCrDcB8pRCFji5fx8wg3OnJra+QyrjCUrBc+c16RUTdLn+VARp+JnLgpEtSr6EGQ+SXQ\nZpetdCmiLQiflCLaAgEoog2QEgbhhBBCiInTIkE5S3/qyAkhdcAg3CtDqnw7hvRZDmT0mbhHRHYU\nOOjj51xW2cqbKjBRsS8SFIeevzxWdm21+ZwgSpoypBYzpJT3aXTZid21oyqQVuqzoR47gsC1DSrq\n3w13+t8nCwWVwyCcEEIIcYL55c40ijvk5q64dbfc7GtKVsw2IYRYYBDuFRl3CumzHMjoMyG1MPOE\nW4sEAaU6cqtsxaRRZSvWPOGyYO6CS4Ui2gApYRBOCCGkfsLKjgIHfYIqBuRWkpBB9WwrceifzMeh\nB+SiMp/4JZXxen2jy1rCtsOvPkJlM8y6AjBPuHdkzKVMn+VARp8JqcVbau0+ZraVNIA246cFxbgj\nDz0AGjN+7HKSR4FDqmgLwmdEFW2BAFTRBkhJ8/+bQQghhIjClKGkUNSIl8tWgFLteCPJVQghdcMg\n3Csy6mbpsxzI6DNxTyU5ipUgjoedicV6bqbin31uigTFyq51O1clnFx7lFL5uNdxoyw76VTqv9ZN\nP9GU2KnU7h+6L80vWWls6wkhhJBGpbxIUB7FL3iWFwmy5i+XoUgQIRJATbhXZNTN0mc5kNFnQmrx\nhhrMuGa2lSR06UrK+N1aNCiH8dU8g9aRv60GPEEEGVZFWxA+eVW0BVLCnXBCCCH1I6JYj8jsKCmE\nlxHGWiSoVraVoIoE2fnrdFxRmVyC8tmP8Z1eH2ZWlxyK6Ta9EEnJSnSLBDEI94qMuln6LAcy+kxI\nLY5Rwp+zXLaiQQ92wigSNFHxOEADIuPal1BEWyAlDMIJIYSQRsGabQVo3iJBhEgAg3CvDKny/ddM\nn+VARp+Je1orHMva/B41qYnbIkEAsEMFpiti7YNNnyCKBO1XixlSqmVHEVUoKIhrB9VihpSoyE68\n4GR8TQValOp9/PRFWNaYaP0nyiCcEEIIaQYqZVvJoZgOsVy2UumREBIajrOjjIyM4F3vehcWLlyI\nuXPn4rOf/WyQdjUOMu4U0mc5kNFnUoBrvg3mLnjUMbOtpGCfbaVS4aDy761Z84TLgl2e8GbG3AUn\noeJ4J7y1tRWPPvoo2tvbkc1msWTJEqxbtw5LliwJ0j5CCCECcLzmu8kUggY8Xn4uahIZUUWC3MxX\niaClOaKKBIUxhyhZi5+4tTXq/tSJqzzh7e3tAICxsTHkcjlMmDAhEKMaChlzKdNnOZDRZ1IC1/wK\nvKaKtsA7pmwlDaDN+EmgGHDnoQc9Y9DzomdR3CmXgcOqaAvCZ0wVbYGUuArC8/k8Fi5ciClTpmD5\n8uWYO3duUHYRQggRDNd8CTBTGkatSBAhEuDqi5nxeBwbN25Ef38/3v3ud0NVVSiKUtrpjVVAy0zj\ngl6gdWFRW2rurDVb2yQq9rDtf7tDiZY9YbTNY1GxJ4j2yEYgfwgAsPYX23HJylUgRRyt+d9dBUya\nqQdn7b3AjIXAiUafzar+eLLRfsloz1H0u88fjfYJxvktRvsko/2y0T7R6P+K0Z5lnN9qtGcbbet4\nSQDbjPZM4/x2o3280baOlwTwqtE+1ji/w2gfZ2mbVS0BYLdl/CyKu+QzjP6vqXoAa473hmX8LIBd\nRtvUme8y+pu5yN8yzpttc76pRvtPRvtoo/260X6H4Y8532Tj/JtGe1qF8ZKW+Uwd+B5Vz6aShG7X\nvrLzB1U9iJ9iXL/XOD/BOG/2n1Tmj3n9fqPda7QPGG0zN3m/pZ015rOOf1DV7eoz2mZ1zz7DHrPd\nZZw/ZDNfT9l8kyztHIBuo33EON9t2GPumJvjV2rnUNSYDxrnzXatNWrAaLeXzW9t5wC0GW2z0qfZ\nHjHarTZtc760AiQVYLTs/Kgxfspom7vlKUV/fs123DifMdqFLCtGO+mwnTPaCZu2WdUzbtM2x4PR\nRnn73wFsBDDTaJ8L0cQ0Tavr/9k77rgDbW1tuPHGGwvHHn74Yaz8uxW+GUcIIWGx6v2juGTlOqxY\nwTWsErZr/n7j+bJLS4gmOi56bpE2VCoSZMXcUY8b5ytlWwnT5yhcG9TcURjfLxvCsMOG3//+YeHr\nvWM5yv79+3HokL5jNDw8jN/97ndYtGhRYIY1DDLqZumzHMjoMynANd+GnapoC8Jlj6o/mkF2CrqG\nvB3NK1sxd8RlwtwFJ6HiWI7y5ptv4rLLLkM+n0c+n8ell14q/D8IQgghweB4zU+WPQLR2MH2MxOJ\n9VwK7jLCiMyC4sfxBOxtajEeNQCjqF4kKA79i6DmDnkUMp/YHa/ms5t5vV4fdjYVvyvH+Jk1xq8+\nEcuy4vgpP+WUU/Dss88GaUtjImMuZfosBzL6TApwzbdhliLagnAx9efVKC8SVC5bKS8SFEcxQI9i\nkSBTMy4Tpg6chAorZhJCCCHEH2LGT8poW+UppkQlV6E/EM2AnJAAYRDuFWv2CFmgz3Igo8/EPa0V\njoUpF3ErTfD6ZcxtajGbS5jyGlFFgvaqerYVP+zLoHqRoDh0iUt5kaB65vIiTdmnFjOuuB3TT5uc\n4Nf4w2oxq0oQ40eFiEW9ETOHEEIIIU2JnWwla/xeSbZSKSAnpElgEO4VGXcK6bMcyOgzIbUwd8Fl\nwW4X3CtW2YqpEa8kW8mV9QeCD8rNXXCZqLQLTgKHQTghhJD6qSVHCVouErTExc+xGvE4bPoEaYc1\nAK+WbSVe4dpacznB65hhZnJxcq0TwpCdhJkFpUFwVbaeVEDGXMr0WQ5k9JmQWphVOmXBrKoZJqZs\nJQ09J3kbilpxQN8pzwIYM36yKO6e+4FZSVMmuN4LgTvhhBBCCIkm5dlWNOiBdxRkK4R4hEG4V2TU\nzdJnOZDRZ+IeN4Vr4PK4qIwo1T7iPkWpfU3UJCVeJCgzFfs+ojLcBF0kaIrij51+XO9mTC/X9ijB\njl9vv3ppEMkKg3BCCCGENB7NViSISAc14V6RUUdFn+VARp8JqcUWVbQF4bJLFW2BM8wgOwVdQ56C\nHpybUY4pWynPwFJJR75fDdjYCDKoirZASrgTTgghpH4qyVGs+CU7cTuml7mqyS5SCFaCE7Xjdv4C\n0cjSEkSRILevcbX3i5UgpDl+XTsMdxGh1yJGQcwRYdmJHQzCvSKjbpY+y4GMPhNSi5MV0RaEywxF\ntAXecVskaIKit2WSrHQpoi2QEgbhhBBCCJGDKBcJItLBINwrQ6p8O4b0WQ5k9Jm4x285ittrnYzp\nRSpSfm6TCsxT6puvEY9vU4sZUsLOjhLmXNYiQW+p+m54PUWCqs3nBFHSlCG1mCElzCJBYcwRYckK\ng3BCCCGEEFO20gL9y51Osq2Yu+ncJSd1wCDcKzLuFNJnOZDRZ0JqYe6Cy4I1T7gsmHnCrUWC8tC/\n4NmsshVrnnASGgzCCSGE1E+r8Vl91ibyCFqOEnSRoGrjRi0jStjFc5pBglLruBVr1U4nRYKqyVbC\nzHzi9lo7mkF2ErGol3nCvSJjLmX6LAcy+kxILV5SRVsQLq+qoi0In7fU6udN2UoaumylDcUUh4C+\nU54FMGb8ZFHcPY8qh1TRFkhJxP4nIIQQQghpEKzZVgA90B5D88pWiK8wCPeKjLpZ+iwHMvpM3NM6\nqj9mE5XPZ21uM1b5iqjMKvV8TL9YCXa+IGQUXo7PVWr3D2puURIUOx280+e9xXh0KltJo3JAHmZB\nn6MU/8es9n4JU3YSsYwoVhiEE0IIIYT4jV2RoFrZVqy75aSpoSbcKzLqZumzHMjoMyG1eEEVbUG4\nbFNFWxA+b6j+j2kG2SnoGvIU9ODcjMJM2UoGupwlg9Jd86B5Ww1pImKFO+GEEELqpqV1DACQs5Gj\n5LO5isdL5CtOJCslx21+t+vj17WAHjy1VjgedMYWL3N5OZ6wtMMu1iPquPU1rie7i9trMihKVkzZ\nSt5yPoFiEB+DdylIJdz6DAd9qj0vbq9vcNmJHQzCvSKjbpY+y4GMPhNSi4WKaAvCZbYi2oLwOUYJ\nd75aspVcWV+rbMUvJio+DkacwiCcEEIIISQKlGdbMYNwa5pDZltpGhiEe2VIlW/HkD7LgYw+E9ek\nzewoFrIWqUnORmpila84kqyUHLeMGWaRIADYoALvVMb3C6JQUBSKBG1SgZOU2tdETVLipUjQDhWY\nrtQ3pp/2lWPukI/B/yJB+9VihpSg5CGiCgVFWLLCIJwQQgghJOrEoKc/jMFdthUN3CWPKAzCvSLj\nTiF9lgMZfSakFuYuuCzY7YI3M+YueJTxu0iQNU84CQ0G4YQQQuomZWRHsZIokaNUlppkbaQmVvmK\no4wrYRYJKj8XZqGgqGVQqXWukY97lbUEIZFxcm2UiwQFNa5XmwTDPOFekTGXMn2WAxl9JqQWT6ui\nLQiXzapoC8LnNVW0Bd4ws62koeckb4MeoJsRXx5FbfmY8fseNbyc5KRAxP4nIIQQQgghvlAuW8mg\nVD9uylbMoDxedi0JFAbhXpFRN0uf5UBGn4lrJib2I4ckRpBC3khenEtYbi3p4q+5XFE6krCVoxSl\nJr5JVqx4KRIEAEsUSz+bPkFkZhElcVmk2PePWoYTv44fr9Q/jte54aCPX8etRYImKWKKBDm1NQhp\nSgRgEE4IIaRuksgjiTGkMYYc4sggiVGkkSmkcSCERJIoFAmSHGrCvSKjbpY+y4GMPhPXDKMVGSSR\nRwwJ5NGKMfTgMCbgbXThMNIYRaxke63B2aCKtiBcNqmiLQifnapoC8Jnr6pHhCnoGvJ243czSjRl\nKxkUs7BYv+xJ6oI74YQQQuomi6TxE0cCObQgixZkkUQOaWOHXDP6jcTSGNXSyMEmowkhJBqU5yQv\nz0NeHoBbUyASxzAI94qMuln6LAcy+kxck4KeojBhBNYa4hhGG2LIG+F5rhicx7PowhByiGMskcIY\nWsbJVnJJd7pxK4FX6gSApctQiD7CrNYZtPbbbsxTlcrHvc7n1/EgdNNzlPrHqfeaeq/16/jRSmV7\nyq81A3JTS14elFurduZQGpiHmX6wQfThDMIJIYT4joY4MkghY7SSyCFuBOMJ5NGGEbRhBHnEkEEL\nxqAH5eAuOSHRJQb9T9T8M/VaJEhyqAn3ioy6WfosBzL6TAIihiySOIJ29KMLA+jAEbQiiwTi0JDG\nGLowiAl4G33xt9EeG0KisO0WMf6girYgXF5SRVsQPq+qoi0In7fU+q4zg/IW6Bpyaz5yoFTKYu6c\nR/DPWhTcCSeEEFI3aYwCALI2O9g5y20mUdInhjGkkEEeMWOnPIEcUrEMUrGMLltJ6NlWMmjBqKW8\nn1WyYiXoSp0AkE9lgNZRY7AQq3WKkrKkALQGPJ+fVTz9OG712e04XucWlaLR7nWud8xK2Vasx62y\nFetueZhVNSNAxMxpQGTUzdJnOZDRZxI6GuLIIlGQrcSgGUpxXbaSwBhaMYYOHCnIVobRCk3UB7ln\nLxUzrygWKKItCJ8TFNEWhM87FH/HKy8SVEu2YgbkGqSSrTAIJ4QQEhFihZ1vQCt8oTOFDBLIF7Kt\ndMYH9d1xLWXJtiLRnZuQRsOqJTd3w6075NbMK2Z/CTKuMAj3ypAq344hfZYDGX0mrjGzo6Qsx6wp\nCHOwkYWU9CneisrH0RDHKNLII1bMthLLIQWLbMUsEpSwFAkKoFInAGTUJxBfcq5xTYjVOoOQozi5\n9mkVWKi4GzdouUjQMo3NKjBbqW+coGwK+vhuFThGCW4uu3O1ZCtmkaAUikF5g2Q+cQKDcEIIIZGn\nUraVJLJIIFciWynPtiJMtkIIqU0l2YoZkOdQWbZivbbBYRDuFRl3CumzHMjoM2kQYsKKBJm74NJg\ntwvezJi74DJh7oKLxiwS1AK9Omcl2Up5/waWrTAIJ4QQUjftOAKgVILiNlOKW8mKlTCLBAECCwVZ\nx4xCkSAg+EJBYUpc3B73s1iPqONw0MfPubxkODED8mqylSSK2Vasf14RlqzwczqvyJhLmT7LgYw+\nk4bHlK0Mow2D6MAwWjGKFuQRKxQJ6sFhTMDb6MJhpDGK2LjtNXuya9YHaH0EeVYVbUH4bFFFWxA+\nu1TRFlTHqg1vA9Bu/G5GseaOeQbFLCxmgB5huBNOCCGkSTFlK2mY2VaSyCOFsXGylUzcmm3F3E4j\nhEQSU7YSQ2lBoPIdcmv/CP5JMwj3ioy6WfosBzL6TFxjZkexylH8ypRSWtxnrOKY7osEwVWRoKwh\naimMdcHpJbYUjgdcKKhEvhJmkaCzldp9nI7bKBlUTlXc9a/Hvqgdt+rgw8yOUn7czj6n87kpEhQB\nGIQTQgiRDqdFgvQaI6lCthX48OVOQkhAuC0SJJiI/C/QwMiom6XPciCjz0RS9LSGR9COfnRhAB0Y\ngS5LiQFIYwxdGMQEvI3WNb9Fe2wIicK2W5PztCragvDZrIq2IHxeU0VbEAxmkaAW6IF5CxAltRl3\nwgkhhNRNGqPjjjnJamKVlHjJlBJUkaC8USQoViZbScay6IgPlRQJyqAFo4k0Cnf2AAoFuZasWPFS\nJCgFoNXsU7lL1XN+ZWZxMqZfEhc7n5u5WE/C0g47O4qTPkFJZATDINwrMupm6bMcyOgzIWWUy1aS\nyhJkkEWiTLbSgSPNWSToDEW0BeEzTxFtQfjMVERbICWuVoldu3Zh+fLlmDdvHubPn4+vfe1rQdlF\nCCFEIFzvK6FnWxlBK4bQgQF0YNiQrcShlchWetCPNgzLI1shhLjG1U54S0sLvvrVr2LhwoUYHBzE\naaedhvPPPx8nn3xyUPZFnyFVvh1D+iwHMvpMCjhd79sKxXr8z2piJ1nxK1OKE8lK+fXD6ga0KWcU\n5tYM2UoesfFFgpBFR+JIQbYymmhFBkmUC1KdFAoSViRo3TrgTMXoU0VIG2ahoKCLBG1UgfmK97nq\nuSbozC92x19XgVlKcOOXn7MShWJFgnC1Ez516lQsXLgQANDZ2YmTTz4Zb7zxRiCGEUIIEQfXe3dU\nKhKUQbJQJKgVY+jBQN1FggghzUfd/xPs3LkTzz33HN71rnf5aU/jIeNOIX2WAxl9JhXhel/E3AWv\njlkkKIks4iU74+VFgrJIYiSWNooERTD9obkLLhPmLrhMzFJEWyAldQXhg4ODuOiii3D33Xejs7Oz\n9OQbq4CWmfrv8V6gdWHxZm6mPGObbbbZjkJ7ZCOQPwQAWPuL7bhk5SqQUqqu9wA2rroXHTOPAgC0\n9Lajb+GxmKjMBwDsUzcjhziOUuYCAPaoWwAARynzkAKwX90EAOhTFgAADqgvIY84JiinAAAOqi8C\nACYopyCLBN422t3KIgDAIfUF5BBHr3IqAOCI+jwAoFc5FTkk0K9uBAB0KqcBAAbU50quf1t9AQDQ\npSxCDkkMqs8CANqU03Xf1WdKrh9Un0EecXQoi43x9P7tRv8j6lMAgLRyFgBduqIhgaRyBjTEMaBu\nBJBHp7IYceQxoj6JGIAuZTG6MITD6jPIIoGkcg6ySGBYfRoAkFLOQi6ZQEZ9XH+elbMBABn1cSRy\nCSSX6e3RR9YAAJJLzwEAZNesBwAkzl4KAMitXYcEgMS5S4zrnwAAxJeci1w2AW29fn3sHL2/tn4N\ntFwCMK7H2nX641nL9McnHiu2s0ngD6reNgP3P6hALga8y2g/bpw3v+y5wWi/02g/ZbRPt1wPAIsV\nXVLwjNE+zTj/jKrnezavf9YyXhbAc0b7FOP8RqO90HI9UCzO87zRNr+Y+YLRXmC0y8d70WifbLRf\nMtpzjPYmm/HmKnr09bLRPtE4b6ZGrDReEsAfjfYJxvktRvsko10+3itGe5bR3mq0zcI85eNtM9rm\nlzS3G+3jbcZ71Wgfa7R3GO3jbMbbaWlnUUyLOMM4/5qqv57meG9Yxs8C2GW0pxvndxn9jzHabxnn\njzH6/8loH22cf/7fgX0bga6ZevuScyGamKZprr4xkslkcOGFF+LP//zPcd1115Wce/jhh7Hy71b4\namDkkVE3S5/lQDKfV71/FJesXIcVKyRbw6pQbb0H9DV/9Yrd447b6bSdpCu02w22G8eufxBjAnog\nbwbhbnXt4+3TUx/GjZ3yuOULnOVFgrK5lsrjlGjCbfz0kvZwzfpiEG6nGweCqdYZhJ7cybXPqsXA\n2+1c9cwXhePb1GIwHvS8Yczh4PjvL35Y+Hrvaidc0zRcccUVmDt3bsUFmRBCSHPA9T4MTNlKGoBW\nkK2kkEEC+RLZSibeglEtZZGtRKTaCCGkblwF4evXr8d///d/Y8GCBVi0SP8474tf/CL+7M/+LBDj\nGgKJdgoL0Gc5kNFnUsDpel8pO4p199e+mE6wWU38KhJUPq4undGzswRVKKhSkaBULINULBN+kaDz\nziz4a7dbDgRUKEjUTrhdbnQnGUrqmU9URhTrcVNCE9T4fo7VRNlRXJmzZMkS5PP8NjchhDQ7XO/F\nMq5IEHJIylQkiBAJ4F+rV8wve8kEfZYDGX0mpAbmlzfDZXyRoJGQigTl1631bn6jYX6BUybML22S\nUInYxjwhhJBGoh3DAJxJTdx+MdOtrCOIIkHl46YxgvaCBEecpCYfUpEgpDJIto5WtjXoQkHWMZ1I\nVuyOu5WBpAC0VujjpHBPPTbVU/jG7+NWn+36+1msR2IJipUIm9YgyKibpc9yIKPPhNSgR1ko2oQS\nzCJB42UruRLZSh6xumQrZrpDqTBTHsqEmeaQhAqDcEIIIaQpaKIiQYRIAINwr0iWSxkAfZYFGX0m\nrklDlyq4lXl4yd3tVnZSLRNJ8Xdn2VEOqC+j1ygu5CwLjBhJjTmOhjjGkEIGeUPEki8G5/FsMdtK\nQs+2kjXOmoyse7JQHKicRIkcxcZPLznKrWM6kayUHPeQn/wPql4gqJ5ry8+FKS/xItnYqhaLBAVt\ns59j+WmTABiEE0IIIU2Onm0lXrFIkFW2Ul4kiBASHAzCvSLjTiF9lgMZfSakBuYueGMzvkhQClm0\nVAer85UAACAASURBVCoSdN7JGNWG5CoSZO6Cy4S5C05ChUE4IYSQummrkR0laDlG0EWCym0Ks1CQ\nX5KaIIoEZZFALmHZKQ+iUJBbyYoVUUWCvF7vl+wkzLlYrKdumCfcKzLmUqbPciCjz4TU4KD6omgT\nAsXMtjKMNgyiAwfVF5BBEnkACeTRijF0YQi9GEAXDiONUcTQZEWdNqiiLQifTapoC6QkYv8TEEII\nISQaxJBDAiNoBaBBA2xlK1kkCzryHOKQQrZCiEcYhHtFRt0sfZYDGX0mrqlVuMYvuYgzOUawRYIA\n4GjleKDgc7CFgvzOlKIfdylZURYV5rYWCSqXrRSKBAHIJfSc5Bm0YDSRRqWA3EmhICcZVwIpErR0\nGQrVRt0WCSo/FzXZid2Ypyr+z+X1miBkMcyOQgghhJBGRs+2kqhQJCiLBLRCtpUOHKmrSBAhMsC/\nBq/IqJulz3Igo8+E1GC/+rJoE0JlWN3goJeebWUErRhCBwbQgRGkkUMccWhIYwxdGMQEvI0e9KMN\nw0ggi8Juc9T4gyragvB5SRVtgZRwJ5wQQkjdpIxiPVacFOjxJhepX+LhtkhQ+TUtyCBdkIYEWyjI\nm6zHn6w0WWRqFmSqZJ9VtpIwCgTFkS/KVhJHitlWEi3G2LHScZKV5wu8SFAqA7Qa72u3RYIAb4WC\nRElZUgBaA54rCBkJi/VIjoy6WfosBzL6TEgNJisnizYhVDqUxZ6uN4sEZY3yQEXZSm5ckaAMWjCK\ntHjZytlLxc0tigWKaAukhEE4IYQQQkLALBKURBbxwhc6U0a2lRQySCFTyLYyEkvLVSSISAeDcK8M\nqfLtGNJnOZDRZ+Ka9orFeuqXV7iViwRdJKh83N3qdkxVTqxqh1+FgqJQJKhffQGdyjsBlPpVPq6X\nQkFW2UrckK60IIuWeBZdGEIeMYwZ2VbCKBKUUZ9AfMm5Rn+XRYIAcYWCvFz7tAosVJyP6UUq4vQa\nCYr1RMwcQgghhMiGKVvRA3utRLYSh4ZWi2xFz7TCbCuk8WEQ7hUZdwrpsxzI6DMhNTB3wWXB3AUP\nl6JsRQ/P9R3yVEhFgsxdcKmotAtOAodBOCGEkLpxU6zHS5Edt4Vr/JSKRKFQkF/PS6kN9RcJcjqu\nn5Ka2kWCjGwrAosE6ec8FAqyjuu2UFCUiwQ5HVeCjChW+DmOV2TMpUyf5UBGnwmpwZ/UbaJNCJV+\ndaNoE0rQEEcGKQyjDYPowDBakUESeQAJ5NGKMXRhCBPwNrpwGGmMIoa8qzmya9YHY3yUeVYVbYGU\ncCecEEIIIQ1IqWxFA0qyrVSSrQyjldlWSGRgEO4VGXWz9FkOZPSZuGYCDhiBTTFjhZMiO1bcZj7x\nUqDHrVSkvD1LmQ7UKF4TROYXL3IcLwV9Usrcwnzl9gddKKie11zzoUhQ4oLTUZ4hB3BWJAjwWCjI\nOq7bQkFeigSdrdR/rRMpi9dx3c7nVuIiCAbhhBBC6mYGdiGLBAbRicPowiA6bINNQsKiIYsEEeng\nu80rMupm6bMcyOgzcc0YWpBEDr3ox3TsxknYguOwAxOxH6kKu4mNzi71VdEmhMoh9QXRJviALlsZ\nQSv60YUBdGAYaeQQRwxAChl0YRAT8DZ60I/4Y48ggSwATbTh4fG0KtoCKeFOOCGEkLp5C1OQRBat\nGEU7jiCNUXRhEF0YBPAmRpHCIDowiE4MohMVM1Y4kK84k6z4XySo/Po0RtFWsUBReHKMMIsEtWAM\naUN+U07QhYL8ktS4LRLUHh9BR+JgXUWCAG+FglxLVqx4KRKUAtBq9qncxVNWFj/HDSKDiiAYhHtF\nRt0sfZYDGX0mdRBDFi3oRyv60YM4ckhjFB0YQjuGC1+Om4i3kUUCh9FphOgdyDegbGWGMlO0CaEy\nQTlFtAmBUqlIUEo5E3lk5SoSdIYi2gIpYRBOCCHEN/JIGEF2FwANKYwZe+BDSCGDPvSjD/3IAziC\nDhxGJ/rRi7FxRdEJCRuxRYKIfDAI98qQKt+OIX2WAxl9Jq5xUqxHD8o7EUce7RguyFY6MYRODGEa\n9mAULTiCDgygC8NoRXnGCi+SFa8Fdqwyih3qdhynTHd8vRe5SBSKBL2lbsFRytyKY4oqFBR0kaBh\ndQPalDMK89YuEhRDxk62YrUv4EJBnooErVsHnKkYfQIoElTP9X7JTqplbBFMxMwhhBDSnMSQQQr9\nSKEfPdCgB/BF2UoGaRxCHw4hiwSG0IEBdDesbIU0F7psJYGM0SpmW8kiAa0k20pTy1aIrzAI94qM\nO4X0WQ5k9JmERrlspQ3D6MARtOMIUsigBwPowUBBttKPbgygGxnBshVzF1wWzF1wmTB3we1xXyQo\n8rIVcxechAqDcEIIIXXTVpCj1C8dMRlCOwbQhSSyaMMw2jBSIls5Gm9iFC2FTCthFAlyYne16/2T\ni/hjgxUvRYKq2RREVhNnsp4IFwlCmWwloRcJGjdWsvJ8TgoFRbpIULVzTuQsQUhZIgA/J/GKjLmU\n6bMcyOgziQB6tpXD6MabmIbXMR17cRQOowM5xJFGBhPxNmZgF07Aq3gH/oRuDCBuE4D5zXZ1dyjz\nRIW96mbRJoTOkPp03ddqRoGgUaQxjFYMoxUZJJEHkDCyrXRhCL0YQAeOIIUxxJD3z/h6eXyNaAuk\nhDvhhBBCIkseCQyhEwPogSlbacNwxWwrer8uDKAbObSJNp1IT8xQjVeWraSQQQoZtGO4IFvRP90p\n7pKT5oZBuFdk1M3SZzmQ0WfimvYahWucSj4qHbcbx8y2Ylck6GgfiwSVz32KMhGo6LP/hYLcXhuE\nHGOGMgOoIDkq7xdEoSC3/tjZ5nbMPmUBzOfDrfTFiX16wB2rLFtJHEHe0JyPImWMFUMuYRnHplCQ\npyJB550J0+dAigQBzrKuBFEoKMKFexiEE0IIaUDkKhJEmguzSFAWSeQQt2RbySEOrbBLrgHIoAWj\nSDPbShPCV9MrMupm6bMcyOgzaVjMbCt7MBU7MBOv4xgcRC/G0IIkcuhDP6ZjN07CFszAa5iAA0iV\nfdHQCVvVNwOwPrq8pb4i2oTQGVSfDXlGfed7BK0YQjuG0IZRI5tKDEAKGXRhEBPwNnrQjzYMI4Es\nAM03C/Lr1vo2FnEOd8IJIYTUjZNiPcXfa0tQ3Eswgi0SVD5HGiOufPZSZMdt9o4gigSlMVpRcuT0\nerv+UclqUmlMJ6+x3ZjlY9UvqYmVZFuJG9IVa7aVPGIYS/hTJAipDJKto+Pt9KtIEOAs60oQhYLs\njg/aHA8RBuFekVE3S5/lQEafSRPivkhQP7oxZCNbmaNMCd8FgRytnCDahNDpURaKNqGAKVvR/xko\nLRIUN7Kt+FEkKLn0nEDsJ9VhEE4IIUQa3BYJOoxO9KMXY4KLBBFSXiQobuyQN3SRIMlhEO6VIVW+\nHUP6LAcy+kxc04XDAMo/XncnKXErQfFLsmJiFglqQRatFYoEWWUrj6sZHK+8A+WylSAKBUWhSNBO\n9TVMV2ZVtcGpHVa8FAoKukjQAfVl9CoLxl3rZ6YUPyU1fhQJGln3JFqUs8fN5VeRIL3tIOtKEIWC\nKEchhBBCokwxUDmEPsSRQ5uhI9eDcl22MgVDOAEjGEIHBtDNbCskElizrQAaYkBBtpKAhoRFtqK/\nz5MYQZzZVgTDINwrMu4U0mc5kNFnQgzMIkFD6EQO8YJsZYHSgmQF2Uo/unEY3U0nWzF3wWXC3AVv\nXNwXCYJyBnLQQNlKuDAIJ4QQQqoSw7CRXyWLOFIYQyeGCl/uNGUrwJsYQRr96Cl8uZMQscSQQwI5\nIwWiLlXR86kkDcmKWSQoq8UxpqUxquk5yRmQBw+DcK/IqJulz3Igo8/ENW0Vqik60yaL141bcVox\nc6M6gFOUCRhBG4bQWZCttBlheitG0Yq9mIK9hSJBh9E1LttKPSkXK/cPtlLnq+puzFBmVuwfZppB\nv9Ivltpf2Z596kZMUE4Z19+Jtr58bi/pCr3o2quPo0uvRpAuZFsZVf+ATmUxkjH9fVwoEpSwFAny\nUKkTcKYdD6Rap13awwjAIJwQQgipE1O2MoAemNlW2ozd8RQy6EM/+tBfkm3lMLqQQ5to04n0FLOt\njKAVMbQZrVyJbGV8thV+B8IvGIR7RcadQvosBzL6TEgNTlEmVDmry1YOowt7oSGFMXRgGJ04XCJb\nmYY9GEEaA+jGALpwGF2I6kf/5i64TFTaBW92WpUzkQcwhgSOIFGQrSSRK8hXCtlWEMdozCpbIfXC\nIJwQQkjdtA+NAAByyWKWBWuFPj0lmnE8ApIVK07T+HmRjugZyNsRRw6tGEW7oSPXZSv7MBn7CkWC\nBo2MK6Zsxcu8QVfqrHa9X9U6vVxrJcxKneXXl9rhTypGuzH9qdRpHUev2jmKVEmRoATyaI8XZStj\nicpFgqzrAOBctlKw1a9qnXZpDyMAc9N4ZUgVbUH40Gc5kNFnQmrwvHqoruvySOAwurAHU7EDM/En\nTMMh9CCDJJLIoQcDOBpv4iRswQy8hgk4gBZLQCaKHeou0SaEzn71ZdEmhM6wuqHK2VhBsqJ/HbkN\nw0gjhzhiANIYQxcGMQFvowf9aMMwEsgC0EKyvnHhTjghhBASKsVsK/sxEXHkClKVNhvZyiH0GNlW\noilbIbKglwUaQ6qQbSWBHFLFckAF2Uo2Xp5thZTDINwrMupm6bMcyOgzcU3rkP6oJfOFY9lE8fdc\nMmP53R/JipUw5CvW9plKCnCREcappGAEbRhBGzQA7RhGm1EkqJJsxVokKOhKnScpkwGM2trtxmf3\nchF3cgy//D9aOQFFWYi7zC2Af1lNvFTrdCupSSunwnyd3Upf9Gt0sYq1SFAyli/NtpLQVeYZJJG1\neFQuWynM4VO1TruMK1GAQTghhBASEfJIYBCdGCwrEtSOI0hJVCSINCLOigSNz7YSh6yf8LjShH/0\nox/FlClTcMop8n1z2BYZdbOy+JzdD+y9GdixEHj1FODQtwBNIo2bLK8zqQjX+8o8px4OcbaYIVk5\nCq9iJl7FDOzFURhCG2IAOjGEo/Em5mALTsQreAfeQAcG4acWd7u627exos6uB57Foxd8Bb887kY8\n84n7MLhjn2iTQmNIfdrnEWMwCwQNoAv96MIRtCJj7P3qkpUj6EM/JsYPoCt2GCmMQTYduaud8Msv\nvxx///d/j4985CNB2UNINMgNAK8vAca2FI+99TFg5Flg6jfF2UVISDhe7/v1h5jlbtJi/d36SbBF\nslIqX7FKVmD5XXzGlfLr0xhFu3Fd0IWCKo0TdpGgVoyhHcMV7Q+6UJAzuY8/coznv/oYnvz0A4X2\n9v94FLvvfwp/vuFz6DzuqHHz2slDytthZjXxUiRI37HWn48gigSZY2WMxIdVZStGn5FEazHbiodC\nQXaSlSjgaif83HPPRV9fX1C2NCYy6mZl8Ln/e6UBuMmh/wTGtodvjwhkeJ2JLVzvK7NYiUYperNI\nkDXbykH0YgwtSCKHPvTjWOz2nG1ltjItAOujRWZoFM/946/HHR/dP4iX/+U3AiwKn07lnSHONj7b\nyqghS4kBSCGDDgxLkW2FmnBCKjG8zuaEBgw/AaSOD9UcQgixp/mKBIXJ25vewlj/cMVze9dLsuki\nDDPbSgJjAPKIFbKsJI1MK9YiQWZWFj3bSuO/d/0Pwt9YBbTM1H+P9wKtC4s7aqbGtJnaIxuBiddF\nx54w2uaxqNgTRDv5DtiSnCbevjDaB/5djr/fvJ73ee0vtuOSlatA3LHqBmDmOwDEgd4uYOEcQDlL\nP6du0I8r7zLahuxUOVOXr6hPGO0lxvnHASQA5Ry9/egf8oXz2UQej63Vjy9ZrstX1qwBcokYli7T\nb8bqOv3xXCWObCKBdar+kfRZiv5Z9no1izwSOFvRb31rVX38s5UWZJHAE6q+U3yGopeU/4OqZ4s4\n3dj9flIdwaaNOVx2XTcAlPTPIoGnVD1ryjsV/fzT6hDyiOM0pRMA8Iw6CAA4TelEDgk8a7QXKD0A\ndL15DgksMq43+y9UepBDopCjfL4yEQDwgnoIOcRxiqJ/YrFRHQCgV/U8gnZsUIcRRwdOUzrQgSFs\nVvcjjiEsVkYxGfvwpDqMEbThBGUaBtCNTepBAMCJylQAwGZ1L3Zu7McF180BALys6hrpk4zzZvtE\nZSpySGKr+iaA4u75VvVN5BDHbEVfT7eobwEATlCORhaJgt58plGV81V1F/JI4DhlOgBgh6oHwMcp\n05FDAjvU1wEA05XjAAA71deQR6JQ1dM8f6xyHFIAXld3ADCznQC71B3IIY7pyizj+p0AgJ5ZE4BY\nrOJ3fpLpGNqNbDi71VcBANOU2cgigbfUVwAAk5S5AIC3VP3T06nKSYV2HnFMUfTn702j/2TlZOSQ\nwz51s3H9yQCAfepm5BDHUcZ4e4zxjlLmIYEEDqgvAQAmKvMBAAfUl5BHvFDhc5+R37zPaL+tvggA\n6FYWAQAOqS8ghzh6lVMBAIPG+R5lIfotecI7ldMAAAPqc8ghgS7j+sPqcwCALmURckhiUH0WANCm\nnG6M9wzyiKNDWQygqDM32wNG/3bldOSQLOQmb1POAKDnKs8jgRblDGTQgkPqRiSQR5fyTiSQxYjR\nv09ZDA3AgLoRY2hBXFkCDXGMGQtKSjkLuWQCGfVxAEB6ybkAgNGvrUbuhU2Iz9DfX1j+5xBNTNPc\nfdNs586deM973oMXX3xx3LmHH34YK/9uhW/GNQRDqnwf28vg8+hLwI5FALKlx1NzgOM2ATEJ6lzJ\n8DpbWPX+UVyych1WrJBsDatCtfUe0Nf8FRNX6g3rlo7194TNcQd9NMvvVllnmLrx8uufUDM4Q2mt\ncb0/1Tq9VMys3F8rZFvpwBBaLOubmW3lMDpxCL3IGIreTep+zFGmVPTFS/rBoJ8vtzY8+N778NqD\n44v0XPB/V2Lme+c7tsHp3F408Xbje0nj2K9uRI+y0Ncxy/HyfgE0xJFHElkkkUMClu+XoDzbSgI5\nyyJhl6Lwf9dtEr7eSxBJBIxEQUoBGXxOzweO/n9A8ujisbazgGN+KUcADsjxOhPiEjMAb0yK2VZe\nw7GFbCtH0FrItjINe3CykW1lKt7CaUoHmlGLW86K+z6EGe+Zq++IA0j1tuGcf39fIQBvdswAPLqY\nspV0SbYVswiQNdtKHw41TLYVV3KUD33oQ3jsscdw4MABTJ8+HV/4whdw+eWXB2UbIWLp+kug873A\n6AtAvAtIzRZtESGh4Xi9N7KjeNoJt+lvm3HFkikh6CJBldqF6z1kXXG7++3XbrkVt0WC+tFdkm0l\n6EJBXnZh3e66pvsSuOjnH8LArn4M7jmCifOmINnWgqzLQkWV2rVssstq4rZQUJSLBAHufbNSOZtM\nrFAkKIG8Ub0ziwTyaI/XLhIUBVwF4T/+8Y+DsqNxkewjewBy+RxLAq3v1H2WLQiX6XUm4+B6X5nH\n1QzOVpqvBLddkaDN6l6cpaTHFQkql600C93Te3Bw+yEk25rvNa7GIfUF9CoLRJtRJzHkkDAKVumy\nlbhRHKhakaAowOwohBBCCLEQM7KPt+NNxPEqutFpJJOzy7ZyCD0YQgeaIWMFaWRM2YqeRSWOvG22\nlSjAINwrMu4U0mc5kNFn4p5KchSrbNrDFzNtfx8p/hp0kSC9XRxshZIAoF8XdKGgICQrJX45GGex\n0gkgP65IUHsV2coAujFYViSo2nzufQ62SNCJyjSgQoEiJzZUs8OL1MSZRKReWQcwRTkJqCC9CaJI\nULVxgygUVKlIUNzyxU6RMAgnhBBSP9sBTALQB26CSoBZJGioTLbSjiNIIVNRtnIYXU0nWyGNSMys\n0Yn/n703j4+quv//n3dmsm8ESCCsIRBAEAgii1hhQNBqcf1YtYKCorWl/VT9tN/Wjapt9VN/re1H\nq11Q645abV2KO0KQRQUVKEtYhLBvIciShSwz5/fHnZnMJHOTO5nlTjLv5+NxH5m5c+4573Pnzvue\nnPs673e8LNhMkDAPUcQ/dnaiIH1ODBKxz0LobANWAh8DG4Aj0MoEWIfHG3s8UdjgiR0enKZoKzsp\n9EVbqSYtINrKYL5mIDvoySHSqSZeBkBG7PbED08kjpUGD0PaeYmPGQOZCRcEQRDaT0+gEv3p/S7P\nZge6oc+Q9wC80UxCjI5iWCbFRBmDejQDyYq/lMVfsgKBUVdSayG92iNHiXKM8mhLUMwcm8ppX7Ia\nM3HCm8tW0jzqcn/ZigubZxFoBtVkBMyShyNZCVWmYSTNSKUuaJ/Nnutw7AjnWH9CldGkUEear8/t\nl9AE2uBo9r79UWCM6jUjfzEb090K4suajkgi6malz4lBIvZZCJ3B6BObtcBRz1aFPiN+BNgEdAHy\ngQLo6JnSJ02y2oLYMsrZpV3HeWUrJ8khWJIgr2xFAdV+shUXaRG1vz14M3YmEt4snUJskUG4IAiC\nEB4akO3ZitDXLVZ4tmPAcc+2DUhDnx3vBXQHg8kuoVPRFG3lKN1IooE0asmkijROB422cpIsTnX0\n/9gEoQ1kEB4uiRhLWfqcGCRin4XQOen521z+kePZNPQB+DHgG4LLVnqgS1dSCDk6SrSTBEGgVGXl\nF+A8V38d7URB8ZAkaE1pDaOdWS3Kt3aMGUmBN0mQDRcp1JNGTQvZijfaSpUn4kqskgRtLT3IQGef\nFvWY/Z7Ck4uEJseIVP8rS7eR7zzD8y66SYLM2hSpSClG0pd4QAbhgiAIQvTwDrS7oYcCOEXTgPwU\nTbIV0GUrPdEH5Vkxt1SwAP8kQaBIpj6obKWAg506SZCQmMggPFwScaZQ+pwYJGKfhejiL1sZij4r\nXoGuI6+kSbayBV220hNdR96duLlbeWfBEwXvLHhsCJSt2HB5pCrGspVoJAkKNgve2WmaBRdiSZy4\nNUEQBKFD4k3WYyT/MErc480LkoM+S+5CH4B/gz5TXguUezb/aCvdgfQQ2wpHstL8fQwTBcV7xJVo\nJwpy4fDJVhSQTi1pQZME2TyLQK1PEtT68ZGRy0RKjhHLJEGt2RROVJNQEwW1Zp8VSJzwcEnEWMrS\n58QgEfssWId3oD0EmACUAIVAJvoA3RtpZRnwKXqSoJPEPOR06eexbc9qviitttoEoEm2UkE+5RSy\nnwKOk0M9SThwk8NJ+rKPIWylP7vpyjGS2qn/3V56MMLWxz+HSrdZbUJCIjPhgiAIQnzhla10RY+2\nchp9dry1aCs9gN5ItJWEoEm20oiNZOrJpJoMqkmn1k+2QkC0lZqARyiCYD0yCA+XRNTNSp8Tg0Ts\nsxA6XjmKUTKdOr/XYUQs8S3udKHPgB8jNkmCmr13nglUBykXhURB0Y64YkayMslphxCS9QQr13bb\nZiQYrR/rnyRIj7LS/iRBo5w5QftsJjpIqHaDdXIR/3qKnH3Rf0yhH+tPa/KbaMtoAtsKfo7sBuWt\nQgbhgiAIQsfBjq4L705CJQkSzOGVrZxoliQonWqS4zxJkJB4iCY8XBJRNyt9TgwSsc9Cx8IrWykC\nxgGTgDPQZ8O98cm3oevIPwY2AIehlfDFbVL6RTgGdzxWl55uu1DconkirXRnD/3YTV+O0J0azwpe\nb6SVwXzNYLbRk0OkU82W0kMW2x179pd+bbUJCYnMhAuCIAjtxytH8Y9MEk4ynRSD/XUG+5vX4w2B\nGKkkQc3fVxFcghOFREEBEVf8zkssJStpNJCFXm/LKCCRj7oSDcmKP2aSBFVSSxE1YScJCrfP/oRz\nvgLrCX5sEg2keH5k0UgS1Nrx4chxwknoQxw8/ZBBeLgkom5W+pwYJGKfhc6Dd6Ad4SRBztFRsTZu\nmehMstqEqNBakqDxzjRokSQoi+PkdNokQX2dRVabkJDIIFwQBEHo3ISaJKgAfVDeHYm2khCYTRJ0\nKKpJgoTEQwbh4VJdmngzhtLnxCAR+yyEjleaEakoKJFKuBNOkqCdns2OHiYxH31AngKlm8E5IoT2\nIiVZsShJUOly+JbTK8cIHDJYlSgo2kmC1pWeZISzq4kkQXaqPZKVYEmCWmsvGomCwpGL7CzdR39n\nYRs2hxPdBKxKFGRsk8hRBEEQBME6vLKVfPRoK6fQB+XeaCsVng30gfspmpIICZ0ef9mKC5tftJUa\nkmnwRVtxg0+2corMTitbESKLDMLDJRFnCqXPiUEi9llIbIIlCfJKVo4BJ8AJsAJ95turI+9mga0x\nwjsLnkiMcHY1+CS0JEGnPKES9SRB8S1b8c6CC7FFBuGCIAhC+/HKUfyzm4cqzTBK7hOqfCMaSYKy\n0COoNJetnCZ4kqDuEJCYMZxEQWaixliUJEh/3/6oK9GWrATYGYWIK0ZJggJlK3XkUYkLG9Wkc4os\nqknHjT0ibUN4CXpimSQoWn3wJ1QZjf5oy1okTni4JGIsZelzYpCIfRYEIzwD7VIXMAEooUmW4qIp\nQdAy4FNgB3pmT2WFsZHjk0+stiD2rC89HvIxXtlKBfmUU8h+CjzRVBzYcZNNFb05SDE76Ms+unKM\nJL+Br9WUl+612oSERGbCBUEQBCEUgslWjqFrx4/RFG1lG/rarx5+W+KpOxKQwGgrSTR4JCv6LLke\nCrHGJ1s5STYnyfLIVoREQgbh4ZKIulnpc2KQiH0WQuek52+wCCTN90dBahH1JEEQ0B9nH4L3Ocez\nudAXdLaWJCgPfUDubTPE6CixTBJ0wRh8UiN/yQpEP1FQQFsxjLgywZkM1Jgu35rswksdKdSQgQ0X\naZwmhdMtkgS5sHkWgWZQTUbA4s5QEwWF2uchznwCf7jmjzUjFTHbh2gkCjIjWbIKGYQLgiAIQqTw\nDrS7oUtRatAH5JXog1lvkqBN6EmC8tHjkmcR72v3hAjg9gtrCIpUTw7PDKpJotEXbUUB1X7RVlxx\nEE5PiDyiCQ+XRNTNSp8Tg0TssyC0QenWEAp7ZSuFwBhgEnAG+uJNG02SlWXAx8AG4DAYriOzm75j\nRgAAIABJREFUgNKVVlsQe9aWnopRSxqnSeMo3dlNP3bTlyN0p8Yz4PYmCBrM1wxmGz05RDrVRGOh\nwY7SfRGvU2gbmQkXBEEQ2o83Oor/3SRSkVLMyC6inSSo+THVNPXZjESmeRlv5s5B6INwI9lKsyRB\n7Wor2OtQz5Fff7VmI4ZoJwqyKuJKCnWke45pjwQjnERB+rx4GjZcpFBPGjUtZCveJEFVnhn1SCQJ\nSqWedGqDlI98kqD2HB9eoqDgkV/iARmEh0si6malz4lBIvZZENrAOTBCFfnLVmzoSYCOebZgSYJ6\noA/KY5wkyDk+tu3FA2c7M6w2ISBJECiSqfckCaom2U+2UsDBiCQJKnYWRLYDgilkEC4IgiAIVuKV\nrXhnyIMkCeIELaOtdOIkQYI/TdFWoBs2XL7EQGkdPElQoiOD8HCpLk28GUPpc2KQiH0WQieYHMX/\niW+o0pRQ5SjRThLUrK7S/eDsH0Jd7ZXIGCUJMoq2EqUkQaUbwHl2kDIm64pGoqBoS1Y+LW1gnDO1\njWPNRdyIVqIgr2xFgS9JUJNsJfQkQZtKjzLU2cO0zaEm2Gl+fCwTBZmN3mIF8WWNIAiCIAhNeAfa\n+ejr8U6hD8qPostWvNFWoCnaSh6Qi0yCJgD+shUXNtKo9cQh16OtZFNFNlWeQD3pnCQ7LNmKEFlk\nEB4uiThTKH1ODBKxz4LQBr5ZcCsIliToG6KaJMg3C55AeGfBOx5GSYJq/QbnwZMEeWfBhdgig3BB\nEASh3TQc0/8mGclIjKQjZmQn0Y6UYqb+1uqKdqIgI4mMfz1eLXkhsU0S1JpNEUoU5H9NxVKy4k+o\nEVeavw9VghIpyYqX0JMEpdPgd0FGKklQqHY3Pz4cqYnZiC1WIHHCwyURYylLnxODROyzEDKHXaAi\nH7Y4bindb7UFBngH2sXAWGA00A/IQNeVexMELQE+BXagZ/5s47srXRstg+OXVaUNbRfqYHiTBFWQ\nz276cZAeHCeHBhzYcbO99CC9OUgxO+jPbrpSSZKfVluIDjITLgiCILSbp6sgW4PBDTA4GQYky43F\ncjT0hZ1Z6DPk0BTysJLgspVe6Is742uiUIgKepKgajJ9spVvOEgNSc2irRwOkK2ckrSuEUd8Zbgk\nom5W+pwYJGKfhZBJA04q+KJW3xxAfxsU2WCADbr7Zdt2GEgQIiZNiUaSoGbvnZk0RYSJdqKgUGUt\nkUgSlIs+KPckCXIWETwCTiTtNiGFMZSsRCFJ0PlOO6AfE6okomW5yEtQQo3SYqaeIc4CjkIbSYJs\nniRBmSEnCWpfnyOfKMhI+mIVMggXBEEQ2s0N6BOsezXYpfTXO9z6BtDLBcUOKE6CAhtoMpFmLW0l\nCTrq2cDSJEGCNbSdJOgUOZyKWJKgREcG4eGSiLGUpc+JQSL2WQgZDX2M1ssG44EqBXtsUO6GPW44\n4NK3ZXWQY9MH48VJUGQHRwcckJceAmdPq62IEEZJgryD8hNQuhmcvdFnvXvSlCQoviYUI8qKUhff\ncnbiDgZhQ+kxRji7NtsrSYKijQzCBUEQhHZz2PM3ze/JcR839EF/oF8B7AH2Aifc8EWdviVVQT+P\nbGVQEmR6lAFpfrIQLVTpSDSSBDV/X02TPCPaiYLCqSdSSYJqgST0AfouDGUrYclxIhUdJ0JJglJr\nIb3aI0cJMeKK/r79iYKiIUExc2wqp0mnps1jmycJSqeGNBNJgsz2MxqJgoyTBFmPDMLDJRFnCqXP\niUEi9lmIKElAf8+mgFM2XbLSXLbyUaMuVRloh2F26GGPX9mKs7vVFsQIj2zFeSHBkwR1YtnKpElW\nWxB7Rjm7hFTeKEmQV7bSPElQFRmcIEdkK82QQbggCIIQdTSgh6Zv44HTdtjpbpKtHPRsKxqaZCuD\nUz3RVuJ0QJ4wBEsS1Ey2wglaJgnqhowyEoJA2YpRkqAeVIhspRny8wiXRNTNSp8Tg0TssxAynlw9\nATeTJL/XfsFRcPhJVtJcumSlj+f9AQxkK+iylWIHFDkgQzNO6BKVJEHNPiutAt+kYbQTBcVBkqDS\nHeAcEqSeLHRJSiFNg/Dm0VZs6HKVPM/fdBO2mkkUFOUkQSu/AOe5+utQkwTp761JFBROxJU1pTWM\ndmaZLh9KkqBUX4Kg023KVkJt259woqZYhQzCBUEQBEvxl6040KUqu9EjrhxRHtlKPVCvy1YGexZ3\n5km6Oeuxo8+Q56PLVqrQZSuV6P/8HPFsAF085fI9rxN7EjQhcGP3zINn4MLm056nURtUtnKS7ISK\ntiKD8HBJxJlC6XNikIh9FizHG20lH5iUDKeULlvZpWC3yyNbqdOjrViRJChE6WyHxzcLbgZvkqAu\n6DPkp9G15BXoj0yCJQnybnE0QemdBU8kvLPg0UXzLex0YTOUrXijrXiTBNUEPELpXMggXBAEQWg3\n3ugo/jcTI9WBvzQlyUwZjyyiJ7psZTxwEDiEPlPunyTIK1uJeJIgs+WikSjISHYRD0mCmn9mVJc3\nBGIh+iy5UZKgruga8h40nY/2JCVqy+4oJwmC8BIFhSpfiaVkJZwILUZ1NZetNElXmpIEubBR5UkS\nVE06DS30Yq3b3ZZ0xkpkEB4uiaiblT4nBonYZyGuSQL6AUPRlQ9tJQka5EkS1CuCSYJKT0FMJg3j\nhNId4BwYgYr8kwTp2gN9QO6VrVR4ti3o0Vby0P/7yiTmspXSz8E5PrZtWs0XpdWc7cywrH2vbOUU\n2YAi1TNnnkE1SX5JghRQTQanyOQUWR1etiKDcEEQBKHDYTZJ0CedJElQp8I/SVAh0IgebaUSfZbc\nu9Dza/RHI3lAAZ0+SZDgRZetVJPJUU+0FW9yoMAkQYd90VZOkeXJ8tmxftwyCA+XRJwplD4nBonY\nZyFkfMl6/Pad8nsdEB3F77VRBBXDyCpG9YeYJMhRBf1DSRLUrHFnCk3JeqKdKChS9YeRJMjZneD9\nba2u9khksjxbMbpu3F+2ssez+S8CjWKSIOeZNJ3jUOshvERBRlFXoi1ZmeS0g4lkPcHq8ac16Uc4\nUVe8WnIbLlKobzVJkHemvK0kQfGADMIFQRCEToVRkqBypU+4BksSNNwO+XGcJChh8Jet2ND/4/LG\nI6+iSbYCnS5JkNA2/kmCQJFMfdAkQT053CGSBMkgPFwSUTcrfU4MErHPQqcj0kmCSmvBmdZyf2el\ndDc4+1vUuL9sZRAxSxJU+gU4zw7D7g7I6tLTjHOmtl0wrgieJCiDGlI53SGSBIUUZfX9999n6NCh\nFBcX8/DDD0fLpo7F6XVWWxB7pM+JQSL2WQigM/r8LA1G2eHyJPhxOlyeAiM8SYC8spWFJ+D/q4BX\njsNXtVDlJ3lZV2dcd2dk3eG2y8SMVHS90VmAEyjxvE+mKdrK58AHwGee96dbVtMW67aGb2pHo2xd\nvdUmhIlGA8kcJ5f99OZrBnKAnpwk0xOfXJesDGInwyijD3utNhgI4X9Fl8vFj3/8YxYvXkzv3r0Z\nO3Ysl156KWeccUY07Yt/3MettiD2SJ8Tg0Tss+DDrM/3Zsw0FXLQYL+Z8maONZup07+8V/kwET2n\nzB5gjwYVCrbW6xunmmQre4B6ly5biXq2zmiEKwyx/uPe2WYI1J9D1LN1tllPCrrmqB8tkwQd9Gyg\ny1by0WfJ/ZMEGdh8vILgOniTmvBwsnX6X1Ox1I3XHa8ly3NiohH2sD3HhBNy0IWDRpI4Ti6VdPMl\nCUqnliQayeU43wQ9MraYHoSvXr2aQYMGUVhYCMC1117LW2+9JYNwQRCETkii+XyNJjWDf5Kgcjfs\n9ZOtbABUWrw8zBaAtpMEef+R2A1cYI2JgpU0JQmq8CQJSqUu4J92qzA9CN+/fz99+/b1ve/Tpw+f\nf/55i3K3Xt2OZz8dmKVv7mDK5dLnzo70ufMzbkSj1SbEFWZ9fsmttwKBE4P+Okf/G53dYL+Z8maO\nDad+/zJuB2QAIzyby93Anj372Vm+m08OHaLxhmuAwOQrARUYvTZT3mi2NZw6zZT3b8vvP4wdm5Zy\n+pwpLY81216k+tne+hsasB3ch23vbkhJpbFgQpvt7vhmKae7T2lfu83fG5xXwzIGImGXanqt/J7m\nuFXTAW6XXwO2pv2aX6V2gu/fv+N9HKe/7TGhqR63Xxn/18pgv9vg2NaOd4VYr9Gx/pippxrrMT0I\n10wsGa+qquK7k1aGZVBH47uT5gDS586O9DkxqKqqstqEuMGsz8/67nfbVX+Dwf54llx3Ae5Glxsn\nCnPu/651XsBv4InL4LUZcj0bYEaDMOcn32XloRDb6OB8f87FbEwsdx8X/t70ILx3797s3dskZN+7\ndy99+vQJKHPZZZdFzjJBEATBMsTnC4IgRBfT0VHOPvtstm/fzq5du6ivr+fVV1/l0ksvjaZtgiAI\ngkWIzxcEQYgupmfCHQ4Hjz/+OBdeeCEul4u5c+d22gU6giAIiY74fEEQhOiiKaVU28UEQRAEQRAE\nQYgUISXraY3OmNShNW666SZ69OjBiBEjrDYlZuzdu5cpU6YwfPhwzjzzTB577DGrTYoqp0+fZvz4\n8ZSUlDBs2DDuuusuq02KGS6Xi9GjR3PJJZdYbUpMKCwsZOTIkYwePZpx48ZZbU7cI/6+85No/h7E\n54vPtwAVARobG9XAgQNVeXm5qq+vV6NGjVKbN2+ORNVxyyeffKK++uordeaZZ1ptSsw4ePCgWrt2\nrVJKqVOnTqnBgwd3+u+5urpaKaVUQ0ODGj9+vFq+fLnFFsWGRx55RF133XXqkksusdqUmFBYWKgq\nKyutNqNDIP4+MUhEf6+U+Hzx+bElIjPh/kkdkpKSfEkdOjPnnXceubm5bRfsRPTs2ZOSkhIAMjMz\nOeOMMzhw4IDFVkWX9PR0AOrr63G5XHTt2tVii6LPvn37ePfdd7n55ptRCaRWS6S+hoP4+8QgEf09\niM9PJD8YD32NyCA8WFKH/fv3R6JqIU7ZtWsXa9euZfz48VabElXcbjclJSX06NGDKVOmMGzYMKtN\nijp33HEHv/vd77DZIqZWi3s0TWPatGmcffbZPPnkk1abE9eIv088EsXfg/j8RCFefH5EzriZpA5C\n56GqqoqrrrqKRx99lMzMTKvNiSo2m41169axb98+PvnkE0pLS602KaosWrSI/Px8Ro8eHRezBLFi\n5cqVrF27lvfee48nnniC5cuXW21S3CL+PrFIJH8P4vMThXjx+REZhJtJ6iB0DhoaGviv//ovZs2a\nxeWXX261OTEjJyeH73znO3zxxRdWmxJVVq1axdtvv82AAQP43ve+x5IlS7jhhhusNivqFBQUAJCX\nl8cVV1zB6tWrLbYofhF/nzgkqr8H8fmdnXjx+REZhEtSh8RAKcXcuXMZNmwYt99+u9XmRJ2jR49y\n/PhxAGpra/noo48YPXq0xVZFl4ceeoi9e/dSXl7OK6+8wtSpU3n++eetNiuq1NTUcOrUKQCqq6v5\n8MMPEyoKRqiIv08MEs3fg/h88fmxJyKDcP+kDsOGDeOaa67p9Ekdvve97zFx4kS2bdtG3759eeaZ\nZ6w2KeqsXLmSF198kaVLlzJ69GhGjx7N+++/b7VZUePgwYNMnTqVkpISxo8fzyWXXML5559vtVkx\nJRGkB4cPH+a8887zfc8zZszgggsusNqsuEX8vfj7zor4fPH5sUaS9QiCIAiCIAhCjEmcpbCCIAiC\nIAiCECfIIFwQBEEQBEEQYowMwgVBEARBEAQhxsggXBAEQRAEQRBijAzCBUEQBEEQBCHGyCBcEARB\nEARBEGKMDMIFQRAEQRAEIcbIIFwQBEEQBEEQYowMwgVBEARBEAQhxsggXBAEQRAEQRBijAzCBUEQ\nBEEQBCHGdMpBuNPp5JZbbrHaDMHDnDlzmD59uuHnu3btwmazsWrVqhhaFTo2m42FCxdabYYhbZ3n\njkppaSk2m40DBw5YbYoQp4jPjy/E58cG8fkdn6gNwq28ODRNQ9M0S9oWgmPV97FgwQLOP/98unXr\nhs1mY+XKlTFr+8UXX8Rmi93/uZ3hunc4HDz//PMB+84991wOHTpEQUGBRVYJZhCfL/gjPj/6dIbr\nPtF9ftSuls5wcSQCDQ0NMWlHKRWTdppTW1vLtGnT+N3vfgdYd2OIBVad40heQ5qmtehHUlIS+fn5\nnfq76wyIz+8YiM/vPIjP7/hEbRCulGr1Alm4cCHjx4+nS5cu5OXlMWPGDLZv3+773Pu46rXXXmPG\njBlkZGQwcOBAnnvuuYB6du/ezbe//W3S09Pp168ff/rTn1q09dZbbzF69GgyMjLIzc1l/PjxrFu3\nzvf5jh07uOqqq+jWrRsZGRmMGjWKd955B4Djx48za9Ys+vfvT3p6OkOHDuUPf/hDQP3eGaA//vGP\n9O7dm4yMDK6++mq++eabgHKvvPIKJSUlpKWlMWDAAH76059SU1NjeI6uv/56Zs2a5Xv/zDPPYLPZ\nePrpp337Zs6cyXXXXQfAN998Y9rWP/3pTxQWFpKWlsbp06dxOp3MnTuXO++8k7y8PHJycrj11lup\nq6sLOP5Pf/oTQ4cOJS0tjcGDB/PQQw/hcrl8nx87doxrrrmGzMxMevbsyfz58007ivLycs4//3zS\n09MZOHAgr776qu8zp9PJrbfeGlBeKcXAgQN58MEHDeu87bbbuOuuu5g6daopG7wsXbqUkSNHkpaW\nxqhRo1i6dGmLMvfccw/Dhg0jIyODfv368cMf/pCTJ08C+uO0G264AdAfadpsNm666SYAPvroI5xO\nJ926daNLly44nU7WrFnTpk3vvvsuY8aMITU1lR49evCjH/2oxfWjlGr1Oty0aRMXXnghubm5ZGZm\nMmzYMF588UXf51VVVdx222306dOHjIwMzjrrLN544w3f597f5cKFC7n44ovJzMzknnvuoX///vzv\n//5vgC11dXXk5uby97//3VS/CwsLcblc3HjjjdhsNux2u+9cNn80+dlnnzFp0iTS09Pp2rUrM2fO\npKKiwvf5/fffT3FxMW+//TZDhw4lMzOTKVOm8PXXX7d5noX2IT5ffL74fPH54vNDREWJ2bNnq2nT\nphl+/swzz6hFixapnTt3qnXr1qlLL71UFRcXq/r6eqWUUuXl5UrTNFVUVKRee+01tWPHDnX33Xcr\nh8Ohtm3bppRSyu12q9GjR6tx48ap1atXq3Xr1qnp06er7OxsdcsttyillDp48KBKSkpSv/vd79Su\nXbvUli1b1Msvv6w2bNjg+zw/P19Nnz5drVy5UpWXl6tFixap9957Tyml1KFDh9Rvf/tbtXbtWrVr\n1y714osvqszMTPXMM88E9DU7O1tddtllauPGjaq0tFQVFxerK664IqC/ubm56sUXX1Tl5eXqk08+\nUSNHjlTXX3+94Tn6+9//rnr16uV7P2vWLJWfn6+uu+46375evXqpp556KmRbr7zySvWf//xHbdy4\nUblcLjV58mSVnZ2tvv/976stW7aof//73yo/P1/dcccdvmPvu+8+1b9/f/Xmm2+qXbt2qXfffVf1\n69dPzZ8/31fm8ssvV8XFxWrp0qVq06ZNatasWSo7O1tNnz7dsJ/e77pXr15q4cKFatu2beree+9V\ndrtdrV27Viml1Msvv6yysrJUVVWV77jFixcrh8OhDh48aFh38zZWrlzZZtn9+/er9PR0ddNNN6my\nsjL10UcfqREjRihN09RLL73kK/eb3/xGrVixQu3evVt9/PHHaujQoWr27NlKKaXq6+vVE088oTRN\nU4cPH1aHDx9WJ0+eVEop9cYbb6jXXntNbdu2TW3evFndfPPNqmvXrqqystLQpvXr1yu73a7+53/+\nR23dulW99957ql+/fgHXj5nrcMSIEWrmzJmqrKxMlZeXq/fee08tWrRIKaX/npxOp5oyZYrvt7Bg\nwQKVnJysPv7444Dz2KdPH7Vw4UK1a9cuVV5eru6++251xhlnBNj86quvqrS0NNP9rqioUA6HQz32\n2GO+c6aUUkuXLlWapqn9+/crpfTfbFZWlpo5c6bauHGjWrFihRo5cqSaNGmSr+377rtPZWRkqIsu\nukh99dVXav369WrMmDHqvPPOC7BR0zR1//33t3VJCCYQny8+X3y++Hzx+aFh2SC8OZWVlUrTNLVq\n1SqlVNMX/8c//tFXxuVyqaysLLVgwQKllFIfffSR0jRNbd++3VemoqJCpaWl+RzyV199pTRNU7t2\n7Qra7r333qsKCgpUTU2NaVt/8pOfBDiY2bNnq6ysLN+Fp5RSH374odI0Te3YsUMppVT//v3V3/72\nt4B6li1bpjRNU8ePHw/ajvcclJWVKaWU6tOnj3rkkUdUQUGBUkqpzZs3K03T1M6dO0OyNTc3V1VX\nVweUmzx5showYIByu92+fQsWLFCpqamqpqZGVVdXq/T0dPXBBx8EHPfcc8+pLl26KKWU2r59u9I0\nTS1evNj3eX19verdu7cph/zLX/4yYP/EiRN9Duf06dMqLy/Pd/NRSqlrr71WXX755Yb1BmvDjEO+\n5557VGFhoXK5XL59ixYtauGQm/Ovf/1LpaSk+N6/8MILStO0NttzuVwqNze31bpnzZqlxo8fH7Dv\nrbfeUjabTe3Zs0cpZe46zMnJUc8++2zQNpYuXapSU1PViRMnAvbfeOONvvPsPY+/+c1vAsps2bJF\naZqm1qxZ49v3ne98J2DwYKbfDodDPffccy3s8nfI9957r+rbt69qaGjwlVm/fr3SNE0tX75cKaU7\nZIfDoY4ePeor8+qrryqbzabq6up8+4YOHaqeeOIJQxsF84jPF5+vlPh88fni80PBsugo69at44or\nrqCoqIjs7Gz69+8P6I8a/SkpKfG9ttls5Ofnc/jwYQA2b95M9+7dGTRokK9M9+7dGTJkiO/9qFGj\nuPDCCznzzDO58soreeyxx9i3b5/v8y+//JKJEyeSlpYW1E63281vf/tbSkpKyMvLIysri7/97W/s\n2bMnoNywYcPIysryvZ84caLPxoqKCvbs2cMdd9xBVlaWb7v44ovRNM3wcUlhYSGFhYV8/PHHbN26\nlePHjzNv3jxqamooKytjyZIl9O/fnwEDBoRk6xlnnEF6enqL9saNGxegwZo4cSJ1dXXs2LGDTZs2\nUVtby5VXXhnQhx/84AecPHmSyspKNm/eHNB30LVdY8eODdq/5pxzzjkB788991w2bdoEQEpKCnPm\nzOHJJ58EoLKykjfffDMqERE2b97MuHHjAhbYnHvuuS3K/etf/2LSpEn07t2brKwsZs2aRUNDA4cO\nHWq1/vLycq6//nqKi4vJyckhJyeHEydOtPiemts0adKkgH2TJk1CKeU779D6dQjws5/9jJtvvpkp\nU6bwwAMPsHbtWl/ZNWvWUF9f7+uPd3vppZdaXKPjxo0LeD9kyBDGjRvHCy+8AMCRI0f48MMPfY9n\n29vvYGzatIkJEybgcDh8+0aOHElOTo7vegHo1asX3bp1870vKChAKcWRI0d8+8rKypg3b15I7Qvt\nQ3y++PzmiM8Xn2+GzuzzLRmE19TUcMEFF2C323n22WdZs2YNa9asQdM06uvrA8omJycHvNc0Dbfb\n3Wr9yk+PZrPZeO+991iyZAljx47ln//8J4MHD/bp/4ItCvDnkUce4be//S233347ixcvZv369dx8\n880tdHOt1eG197HHHmP9+vW+7T//+Q/bt2/nzDPPNDx26tSpfPzxxyxdupTzzjuP1NRUJk2axJIl\nS1iyZEmA7s2srcGcsdk+vP766wF92LhxI9u3byc3N9fw2NbqbY3mx916662sWbOGDRs28MILL5Cf\nn89FF13Urrpbo61rAuDzzz/n6quvxul08uabb7J27Vr++te/opRqcQ03Z8aMGezbt48///nPfP75\n56xbt478/Pw2jzNzHtsqc++997Jt2zauvvpqNm7cyIQJE5g/fz6gf8c5OTkB3+/69espKyvjvffe\nC6gnIyOjRd033HADr7zyCo2NjSxcuJC8vDwuuOCCsPvdHDPfDwT3Hd5+CrFFfL74fDOIzw9EfL5O\nZ/b5UR2EG61sLSsr4+jRozz44INMmjSJIUOGcOzYsZB/uMOGDePo0aMB/7EdPXqUbdu2tSg7duxY\n7rrrLpYtW8bkyZN55plnABgzZgyrVq0yXCzzySefcNFFFzFnzhxGjRpFUVER27Zta9G3srIyTp06\n5XvvjX86bNgwevToQd++fdmyZQtFRUUttpSUFMM+TpkyhWXLlrF48WLOP/98QHfSixcvZtmyZQEO\n2aytRqxZsybgYl21ahUpKSkMHDiQ4cOHk5qayo4dO4L2wWazMWzYMICAkFD19fWmFqAAfPrppwHv\nV61axfDhw33vBw4cyNSpU3nyySd5+umnuemmm6KyenrYsGGsXr064Fw0D3O1YsUKunfvzq9+9SvG\njh3LoEGD2Lt3b0AZr0Pwv64rKyspKyvjzjvvZPr06QwdOpSUlJSA/9SDMXz4cD755JOAfcuWLUPT\ntIBz1Np16GXAgAH88Ic/5LXXXuOBBx7gL3/5CwBnn302x48fp7a2tsX326dPn1btA7j22ms5ceIE\n77//Ps8//zwzZ870fT9m+52cnByw6MvoXHz22WcBK/TXr1/PiRMnWh3cCNFHfL74fPH54vND6XfC\n+/xo6Vxmz56tJkyYoNatW6fWrl3r27Zs2aKOHj2qUlNT1bx589TXX3+tFi9erM4++2xls9l82iAj\nPdfAgQPVAw884HtfUlKixo8fr1avXq3Wrl2rLrjggoBFOitXrlS/+tWv1Oeff652796tFi9erHr1\n6uXTonkX6UybNk2tXLlS7dy5U/373//2LdL52c9+pnr06KGWLl2qtm7dqu655x6Vk5OjCgsLA/qa\nnZ2tLr/8crVx40a1bNkyVVxcHKBde+GFF1RycrJ68MEH1YYNG9SWLVvUG2+8oW699dbfLnfYAAAg\nAElEQVRWz+OBAweUpmkqKSlJffXVV0opXQvlcDiUzWZTBw4c8JU1a2sw3aZ3kc4PfvADVVZWphYt\nWqR69uypbr/9dl+ZX//61yo7O1s98cQTasuWLWrjxo3q5ZdfVr/4xS98ZS677DI1ePBg3yKd66+/\n3vQiHe/Cj61bt6r58+crm83mW6Tj5bXXXlPJycnK4XCoffv2tXrulNK/37Vr16p33nlHaZqmnn32\nWbV27Vp16NAhw2O8i3Tmzp2rNm/erBYvXqxGjRoVoA9ctGiRstls6umnn1Y7duxQzz33nOrTp4/S\nNE3t3r1bKaXU6tWrlaZp6o033lBHjhxRVVVVyuVyqfz8fHXllVeqbdu2qVWrVqlvfetbKiMjI+C6\nbs5//vMf5XA41B133KHKysrUe++9p/r27atuuOEGX5m2rsNTp06pefPmqSVLlqidO3eqr776Sk2e\nPDlgccv06dPV4MGD1Ztvvql27NihvvjiC/XYY4+pJ598MuC7MtJZXnnllaqkpERpmqY2btzo22+2\n38OHD1ezZs1SBw4cUBUVFUqplvrAw4cPq+zsbHXdddepjRs3quXLl6sRI0aoyZMn++q577771KBB\ngwJsW758ecD3I0QW8fni88Xni8/3Ij7fHFEbhM+ZM0dpmtZi866mff3111VxcbFKTU1VZ511llq2\nbFmAQL+8vFzZbLYWX/ygQYMCvsBdu3apCy64QKWmpqq+ffuqxx57TDmdTp9D3rRpk7r44otVz549\nVUpKiurfv7/6+c9/HiDw37Ztm7riiitUTk6OSk9PVyUlJT6HfOLECXX11Ver7Oxs1a1bN/XjH/9Y\nzZ8/Xw0YMMB3vNfJ/f73v1cFBQUqPT1dXXXVVerYsWMBtr/55pvqnHPOUenp6So7O1uVlJSoX//6\n122eyyFDhqhu3boF7MvLy1NDhw4N2GfG1jlz5gR1jk6nU82dO1f9v//3/1S3bt1UVlaWuuWWW9Tp\n06cDyj311FOqpKREpaamqtzcXDVhwgT117/+1fd5ZWWluvrqq1VGRobKy8tTd999t5o9e3abDtlm\ns6kXX3xROZ1OlZqaqoqKitTLL7/comxDQ4PKz89XM2bMaP2kebjvvvt8157NZvO9bs35KaXUxx9/\nrEaMGKFSUlLUiBEj1JIlS1os0pk/f77q0aOHysjIUN/5znfUyy+/rGw2W8AP/vbbb1f5+flK0zR1\n4403KqX0xVmjRo1SqampaujQoeqf//xni+s6GO+++64aM2aMSklJUXl5eWrevHkBi8u8363RdXj6\n9Gl13XXXqQEDBqjU1FSVn5+vrr322oAbW21trbrzzjvVgAEDVHJysurZs6e66KKL1NKlS5VSxr9L\nL2+99ZbSNE2dddZZLT4z0+/3339fnXHGGSo5OVnZbDallO6QbTabzyErpdRnn32mJk2apNLS0lSX\nLl3UzJkzfQ5cKaXuv/9+VVxcHND+8uXLW3w/Zq4FwRzi88Xni88Xn++P+Py20ZSyKNp7J2LOnDns\n37+fjz76yGpT2s2UKVMoLi5mwYIFVpvSKpWVlfTt25dXX32VSy65xGpzhA7Mzp07KS4uZsWKFS0W\niAlCa4jPjx3i84VIEY8+37LoKEJ8odpItGE1jY2NHDp0iHvuuYc+ffqIMxbC5p133mH27Nlx44wF\nIZaIzxcSjXj0+Y62iwhtoXWCdM3x3ocVK1YwdepUioqKfCGRBCEc/vu//9tqE4QOSrz7SzPEex/E\n5wuRJh59vshRBEEQBEEQBCHGiBxFEARBEARBEGKMDMIFQRAEQRAEIcbIIFwQBEEQBEEQYowMwjsw\nc+bMYfr06QH77rrrLnr06IHNZuP555+3yLLIEayPgiAIgnW0xy9H25fLvULoiMjCzBjidDopLi7m\nySefDNi/a9cuioqKWLFiBRMnTjRd36lTp3C73eTk5ADw+eefc8455/D2228zbtw4srOzSU1NjWgf\nYk3zPgqCIMSaOXPmBJ3UyMzM5OTJkxZYFDumTZtG3759eeaZZ3z72uOXb7zxRvbv38+HH34YDTPl\nXiF0SCREYQyJdEiorKysgPfbt2/HZrMxY8aMsOqtr68nOTk5rDrCxWtD8z6GU5cgCEJ7mTRpEv/4\nxz8C9tlsifkwuT1+OVpxySN1r5D7hGAFielBOgBOp5NbbrmFX//61xQUFNCtWzdmz55NdXW1r4z/\n47c5c+Zwww034Ha7sdls2O12ABoaGrjzzjvp06cPKSkpDB8+nJdffrlFWzfffDPz58+nV69e9O/f\nnylTpnDzzTdz7733kp+fT25uLr/85S9RSnHffffRs2dP8vPzuffee031Ze7cudx5553k5eWRk5PD\nrbfeSl1dXVAbCgoKKCwsbNHH9vTHv64VK1Zw7rnnkp2dTXZ2NiUlJa3Oyphtq63vSRCEjk9ycjL5\n+fkBW/fu3QE4duwYffv25fbbb/eVP3LkCAUFBQE+0owvjKTf+dOf/sTQoUNJS0tj8ODBPPTQQ7hc\nLtP1zJkzhyVLlvDcc89hs9mw2WwsW7ashV/+6KOPcDqddOvWjS5duuB0OlmzZk3I5ziW9wq5Twjx\ngAzC45jXX3+d48ePs2zZMl555RUWLVrEww8/HFDGO7P+2GOP8X//93/Y7XYOHTrEwYMHAbj77rt5\n6qmnePTRR9m0aROzZs1i1qxZLFmyJKCef/zjH1RWVrJkyRJfKubXX38dl8vFqlWr+MMf/sBvfvMb\nLrroIurq6lixYgW///3veeihh3j//fdN9eWbb75hxYoVvPTSS7z55pvcddddQW1YunRpQDpo/6cH\nofbHW1djYyOXXnop55xzDmvXrmXt2rU88MADpKenG9psti0z35MgCB2b1mZxu3btysKFC/nzn//M\nokWLUEpx/fXXM3DgQH71q18FlG3LF0bK79x///088sgjPPzww2zZsoVHH32Uv/3tbzzwwAOm63ns\nscc477zzuOaaazh06BCHDh1i4sSJLZ7qVldX8+Mf/5jPPvuMTz/9lOLiYr797W9z7NixkM9zLO8V\ncp8QLEcJMcPpdKpbbrmlxf7y8nKlaZpauXKlb9/kyZNVSUlJQLkf/vCH6pxzzvG9nz17tpo2bZrv\n/TPPPKMcDofvfXV1tUpJSVF/+ctfAuq54oor1NSpUwPaGjJkSECZyZMnq9GjRwfsGz58uBo5cmTA\nvlGjRqmf/exnhn321jVgwADldrt9+xYsWKBSU1NVTU2NoQ3N+xhOf44dO6Y0TVOlpaWt2uollLba\n+p78OX78uPrDH/6gLrvsMvXWW2+p5557Tt13333qhRdeMGVXtOoSBMGY2bNnK4fDoTIzMwO2Sy+9\nNKDcAw88oLp3767+53/+R3Xt2lXt2bMn4PO2fGGk/E51dbVKT09XH3zwQUCZ5557TnXp0sV0PUop\nNW3aNHXjjTe2OB/+957muFwulZubq1566SXTx3jtidW9Ip7vE0rJvSJRkJnwOEXTNEaNGhWwr6Cg\ngMOHD5uu4+uvv6a+vp5JkyYF7J80aRKbNm0K2DdmzJg22+/ZsycjR45ssa+ioqJNW8aNGxcwSzFx\n4kTq6urYsWOHoQ2R7E9ubi4333wzF154IRdffDEPP/ww27ZtC7utUL+n1157jXnz5nHkyBFOnjzJ\nDTfcwF133cW8efMCZtpuu+02Q9taq+vOO+9k3rx5uN1unnrqKZ544gluueUWGhsb26xPEARjJkyY\nwPr16wO2v/3tbwFl5s+fT3FxMX/84x/561//St++fVvU05ovjJTf2bRpE7W1tVx55ZVkZWX5th/8\n4AecPHmSyspK33Hh3mcAysvLuf766ykuLiYnJ4ecnBxOnDjBnj17QqoHYnuviNf7BJi7V5i5TxjV\nJfeK+EAG4TEkJyeH48ePt9jv3dc8kknzRSKapuF2uyNul6ZpZGRktNiflJTUolzzfYApm1QbC3KM\nbGgPRnUtWLCAL7/8kunTp7Ns2TLOPPNMFixYEHZ7oXxPV111FS6Xi7KyMq655hoA9uzZQ1VVFTU1\nNTQ0NPDoo4/yzjvvtNlusLr27t1LVVUVK1asYOzYsfzoRz8iJyeHRx99NMxeCkJik5qaSlFRUcDW\ns2fPgDIHDhxg27ZtOBwOtm7dGrSetnyhWVrzO96/r7/+esA/DRs3bmT79u3k5ub6jonEfWbGjBns\n27ePP//5z3z++eesW7eO/Px86uvrQ+5XtO8V/gP8eL1PQOv3iqqqKtP3CaO65F4RH8ggPIYMHTqU\nL7/8ssUPb/Xq1djtdgYNGhTR9gYNGkRKSgrLli0L2L9s2TJGjBgRkTbMRntZs2ZNQL9XrVpFSkoK\nAwcONN1WJPozfPhw7rjjDt59913mzp1r6Fyjde66dOnCypUrmTBhgu8fmvfff5+JEyeSkZFBUlIS\nt912W9AZtFDqKi8v9y0OKioqYvfu3e22WRCEtn2d2+1m5syZjB49mldeeYVf/epXfPrppy3KteYL\nI+V3hg8fTmpqKjt27Gjxj0NRUVFIUV2Sk5NbnR2trKykrKyMO++8k+nTpzN06FBSUlI4cuRIi7Jm\n7hfRvleceeaZbR5v9X0CWvfvWVlZpu8TbdUl9wprkRCFMWTevHk8/vjj3Hjjjdx2223k5OSwevVq\nfvnLX3LTTTeRnZ3tK6siEM4pPT2dn/zkJ8yfP5+8vDxGjhzJ66+/zttvv83ixYtbbSucfcGorKzk\nRz/6Ebfddhs7duzgl7/8JT/4wQ9IS0szXU84/dmxYwcLFizg0ksvpU+fPhw4cIDly5cbPtYMp622\nKC0t9TnoqqoqnnzySZ5++mlTx37xxRecPHmSqVOntlrXmDFjfCvvV69ezeWXXx5Qz+OPP84TTzxB\nWVlZSLYLQqJSV1fH4cOHW/zevbPhDz74IGVlZaxfv56ePXvy/e9/n+uuu45169YFxK5uyxdGwu9k\nZmZy9913c/fdd6NpGueffz6NjY1s2LCBdevW8dvf/tZUPQADBgxg6dKl7Ny5k+zs7BZxuHNzc8nL\ny2PBggUUFRVx9OhRfv7zn/v640883iv8iaf7BLT/XtH8PtFaXXKvsBYZhMeQfv36sWrVKu69914u\nueQSTpw4wcCBA/n5z3/eQtsVLKZ4831GZfx58MEHsdls3H777VRUVFBcXMxLL73ElClTQmorlH3N\n0TSN7373u2RlZfGtb32L+vp6rr32Wt+NoLV6mu9vb38yMjL4+uuvufbaa6moqKBbt27MmDGD3//+\n94Z2R/Lc+bN06VKmTJnCwoUL+eqrr/jLX/7C2LFjDcv7s3DhQpYsWcK6devarCsrK4tt27ZRX1/f\nwrFWVla2qnUUBKEJTdNYvnw5BQUFLfZXVFSwZcsWfv3rX/PGG2/4BuWPPPIIK1as4NZbb+WVV17x\nlW/LF0bK79x7770UFBTw+OOP89Of/pS0tDSGDBnCnDlzQqrnpz/9KRs2bGDUqFHU1NSwZMmSgDI2\nm43XXnuNn/zkJ4wcOZLCwkIefPBBfvGLX7Rar9F5jtW9It7vE9D+e0Xz+0Rbdcm9wjokY6YQdaZM\nmUJxcXFEdHUdnaqqKvr378/Ro0dbdcBTpkxh6dKlQT97+umnmTt3bpt11dXVcc899/Dggw+SkpIS\nsT4IgtA+xBe2jpyfJszcK8zcJ8zUJfcK6xBNuBB1IiGt6SysWLGCMWPGhJU59cSJE6bq+vvf/859\n991HSkoKb7zxRrvbEwQhMogvbB05P02Ee6/w3ifM1CX3CusIeRBeWFjIyJEjGT16NOPGjYuGTUIn\nw8xjt0RgzZo1PPTQQ1RUVPDBBx8Ylnv88cfZvn07//u//+tLuuTlnXfe4fzzz2+zrnfffZdf/OIX\nFBUVkZeX166kGYIg/j6yiC9sHTk/OmbuFW3dJ6ZNm2aqLrlXWEvIcpQBAwbw5Zdf0rVr12jZJAiC\nIMQB4u8FQRCiR7vkKPK4SBAEITEQfy8IghAdQh6Ea5rGtGnTOPvss3nyySejYZMgCIIQB4i/FwRB\niB4hhyhcuXIlBQUFVFRU+ALzn3feeQD89a9PUVw8IOJGCoIgxIKqqiouu+wyq82IG1rz9wBPPPEk\nQ4cWWWihIAhC+4gHfx/yINwbJzUvL48rrriC1atX+5xycfEApk1bHuQo/1TnaSZeZzU7PtvgtX+5\nbgb705te2srA/Q+gD3SZ27S/i1/xzBBfr58D5z6rv041KJNq4rUGfATsR38+cQEwhMBvKDCrfeBn\nob42qscMD8+BXzxrvrxRsjUz+9tTxugz/9crgXV++/oDZxN4LfiXf2UOXPVsy/2nQ2zX6HU06gm3\nrj1zoNez4dcT7LXrENQ+D9SC1g9s3wMttWV5U/jLJYwObmj2vrHFZ3PmwKxZ6xCaaM3fAwwdWmTg\n8/3x9/+OKOxPMygTanmjtpp/di/wcJD9/hjZYVSn0bFGxDLFx/cBMyEDQ/3hNv9NhlKnmWONypip\n827goQjZY+a8hGprNI79P+D2EOoPtS2zdbWn3vbVv3ix9RMIIclRampqOHXqFADV1dV8+OGHEUt/\nHhPUVv2vbUjk6swsDL+OauAt9AF4GvBf6APweKVnodUWhM944HpgNPr9bDfwT2AJcDxI+dzCmJkW\nNyQVRq9ue09IvhHIBrUHXM+AOhW99oSQ6fD+Pmr0ttqAGNPfagMsING+Y4AeVhuQkIT07/Thw4e5\n4oorAGhsbGTmzJlccMEFMTaltdmK1va7QXmyPjmGhD5znGqw3+b33syMd/PXx4H3gSqgK3A5kGfC\nBrN2hzMTbrQ/mcCZfi9m/mmNxux3e2bCG9HP51T0GfAvgfVAObALGAqMATI85R00nf9w7DOatU41\nKNPaLHcwml8j4dTlf21HhTxw3AS1L4I6Au5nIOl6cOQ2FTE1EeIf0szfYP+Dzcwuus00ljBE19+3\nh1B9v5nyZmbam3/m/8OIhh1GmLmGjTBTv9GPzWaybf8yoc54horR7zxSmO1zOITqn8wc63/ejb5z\no2P9+9xgUMboezX7fRj1M9x6g9Uf7WswMoR0ix0wYEBAGtSOxV70R99dQeseuWqTu7RdxoijwDvo\nA6KewKUEPimNVzLD6HM8kg6cB5QAnwFlnm07MAIYBaR2sj6bwRaDPttyIP1GqHkR1EGo/zvYrwct\nP/ptC63Ssf19NMluu0inIgF9X8J9x9A04yTEkgTKmLld/2MrhkgmA+ha0r7jjgGL0AfgfYEr6RgD\ncIDB7exzvJMFTAGuAwai/+O9FngFcJUk3kRpWoy+Zy0dkmeDrRCo8khT9sWmbUEImWFWGxBjRllt\ngAWcYbUBFjDQagMSkgQahH+t/7EVR7baAmfoxxxHX4RZB/QDLiT6T74iyRin1RZEly7At4HL0J9Q\nnAbKnfAmum4/Uch0xq4tLQWSZnrWa5wG1wvg3hW79gXBNBOsNiDGTLbaAAsYb7UBFjDSagMSklgu\nsQ6B5iNSMzq61sTPp4DDej3J/XUJqZHG20i/baaMmfJ16APw0+jrXWYQqDc2W2drn0VDBx4qoerD\nI6Wzbs8xRq8L0b+jr4HlwDfo+v1C4BxaPrGMtg48Urrx1uoye3xUcIDju1D7Frg3gPslsH0XbIP1\njyOmD4fgPsUVirFCTAhVi2xEOPrw1j5rTUfe3jJG7RoRqSe7Zs6j2cRNZrS8HUW/G452O5LtmdF7\nG2F0bKjfjRlNd2u2hXMtdE59eILMhHtmwe0DQIvw/x37S82XPQ28C9QAvWgagHc01pRabUHs0IBi\nYGypPgHmQF+4+Q/gC6KzJiheOFUa+zY1OyRdAfYxQCO4XwX3ptjbIQiGfGq1ATGm1GoDLOAzqw2w\ngP9YbUBCkiCD8B36H7uFmqdG4GPgJNAdXe7QEQfgiYodPVrKTGAQ+qTpl+ihJUW+HFk0DRzfAftE\nwA3uf4J7vdVWCYIgCEJE6YDDQDMhofwfz7mBnfrLlEH6YArCC1Ho/7q7s+0yKcAn6NFQstDDEGa0\nUt7Ma7N2hyVNMXj0OGUyQR9LNpp4LBpu+EEzZaKRKGekU/+bCnwHXRu+FKhE/+eqEH2mPCPIsaH2\nIVKSFbPH+ON/fJ4ztGMjigaOaVCXBI3LwP0m2BrAdnZLe1qrw0fzizzWj5gF85i5LZlxZmZkI2Zl\nIP7lJoVRlxlpSgQDB0QEp9/r9tjm32cjOYuZ0KKxlBSc13aRuPEhZqQmZmQtZ5k41qhds99TpGRK\nZsIvGtUZXyTATPhBoBbIBXtXa0xYjR5/Ohl9sZ9EAur49Aa+h64NT0KXqPwT2ETiRVGJFpoGDqc+\nGAdwvwPuRHxMLAiCIHRGEmAQ7pGiEKX0pHtL2/gcPT26BkwHukXHjJjyWanVFsSeLaUt99nRF5Rf\njT4T3oAuJVyEvoizo3Oi1GoLdBznguMi/bX7A3CvtNYeIcFJtOuv1GoDLCDRdP+gZ6sTYo3FcpT2\nZMn0x8SjPa1cfwJmKwo9G6aZ/cl+75tLR07Q9Fs+F11L7F8ms1n5UNo1a6uRpMTh99jGEWJUiOQG\nSK0zX77RbrDfz1AjKUssoqP4ny8jaYr/99y8vVT0Jxzb0GVHFegD8dGerXnZYPVHI2pK83Kh2mEn\n+M/KisgqjnFw2g6Ni8C9GGwusE1qaYMhza+vaGfcEyJPKBmSIfT7hpF8pfl7/x+Gmbo6iuwkFpjp\nsxmpUahSi1DL2/3KtUcSE237oi2FiUYEleblQs3oaVSPPx3Pr3dATXgoNIDaq7/UBkSnif7O4Pu9\nCzEb0AffZwUv1iGZOKntMp2NYc62yxQBfdD/8dqIvnBzJzARfTFuR6OL02oLAnGMAezQ+Ba4l4Jy\ng20yiTmYEazjW1Yb0A4U+k3J5XntRn8QbkMfcNox/h05Y2BfvHGu1QZYQCImZbKeTj4I34PudApA\ni3E6yk/RJQk5wDRknJAoJKPnthiAPiv+DXpYyjMRHxcJHCV6GMOGN0AtA7cbPc2p/MCEREShh9yq\nQM8Cd8KzVXu2GvTkFPVt1KOhO68U9EddGUA6+uPabPSIAl2AXM9n8nsThEgQR4Pw1h4F+mNmNbqX\nXfofe6F+WKhRUMzs31cKhc7A/bvRpQl24CL0gbgXMxKUdiXr8ZOdGEhNbH6v7QYSFLuj7Uc4ruUr\nsJ/X+myQqzH4peUKkKY03Rjc/vsDXhtcov7yldbkKGYin5iRpqwrhTOd5ssXoWdDXQWsBTaghzKc\nRNOseDSipjSXhIQqHfEvf7AUcp0GBds4NqrSlBGABg3/ArUcNAW2qfpCTtNPIINFTpFkPdYRjqTE\naL+RJMSMbKS1ZD2f0RQ9w0xdkRqwKvQQW/tB2w/qIPrgu60BthfvjLfNY5NCv+Zd6DPjdZ7tZLPj\nytFnFbwkAd1AywPVHchHTy2cQ2T6Go5kJVKsoO0nHvGYDCYcWcsmoCTCbTUnUkl5opHcxxriaBAe\nDXbpf2xRkqIEo4YmHfg5dI6FmEL7cKAPuvuhr236BngbXZokGYLDw34m+kD8n6BWeJ6uT0Vm6ITO\nxUn0ZHPl6Nq2Gn13wFKfdCAPtFzQctAHw1mgeWezU4Bk0FqJw6Bc6IP5OqAWVI2nrSpwL9flnOo4\ncAz9P+xDoA41qyQVfTDe27P10e0QBMGQTjwIr0cP5qyBrV/0mvHOgoPuGFeh+7G+dNqBVluz4J0S\n7yx4e+gJ/Bd6qEqvVnwP+kRLdvimRY1QZsGtwD4cfSD+etNAHBmIC9HGTAzpcDgKbAa2AgeafZYF\n9AFbb6AXaPmewXaYaHYgzbN1CfwJ2c4JLKtqgUpQFeCuAI6ghwKuQZ/42uVXOAd9FqIvegip7nSM\n32cC3uNCmgUXIkUHGYSbWf3bvMxeQIGtFySl6LvMyDzMJOgxer0Lfdyfgi5DSWujfMivm0U68ZOO\n2FKbHknaA2QnTWUchhKU0PYbYSQ1MSrTaBA1xV/K4l/etGTFX6pi9ETKjGTFTNQUM5IS0L/H89Fl\nKkvQnyL/G339z5BWjg1VgtJasp5w6go1CkqsIqg4hgFXNQ3ENQ1sU9opTekIg4PORKi3HzNRM0KV\nr5iNaBJqFJRQr6Ua9P/Q/4N+E/GrUxuob44BoHXTr20jonFHb/E7SkOf5e7TtEsp9FnzA+DeB+79\noPaj69M3eDaATNAKQSsC9yDaP1NudA6MEgN1DGlC/BCtaC2hJviJdnIf64lfy8Jmt/7H3j+6zews\nhSKn7kO9eUS+Rad+CtdQuook50SrzYgt/yltypoZDn2Ba4Bl6E+Zl6HPio9H/+ctnqgshW5Oq61o\nG/sw4L880pTloGygOa22Sui0fEJg1sxwOIJ+49hA0yAjGbRhoA3VB6uaZ5BhVVYPVynYna2X0TQg\nC+xD9K0RPXoRR/QIZWoPqHKgCtRGfQN0PXkx+kxEb+Indclyov/EI95YS8uYukK0kUF4pPgSffK3\nHzAwNk0KHZRU4AL0AfkKdLnnYXSf39NCuzoy9uGA0hdrupeh38wTMJSm0EHYhT6YL/fbNxAo0Qex\nmpmnv3GOZgN6gtYTGOuZLT+qD8bVDs+g/IhnW4muXx+MPiAfSDynGheESGHBIDzcJs2seG/E90gv\nuV/TP9fhyE6Myg9z6lEv9njKnI/+tC5UqYlh1BS/xyvN5CFJARKUpkc1KQbSFH/sdj/JSoiP55LP\nH4MufG9eafDyLv+T5zfb63I1HWAkZTGSrxhJVqCZbOW0X4NGEVXMyE4mOtsug8F+o/pHAv2B94FD\nwIfoExGjCD4hFG6yHjPRS/zL9HC2XSYcmUrEpSln0jQQXwo2O9g88X7lCXQHIlT5oRmpiZmkPK3V\n6X/8+SbaNqIcfZX2Hs/7ZNBGQdI4sAVJJmBGgRNtHE5z5Yx8ng8NGvOAPGAcqEZw7wH3NnBtQ1+5\nvs6zOUArBjUcfaY8uR2GG0lWWhs3eLnA73V7Ip9EQ/4S7UQ//rPg4dTvT/O+hxV7uo8AACAASURB\nVJrgJ9rJfaynk86EH0QPu5QHtijHB29EX4wJMIH4XmgnxB85wFXoE0Frga/Q12I50cPxCqFhHwG4\noOEtPbMmdrBNsNoqIeE5CnyEHrsWIFW/LrVxeg6LeFFhxBLNAfYifeNC9FnyLeDeCuwHVQaUoQ+s\nhgAj0GfIDWZ7BKED0kl/+t5ZhihGRfHyUSmcQs9hkCCLi+tKP2u7UGdjbWn06rYD44AZ6E9kDwFv\noj9hsZKjpRYb0E7sJeCYob92fwDuL6y1R+hkLAuhbB36o66/oA/Ak9GTS92uZ3uNdRK59tBQGv02\nNE2PO247Dxw3g/12sF2IvvizAX3R6svAI8A76M5RGdcXNqF8x52FtVYbkJDEaCY83FXwZh4r+j16\n0vbqv09bX3NRUEJN4uN9XQXsQJefODFOymMkNTEhQfGPepKcGigBMZKdGElNHPjvN5CpmEhYolFH\nGrVtlvPiMpi5cNn9pCZ+r/3lKy5H0357gBylyc7mUVYCpCp+58WUTMVIOpJM03dkVMaMrIVW9g8E\nCtDv2XuBD9ClKWeh/7tspp7WkvWEGvnEv8+hJvqxXJoyBk67oPE9cL8DtiSw+aUsFXmKRYQq3zCb\nxK2t8maim6QZlAl2vBlbtqEPGE8CGmijIXkqaJnBmwjWtJlbZ7Tv4hrGi8bblKC0UqbV/Tnoj5Yn\n6PHJXRugcQN6WKkvPFs3/TftLiG0SAhmZCp2gncoHhP0RAo7kdHhtyYhCVU6EssIKtbQCeUoSl+N\nDaBFeSZ8LZDm1CVrvaLbVDyR5hxntQmxZ4wzNu2kA5egL/RdDaxHX7c0hdivU8p3xrjBCOMYBzRA\n42JwvwU4wDbcaquEDo+zjc9rgXfRZ28BeoH9En2BYkeMgpnitLZ9rQs4zgP1LeAwuNeD2gBUgnsJ\nsBT9JnyW528kHvA7I1BHR2OM1QYkJJ1wEP4NerzADKBL9Jo5ip7AzI7+D7sgRAoNOBs9UsoH6Esc\n3gQmo0f0EszjOBd9IL4M3P8CksA22GqrhE7LHuBf6PGxk4ApYB/ferZKwRyaBvQEe09Q0z0RVtaC\n2or+1GEb+qKss9AXGcoCLSH+iaNBeKRM8cyC2/pCktZ+qUlrr1PQF9AB9CptmjEMJwpKZtPzeP+o\nJyl+EpTk1MAEOP6ykxS/aCV2A9mJkTTFi9tto7HeQUN9Cg2NSTQ2JtHoSsLttuN221BuGwpwfboc\nxznnodnc2GxubDYXDnsjdnsjDkcDSUn12JP0183zSjQaSVP8JSh+ZQwlKyl+5V3N5SjBo67U+UlQ\nTMlUHH7GLy+FsU5vJ4IT6f2D0NcaeAfiHwDnAM0nc1uTVoQqYfG/JneXBo+QEmqUFaulKfbJoBrA\ntQrcr4F9JjgKmz4XaUocEI5kMdTXZiJsNX/s5P++lJYzpW6wfQLuTwAFWm9IuhJsXc3JS0ItY2Z/\npKgt1Z/4QsvfSkQlKKHst6HPeheDqgLXenB9Ceob9O9nGXAGMBY9BJWZRxD+ZUpp+o4jeYKtkkWY\niXCyDn32x2z5UCOoND8mVPtCjaBiRppiPXE0CI8UntVstt7Ra2IP+qAoBRgavWaiSWOjg9raDE7X\nplN7Op2602k0NpoMA3U6E6pz2iymaW6Sk+tITjlNSkotqSm1ONLqgg7OBQMygMuAT9GlKSvRZZFj\n6ZS/3qigaeCYBtTpN+qGl8F+gz5QEoSwqQP+pYfaA9DOheQpnlTwQtTRMvUnXvaJ0FAO6ks9ygqb\nPVs+eja0kYjTFOKNTnhFeuKDa31aL9ZeFLpWF/SnXpHIohgDlNKors6ipiqLmupM6uuCrcp3k5Jc\nR3JyHQ5HPQ5HAw5HIzabyzfjDUC/AmCrb4bc7bbhcjn0mfPGJBoakqlvSMHlSqKuLo26urT/n733\n/HLlOs89f1WFDHSOp/ucPpE8zCIpigqURJhUtiXZpizLtjxX0njsuyasWf7qP0Bf7C+e5Jkb7DuS\nfeVxuJIsibJlSQYliiIpiWJOJ/c5p3NAJ2Sg5sNb1dhAo4BCagB98KyFVWnXrl2Fql1vve+zn5cd\nRvaPYhhZAsEEwdAegdAegWCi+7mSthe8EzCQLKzjiIPnbYQO9SuURlZaDSed8F6EpoHnV8HMQOEV\nyP81GF8Erc/v6aNeRJX5DeBvkS/jIOhPgH62+/uzemB7wbsdmgb6GeAMmDvywc0vkEE13wJ+gPCe\nH6Z2xxltZ0u7FA/VLtJHy9FhI9wpLFAtFOgUSgQJSywDGvhmpCN0Q0Gph5pyDel3I4gRXi+VxQUF\nJRRJ7M/7/IoCSll4xa8ktfEpdBSbamKakNiNsLU9ys7OMIVC8UQ1LU84uEM4uEMouEswsIffm8Kr\n1VZHcYMcBvmCTiodIpUOkUyHSKbCJJID5PNe9naH2NsVb7qu5wmHdoiEt4hEtvD70yX12HBDWQFI\nGyrtRFFXUSgormgqKSUy4FFukpQLNRWn9Srqpancg/DEv43cg98BPkx1nribZD3NKKj0FDVFA8+n\nIZWB/FuQ/yr4vgQe6wOxT9ttIar107XQqiQ7rZp3wnVENi8JTIDvc0I/gebYMs3QTtrxRnejgOK2\nXDOUvbooKwOQi4L5ASi8BtlnkfD1j4FnQLsX9PdC3s1HeL1Jf8ob1UdlNEttqVWm3puwMzhinvAl\nhJs3CVojGbZqwEQoAVCkA7wek6yZXYRMxkd8c5ytrdESiknAv8fgwCYD4W0GgpvoemM6q9uxXzIY\nfaBmOUMvEA7uEg7u7q/LmR4yWT97iQHrN0g6E2Rnd5id3WFYBp8vRWRgi4GBON5gqjuoK8/G4D3R\nTrdCvOGfQ8QXriMG+buBu2i9920xBseiLa60w9AMCHwGkn8DhauQ/SroXwStHomzPm5txIBZ4O+A\nHGi3g/6boDvp+PU4EjEIRTvdisagGWDcB4V7gXkoPCtUFfNFyL8I3A48wsGcIjFuPW/4zxDDpo/D\nxBEzwi0qSrv44POI+EoEMXq6DKlEiM31CXZ3hrAtMp8vycjwOoMDG4T8RQ+73tZEB87QNPD70vh9\naUaH1wDIZr1s7Y2wuzvE7u4QmUyAjfUAG+tTeDwZIoNbRAbjeIOZ7jDIO40A8DGkz3wReBa5L9/b\nyUb1EDQPeD8Hma+AuWBRU75A3xXehztcRjyqBdDuB/2TffWTboemASfBOAnmhmWM/5Kiqsocwvk7\nx9HiEvXR7ehxI7w8ZLhgrZ4pnlm9FBSnCJOfouzreylSyh6MVq7HSRGlTgqKqnrio1Qdxd6WSIRZ\nWDnNXkIkmTQKjAytMD6yzFBwc99wdVJNUeEmWU8wegfUSNbjmKCn0novRIZ3Yfg6pgnxxAhbO2PE\nd8bIZAPENyaIb0zg86UYHlpneGgNv694XdJlmSTUc3BSV8l4ivuoNJW0QkFRqSnZ6HvB/i88qpqK\ncg+6oaC0kqbyKEJP+VfgLSQnyGOU3nuN1GvjdLQ43wythTrLNFPeNfzg+T1I/BWYK1D4Gjnzs608\nQB810Q6VAjdUFqekPG5ehy+yr8ClvRd8H2a/g21VYjiaWF9vGSeofcJotP59nNa3SinFTRmcyowC\nnwDzUcg8B+bPEA/bfwWmQX8/FB51qEhFNWPd6c9tNxXCDR3DCaoXvFWKKG6T9dR7DBXNJPfpPLqr\nNU3DMsKNNnjCryOD4ULIIOsuQDodYGVlht0d0UPX9RyjI6tMj17H5xWDvde+6TUNocuEt5mdusJO\ncpj49hjx7TEymQArq7OsrM4SDm8zPLLGwEC8906ylTiP2BS2jOE/ITzxkWo79QGAFoLg5yHxl2Be\nJ/aDb/CF3zvW6Vb10bV4FXnAAP0xSbF+K/c9vQ4tDMZjYD4iiiqFnwJLUPgHYALxcrSD59dHH0Uc\noRhaGlgHDDDaoHjwS2tarnL0aqz1x6qBQkFnfXmKy5fuZHdnGE3LMzG+wPnbXmZ66sa+Ad4uxGMv\nt7V+G5oG4dAus9PXuOu2Fzg59xZDg+toWoG9vUFu3jjDhbfvZWNlgly2zd+Tz/yovfU3g0ngN5H3\nxg7CE7/ZgnpvxlpQSZdDHwLf54Eg2/GNTremj67Fm0gSHhO0ITHAbxXsxjrdgvZC84P+PjD+V9A/\nAQwhEmj/APwF8vHVGfrm4eJnnW7ALYku8oRXC026SbRwzZpOgdeoXKRRdZRVZMynH0nEpZbxKcuO\nSXmKYRE3FJQQynqFjuInw/bOMIuLc2RzfsBkfGSRY+PzBL0pZR9VUcV9sp7y8k5IkippYyU40VHq\nTtZjz2sQiKSZiiyRy3tYiU+zFp8mlQ4TX5skvjbO0OAmY2PLhILFtqnHyyi0FY+S6EhVU1GpKRlV\nHSWYwrD+r4yiplJQypck+sGFgoqKZmgqIPfebyEe8UvW9IMIxbFSvW4oJYbSrk4pq6hoGzVlAozf\n5+O/7qf4td3H4cKNSkm9XA43+6rUFCeP5xXEIDNFA9xvVKY71ktx7BU6SgZnipvTPq1a3ypqiqsy\nHuBdYD4Imf8EZhJ5+f8j8CPQo1C4k/oT/6hwc6/WqwLSKqgdfr1oJFlPI3SWevbtVGKk+tBFRniz\nWLSmbQgnv2lN70WMbhWHpBNeyOvcWDpFfGsCgEBgj5PHLpQojxwWxqL3HPoxVXiMHJNji0yMLrKb\nGGR54zjbOyNsbY+xtT1GKLTD6Ngykch2yyKJxgfe35qK2gkv8FFkoOYLiKb4BkL1a+Q6HI+2rGld\nD+MYwWC6drk+bjGsAv8fkAftYdAfpyST7q2AwWinW3C40Aww/gjMvAzeLPwYWJVsu0wjA2+O4gDO\nhzvdgFsSfSO8FnYRPrgOvKO1VbtFMhFi+eYc2awfTSswNXmDsdFl/NqtbTTY/HF/+BKZrI+NjUk2\nNidIJAZIJAbw+xOMjK8QGdy6dVRVNGTg8DCisvUKcg9/sINt6qOPnsQeMlgvDdqdoH+MW6cj6QPN\nAO0hUcDZN8aXkHviJGKMl0sb9tFHfehSI7xas5y2LcnEmK4//Fctsc7LCB3sDsSwKS9zIQYPRCvs\nW+SQ6XVSUOx504TtjVEWlk8CGqHADmdn3yRoSQ060U5URRUnRZTyxD82nGgqKlZjbzARvbNmORtO\nCXdUVKSgVNk3o4QkPOQJeRMMT8U5OX6JpfgsK+szpNMhlm6ewreaZHJiocQYV+t1UlMxwsX1ie/9\nHM+j75PjlaipFCkoJQEvJwWVkjLKvBt6hZuB9XaZB4BRZBzZFUTM5nGK96hTXWo7VmIwFz24vh3q\nKN1ATTlCI2SOPlqViMfBqDaykP9bIA7MgO83iga4GQNvVObd0E7qpabQhvXNYC0Gw9Ha5dpNR3FT\npl5qioqS/jgGnqhV3qap3A/Zn0HhaYT++leWRvxjkJ9yqLQc6v2m3oet4pw3o8TyHJJ0ohrcqJW0\nC82otBx2W92jS43wepFFpEs0qqcPrBM5RPoNxKg5RBQKGkuLc2xtjQEwMbrAycmLDSfYuVVgGHmm\nxm4yMbLAenyKpfUTZDJBbtw8i28tycTE4q2jqHISGbD5beQb9dsIXaWfl6aPPqqj8CRwAxgC43dA\n696XeB+HBM0rAzi1B6HwDJjPgvk25N9GwuSPAYMdbmQfvYYjYoSvIF+SE63tLC8ig1ImcGa52F7w\nFiKX83B9/iypVBhNy3Ni5jIjQ+sdS7BTjnq84J2CrptMjC4xOBInHh9jZW2GTDrIzRtnCAQSjE0u\nEoq459PbXvCewxjwBGKArwPfAj5CMapTDbYXvI8+bim8IBkV8YDxOdAipZttL/itAjde8KMG2wte\nCVrAkjZ8WCgq5s+RVNqvAe9Bkv70YvbUWl7wPtqBHjHCnQxr2525LBPdoqLUSzupVN6kOCDzHVX2\ndVREKVJC6qGgZDI+rl27nUw2gNeb5s4TLxEOiLHolKwHSikVqqKKx5GOUjtxjwon+ooTvaS0TGWq\niVMZJwpKvoRCkqtYprycR8sTHtnj2PB1ljdnWFo7QSoV4ub8WcLhLaYnb5SoqaiJf0qukb94PMdE\nPx6ljKqgojbOo7Q15cId3wrKSgD4HeDriHThk8CHgBllu9u6ytvRDL3E6dapl2rSql6s8q3ZR0tR\n75/lRCNxqrMZKRKQd8l3rcP9qtAbwd27o1XUFOos41S+VXDLaug2Okq95V0l+lHnI8DHofBuyP4A\nzNeBpxGFpSjwIO45buq7oN2JftzQNJqhnRxGsp5myncXjggL0jbC3fKyXGDd+gUplXkrxy9iLTtk\nKhXk6pXzZLIBgoFdbjv9yr4B3k1Yir3d6SbUDV0Tz/jd537BzORVdD3H3t4Ql67cxcLCHNkaOuPp\n2LOH1NI2wQ98ErgN6Y/+BeGKV8PVWJsb1Ucf3YQ08PdADoz75VexWOwQ29QF2Ih1ugWHj2zMfVl9\nFIzfAuNLwAlkQO93gP8bCaf3Cnr8HdejOFpGuDbduiovW9M7OBQPWSIR5trV28nnvUTCW5w9+Tpe\nT6u+fPuwoesFpsdvcPttLzM2uoSGyVZ8nEsX72ZtdQqzcITJ4gaSTfM+xD3/Q+D1jraojz66CP+M\neF4mwfOJTjemj16DdgKML4L+GYTvtwr8DfA15L7qo4+D6DAdxY1wfa1tJvtGuHdKPiuaCREGEE/h\ndWv5fmudUzjykaiyvhjyCKgUlEB1CkoyGWJ+/iyFgsHwwBrnZ1/ZH4AZVMr7y+goTrSTepP1ONFR\nnNafiZ5A5DZK4YZqosIN7cRpvkTRpKx+N+U8Rp7B6beYHZnn2spZtnbGWF2dZSs+xrHpeQYGtkgr\nCiwj0Xdgn7NToh8VJQoqynxWTQCEQ3IfFfV+h7kp/yEghDg+forc7w9WaMK5aHHeibLSDDWlGTWV\nesu4wRFxSfQOmpEKcUrg1qgiytuAxQP3fQaCZe+ZkvdItPL6TtFR2v0WV8eGNEJNaRUdpV7lk6bK\nRyuvV1GxTg24G7LnIf8c5H6E3FsXQXs3mI9Smy9eb6KfeuF0MerNAusmqU41dIqa0l04Aq+dLUTH\nNQR6pGZpV7iK/H+ziMxbG5FKBZm/do5CwcPwwBqnj7/ZV0A5RAT8Sc6eeINzc68Q8O+RyQa4dv12\nrs2fI5vp3ge3KWjAO4FfseZ/DjzDrZGZuY8+DiCJjFgGPI+BPtHR1vRxBKB5wPMI+P8X0B4ACmD+\nFPjfkY+9fmfbh+AIGOFt4INfsKZuEkP+LNbwYdJp/74BPhRZ5/Txt3oiF8TNWC/x3NxhMLLFnWde\nZHpqHl3PsbM7wrVL59lcm8A0IRl7vtNNbD3uQpRSdOBVJLmPOor0Suzw29RHH4eO7wK7oM2B4UIh\nIhVrd4O6C6uxTrfg8NEq3r8WAeNTYPwhRb74N4G/pJhgsFvw00434JZEB+goTt7Fal7HajG5FWv1\nZHFTIxQUGymEyuVFuLO+GuV9xWU1KY9fpaAYCjXFopDkcgY35s+Rz3sZDG9yx/GX0bWDFJSQQvtQ\n1VCkrowyX68iSn3UFBUB0iW0mkpoFQXFqXw1OopjIh6H9fuJfzSYG7vC9OBN5pfPsrE9ydrKDLtb\nQwylXzpw/cvrcVJQcYJjch+P8izUS6+ol75yD3IPfxeJmmaRpD4GJfe2I41ERa9TU/rqKF0IN5RF\nJ2qKCy6H/iYUXpHtwU+Drlcuri7rFO+zdtBROqWU4tR3qP2A233aoXzipkyrlE+yVE5s5qbOijgG\nni/KvZb9V0SD/j+C9k4r2U/QRR3tVlAxaD1to7w9raq/XmqK076dxxHwhFtGuN6iJD228McZwFet\noIV3R+s+RKGgsXj9NJlsgFBgh9Mn3ugpCsqJ6OlON6Gt8HkznDv+Bqfn3sDnTZFKh1k+8fssL81S\nOIoDN+eATyP3+xVEOSUHnI12sFF99NFuZKBgyRHqj4vKhRuEom1rUVdiKtrpFhw+gtHW16lpYNwH\n/v8ZjPfIOvPnkP8/EJ3xTtsAj3T4+LcmjoARvioTowVGuEmRinJ789VVPIQJywsnSCXDeD0pzp54\nHUMv1N6xj0PHYGSL82dfZmJsAYCNjSkuX7qL5F6owy1rA6aBX0e8P9cRz3j3Sqv20UcL8CNgGzgG\n2sOdbkwftwo0P3g/Csa/R9IaJ4BvAF9h357p45ZBlybrcdusApKuHvBNFD8pGg0FrgC7SFrv02Xl\nSxLxKPMvfw/e90GgNClP0K/MK9SNnbVRdrdH0PUcd869RNi7d6CMSkFRaR/VkvWUKqLklDJOSilO\niii1QzVXY9c4FT1ZtYxTEh83yiduKCvquafLRpuXqKAo5+lEU3FK/GOQBx3OTb1J4MUnWTv3OyTT\nYRavnWZsdJmpyRtk9crnqSqoGGFlvt7kPvWG75qJtJ0APoMk9VkA/iEGvxs9OJi/G6gp7QjHHwGX\nxNGAG8qiGwpKNUWUNfY5sL5fFRqKE7WkfDkXg0j04Ppmkvg0Q01xs74ZXI/BsWjtct2cfKdeBZWt\nGISjjdXjutwkeP4dFF6yKCpXEW3xRxClkmp9fzsUVJ5Gsn12Au1WOGlWyaV96PHXzgaQB4ZAb0Ga\n2HlrejvO93gT2NuNsLR6HDA5OXuRcGCv9Qfpoy0I+JOcP/Mi0+PzQIH1jSkuXr6bZOKIecXHEEN8\nANhEsmsepML30UcPw0Q4VwUwHgB9ttMN6uNWhaZZiaH+p6KKCj8G/gK41Nm29XEo6HEj3A7dtEBS\nqoCMlQA4X8d+lhe8FrJZL8s3TwIaU+M3GRyI19nA7kEtL/hRxED0AXTNZGZynrOn38DvT5DJBLhx\n9RzrK1OYnabztRLDiCE+HZXo0LdpTn+7jz66CheQTIZ+8Dxe/+62F/xWgRsv+FGD7QU/LGghS0Xl\ni8Ak4gH5a4SmUl0EoXXolBf81kZ3+eUd4ZB0QV8V41kbrz+0Vx5GXEA8fiMIP1arUKbCvFdRQVGT\n8qg0EJ+Z5eaNM+TzHobC65yeeBsNdxQUt8l6nGgn9aqmqHBDTVFRLwVFhRMFJaOMjnWirJS331Wy\nHofzV4+nnr9axhPMM3J6nRurp1laP87G2jTJ3Qgzx6/h88n1LqfI7MNFwEb9lx2pKU73dbPGsr3/\nKPBbwD8ikfvvA7/GwTB9p6gp7VBK6XGXRG+jGQqK03yl/qgAfE9m9SgEw5WLV6OjuJlvBx2lGQqK\nmzJuuvt2JevpFAWlYbWTMpRf34aPPQfZP4T8TyH3FDJg8wLoH4XCvdQO0bdbQaVZNEMLaUdyn86j\nt187psUH11rgCb9qTc9TFxWl8PSPa5ZZWZ0hkRzA48lw2+zrPaEFXg2XYjdqFzpiiMdeKlnWdZO5\nqcucPfkGXm+aZCrClct3EI+PHh2v+EJMPOLDSNblvke8j57Hi8jNPALauxqrYjvWwvb0AG7EOt2C\nw8durHPH1gzwvB98/x60U0ACCl8HvoYMJG4XatsyfbQedRvh+XyeBx54gE9+8pPtaE992DfCx5ur\np0ApH7yFSCcCrK4dA0xOzF7C6+mur7A+mkMkvM3tZ15maHCdQsFgceEUCzdPUcj39vftPiLAE8AQ\nfUP8FkRX9fdNI4tkpEK0mbW+MHwfXQx9DPT/DvRPIeGUC8D/iaQ4Piqenj7qpqP8+Z//OXfddRc7\nOzstOHyt0GEl2OVM9pVRmKg/KY9aZgOhogwDxyl6wp32jRStkOCHHsYeuaYm5QmRED3whVOAxvTY\ndSbCK3VTUBpJ1uOsiFI7QY+bZD33RsdAaVclONFOWqWC4kQtKa/XTbIep2uUUY43E70Nm5t3YF8D\n7px9iYXwCW4snWF7e5RUKsSJ4xcJBpKOtBY1uY+qmuIpUVApzmeVeVIqr6VNoZW7ozK1OeL/iBji\nP0CoKe1STWmHIoSbMn2b7ABa09/Xm6CtXhUUHNaXPxc/A3ZAn4bg3dUph+XVq9uGo5XX10tHaVXi\nHjfrm8G5qLty3ZCIp1Xz49HG920pNOABMM9B5jtgvgV8B3gd+CTCn622byU43SS/4lDGzcmpzsVm\nE/I0o4hSLzWltr3TbtTlrrtx4wZPPvkkf/AHf4DZ8Zj7NnLBQ6C5yTZVBVes6Wlaas+srsyQyQQI\n+vc4PnGl9g599Cw0DcZHlrnjzIsE/HtkMgEuX7mLjY2Jo0FPUT3ia8h7oK+acqTRXf19s0gDP5FZ\n3+P0PCewj1sL2gDovw36E0AIMVr+Anievle8t1GXEf7Hf/zH/Omf/im63g2h9nVr2iQVxaTIB28g\nEWTuRz+puD6RCLOxMQmYnJ55q6cyYtbChdhip5tw6NiIveKqXMCf5I7TLzEyvIJp6iwsnWJ5YY5C\noRuemTrxZqx02TbEBxBhon5CnyON7urvm8VzSCTrBBhnm6sqHmtBe3oI87FOt+Dw0Y28f00D/R4w\n/kfgbqTz/S6S5GezBQf4UQvq6KNeuA5effvb32ZycpIHHniAWCxWpeQ3kPg1SLxtGrjTWr4EhCkS\nr1+zpndbU3vw20es6c+s6a9Z058gsg1RxAi/ArohZ+EBkla7PFGZbsXk3pywlpet7bNRadqVGGwB\niagYFomYKFfdY5V/3Sr/oFX+OVn2/uqDgAzKNK68QPDjspyPPS1n/ejDLC6eguefYmRwhYm7BgGI\nx14GUoxF7wFgN/YLACajdxIkwVLsbQDGoicAuBm7SJL0fpr4RWv7yegp63TeAuB09AQGeS7HrgNw\nZ1Syh16M3cRLjtuix4DigMrbo9N4yPNWbAmAu6IysPXN2DImGmejs+Tw8GZsmQIGZ6LC0bkQu2n9\nDz4SBLkSuwGY3BadsY5/A508d0XH0SnwVmwZgNuiMwC8FVsij8Ht0WnreKvW9mPkMbgQk8yUZ6zz\nvxi7SR6ds9HjANyIXdrfnsHHlZgQ+e3rczV2DYCZqNxf87ErZPFyInrG2n4VgOPRsxjkWYhdsK63\n3H9LsbfJ4mUqegcAm7FXAZiI3omHHNuxXwIwGH0AEMM8i4/h6H0AbMVe2GVwSgAAIABJREFUBGAo\nej+nZ97G98I/s7I+y867HieT8jN+6WvgMwlFZUBYKva83C/Rh8GAdOxZubofeBSAbOwZjIwXzwcl\nnbA9CFh//wfE9n3G6jQf/LBMn41BRoOHo7L8fEykVh6yll+IWeWt5Ret5Tus5Zet8vb9v/iipLK/\nKyp0EdsofyIK/wBcjklA6nej8vxdsraftcpfsZZtibNrMYn+zVnLF63tx639F6zlSfv4VnvstNnb\nyvYUsGYt2/SAdav8iLUcV7Z7lP0Hre07MUi+CFmRC/3xdy7x+Q99gT7q6e+hcp9/m7V8GeEtnbOW\n7Yig/Q5405ragyRfteq4z1r+pTV9wJra74THrOmzwCCS3ATE2AZ5R4BwwLPFeowA8FTxHZGzzi0Q\nlcPuKcsg94i6HI9B+sXisj2Ab9zaf8Vatu/xpZgw9+xnYN3aPhuVe9Ie9HjK2n49JrQoe/+b1vaT\nVvmr1rJNEbGfsdMVlj3IMwpwxtrudtk+/pUYbL1YlGUsP579DNvtt9t33Fouf+Ztg34uKgyB69ay\nfX1uWOVny8rPWOUXy8ovWuWnrWX7ek1Z5e3/Y9TavhqTPmLMWla354BNa9mH/J9xq/4hq/yGtX3Q\nKm/fH3aae/t+sO+PvZiMOQtZy2r5HJAqK5+OiWvUZy3bNo3XKm/fr97PQP5uyP5vyDO1APqHobCD\nhPOt/e0xEI7LTyvLHuAZa/lRa/oUcmBbitkevGk/b/b+77GmtlPyEWtqJcTivdb02bLy9vJD1vQ5\n63h2Btvnram9bD//91vTn5ft/wtr+s6yZbs/+TvgbaSPAvh9Og3NdBln/JM/+RO++tWv4vF4SKVS\nbG9v88QTT/CVr3xlv8wPfvADPvShSiNsVbrIoDI/6jA/Vbb/VIX57wLPg+dD4HmkeE2hvvmXgTeA\ndyD34bhDeWW9d7w4Qnl4rKj3PYDwJuPrY2wsT+P3Jrnz7AsM6UU+pcr9tstDYxkz1W0q19hNJk0P\neQpoZPCTwUsGP1m85PDQCk6ORh4vObxk9qc+MhSU4IsTD9wNb1yVEsyVkXlVLrdTObVMWinjtG+6\n7vUyn0wHuXT9LjKZILqeZ2p2nsjAdvU25JU6U0qdCg88q6wv4Yenyv67VBvmc0AcMcT3kEybH6XU\nK15t30bLtGp9+TZr/gufSvP5x57m8ccb0I4+YnDT30O1Pl/lXQZdzA8o8yGH9YMO68cc1tvPwrPA\nv4B2HHxfgqDyjKiZkJ2yIlfb1m1yhSqa4Yc3IkXotL4d3O9m6nHqI1opb3hY/HUzYXHFX7dWnAU+\nTelzUA2q+ed0gbMOZZzWO+1bablWvc2UcTpuscz3v5/veH/v+jH98pe/zJe//GUAnnrqKf7sz/7s\nQId8uLDoKNpY9WK1sGBNG6CiVEIu62FzVTzLx6cvdxUNxQSyeEkTII2fLD4OGtwmHjJ4yGOQw0Me\njcL+VFPqMtHI46GATh5j/5fFi4lBBqPE0JS6c/jI4CONhzx6mRL2UUPQn+Ts6de5uXCa7Z1RFq+f\nZnRiidHx5baNpzwUDAO/gRji15HBmu+n10VP+7DQff19o8iz743zvP9oc8FNxMu7h3jfs8rU/hWs\ncgXkWbV/HuS7yYsELmxPcND69Z/r7oQWAuO3oPAaFL6DsA3+L+BXgXs627Y+XKHhb2XtUDuzSs20\njHDveLETqVS8mmrKLkJH8QInre2Ono3il5Q/UPQ0m7EfEYi+GxDP9PXlM5gFg5GBVSYHhI6heqbd\nqKC4KVNer+rxVtcb5MngZZcIe4ySVzxUGgX8pAixR5CkNZ+saRu+Flvj7qgzF99EPLtiagdIEiKN\nnzR+cpZfPEHYaneaIAnr+Gk0Sj3hToooqle/PEmQqpaiqsaoHwRO6jBO69djrzIZvfPAsZ2UVUrq\nNPKcP/4Ki+snuLFymo3VaXIpH9Mz8xhGoWL5fTipjCgo9QmUS5Y08Zy+GitSU1TYnqQp4FMIG+EK\n8hxFaxyyG5L7lG+z0VdHcUTn+vt6lVLK2/kqsA36BPhud52ErWqynt1YUT2jU17xDPIK3ECiUnGE\nGlYaLG0NEjGhdA4iDtZBZID2CMIutS95ryTlcRLNUPuElViRwnIYnvCmZV/vBnMOMv8E5kVEyupt\n4OOURpzKoT4vP6FIUzkM56GbxD3NlHGjstJ5dZSGjPBHH32URx99tHbBtiGHWM8aaMO1CjvDpjjb\nBniT2NuLsLU9hqYVODV1ofkKm4AJJAixy0CZ8ZklRIIIO4RIoGOWGI+teNVqiDHrIUmIJIMW7aaA\nZhnlQRKESBK06DB+thhBJ09o3yBP9bSjuByaBjPj1/EG0szfuI3tnVHSV4McP3EJn68db85DwgSi\nlPVNpM/3Ae/raIv6aDE63983CpN9L7j3fb3tBc8iUdtFYAUZ61TJTvIihnLI+gUperW9yIemZv1s\nj3jeqj+FGPEp65dAvOrqr3xMvg9hko4hRvkYpYZ5H4cHbQD03wXzF1D4HvAKcA2hp5zpbNv6cESP\npK0vh9UDacOgNXEKduLHJqgothfcNGFxeQ6AifFFAr7OZDQpoLHNIDtEKFh/rxi3ewyyTcAybt3o\ngTuhmhe8GnRMgiQJkmSUDXIY+wb5HhFyeNllgF0G9g1yLxk85Drep9te8GYxGNnitjOvcGX+DtLp\nIFevnOf48SsY4S6UGankBa+EaeATSCIfe1zd3VX36KOPQ8AVYBmIgKeFoXlVQ7qdSCGOohuI4a0y\n93TE4B1FxiuNIh7qAJUN4GbS1uejYoBvI6/eLeu3iSg/Llk/GyHk43wSiZaFHNrUzbC94L0GTQPt\nIdBOQ/7ryA30VWQg5ONUvxGih9DAPsrRRUZ4PYl7NmRijBWL1pusR6PYcdyhbHMorweK3spguEgL\nsekiO9vDpFJhvJ40M2PXSmgkpfMq7aQ+CopaBkqpFl6y7DDAFsMUrLi6jzSjrDHEFjqmqyQ+KsqT\n4NRC+QBJG9UGYIZJAOtkLf74NoNsMUQWP7vW4BIfaQbYJkAS3XL/ONFMwDnBj5sERXVTTeqktQD4\nfWnuPv0LLty4h529YeavnWN6Zp7h4Q0OQLmkRlipU0nco94VB035Q0jqAyKG8WHge8iAdS9wl7XN\nDe3E6ZltVxKfStv6vNdDhtMf5IaC4jSvQPupeHv1d0FQqadZOopjEjeH9fUk7skjYywuIp5v29ut\nIQbtCeCY9bNPu1WDNKsNxhwCZsrKmIhxvoZ86ywjHwsJxAF7zSoXstp73DoHmx3RDUl5nGgqzQze\nrLbNyTen3hctOZ8xyH4J8j+G3FPI4OQrYDwB+QmHRqhQ3xX13mBuR/XWCzfUFCc4UVM6n+yii4zw\nemAZK/po9WLVsIz8LyOUDrqvE4nYzwg++i7WV0VK5djEPLp+eIMNhX8dYIXJfb53gCRjrBEigacN\nD8TLsTj3RZugAVWAhhjPE6wywiZpyyDfZogMftaZQKOwT6U57AGdS7G3mY7eXrugS3iMPKfn3mRh\n+SRrG8dYXDhFJhNgYmKhe7xGL8fgvqj78ueQcPa/ISyAAP0oaB8dwobFjTXEM9hKrMSKMpqtwjbw\nFjKuzrYLNGAOEbyYo3pGz3birRicjx5cryEfHhHgFPI+NREPuU2dWUCM8kvWD8SDfxwx6kfonv5O\nxVrs8CIe7YKmg+dR0M9C5r8By5D/D4gE9EMcvPAx+t7ww0dvG+FGE0a4TUU53nRj2I6Pks348fuS\njA0vN1+hS+Qw2GaYtNU7e0kzwiZDbHVlv+YWMnYqTYBVRtlgjzDbDJG0aCt7RPCRJsxOide716Bp\nMDt9Db8vyc2l06yvTZPN+BidWeoqVZ26cBeiyPAsIjEbQMLSffRxqLD0g7V7REGiWxFHJHKvU/R6\njyHR2VOUetd7ARpFaswdyDnFKdJqFpEBpetIWpAQ8oExi5x3L7+4uhX6cTD+CAr/DOaLwJOIfv8n\nKZUD7aMTOCQj3Cm86Pbw5eFGKzuUd7QyHcXNqHNVmtAx1Fg0hEKRYtBfNfwGP3g/b18U7fJTExcI\na0IfCbmgnThRUFT9cHVf+7gSBYywwSQmOjp5pllilPUDfG+VtuGOjlGbgvLuqB/KlFrKkXekptTW\nA8+UKaKESTDJKnsE2WSULYb3B3R6yTDANiESyiB9VUWlNVQTSSCUPLDeDa3FCXb5udGrBH0JLt+4\ng+3tUbJZH8dPXMLjqfJflIugWEiULTsrp7h429lJf+rF+6yGvAx8H+GL28MInJ5TFfXSVOpd77St\nT0fpIJzUC1S4Fc3OAZI4i8C7hNLViHoWDst2cihoXD88jnwn2JQNHaF03Y1QTuzH0w3Vqhk6iptA\n6Tuj7so7USQGkHMC6UJvInT9q0g/8ab1CyPv45MUDfJWUU3qpZfYyYca2bfasVtFO6l7yJkf+DTk\nz0H2W8gFvwn8JvK1B85e8HqpKZ2EG0WUdtFlGkO3X1EH2HSUkcZ2TyFf4h6Eq9ZMSzYnyeV8BPwJ\nxgfb7wXPo7PBGCmLWBdhhzHW9hVIjjL8ZJhmiQlWWGeCOMNk8bHBOFtkGWSbMHudbmZDGIzEOX/q\nZS7O300yGeHa1fOcmLuIksOnd6AhmuFJ4ALCE/8k7vNH9NFHU3gdSIJ+DIzZTjemFAnEA3wB8aYY\nwHkkAaD9fBxlb7AXsflOIR6CZcQpexnhl79q/QYRKttJei8a0M0w7obCLOT/EQlNfAXJhvlB+l6I\nzqAHr3oBGZoNGA0a4WvWdIamPkPMgsbKk5I6fnLyZtsVsFL4WeIYKYLo5JliiSmW6x5A2Sx+Gduu\nXaiNMCgwTJyTXGWCZTxkyeNlkzGWOEaSYMtVTm/GLra4xoMIBhKcP/0Sfn+STCbA1avnSSddCIW3\nC3Za+0agIYPxjyPG+L/QAi3cPvpwgxdk4n2wPdUvxerfp4AY3t9ApDxB6BqfRTJ6d/MH6uux9tSr\nIcpK7wN+G/g1hM4WQDjyLyLSp99HPOeH6cBcjh3iwQ4Z2jAYXwTtA8iX4FOIMf6dzrbrFkWXesKr\nhSa3kB5tALxK8+sJMdoiFKesdY6hQyUZjqKOYifG2d4aoZD3EvLvMhVZKKGXOCXoqZeCEiKBCeww\nwIYVowuyxzRLDFE0hlXaiZMKihtqigqn9SESDFRw17ihoDiloVfLqO13Stxjlxm0IgHbDLHGBBn8\nxBm1lGHWCSo0lWZUTQKk9/87N7QWJ9Si+/i9Ge449SKXrt/JbmKYxWunmDtxgUi4SqTDgZoCkPYU\n21RqA7ugptj6ws3g14GvIZGnHyDp7e2/3Q3tRIUbqkkzSin9ZD2HgHq5E24UUZT711iH/DXZHri3\nuKleRZRqdJQgRe+sG3WUBPA0sGotzyGKcWoUthtS2Dt1X+r5NkJHcVMmh3yInEUGd99AGBOXKSqv\n+JDB3+cpFVNwQxdxk6BHXa/2ffWqplRarrXPoaup6MBjkD4F2a8jvKhnQT8P+rkq/7P6rlCfwWbd\nXm5oJPWWr7fOzqAHPeEWH5wGveAgMkpQ5Kk1ANOE+NoYPBzl2Ph827zgJrDOGBuMAxojbHCcG3g7\nyGt6KBru2LErQQOG2OIMFznGTTxkyeBniRlWmSTTggfwRLQJMfk6YRh5zs29xvDgKoWCwbX529ne\nbq0ajSs8GG2+Dj9CRYkgkqBPcTjJ2Pq4NVH4pUy1u0Gr8nXaDGaj7sqZCDPmm4gBHkKEKT5OU6+v\nQ8e90cM9no58qHwE+H3gA4jueAa5nl8HvosY6O0KAh+LtqniLoNxBvx/JAoqHIPC30D++3RDJslb\nBT1ohMetaYO9mJ35y09Tqg17O4Pksn783iSjg6u1d2gAJrDCFLsMolFgmgUmWD3SlMFmoAHDxJnj\nGmOsopMnTYBlptlglEIPXTldNzk9+xajI8uYps78jXNsb3bAEG8Fwkio2YcMxvpZR1vTx5FFAcyX\nZFZ/oLNNSQA/BH6JBG7vAJ6gqcRwtyT8CEXlN5HEj3cgTs0V4MdIdvbX6FPdmoEWAe/vgf4YoIH5\nE+D/BTpLO71V0INGuO0Jb9Agsb3gszR89qYJW2si9zD8xj+2xQteQCPOCElC++on3TL48uex7h78\nKMb4FnNcI2J1JHtEWGecRIN88euxKy1toxtoGhybnmdi/CagsbY4S3x97PAa8EKsdXWNAR9D/pxX\nEFm2PvpoKa4Au4hGXhNhzlq4Gau+fRVRgVtCjMgPA4/Qm4OsAV6JdboFgnHkOn4OofMMI+NNXgW+\nBTxP6+zGxViLKuoRaBqQB+PfIbyg68D/g4Qb+mgnuogT7ja9nTUok+H6paYCFPngJ5VyDlxAr8oD\nNxQ96j2DdCqIYWQZiyzjQyQKfQqXWc2M6S5jpipFmGKZabL48JBljqv4yZSUkXIKZx2Vs16bH+6k\nr+2GHx4ixYCVLMeJB66iXk54WnlbqWXUc8woZcrbrPK6gyRJ42OZafYYYJdBMvgZZnP/2qj1JvbT\nuZXz6VP7/6MTh9wJbmQfHfnkGpyYvILfSHFj+Swby9N4CnkGx9cqf/xVicDnc8Vr6Uq6sBWccBW3\nAb+CeAh/ivT1lXT6m8mkWS9XXN3Wgy6J3oaLrJeO/PBKf+gr1qZ7waO5y1rpJvtl+baksqyW8yOD\nL3+OhDFngEeRb4Jax3MrlVirvFOZeqF2R4fFCa81bz/PAeAdwH2I1PDLwDzyDXYFcbDdDRaDs3Tf\n8jqduOJq31dvVs1Ky5XWu+GB18v9biYikAeMk+D5I0nuY15GUt5HEfWUat7GXpIx7C704GvHpqM0\n6Am3VQTnGm/B2roY3aMjK4w+dl/jFVVAAY1lpsngx0OWU1wpMaS7Ae+OdlCxowH4yXCCeaZZ2OeL\nrzDFJiOuKSqnoifb3MrqmBxbZHbmCmCysjrL+soxzHZzqx+Ktr7OO4EHESPlhxQDW3300RSy7IdX\n9Nb2yQdwInpwXQHxxP4MubfvRQYhH4VcKPdHO92CytAQg/vDwGeQvsVA5K+/hygyqUmQ6oFb3v9R\nghGVqRYG/fdAe9TaEAP+K7Vyg/TRGG4tIzwB7CAOlQb54LmMh53dYTStwNjoSu0d6oAJ+4loPGSZ\nZhFvmc+yj8agAWESnGCeYcvy22WAJY6VeN67GSPDa5w4fgkosLk+ydryTPsN8XbgPYgKQhb4V/p8\nzj5agLeBDGizoDeRSbkR5JDIzkXECHwf8DA9+XbtWQwh1/0ziOa6H1Fk+hGivNeoMX6rQtPFKNc/\nj4RCLgL/gWKWwz5ahTbGDZpRpChvll1XHrGiNTAG65dvsvXBJyn1UDhkyfQHDtI6EptDgMbI4Coh\nzx6p2HOMRu8FnKUI3WbMXGFqn4Jykiv4yDrua+9T3j5wR0dxkyXSCc/EsrwvWv3/LaWdOEkXFv8c\nlV6itt+pTClVpDRSoJZTZQ3tc4uwxxBxlpkmRZAtRgizyyjrJdclqRzjWuyqlTWzfnlHp2vaCJVl\nYnAJ74kMV27cQXxjAt00GZ1edB6X4CKzpiM15fmnKmfNdArP1jP/UeDvEf7sD63lWsymVtFUysvZ\n27pXxaoH0UhmZBtONBW1niCleM0qfk/tLMpuKCjl94u6bS1WzKioA88g93EAGfcw5fJ4bugy9dJO\n2vFGfy5WmjVThdsMkvWUd6JXOFFH1PkAQkN5GKGpvIIwWJ9HJA/vRaLg9geSE6VkIQZz0eplnKgp\n5eWc1jdzvVolXVhybjHwRMsqPAvZP4T83yMG+F8io+zvd2gANEZNcfpz3UB9gzkdz02ZzqDHvtXt\nUReD8qVWL2wqylRjRzcLGrvxIQDGRxYbq6RSvcA64/uDMOe4iq/vAW8rbIrKBCtoFNgjwgKzpKqR\nqrsEwwMbzJ24gKYV2NicZGXxeO95xL0Uw/WLiCHTa+fQR5cgjZCxAc9dh3vY71OUH/wUDb9b+mgx\nvAgv/LeQwZwRxHz4CfBthDte6Fjregv7yX0eRByh30TCC30Zw1agx4xwe1DmUGO720b4dGO7J3Yi\nFPIegv49wkFRKrG94M0gRZBdBtAoMMVS13HAy1HLC94r0IARNpnhJn5S5PGwyThbDB3gitte8G7B\nQGSbk5Yhvh0fa48hXskL3kqEEc+hgbAJXm/v4fo4qngb8Z7NgT5Yq3DzOBUVzeofI2MaBhBN617S\n/q4HTl7wXoCByBr+BmKMDyDB9GcQBZubVP74t73gtxIOeMEVaB4wPokkfTCQ0cf/BbpEsa2X0WG/\nvJvR8SosT7g+JC2vJ9yYRZRRNESRwTEUWKRCBMOlVJDVzVkAZkbmCWuyrVQRxYmO4jyfJEDC4sbM\ncJNBtqtmz1ShHlvdptI5ShVRalNTVHjy9X3p5ozatJO8A02llIJSXJ8pyZJZWQ0mU8bpNhzoItUy\nXQ6wzTrjrDJJgghZfAwR3+fktzozZiv2HY2s4jmR4dL1u9mOj+HR8u2jpqgfJa3ME3UCGVj1z8Bz\nSChZVWF0oxpRL02lvJyNHnNJ9D7q5TI5ZMnUXhdDSr+rucyYbjNmGogRt4X4gz6FeMKd6CztoKO0\nQxHFCW4VUZzWNzPvhoLilr5yP0JHeRV4Efn/nkX6mwcpVbFpRBEFh22NZNxsRRk3Y23qpq88COYU\n5P8OSWv6H4DP4iwJWv4y6gYqSHexDHrstWN5wrUGPOFxpKOeoCHuZybjJ5EYQNPyTAwVqShrsdfq\nr8xCFg/rlo7SOCsM9og4/o9jRy+OpwHjrHGc63hJk8XHGhPsEcYELsS6c0DKYGSrhJrS0sGaz8Za\nVFENnEdekCYS3t89nMP2cRSQAfOizGp3tv9weeAbMRn0ZyehOgoKKNXwfKzTLWgdDKS/+QwyQDyA\n/Jf/imTztdWarsY60brOIhNzV06bBeMPgVNIZ/1fEM94H42gx4xwy0OsNRBytPXBG+TsxTfFPTc4\nGMdjNM+FsnngJjpBEozTnqybfdQHPxmOc4NB4oDGNsNsMobZxdk2ByLb+4Z4fGPicOQLW413Ic6U\nFDJQs5Xe9j6OMC4hN8tsY++FemACLyCGWhB4nIN64n30BgyEM/6biBfciyRX+h4SkaucRqMPG1oY\n+DzwboRc/x2EbN/nideLbogNVEC5q9pupuUp9lSgo9Sat+nkM1SlsqgJemz6g2nC8pYQySdGFkuo\nEzPR09gBfT9ukvUkrOYMkcWHlwwz3CTsmMTn4L6VyjkpoqjrVXqJL1U5JGMoxo/H4Xn6xAPA1sGN\nOaNynXmPOq8r80oSH8OJglI8l7SDOkp54iEnqopPqTfpQFlRFVTW2WOJadIEmIzeicEafjKuFFGc\nKCvO65vrvMYiqxjH81y+fgeb65N49QyTE4slVKASKEyTfK4yjSgbfS/7b6Oc8pC0Syb+E8DfIkbO\nc8BjVco2m6yn0mWpnXeqj6bRStUsED444DlfP0Wx2ny5cR1BKAwLwEhUPOCjOFNQWkVNKZlXvqw9\ntTtq3akDd4GC2id85D3sP0wOfYVsUxqbc6Cv1Tvv9DzXS1+p1l+8F4nEPYdIzV/FkucD7sH5/6jW\nv7ihrdRLNXGTxKfeRD9q+VDUoRFOdRrAxyB/DLLfAn6BjFL+LBImqgTVmaX2Ba3yGqk2SG+MXesx\nT7hlhNdLRzEpesIbGJSZ3guRy/nw+ZKEgs3HylP4SRABTI6xgNEfpt2ViLDLSa4SIEkeDytMsUOk\na0U8hgc2OHH8MpLQ5/h+UqmeQQAxbjyILG3jTK8+bgkU2DfC9fPtPdQV5H7UgA9Ryh/uo/cRROgp\nTwCnEYfuy8DXkczt3drpdwOMd4h6CgNI6tL/iIQV+nCDHjLCJZUNIAMz60ECcegFaEhYJbE1AMDI\n0MFU4SuxN+qqK4/OljWMfpxVAj0Y94o93ekWHB685DjBPMuxNwCNOKNsM9i1ffLQ4KaVWROWlufY\n3mwwsyzAMz9qUavqwDiSJRkkAcqyc9E+bnXcBBKgjYA20b7DbCAD+ADeCaRi7TtWN6IT/UCnMIhE\n4O6JSV+URLKgfp9inpGjinSs8X21WTD+BySF6RaiJ16fbXSrogN0lEZCBBoSN8kCPirKPFSjo9jj\nHY9RzPHgEApUE/T4yFAoaCR3JLQyNbSAn3QJDSRLep8mUitZj4lkaSxgECTBHPP7wZlSRZTivur6\ncjqK30GZxZ9W6CipopddjU5qTuEppwimUkbbA82m9yjXuuSfNRzWe4rtyfqL83lPMYzk9ygUFL9K\nJ1FpJpVpKnJod4oo9awfZ49jLFj0lCBb6EyWWYhuku8cBqaGF9AKJjeWzrK2OEPQSDI06JwfPh+o\nHGIu+LLoFj0rWxKGrvMZrje5z3nkhfcikvHu15HnthmllPKertI+PeSSOHpwUsqqpqBlecG9t0HQ\n6kndKI7UQxtJI1H2ApIW/R2Ik8/er2V0lMpUE12hRxpKB254KvMXPA4UFMNhvRMVTUU6mMKIJCpu\nyysUFKe6Sqgt6nxK+T9bpZTiVKZemsokkoHzAkJT2QB+AJxBqCvl/VE19SWnY9RLWXFa34xqinoP\nZpXlelVWABgAzxcg8y0wXwb+DvmieT8HVVLK0UiCn6OBHnrt2FSUQZw12BxgU1GO1X/UxM4AZsEg\nHNwm4Dt4N05Hb3ddV9qioWgUmGS5i4f6lUFD7hRDftFHrHmd2s/WEcGd0QkG2GGOa3jIksHPArNk\nupR3Njm6yLGJa4DGjZtn2N0bqLsO/f0faH3D3OK9yPiNBPBv9BNr9FEBliqK130fXBdMJNNiAlHV\nere1/o5oe47XpTA+8P5ON+HwcVtU3m23I0oq70Ded5eBbyHZN49anxSMNl+H5gH910F/3FrxQ+Ab\n9EfaO6P3jPBGkjE0YYTvbgt/ZWxwpf6dFRTQ2EUMoTHWusZregCKsb0/0MlAAhDesp+vrJxH2feI\nwk+GYywQIEEBgzgjJNs2UrE5TI9fZ3RkGdPUmb9+G+lkd7azInQZVrRLAAAgAElEQVQkAUoQyaj5\nQmeb00e3YRtxSXvBc7I9h3gbGYjpBX6FI92v9VEFXuAhREllBvEY/wKRNVzvYLu6FZoG+vtB/xxy\n8V4GvgLsdbZdXYou8vs7JWWwYRnhxmCxqJvQtp+i9uessq0kFFikQviU8J8nnyW5KwMoZwav76tw\nqGoc67HXmIneBpQqopSqlaTZYJQCBiH2mGYJDWf6ihMFRaXBAITySoIeRe3Er9DMNdV5r9LPTYoG\ntPoppinb88jXvqn8gNizEH2PVdb+6Th7xk2rnjzSgVkeBK/SHq/ygjMDRReDL1U8gUyg2FDDX5k2\nUr5cSfmk+vpQxfWvxta5JzpmlckRZpdlptlkjB2G0DAJsVfx9N2oqbQKaqIjNDg5fQEzr7O5PcHS\n9TlOnXoLn68sI6tqXCjPRe5HP8HzwUekXiWMXOoAcggpO1EB6kEASW3/TeAlRF60Uk4INxSU8jZU\n2qeHXBJHA2o/7yZBj7r+kjU9DV5lfb3JcJwoJEnkngN4lFIHzuUY3BU9uI8bOkpEoZ0o1EdVycSn\nrPeUUFAc5o3KdDpXcEjgpSIZ+xm+6HsByOedv0TUPkKdz5WsV+gryru2hLKSUhqlqqy4UUqpl47i\ntP5irBjxsI9lDxy/BvwEyT3yfcRbfh+l19KJwtEM7cRpfatUUzZilRVS3NRZEech+yXIfw24Dvwn\n4HeRsFI1tIqaoja2OyPW0FOvHYWOUg92EMMvCNQZkd/dGcY0dUKhXfzexgdQpvGxZ6mhzHKjcwwO\nDbmn/cj18CF3gIlcoxRyvTaR6EEcuew7iCb/nvVLWdNda9u2VXbD2ncLeYmlKXLMbW+6Ten30dNU\nFg2YZokx1gCTbYaJM9p1AzY1DU7OvE0kFCef83J9/lzVF2nXYRZ42Jp/ir4zpQ8LthF+rvVV55Gx\nCCaiJd0mR3sfPQgNyVHzWUS+UEMiJt9GpA277QXQaWjTYPwBEkKIA/8ZkRrqw0YXecJrwfIO63Va\n0jYVZaxqqYrY3hZliYEqg9psL7gTTGDT0rMaZLuzaijql3oB+VDMUSqt6cKREn1XlY0FDnLlbP64\ngXyQ2p5zGz3Qcdle8HIMsIOHLCtMkSLIOuOM7t903QFdNzl74g3evHo/6XSQ6/NnmTo5j65Xv/C2\nF7zjeCdCSZlH+OGf6Gxz+ug0Cgg5F+Bs66t/HbEXhhAaQjlsL3iXwjTBLOjkswaFnAezoFPI65gF\nXZJ4mUXvh6aZoJlouolu5NGMArqRx/DIvKax7wW/pVCL9+9F+qWziIrTCuIdv4I4DXrIz7EPNzrh\njUAbAOMLUPhvYL4J/DUSUnigPcfrMXTYCK8nRGAZ4Z6B2nQUNXxiZ5gfxzEMqY5A9xliJBfyGpt7\nxwCTsYHVEgpK0CGZTiVFlCQBsvjwkGWS5YqJe6rNqxSUgXSRpgKlyide1UNoN9XmZ9sGb8HalqbU\no+hCEcUVnO4mo6yMhnjCg8gtYLfPlGNqOxQpK8qHgzet0FT8Kk2llF7hUxRVnFRU3CXWqUxfMcry\nVAdJEGKP65wki58NxhhmY5/O0g7aiYq8mx7fgNvmXuGtK+8gmYywsTDNzOzVA2Oc1aRJJdQUJVys\nXu2S761cG1VTPgr8DSJZ+BJwr4t9ncLXTvv04ouz5+DmleNEQbFv1mUgCdow+Efd/f9u59cRRQxb\nD7ySCoqb+RIKStHLUfKuUWgnfnW9X1FEUR6ScjqdaUI+6yG75yOTCpJN+8hm/GQzPkyzFUHuAh5v\nDq8vg8ebkak/i9efxvDm0LSyvkcVQfErFBTlT1GjcJlUsT8uoawo1yKrlClRVvG4oMHVu94Nra28\nTAQZuPkSImW4gCSPvB+4jWL0udYx2kFfaRVNxaltdSUD8oL5Wcj8K5g/Bf4J+dKNUj0kfvRVU3ro\nrCwD1KiTjtKgJzyzFxIqSnAHr7dyJkiA67HLnIieqbjNBIuGAuOsoR+Wy9fmetv3bx4xvJOOe9SF\n2AsQfbCJCkxKqSpeipJPXqVMF41dfSkW5x1RZ83tAGlmucEiM2Tws84Eo6zh7aJR4T5vhnNzr/HW\n1fvY3h7F60szObnoWD4bewZv9H2H2MIqCCFpwr+FDNKcoKHEW30cBVhecP10a6vNI3rgJmJEOd1f\nr8Tg3mhrj+0Cpgm5jJf0XojMXpBUIkghX/kVrul5PJ4sHk8O3chhGAV0PV/0fGNiomEWNExTp1DQ\nKRQMCnmDfN5DLuulUDDIZX3kfvIMPBw9UL8vkMYbSOMLpvCFUni83dPXNY3XYnB31F1ZDbgDmEO8\n4lcRg/wqkgAo5LRjl2E3BpFo++rXNDA+AoVRKDyJcL7iwKe4lT0gvWeE10tHsUcv12mEp3bkyRka\naJxakCBMAQM/KQb2xcoPAbYhW0AM727vG7MUKSk2Z1xH7s4eoKrY8JBnhpssMU2KkGWId9fw+WAg\nwZnjb3Jx/m7W147h86UJDvcI0XoGeBAxwn8MfJLGB3320cOwOKV6ZedHw3gDsQkiFMchdBimCdmk\nn9ROmPR2iHy2NCeCbuTwB5L4Aym8/rT8fBkMo1D/IE0FeTwUChq5rJe9q0vo04tk0z7S6QDZtJ9C\n3kM6ESKdKFqYhieLL5TCH07gCRe95bcMbEfBFeAZJIP7kwh3/HZ6agReW6E/BAxC4R8Q5ZRt4Le5\nVTvzLjXCy5uVQ8RaNfCGix7eWiHsFGKE+jhIR1HKl4QFyWCakNmVzmVqYJEgiZJEMSo1ZSZ6HDtA\nX6qIkmLVGgV8nOuE9xP6qFSW2vMqBSW0V0q21lTbqUCRb51HBk2mKFVEcZOgx0USgOhZ9pOXlsDp\nblLXl1NTbPjL1nuRTs1P8f/OWG0yQXW6ePKl18XIFeNnnkBlFQE3iigqjeQ9UR9QOWFF+b5hLnGV\n0+wR2aemtHosgCsKCqWhYBsTkRWS0yFuLp1haWGOOe9FQuHdg/U+/k7sG8gpoU9KDREHKlEHyqDe\nU430uY8gFLNFJInGR6qUdQr9li8HHMr00SI40ZSqJeJxWp9DBgcA3tNi2DRCO7FhU0gSSFp6EDWU\nkbLDqlST90Yrry+ZL958XoVeEVKS3qi0E/WdYpAnm/GyFx9ib2uQnGJ4G0aWcHiHSHiLcHgHnzeN\nR3NSX2rOCEcH/DD2iVOIJEixf8jmPKSSYfZSEZLJMMlEmHzOS3LbS3JbHGUeb4ZgeJdAJEEgnEA3\nCuQVupsvnC49noVMuni+eeXdnFZUU0qUVVTKitoHpZQ+yA0dRZ1/d7R2Gaf+5V5ExemnyKDNlxCa\nyiOU3iNONI9201ecKCjj0dpl6k3iU97H7+9/OyS/YCmnXAX+Cvg9JGWpE5qhpqhshu7q6LurNY7Y\ntaaR+hL12PbrGHUpcaSTQQp5g4AvQdBf3fByQpxhTHSCJBjYb3+bYNNPTMRQjdNTHuSKyCKGfoii\nqorNce8imkol6JhMscQqE+wwxCZjjLBBwH3qsbZjfHSFdCbI2sYxbtw4zanTFaQLuxE68DGEH34V\nSZrRYlZCH92Mm0AO9EnQw62r9iWpljPA8dZVWw9ME9J7QXbXh0ntFa01jydDZHCLocENgsE9iep3\nuBP0enJ4B7YIDci7zTQhkQ6RTERI7EVIJiLksj524qPsxEcBk0B4j8DgHsHIHoa3yzvxZhFAtOXP\nIKpOqwiV7gHEK34rRQicoM2A8d9D/m+Qka3/GTHEJzvbrkNGjwRIFCO8HtgMkPH6dkvuyHFGIms1\ny87HDsrtqIl5RnBWVmkaGmKUahSpJxnaboDHXm5v/SUoUJROtLzgnaCP/TK2U7uQAg2YYJUh4oDG\nJqMkCbalbY1iZuoaA+E4+byXG9fPks+Xdgfp2LMdalkNDCKZkEHCvpWiMn0cUVyVidFC3cBVxLlu\nIBzeWngx1rpjYxmwWxFWrpxgbf44qb0ImlYgPLTF7NwlTt32BhPTC4RCex2hd+zGamfK0jTwB9IM\nj64zc+IaJ29/i9nTlxiZWMYfFEdWai9CfHGKxQunWbk6S2JjgEKuS02Ql2Otqeck8GnEGM8DP0eS\nSHYjA3A7dvjH1IbB+BISOtgG/hI76nKroIs84dWUFWwjfKA2BUWdt3eboJjR0YYSJikZmU6alEVF\nmYgs7dNQQg7qJTnS+9tsGskOEUx0BthmiHgVBZXKCXqcKCgl9BNb8g/E8Ba5aoHKfFDnnRIcONFR\ncFi/R9HwcUNBUVFOO7GRdiijrk8i5x1GBnJqgGldF6V9AWV/f7oYhjLCCtXEX/lEnUK4fnKEajwu\nlfYNMY9OgU1GiTNy4H6oBbe0Exs51zQVAzS47firvHblQdLpEEs355g8cX3/Re8jh9+6//P+yueu\nJt8oHb7sIuFGacOLcPOM34nkf7iASIP9GsVxBLX2LW+H/VzcumODugzV/jjrBe09WVkly00iHnW9\nn2JSnndSzCNS7u9Rl4M4qKYUO9iAQjsJRZQkbkaxQ/OZGVK7YeKrE2RT0ijDyDI2uszo6AoeI1/i\n8S6nrFSaV9GMt1ztd/Ik9t9P5f2Ruqz2PXnNA8EdCK6SnzDI5Tzs7AyztTPK3t4AmUSITCLE9tI4\nocgOoaEdggO76LqJX8k2l/YX+xE1kV6JsopCWckolJWCp06aijqv/sdu+pRa6ksfR6Tt/w1J9Pok\n8C5Ec7xWXTbcsIuaUVOxI+rQHjWVcuzvH4Ts70P261B4A/gq8ATSyTuhVdSUzqOLjPBqaNATrtJR\nXCKb9ZJJB9H0PEPh2l7s09G5kuUCGinL4znGqvsD1wM7O6WJGKbqwMZDQPSuwzvWARSQ/zVPMemP\nB+lAlGycrcZD0cZC3xowygYaJhuMsYUorNRjiLcTHiPP6bm3uHD5XrZ3R/GsZhibXAYgEO2S0WlO\neBThhq8ihlRfdvaIIw/ckNlWpaq/jAzeD1FZE7wS3hlt+rDZlJfNpen9gY0eT4bRiWUGhjYJ6h3M\nJVEBw9F3NF2Hx5NjZGSNwZFN8nmd3Z1h4tujJHYHSOwOktgdRNPzhAd3CI1s4w2kOzuo84Fo6+s8\ni4w1eBpxIPwEYVe9i+7gJAxFO3dszQvez0Duu5D/OfD3SEIItw9l7+LoGuEmDRnhiV2hkYTCu+ha\n/ZZtghAmOmF2CLaDA2zTT0T/sOv50W2DSr8JIZ2Yj669HjYtSTXEPV3SWL8vzdzxC1yZv4ONtWn8\nwSSRgUNU82kUfkSN4JvAL5GIZp3f6X30EpaQL+0x0FvwRxeAF635BziUzNaFgsbe6gh760OAhm7k\nGBpfZ3RkuWbyrKMCwygwNLxBeHiLXM5gd3uYrfgYmVSQ3fgwu/FhvP404ZEtPMNptKN0XULAh4G3\nEDnMqwgd+j3UzuZ+1KHp4PkE5CNADBFc3wM+yFEm0XepEV7eG9pGeJk3slqYyE74MoBkPoOyUGUx\nJKGOUk+tSOc+FN4sCf+VqqMU5xdib3M2etyqPsmaRUCf5eY+PUVN7qPSTkqS8uSVeZWCovJdbfWT\nnHV+Kk1Zpaqotr8THaVORRQVsbcger5GoXpHlDsppbhJCJC29gkhHyn2ANUsqMIB4VzxuhphJwWV\nyqKuv4jt8XC0upxHrfCv7f22DfFhNkvujXpQSfWk9j7OfIuJyAq5ST/XV86wfHOOyOnXyf30aUJW\netSSfZX/J5+rXGe2RDXFwbppRinF3vcUIgH2KjIA6tco0kqq1VnpPuwGb9SRh1MiHo9DGXXe5orO\nOdNO6qGmXEReLSPAXThTVsqXX48VdbNdUFBChqxP7wXYWJghl/UDJqMjK0xN3sAw8mXKWmqynmKf\nopZxUnFS0So6ynrsVcai9xxYD2UUFDUpT8n6yvNp/OCBwdFdpkYXSaUDbG5OEN8aJ5v2E1+aRFvJ\nMzAUZ3B0o6TfUZVVMvniBo+neM6uaCpq0h/13nk2Bg9FD653S3erpXzyEDIA+IdIJO/fgPusX6Xy\nbuqsVsYNHWUzBiPRg+udKChukvjU7YfUQHsUcmHIPQnEQEuA/jHIOxnivZ3Qp0deO7aFWYf3o4FB\nmabJ/8/emz03st13np9EJnaCBPdikaz1arnarH29kmDLYfXi7nG7/eD2WC370W/z4BfHPPpfmPex\nu8fdjonoGM90dHTbllqQdLVda7na7lr7QhZZ3LEvmTkP5xzkSRQOkSBBAKziN6KKicTJRAKZefJ3\nfuf7+34pV4REztTU4NVeJXKaLviQFVGUOkgb8d3OiHZxbtFAqMI0EPdkEiasDhIQGXGhHW5xwCy1\nCdJGvTT/kOnpPTzP5sGjm/jeOekePgPkEef/9T5tL3COIakoXDm2VSS4CHt6EAHRGV7qvg+HW/M8\nvb9Gu5Ukmaqxfu0Wl1fuh2RTX3SkknVWLj3kpff8ksurd0mny/iezdH+PI9uv4edB5eplzP4z0ti\nPI8o2vwoInH0c+Dv6aeE+2LA+aSgp2CD/xp4f8fETnOfEudk2HACOorKEg8QhLfrCTzPIRGvR5Zr\nU1lwwX4RAfzMsOUaEoiHhArAx9wJ9c2Cjws+4lLxEEG4yop7nPo365cFHwSz7ONLxZQD5rDYnYjR\nsGXB6spdGvU0jUaG0nv/DRn/weQbbjgIfvj/h9B6vsLF1O5zBx9BpAXBOzol7iDobHMMLnHZ5R55\nHNyWzfbGuiy89Jld2GJ+cUs4V54TqCz4qBCL+czM7DMzs0+pPs3h3hzlwzz1cpZ6OUs82SCzcEhq\nunx2fZPKgp81bEQSYQlhQLaNCMQ/DayO5hA6UFnwSYH9AXBT4P0t+L9ApNX/gJHwxkaIMQfhx83n\n6FCZ8Gy06aCUtsmi9p7WJpZ61iihUZEumdk9MscY9Og0EjV12CRBmzhxmsyxY1RBCVFQNCpCuhzQ\nY0IqKA5BAL5JOJjU25UN601mPab1RFgfBVHOkz6zaZrCMqmmpAxt1PYWgoaUJZhB0H4XfXO7rVVL\na1PKepaqGmEUPgjHO00VjxiH5Dlgjjl2O9ebafo2CrrVUaJsr7dJ2zVurL/B23c+SulolqnMIfNz\nT430F5OJj05TCU3atLUO9DRKKd3bXkPwen+KkC38g673jzPrUcsX6ihjhImCok7OAaKTS4M9F412\nYlqOI9wxQUhdKhNmk/EOIMs45HJvCkpuJuiEM1SpVzIcPFrGcx3i8QaXV+8xnwmK9XXaielZMwl0\nlOPWD0pH0dvr3zlMUwnoIolUk/nLO7SXHLb3V9jfX6TVSHL4eInKdp6Z+V2y+aMOn76RDbY10VQa\n2nJLW8YxKDqdhI4SVUVF4T0Ieso3EHKZrwIfRBj/9OuXTqOaEoVqEmV9FPrKce2MuAHe16H5Nwjn\no78B+9+BmzS0P3/UlElIwEWAFoRHhaKjDJARa1QEf2E6exB5m3eLGwDU5dU2y97wSgiU5JrLRGTA\nFYq3xn0EEeAjntsVRBToIIL4E17xPygO18jGAubZIcchPjH2mKc1IZ1GOlnjyuV34bUiT7auUKv1\n5slPHD5HQEvpL218gXMFSUWx1gYzbOuFdxFZ8FngpRNs//3v9G1ytJdn6/46nuuQzR5x/cZbZDKT\nKA7dH9vFN/s3OmM4TpuFxS1uvvRrVlbuE080aLcS7D5ZYePWTY525/C8IabFf1Qc3r6iIo2oafk0\n4gHxa0RQPqrLZrc4og8aELFVSPwJYmR8H9z/CCespZpEnIMgvIWosrMJp0KPgU+gYx1RGcX3oVkV\nQXhugCAcwCVGiwQWHnkG29YIJUPoMVEB+LlDG5FAayE6NiVpOAG/pzL0yVKWgfhCZJ3vs8bczA5T\nuX18P8bDxzfx3HPQVTiIQnoQ3PC9MR7LBYaMx+KPdUo7S5/Anv4jDF10wfehvJVn/8klwGJ6fpf1\nK7cuuN9DQizmk5/dZe3mLZbWHpBI1XDbDvtbSzx+9yaV3Rn8YQbjo4aFyH7/LiLnuIPQFH88zoOa\nAMSWwP5TRJblMfBXcNZO5CPCiFJvUWknvdqoYWAGHCvadFADkT1OEUw1QmhqxHb0ab4m9Voa34+R\nTpSZcsRn9qOgAPxGIc+B/PBZ9jsUE32qLWOgoOQqwUUU10e7LcSo2EdwxNSuuqnmFcPysNRRDM+N\nwhLBTIMOU/wYRQXFRDuJcpzdU229vsMBYkCWkcfQQvwePsRDEyyauY+mmvKVQoazGn1f4y63uUmd\nTIeaEutTeRtl6jfq9m3D9i/9m2Xevlum1phib3OZy6v3sKxwG918xHW09ZoyQT2klKJfANrDMopS\nShSayjriIfZL4AfAv+JZEx/T9udgnPF8wcTt7HWNyEx4Yu1Z47VBqCmPEM/uaYR9uEkR5RmznqBf\nSP3OJ1HVczoFJe1X2d24RO1wGvBYvXyP2fxuqP83PRdMdJSEQSlFNwaLQk3RobeJ0l/kCmuoIqtn\n6W6DKaLo2zcNdJSE9gBoatSU0O9iNZmeLnEpt8FeeYGdpyvU61lKW/NUd6fJL+yQng0447qaisn0\np1EP1re+8lk6D0ydpuJEoKkc915UmsoV4A8R/PBHCMW+DyH6tu7+LAqtIwplZbUw2LanUVAZpF0H\nc+D8KTT/I/jbwF+B/e/BnTa0Px/UlHPw2FGBzwmoKKZz0wP1qtj/zIBZcCHXLbadp7/NfSSoi7MK\nDJcF8WKjjrg2XMSAIc1E3AExfFbYJEGDFgn2mJuERD2xmMf1tbeIWS5HR3McHs6N+5Ci4bOIIGqH\nQAHjAucYLkIjHLAvn25Xikqngpkhwffg6aNVKod5LMvj6pV3mc3vDu8DLtATlgW53BHXrr/N2vot\nmRmPs/tkhSe3rlI9zJ1fNZUU8DsIJ1cLIcNa5NkaqBcJ1rSkpiwDu+D+FQyLfTAmTEAI0g8yW2Cd\nIAifObZVCDXpXDad6e+SqeMXxQM8bOI0h+eCaCFutNMURp4hivfGfQSnQBsxo9BGXP0RZQy/Vzzb\nkyEC8Q0cWrRIcjABgXip+DNSyTrrK7cBeLK5TrMRkRI2TiQIaCk/4XmZtXyBsQW4YM2DdQqVoj2E\nO2YCOIXCk/vdV0OvfR+OHi9QK+WIxVyWrz4gN3UOzK4iYrP47rgPoS9UML56/Q7Law+IJxq4rQR7\njy+xfXedRnnA6yYC738ksBAShl9FzBBvIugpZ0G1e1o8g52eAaws2F8HLgP7CGrK+eUeTm6OvgMV\nhGeiT0Nuyr+zGKcnk9p0ecxvd+yDFzJbnSp0k0GPXqXekFNnMxySjaKIopnypLrpJCn5nRqI5w6E\nKSjdBRomOooedDQMywNSUEJtKtpxma4gfdYyyhTcMNVR9PGaic7SQmRLVdum+BfXi+XdgBKSbDbI\nNJrPHkcEmOge3ZSQBLDOfe5xgzppqmRJaV/OtJ+oiDZ1HLSJ0yJJk5WZRxyW5zg4WmDj8VVWr9/u\nWRvnJg0KKu1gfUt/o62dRFOl/XGKKL2gtn0PQnruLsKZrtDV7oKOcsaIYspDhPXQIcQ6q0GzQRVR\nUghZQhBc8NkebY5RR4lr5jupdKPzOu1X2Xm8QrOUIRZrc/3aW6RTta7+XzPuMTwjEobni8m4Jwod\nZVjqKGmqIZM5HSZ1FJ1GYm5joqNodBHDfkxtFE1lObfB04MVnj5doVVPsf/gMumpEvPLWzhJTQEr\nq/1eGkW1mq5jS+WbprY+ktFP9+thLL8PQaf8RwRF9ZvA54GbREOUHFKC3n3ssBRUuo9jUKWVENLg\nfA2a/wn8hwTUFJMm9eRSU87BY0d2YNYACg0D0lGajRSeZ+PEm6Ti0S2ePCxWCu8FfKYMnVRkqAGG\nD8NitZwVCqesjZoYlBGDCR9zByTxpS+PptgnRYMltgCfI/JjNfOZKXwUEFmmtZW7xOMNavUpdp9e\nGtsxDYQvIGLB+wQS0xc4h5BZFWfl5LuoIaTfLISU5SkQL3weEBnwvc1LVI9msGIu1668Qzr1/Kg2\nKKwXboz7EAaGZUF+dpebL/2axcXHWDGXWjnHo9s3OXiy0LfQ3P7iKyM60gEwBfxr4GWEYMOrwGsM\nz7hvuTCkHY0IVgoS/ytwFSiB+9cI+9HzheczCFdZ2ohBeE3ywdPpwbSA2tJHPksF+zR3gk+QXVVF\npRcYDeqIS8xHDIImQJwkTb1TX1BimuYEmBPYtsuVy7cAn/2dpQ59a6KRRbghgnhYTSi96wL9IIPw\n0/DBxaUrtJgHqBU6DvXdHOUDwQFfWn90biUIn2fEYj4Li1usv/QuuVlBWSjvzfLk1jXKezPnjy9u\nI6h2n0NEb28C3+bF5YlbSbD/CKxriKza+QvEJygvbzJrUFdXj4d+r2kbj4COMWtoQ1eF9IEgBk9l\njkLTf+aqdjEwqJPmXvE+Xyr4ZKgeM+3Y25SnQyGJI26uGoLaZKKZnFYdxaSUEoWOoqG4AYV+z8Mo\ndJTTqKOY1ne/Pk5FRUcVoX6kzJEq4Qms1171KLyiN+5xrENEmmpHP/yIGS6zEWm74800+isW6OsP\nir8gX/hIZ30y26A6/5DN3StsP17npZu/xo0FJ1RXL9CVUnTqV8jEJ6XdC2dl4vNJhC70DuKB9SnD\nvuF5M2I7B9BPnKn/byPm34HkpeCmHEQRxQduy+WPEI2CMhWeEc1opjyx734L72NfobY7Dfisr91i\nOnsY6vP1mdGM4blgUtwy0VHCSiknV0eJAr0fuFt8wPXCFeBk6ii6+U4UyoqJatLQOlv9dwmZ+5ho\nKk6T2ZUDarMZHj25TrWa4+DJEomDGnMrWyTTdexk8Jt6r363M+MxsNEPhFVUzgIfQbhs/gPi9vgG\n8FuEa5wGVVB5WISVwvFtTmP6040o7SLtKwH+H0Hrb8G7A/y14Iy7JpOYyZKwPAeZcI0THgUqqzlF\n5CGGyoRn0tEruNrYtIkTwzPy5SIhhghYPc57ke/5hosYAKmCzQHqgM8KSzyRzpo22yyNvVATYHXx\nHqlklWYrxZPtc8BLigG/KZdf59mB7AUmHE8RneM8WIl+jUeO0lYAACAASURBVHtjG5GkmGYoVuDt\nRpy9jWUALi0/ZDp3cVGdF6RTVa5cfZfVtTs4TpNmPc2Tu1fZ3bh0PrwQdFwCfh/BFS8jCjaj5Wqe\nP1hxiP8hWDeAiqSmTDivVyLyVVev1/nMZz7DRz/6UT7wgQ/wF3/xF2d5XBoGpKOo5ELEKUevHaPZ\nSmFZLqlUdHWThhyifaQwQ+w04ZFK+hwyPG7XGaNvFvy8QuhNiupBNTiSg+bCGCiCFrDAUxxaNEly\nxPRIA3GVBdcRi/msrt4BPPb2lqlVzgEt5TKiUNNDaIdfIBLG1+frkNKEnIIPfl/+fR+nToJ57RhH\n1/8t+DGy+UPm57b6b3TOobLgzwssC6anD7j50htMzwsZyfJBnp1ba9QOs/h+wPufeEwB/wy4hkgg\nfRd4m5OZ0fXLgk86rDjEtECc8xGIR6ajpFIpvvWtb5HJZGi327zyyiu8+uqrvPLKaaKTKPO/MjC2\nMyIo6ldFrGbylDJKaHpSM2KRDmbtqjiGbLpM0mqEpgJNxgpJGuzJ8voFdjvtTOY+uiJKvJs2aCGC\nPp3GpCfkTZST496LQk05Th3Fl39biMDFxzxAiCG+g0VAq7EwX1lRqqhNFBoTfaU7a22irURRflEO\nm7MIBlQMqIaf3ZnQjzF8akp4WrfOKo94wFUapGlRI0f5WJUV8776G/S4hhOnt5lJHbCy+JDNp1fZ\n2bjMjZtvEouFL5C2re1zUBOftsEQI4qCimn5C8A9RED2GCEz293unCXCzhqD9/nD4vPoJ04F4ctm\n2slx1JQ6QmnKIqCiGCkoQeSSmgonZNLJKr4P+5sreG2HdKbE+sodslZvCkruFHQUfb1ONelHR/Gw\n8LFwcXCJ4RPDxcYjho8l/4Lem1n4gC9be1h42Hg4tOXWLlbnvZPRUdIhg55kzzY6paQZgWoSVlMJ\n2tQiKMV0frsYXFm+Qz2/wcbmVarVaQ4fL9M6KJFf2SaeEPFCNRskGuwQNSU4B7qCCnSpqGBQURnm\n8r8AfoyofXkd8Vj6BIP1acepmgzS5jja52kMfiJRU+Lg/yG0/hN494D/APafgDu5HhcDPXYyGXEx\nNptNXNdlbm4UX+yEmfCIGuHtmugUMqnolJIWDm0SxHC5fxrR7CRB9nWc8BAXdQmRkd9HKMzUEMFu\nE3HzyH/Fbe11U7ZR2x/If4cEWeVJ4FEMin3E97KADBR/OL5DSdLkkgxGDpgNPZjOEnvFXxrfu7Tw\niHSqTKuV5On2KbKUo4JepPk9zs2s07gxnj5fh8o0n1CR5wHiXF/lWRfMAVHZydOspon9+Busrd3F\nssbXsfmIgLhBkiNy7DHLPvMcMEeJaapMUSNDkyRt4rg4+MQIZ00sGX7buDi0SNAkhRBYzFJmmkNm\n+XnxiD3mOSBPlQwNkrRxzmW33gupZJ3rV99maeUhsVibaiXHxn++z9Hu7Pkp3LQQ9S6/iUiEvQN8\ni8HM/jaKQz+sscCKQ/zfEVZNmVyu70CFmZ7n8fGPf5zbt2/zZ3/2Z3zgAx84q+OS8AmC8IiuKoMG\n4dK2dhA+eE0Wiaao0T5NV2QhgtdxqKGowLtO78pqldEO99kCCUQBiK/9UxlzlUmXuttUCbLkCYJs\n+XmAGm0nCb7/mDrlHCVKHFFmml0WmObwdDSoU8KyfK6uvMtbdz/K3t4S09P7xDITLuvzG8CvEQOs\nt4Cz7r6eA4y+z9fhEwThy8c1NOOe/Pvy6Y6kWU1SfipmP+cXn+A4o8+s+ViyFsmRGehubo2PQ7uT\nxY7TxsbtZLhjcuRpaf2GL7PnfqeF+CcCd5ELt/Cgk2F3NK1/X7Z2ZTben7CSt+iwLJiZ3SObO+Lp\nk8uU/Rj7W8tUjqbJXt7HSR6X3p0g3AByCD3xJ4jCzQITJcExElgJoZri/l8Ifdq/Bv6UoUkjDRED\nnZpYLMbrr7/O4eEhX/3qVykWixQKha5Wf4eQmYgh5g9WEE8/EDIF0wQ94uvy70fl3x/Jvy/Jv3+P\ncFh4H8RtaBVFTJ6Tn7lXFH+XCuKb3C/KPrsAc8At2f5jsv1r3xJ/P/8lkjSof+tHtB6twCe+wmx6\nn3rxNfbZZbEgjm+7+CYgdFITNLhdfATAFambul18i8vUO1OMvyoK/tGnChmSNPl+UXRXv/cx8ffb\n3wWnBIXPAwkovgrsQuFjQAWKvxCHV7gq/hbfEOsL0t2t8/7NrtdX5faP5GupV1/cAJpQkInKoswK\nFaaBBhSlyVRhDrCguA/4UJiX7SWdqjCPyIDr7avyta2139W2t+T2vmzfhKKcWS4syu8vxz2FS/J4\npBJZ4Zp2/IlAl7wozTYKVwA3cO7s/D7q/Q/L1+/K7dX7b8r35eVX/JV8/Qnt90zJ8wEUfyLf/y0o\nfAGK3xPHWZBujMUfgJ8KVFO+820xpfGlL1uQDFw2P1IQo44fFhs0aPLpghhQvlYUA8xPFKZwcfhZ\nUQjcv1+2/0XxgDpJPiR/4IPiL9hmicuF91Ily9Pir7EIdHxvFR/TIMX1wjoAd4sPqZPkqvxB7xUF\nOXa9cAMXmw3phJcviPvzSfFtmiQ7138Mj4Piz5kvfIgEDfZlZjxV+AwA9R+9xszebQ7f/wc82bzC\n3IP/jGX5ZAqfIkmTevE1ABKyj2gWfwC1JM6XvgCA/eNvis955Yu02jb84Nvih/zYb4u/PyqK+/eT\nYnt+URR/P14QXcvr8vVL8v1fFsXA74Py9bvy/ZcLon+4XRTJkV8W4GeAU4Tt16EksiTf/eZt/vh/\n/xMuEODkff4H5Xu3ELwuZVH5lvz7YcSIXN5k/HP594cIztCXEdNxb4p92lPiHNaKollKHsNBUTRb\nkq+V6996QQyiHxXFdi8XxMe9WRR0s4/K9m/I9p8uEJuq4n9POCXmfl8cf7P4A3zX4ujK7wEWU2/9\nP+Tn9juUkVbx+wDMFj5MjhI7xTcAuCx51E+Kb+NS53LhPQDsyk5nvXCDNLXOTOrLhSVA3LMlmtyU\nnd6D4j2axFktvIcKWe7Le/hq4Rpxmjwu3iJJgw8V5ojT4t3iJg1tf28WhbKM6kPeLD6VnyeUI35V\n3A19vmqvv14hxnV8miT4VXGXNglWCzdpkuBu8WHneAAeFW8Rp8n7CpeI0+JWcYMWTuf7vFt8B4Ab\nhXW5/QP5e4nf537xHm3irBeuA7At979WuIlLjcfFW53fW/y+79AiznLh/QDsy993sfAyCZrsFH8N\nwLTs1PeKv8Ql0al32Sr+uPO+jUv51Z+yDOT/7Vd5stmk+e0f0bQ85v7lB5iZ3+XgBz8HIFn4LLbj\nds6/89kCAO3vfA8A99O/BQiVFbeWhM99GQB+It7nMwVxXf5TUbz+cEG+XxR9nro+VZ/3Efn6V/K1\n6vPeKIo+7/3y9Tvy/T8owH8FHhfhvwC/WxAFnHdk+2uy/QPZ/koBbhTE/QJwSb7/WLZXfPEt+f5y\nQdxf6n6ble/vyPZz8nWt6321/UxBdBVH8nVCvl8uikReVr7el++n5eu6fK3u/0ZRjNXj8nVbvu8U\ngATE1qAl7kn4D2BVwH8TQaIH+CLjhuX7J5tw+cu//EvS6TR//ud/3ln3zW9+k9/+7e/KVzo/MKct\n6xkEXV1BL1tXQfge8H+ANQMz/5tYda1HM335vyFoEn+G6PtDbQIi0drqQ9yWzea7N7BjLT71vu9i\nWYSk4NY1h48Vud7DokoOC4+b3GKlw1lEmqwILLAbrD8MLFXje4iMcAwxQ6KMhYLmYQWHI8P67tf9\neOBt+Xm6ZWGMwCBIpTCi8KZ1RHHMjCEy5W3CNAALcSOmCfOpTc6YUdZDmCOeMqzXl5MR2iwQ0IdU\n1h/wtTbVbMDuqiYD+lRJmwevaVKbVcNyTdOZ6m7TwuE+1/CwyXHAFBXjPgfZb782OgVG/7yyl+Xt\nOx+h2Uwzv7TJ3IJ4iOvcz9D+K8H+G/WgTauszXTVtb5Dn6CqG5ajtFHLPuKh9Bgx9v9M8N6fvNzg\nj7Ov8pWvfIULPIvB+nx95lLv/5cNy0vasnou3AL+b6EBbH89/LjQly8Z1m8Av0QU5f5+/21jC0En\nOr8cdMhHj+doHE6RTFVZv36LaSvolPPaNHcuxAkPLkqTS6ZJ0jZBAw+LJkmaJCWNBMAnSYMkdXKU\niMtOOYpLpml9FOddE9fbw6JGmgZJGqSkhKDON/dI0pCZ8hYWZolCXX4wvL63vGFVu76axm37r9f7\nu+72rmuztbXK4YHIaiXTVXKrOzgJ8bs3Xa19PUwRjNS3DaM/O275EOGsuYl4Tr+CCLOibGvibg/a\nvjtuGHQb0/pB2vg1aPw1IkO7DHwd1T994xvfHHt/H5kTvrOzw8GB6HBqtRr/+I//yMc+dkrrsb6Q\nnVQsIh+8hfjh44SfAQY05Y2STZV72nD3guoIMlSI4fPz4oBcI0XL8+G0JpuR4CJuxqcEAXiSoGi1\n16xmHxT3+rcJQQX7qigqRfAbKG30fQbjr40Yxe8QcMTHWMAXp93hh5eYoXWG4tYqa3ccYjGftUv3\nANh7ukyrORq++olhIR5GIAK06Cy0Fw7j6fN1SH3wUIAeET5wVy6fwvCxWU7ROJzCsjwurT7AsnxK\nxZ+dfId9IJI8GUrM0CCNTwyHFlMcscQWc+yRpdoJwEeBt4q9FWBiclAwzRGLbHOJTebYJUsZmzY+\nMeqkqTLFkeSTt7HPBZe8Uvwxtu1y+fIDLq3fx3ZaNGoZdm+vUd3PnQ+ueBL4KiIR2UaY+tw+pr3K\ngj9vsNJgfw0xFbAF/A2TFGxEpqNsbm7y9a9/Hc/z8DyPr33ta0MeQfQ6lB588OMqhNUDdZogKaO1\niWsGPQmaVOqCOD6dOuhUXusV2Pqyql5Xo+U8hyRpyBLNZqgNhCvc4yob7RMEcBWiqaCYst3HbVOX\nn9UgHOgrXrMqqlSIaoKj779XMWmUrHi3qoFHmJ9uIzLQ3Wo3EM3EpxtRnlVR2tQQake6akqXoU/C\nDtL8rqMZ1Ngnzzb1UjFJ0qBMliPyHJJnjp0OP/x4dZT+Bj36cpxWRy0orEYQVilITm1zMD3H3tEy\nO09WuLr+Lq5lMPFJacegqaO42r3ptbULKaX9wiZFlEFVU9YQD6ZbCDbEF+T6C3WUEIbX50cZKOpt\n1MmSfLjEsng7ikGTWt5H9K8Zni3KDLUPoindkCdDFc+z2NsUXL7lxUfkkyrhUutkuk3Z77A6SrXn\n+rAKSpsKU1L6VhSfpKkwxx5JGliY1VGShoDiNMY9+v0+RZm87HyPMwMTGelSp12TOBWmKDNFkyQt\nklL91SVNjTTVjrKL/lvome2waopu1hP0KaYZO5NxT0+llK72VRqdY7JzLvnMLpubVzk8mudocxG3\nlGD68m5HLcXOhn9rXUVF19kxG/wYMmGDKqX0wu8gnqk/R7C9PgJ8qMdHJgjujUHHeFFMfMCscDLo\n+ij7DCELzr+H5v8J/mOw/hZif2RqPFJEDsI//OEP89Of/vQsj6UHzrYos1EXZ28qojKKD7TkzZyT\nPJGPFQYk+qvA8yxtZj1EX6j6lBjiBmsZtxgIhYi/77FQGWWVEbcQx+siKDiq+HNCoHjj7CMCgjii\nYxuTysY8u9RJ0yRJiRlmzqD6e6EQvQjvyqXbHJTnKZfzlMp5nNzkZBp64rOIcpO3EQWas+M9nEnE\nePp8HVK3NXaCTLhiFd7gxNrgh9sLuK04iVSdpfmApthLP/+kELmSVCj4zlImxyEOrjHAHiUUn3xQ\nJGiRYJ9pjmjhUGGKElO4MjgHcGiRpI5Ne6KKOnOF8IyPY7usr90hdVjm6eYalfIMtTtZ5i4/ITVV\nM+xlQmAhlKGyCJ+EXyCC1U90tbtSGO1xjRrWNMS/JgPxu+D9FwTPdLyY8NyPHNZYJkHKLgxo1BPQ\nUY76tBRoEwcsUtRONh2oArazvGcbBNQOkT4RGeRJPtOKG56DTsKiiZgFOGLy5OSqBM6aY1J6ieHL\nGgSfKlnqwxIpPyESTovlxccAbD5Zx/Mm6ZHaAzOI4NsHxhlnXsAAj04mPGaynzbAR/BgAa6f7NOb\n9SRHe3OAz9zKZmS64iBoEafENA3SgEWSGvPsMsteSB/8eUCcNnkOWOQp8zwlQwULjzZxKuQoMUON\nNN5EP6hgeuaAKzffJpUp47Uddh6scrA1fz7oKS8jrO1jCAnD7zEeZbZxIjYH9h8DKfDf6tt8FJhQ\n4RrV48kg3E73P1InaE6eoL0Wv9uauL7lebRbScAjlwzk3sJmPeFlFejMcNiZunqzuM0nCmJUHzLo\nqWjzIhX5lcTHCQ60TzQ6ioma0qtdQ1unDHNMxjf6tE0Uaoe2vliGgpreNZ0Xfb0eqEYx30nIY/IQ\n36eKOI9Zeme1uo9Zfx3Ffj7CeKr4s0A1pfO7zhF8z7oQ8AmgTTto09w6NUUvNEqHJi3R2pjNdhI0\nWGKLbS5xRJ4pHoeMQXptE2W/CpvFd1iSSimmNvrU7qW5h+wfLFBvZCnv5llcfPLMZymTLICkRkFx\nNQqKpxn60NZu4Ci0kyht1OvPIMQ67iHuyfMinfncQD8pOh3FQlSRuzJ7JTsKk1lP9/I+ot9Qhfmx\nrjYaNSWm3ZvprLh3fB8O7i8AFrNz28ym90M0kkbxhywUhHqKfr/lDGY93dQUwfvOUpUHEpc+AKpQ\nU3/uJEP0yGC9Q+9izChFmlGg37M/LZb4jUL+mfXQ3afUtOXeRjwB5WOPFg5lpjhihgYpmqRokiRJ\ngwxVSYfrb+Kjf09Te52yYmqvG/2Uij/rzHg8YwAUrzF99Vds7Fxh5+kK5d05mpU0i2sbONLgxzZI\nGpoMfjy9oN4xmJUNil6UlQ8h7ou/R2jotxDa4nHgYRGuF0Q7I63DgCgmPse1GxY1JdLvtSzkC1v/\nGKXxmWOyh50dOsqAmfAIdAlFRUkkG8Qimi4oPvj0M9FwBKiLo8TwtaZ9xHdXAbgqhJzwZKQRagDh\nEC7gnKSsuI+IEzzEcY6pHnGOXZLUcHHY42TTxsOCZcH6JaETubuzTKt1dkWjQ8EUgXrqj8d5IBd4\nFpKKYg+YBQehfANwkxM94ZqlNLVqDttusbi40X+DAdDC4ZC8pJ/4zLDPkhaAv0iI4TNNiTUescQT\nMvIB1iDFPnPsM0trQk2BLAsWF59w9do7OPEGzXqazTvXqB6d0hFqFLgM/CsE3XMToSl+lvTYSURs\nHRJ/Ou6jACY+CJfDndiAnPAIdJRmQwThyVS0zs8lRpsE4DOlpbA/UYh406lgcthqDD4i86NGhhnO\nPACP+pVPjRgik63GYE1ExnLQUfoQUOglCuESFMGOKQi3gAV2sPBkYdfwDkRlwQdBLntIPreD79s8\n3b48tGM5M3wCcb88hKf3z+uo9XmEpKLYJ+BsqiD8pWNb9YTvQ2VbZH0XFjex7WdH/SoLPtB+gTYO\nR8zgYWPTZplNcpQmPleisuBniQRN5thlhY0OVaVFgio5yuRoER9pMB6V95/JVLhx4y3SUyU8z+bp\nozX2nixNPj1lAfhfEM/Xp4jMuNIGf1FwFhyzE2AMdJRBsmM9OOHHVQireHpWe09r42jTP25JOmUm\nK6EpP9OyL6fXUtRJa1GgaeowqY8sVeFhg7Dut94mCh2lW5GkjBh4qP04iCl4vV0UOsqg6igmmCgo\npnNmoqb0Oh41XFRFpw0Cekr3rOtp1LuiVKB3n4cWwexLTRxjXGvvOgE1JZ0djHai01RMKiZZqizw\nlKcsUyLHFJsdepWuCmD6DNN+T9rmyvJtDstzHB7OszD3hES60XtbJ1hOahQUV1NN8RztaaZP056G\nmqK3yyHUAn4Kr/+DIzSlL3CGiNr/yyA8vtizLz/2PB/I99+rtdMTB1NmRZSjvVncZpxkosrl2Ycd\nd0mT1ncUCsoUJUpMd4r6pzlglv0QlcW0/7Aiikbl0jpPMx1lsI7QNYQDpnsfuukovTXAMyFqSm/t\n7oS2PkMND4sjZthnFg+HKlM4tMhSIUEjRCNxQvQSff+9f7uwUkpAAzFTfNrHr7fh6vq77O0tsb21\nSmlvjmYtyfLaI5x4O/Rs01VTHIOCiufoiRTD/TKMyC0F/B7CW2UfKBIoqZwGw6SmRKG76oiklDJZ\nOB+Z8Ch0FI8gCM8d11DuWWXCk9Ey4TV5dlNd04b/VOwdVHXgE9yEw7woFAVFD8BHdDaL45g5VZx6\n1Sepws0RyeUWf37Mm0qyURWYjmGAneeAFDU8HA4YTubqSfHtE22XStSZnxPawk+21ic/K/RRIA6P\n35rw7vCFwgkz4dI1mMsMHKh4bozDHUHpWl2+h2WgKSon5SgQE5Wz1EkDPotsM8f+xGe/dfykOHox\n/Rg+eQ5Y4TF59rBp0ybOIXn2maN9xvnDKB4JOiwL5ue3BT3FadKoZXl85wa1SkSPk3FhCvjXCAnt\nzSL8D0bjX3KBDib8qaPoKBGC8AZBwBvh/mw0BMUlFTEIr8sgPD1oJO0hfuVube7T4oggAM8x8Wdy\nKLAQQXgKkWn3EL9DL83yUaNMoJgi6J4jhQUs8wTwqZAbKi3lJFhc2CQWa1OpTlOtRBgVjxNp4Dfg\nvZ970aQCJhU+HQthe8A6BxWErw/+qUe7c3iuQzJdZWZqUEeyZ+Fh0SBFmwQxXGbZIzsRndX5gYXQ\nKb/EBlMcEcPtKKpUmIrk+DlKZDIVrt94i1SmjOvG2bx/jcre9GQnItIIjvgM4jl2EYiPFGNWRzFV\nxyvIKNNJ9Z+SVAFp1twmIdUYPNei3U5gWS6peO1YRRQIW9VPUQpNEb5ScFCC3Bk3yIpbepFkDHFx\nK0MaBZPVvL6+l4KKroLidL3u3t5EQdHXD0hHKXR/hsKgdBS9zaDmQYKeH6jNVEEqfZ1JdrzwEv2D\n/TiiI7MRl4Q8Dn0I6TqaIkhyMNqJrj5gMvHJs88BcxwwyxoPQ9dqFIMevc3VwjXUhTKo0U/arrKy\n8JDH29fZ3brEdPYAy+pSJrA1CopGTdGnbI1KKYOaWPRSR9GXvwCfvzE6F8ILQG+DHhA3cx1IQjwb\nzCz1M+hxQZrJCn3wARRRPNdi/6Ew5rm8dJ9pK5z91ekl+cIaKkoxUVDSVDlgFp8YCRqssIGDazTr\n0akpUdRRkgaqhYmCEkUpxRTQfqXggPQh6G7jGqgmJnUUvQDVZE9vMutJ0cTD4pAZmQ2PUyZOipp0\n6fRCKigmgx7Tev2zrhWuos6xmbLSez0OJK6+ydb2Gju7K5SeLEAtxtLKIxxNHcpE1QhRU/Q3nAhU\nrpNGdCngawX474h76FsIt83TeoJ05yxN97CJgnLmJj7jx4TnT1UmPIIGsrpyI9Rwuk1xMaeS9Ujc\nfE92KGlqg08jCv+F4WmD65xvm4k/g2cGC/H9VV9fRwxYxplxUIW3PiOlB+mYZR+HFk2SHA6JlnJS\nLM5tEncaNBoZjo4u3HAuEBUyC878YMVTe4hAfAEYkAVQ28vheQ7ZzBHZ7OnoFx4WB8ziYePQ5DKP\nnzvd73Ehhs8sB6zIzDj41EmzywIVshOjpGJZcGn5EWurt7Esj9LhHI/v3wzVu0wcEsC/QFC5aoiM\n+AmE4C4wGCY4hFO+60TjhKsgN0Ln6zXFUCuZiKqMoooyn23/WvGYIZayia8zHGk9VZQIgnYzpvu5\nOH4TNwEViOfkcgtBTzmD511kimCbYEA4BoW+GD4LUt5tjzncU9zim8V3T3csMY+VxQcA7Dxdmewp\n2QtMELQgfBBIVUPWBtvM9yxqe4IyFUWS8Lj7wsOiSRIPmzgNZtnHnhhd1ZPhR8c948aEGB55DrjE\nBknqgEWFKapkaWOfOhgfhPd/HPIze6xffxcn3qRey7J9Z51mbbzGaka8WxTPrH8GrCDilv9BWEzi\nAkPHhJr1gIhmpAizZYg2eylWTGGchlZGIV5LBCaZRJkkjVCWopc6Sl2m16c56hgJBLtvkpD58URd\nM2ipE2Tl97TjG1QFRS37iFGpUlrxCM9bRdmXgYLia8ttLYBtGWbn6y5UW8+ujxuuJo1pEB5P6afV\nRDsxre+ldtGS7XcQgfkwBymq+BLMVBv9HCcQHVqXYVKmEjyQXUejY2gmPs0IFJKw6smzJj5lKe1V\nI808e89sbzLf0fcbw+1M1+rTtlGMQlSbpfwmmzvrNJspSod5MvlgOj5k4qNRUAZWShkGHUV8gfHO\npLwQMD1y9BGr4mPP9qeg6LuUtZzclO9P9W6f0K6vDFWO9mfxXZts+ojFzBYWYYUSoEvHu9qhlej0\nkiwV9iUFJUWNFTaI4R9DWRlMHeU0dBTH7Z+ZaNu9O8wpIC9npY+no/Tuk8K0k/7qKM3Qdw7a6N9Z\np51kqVEjxQ6LNElSJyP/r3QGQCbaiW2gl2Sodc6V3qaqTbWH15uzf3bKZep6mXsP30u1luPpvVUu\nrT4gMx2cZzvb+/w0tH4x/Mg9gwxPAnGfpIB/jpAtfIxQTRkGNaUbUVRURmriMx5McCZcdTgRR40n\noqP0z4QrfVcI8/YUPlswHJ+yNPcZTuGg0qOGsRvxfGkSZ9RU0aYaoAw5Iz6wZLaUKhzXuVrmCRYe\nVaZonrDDvlw4vV5fzPJZktnFpzuXL7LhF4iAffl3LvomdcQsoQNcir6Z74uCTIDLCw8isV/WCzee\n3Q9wQB4XB4cWlzSZ0POOLxQmOIKRSFNnjYdMc4iFR4MUB8xSI32is7AyhL5PR9xpcfPqG+Rm9vB9\nm81H1yjt5ierP3xfIViOIwJvRU35By6KNc8Iz08QPgAdxZV0lFQEOooro6gk9cFsgFW/NYxaL5eg\nQPM8O2GeNXSnTR8RiI+r1k6vAxjDXZagyazMKIoCsfEhP7NLPF6n2UxRPhovT/0C5wEqEz5AEK6y\n4KsMlPWqHE7jtuPEEw3yU7v9N+gBlahpE8emTf45oKCcR1iI2YhFtklRBSyqZDkkjzcBD81YzGf5\n8kPmlzYBi8OtRQ6eLE5WIK5DUVOWEUnOv2cylMieM38YEgAAIABJREFUM0zwEFcLwqNMMauAJ93d\nJrjCbdr4fsAJzybK2LhGQwQbtzN1laXcaae3f71Y4vMyU9Ax6PEJKAu6ljeY1UpMFJI6QZbfJzwn\nNSAFpaWt16km7bZhvWHM8T3gCz3WO4YMuU5TSetF5DpNJQrtJGpAnSEoiN1BOKhGzd4brq/iLSi8\nT74w0VFsw7IyFaqFmVWJZHAy21ldlae/wY5+DZpoKpd4wgGzUibNCU1nm7bR93uveI+1ws0exzGY\nUkrbsllZeMiDzfewv7NEfnr3GaUUW1MN0KkpkZRSohj3RKGjxDiTeoIXE8f9+P3ayEy4PdubdtK9\nnCKI268TbBNSRwnutcyUeFj4PlQeiILhhfknZKwgKZPrSvvpr3eKv5LqGWJ9lQwtksRwucxjErTI\nSzWR7m2jqKOY6ChJVzPo0TrnRD0I+Du3i6/99bv6VwN8uxXUMRH8/eb34ctfFMtu16l0nSDD0EhG\noaP0V0HR14fVTnpTc2paG9Wn5DnkgBn2mKdNHBebDBWyVCIZ9LxT3Oj0fSbKXe2YzsJk8IMF2YX7\nZONlHm7cpLKfx2/FmF/bJBaTJ00zy7ENhj4tR/9sg2rUoHizCC8XwutSiGLN/wZsA99GBObdyc52\n1zaDYljqKOfQxOccZMIj6h3rQfgx8Fwb349hx1o4dv+ori2n8gfSd1VBuMfpM7GK5zz+gfz5gcqI\nq0D8jIo1I+EQcR3YjLxQ08brZMN3WRhrNnwuv03cqdNopCmXh00uvMDzA6XjGmcg675t+fdq9E3c\nepx6PYNtt5meOZkueIOEDAJ9lnlCgh7FMmcNGWTHWojnRVP8s5pgtcBq0wnGj/tntWV7uT0NuZ+2\n3IfHuaqZyFDjMo+ZlhIfVabYY/5UxerDwuzMLqtXbxOz21TL02zduzK5yilKNWUBQUn5ByYukD3P\nGP/VaIQa9Uago+hT/32C8EGoKACtDh+8tzOmyoKHoBITp1UR8QjGIicZXZ4RemXBJw7d1JQSpwrE\nO1nwQaGJ/IzDP2eGQxxatEhQi1IwoUFlgoaBmOWzPC+44bs7y0Pb7wWeN6gM8mx0ecKK/BcHlqJ/\nUv1AVG7m8ztBFjICVBZcKJKKfWSo9qwZOhP4PrG2T7zqkTrycGrgNMBugeWB5Qf5B98CP0aQ4T7m\nnx+T7fXVPnzlM+A0IV6HZAkSFXDqMuifWC6FQAyfOfakSk0bF4caGZokjh1PDLPvMyGdqbJ+7V3i\n8QbNepon967Sao5BUkuhOwuuI4kIxGcQiaVv0F0peoETYoLoKN0XnyFy6XXELiJgVW6KoemMcEV5\nqymi2Uyi0pnqCxmIaNNccZpyWk1Y6AaV1u2e7S19dGghAr8a0WgnvWgquu51tyHPcfvSaSfafmva\ncdR0mgq9lwdN4juGIDdjUFwx0VTiUYx7MLR55sMJijV3EdQUFaAr9FI46UaU9qY2VcRwN4n4DvJH\nTmrnQDfxaSZ7U03M6ijB+kTXyK+NzSJbbLJGmWlylKWyo9tzG5NSSj8VlChtlmcfs/H0CrXaFI1q\nClu7MJI6VSZk3NPuuf5USimm9y7oKCNGr4BDChPHZoNBtIJJHUXF7cuEp8m1NrFUcI1n7CpuO8Ze\nSVjbXpp9+IzqVbor6ZLpoo6IvE8GnxgZyizy1Eg7MS1Pact6AK/TTtLloEeOq+L87uhRrVMzr574\nFxrCRLiunxEhsxD3hPI8sMCKyay73F+iptLokHHqnei9oeXOTJSVMO0kra3vTzvR1VQcQ1/WrWSS\nZ5895jkkT5MkPlbH5Ee10dsHn9v/x+uuF7OjFKcBmWSN7PVfcfvByzTqGbbuXmHp6qNAwceQgwxR\nU0LvnGG2LoVw1vx/Ec/S7wG/iZjljUoPMd3PJgxKQTmHSinnIBMeIX2omkZI9LVbUhkl3j9r0ZJy\nGw4tY6HNq0XDDepzuikbl3Bh3wTRUX407gMYBHrArQpcT5C8Kb5zyuOoENBSRnzXzXBIgjouDpWQ\nbtvxeFi8M9TjsGMec7OCN7CzO4CExQVeIMiI2hqggHdL/h1ggqV6OA1+jOnsPslEo/8GGu4UH9Ik\nIc14Wiywc3bds6SJ2Mproovr3ZlpUw69Kggf0mfjQvF7BDSXNkHSyw+3tbQ2lsvEUVeEh8IOc+wQ\nw6VFggPyIdlEhfvFeyM7rrjT4urVd8hkj3DdOE/uXaFeHWzWcij4dbF/myzwLxGD3S1EIH5Rg3wq\nPB9BuBoKRhhZdYLwCHSUlszUDMzzUwY9p+mEVIZVL5S5wMmgyxe2GJ576SDwGZuJjwUsSieTI6bH\n+mycn9sGPI5Ks7RbE5aSuMAEQGbCrQEcVhUfPGIQ7vtQOZgGYGF2q0/rZ+ERo0UCpDHWmUgR+j7x\nmodTF1SQmAp0VHZ6nFBZd1cei0wSdWgsLiQrkCiD3QDLnaxoPElTKqjUgBhlcpSYGmu/aNse6+u3\nyeX28T2b7fvr1MoD1ESMEjMIakoceAj8mIkbcJ0njPt2PgZnE4R3NMIjZcLFZ8ePIXe/UjAUU5wm\nC94moKdMYAD+mXEfwElgEZh36MY7EVF47xCOoYF4eHXTYUaAHEc4tHBxqEYseOulh3xaxOMtZqb3\nAYuj/QEk6C7wgmDAILwlN7GJrGjYrKVoN5LE7DYzuUELMn1WCu8FLOI0STFYFr3/7n2cusfUXpt0\nycXyBU/bjRMKeEeJwmePeVMliWJAAvx4wC2P+RBvQObQJ3XkYTf9ieGQx/DJs0+WEuDLM5nqSBle\nLVwb/THFfFbX7pLNH+D7MbYfrNE4GmFG/IOF6G3ngS8jzvu7wFtnckQvBCY4FaUF4f0UrlSWIMMz\nPMKYE+Z5qexbJl7qcLt1PqrOLwtMeqphqSh9uaEF6A0CDteh9hW6JQf19vRoo2xiHcJZ2+7A0bB9\nVVsO8cA15oy+WxMPfNC6Cz3Bq5+ykGqcdgwmrnhaW47GrOvCcVe1jcjg7MkDczBLDg7K/Tbx1PT1\nVcRgwA7XECTsYE4voZHFwzzwYNpUvx716dRkV1Cgbz/HHtssUyLHPE87z3JdHszEr4zi3Gly7uuu\nuViee8Th0Tyl/TzLC4+Ixfywe6YmV+hoF4yryxVqXHEc7co7rWPmRbHRGcM0DaTWy87PyYvzcZws\nodacJcRUuc620pYzUwGLtnEgepWZ/B5ZK1hv4m7rr9vYeNKQZ57dEK97UB64vj5TqWO5gvcd0xmO\nTVFsaYPR8TjUv5ykbkbB1G+a+kcIJb5CnPIUoQDdboNd9klWGng2eHFopjXut9bnmbjiJsfMcI1W\ns+d6U+2KQ5spSuyyQJsEDVLkOAqdG1NfZnLSjIqe21uwvnKH7dgqe3vLHD1aYGF1g+xMaTL44fp1\ndBXBCf+fwBuIeqtB6llNz8soHO9B2xBh/ZhwDjLhEebuVdM+15zvg9uOlgn3CQKM7mI3Hd/5tjay\nV52Oz8mVURTnDibuYlH48bgP4DRQ2SQYiB9evD2kz3cR18YYZjimKHWUUhoROugHxbtnchzZdIl0\nsozrximXLsx7LqCg9ESBWMTrQibOB6GiKMOoXH6wLLiHhYfN/eJdZjgY3i3s+zh1oTrSCcBVdnkC\n+LbFn5xwQ0Vb0bL3li8CcqcGiYo3EVSVOG2W2JL0FIsSM7xV3Bobw8KyYGn5MfMLwtRn5/FlypI+\ndab4ZXHwba4Bn5PLPwI2h3Y0LwwmOAhXY7rh0VFcqREes9vYsf69m4dNDDe6U6b6NU/TcaoB+BgK\n+F4ICGmQQMd9HA5gp60XOCEsYEYWvg1SoDn047BgYfYJAPv782M7jgtMGiqILEQarIh6nkoZJaI0\noVtL4Hk2yVSNZDI6lUTUKCr35MbQ9MDtlsf0ThMljtQeI+3kzKAGFDFoJ8GTGXNFVUmWPOzWeEcb\nMXymOSLHIeB3pAzH5bRpWbC0tMnM4lPAYndjhfrBhHLEX5b/fOA7BAPjC0TCmHOtx2W5W73b9Jq2\nUDFylmfoKLrjlN8SUa3jtIzTUyrr7RKjKV0Gna5AXJdN+s0v+NDuiqgamF0yj3PP1INCVfVuorJA\nJCnCIwMFRZ9VMlFTdOjt30cwVuhlWgpmaoo+aafvU5coNPHpdZrKibrG7gNRWeldeg/gtOnVwqp2\nXMnebULrnT7rHQTXRkoW6nKNOsXJTeoumf0dL13CNQqNEIWlwTw77DNHkyQuNkmaoWle3enueuEK\n6ubqd790f7bJ6VOtX5x5wqOt61Sr07SbDnbCQGUJuWcG60OOcY7240WRKzS9dzHoHTG6T0JZLNoz\n4ftEods90yd44F+R74dkDIN+OZ0VvdPRvqAxzE1vk6FmlCXs1vxO0qRFEguPLxRsbNkDRqGahNwz\nXbne98ntt4WSCHQMd5w25j5fX693niaaChHW6zBEA4XrBI6k3W2i9Hm6oaNab9HJrzktmNlpCj1z\nG6q53jSVXs6Y4qOCNlVDmyhSqjVcMlSZokyssI6HTZ00SepGdbTTwImQ3Lu8+JCE1eTp9iqljTkS\nNJjKH0WjpoTMf7Qnsula+FSh7/EYt/0c4lq9C3wf4ao5DDr7aSgoUdw2JwAT/NgZfia8LakoTrx/\nFsOXP81xVJSuDYKA7KRaww2CDOnzkgWZVMhCIkA8+0etD62oMDYjPdc2HnlpC14eYzbcsV1ZoAkH\nBxfZ8AtAh4piRXRUVfftFJHMNX3PolESkUF+ZneA4/I7wV2GyukDMt8nVfKEEyXSTOdF06fvkjf0\nEdx3WpAsj5emkqTJHLvEaeJhUyPTMe0bBxYWtlhaeozKiFcOR0BNGRQW8CXEjFQVYW9/WrfwFwTn\nIAiPwAmPGoRLeULH6R+Eq2moftOO3/mO+Gv5BBy+k/TRuuvnhAfgr4/7AIYFRfkR1nfHUkSGTo+W\nGrzAyOejhJW9T5XssRbOZ62Vm8/vAHBwuDApogkXGCsUHzxikDEgH7xRSoMfI5MukYhHL9qx8PGw\nsWmRpMGbxe3+G5n25flkDlwSdU/IfDuMXLJ0UBR/PoIPSYAvk1hOE9KHvuCMe+PpGG4XH5NnnxRV\nwKJBmkYfl82zxPzCFnlJTdl5vHI2qik/L55uewf4bcSAeBf4ARfShREwoaV/EETWTv+jVE17qKPo\nU9heQ9zlCadpnJIKpsITcpcVkjRCU1769H28JZ0P1S5aiKkPkwpK3bBclfuwCBd1mugrgK8rn0RQ\nQTEtmxRRTAPZBr2lto2KKIb1pm6kFYGakumngNLrw4+jJzQJrK8V9N+7pb3W1+v7GXR9FcjJ49V+\nmEQ9GMU1ksEb+nUXRSlFbKOrDiTkIYhp1ypZGqSMqiZxGXTo24o2/VVQorSZzhwQdxq0Wkla1STp\nbKVzfJ32Gu1EV0rRVY9CY96oFfET3PM9fzCR03RYBMooBjpK91SzYnysESRgdJdMTRElSYPykZA9\nXJx+0qGh5Ayulep9HyVVazHHXsdZM9eho5Q72/SjoFiuz9ReW8gOAlaDoH/TebT9nJSPW38W6ihH\niKCqVxsTHSVlaGOgqVhqJkPSVCwEZzy/1cCLg+dAMqSmYnbG7L08WD+Voco0JXKU2GGRI6ZpkSRO\nkzQVqTLbez/d+zK1G1RRZWXxIY7fZmdnhaNHCyyuPyKTq5xANcUw6ktD38nRftdRCvgq8F+BBwhN\n8Y8Yto/ybDYlVoellDIBeD4y4erERqaj9M+CqEx4t+RbNwqvyAU14jtpvc4AX3dUaCKogBsIqtfb\nCDnQhFy+K9/b5ZnxwfmBRXDdKF5+DxSunsFnn0ZF55SYlk/948x7BCf87GBZAS2gdHShknIBGYTb\nETPhul19H/ieRV2an8xPR89ku5IvlqTWeRZ8qDA4fcpyfbL77Y7ut/T6ORcofGCEH9btwgnYLXDq\nEOuuvTpDvL8gLioLyFJhjj0sPFokqDCFP6bp6oXFTebmtwCLnUer1CtDzIh/vDCc/cwCv4X48X6J\nMPS5gBETHISryHqIdBQVhDvHD+eEG/CAnHAVvJ0kCPcZ6OueJarAfeDnCNrJLeAR8BSRrDmS/w7l\nukfAbdn+p3J5n3PzfBGII7LRipYySuh1ACNEhio2bVokaI/xostPiyC8XJq5oKS88JCZ5Ch0FL0o\n81L/5vVKBt+PEU/VScajpQyEwp6YVps5heSDCsBjngzAlXvvBfqinRC/meVD6khQVBgDRSUpi9ot\nPFzilMmN5RknVFMeM5XfF4Y+D9do1SYoc6ewBnxSLn8ftImhC3RhDEn6qPPFEdVRlH2upTU1fITb\nFm8knIZxGsrBlTxZC4cWcfmeaQrr2/8TCp+XLyzEVKI6JgVTJbta1iXrmkSbggRq2usjfVlvE2G5\njYg9N0GW7AmILICY7UrIfxbwJvB+eaiKpVEhYOFsIYLxBYSxVq7rsxRahuXQ2D4KNaV7hWlqyz5m\nWT0UKwQGPtrnFTehsN7jOEzqKKb1+rLaTwIxgGyLf442mNSVUprJsNKJQiNEFQkPME3XrYPLNEdS\nKSXOlBx96LSTB8V7XJdfOkx56W3uc9w9ZWozlTokEa/RbKVpVtNks+VwG7s3NcU+jXFPN3SznguM\nEN3Bg+y54tPBOQmpnWjLTUTfkEVk3nq0SaSCe6RVEm9M5/ZD13K6BwUFBLWkQoaWdMacJ9AUv1N8\nyG8U8p12+jadZY2CktsNrk9L9wAyUVBMy1GeC2egjlK8ozkGd1MfTIooFcN6ne5g+j5am46aigOW\nIygq8YZPvFHGk5ePnY3W1wzS5u3iFh8sLDzTJobHHvO0ieNjkaV0Jsopx8KCtZW7bHg+R0dzHD1Y\n5NL1+8QTrdBv7bZ7d2ihPGFbuwd/XIRPFuR6w2dHuY5Um48BO4gp8+8Av8vgyiRnbegzATgHmfA+\n4wTVLEnf7EInE24fn6725M/Sj4oSgiWP5ST3o3oOjEEbtonIdr+BCMAtROB8EyH9eQ1YIQimpxBB\nck6uu4QwznoZeK98nZD73ZD7fcxEeE4cD93Ep3pcwzOA+rwRB4GKklIjM1ZjilktG36BFxU+nUy4\nnTu2JRBI5kVwt/d9qJTEPrO5oz6tBTws6jIdkDlph+D5ZA61qGWCn7YTjzah3y9Rg3iVkT9YbDzm\n2SFBA58YFXIhN+FRwbLg8up9stkjPNdh+/66MegeGyzg88Ac4tb+Ludsinw0mOBuYcAgvI+SoXDL\nFPvqp47iDUBF6WTB4eRUFD0IHxF8xCD1dcTzLIYItj+IkNydPuZwPtRjncqarwAfAG4gAnYXQW/5\nqfy8ib4HVR/W4pkRfycLfhZoIR4mytRiREjSJEFD6uE+m6K4fqZfOsBMTvLCS/kLSsoLCxVRpUXK\nsx/U9HaUILxl47pxHKdJIhktDSYCcJEFd7o6A5UFP/5DfTJHLrba9Byb73Sy4OOG6h8tqe7ahmQF\n4vXh6zuqLHgvxPCZYxeHZicQH4epj2X5rK7dIZGq024l2H6whu+d4jhUFnyYcIACIj57hJhGv0AI\nI6KjDMpZ0knSfQ5RBb5Jranu3SGnrX3PokGMWMwlHmtHmp5KEtBW9Ol/fRmXoIOta4dtUkHpnoJr\nyX342ncxKKL4Xc+PkCIK0Zd9RGGlSiZlCDLYNXorn0SBvl0CQQurILjjdeAdRCB+HRHvRrn49Cun\nZqCmxLt2FDdNW0VZThIopejaw3qM2jjFen052bU+DcTA0r6bnQxSPbpxhYkSkuwaOIZVVJ7dfoYD\nnrJMjQxTVCIpB0QxvhikzUz6ANtu0WolaTcS2Knen6uPtI3GPRjoKN24MOuZMCieRi7afaqC8HmM\nlJVkStwL9aq4kXO5A1JWM5TZ7qaggPJJE/dNnn2SNEJUk3SPbURbeVC+oKBYnlRBqRBkH3QKip6U\nj0JNGZc6ip5g7R6rm94zqKAY+z8TTUXvg3WzNrneAnL7LVynhRcHJ2egsg3Yf0WBTZt95qmSpU2c\nDOUOfXVQmMzN2qH1PdrYsHrlNg/vvkSznqbyaJbF9UdYKivW67O0jHl4IiGCoc8gdBSFFPAV4L8D\nv0Jk6lYi7CcqolBWiLB+TJjQx466GSKkD3Q6yjHwXbGfflQUCIpxomTCiz/QXpxE6WLE6hgeIhhW\n2e91+S+iSTQw2GA2i6C2XJaft4e4D8fhFh8J6jpSbpoSxUdn/LlNxIN6xB3EtIwEaqSfmaW4UxxN\nWbtlQW5KRCHlygQaUVxgBFDBbEQDKVW8EiET3q6JmzqXjVZc6RHDwyYuZ4q68bNiqcdWAZI1txOA\nE2fCp//6Y+geCcOEH2TFh6mg8svift82FjDLLllKgEWVKVpjKHJ3nDarV+4Qs9vUylPsby2dbEev\nFYd6XCFcAT5OYG1/0kzfc4gJGxMoRMyC60370VE8Md6w7f5DOUVHiUeNkNU44SQB9UklDU8AD5EB\n30cExDcRj7yzvh8sBC0si+CHVxGB/Hvl+omCkg9rIqpVR3mALQYbDQ0BCZrEadIi0ZOSMipMTR1y\ncLhAuTxDZv74IOcCzyOULFEEPngL0Wk5/Zv7noVbF5FwNtv/utIVUaYoDUwysFtewAN3GE+ayyMw\nc6gRVM+rmiVf/lP0jpg81iRi0JBEzMqlmNg0nY52CpyGUFDJ7rWp52xaqdHQQyzEbEmLOE1SVMmS\nGUOKKZFscnntHo/u36S0N0c80cSeG5P+rQmfQBSKPUHww1/hXFxfZ40JDcK7rASPm55UA1/DAFSp\nKCijnrjdwqZtnJISBRfiBk5R60xj6e0dN1gufEou+Ij0rjoefWbLVL2u6Ci91vfYttaVlNHpGSaT\nHZ2C8gZiBtRGZL9tgj6617am8cE1egfu+inoZcpjy203ELPJbyGoKYuG/XXvM7ReNyTqouk42hSp\nZVJEMVX160o1ykzDgcICwXnppXASdb1JKSclt1FBuPx++phRv+4cW79mzWY9JoqIvpylwgEJ6qRD\nxcjvKax0DjjKFO6pjHuyYiq/Up3C8lxiMf/Zz3V6TxeHjHscLRPmaA/iC7OeCUHcsKyC8Gx/Oopq\nOkcQLCqkgvOfTlaplzKAxVT6kJwtgnATHSVNlbb0xbRps8Q2MdkZ6O2+VAA6Zj2aIspBHacuczJt\njVamJ+D3tOVDw/Kg6igt2a6C+G2Gqf6QgEIGoXCRQWRS9PjW1I9GoabodIkIFBQTrS+u2ksFlXTJ\nJVUBe+ZITLMBdnIwCsrnCxnUheZEoqlsc0ieMtMyEB+MmjKM4s5MtkbrcoKtjSvsPVlmIbFBShpW\nualg/22NjqKH6d6Xvkzn4dc2DGKi0FSOy+UUgL9DSLG9Q1BgdhoK6WlUUyYAE3Y4CuqMRrgw1f0R\nORPeP/XsDkBHwZL/VIZhEOismzPGY4IA/D1n/3FGxIBVxOnaRvTtMFyK2KmhMkQe4uaNOEN+aqgC\nzRFnBzJUOGCWKpnBFIGGiLjTIpWsUG9kadQzpDMTS1i6wJlARdYRbjYVD0eoj2xKM5PpbH96AQQ1\nFHkOOgF4VNhNOmY81smowdHhITr0A8R4oFslxCHQldUlOFXfYhFkxH2CuiQX0Q+1EBGa+neg7SMn\n/00zWRFEG3wp9Wp5Qle8MQW+ffZZcQtRXwPIQHyKLOVninrPGtP5fZrNJPs7y+w+usTyjYc4iRFO\nt/dDFvgy8PfALxDFaOYa2BcCEzoZ0JUJPw5DpqMERj1+pBuo+ENtw0ExAOvmNDhCOMiCkBM8rcfW\n26fc3gKWENl4EIH4nrn5eKDuDJkZL26M6HPVuG+ExfYp6h03OFfrEm6fORE+jGxGZBVrVUNF0QWe\nY6hB1wBBeAQ+eLMi9cGz/d1CfCxpUS8oBib8U/FZycJEvUXMlZICfeqTToU6ojN/AyE7dYgIwFOI\nYGYFMb14DVGIs4AYrCht2SSB8UNSbqfsyme1fdwA3if2U0TuI454NB8gXBB/jchmbhOtYG8UsIG4\n5Im7kD7yibUGfzj/rBhNylKHCsQVR7zC1FjkC+cXn5CdOsT3bHYeruC5ER8mPyye6XF1sIaQYfOB\n7zFSSu4kYpLGsQFsV8bhdv8j1Asze6ijKASFmceb7yg+YAyPuGlKva1NT6kMRBszpSTKehNlRVvu\npl3o165JEaVEEDTP0VsBZVA6iqIbdkPfNkph8ozc1zaiL38ZMVDuRafp3lZ/DHYboOqnR6etRDJQ\n0qewVDa8LLd1+7Q3rTecz57LdbmtBbSEOYVCU1cNMVT+P2vW058i4uCSoSofGg4J+evaeD2nYqOo\nppwE2UyJ3f1LoSDcZNzjaBSU0HxV6GIYUCllQlMS5xM61SRKbxCBjqLuKdUpLMt1ITpKcMM4bZd2\nI4lleSymtzqZbd2gJx3qYcS0ZoI6+S6HTJ12kqFKTl6XGbcKns+U5IFbLsTLRFNBGYSOUkdMZ+qO\nvnEERUTPdre1Nqb+zgSTsRmEaT917V9J/nuICOTziE7cZLKkj6/rhvUmNSkTTUVXTdGPOSVmJtIl\nH6dVxpWJOt3cx4QUFpkThkcZajxinRqZTka8F+0lrHZy8sqs8H5ssODK6i1u3f0grUaKg40lZte2\nFDPHOM6tJ1rB/dM2cEoGVU3ppZQC8EUEJWUP+BnwacM2Z0FBmbCod0IfO+qCHYCO0qcouZMJjx0f\nKKhMYCxiQNHRCR/UNMDXtjnDs7CBCKYzCO71MDBMOssiot/2EKZBk5JQAYLZlRYULo/oM5WN/Yhl\nZxXnVXfMfKmwOtJjyKZFoFOvZS70wl84qGgzwiyIatonE96oijm/RLrWqTE4DrWI5jyfLYRT3cmq\nR0wveBwmWogA923CtatLiEHICCghBcUVVK7UOUTHvSqPQ1kWlxFa0HcQurTDl+8eDJq4Wrwu1FOi\nnp9PFE7OQVQZ8RQ1qSM+1RF7GBVs2+PS+kNiMZdqaZryboRpo89/6ewPTMFG8MNt4F3EdfOCYsKD\n8AiHpwLZvkG4LNDoQ0fxOkF4xKhaHeKgQbg7ynlRAAAgAElEQVTeQZ1RwFUBduXylbP7mFPBQsya\nZhDx5z0mSNFLXVN6FnwUGINxj8oINkctz6IhHm9i2y0816HdGt9xXGAcUIFvnyC8jegobEQAegzq\nVREdpjLRsowtElh4pAaobIy1fRJVT/RZw+wjfESm8C0Crt40gmayTCSH6DNHDHFMlxHHtYjoM1sE\ndskbjFyGt4Mucx+nKYLxUYzwlWpK4Kw5NXJDn3iyyeLqYwAOt+dpVManftUTs8An5fKPmDg7+VFh\nwhLzCiqi7ZMJd7Smhm+iFBXU5R+PtXBwjVPzlmx5XBu7HUTcxR9C4Ys867JookGoZXXBWXKdYVtf\nW9/u6uT1R0svGskd+XcO8fMMSkExDVduAS/1WB+FjmJqvwrcRjxvNgmy9vp+9OMPKbF0/y7azRxS\nSjGplJjoQkk6lJTibShc0db324/pWohKWbER14a2Xr/u9Gp/Hd2UkKjGFEnJC3eJY+Fj43Gn+JD3\nyCmAKKY8OgY3+mmDJbLhR+U5WvXk/8/emz1JjmVnfj8AvofHmntmZdbe1dVV3V3F6u7qle2tZnMb\nymzMhnqRaLQh+aKHoYl/wbzykSIf9So+SqYZjWTkzJAar97Y+1pL156V+xKZsXn4DkAP517HBcIv\nHB4evkRWfGaZDkdcLA5cHJx7zne/Q7nQsr6/TaUUczk2Fs5arOcEc0bAwAn3KulpZx0FXyPKVBlt\n8qWox3R35AGrVnZiE46HLfcV+apKgyWaB6LhZoGeX9T3+HItB2HI0lZf5ji6xGkkJr3kgWW9TSll\nCzGC2uCV1O/1jWNkKdaThSKQgSlU31LqUMPaJ1VQThHxFdtIRHwT4R6aClMwvjpKlmWGr9fFfbwe\nrN7v0BPRHOuY70f1Nl+oTe60LrHPRzxBnzxtKpTZH/giWfjiZuGeA7STwbJ9kFlZbuKfyrP54AIP\nb57n0lPvU8hFF9tUTenV/wX3q1+T5b55bpYiPjZFlKxKKX3gs8gch9vAT5Do+CSXPQsFZcFs/6MT\nCR9xYbPSUcaOhOsnatxIuPZ2pzQ4biE23uHoaCjTRBGZKA0y32jemcwBdL+a5eSRGarmaDgwiADO\nMxpeKUnOvd2ujGh5gkcH+s1ZBmdEpzflCVMQhtBpl4GQUiWdXiLMQDlulewa9cV2X9RQ4Ohe7FtI\nOlDroJ8iijAfB4ghEWN+AUlxhshkzvcRZ2uexj2UKWeFJjNJuXoEbPAAlz49CrRYmnmm99zZG5Qq\n+/j9PPdvXlosqp+DON455MV/LbX1I4nFdMJD5dE6Y3DCRzrh4u26R+mEh1D7KofjAk7ZCb+jPlc5\nevs9LAp+FFhH7HcXsdULAfWE1FaYHU9G80tn/HTqqKCu+vbszIjwEUpFcZg6nQVLnZ5gitBOeIaB\nV0Z5wrAnqaRiqY3rptvyUPEWXPzERM3h0FHw5T113jkmt+MhEZ86QHjXT5LpkkwbtcNKyBURzviT\nyGTAEJmF/xskOzAnZzB0wPWhsA+OP/wkjiIKriGO+MOBAlVnxkXRHAfOXrohFTX3l2k+XB3aTkfB\nZ44VpJomwA+YH31pTphzYN52+MSMxbRUgqkTnqaOkuKEm+ly/Ujm6FuF/Ae0cn2aeqNxUmfaCdfa\nrOahjJSKSbVIBmNtNJIGcFctrxntbKdko6nYjmUiSwfKwsjUsolnkHlINzg4gLD93mScyxTIiCml\nZKGLDEvnak1dXdFy3BRplrRw8hx84sWoiBfuyaJ6Muz78O1luUyTbdbpk8+8H1ubLJSVYdBOeFc5\n4TZai1WTNFbQJ+Pw09RRPsGUYVoMfX/001w52CSpfKBt4xmitLXh0xSVukO3U8YHquVdKrRiNR/K\niQI9bUr0kcl0moaSdMYrxvflzh65TkjODyEAR0fnsyifDFv2kYmX+hAryKVoYC/cY6Og2NZnga3/\n2wryJM8prSjPsvp7A6Ge3EBoKucQ4z8JBWVMxQ5NTXEDWN3s0K0grsYEyqhp1BJNHcnR5w4X6FCm\nTCvWp4a1Ty7bjmdrb7ZZyu9z8eJH3Lj+NHt3N1iq7FIsd/CLBt3FoKCYy0Hf6ABmJdJxlVKSfzP7\nyGeRDNA94NfAq2r9NIr4nNBRsmAKdJRQTcwcERXRkXAnI7+k/n3Gp6LAVFNyWjo2qRR1VPhgdJND\nQ9vrALHRCwEH6g+ZDyVlhigm6CjvzkwcPUKp0AJCut3iYqVNTzBFKGfEyRD2zaiM4nfFwa+UG+kN\nYaANvpqQJbTh268F5Fu6smCmTezoI+oQLcQJvsTBqpRzRj3bZRmNAkJTOYP81jZCQbjL4d6hkyIU\nR7zQPHj8f6kffTh2iSbLSq9yh7VYTYZZYHl5h/X1e4DDg1sXB4FJjf63vzfT84nBRWgpLjLp7P78\nTmXWWFAnXL99x3DCR0WxdCTcSfduwjHoKI4+zXGdBVOecArQZSYyiBItJM6qz00WRCklmkkzO8zh\npaSjhX1yc7vurhuSy/UAh96JQsrHBDoieHROeNCRqEy5lO6E+7iqNkTAEqMddpDJfW4Aga4jcFho\nB3wfCSJdYvJKaosOPRnyEhGvfwtRUsl2+Y8UgRs54k4wfau3xD5lmoS4tCnP3M6ePXeTXKFDr1Nk\n+/6ClapcRyLiAD9iPgOzOWDBAvMa+upnCAeMcMJ1gQ8dCc+5vdTUesQJjz8eySIoslOlE94mewrG\nLOqjqSjJNgZ6xvpkIHaYkokPg6lFa9ipJrZl288w21weci5ZYSmlEtufzlzqQj7aVpud9VD+cJbC\nPcPah1DbIFLAse3HxLip02Hb6hfyiKh4VrqHrd/r7XP4uPgEePh4fLJ2bujBbVSYcc/BRlkp5Dv0\n+wX8Xg63kIEGY/CPelaaylineYKZQnEoXKWMYiu+oZu6yAvbPdimUOoS9F1C38N1fFaL2zjEtb9N\nGoAz2EWbJZNykpigOfgehnzrFSBUc0htiihmgR6zjVZE6QNvIfxXrb2tq6jZCvfYitjYCsBlsXG2\n58J4n9Zyxjkl29soKLbzM+W3i4hiyrZq/zby0rpMdG+zUAgngGtSU+536KosxO/WIP4j9GGHOxq2\n9XCQOlLgHne4QJciPQqssm1VO8lCO0k7VrSsbpwLFy59xPUPn2X3wQZnqk2KS3KD/N/9PJqQ3Tfo\nKO2YUopxw/sWaopNKSXtb7pffR4ZmG4jKfcnhrQ5yuUFwMcnEh7qSPgoOoq0y0pHkX1nb6oOMjXs\nIqdT5vhMqE/CIXK8F6acveaFzyp0MScFgZwaDvXnaKnyeXkRnETCPy7QdJQRYWDtkGoOrwV+R1FR\nSo2oSqAFepJcVm3wmCLKYd+eAeJgaAf8Eh/f+Qh5xBHXmQ2tonLQ/50uFDUlPwPVFJeQM9zDIaBL\nkeaMZ9+Wyi02TgstZev2uQO0lLkiD3xJLf+Mj4V2+II74Rk6R0Z/PRw44elPWDhwwkc/iU54SE74\nFB9yo/jz1HB1ivvW0HU4tlkASooD9W21PCvnWDv8M7aPOiLt4/FufT4aNUJHgX7/uA4jTzAeMtJR\nMhbV7BtOeDpCNf8hjGmHp2Gp2RGbr3X8x0WIyLDtqX1cZOEic0nUp00TcRApxseQa9EE3oGMFP0j\nQ+iIfGG+Bd/9b9M19Hn6rKgfOI+Kmuun71Iotul3C+zel5BXr/79mZ6DFVeQvtBDJmk+4ljQx38M\nOkoGJzw0IpiOioTb0+i6WI9dHWUgwJBUR8mS/jO3s8HYTz8j70LTOXQWtMDB+kHjsiKyUE7MNllc\nJrO9LUPUU989JFi0z8GsdBqFJqYoY/zRqo5ChvXDDpzEuHZ71PkExCJkpvBHzje+pETRRlFQbO39\nhGkYSsfKeKxxoZ1w37ebJy+X4Vg5c/iWsCULavkeTeQty/omqElwucrB+2J+11GxKnGDUIruc8Hr\n0OzIEH6ltDOY52CqoxSUwx2qslRF2lTZj1FWkk55xW9KdcyuL1SUDhKttVFHbIoo1xF5PgehoDSH\ntLFRWcyo4JjFesIMBt9JM8g2KWCTjtKxrDfvlW9po89vFbkmLSTas49MEnKYegDEUTK0Xh+WdntU\n9pUdWhpeMMdEcr2NXmLa1b6i/TVYoUeeVbZxCVOK8sS3Hdama/Tz1EI/Ljx24QM+uPo8ew/WWVnZ\nIuf1KHhyE80iPr6hjhIr4pMznuWsxXqy0FZywJeB/wPJGL2ApMZtRaZO6CjTwBiR8ISaoR3CJxiV\nnhwnEg6KE75AdBSzyNq08MQU961hFjObw3ydA6jp2aKznCwyxlj0qOAZkfBnaxdmd2ADOaXFeBIJ\n/7hgTDrKyEi4eHdLpfTCO9rWlw+InA5HoSUPZO1LIxrasEOk+nCRY8MXPELJ7NFwEadb01PuIwOX\nWdhdXeYe+OYXwJuBXvUq2+TpEODRnGr++iAqlX1WNqSk3+adCxS+/sWZHj8V68Cn1PJP53ki08dY\nTvj169f5xje+wQsvvMCLL77I3/3d303rvBTG8D7SmuooeAZveVwn/FCY4q613Tgm9j0VOlCyELQw\n3b9myY2Zw+xwPRcimDUPxoDW8g+CBY0RfEwwO3uvnvBRTrj2lVN8lTDUdJSQSnHU8F074RkqGYQh\n+bZ6IA/zXGolFBDqxfIh9vFxgYNExM8hHsou8CGzkYh1GNj6XBucKStiyfwnqVzUoTTzasUbZ+7h\n5Xp0WhVa2wvWKV9BHJlbLFD1vqPHWIH5fD7P3/zN3/DSSy/RaDR45ZVX+Na3vsXzzz9/xKd1CE54\nalP1Rwsf3EzN23ysoal2xQmvfYrDyXUERAY9w/YHaBdDdqft1DQzLlcZHg232cjDDgj0djrLOTV7\nmIGaUt+Bmq76lmXbcY81DPpYAZlTsZNSQqJnweHd+u1DR8Oz0Fds0BUOg/DECZ8nZmfv9TBbhVxt\nqWPthC8n20R9ze0AOOQKXcpu5Fyb9JIiXUKgTRmHgBV2cQmtBX0AKjsyITNw4dv/BLXPqz/YKCjm\n+l0kmqsnYuZVWxsFxbYfIxoRGutN+l3LErHoZXgc85aXxo9y8HX1t1yCjeHYFFFsNJW+pY1N+eQ8\nIpHVAl4HHudgwaBJYPnN9V9LxqPYlEI3oSc+hF8crUqS/G6nl0TLLZbYZZV9llhib6DOZu6nkoGm\nYlKqshTxKXse587d4NbNJ9n7T79i5X+6jOcF4xfxMZVS0tRR0gpxJbepAp9BIuE/A36X4XLBHyc6\nyvnz53nppZcAqFarPP/889y6NfuCHjGM4a9ni+0dIhJ+GJ3wKUD3y8POGVo06JjAQlSxnUckfA4z\nUnUkPJxjD3K0E34SCZ8rZmPvQwZemjOC95AhEt5TVJR8MX2iZaCsZJnWATnaYXCVcQ0Po2KiHW4X\nkeB7FIzzrKAL/BSQF8GHzDw1WmyETLtyWIV9CoqW0p6xWPzKyhaVyh5h4LGzaNrhLyBSb5tIldVH\nEId+y129epWf//znvPrqq6MbLwyO/kGqfXmCjY/4dMYYj0yEJ6a8f41FelfVzsz7DGYDc6wxL074\nIt33EwimZ++18L4HTkrOLCRywlNEVAZOeGGUEy6vvix8cM/3cQJVYy1nRMGzoIek00HoFQsWhcuC\nr8/7nHOII76EdJcPISON/9CofZWBdySKKdN1woWBI1pgPYr0ZthRHAfOnb8BX/g6ew/X6XUXiMya\nJyrg82sWQCrt6HGoO91oNPjjP/5j/vZv/5ZqtZr4639AhvsukmO4QKT6/A6SW3pRff+J+vyc+vyu\n+nxcPsLXIVhD6pkCjbpsflZ9v1qXNJ6nvr9Rl88X1fcf1enev0v+t8VTDn/0Gjt3f8lqTaI7d+pv\nA/BMTcIbH9avAQ5Xak8C8PO65Ahfrslse13K9spnZPf17wnDpaays/XX5bOmfl5dcQBrKnJTvwZs\nGt+3kEIwahKKloJSZ0+9A/sBfE0Zgx+q9fo1qOcrvKI+f43Yp2fV99eRLN4n1fd31Ocn1Od76lNd\nbd5HXodPqe9X1ecTh/yuy9u/YBzPM87vbfX5nPp8S33+lvH9NpKRAviF+nxJfere89+pT319vqU+\nvwdUfPhtFb3SlYhrKsReV9nqwf3Q139VfVci5bUN47sLtYvq+y2gDLXH1Perqv0T6ru6wDV1g+pv\nAyVFXwLqv1J/1/3pZ+r7N9T3HwDF6KVfV49H7avy+Z26RIxf+qZ8/369R4c2r6qZVD+st2ni8jn1\nA5P9+VdKd/HJmnAB36hvsoXPau08wECiUDvj79clFHFWdfir9Y/oUuKyel5uqh98qfYMAHfq0uOq\n6gLcr79FmyKn1AOyrS7AmroAu/Wfyw/5/O8D4P/gO7Su3qNc+wIAnfoPACjWZALRQFLrc3IB/O98\nF1ol+PJvy/of1OXzizX5/LH6/nn1/ad1eOcX8FCuw3e23+dP/pd/ywniSLf3MNrmPwQ+rb7/WH1+\nHnnD/jPwITgvytuoVxcKxmpNmt2ry+eZmtCyunWJiOl7+os6TqeF8xW5553XfgD7Vcr/+imKdHmg\njHKhJud9s/4eBW5yRj2Et+vvsss+L9ROU6HJT5UReK4mxuH79T7FVpfHXwJC+N4/AfeMZ1oZndqL\nwD6oLk9tzfj7Q6hdAApQf1P9/Yxqr8ob15RzUd8D2lBTA42BDSpCbx9eUxH5L6jP7wTQ6cFX1FX9\n/9SnnmL3A/Wp37DJd4j5PedH7b+mPv8F8DrR/n+g3kVfVSPlHytn+Lc9KBehrjiJ31D04noHsXn6\n9yip11oVWAJlktDj/fqWaq8CsvW76u/ngHX1vQu1N4EnoX5ftX9Ctdc29xn1Xb1kBjb0TTnuwOZq\nG6xeOnX1Uqkpm1r/IYR5+MaXId8PqP9K+sfXai6+5/F99YM/XZPB34/qEqZ/sSau1U/q+zRpDmyu\ntsGfrq1ToMCb9U0AnqxdAeDt+h32WOXJ2mMs8YBb9ffV3y/jk+Mj9ZLZUDb0Rv19upS4UHt28B3E\nRhfosll/A4BKTXrAVv3XdCgOfKCH6vmo1l6hurpN47/+kodvNFj7H+T56NR/QNgtkfu6+FCOsqnu\nV79GUOrA978tF+ozvyufP6yL0/G5mnz/tbTnZfX9bfX9szUZUL2uvj+j/v6m2v459f3DutCPKjWp\nrPqTukzcvWT8vQVcUd/vqP09VhN7ckt939D7/19h8xew9IR8H/T0+cEJw/HyLL1ejz/6oz/iD/7g\nD/irv/qr2N/++Z//md/5ne+ob+ZoasNYPmssPzF82b0OwX8E57Pg/evIi4SDy/+IGO1/h0x4gcjH\nB868cI0wcNj8zWVcx+fV518D4GneH7R5ZuCOSho+wOMJPuDpgRsJT/DhYPnKQzXFvQevfVc54U2E\n96dxzVi+lVhWhhafiBN+z2hjVKjZfRAt300Ed8xCNrtItu4niKOrWZumPkDLsmyT+7NxvK8yOhpu\n3n0zuZazrB+23FDHWkZ+j9nGnEKyQhzm92UjdV0x09i25dXh6+tN5axrbd9R265Y1tvaD1uuID9a\nSYSFRpu91egK73nR1UgWftgzrpS53DKuprn+Lme5x3mW2ONW/f2BA960tG8Zx2vGlqP2DYafn7ls\nns+9/XNc/eiTVCq7nH/iutE+atP1I2JosxGtbzeM3982yKONRHzdTGmrwde/Pd3hTza/yze/+U1O\nIEiz95DV5l8ylp8wlp9H8sz/G7gbsPKXstq08dqW7yOj8DXg3xCNxAH3xYggnWu4dDtlLj/5Di+W\nXzeOenWw/DTv8ZBTgMOL/GowD8Jsc9kw5hubDQo9fxCFq/+HyAk/YNs17iF97FfIdhcQZ8K08yb3\n2zTm+8OXe8ayyf1uGe+FYQFiH6m30CBSG1S5B/II06NCNIyC+J38EZETnuSElw0GUdl43GLMItPm\nFS3rbcvVxPoQ6TJt5GXyJPGuZtrdqmW9ze6a9v4tUGN9wiVw1O1vnM4RumJLTLu7l5hpa9q2uA2u\nDl2v7ajIyD9OnzwVGoQGWSG+z+qBbZP7tNljW/t7//QW9y/9CWHocurJG+TLErVqdYz9GPa11zYm\nkTaMG27Oh07OjR5idzOt/zXwfcTH+1fE5xnY9pNh+Z/+53+eu70fKxIehiF/8Rd/wac+9amhBnku\nGIOrm220Ear/j0iZ5SjaZ4S+mT5zqfNy5NCDgIWomzgrro+JOdxAbfSz8GSndg6KCz6quu0JpovZ\n2HuVnhrFB9cTQ1KoKGEIve5oOopMZHPw6Fv18jVcPyBvOOBj4TqyXZWjnUw4Ag3gjvp3j+wSr1q6\nfAOJM5xHHPOFgoNU2NxCBihXkes7zZeEB2EgWe/Srk9r1WOk1vEh4QBV9thmgyZLFGnPzBZ7OZ+V\njYfsPDjN3v0NNq7cmclxM+F5JPX/ALjLAnbMw2MsJ/x73/sef//3f89nPvMZXn75ZQD++q//mt//\n/d8/4tMaw7PO1FT9MRz+4JizhW1GeahIv6M44XscjtjjEoUeMmyfVsdC7y6HRLP7TE+m8AnL+mFl\nOCaBfo3q99fUWHK2HRvra6eREXSyC417UuO018dyhxzXAlsxiayInoVwIk54stjPONATMrVKygnm\ng9nYe/WUu8Xo2RjWdbQTrgv1GG104abQd+iHLp7Xo+j1YkpBpjqKflUU6MY44QWjTcWX9fmWEus0\npKdqLxBF0yxRa+4i0W0HcRD3h7SxFeUxIuRNY/2esWxGvFvI5bmG+KRbHEQZGb/kkQi4q35SX/2s\npvpJu+rfVbVdCSle+DYShKwkXo8t45zKRoRxxWgXK5JmRrltiihZcEqdeBfhLT6J/DCb+TPXZ1DN\nqL1MNF/YGM/luyHOTp8wB/3V6C4k1VHiBXQKQ5dtRXyqNOhQpMUSAR4l1Tls+zS3LcSK9dgK+hSN\n9tGPW6t9lmr/FrsP1+k2KtB0KVba2ZRSzMJoOYtSChxe1SSH6Ib/HHgD+Poh95NcXgCMdTpf/epX\nCYJZvhiPSKHE0U1GezLOYSLh42KKuy4SGdYFml5xKGjzMMtaEVbMIxI+B3GQRYiE+4EYd60XfoL5\nYDb2Xns6I0LFOi2WFgn3pe/mC+l6Sj3lwOQz6C7lOofUBtdFedZJrWg7KToI4+U94kUtz6hDa0ny\nLKfvIFHzLYS+olkf76l/S8j8nqdZgHeLi0x0vY2c5A2k3PkM4HWhP8V7CjJJs02ZHgX6tEdmbI4K\nuVyfjVP3ebB5nu3N05y7skCSJJ9COvsNZKC6mt78uGBBNcD0aWVwBHTTkVZGCBqjGPDjOuH17zO+\nYzbFq67fURnKTxwaV6e4b42QKDi0CCUE6prLOcsnZozH4KigIzoe/cHEzFnD9+UVn8v1R7Q8wfGH\npqNM7oSjnPBCPl0ZpadcyPwoLfswJNdTD5/hA+n5w1bsIcZLKrFMBT4y8f7/QqLUPjLb6nPAHyAT\nM59C/JSsJstT7Z9Aps3+PiIS4COR9H2EH/5/IrLN6Vd5BvCICvrsEefbT4j6j4avD1y5rdOuppnD\np6pmdHVmJFm4r2albmzcxXEC2o0q3fYMeVSjUALUhNtB4atHAAsWmNc4BB0lxQl3HITQFToEoYvn\nBNa0vXbChS1oEeZXqwfZcm3lbCkvEutHXXVjPzmzbYrV05GJVSQI01HrppGR0RN6ssI8Vt6yTGL9\nHnJLywyXBU6jvpiTh/LjXgDbet0V0354lvtvO9aw9om3pxl96XvZQjHWPmxZr1ObyaI/Weglk1Jh\nNHS5+lzOXiLPzxKK6qeMjk/8+zkh2Y90JNxC6tXNzQIeCRvqqcFaGMrKUqFFgW6MghKl6UP6auMl\nGhSNaHjFCF0U2j2cPoMCPW6yaM4weolevmqca9/SBuJkbZNqYqGgaPbKQ0T5SU+630AUplaR4IvJ\nctHIUmxymE31EG74byEMm4+QSPnrwG+QObTPqvY9w2T0DUqNOTm+bDx3ziRV2s3H/zTigN9Hrrme\nhGl7d5r3wGaDW0T3xziWq/bt+lBudAjyYmO6xbhX3jX6VcGyPIqycooHNFimTx4nUUzKXO4Y25p9\n3tx/x0JBMdu4BHj4eDmf5fUtdh+eYu/BOtVL0axhTf1KLgdmwKRk9KS0Yj22oj5p7+wXkVHnB4h0\nYVYnZ4HpKAsaCc/gWWvoXzAiW6PnUYQjqvCNEwkPNSd83Ej4FFNZOmq8z/QCqE+NbjIxtA1fiPkX\nYSQ5Ns17F4Pmgc+YFaKd8xz9uemE93qjnfATPCrQkfARM+t0V0gJCoa+9N1RkXBwyNEbSbnylGMQ\nJJ55LW83FD2ExwEHZZsmRIgIPv4XxAGvAl9GotbTzMy/gpii84hKylcQv7ePOOP/GXHQ5wYt7QJC\njD8CszFQv0nCKGtfaE63iI9HMKiAuc8wadCjRdX40asbD4CQxs4qfm9WL70MOI10xB4yInwEsKBO\n+CHoKKOc8IxV+Fzl+AfjXJpxr+KUnfAcMvCfJiVlmugjk6BBuI0LA3Mi7bQRzY+cGUKgr+JhuTmG\nirs9idqMdqZOcPyhPKYjccIVJzyl3+h4ST6Dp+aod0owTuRMfBc5zyMkTgcIFeQnavlJ4BsIG2PW\nIkrrCN3li4jv2wS+jWiOz23YvIpccx9xxKdpN9UF93zITZmWUqaJQ0CPAv4M3bV8ocfS8i7g0Npe\nBEKoAa2//H5qq2ODBQvMaySI3qY/kPQNRjjhvoqO6AenF+ZTU+2OxQk32/i5aJffratCAGnSJcNk\nTPQOdMTT0t6kUyRtuo2ScQqJTGwRpySmXcZx8D4yOScNNtqJ7bKYbR4id34FMfij9nPguhh/jOna\n2pZzI9r4UjSjdpGDM/CzUpBGLSfba5/EiY7hW9qb1JI0SsgoakqXPCEuHn08An5Tv8uztYsH2see\nhQwjStv5mcu6TRhCpyN5ylyxF0uj2uD3M5ixE/rJAkJrOQFeYbg6SpKOUj7YplgST6gbiJEv5Vqq\nD0d2XqfgQxxCPIp08PATKf7IeS/qOkPvydEAACAASURBVA5A3iemLVz/aVSQLaY/3CIKCedJp6wk\nlnspFBQfkUi+jrwuPovYda3NkaX+QxbYxgzvEBUtNNsUgS8gBeLeQ1gCN5DIfMxqmL/ZgDmeig0k\nbPbY1kYvLyPRpwai2Z7lxWPeP8PU1N+ICvjEqCx6WdnlQjPEDUIKxfjArxCjiAxXRzGXbVSTEm2q\n7LHHKj3yFNTFNGknNqUU03ba2pvPSKf+A5ZrL6v9eJxav8f+3irNrRVWTz/AcZJ0lMio9oz1MQ5t\nLjFEnIQ6opefAb6DZJyaxOUpT+goR4WM4W2z6YiXrOPI0DhI5hYP7G6MSLgpITcODMdqGtDR4weM\nr/w0b/QRfVtIGPJ5QrOiZikJMIcMYEeR9LJECaeFXr9AGHp4Xh/PO2699wTjQ0fCRzxc2i+xSCWF\nIQT90XQUTTMcqYwSKjaYQT8YiRbi1HkcmW51gPC/ryO+wxeJlz6aN1wkIPMlJGiyj0TFr6VtNC14\nRLUAHzDdmaMyxQwnBHfKA3yZoBnSJz/TaHhlaY9CoU3Qz9Hem4TAf8QoEC/zfcyx4E54Bk64dlZG\nOeGKjuIfoRMeuooTfpirqEdjU0ibVZCggE+8ENtRYVQU/LAIEQfcR7KLR0ypPBxC+Vfb4JF3wnXV\nSh0RHBYFn/o5tMXYF4vHlUx1gvGQwQkP1D8X+zMYOBA6uI4/YvAmHnVh1EBTv3qGOOC1Fw+uA0TX\nD4SjcQQckRD4MRJdziOO7pTEVlLx2dFNWEGUVB5HLt13gTeZ+ZQWIcpX1YEnUNcbRMFToEScxAmf\nOjdc5Ha6U6z6pKPgGo4Da2sywWF/ZyHexhH0xLRHgBc+58C8zXNWHkg4hhPeMXY3ZLeOKw+Jr3L6\n46qjxJZzhtcdBmJw88SjNDaagn6GyuqcdVTc0t6kU5STJYONd43psuQQY/g6Qkk5w0FRlmnceBtF\nJIs6ShkZMDSQS/EMB8/ZTF+mqayY2TAnS0oqrZCD7ksFhlcNGnc5Cz0mT1RNw+J0ZKWEWPtwbHtZ\nbiodmgI9fJknP/IYWagm42C/JfzDUvlgAe7YOdvUUWISMikHGsbNOgm8HyHSCGMmhjjhyWfHrNqV\nP9jGy/kDu57PdwaaymZaX6/rqn5ZYV9Z+P6BNgBOH3AUL9wnHlU1KQx6fUhUJadEJF0CcTrGsG2B\nXUMpRaubvIcE+lyE9qGV+CBu780nxezWPct6G2x3zNxPUiHS/FuZSEP8PeAXyE//HMaYxEJNqZgH\nz6JekqZ2sqzWabHzZay0k9jyMNoJ9m1zKtvhhLC016VfjEZeplpKFqWUTowiEt0trd6zzhZNqvQo\nsMpOzBk3KSXmtvFlf+Rybsj69dVN7t27RHuvgufHB7g5g4Li2pRScoln/6gom48h7+Qd5F6vjmi/\nwFjMSLhjkHFHQTcdEdhwvGyRcG8QCc/mRNS/pw+QqXkE3TenNIDWfOqAo5+5/t4R7w/kRaIDF08w\n0yrP6VD2pD5M92taGKP7HxVCoK1GkToS/l795uxOQKHZFhWAcumgE36CRxEZIuHatqdU7Qq0RnjK\nTDkxtQ6uGmIeFvU3h6zcQ2yFl36eWbGNTMIE+AzxuTGzxutjtHWQANDn1fK7wC+ncVJpyBGlUe9w\nqHds/RcZGhlUpXx7ukopRTrk6BHiDmiDR43dIQL4+XyP8tI+4LK/u0DRcJeIknJ9nicyORbTCR/H\nC9Ejn1FOeCISboOrjpk5kqeD9eMG/rSXqegO08AVxEZsEauEvHDoIBEfH8nknk1vPjvoNDgcGccz\nE5KT0WaAFhVCXHJ0BwPRWSMModEUQ1+uNEa0PsGjgQxOuJmNskDzwXOe/UUQ8cF76TET7UyNY5c1\n72+JiakoAfAv6vMKEvQ7bngMeBW5FG8ikzZnimUk0NVhui8/da9df7rccAcoqfxHe8Y1pJdW5ALu\n7y2YSoqukHprrmcxMRY0eJ+R6N0nGkZ0E+sVBmlrNTGz6xfUvHlb6lzTUextfIMjUvtiEJ2yLY1S\nHLI+R6QDXcBKZXGM9flEKs+ckGxSNUw1r8vIJJmbiKzVMIUvm06+7ep/2rJ+XDqKZuRcV8daQ4o/\nVBJthu3HXF9OhM2tBXrMdiXLstlev4QLUDuXob3ZjYqW9bZz0/t0VXsp8EpotOkaRRBs1JKkmkgW\nuoiPx57SoS3SGWzzRO2KwdQYTWuxHytbm/1WlSDIkS90cPLBwWfQHz7SjVFTbEopJ+ooCwqz2LoF\n+t6ViNtPBc/ztXmnkOsMotwH0/Fq4ibdwd+KQ+gBXt8X2xwQvVcMekLtaeO7pipobXDt+FloJ+Zy\nz1huGbb8V0jgpILYbE09sVFQbOook3R58248bew3uc+0Wo5LiD1/C/ip2udz5jGMaxRTActCTTGv\nr83uriNFfO4ikR09OMpAO6l90vg+irKipGuLzRC/KB3RVEsZVynFpK+YtJMKTRos06XAEo3BzylY\nlE+Klv2Y7U0azHrtMzB4dqIOWVneg9shrf0lloNNXBXQtBbuwUBW1bisqmHm8hXk2m8iz2lykH6i\njjIJDkFHGTHZXUfC+3767Drd+bLSUQY9bpLJmVN0EM4h+vYB4oxPWdZ0LDSQdGUfyR4+xwJ1yJDI\nyM4y8KBt5QyD0SERH7wYe7vNFo19FQVf2hvR8gSPDpTxczI44SkcNR0Jz2eKhKdbwVw/0BtkQ0BE\n1p6QR7ePVKIEqVK5YP7C2LgIfEot/5Q4VX7q0EUzekR8/WkgUDETn6nORPUI1EDRGVR9nQVyOZ9i\nuQWhS7eRNuyaMQqIg6MVHY4pFsbniWMM71T71CPkiDQnfJQT7hDiEBDiWkt7m6h/Xy0sqBPuIBzr\nKmKLPmTyIj7vTLh9iAxe31XnVEX09xeoLle8TH0O6rNKeemX+Az54F2K9Cjg0o9NFnq/PoG8wCGw\nsyfaD0snTvjHCBmccP0spNFRFCc8rcqqdsJzI7iLXj+djlL/TWJFQ7XNM7ERewPx6S+yOIXK3ppw\n+08gv6eP6J3PTDHFISLT3x9v0/qvxmsfuooiPmW7rSkp03DCd1KI8JWq0AO7+wvkhEOk13lvrmcx\nERZzoD1wlPsHHdTkd/0LWkP+RpSq1g9+t1/AJ2dNiwfkcAnwcdljmcqg0xuFRTzD0uZ7snNXnYs+\nkG0GthlVrajz9lPaGIOLciIiWzH+NmpW/GeRCTINxBG/RDSheFw6SpHhacgsdBQdkdeM30tIVslG\nQbEum6oxieuSNyVNbdfVdn+K6iR1QHgV+TGmOkqWezuMapLWRkvBaCqKuoAxpoXR78w0YpoqiZmG\nNPuwuf2umsW0xD6BcVIB3oBKko3WMlyxJUubVq9Mq13FcXyK1dbQ45roGxcmsCqlDF994G96eT5U\n+I8ZTMvgMPCwc97wt5FpU1PiJ7paZsGN6ChJtYee2kGR7uBvw5Qlcr7qEH2GK251iexyh0ia0FRT\nMoNC5rYmBcVIOrXUbrXD+7haNy4FZRp0FLP6ctZ9mreqjdBSNhFmyK+BZ1FFkHR741qYimCOaV9t\nCiemTTWd4A5itx3khbOrtrPtx3xv+Ay/95ZlpwQE4ClVnZxvqIh48X54+OU+FfbZZQ2fHC59Vedv\neHsTtvXmtq6y+Ae37bO0tMvW/bN0m6Xo2clSuCf50B6GdpLWXtNENzkop3ZMsOCR8AxFQ444Eg5R\nh81Sra/2JX0Axk9Fusxswl8OMYSnEF/jOjKf4TCG+pOH2EYX4XkLsYc5JPr9OLMvu5yKkDipXnWX\n2iwqZMxBEibEoaHePlXikyGfql2e2Xns7krIarm6M+AcnuDjgDEi4WlS4joS7tktWkRHSbd67ohI\neO25xArNW57Qlmtq3imiAMkiIPlzD4MC8IJa/jXxAcVU4RJFeMYomlGzTXxKOU4I8nKdovnK4atM\njnNoGVgb1mp2RfhSuYnjBPQ7Rbs87DxwDnEgHnJs5/0sqBNuRMJH9ehxnfBeFie8r3aZkQysT/Ew\n3OEZOl4uonGvVVMeItSS+0yP/dBBnP13kMFqiGQIP8l8Zbes0LrAIJzCWUFP7J1xNHaXFQJy5OnG\nqCizxvbOKQBWV6ZJ3jzB4kE9bE7Kiz2DEx4G2gmfnI7i+sqgZ30WdZh4gmJeIZKhBKEPPoo4h6im\n+ES895lAR7h3mZ6DrOQKHaZ4DAU9b8efYdjXccJB7YZua2EEhOWZWyWu03/MMKO7mKUMtjmM0RIR\nyiNKUzzQttukoxi70mlrUZ0K6fsFemEO34i8dCyzlFuUB6NNM61vLtd/2JaqmSDkZp3qslEQkmm0\nAhE3I4f8dDMtZs4gT1SOXTZ+Z8+YRW672voXaw3xj5BM6gP1eRpRKNGBA9t+XgeGFY0zh047yDNh\nsnvXkEGA9m2zKJ+YyqQ2Cko+aRNsKcY0CgrEo+BVYhyZ+n0YBIZH7ecwy/pYPoTVaHW3FI2TzX7n\nW6glnUQ4zmwX3z5HCDxAnN8qewR4sf7/Xv0WT6ofbW6bhQqThb6i2zRbS7TbS3hen8ryLm2jB9gK\n9PimTYhxdoy8ii2NbPvbCR1lDhgysz1p7rUTXjT+Zqqj0JeKmUDe7RrqKPFUvnbCRR3loIJKzvch\nDHH1KVn6T/1NqH1CfekRpzcMozAM+zvQMgJH94jYEitEZshGL8lCQZmkWI+JXyH0kVHbmMvJ4nEa\nTyP1ID5E9M/1k14239kmTcUMrpn20nZ9h9lX7U70kKyFYV9t+6l/aFRG9S3tTTpKYtkzfoQ3Nh1l\neMEdTQMp02afZXw8VXBqvH3a6Cvb9V8OouFDj1vap9Ws0m8X8Jb3MhbuSY5ILHnvcT1Rs/064sBs\nEw+cHRN1lAU7HRN5pPf3SD1N7fmNmG3oODJpp98vSDQ8JXWodZLH1uM8zABRp8v2iUozzwBLyKz1\nXeAqMg64q/7lkReB5n7r+UbJxyckos5pTmOTuKqUg6hDnVfHnGXl97EQEiVekpKR00YRue/6gs4I\nbcp0KOPiU5ldgvgANrfPA7Cy+vCEivKxg46Epxi+DCqGgXLCPdf+AEWRcLtL6qgCyJkHZNpJ1Nzj\nQ+Ka+rzMwqanjwTLyLvgDhINfzm9+dHAQRzvHeRFdy69+UTHmWLdDw0dCe/P+G1aKomT1W3PVqd8\nJNaRUd0W8gAdMyywE15AhqZdUtVITTpKJAU7fI/5Dv1+gV6vmOqE64I9bUpartmKQRQ8VMfOky3w\nb6JK5ITP2AdZQbjZTYSW8gDxRR8k2skEEEEeMaBpikzLSOR7jdmyOg4N/WO0wU7c9KnSo/UFmjGn\nbXMQBW/gDrmTT86AE97v53iwLeWZ1tc2R7Q+waOHDBqvGQqiaTqKzQnX1TIhxE3xsLXeeJodHkTB\nIdJ8nZAPrqsaL2JhHlsU/LB4CnHCrwIvMaM5QUuIE54x1lAbluodB2Eokb8pQAaRgerJR3eMNE44\nQFE54f3OLCvXZYCeQHFMRbXm4IRn9TT0jU7wVIelgwqq2R7iQMWK9UQ/sZDvQQvavdLIYiIOAQEe\nDaoU6FpT/j1Fd/A6UjWLFWTsMA4doUjk/eaIUyjMdFzi/VKJ0W6Gb2OOlW3LPXXa55HLqCeS7yBj\ngy5RTiIJD7n8ZbWPqvo0h002pRRbmxgdxbheVgpKgqYT+55lOU/UzU4TRcFLlvbm+qplva198rwL\nRIooanZ3x2jTKQ7vdzZ6VDeRjrFRR3ZYocUSDj4FOoNJyJ1MtJPhxXe6lvPrxM4v3ube1kXC0KNS\n3cUr9VIL9HTaxvnYCvRkUDKw/m2GWYgTQDxsmOKE6yZp88FUJNy1aMTp7KZDGEvHx1LzfR+3Z/DB\ns/QlbWt14lbDshwOef11EXvrILbTLPDYsyzbTsfWZty4kA1ZHqO08+gjMYcSkj29i0xENSkoPWOD\nvLmx7fpmOSFtj9vq5LTvOu5+bOdgtnEg1wsJdVbviCjUXqLf9kfkTDyLr5VFQSU3pE1ecYP6vbzQ\neyf1/7N4n1naaM7qfmqrhcUCZ770C3fEjEuz6YhRbr4g++p1Rz8VZjQ8Da99Rz4D/YI4bIZIe57z\nq5UCSIdYQSIyn0DSha+qf7+l/uXVp17/MjLR8nHEoC4s5WQYAqKHt4KVhlK/OoVju8zlYoXAtpoW\nu8rO0Cg4wNX6R1M9jyBwefBQRcFPHWOh1xMcErrfOelRQx24tryQwxDCUNNRhke5NRXFGZFqzBIJ\nr79rfNHe5gThLC1hvcaC1UpQeO+I9+cQMUJmVonAU/8CMrkU9TcmO9y09cK1w3yUeuHbI8TRPS/A\n9fqEobtYCik6ENZIbbWwWGAnXDvKGZ4Y3XSEE15QTng3kxM+Hi88NPWdDzNCVEVhZk1HyQoP8U/1\nXNISi/nCGAtmtKvI7CUCi0hfOaowVUZss06HEi59Vtid7cENPHh4Dt/PUy41KFeOaRjjBBPAcMLT\nkKkqsVBNHMdmQLMZ5cHmWTnh2n5M4AtpmfGV1FaPFk6rzzFUAyeDw1hxvYkPN+X3eFTZe7YunNYD\n921iGfOAnlPV41hmMxfoSiZhOOGj0oI6mrhLvMAC8bS1U1aOdbdsVUTRafRQde59qnTZsab8v/Qt\nd8BkyO8FckUrjE+J0IUF7hBpjnvYiz4kvpsGPGf4M3vGso0KYs5ptfmD5qG/Zh7L0n5sCopF+aRs\nOMaOje6RdJ6zXO8SEYesAmwg193SvnZxzP1XR6zXoxiV1usZbbql6Mq0DIkWs981jfW2vjxsGx+X\nW8iPWWGXnhIn1DCpIBdrnxj07VHPC4yniNL3c9zflAmZZ87epucMp6/YFFECg5oSU0SxKFGcqKMs\nIjI44abxsDVTUfA0zyc60gjvKIPzVDNJ0iZfPa2/6dUm7UJ9ajNUUOuy2GAbJqGg2No/k9LGJjph\n2vnekPV6GszukDb9cX9oVsdrVPkRYz+158h2wS1wDFuSRfnEpl4yjBYCQpeFyE8ZdqxxsVb7zND1\n5j5dpYgS+IcMwU3D49QDLE01OmbRwY9VJDxfEJei1ykoyUI7dCfvUMwenJ40KpInsk49FjYqfuwR\nEGnGFogc8Fkhh/TZGauhADzkFAEeBTqDEsjzwJ37jxEEOZaWdlmqHtMZNSeYEBkj4RqWZtqWp+8l\n4zEy0FFi0M/vBG9SHSdZMM2JqUKrTZrFR6eOMWoATowpv7s1hXDWkXBX1VsJggXzdHXcasZZ5aPA\nAjvh2iRlIElrJ3wEJ8jL+YrT5NHpp5s8B8jTJcRNrZz57deMp01L3OnCK4fBijp4cmLQAuGn8z6B\nSWCWIy4gUeoM7+f6+0d0fLOC24wjr/tU2FWVDVbYHvmzr9U/HNHicGi1K9x7eBEIOXP25lSOcYLj\ngIxOeFZfPeXvWSPhWVz1GCc8w7zSUTgigZWp4ag54SDXeebToPQ9yvBerb852aGmHdPR/Tg8wiON\n4oQDuGrORRgsVJ3ryN9aUJ8pDXOmo9jmfkPkhLfsFzZJR9lT64yn2kxbdymQL3bpNHNst0+xkRdJ\ntI4lzb/KNj0K7LEcS8E3jWRbp1CkWZTLuLSkRgEOQnrTAT6TjmDWI+5YlvUU+R5CX8hi4I07WTGW\n88Zy2bgu5gz01pAUaRLmLVhBgseJw8ZgU2LJjUs7sSnL2Kgpye9mIR6X6I23jNyLJAXFvD/m+obx\nfVyqkV52ieQPAwjLDKy1WZSn6Q2nmpj9Ll5UymwfHzDq/tzH456aDrXKNiEeXZW3s/V/k6qSVe1k\nVJtOWOSj288CLsvrD3HLAR2KcSUWiyJKL0ZBMXpeFgpK8k1/oo5yggWBdmc+ronPpDuXm7ZXsmD+\n4wmOEMfw3i5wJHyMcXLGSDhAviTe7n6nOqIllNSx08rXf6VmsRhJx3AcFIiipTq6vkB4dd4nMC50\nIR7dlSqIFMEYD2xMG/gwcBDHXxd0CMY7/iQIgbucJ8CjSJvljIKql2tPHfm5bG2fptlaxvN6bJy9\nO3qDE5xgwVA7YuHsRfcbnhnd5FAYk4w0U9Q+Ne8zyIqjcw5snPDY0Rb1pi2YjzQOjoETnoG3qn3k\nPUbejHxJQqH77dElZIp0gJAOxdiks5HQlJSUGkMjUSHOczrGnWyuCIiun3aE50G+XCZSv5kDD3yf\nKg4BGzyYm/1sd0vcuXsFgAvnr+F5JzMhP97IGAPOGipO+Xu0i/TeP7aZ1buboCsf40z6oRESl1if\nCTKp7BwNpv26jiQ3Z4xQLp5dhWhOmOG9PWos8CnrUHCGElc5oqnlIwLnhZI02GuNFoTyCJQj7gx0\nlZP4Xj3FdE5SKlJXbtBP2QJZ6B/O+wTGgb5u+noe0uLX3znk8c3j+szcAW9Q5QGngZBTbFpn2w/D\n9foHR3YeYQgf3PwkQeCxsvyQ1ZWZiZOdYGFxNE64lhhPd7AzOg1O4nMIYpxwHZuZ4LnWOdmMxRxn\njmlwwlvI61rL3s4EmmuZgXw/KSd82t6xrpSZVv11XGThhGuqoOctGHdPj+gWdWJFChZYotDihNs4\nn8tI1cmHyTbRT+xQJCwCTkCnV2G/XyGf6yd4rSYHtzKQDrrHWSrqXEwObpsiTbVNT3PCQ8jvI47X\nGvFKTuayjYtsnr9UVpGRXhm5Y8MecPNOGkF7s7Jk3uCdh8ZgxVatzCYVtR7AuSHDt5yFi27ywB2b\nplUW7retSqbZJlTt2kTv3SXk2pkMJJuEoO2e7Bjfs7TXEz6XkX6gKDGhMfZrLkUXca8YjdhM7rfZ\n18zlpnU52rZNkdtcAGCNLVyV1Unbxuz/PfJGJc3hz4itwmayzZ37j9ForZLLdTl98RZdp5CQRow6\nQ9ecx9E2brpZIKJtPAQ27reNK25rt0AD3Y8HMjjhJh3P5m/oqFzoWKuF2yayHchwZnDCY9CbB9j1\n+oxDmLZQxwO02Wirddb5NBlOx9Ymi2hElmMlYxi2cx21X80c3eDgb47BdiKW65t6kfTzXTHamdsm\nlyfwjvycg5+TTmSrNmxb7g+RdE0iUOtdAqsc7CSwyc0Gyga7Xp/gMBdoGjbWTKscQyf80YiEQySU\nPaL2iONATlFSGhmi4QU1k2+XlcHo08SXakPuukPUKSYd5nuII+8inW0BqClfW9Reo7nWLaKJmOtI\nV5owMlF7fswNdOlR7YB3mel965LnOo8T4rJEg9VYMexsuFQ7Gjbo7t4adzcvASHnLl5fvCjKCeaE\njJFwbW8sTrg43dnUIkYyWjI44TFO+BHI3q2pz/Gf0NlgGpxwPRvk1BT2PRTaBkOmomy1FyY83JTf\nkb56KNwjTK2O4oSHIfRVUNPLLZAN14xlXbTnmGGBT1mHGPcZKeoNY1myfEU85EZzdURLoaTk6BHg\nscPo9gN0kRSldqIngd6HfjH0OCksYkI73+Y1KSJdaB65njzigOeQPjBjB7xHjms8Tp88JVqcYnNu\nPPBWp8JHN58BHM6fuU6lekxrC59gCjCc8DQbn0FaznGVbrJFv9gdOOnpr7wsTngMR6BPfAYx8XvM\nUK5vjugCt9Xyk7M6aIcoWzGDysj+lN87ulx9bobpu34/Txh4uF5/ULRnIaADr8e05OwC01HySG6h\nC702uCplbqOj6MD5QxKp5siadjsStXby0oF2muuc5VZKal+WdSpzkzMU6cbavFZ3+UJNwt17q1HY\ne2PfOInTiDMWEKcsmP04y7PkIB2up9rryX66wqaGuWzSX4xTcgwaRb4/fNk2yK53oDbMkNkyYSVL\nm5ylTVZqis4M9BNtNozjHFZOMLFc/wBqn1ZfbFSWVaKKqVoFJZyMgrKH2WY4hcRcblDlDhfoUaBA\nhyp7tNXfbdvYaC4f1K9zXsnC2Kkw9v34vse7118kCHIsL2+xdnrTKqeon02AjkFBiVXGbBtJ6yy0\nE1ubZDtTonCBwxKPHhzkgusRtMWAZHLCA8LAxQ88cp4qrR1L6+tUokOf3FC9cD/nEWjeWJKOYCzX\nPzDUknT37xK3CxY7Z9LxNDUlB5zxpVjyfeKviCzUlCzz/832fct6E+axrgP65ybb2xg4tnPNA9eQ\nu32BKD4Vo+nYqCa2ZdtJmMs6M72Ubdv6b6D24pA2aeegg0EA7vBRnI06koVGotsEOIoKEqZua6e+\nDG//oP46a7XPWo/f7cgLOF/oDqV8jY1xK6PasKU+J5mDN0cs+CtHWbUgQ/RMOzoZIuG5knA6mq0l\nfH/0JfAUMXGfpfFUUiCiRYwRRLdC70f7MT2iEf7HCZoD1iJeeGcdeRDnVcxLR991saUZBwt65AYO\neJ4u57gziADOGkHg8OG15+h0yxSLLS5e+uhoDPe08D48uLHIJ/ioQtnfMOVhyTD5UUfC/WC4W+kQ\nBVPSbPiARpC1K+gxoghpHRoX1efVw+/iWKAH6Dnuk6q+jgXtQlRSW02GGcn36eCFhz/TDGe7LcM9\nLfO8MNBO+DGNhC+4E66GNn4GXWNdeGWPkalBxwuplBuAm4mS4gBVGohKSpxboqPgqQiRh/8opoHr\n4jL69wbMPIc5NAo+C2h5P9PB1VQdHYWeEgZR8GFwgbPI/Q2R+zHjgVGXPB/xRMwB9yY8ifOHFEcP\nQ4ePbjzLfmuFfK7D5SvvDSqtLSTuAf8A//C3MxNLO8EA+qHN4IR37U1cV7bvp/AAtBPeS5NIch0C\n8ditzlTssdCzCiccdF9Ru9lk8bjhR+ksv4mYx3XkN88EPSRg45I5WjqIgo+DGcU7Wir3kU97IA6B\ntCg4wH5TLl6xkkE2epa4rz7PzPUsDo050FFMD7lvWa+hnpjeXmSIbannUDXfBW6AEoWItTer71Wq\n+zRby2w1TtFcHp6mN5dPsQkss806O6wMIowmXaBsTCKtrEYHLj1ALOwGYgy0P2Kj1tiQvFtV5Pfu\nEb00Skh0Rr9ATLqEOYA1r2MWWoxt/SSz14sZ1ueRrpHkwS8RKY8kCyPZVFRsiiqTUFY2iCaEaCNc\nhJ7RplWNXvpmNcw41WQ0PcTW8cmAqQAAIABJREFUfodV7nIenxw5eqyyTZci3UQ7c/vD0EtGtelQ\nIAzho1vPstvYwHX7XH78fXr5/MDxMfdjUlCaDaNS57gUlHGXze9N4D8BPjz5ygIPFB4ZmHZeF1Qg\nHglP2hptPzrG34w2Pjnw5OHr+MVBuj2u8BBRUDoU1dORUKXwVLo/18fthRHlDex0uRJih7eIK6SY\n7S22zawYvLIPzwGvI6+v8wd/prW+9LimeVw6Shr1xfxesazXyw+AD5BX0xeJm1HzWuRt74WSZXmU\n4pamZK4TKYyN2jYL9cU4h14Bcso37ZegUzTVoUwVqNF0FLPy8DDVFG1zPXz6eFYlExvtJEv75HHD\nEFpNYSbkKx18vFhl476hXBWYKlb9xEg2i38xTps+QkEGof12R7RP2/+ccDwi4cEIyRMNHaS+M7rp\n0pJE1/cbK5nmfRboDiZoPjTmdP+0noEqo/WhdTn7o4KL/OZzRJw0LcA6xUqbWX7yRNBRpR5iQPXE\nRg+x3KeItK1mhPrPEyscIqPuMrcHu0GV21zEJ0eR1kCK8Chwr/7WWO3DEK7dfpaHO+dwHJ/LV96n\nWFzgqWZd4D8iqeqz8MV/s2DW+WMB7YSnXPsskXBV+Kkf2I1Cpkg44HvKcbC8HetvJ1ZoLviEgclP\nqkPeQRzWRUHy5x4GDeAnavkFsFTdmAJ8GBQI3si+Wf3X4x3G7atpQC5TpaP0ydGjAIQD+eSjwk79\nF9a/tZtLBIFHrtAll18gO3kH8RfWOZbyhLDwTriiigQZE3T6yb6d2gqAYrmJl+vR7xXYa2elpOyp\n3Z8f383R0oJ64uBRooCMV/RETYgqRR5H9BHjqS9yHgmzaLnBeffaEjLwqRDx02fsa4bAA05xnSuE\nuFRocI678+OAhw5Xb36CB9vKAb/8AZXK/ugN54U+EgG/h3AJfw+8BZ6m/uhCOcRpTrj2mVOoqK6S\nTOv17W9iR6XSuiPe1n7e1Rtkg359TMgLrwCaBfErZj6lZGpoIQXeekiC+jBMj0NjmyhLPkU+uKu6\nr2VKwpFhX+UP8nRnygff25UIZ2l5wdStrqrPx+Z5EpNhgV47SW4JDKxbf3doGvJAullHJG4afzP6\njFn4o7dapLzcoLG1zu29y+TL4rHaiqO0qKg5lj5dStziEivs8onahcFAu2LQUYpLUVjk3KoaRATg\n6Fn0ebLlEW00DYiTB82/7SG/OymxriX7ckjURj/FY9JRamct54dlvW0WueZ4J982LhJhLhNx3yGb\nggqMTzsxt7con9R+R53XEtGIW6efVTdpG+33lqIdTULxGEZHCXC4xUWa6mTLNCnRZp9qrP2kx67W\nXhl0oTQKShA4XL35HNt7p3Fdn8uX34OlcHCMsSkoDeOmmc+4af8noaMEwD8gef8KoO9tj2MbTTm+\nUB52vzfc6e0TDbrbDKej+B6oiZmdfmmQVo8VgKJAoHbUojyY3BYv1KYMQc6lohVSNIzlGHW2iPQZ\nJeRFXq2zUeKMcWnZaLOi+udXQrgaCMvwXeIa3baYisnQtamgTFKs5/PGcpKOYm6zPKRdC/iR+twA\nvmVsY/7+ss2e2+x0ljYuURT8CaJ3gW0/xnLN/NE2GoxZhC6EwIF+EXDsaiS2Qjx2akq86Nm+svk5\n/MExzGPZqC+2wmjmOVRrrwxexbFzDnM0dsUXK640B9v4Bu3EN4oixoqqJf2JcSkiaetDIif8Ykrb\nrPucE+YdUxwBNd012M7WXNNRNslkdSrL8oQ+2D2biZIiSoBiLR9wavygh0sUzSkyPUmdAmLxLhI5\n/CDObgd5EWiete7M+t9Rwdynr46jJ8i01HloLXWInNk1dd4biCVfBMEKh+jcJBMov8UcyMwIHQpc\n43GaVHEIOMV9KjTndpn6/RzvXXtROeB9rlx5l8rSAkfAfeA/I+TUAvCHHFtpq0cD6uUdphhsbb9S\n5oO5ORXl7ttnjUd0lPSRVj8/prySQ5TdnDBQ6DnwZeRV8R7w/mS7mys2ge8gfvAq8FVmyCAMiTLi\npqLYFOGbc7GmgA5FAjw8+kdapGcUmo0qvp8nV+gMCh0uBO4hvkyZGVZ9OnosuBOu+CXBVraCPTnk\ngQvIxAsvLTXxcn3a3Uqm6pkg3PACHXoU2GKdX9THnMveJ3LEzzBdB0BHlNeQTlpCrKBZqC5I/Evb\nl5r8Wd8mkvi1wdynVjQxHX0XcYJ0Ofl1JKJhnt8iYBm4qDjhuhJqh5nnikNgmzWu8ThdiuTocZa7\nVNI8kwmxWX8j9e+tTpm3r36WRnOVfK7D40+8S7mSscLtPOAjEfB3kH72Bxxr4/1oQDnEWZzwFMqX\npqN0eqOd8A7F1HhD4LlaUnwohk6V0NnBXSYOZmwgExcdJBr+4WS7mxjpVuAgQmQA8UMkTnEW+Doz\nqZEToYEM2nJE92YM1H85RmNHijz5U8yihTCIgk8r6LJ7YOKTYOeBGMmV9a3Fkpn9jfp8ksXyGcbE\nnOkoNsOr8wU5xEtrQa8B7vLoYhyrCE3jKuLkGm0CI/3dPFcBBworTVoPV7i98xhe5apVjcJcXmWb\nhxR5wGlC1thWtJmCQVr0DC+tsBGtX9cn1AfHV+eoqytq2KgcyQCjrShPx7KcvF46Gq3TvHry6DAk\nU7NZeo6j2uaNfyWiAkMZFARSi/UMWw/29OQ4NBVT8xuiAUQhm/LJJMV3DhS9weUeZw36yT4FunQo\n0aFkLTYl+yoP/VszRrUa3qZDcXBeyXNq7C9z9cYn8P08xVKLi5c/IMh786eg2No3gH8CPkL8vt9B\nBqdto91xnUOxkMhKhtBOuBFhS6ap9WC/yXA6St8jdJSD3SsPUvLDaQAhAdJP8/RjBaPMVH7ogRNA\nWARy8eJmlIjshP6sIE5BV/3LoKzkGP1zxRSH2YHPICbovyETI3MIo0KbI1O016SImEPyUW9XyKaO\nskQkwZymjlJGHrOfEU0s/RQSAde30KSdLJvXYhKFqqSNbxLZgaeQQIrZ3lZsbdQ9Tiz3KqKI4gD7\nq3m65ai/2ey5qXzSjfU923JhsD9R+Alw8OnE9jmcamLux0ZN6SbaDKgm6rPdKtNuVnFcn6W1Xfb9\n6AKYanN+jIJiUlOIIwsdxaaAZy7vI9lMECd8GF15gRVRTCwQJ9yGdaAF4UMyhY3XkZJct7LtvbS2\nT+vhCls7p7lw7lqm3ECRDkVadCizWnuJkA/HH4jlEGOh+YPrRKLzs4Dmhi8ROeomR1tP7Aw5QFep\naflHJ/FPR8s9IplEB/ugYtGgK4+Wic4zAPpQ+/LsTydEnPZNThPg4RCwyjZlWjHDPi2sDxFHD0O4\n9/ACt+9eARwq1V0uPPYRrhvQXdSb2wb+XyQ7VgT+FScUlIWBdsJTZl2aEzN9htoQNy8zubu9ImHo\n4Di2cLSEuLsUyKe9mc1CngkM1ZB2kKzKbYSHYQ7gD4nnEF/jx0g0+jbwEjNhVsTwmQxt2kjU/gPk\nCpeBVxFm4UzT7R2iLPgFDv2c135rdBuvq0p1uNAtTe9XhsCu4toWaU0t6Ltce/nAus1NedlX13ZE\ngWhRZgu/Q1R2tTqi7YLjGDjhG8AtCB6A93i25iAWK8PoJ1fqUSnviWb49hme2Pgo01mtssN9iuyw\nxjbrrB/Gg9ZOruaH62oN84J2mHWvmITAt+BEpxhc5EE2q22ag5E5oEuemzxGQ71FyjSpsktujlaw\n73u8f+t5Hu5JfvfMqVusnr2/WCnKJLaB/xsZ4C4RUVAWWDnx4wUViQtSnHCHaOJjk6GOleOAkwsI\n+x6dbpHSCGnMNiWWDsxcN6AYKWPNlVlHeKotogmaE+IZpNv+CyKH/G3gWUTpdhFMbBuhy1wnMpVX\nkMmcM6/p5iPBtwAZqVxIbz4RHHB9FbcqwDSN4C6r9Mnj4lM44gI9aWjuL7G3t4bjBKycejh6g1mh\nS8SRmqnUznSwQE64rRSBUkjpPpCHzJaqMNefQvJhV4lL1zSiB2VvJxo+rW08pHlzmXsPL7C7vjx4\nnkzqgFkpUxflKdDh7fo93NplfNwYHcV0lkxqChuRlz2gpmjVlBJwSX3qXZmpsCT93DLr3kpBsdFU\nxkzb1K9BbVS5syz0GhsFZVyaSrJYj422kkw3eupTzWgfwJV/PeNl/19+4vG1mrz2stBOxqV+6OUQ\nuMdZdlklxMUhoMoeJdpW5R4brSVru1aCgqJxt/4bVlR05EHrNNduPE2vV8J1fc5dvEZ1ZTe+f99I\nkbaHU1ACWyGeLLSTcakpHwH/SFSi75tIH2hbtjmho8wYfQYjfb+dnlLWTvgOEmY12ui0uOOJE97o\nruIWw1jaXfdTl4A8fVpU6NCIPY+xvlx1Ke0GeH3o5B2K1cgTr79nKKSYNmUN8UA/RBzxdaIKxxqm\nGq7xG8x4h6lgm2vI96dC+K+BJHnfQnzM55HXmzksN+kok2TgTbP7BvA54zxFHlV+5k2iMcoTwMvq\n/A1mBitGpDJvs8e25dWMbXrqZHxkkPYM2WgnluX6W1D73MH14RKDLLEDtJc9emU3RusAO9XEZoPN\nZbPfNqmwp8hAOXr01L5sNKquZdlGdzHbPKy/TrX2CgDtsMidu/KSXzq9jZ+XIYBNESVu142XaRod\nJQvtZFj7nyP+yxn1L4svs8DUlAVywm3QJmmM8gWXVPMb2ZpXV7bJ3b1Ar1viYeMMp5bvj94IeSiK\ntAnwuM9ZznP7cDrNWjUljziGpxGnetHqFz8KcIgmg5pvPh35LjGXSR4hUnhnkzMD9YYK+5RpTlx+\nfqLzCuHW5hVu3n8ccCmV9jn32DUKhQWaJZ9EiJQerCMvzMeAr3EiP7iQUCPmYERqoogMwlLUR5yc\nD508nU7JSkMI1MPdpTDSUvcLDl4/JNcZw6afQ6KxHYS4nW2+/0iUHaghfuZPkQTPT5FufhHp4kd0\nqKHwkVfqfYTtoZ19Bxl3vKDOYy7oEGW+l4CnmV6aIJTjOECv6NArTe9lEeCwqzR6SzNWwNrbWqfT\nLuPlelROLZAj0kQ6PQhPapGzsBlxfJzwMJtjDMBlpNrBNVJnuWs4Dqydus/m3Ut8dP9pNqrZUuwO\n8IVaiVv06VDiKk/yJB8cvl/o0uyaq11GrN4CPQOQIQq+iNDFfkpEBjogkhnU71nLzdNR8Glgnwo3\nuDyIxOXosc4WJdqxqMWskfviV3jzw+fYb8vr/dTGXc6dvU7PnWGp0nHRQ2azaQWLF4AvcRLlXlio\nCGA4QuVHZ7f27E2cvMSE2+001rRDjh598iOL9vQLUGiCpyeHqrFwTCc8CRd4HOGsbnFwJuOEuISw\nLF5HItE76vND5BKtI2/MVaL57+MiRIKODbX/LqLqaYYCyshr9nkOJiJnig5C4dSF8J7hSOYdDaLg\nSfREEzx0oLXsTZWGsslpRUPpU6UxUEeZFnQUvNMt8uDueQBOnbuD686nANxQ/AjpkBeB83M+lyPC\njJzwcXME5vIKYkoeSkGHvuEA2NLQZ5HIyR5CVtMSRUYUpW2kyPdWl/HWu7ibffbaa9xsXGZ1eStG\nQTEL8ZSNors5fMo0abDMJmdxCFln28rdjc1S3oj0z9eKkadd2gFVGUgiK6fV70tau33LchY6inmJ\nbcV6xk3bjFu4x1L4INP6LOooWlwnRzwyEkKYZyDh2DH21VyKdpYsSjNsvY12kkwpRsvRW3mXFbZY\nH6ieOAQs0SAEWpRoUYqlNcehtQxrF0+L2ovvhKHD3c1L3N68Qhi65PIdNi7epbzUZJ9q/Fp0jG2N\nlKT5fGEUyYqlKo9K+UQvbyMShA+RfvMFRB2hlWgPw9OcC5amfDSRvMiqH/qtdDqKNvs7ap1xP3UR\ntjBUxXjaS3QoJJR+or65wg598jRYsT47zaIse502pVbfTm0w6RLaBq8gwZMt9W+DyBvO0Mfyhr3c\nMOxf2bDf1X2Z+HgfEWX5ALkkt4nksXMIQ6ZCVPtMm0KPwZzzweVsqn97MJR5vIEIUTyOsAAcEgV3\nDDucz0IdnIAuwgrynO8aJ/c4GK9m+31asaxPo74oOV8nlImY7RWHZj5qtJdIvcRVsExbO9zuJt8p\nTcrssQqEFOnQppx4B5n0leHviE7sHTSc7pKktYQh3Lj5NGHoUl7Zo7DajtEMTRvfs1ELbfY7+T0L\nNcVcfw0RzvcQ3tM4iigndJRJkENI3pvqX4bZFi4yUvoQsVAZdEIdN2Tp9A57d09x6/7jrFS3MoUR\n3qvf5JnaJSrs06TKfc6Sw+f0Ucyw1DreHpGGttY/nSPq70Lt2fmegxVaWkpTezSSOuVJx30EflDv\n8MXa0USlOxTY5Mwg1egQUKZFhX1cwgO87llib3+F63eept1Zgh/VWfu9Fzh79iYdb8wLNkuESOT7\nu0jEewXhf89aRuIEh4COhI/Ql88QCceTh7zbLRIErpWSIPKe5ZGRcIBWJS9OuIH6z0aoZziIQ7iP\neLUOET/8COEgr7Z1RFf8ITIN6i7i+7c5/Dz/AuLAbyBzTf8Q8aUXIgfmI8E13WUuIcGqI7y+9R9C\n7VX1Rb+HkQh4e9khdKcXAe9QYGeghtKeGR2xWf8xzU/997RbS7i5PusX7s3kuJnQQWYng9BQjrki\niolj4ISD5B02kTF+xinPeoLMGwgfNMMzU1nfpf2gSqtd5cH2Oc6vZ++EBXqU2eQBp7nNBZbZ5fQ4\nPHYbGohF1OWRN5CRXBPpmAs2qps58sgDWSJONYGI591HjOic/ch9KtzkkppoIxyYKnussXVgYs+s\n0e0X+OjuM2zuSI6vkG+xeu4Gpy9Mk2l6BGgSVcAECdV9FXlWThRQjgHUSCkcUWVVj0tTiic7DhRK\nLTrtCu1W2cqTyCven0+ONkVK2JVZ+nmXXt4l3wvGK8LjIVmYtxFnPMdUSdtaIbGCaHODjFd2iIoU\nt4iLPrlEYlhFtW2FSChKvzJ/wRyUToZBUoRRQSQPcQ2mTUswfOD2skPoTc8Bb1NkS6VOKjQON8fs\nkGg2qmxtngNCNi7eEUnCRUCIyAI1EP/nBR4peuGCOuHJK3weYcHdzpa2biMGr4iEB95XuzAN+Hbk\nkTXWotTR+rl73Lt5mRv3nuTCyg3ynni5JjXFVDs5W3thIE54igeUadKiwjs8xx63WWbPKBRBbNmk\npnSWoqjM8tKesax+WAh5PfLXBn2ZyMm0UVPM62KjndicFYsanpUTbuPi2ZRSbMonaaopWkaxwEDF\nJIYQQp1zLUDHcLy7peGFdWxUE3P9U7UK9wbri0Z7W6Gbgj4dtthghzXag7YhZZo4iLbxNmtj006y\n0GNgNC0mCB3uPLjCvc2LBIGH4wSsnd5k9dQm/WdfHQQep658chg6ykfAa0SScK8ig+8AuwJK2jFO\nnPYZo0ckUdgYnl4274mDeJb78fVmvytU9ui0KzSaqzSXhqf7W1TwCFQRrHODrGW8OFt1cMz+coEL\nD7cIHegsQ+1bxjnZFKc6RMTs1xFvuIpEbDVsNL3daNEx7F/FsOsVs2iMcdyece36EwRocsa5PWEs\n55PeuM1W2wqjjauOopd7yPtbX4MNZJBTIJuaSpb1xvLX/1AV6e4ZFJRlh91KNJKyFfODOP2jYWmX\npEL1yKkCgC45ejiJrGgjZdthx7UVCRpGU2m3ymw9/QUIYfXcfYKyM7D5zYZBZYlRC81lRi9nbZek\npryFBFlySMqnd4j9pJ3TnLGgTngSOvp9O7VVDC6SpvoAuYkZR8tLK7uUtvZpN5e4evdZnr04rEbx\ncIjwhnjKLSrc5gJ9PFbZmjxTZu7AHByboYye+veoRMgd4tU2teNtYligYAF6tY/LLqtssUFHvYUc\nAkq0qCjFk3nSTsIQtnbPcOve43R7cn7L1W3Wzt8jX1jwMMM+MvnyffX9HBL9rvJo9PuPFQrIA9uT\ngj2OJeaqtfz3iDmpSRQrLfYeQqeZzkXy6OOTY4dVTrGZap9bhQK+B54PuRQ586E4i7yHbqp/q8TD\nzCdIh48MYPQ99xB34DLTvYYquOUAvgedKVNQuuTZYoMQF48+Rdoz6yLdToFb15+E0GVpbYfqxg6t\nYEG4fHeBH6rlz/FIFlkbS/Lhz//8zzl37hyf/vTBSnrThRY/ug3hGG9ZHbHV5YQzwHHg9IXb4ATc\n3X6Mrcap1PZX6/HiPtoRP8Um4HCfc1zlyYE01pFCU1J0xFpHBS6qf6cQo5/UwZ4Q9ddHtxkbOSQX\nuoZMRL2A6G5tIA+eppqo6MRgsDHuS3EMBEHIt/+fBn/97+7x7//Hj/jgjdFD6BYlbvAY7/EJ7nCR\nDiU8+qyxxWNcZ5nG3CUHH+yd5q0PXubqzefo9koUCy0ev/I2j195N+aAt+s/TNnTHBAgqkf/O+KA\n5xDlk9/jkeIILgpmY+8NIe0wjfANg2RkSl20UqUJhLSbZfzALpPhqkkiXYqjq886Dv2SYkB0of6T\n9OYHcBpxxEEcyi3Go7bMGa/NY2AbIIPtG0QO+BpSqWiNqTng127C934Jr31bOeBMnwO+T4WHnCLA\no0Cb0hSrYibR7Ra48dEz+P08+V/9I2sX7i1O8bVt4L8iN+F5ZJ7FI4ixYoZ/9md/xl/+5V/yp3/6\np0d0eFuBnuRTX0JCCvdg/zbkLstqW6paL3vRZvyM+ARNg5rS2I6GV+WlFhRh6cwO+/fWefvWizzz\n1OsUjBCISUdps8oDTh/4ZetsU6FBkyXuc45dVjnDvVhayE5BMJVboglLldX4jMxKJ/pboRXg+FLF\ny+0TL0sP0eQS/a+fWNawGVxz/T0kEgHZFFEgKmuvVUk0IdEse5+EkoLS23aLELry3c9F48dOMT7B\nqmtRAbGl5IbdB98P+ff/P3vvFiTJdd53/vJW9773TM8MegYzuBMXkoAIkAQBoSTKoixZ65BMRUhe\nWyt5QxHahw3rTX5Y74MiNvZlHxx7Ce1uOLyhXVv0amVbkq2bRYgFEARIgAQBDkBycBkM5j59765r\nVl7OPnyZlaeqK7urpm81g/pHZOfJrJNZ2ZWZ53znO//v//3KRb71HxJe/4v/7wa//b8/Svm3TnfV\nDzGoUWKzh1Zi45GjGUnLWqwzk0odSaONDEI7STtW/0wpWK4vcGt5kWZTLFbbbjN77BbOdIvAMNlg\nuotqU2uWaNXF8nG1qceuqPiaNte8HwonaeVl4G9JIs1OIuonJbrpV2lUhkGi9Mde9C7sX3u/Wzs/\nAWyCtwXW/M5CWSDPQtczlVCfXDuLnWvjt7Is1U8wPSGZ/vpRB0xCTBRLHGOO1YSCAmx0yWxAYbLJ\nBE2K9bbw0+NAy52m0WPE/dAccB55XkPEwRBfuk7Z0Ms6dSJF6crR9jt7UbpKoQraLegIgfS262lU\nkzT1qmJKnXh/nJBvnYSLPYX0N8f71I8/34f9lXcgH8KXPg8vfhN+93+Ar78Bf/j1aUoT0kGlUVB6\n2139Werqz3uOaZCPgjBFOtPB66IgplFQ0tVXdqepxMd67QxXL4kBnik0yMzXOh5wnXKoU1BCXfVK\nS344UHu/U73echP4j8hzfgr4LN2O1NuhtfQrjwCGMsKff/55Ll26dECXshsWgSXwLydG+CB4RA7j\nx4jHbMBRXn6uiqraNJoTXL12HyfPXO87Qryn/EDqOTJ4mFSj7Gw5rnMPFgHTbOz/SNcQLnRgR0Z4\n7GnRddItEu6h3gDGyiEhSdSO6lmC5Jzl55LvxKLbkDa0/ZHB3FnvBF25RK+r2XtqH/RfB8VLf7zW\nZYADhCH8y3/6Yz731UWKM5lIlnKeOkVUNKlkEFKgjo3fkal0B1BhOCgoBRu1WW6snKHWlN7Hsjxm\n5peYmlnFNFWqJ9D+yS8d5qX2Rx2ZjoxZYQWEF3iC8ZT+AePw2vvIYFG7JEQYwBMOkCm18FtZNmqz\nHSO8H0IMTEKaFPB3iviMUJ3IkW35lJ8NB8o/sQ0LyBjkQ8TIuI4Y8yM+xV4+DCHwOLlRnaQfKCL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QQZsL2CJFMECRt8DLlZIyYheNC4w+goFhgPgnoX1A8ZSiUFxIaPs5f9JRLvOYQmUGyI540m\nK2snuXL9Ady1M0yrnRv4Xc8LkWnYpE0Wlyx1StSYoMYEJj5TbHGMJWbYSPVKjxEb3HkaFKlTpEaJ\nVifffQILnxxN8rQw8TsJdNocnaHdC893WKqeZHXzONXGFPH/YFkek1PrTE+vkss1j1yJZSCsIFr9\nPyTxys0hnO+zDJxMa4y7FfOIEb7Ejka4EVW9iniMdzDCCxNVbKeN386wvHWC41M3d/h+gwm2WGeW\nJgXWmGF2Ny1EAMOgOWmhqgGZVmSNxvKFe7XLC0h/dQ/JoKOODGSDaN07aWzSXx5Wl1Tsl31Zv+aY\nFh1L1i6zsyfdRozrQrTk6Ta2D1NeLs4/YYrYAAjtpFUyCJ3oHz+gbDQK2IyyJMdOnhxNTIJDc6Ip\nBesb89y6dZogtDGMkLkTN7Cm3dFJwnMT4X9vIffqWZKk6J9AHKARrtNLBhn96cOf3rTZ2mfqMeBd\nCN+FlmaE61MguuSr7u3OIfJQt5Cg/TeAh0idOmzZiad9Rasyf2KV6cwSGzePsfTIf0njygaLpy7S\ntvsn39EDNvX9egBmvot2IiQJHwuFSYDNOrOsM4uMqlvkaDFBjQwuBul0FN1gz/ZOqfYp60jbf7KM\nFtqUIJ2asjsFRaevpNXvpaMEmLTJ0KCAR4Y2Dh4Zto+sFBZ+lJzDxyLAJ4MXLWkBnzpFJFs+14m7\nup1gz932x+fxA4u1reNsbU1Tr08m/4sRki/VKExXyZXqtI0sNYrUKKYGVkLPFKP+WWuARAvnysmD\nfzvTgiHyoLyFBN7EOIXIDcbjijX2Ri8ZpE6vd6XfZ2P++T4iLflaGgVxARmhLe1OfYoZgx8g3rOu\ntj9pzDfnp3Gmm/jLGS4tP4gz2cIw0gPfpS0NUVhc5gwtsmSia9TbwrNl6UIAgjigfFpxT/MWpU0x\ndtQcBBnJbeDodAk9MFOnROr/g07X1f//OAO0WHviFa9F9WMaSCwDu48ozyKGfY5uI7uETEbHDDbd\nmkhL1pNGNRmWmqKVvbzkxjD9pOVXBjTyGRqFDIFjDUQj0dvyxXK+c493qx8b3zqtUehNPiEmNc0I\n2UuSnd3quK0cN2+cod2MRB+KLQoLG4QOtBra9+pURD0A89GfTWyn/aKg6OUQsbneRn60KeDzCE34\nAIIuB6YmHjHuME84SN7aLHAD/BWwt2er3BEFpOF+G3gZaftP7HhEX5RmN7GzbdavLlCrTfPBxcex\nTp1nprQ/gZUGCgefAo3I2MwigoMZXPK45NlkBpOALC4F6h2G82GK/h80FESEnQx1irQ7hnM2lXdu\n4WPj4+BFQxi/Qy8ZRbheluXqAlvVGWr1SRLXkSJfrFGa2qQ4sTX62t4xthDD+0ckjauDqF48QGJE\njVhjOMZRInZp39qxFiCddwYxGHbJseNMNHHXi7TbOTY255mZXtn5AC2JwSrHOM6twWYeDYNWwcHL\nWEyst3D8EMs9oARjBmIAx7ZdPHhUJMZ4HBTpkSRgixOuqZ5zxcnV9CUOBnWQPjNuenqboBHQcNYz\nhga2QTtv4mUNGs7BUj9UNOtap9Tpi0wCcjTxcA6tD/Z9i/WVBTbW5gED0/KZPrGMKoaj4/1eReyt\nWCnoUcQBOgI5QY4ad0ivrsNG3Ghvgfsm2D87/CnuRTwJlxBaylm4HRZCrtjk5OU/YPWBX6XZLPHu\n5Z/gxPRVzi68v68Pl0VIPkoGE2DikqNFDpcsPg5NCl2jZKFatKKQw2YUBiKcNGsf3CTfr2zxZHmA\n5Ba7QLo7izYOLfIdY9sl1ym3+3q2BQYhGdqRwR37wduRN1yQ5p0fFtcqH+yYHXUYKAVbzWmWaydY\nr87RcHUOqqJY3GJicp2JiQ0C+whf0bcq8NnyYHV9RMP7HbqnSaYQCbmHGCfZGWMHxPPRN+QF2cl6\nMBGv8AdI9skvpFc1DMjO1mguTXPr1iKTE+s7ts3yrSEOHm2yLHOcY10ag/D9SpUny/1544FtsjGf\nZ3alLt7ZAOlbYi71QUJXU4G9JV/RfqPKZSjft4dz7RdiqolNV5eggNCWpTm5P+3l+co6T6TIwsQB\nlxtMoaIfSpxhzU48kX8Io5MwNFlePcHS6j2EoQUoijMbTB1fxbRCGsGQNMXXK/BMeX8v0kMCL88j\nN6qAZMA8yfaU9p9QHFIPnzY1mTZN2dta6cS3SSTC8i1ovgXhT4Nhp6uj6J4SfcrrSWR0tgr8W+Dn\n6WPrJTtafqJ7e8tPfraCM0Hx7Brmqk99eZKbG4ssVU+wePwj5qZvYRjpFJQ0DXBd/7t7urSbOFug\ngYOLwsQgJIwoGgE2dUqdlLg6zE6NmNARYuNFVI1kMVCRB1lhRK6TeH2DJaY4jop+HxXV8rGjspwh\nPluA3SkL+9okjNbdqiT9oDpnQju7Hz26PjYtsujzk3vRGU+jo6zSwIgMhWGPbVDA8xxq9Uk2azM0\n6hOEmni6YYRkSg1yEw2ypQa+4dDGZpV52nWNyqJreA9CM4G9RZevIfy93v3x66mAKwi16wMSj5yJ\n8FjvRxycAeKh61VOOAiqSdr+MR1lRJDW5k8i73AdGmtgRdlg0tr1ReSZex9pw+PXXGvvN1ciFRQF\nmXyTdjPP5aX7mDiZtME6jU9vX49zC4MQH4cbnIqS+opVu8o6N5AZ2L5tgQGNYxvYvs/MVp2C2wYb\nlIMMHiypY+jqKPUBymnPtpuyf5+McEJkAhq2Wwy682pYOspuNBUFvi0DGSPo7p5D06CVtWnlHDay\nE51BW5oq1bDUj1Xq3IimyOM6HjZVJqO+p0N8wSCkGUUY7XbevdBO4j5FKYOl9ZNsrswTRLaIU2xS\nWtjAC2y2WuIg6+ovatqsQC1FAWuT/vTDYakiNZK+4TskAfgPIM4YhyTYeJjz7hcFZcQCP+9ATzgI\nqfQkcEO44dZnhj9FBhmRfR1pzL+NKKYMe5qyHFSY32KmtMLKzZO0GkUu33iQlfUTnDr+MaVi7cCm\nhWQ2Mex0JpJ9PiTA6gSHiLltdfaFqUKEgyFbvp+P9nzlMeSKjIj9bnbKYniHGEl0exdv/HAxX350\nqPp+YFNtTLFVn2ajPovrdnslHMclN1EnX6qRKzRpm1rDOCpxt3EWtF6sI4b3hagcYxZpaEdDRn2M\nOwoGYllfAO9qYoSnYRbhklYRb/hDO5965uQSty6eob4+zdbkFJPFzR0OkKux8fBxUJgss8A8Szj4\nPFYejALp2zbLs1PMN9fINkLstqQGVwEyUDXZd/72QaD82O519g3xbxJRZmzN7xSa4GVN/KxBNVfU\nZkv2v3ONM1yGGJFkQg6/41hRWHiE0ffqfw8SYWiwuTHH6uoCnicGdibXJL+wRaYo/b9X34NJ92R5\nH64Scd58jyR51QziN51lPBPaB3eoEW4ATwN/Bv6rYH6a23oJJpGpzFcQ7XAT+IXbv6pMzuXkvZeo\nb02yfus4jdYEH1x+nFv5Rc4e+4CZ4sqBv6sSEK8w8QG/y7tjRoEiYeSKCaKyispK84XH3u14ATrr\n5LsSD3nvovvC5ZrEJ45Wjg1ug3TvtbpDSGNtP8NK4xhbjRk2GzPUWxPoN9swAorFKvlSnUJxi0y2\nPVJKLLtCN7yXtf15Eg+HPvEybmzHGBqxEf4x5HZxrBjIYO8HSNu9kxEOOLk2E/NrVFfm+PDap3j8\nvu/h2L0CANu/IjbEA2yWOMEMa3RHV+6OIGPSyJiYnqK46YtsXog4gmIda4ftegR3O2Ill1hiMean\na5z10BRefWhBc8JODO8DJDsLtV643g0KXcGWMfXRRHV5rw8SfmCxunaC5bUTBIE4a5yMy/TxZfIT\ntb0lZNtPbCLv4nvRtgM8gcyIHqZCzh2GIzbCB4mgB2j0Kd8PTIBaAvc9qD2cVBmEjhL/5xnEA/4a\n4g0HidjthXZ5XivhQy9rqb2b0/nOuWceuE5jbZL66jTV5jTnL3+OTLbJ8dkbzEytYJrhnuko2ZSp\nVN3PnaaUkq6I0t9HbhN0jO6PKpc5V5ZQfX8AI3kQ5ZP9Uk3p/UynhaQlBHK7OOT9U96vVN5lovyk\n1FdZ2u0cjUaJanOSZqOI1+5N8aXIFJpkCw3Moo+TdzFMaLsZ2syAC65GKWlrU4dDJ8/ZKfJ7L1N+\nr1VAlUXLVbc7HIRucgaRGYwbWD3mbb9oJHuhnew0BdnvmDEd5YCQZl32tvmnpdj+qH8Cpd52fQZp\nx68hQcAn6X4GS8k7uVKaQ2XAyHh47Sw/vvZpTpz5GMtI2kFbaxO7Y0kU86ygMFljnh9WVnmiPI1B\nOqVAV8HYsCJajAUTuSpWEDDRbDLZqGMHSv6HSVH0CGywFJ13ytCfybRy2vO/l+lOzTKofB/KT2/f\nD6Snrdf2qyydgNDAFGqJGWz3RynAcyyamQytjIObcXBNneKRlNtdVJP+iWuGoaMoJF18rJh1qXKZ\nezve8JgIaVPXaI9pyXN6r2OQJDv9rrXtZlhZO0ljYxKl5IGwcy6F+S0CE5pGlmYjm554LY12kkYv\neaMCT5R3rtOvXEc83x+QSF2eQwbGim61n2EpJQdBTRwxB9Ed6gmHRGDyr4Fvgnro9kfH8fR5bIiH\n7BjsMwhMU1Ga36Qwu0W4lmV97RhtN8/VG/dxY+k0M1MrnJy6SjFXHZ0I5jG2QSnxctcaE1SXztBo\nTlBvThCE3a+OYYRk8w1yhQb5QgOj4GOaMmjpHSSMLELEoPkIMbyvkvAzHcRGuhcxvONOdsT4dWPc\nyTgB5EBtQLgO5i7J2GzEeX4J+D67ag0bBmRma3jLEzTrJdZuLbCwcGuA9tfAiEwxhYlLlnVmu+J7\nhkFgWWyUSgRFheWHZFs++YaHGYLunB+d9GxDovf3bCe79FYzNEXNJHAM6rk8nmOBYRyailWsvNWK\nZAy61bZiWdvg0NLLg/Q3tdokm+tzNGqJsy9brJObr+EURAJTl6U9MlSRQPwLyGyOAdyH+Efjn2zE\nDN5RxB1shINk+vgmcA3aP4LscLzdLuiG+OsIr+lX2V01ZZcMU6apmJpfZnpuherWFNXVORqtEitr\nJ1lZO0k+U2ducolTk5cpZu8Mgzz2gt9tUAoa7QJ1d4Jaa5Kt5jT1VgkvyMLZ57q8bLbdppCvkSk0\nyecbZPNNQqO/B36k0UAa0YuIMaM3mrNlUQ46CxwjMbzHDesYBwITGeVdAP99yDyz+yGnkcHiFWQA\neXbn6oalWFi8yo2P72VzbZ5r1lkWj13a9WtiQh4EnCsv4ke5GwJM5lnp8qIPDMMQDWvHgkyAESgs\nD0n6E2d61PuDHInEYMydDqM6B6APHqP8NEnSnzgm0dQWPSlQH3QYJib4DihT6CXtQuKp9Q5JfjWI\ndLvrFGhQ7MqcbBBGKlttHiifwjjE4BzXzbG2eYy1jWP4vvQdhhFSmKpSmtvAybYP3pkTe8F3wwoy\n6H2fZKR4GvgMooY1Vj0ZCkdghA9CQelNA+anfDYH/BTw51D7G2g/JEopOgXFTin3Qx4J1vw2MrXy\n+4hqyiTp0zm1ZA6uNq2XtenIUkIpmbhvjUyzirtZxN0s0GwXubpyjqsr53Acl+LEFjPFVUrFLUwz\nTKWcyPbuCXp0eomdQkcZNllPGgaRA9wvCkpafeg2gPvRVpQC18/hujlaboGGW8Rt5Wi7OVQfYV/D\nDLDzHnbOxcm3MTIBph1gGNBqZWipDDSmu6LRAz85z0D0kv2K/O41kHvrhYgU80eI8bLcU79EkjZ7\ngoRqogdgjgLVZC/1045pMMaBIy1ZT9yuR0Z4+wK0n0mnFurlh4F3ER3iB0meWY0e0col6lbVxYDs\nfBV3ZYIry/dRNwtMz3XzvHsNHt07O89KJ8x9i2m2mMLGZ5PJTmZEPUFbmiJWV7K2bLI/O9UGpcgE\nPpPtKhnfJ+P5OJ6kb4uys6VCGclCvIaOkdwrE97ZGZ06rmCEYKhU23obQsPAt0x828K1HDzbwrNt\n6naR0JSbkkYjTEtolkbZGCRhmvC5RUGrTilS5rL0/zr6t40o03Kx89le6C5ST1dpyfTdXwtKNKoT\n1DamcBvJftPxyUw2cCaaeJ7DZmsCWtDSE+voili1lMRrt6NqklZHIYGW5+mW8l9EYoKyyOu8ssP5\n4WAUTsZ0lKPGU8Abwg0PXgV7Z8/0rjgF/AwSrLkK/BHwAhLd2681erMCT5WH+gon7+HkNzi2cJ1W\nvUhja4JmtYjnZdlYO8bG2jEZBeerTBU2KBU2KeW3yIxIjOLNygVOlB/eveIRIwhNGu0irXaeVjtP\n3S3htvO4bn4bnSSGZXtkci2yuRZmzieTa2E5PrWX3uwo4QTBiNyIQaCQ5/gKYnhfoztFvIkkrFpE\neN667XGhAveWD+UyxxhDcB/S0F5CesveWIs+eBB5tuMkUU/tfohTdEGBuzrJ2q0ToAyOzw1CTYEr\nlUucLp8jRJGjFalNOSyxQJFal6F92zAM2rZD3c51VApt5WOGCjsIyPptrCDEDBR2EGKGCiNQYjRH\ny37hG6/BT34JlGkQWCbKNAijsm9ZBJYpZTNpU3XDMzzEqDwFeDi0yFGnRJtMjwxuInlrENIiR9Kx\nJzf/euV9TpUfZL8Rhgb12iRbWzNUq9MdrrdhhGQn6xSmq/iWmTyHhxmse6ECD5e797lIvMUFJPAS\nxGo8h4yXY7riiBm2dxLuAiPcBL4C/D/gvwzmw4hVsQdMIob495G+4D8Dl4Gfozt17h5hGJAv1cmX\n6jjKpdUs0qhN0KwVabaK1BtT1BtJbuNcps5EbotivkoxW2U6u0bGdu8ICstBIFQGrpej4U3Q8nK0\nvDytdkEMby+P56dP31mmTzbbJJttYuc8Mtkm2WwL7OTHvGMoJTp0o/tytPTaBFOIwX0PwqPVn59x\nYzrGkSKP9O6XkDT2A1jUFvBpZAbzm4iBsAudHMApuUw411m5eYq1pQU+cEPuP3kB0xyM16EwyOIS\nYOLjEGJRY5IaE7TIMcM6+W2zunuAYRBaBm3LhExiZXfNdvq+GOAh2H4g3u24auzh7vof6NoZe88D\n2xJvugnVWYPNhVbwqV0AACAASURBVFjutttk2K9kaLeLAJMG+SgtnSxhzzV158bwu5K5HYa0YBCa\nbNVm2NiaZ7M2GyXWEWQLDUpTm1iTLUxL7kbgHrHaiQJuAD9GaIrx41VAvN73M068to8YISN80GQ9\nejm2Lk4APwF8D9r/Hqq/JbQUGI6O0vvVn0YMlndIHsgngWdIpjyPl2VaH7qnSDVqSqukl5PewdRo\nKplcRC3JQnaqhh3UCVoZlGfhNbL4rQytdpFWu8jyVhKBZJo+TrZNLtMkk3FxMi45p4XjuNi2h23s\nTk3RMRAFpXw/H+5SJa1xTlNT0Rt3X1kEgY3vO7h+Ft938H2Htp/B9xwC38HzMlGigp0aUYWV8aPF\nw3CCzrbn2RgGeBg0/Tz4efDpJD+AnoQ4587Cx1FZp5QcRJKZYY4NEO/2rWi5yXaVjxySNGcW4XYX\ntONXd/i+Yrl/8ob9UinZC6Vkr3SUeDvcAP/HoC7wwzfvh3/AGPuCQW5EWrv+acQIfxtqmhGeRk1Z\nQWZwjiNpsf8M+Duktv01jiUbi8vkjm3SWplkZfMkW+40x05fw3W6B+A63WCmPNFJCpvQThQzrEcJ\n0IhoKtOAirIWu1gEQ6tg6fv1tlmnInbRDG2t/dZ8EIO062lt9vGy1VGd622/06iDw6pSpSU6c3vq\nixlt45LtJHzr7QNiiokXJYlTHarJzt+r3+Og/ABXOvvT6S799gNU/Qma1RKNaolmvSijmQhW1sMp\ntgidAMMOqZOldVMbNaYlX9tPekm/cr4MLyF2jq5oMoeMixeQWdStPscOSo8cNSrjCGCEjPC94meR\np2cJWn8L+dtIZ98LAwn0OY5wDq8jGaA+QLjj9+79K9JgWgqz6JLJSoOsFJgtkbLzosV3M4Shjdu0\ncZv9Rs8Kx27j2B623cax29iWh235ZKw2luVhWwGm6WOZAaYZ4hhtTDPENMKhPexKgVImoTLxQodQ\nmYShRRiaBKFFGFq0wwxBKEZ2ENgEoY0fGdx+4OBH+wfzUCgs28N2PCxH1nbGQ2UUluNjOT6hoXUS\nGo3EGLEXcWDUEEP7erReYntynzwyLl1APIKxZPnYcwEqhPAqeO9D+J7Q2CJ8/HHAgb7UYwyIR4G/\nBC5DsAbW7G4HCB5A3o8VhJYyYPy4XWiTP7FOe2WCdivPjYvnyJzwmZ5cGaINNKLsDCax4R3zj5sU\naFLAwsclQy4yysdIR4CJR4YGeXwcvGjpL2wYm92qq06v1/4goRS0mgVq9UnqtUmazYRfDgon3yI3\nUYdciOlIg61L1B4Z2ohz6UOkT4mnRnJIU3iWu8pKHEXcRT9vBvgl4P8C9zWwFiGzB7UUHQWEnnIF\neAPxHv4pYuScrcBXygefhMeATN4lk08ab0e1CQIbz82g2hbtdhavncHzZAkCB8/P7kjL2BkKwwgx\njCgJTxS1E37nJczPl8XojiJ/QhWHyO8HlAwQbF+MbNvHtjxMx5ey42HYoayN7R6cA5G4eu0l+OIL\n+3/endBEZllukhje/SLPp5BncQGYJzG6YW+G9/UKnCrv4QQjgnALvA8h+AD8i3T/KBkwHgDjYX76\ny/cC3z2iixwjQRYxxN+G5utQ+rnBDnOALyFZkH+EKDY8OdihVibg5LlLrF4/SbNW4qNrjzC1tcrp\nExfJON0G83LlRxwrf2qHsxnYBCgCFAYWIW0yBNgRXWWS2FDP0yBPkwzu7SmsHALerNR4qlzaveKQ\nEP52BpcsDYq0ydCOtnspJTGEVuIjEoJhJCGoB0XuT0e8WnmHufLj6deuwG3nqNYnqdWnqNanCPU4\nIyMkX6yTn6hhTbidGYrmUVNNQAzvS4gz8TKJE6dZEU74fYjzJu7O70bnjWpDcH33eoeAQzLC0+YC\n0igovTy6tGlLvZxHosu+DHwdGv8BGhN0EkAMekk7TdtkEP3wW0hWqFuI8/094BGkwY+ZCmlJgkpJ\nIxHmkimyVkkr6/VzWoSN3e2+NXOaIoodyN20wbJdHFxsBRYKFZio0AQFKjRRgVYOTVRgJJ8rAxUm\nofVKWajeIJ/QIQwc+kNhmEJENIyobEZlS7iWhhlimLJtmArDDMWYN0MMKyQIk8CUEGkz2jgEEWVE\naCOa+ojf02Dr03m+1ijvhdpwzYYPnJ3r3C7tQiHqI6vRshKt+xncDjCNNJIzCMVEp7Bu0T2VuBcq\nyBr9G+KDoIjs5zlVG9THEF5EXDy9EjCzSDTfg8BZScmnIOuMvZMHgzRFFP3GNXrq/ATwNrTeBO8F\nMPLdGVlzKeVFxH5/F/ib6FQ7eMRrrYSa0jhRkIQ+RReaDpvVOTZrMxTmqpycu4xpxS/aR9QiLcQ0\nFZQJ7eUVSonCwadAo0NZiT3kANc4HWl0hDh4UZ2APK2OWalTSnRP+iBKVzr0OoNwui+xQi6Ks+qt\nn6ZSJQGRoDBpd2ghJj52JzOz6qTI3I7Yt+13TG2TFvlOkOWwVJZh1VfWqVKN7rFLFqXA9xw2G9O0\n63na9Tyh320+GXaAlWtj59u4gY1rGLjtCcJrc0mlQZKvDUsjGaS8iTh0riLOHL3PmEUEKVokE4Fr\nQ55/0CRph5mUbVu/EEm8BG8iHGMfyTVztLiLPOExvog8QW8CX4Pgn4A1v3+nt5BMUPchEfnvl8WA\neg3JGvUo8ClAn406IhgGmHYIjrxxOl+wizuowbKS/UoBykiM8Fjr6qEHgKudiB/DoLtMuoJI0Gsw\n99kfjmKWis+W9+c8PnQyXy+RGN394rcsxOCeRQzuKRIv92FILs2XD+jE+wzlCcUkvATBJaSn0XuZ\nDDKvej/CWRiQ3jDGEeIE0sheBPU6GEPMQi0i78SHiGzhT0enGwCGAeR8pk+tUL81jbtVpLEyxaX1\nR5iZX2JqZo2p8oDu9e4zdygVQplQ5LUX14gSAUkyoKRbrjHZMcht/I40YoAZlYNI7ePgGs1HymKA\nS7xnrC1iEmBFvGsxlCU41Yyuqj9feztkllVXUGl3PFndiXvUvs207o7CC5+j2czTbBapNSZpNYoE\nfrfjybACnIKLXXDBCjGdpM1p147YtFKII/Aq4u2+Sbc25TwSmD9PMohtlQ/xAg8RagPCdyD8Ad0O\nmcWjuqIu3IVGuAH8ApLO6X2o/QGU/qv9NcRBfrkHSWKILiD3961omQceQzzko3Gvh0ZsXHerqo4x\nENoknu0lxNBeQRrGfj9jBrEN50g83FN0ywneqTz2/YZqg39VDO7gshjgXR5AA3npziGG9yIM4PEb\nY9TwReAihK+B8TmGkqa6H7nl7wEvIu9XOrtgGywnYHJxFa9RpXZrBr+ZZeXWPawtL3Bs9gbHZm6Q\ncdq7nygV3cZpjmZHPE+MUjG9VUfXw8bbIVlLYhrHfmPVMc6NaKHje06MRdUx341OzTDit6uesw5m\nVG+/Lv0sQMcP7mF3ztaty3643iulwPVybDRnaTaLNJolGq1SRz4whmn6OEWXTKFJptgitI2O06k9\nKvzuj0hUsfQZUQMZiJ5GYtw6hvdhXuAhItwC/4cQvAvqqvZBEXgCoS0cRxqHo8URG+Fp1JRecUzd\nTag/Wfrl66PUCUTm4N+CugTVfwX8Q7qs4UGmNmopZX1adKMCi2Uxxn3k4b+GGFwvRcsUMiW6iEz3\nxPZA2pRqV1lrkOzukXiYS7Z1Opo3iCLMsKoxOl6vwDPlweunGY+D7B+2vNfj08rvVhIN1fgZCRGj\neguZ7tPLdfrDQJ6fyWg9EZX1mKNWdI7NAa9tp+m/vUzhrVVgsrxznYOmoPiAqoK6AuFlJDDjBttH\nMieQlysWsO3Vl+6t36/tGU1O7p0Dvd1OS6udlpStXxs/jVjTH0LwDdj4e0mVtPZSb8vOkvBf/xx5\ndB6n+9Zr7XpYS4z85Q3N4FdgTTUIGxlCz+bWX3zIrWdewCm2mJ5dJV+qYRjpSXnyKSooaYoo3UnY\n3MgcD3HwOwatFZnKiYEdC/HtPz6uXOLe8llAD4E0Is+41THcY+93iIkXecWJKCUxeikryf7hkvik\nKbHsdqxkRS7itbK0W1ncVgG/6aDCnkH66xWMZ5/HcHwRNrEDlKVw3QxuLQO1qXRqSe/2IPSSQSmx\nejkkkaO9GZX1CUAHcQbOI46dflRZ/ZzXKrBQvr3r3CsdZT/6EbUJwY8QadMrWgUHoS88gcyExoOr\n0XAq3oWe8BgZJO/8v0Pyq/4BtH8ZMjsF1OwR09HyOPKgX0bshU0k09R55Bc/hUwFxbI/d/FduOPR\nRu7fdcSw3kLoJFvIZEuapLBJYmAXo/UkYjDE7f0IyyYdGZQP4U0Ir0UUkyskWSJiGIjAeRy+f4Z0\no2+MOxcGkgPi94E3IXgarCFyQBhINs0cIjH7A4Q6+F8wUA4g/TxmzsfM+YRtC/IuAeDV8yzXFzEt\nn8JkFWPCoFisYuxnphyMyBNOV7Bit9ysH19mxPdWnW2B6nihd4Lu6db/AxeHRvSD+dt0wvtLFKYF\nVh4WlAI/sHHdHK6bp9Eq0nZztFu5bR5uEGqJlfU6izdbxVqQdqetxRgdqdkWG903SAL29TGtgRjb\nx6MlT/IQ3I39i1KibhW+B+GPkU46hoVQFR5DDHB9pmI0jO8Yd7n5Fxvifw68CY0/guBZyP00+zY9\nvVjevs8kSf0dIsZb7CFfJ5kuei26jOMkiVMWovIo35lhvOCjjPjerCEGda83exNtVF7uf44CMtMx\nSWJ0TyIN4G5BjaOO2At+UFAhhKsQXAPvuqzDm2wf2WTBWAS1SDKlNALTv2McAo4h6YrfgMafQum/\nBmPItvtepI19DXGQ/QFi258d/mrMTMDEVx8n9G/ibhXwNnP47Sy19Rlq6zOYZkCxuMVccZnJ0jpZ\np3UI7IrEcNaDHfump98BaYbzYvmBPV3dQSJUBs22JGlruXnq7Qla7i5ZkR0PJ+vi5FyMfIida2Pa\nAV5by/L5wpcO619IRxt5Xq9Hyw22kwQmkGc7VsfSm85hqSaxF3yUodpCQ/Teg+B9upkRDmJ4fypa\n364q3OFihEy9ndRRdBqGfslVdscEwhGfBV4E91VwP4TmL4N5XKroD2sppZxGR8kNsD+HcH3nkNZw\nFTH2NqJ/4Ua0xDARQ24quuzpaHuG7ucqjVIySJkB9u8X9kJHSdu/kxe5jdzThrZuIAZ3s6e826DY\nRAztfLQuIPcz3taPbyGJcpYHvNaDVg05jO8emFISAisQxA97vPTLyzyPGNr3ICTGY1GyC/3H3om+\n1u8ieuv0e8gOL/Dr7scgyleDlD3geeA9eXY2K8CXh0+8No/QQH+M9Nv/Dnm0vkRCNe9NAKRfxfRk\np7ymlZnywPQgMCGEMLCoVmeoViX5imEFZItNnHwLJ+9SzNUwTXmO0+goupc727W/vwrKIEnY9oI0\nOkkvgq56Or1Ep53095yn0VECLMLAxG87NL0CQdvG9xw8V6hBoSda7H1hKLBCWQzAUmCGBO0sgWfT\n8oqwrB27X1SR2zlXE7EFVhDVtTXECdTbP+VJcj9MI31RfM6l27ju/VIiGeTY2znGVyQydB/QrakI\n8vI+iEx53U93wzCIKtPRY4SM8IOEgUjRnAb+BLgF7f8T7DJYX2BPP8NKZTgViSyJlzyHGIwbJB7Z\nDcTgj430j/scP0HCKy6S0B1iI7HEwXpf3q3AY+UD/AINAfKy6kZ1XG727G9qnw+KLN1Gdo7kd8xG\niwFcrMCZshzzSaGRtCqQKw9/nGpBeEsWdROCtKxCICPNU8g00GK0HoYrMMbdjxzwi8C/AV5BZkMe\nHP40eeCzSDsb00b/GPgMMms9KN6owNNlKQsHBKwQp9QUuVfXxggNgmYGFVi0tkq0tsRDs4bCybpk\nci6FbI1stkUm08LOeJj7SmPZP6xXzjNTfmLfz6sUhKGJ52doezm8KDOy6+XxPUeMba8PX7v7LJi2\nj+kEmBmfEDCcANMOaLczidRtiipXKt6swFPl2/vHdoNCDO7riNG9HK1743wNpHmcQ5xxRQ42oHKj\nAtPlAzjxkFAbEsunLiLGd2+A1T0It/shpL/QjZ3RfId2wifECI9xBvht4K+BN8F/UTQj3b8DmUcY\nOkXkfiBDd7QyyHO0iXhs6lq5inhaXbZ5arpgIB1OTltno3I2+s4MMsHgRPsijXGsaG32LIZ27jpo\n2ZplCkxBRFyUJYgWP7reuOxpixut2z1LK1q73L6RG//v8dLrwY5/D4vBvLljbIfyIViBYBmCW+Av\nQbgkATJ9MYM0miei9UmGUrwY4xOMMwgl7BvAH4P36+DcM/xpYp74IhKjcw2Rln0HeBqRJ9/DGNCw\nFEbBo1BqiJHpWZg+eM0sXlOyHHtuDs/NUWdKO1KRcVwyjks20yTjuDh2m4JdJ+O0caw2Wbs1soY6\niFEtGZAd3CCLHzh4gUPLz0k2ZN+hHWQlO7Lv4PkOSu1uHBtGiJ1pYzoBVsbHcjyULQo2puMTaka6\nnoXyKLrzbQhIjOxlEqWsfikJ8ojBrcvS6rgblUyUArUO/scQfiz5HdRGT6UJxMt9PyJbOgIJj/YR\nR2CE69MCg/ImGjt8Nsz3xcFbX0YEvf8K1ApU/wjxkj8P1QeSt3cg2klZgiR66wwSvT9InYloATEY\nPRLaQ1tb62WfhIJxIChLVunDgIH8Ho622D37LK0cDy76BaTEA4Je434g+ktZZsP6nfOwyqnXtkP9\nPX13WdaqDazIu6JWQC0jPcoa/T0PNsLljYmKJ6J1r3UTj8pgsOnCYeuk0VR6j4/r3V2N++gg7b6l\nKaX08jxjPIdYMOdh898Av4k8Zymn303p6gTiAPkw+spXgG8j9v5jdMvJT2vlUlmMdoBScn2eVt4s\naZQV/bGPmRYKsALJvRAaoKDt5Wh7OWoN3TjvhhElNDOsEDMqm1aYJEDTEqWZpi9J0qJMx4nDUJjj\nXeGbUaI2kHWobGGQKQP12AuoWwYokyAwITSiRG8GYSBrFcr+4adgJZlb51JMBaFJh9oeiFyi5+e6\n7+FeKBKD7C+Uhbo0aP0mSeD+JhL7tYk4zvo1kQ5iR8QKWbFjKD5vPVoO4v9MrVOWYM+B6w9ZBvAD\nhF4SK11dZntWuhxJ0P19CJdMT44Re/H6fcmwfcTR4xPmCddxP+IV/x5QQR6IP4T2AthfAvNTjNzP\nY5B4sSF93GIixriHjMR177NP4rGOywHbvdi6h7uTrKfP9cTrOGt9vNYXS1t3pm/p9rzHxrZuYNvR\nd/Zr18ce6/2FCkFtQbAaGdqrEEbrLqNIh4G4bo7RbXTP0s2vHl3v3Rh3EgxE2qSFKF7938A/Rizp\n20TscYwTmywhM+AXkUf6PsQemE47wZDQ28xsEkVnZNtixAYmlhWgfMlmbISGZDzWjF0VmuCNqKCm\nEcpsgKllQ46M6yQzsgwWfM/WnCWaR9zX2o7dRV0OFz7SHG4g48E4mH+T9BtSQAztKWTibwKxM3Vv\n+N3ah6kqqGui1a2uIlNPvf9sAXnJzpBIxo2WjOBBYsSszMOGBTyDkAK/B7wG6hZ4/x4ogPkk5J4C\na4cMe9UKTJQP4VqHgIm85DkOJhjzU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+ "text": [ + "" + ] + } + ], + "prompt_number": 25 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The plot on the left is the deformed landscape with the $\\text{Uniform}(0,5)$ priors, and the plot on the right is the deformed landscape with the exponential priors. Notice that the posterior landscapes look different from one another, though the data observed is identical in both cases. The reason is as follows. Notice the exponential-prior landscape, bottom right figure, puts very little *posterior* weight on values in the upper right corner of the figure: this is because *the prior does not put much weight there*. On the other hand, the uniform-prior landscape is happy to put posterior weight in the upper-right corner, as the prior puts more weight there. \n", + "\n", + "Notice also the highest-point, corresponding to the darkest red, is biased towards (0,0) in the exponential case, which is the result from the exponential prior putting more prior weight in the (0,0) corner.\n", + "\n", + "The black dot represents the true parameters. Even with 1 sample point, the mountains attempts to contain the true parameter. Of course, inference with a sample size of 1 is incredibly naive, and choosing such a small sample size was only illustrative. \n", + "\n", + "It's a great exercise to try changing the sample size to other values (try 2,5,10,100?...) and observing how our \"mountain\" posterior changes. " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Exploring the landscape using the MCMC\n", + "\n", + "We should explore the deformed posterior space generated by our prior surface and observed data to find the posterior mountain. However, we cannot naively search the space: any computer scientist will tell you that traversing $N$-dimensional space is exponentially difficult in $N$: the size of the space quickly blows-up as we increase $N$ (see [the curse of dimensionality](http://en.wikipedia.org/wiki/Curse_of_dimensionality)). What hope do we have to find these hidden mountains? The idea behind MCMC is to perform an intelligent search of the space. To say \"search\" implies we are looking for a particular point, which is perhaps not an accurate as we are really looking for a broad mountain. \n", + "\n", + "Recall that MCMC returns *samples* from the posterior distribution, not the distribution itself. Stretching our mountainous analogy to its limit, MCMC performs a task similar to repeatedly asking \"How likely is this pebble I found to be from the mountain I am searching for?\", and completes its task by returning thousands of accepted pebbles in hopes of reconstructing the original mountain. In MCMC and PyMC lingo, the returned sequence of \"pebbles\" are the samples, cumulatively called the *traces*. \n", + "\n", + "When I say MCMC intelligently searches, I really am saying MCMC will *hopefully* converge towards the areas of high posterior probability. MCMC does this by exploring nearby positions and moving into areas with higher probability. Again, perhaps \"converge\" is not an accurate term to describe MCMC's progression. Converging usually implies moving towards a point in space, but MCMC moves towards a *broader area* in the space and randomly walks in that area, picking up samples from that area.\n", + "\n", + "####Why Thousands of Samples?\n", + "\n", + "At first, returning thousands of samples to the user might sound like being an inefficient way to describe the posterior distributions. I would argue that this is extremely efficient. Consider the alternative possibilities:\n", + "\n", + "1. Returning a mathematical formula for the \"mountain ranges\" would involve describing a N-dimensional surface with arbitrary peaks and valleys.\n", + "2. Returning the \"peak\" of the landscape, while mathematically possible and a sensible thing to do as the highest point corresponds to most probable estimate of the unknowns, ignores the shape of the landscape, which we have previously argued is very important in determining posterior confidence in unknowns. \n", + "\n", + "Besides computational reasons, likely the strongest reason for returning samples is that we can easily use *The Law of Large Numbers* to solve otherwise intractable problems. I postpone this discussion for the next chapter. With the thousands of samples, we can reconstruct the posterior surface by organizing them in a histogram. \n", + "\n", + "\n", + "### Algorithms to perform MCMC\n", + "\n", + "There is a large family of algorithms that perform MCMC. Most of these algorithms can be expressed at a high level as follows: (Mathematical details can be found in the appendix.)\n", + "\n", + "1. Start at current position.\n", + "2. Propose moving to a new position (investigate a pebble near you).\n", + "3. Accept/Reject the new position based on the position's adherence to the data and prior distributions (ask if the pebble likely came from the mountain).\n", + "4. 1. If you accept: Move to the new position. Return to Step 1.\n", + " 2. Else: Do not move to new position. Return to Step 1. \n", + "5. After a large number of iterations, return all accepted positions.\n", + "\n", + "This way we move in the general direction towards the regions where the posterior distributions exist, and collect samples sparingly on the journey. Once we reach the posterior distribution, we can easily collect samples as they likely all belong to the posterior distribution. \n", + "\n", + "If the current position of the MCMC algorithm is in an area of extremely low probability, which is often the case when the algorithm begins (typically at a random location in the space), the algorithm will move in positions *that are likely not from the posterior* but better than everything else nearby. Thus the first moves of the algorithm are not reflective of the posterior.\n", + "\n", + "In the above algorithm's pseudocode, notice that only the current position matters (new positions are investigated only near the current position). We can describe this property as *memorylessness*, i.e. the algorithm does not care *how* it arrived at its current position, only that it is there. \n", + "\n", + "### Other approximation solutions to the posterior\n", + "Besides MCMC, there are other procedures available for determining the posterior distributions. A Laplace approximation is an approximation of the posterior using simple functions. A more advanced method is [Variational Bayes](http://en.wikipedia.org/wiki/Variational_Bayesian_methods). All three methods, Laplace Approximations, Variational Bayes, and classical MCMC have their pros and cons. We will only focus on MCMC in this book. That being said, my friend Imri Sofar likes to classify MCMC algorithms as either \"they suck\", or \"they really suck\". He classifies the particular flavour of MCMC used by PyMC as just *sucks* ;)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "##### Example: Unsupervised Clustering using a Mixture Model\n", + "\n", + "\n", + "Suppose we are given the following dataset:\n" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "figsize(12.5, 4)\n", + "data = np.loadtxt(\"data/mixture_data.csv\", delimiter=\",\")\n", + "\n", + "plt.hist(data, bins=20, color=\"k\", histtype=\"stepfilled\", alpha=0.8)\n", + "plt.title(\"Histogram of the dataset\")\n", + "plt.ylim([0, None])\n", + "print data[:10], \"...\"\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "[ 115.85679142 152.26153716 178.87449059 162.93500815 107.02820697\n", + " 105.19141146 118.38288501 125.3769803 102.88054011 206.71326136] ...\n" + ] + }, + { + "metadata": {}, + "output_type": "display_data", + "png": 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+ "text": [ + "" + ] + } + ], + "prompt_number": 37 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "What does the data suggest? It appears the data has a bimodal form, that is, it appears to have two peaks, one near 120 and the other near 200. Perhaps there are *two clusters* within this dataset. \n", + "\n", + "This dataset is a good example of the data-generation modeling technique from last chapter. We can propose *how* the data might have been created. I suggest the following data generation algorithm: \n", + "\n", + "1. For each data point, choose cluster 1 with probability $p$, else choose cluster 2. \n", + "2. Draw a random variate from a Normal distribution with parameters $\\mu_i$ and $\\sigma_i$ where $i$ was chosen in step 1.\n", + "3. Repeat.\n", + "\n", + "This algorithm would create a similar effect as the observed dataset, so we choose this as our model. Of course, we do not know $p$ or the parameters of the Normal distributions. Hence we must infer, or *learn*, these unknowns.\n", + "\n", + "Denote the Normal distributions $\\text{Nor}_0$ and $\\text{Nor}_1$ (having variables' index start at 0 is just Pythonic). Both currently have unknown mean and standard deviation, denoted $\\mu_i$ and $\\sigma_i, \\; i =0,1$ respectively. A specific data point can be from either $\\text{Nor}_0$ or $\\text{Nor}_1$, and we assume that the data point is assigned to $\\text{Nor}_0$ with probability $p$.\n", + "\n", + "\n", + "An appropriate way to assign data points to clusters is to use a PyMC `Categorical` stochastic variable. Its parameter is a $k$-length array of probabilities that must sum to one and its `value` attribute is a integer between 0 and $k-1$ randomly chosen according to the crafted array of probabilities. (In our case $k=2$) *A priori*, we do not know what the probability of assignment to cluster 1 is, so we create a uniform variable over 0,1 to model this. Call this `p`. Thus the probability array we enter into the `Categorical` variable is `[p, 1-p]`." + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import pymc as pm\n", + "\n", + "p = pm.Uniform(\"p\", 0, 1)\n", + "\n", + "assignment = pm.Categorical(\"assignment\", [p, 1 - p], size=data.shape[0])\n", + "print \"prior assignment, with p = %.2f:\" % p.value\n", + "print assignment.value[:10], \"...\"\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "prior assignment, with p = 0.31:\n", + "[1 1 0 0 0 0 1 1 1 1] ...\n" + ] + } + ], + "prompt_number": 38 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Looking at the above dataset, I would guess that the standard deviations of the two Normals are different. To maintain ignorance of what the standard deviations might be, we will initially model them as uniform on 0 to 100. Really we are talking about $\\tau$, the *precision* of the Normal distribution, but it is easier to think in terms of standard deviation. Our PyMC code will need to transform our standard deviation into precision by the relation:\n", + "\n", + "$$ \\tau = \\frac{1}{\\sigma^2} $$\n", + "\n", + "In PyMC, we can do this in one step by writing:\n", + "\n", + " taus = 1.0/pm.Uniform( \"stds\", 0, 100, size= 2)**2 \n", + "\n", + "Notice that we specified `size=2`: we are modeling both $\\tau$s as a single PyMC variable. Note that this does not induce a necessary relationship between the two $\\tau$s, it is simply for succinctness.\n", + "\n", + "We also need to specify priors on the centers of the clusters. The centers are really the $\\mu$ parameters in this Normal distributions. Their priors can be modeled by a Normal distribution. Looking at the data, I have an idea where the two centers might be — I would guess somewhere around 120 and 190 respectively, though I am not very confident in these eyeballed estimates. Hence I will set $\\mu_0 = 120, \\mu_1 = 190$ and $\\sigma_{0,1} = 10$ (recall we enter the $\\tau$ parameter, so enter $1/\\sigma^2 = 0.01$ in the PyMC variable.)" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "taus = 1.0 / pm.Uniform(\"stds\", 0, 100, size=2) ** 2\n", + "centers = pm.Normal(\"centers\", [120, 190], [0.01, 0.01], size=2)\n", + "\n", + "\"\"\"\n", + "The below deterministic functions map an assignment, in this case 0 or 1,\n", + "to a set of parameters, located in the (1,2) arrays `taus` and `centers`.\n", + "\"\"\"\n", + "\n", + "@pm.deterministic\n", + "def center_i(assignment=assignment, centers=centers):\n", + " return centers[assignment]\n", + "\n", + "@pm.deterministic\n", + "def tau_i(assignment=assignment, taus=taus):\n", + " return taus[assignment]\n", + "\n", + "print \"Random assignments: \", assignment.value[:4], \"...\"\n", + "print \"Assigned center: \", center_i.value[:4], \"...\"\n", + "print \"Assigned precision: \", tau_i.value[:4], \"...\"\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Random assignments: [1 1 0 0] ...\n", + "Assigned center: [ 174.74278858 174.74278858 126.25164007 126.25164007] ...\n", + "Assigned precision: [ 0.00034557 0.00034557 0.00012237 0.00012237] ...\n" + ] + } + ], + "prompt_number": 40 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# and to combine it with the observations:\n", + "observations = pm.Normal(\"obs\", center_i, tau_i, value=data, observed=True)\n", + "\n", + "# below we create a model class\n", + "model = pm.Model([p, assignment, observations, taus, centers])\n" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 41 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "PyMC has an MCMC class, `MCMC` in the main namespace of PyMC, that implements the MCMC exploring algorithm. We initialize it by passing in a `Model` instance:\n", + "\n", + " mcmc = pm.MCMC( model )\n", + "\n", + "The method for asking the `MCMC` to explore the space is `sample( iterations )`, where `iterations` is the number of steps you wish the algorithm to perform. We try 50000 steps below:" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "mcmc = pm.MCMC(model)\n", + "mcmc.sample(50000)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + " \r", + "[****************100%******************] 50000 of 50000 complete" + ] + }, + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "\n" + ] + } + ], + "prompt_number": 42 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Below I plot the paths, or \"traces\", the unknown parameters (centers, precisions, and $p$) have taken thus far. The traces can be retrieved using the `trace` method in the `MCMC` object created, which accepts the assigned PyMC variable `name`. For example, `mcmc.trace(\"centers\")` will retrieve a `Trace` object that can be indexed (using `[:]` or `.gettrace()` to retrieve all traces, or fancy-indexing like `[1000:]`)." + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "figsize(12.5, 9)\n", + "plt.subplot(311)\n", + "lw = 1\n", + "center_trace = mcmc.trace(\"centers\")[:]\n", + "\n", + "# for pretty colors later in the book.\n", + "colors = [\"#348ABD\", \"#A60628\"] \\\n", + "if center_trace[-1, 0] > center_trace[-1, 1] \\\n", + " else [\"#A60628\", \"#348ABD\"]\n", + "\n", + "plt.plot(center_trace[:, 0], label=\"trace of center 0\", c=colors[0], lw=lw)\n", + "plt.plot(center_trace[:, 1], label=\"trace of center 1\", c=colors[1], lw=lw)\n", + "plt.title(\"Traces of unknown parameters\")\n", + "leg = plt.legend(loc=\"upper right\")\n", + "leg.get_frame().set_alpha(0.7)\n", + "\n", + "plt.subplot(312)\n", + "std_trace = mcmc.trace(\"stds\")[:]\n", + "plt.plot(std_trace[:, 0], label=\"trace of standard deviation of cluster 0\",\n", + " c=colors[0], lw=lw)\n", + "plt.plot(std_trace[:, 1], label=\"trace of standard deviation of cluster 1\",\n", + " c=colors[1], lw=lw)\n", + "plt.legend(loc=\"upper left\")\n", + "\n", + "plt.subplot(313)\n", + "p_trace = mcmc.trace(\"p\")[:]\n", + "plt.plot(p_trace, label=\"$p$: frequency of assignment to cluster 0\",\n", + " color=\"#467821\", lw=lw)\n", + "plt.xlabel(\"Steps\")\n", + "plt.ylim(0, 1)\n", + "plt.legend()\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "display_data", + "png": 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L9npkcgJjE1M0NOh+RrXNEly43Tr60pWTuWmmUwrlESW5tBEDHc3a3UZOCCQy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\neX1Wr16N4OBgjBkzBgEBAfjoo4+gVCrh6emJn3/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okvP159dtXeDp14X1hDuV3lVdTreH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Sz/2RwJJvnnswBavDs+hyehnJRacUeCoaWmnu++XsKq2O9V10vtI2ytinQBAEWiRSVDe2olUi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+ "text": [ + "" + ] + } + ], + "prompt_number": 47 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Notice the following characteristics:\n", + "\n", + "1. The traces converges, not to a single point, but to a *distribution* of possible points. This is *convergence* in an MCMC algorithm.\n", + "2. Inference using the first few thousand points is a bad idea, as they are unrelated to the final distribution we are interested in. Thus is it a good idea to discard those samples before using the samples for inference. We call this period before converge the *burn-in period*.\n", + "3. The traces appear as a random \"walk\" around the space, that is, the paths exhibit correlation with previous positions. This is both good and bad. We will always have correlation between current positions and the previous positions, but too much of it means we are not exploring the space well. This will be detailed in the Diagnostics section later in this chapter.\n", + "\n", + "\n", + "To achieve further convergence, we will perform more MCMC steps. Starting the MCMC again after it has already been called does not mean starting the entire algorithm over. In the pseudo-code algorithm of MCMC above, the only position that matters is the current position (new positions are investigated near the current position), implicitly stored in PyMC variables' `value` attribute. Thus it is fine to halt an MCMC algorithm and inspect its progress, with the intention of starting it up again later. The `value` attributes are not overwritten. \n", + "\n", + "We will sample the MCMC one hundred thousand more times and visualize the progress below:" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "mcmc.sample(100000)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + " \r", + "[****************100%******************] 100000 of 100000 complete" + ] + }, + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "\n" + ] + } + ], + "prompt_number": 48 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "figsize(12.5, 4)\n", + "center_trace = mcmc.trace(\"centers\", chain=1)[:]\n", + "prev_center_trace = mcmc.trace(\"centers\", chain=0)[:]\n", + "\n", + "x = np.arange(50000)\n", + "plt.plot(x, prev_center_trace[:, 0], label=\"previous trace of center 0\",\n", + " lw=lw, alpha=0.4, c=colors[1])\n", + "plt.plot(x, prev_center_trace[:, 1], label=\"previous trace of center 1\",\n", + " lw=lw, alpha=0.4, c=colors[0])\n", + "\n", + "x = np.arange(50000, 150000)\n", + "plt.plot(x, center_trace[:, 0], label=\"new trace of center 0\", lw=lw, c=\"#348ABD\")\n", + "plt.plot(x, center_trace[:, 1], label=\"new trace of center 1\", lw=lw, c=\"#A60628\")\n", + "\n", + "plt.title(\"Traces of unknown center parameters\")\n", + "leg = plt.legend(loc=\"upper right\")\n", + "leg.get_frame().set_alpha(0.8)\n", + "plt.xlabel(\"Steps\")\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "display_data", + "png": 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SzpURFxdH8+bNy6SnpKSQl5fHgAEDpDQhhJ50x8rKSu9amZqaVuhMR0dHk5CQ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FeXbmDx1gKs+Vdf9ryssQsnpZp1Aw0yBVbsLMLlOs1n85FdV/DxqRr8pbdLXkuvlWbupxfQ0qXA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\nZvAJQ+h+5t7cvmtGBEEQGjxlp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TqFqqoqPPfcc/z7Xb58GbW1taiursbq1avxi1/8AidP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\ngiAIN4GSd4IgCIIgCIJwE/4/A0GofKoLPsoAAAAASUVORK5CYII=\n", + "text": [ + "" + ] + } + ], + "prompt_number": 50 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The `trace` method in the `MCMC` instance has a keyword argument `chain`, that indexes which call to `sample` you would like to be returned. (Often we need to call `sample` multiple times, and the ability to retrieve past samples is a useful procedure). The default for `chain` is -1, which will return the samples from the lastest call to `sample`.\n", + "\n", + "#### Cluster Investigation\n", + "\n", + "We have not forgotten our main challenge: identify the clusters. We have determined posterior distributions for our unknowns. We plot the posterior distributions of the center and standard deviation variables below:" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "figsize(11.0, 4)\n", + "std_trace = mcmc.trace(\"stds\")[:]\n", + "\n", + "_i = [1, 2, 3, 0]\n", + "for i in range(2):\n", + " plt.subplot(2, 2, _i[2 * i])\n", + " plt.title(\"Posterior of center of cluster %d\" % i)\n", + " plt.hist(center_trace[:, i], color=colors[i], bins=30,\n", + " histtype=\"stepfilled\")\n", + "\n", + " plt.subplot(2, 2, _i[2 * i + 1])\n", + " plt.title(\"Posterior of standard deviation of cluster %d\" % i)\n", + " plt.hist(std_trace[:, i], color=colors[i], bins=30,\n", + " histtype=\"stepfilled\")\n", + " # plt.autoscale(tight=True)\n", + "\n", + "plt.tight_layout()\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "display_data", + "png": 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cRzscuyCgLPMy7uVc1UxA7STl3AMcvy5JOXZ18OCAac1vf/4n0Mo86L2iXobP\nh/O0FBFjjDFNKM/ORcn/HVJZhmpr8aCoREsRMcbUxYMDiZH0TTFEdX+tlWkjSedCwzgXdTgPTN9J\nuY6qir3qTjlyVm/SckTtI+XcAxy/Lkk5dnXw4IC1quLadVBNjcoytVXVWoqGMcYYY4w9Ljw4kBhd\njFzz/p2Iqxu/VlmGamu1FM0jhjSKbw3nog7ngek7KddRKccOcPy6JuX4pRy7OnhwwFpFtbWtnjlg\njDHGGGPSJ9N1AKx9UlNTdR2C3uBcPMK5qMN5YPpOynVUyrEDHL+uSTl+KceuDj5zwBhjjDG98XvK\nzzC27qKyjK2/N6z6emgpIsYMCw8OJMbQrntThXPxCOeiDueB6Tsp11FtxZ713uetlhm4ZVW7BwdS\nzj3A8euSlGNXh9qXFa1cuRL9+vWDn58fXnnlFTx8+BClpaUIDQ1F3759MW7cONy+fVupvJeXF7y9\nvXHgwAFxeXp6Ovz8/ODl5YV583h+e8YYkxruD5i21VZV435Bcat/jLH2U2twkJeXh40bNyIjIwPn\nzp1DTU0NEhISsGrVKoSGhiI7Oxtjx47FqlWrAACZmZlITExEZmYmkpOTMXfuXPGXcqOjoxEXFwe5\nXA65XI7k5GTNHV0nZGjXvanCuXiEc1GH86B93B+0j5TrqD7F/tv/ex9Hh7ys8i9z4f8oraNP8auD\n49cdKceuDrUGBzY2NjAxMcH9+/dRXV2N+/fv44knnsC+ffsQEREBAIiIiMDevXsBAElJSZgxYwZM\nTEzg7u4OT09PpKWlobi4GGVlZQgMDAQAhIeHi+swxhjTf9wfMJ0gAmprVf5RLc+yx5g61BocdO3a\nFW+//Tbc3NzwxBNPwM7ODqGhoVAoFHBycgIAODk5QaFQAACuXbsGV1dXcX1XV1cUFRU1We7i4oKi\noqKOHE+nZ2jXvanCuXiEc1GH86B93B+0j5TrqJRjBzh+XZNy/FKOXR1q3ZB8+fJlrFmzBnl5ebC1\ntcXLL7+MHTt2KJURBAGCIGgkSACYO3cu3NzcAAC2trbw8/MTX6z60z38+PE8zijMg6L2HnxldbNH\nZNbeA4DH9ljXx8uP+bEUH9f/n5+fDwCIioqCNnB/wI8BoJ+ZLYDH3z9wf8KP+fHj7w8Eqr/Ysx0S\nExNx8OBBbNq0CQCwfft2/PLLL/jvf/+LQ4cOwdnZGcXFxQgODsbFixfFa00XLVoEABg/fjyWLVuG\nXr16ITjCbZCmAAAgAElEQVQ4GFlZWQCAXbt24ciRI9iwYYPS/lJSUjBo0KD2htkppaamipVAW7L+\nuRZX/52olX31en0qfD6a36ayusiFvuJc1OE8PJKRkYGxY8c+9v1wf9A+Uq6jqmK/deoc0ib8Py1H\npJrD6EA8lbBGfCzl3AMcvy5JOXag/f2BWpcVeXt745dffsGDBw9ARPjpp5/g6+uLCRMmID4+HgAQ\nHx+PSZMmAQAmTpyIhIQEVFZWIjc3F3K5HIGBgXB2doaNjQ3S0tJARNi+fbu4DjNMVXfLcb+gGPdy\nC1X+Vd+v0HWojDFwf8D0172cfBTvS0Hx3oMo3nsQN1NPi/83/ONZjRhTZqzOSv7+/ggPD8fgwYMh\nk8kwaNAgvPHGGygrK8PUqVMRFxcHd3d3fP311wAAX19fTJ06Fb6+vjA2NkZsbKx4ijk2NhaRkZF4\n8OABwsLCMH78eM0dXSekyZFr5e27uJ32G2oqHrZYRpDJcOvkbxrbZ2uuJf6Aa4k/qCxj5twNTx/c\nKulRvKZxLupwHrSP+4P2kXIdlVrsFYUl+O2N98XHZgCa682GH96utZg6Qmr5b0zK8Us5dnWodVmR\ntkn9NLK+evh7KU6Mm42Hxb/rOpR2qR8cmHXvqutQGNNb2rqsSNu4P9BP+nhZUVsNP7wd1t59dB0G\nY4+NVi4rYrrT8GYTQ1V9txy3fvkV+1b/CyXfHWrx715e55vppCVcL+pwHpi+k3IdlXLswKOblaVK\n6vmXcvxSjl0dal1WxJgu1dyvwK+vL0FO7T2Y/jEjRXOG/bhZi1ExxhhjjEkfnzmQGEO77k0VXxUD\nA0PD9aIO54HpOynXUSnHDki/z5B6/qUcv5RjVwcPDhhjjDHGGGMAeHAgOYZ23ZsqUr9+VJO4XtTh\nPDB9J+U6KuXYAen3GVLPv5Tjl3Ls6uDBAWOMMcYYYwwA35AsOYZ23ZsqUr9+VJO4XtThPDB9J8U6\nej+vCDUPKuDv0ANlWZebLVNdfl/LUbVfS31GWeZlVBRdV7muhVsPWHm5P4ao2k6KdachKccv5djV\nwYMD1mndzriAilZ+w6FL756w6uuunYAYY0yCSr4/jOyP1us6jMfm7NylrZYZELtU54MDxrSFBwcS\nk5qaanAj2JZk1t5TefYga/FnrW4jYOPHnWJwwPWiDueB6Tsp19HW2lx9J/X4pVx3AGnHL+XY1cH3\nHDDGGGOMMcYAdGBwcPv2bbz00kvw8fGBr68v0tLSUFpaitDQUPTt2xfjxo3D7du3xfIrV66El5cX\nvL29ceDAAXF5eno6/Pz84OXlhXnz5nXsaAyAIY1cWyPlb4A0jetFHc6DbnB/0HZSrqNSb3OlHr+U\n6w4g7filHLs61B4czJs3D2FhYcjKysLZs2fh7e2NVatWITQ0FNnZ2Rg7dixWrVoFAMjMzERiYiIy\nMzORnJyMuXPngogAANHR0YiLi4NcLodcLkdycrJmjowxxphWcH/AOrvivQdRlPiDyr/rP6aipqJC\n16Ey1mFqDQ7u3LmDY8eO4bXXXgMAGBsbw9bWFvv27UNERAQAICIiAnv37gUAJCUlYcaMGTAxMYG7\nuzs8PT2RlpaG4uJilJWVITAwEAAQHh4ursOaZ2hz7aoi9TmrNYnrRR3Og/Zxf9A+Uq6jUm9zOxL/\n7weO49y8j1X+yT/dCKohDUasTMp1B5B2/FKOXR1qDQ5yc3PRvXt3zJ49G4MGDcLrr7+Oe/fuQaFQ\nwMnJCQDg5OQEhUIBALh27RpcXV3F9V1dXVFUVNRkuYuLC4qKijpyPIwxxrSI+wPGGOtc1JqtqLq6\nGhkZGVi3bh2eeuopzJ8/XzxlXE8QBAiCoJEgAWDu3Llwc3MDANja2sLPz0+8Bqx+RGcIj0eMGKGx\n7T31pC+AR9+m1F+PaWiP9en17cjjevoSj9TfH1J7XP9/fn4+ACAqKgrawP1B+x7XL9OXeNry+Fqu\nHDaoazN13V535LE24j/+8wkYmZtx+9YJ45fS4/r/1e0PBKq/2LMdSkpKMGzYMOTm5ooBrFy5Eleu\nXMGhQ4fg7OyM4uJiBAcH4+LFi2JHsWjRIgDA+PHjsWzZMvTq1QvBwcHIysoCAOzatQtHjhzBhg0b\nlPaXkpKCQYMGtTdM1oqHv5fixLjZeNjKbwF0ZgEbP4bzhDG6DoMxjcvIyMDYsWMf+364P+j8rqzf\n2al/50BTrPt5Yci+DTDuYqHrUBhT0t7+QK3LipydndGzZ09kZ2cDAH766Sf069cPEyZMQHx8PAAg\nPj4ekyZNAgBMnDgRCQkJqKysRG5uLuRyOQIDA+Hs7AwbGxukpaWBiLB9+3ZxHda8xt8SGzKpX/+q\nSVwv6nAetI/7g/aRch2Vepsr9filXHcAaccv5djVYazuiv/617/w6quvorKyEn369MGWLVtQU1OD\nqVOnIi4uDu7u7vj6668BAL6+vpg6dSp8fX1hbGyM2NhY8RRzbGwsIiMj8eDBA4SFhWH8+PGaOTLG\nGGNawf0BY4x1HmpdVqRtfBr58eDLioCAuBVwfm60rsNgTOO0dVmRtnF/oH18WVHb8GVFTF+1tz9Q\n+8wBY51B7voduJX2m8oydoP6ocekEC1FxBhjjDGmOzw4kJiGs1wYuszaex3+xcs7GZm4k5Gpskz1\njOf1fnDA9aIO54HpOynXUU20ubok9filXHcAaccv5djVwYMDxhhjzABRbS1qq6tbKSUA+n/1MWNM\ng3hwIDGGNHJtjZS/AdI0rhd1OA9M3+lTHX14/SbOL1iBqjvlKsvdu1w3V7rU21ypx69PdUcdUo5f\nyrGrgwcHndT9/Gu4l52nupAgoLpM2lO7McYYU9+d3y6iqvSOrsNgjOkRHhxITFuve6u6dRfpM/+u\nhYh0R+rXj2qSoV0P2RLOA9N3Uq6jUm9zH3f8tRUPUXnzFh6WqJ4B0NjGCmbdu7Z7+1KuO4C045dy\n7OrgwQFjjDHGWAfdu5yPo4EvtVpu6A+b1BocMKYtav1CMtMdQxq5tkbK32BpGteLOpwHpu+kXEel\n3uZKPX4p1x1A2vFLOXZ18JkDxlqh+O4QHhQpVJYxse4Cn+ULYO7cXUtRMcYYY4xpHp85kJjU1FRd\nh6A3Mmu1czN1ddk9lB49pfrvRIZWYmkJ14s6nAem76RcR7XV5j4uUo9fynUHkHb8Uo5dHTw4YIwx\nxhhjjAHo4OCgpqYGAwcOxIQJEwAApaWlCA0NRd++fTFu3Djcvn1bLLty5Up4eXnB29sbBw4cEJen\np6fDz88PXl5emDdvXkfCMQiGdt2bKlK/flSTuF7U4TzoDvcHbSPlOir1Nlfq8Uu57gDSjl/Ksauj\nQ4ODtWvXwtfXF4IgAABWrVqF0NBQZGdnY+zYsVi1ahUAIDMzE4mJicjMzERycjLmzp0L+uMXF6Oj\noxEXFwe5XA65XI7k5OQOHhJjjDFt4/6AMcY6B7UHB4WFhfjhhx8QFRUlNuz79u1DREQEACAiIgJ7\n9+4FACQlJWHGjBkwMTGBu7s7PD09kZaWhuLiYpSVlSEwMBAAEB4eLq7Dmmdo172pIvXrRzWJ60Ud\nzoNucH/QdlKuo1Jvc6Uev5TrDiDt+KUcuzrUnq1owYIFWL16Ne7evSsuUygUcHJyAgA4OTlBoaib\n4eXatWsYOnSoWM7V1RVFRUUwMTGBq6uruNzFxQVFRUXqhsQYY0wHuD9grO0EYyNUtPJDaYKxMcy6\n2WspIsaUqTU4+O677+Do6IiBAwfi8OHDzZYRBEE8vawJc+fOhZubGwDA1tYWfn5+4jVg9SM6Q3g8\nYsSINpW/dzlfzF39tyX111vyY80/lpVXYdDVa7ifW4hfzv4KABg6IAAAlB6buzoj4+plAJqvH/X0\nqb5q+3Fb3x+d8XH9//n5de/9qKgoaAP3B+17XL9MX+K58PAuqhv8crCq9s5X1kUv2lt1H+tL/Bef\nD4efVd2PoF14WDeg7mdmo/R48seL4Trj+U7Vvkk9fik9rv9f3f5AoPpzwO3w3nvvYfv27TA2NkZF\nRQXu3r2LyZMn49SpUzh8+DCcnZ1RXFyM4OBgXLx4UbzWdNGiRQCA8ePHY9myZejVqxeCg4ORlZUF\nANi1axeOHDmCDRs2KO0vJSUFgwYNam+YBu3Obxfx8zOv6ToM1sjQ7/8Nuz/113UYzABkZGRg7Nix\nj30/3B9IV0XJ7zg+JhxVpXd0HQprxGfl2+g1e4quw2CdRHv7A7XuOVixYgUKCgqQm5uLhIQEjBkz\nBtu3b8fEiRMRHx8PAIiPj8ekSZMAABMnTkRCQgIqKyuRm5sLuVyOwMBAODs7w8bGBmlpaSAibN++\nXVyHNc/QrntTRerXj2oS14s6nAft4/6gfaRcR6Xe5ko9finXHUDa8Us5dnWofc9BQ/WnixctWoSp\nU6ciLi4O7u7u+PrrrwEAvr6+mDp1Knx9fWFsbIzY2FhxndjYWERGRuLBgwcICwvD+PHjNRESY4wx\nHeD+gDHGpE2ty4q0jU8jtx9fVqSf+LIipi3auqxI27g/0By+rEh/8WVFTJPa2x9o5MwBY6xtBCMj\nVFy7rrqMmQnMHHiWCsYYY4xpX4d+BI1pn6Fd96aKFK8fTZsUjdSgV1X+3fr5TLu3y/WiDueB6Tsp\n11EptrkNST1+KdcdQNrxSzl2dfCZA8a0qLaiErUVlSrLUFWNlqJhjDHGGFPGgwOJaThXtioy087/\n0tbPG83aXi86O84D03dSrqNSb3OlFP+djAu40bsn0OC2UG+Y4MbhNPGxYGwMy949gRrVXyjJLM31\n4lJVKdd9Kceujs7/CbITup1+HoW7vlNZ5qHippaiYYwxxpgmXfsmGde+SW61nGBk1GqZwd+shdnT\nuh8cMOngwYHEpKamwvNWJQp37NN1KDqX2eBXPQ1dw19cNWScB6bvpFxHpd7mdsb4qZWzBgBgZGqK\n2urWy8mMWx9odISU676UY1cHDw4YY4wxxjqps29+CNNuqs8cPPHys3AL73w/OsjUw4MDiRkxYgRK\n/u+/ug5DL0j5GyBNM6RvNFThPDB9p606WlF8HdXl91WWEYyMQFXVbd6m1NtcQ43/fm4h7ucWqizT\ndViAWttuDym3z1KOXR08OGCMMcY6mXL5VZyeOk/XYTDGJIgHBxKTmpoKT10HoSekfv1oi4xa//mR\n2qpq3Pk1C7WVVQCAtHO/Yoif8jc/giDAyrs3TLvaqtxW1d1y1D5UPb2qYGwMU3ubVuPSNUO7LpRJ\nj5TrqNTbXI5ft6Rc96Ucuzp4cMCYnsn+aD2KEn9QXYgIN1PTQX8MDi7W3oOsUadhZGmBEce+AqB6\ncHD33CWc/csylWV8li+A83PBrcbOGGOMMWlTa3BQUFCA8PBwXL9+HYIg4I033sDf/vY3lJaWYtq0\nabh69Src3d3x9ddfw87ODgCwcuVKbN68GUZGRoiJicG4ceMAAOnp6YiMjERFRQXCwsKwdu1azR1d\nJ8T3HDwi5W9QVHlQUIIHBSXtWqcjuaDqGjwsuaGyTO2Dh2pvX5sM6ZsdfcH9QftIuY5Kvc3l+FtW\nsGMf7l7IUVlGZmoCn48XwMLFSa19SLnuSzl2dbR+/UIzTExM8MUXX+DChQv45ZdfsH79emRlZWHV\nqlUIDQ1FdnY2xo4di1WrVgEAMjMzkZiYiMzMTCQnJ2Pu3LmgP37YIzo6GnFxcZDL5ZDL5UhObn1e\nX8YYY/qB+wPGpK+q9A5upPys+u/QL7oOk2mJWoMDZ2dnBATUXd9sZWUFHx8fFBUVYd++fYiIiAAA\nREREYO/evQCApKQkzJgxAyYmJnB3d4enpyfS0tJQXFyMsrIyBAYGAgDCw8PFdVjzUlNTdR2C3sis\nvafrEPQG56IOvz+0j/uD9pFyHZV6O8Px65aU676UY1dHh+85yMvLw5kzZzBkyBAoFAo4OdWdbnJy\ncoJCoQAAXLt2DUOHDhXXcXV1RVFREUxMTODq6ioud3FxQVFRUUdDYoyh7sdxKm/eQuV11b+W3dol\nRYy1FfcHjHVeVFWDsgtylGddVlnO0t0VXTzdtBQVexw6NDgoLy/HlClTsHbtWlhbWys9JwgCBEHo\nUHANzZ07F25udZXN1tYWfn5+4jVg9SM6Q3g8YsQI7Ps0BjkNZi2o/zaBHxv243ri8w+Bn8e9ppHt\nV1zKxCSMB6Bf74fGj0eMGKFX8Wjzcf3/+fn5AICoqChoE/cHbXtcv+xx788bZgA02974yrroTXvH\n8Wt//1RTgx0z/9JqebfZL2HMpOcBAL+c/RUAMHRAAHyNuuCHL7cAAIYPexq2A57U+fuxsz6u/1/d\n/kCg+os926mqqgrPP/88nn32WcyfPx8A4O3tjcOHD8PZ2RnFxcUIDg7GxYsXxWtNFy1aBAAYP348\nli1bhl69eiE4OBhZWVkAgF27duHIkSPYsGGD0r5SUlIwaNAgdcLslEr+77/49fUlug6DGZA+b81G\n95CnVZaRmZrApn9fLUXEWpORkYGxY8dqZV/cH+ifG0dP8e8cML3VY8oz8F//ga7DMBjt7Q/UuueA\niDBnzhz4+vqKHQEATJw4EfHx8QCA+Ph4TJo0SVyekJCAyspK5ObmQi6XIzAwEM7OzrCxsUFaWhqI\nCNu3bxfXYc0ztOveVJH69Zea9LhzcfnzLfgl7HWVf9krv3ysMbQFvz+0j/uD9pFyHZV6m8vx65aU\n45fy+1Ydal1WdPz4cezYsQMDBgzAwIEDAdRNTbdo0SJMnToVcXFx4tR1AODr64upU6fC19cXxsbG\niI2NFU8xx8bGIjIyEg8ePEBYWBjGjx+voUNjjDH2uHF/wBhjnYvalxVpkyGdRr53OR+1VdUqy9xK\n+xWZC/9HSxEx1jbdxg7D4J2f6ToM9gdtXlakTYbUH3QEX1bE9BlfVqRd7e0P+BeS9Uzu+p0o/Or/\ndB0GY+1WeiIDJyf/RXUhmQx+X7wHi549tBMUY4wxxtqFBwcSk9lgliJDx7l4RB9yUfvgIUpPnFFZ\nRjAyeqwxNJwFhjF9JOU6qg/tTEdw/LrVMP5bJ8/i6uZvW13H8ZmRav8isyZJ+X2rDh4cMMYYY4wx\nrakoKEbWe5+3Wq5bUKAWomGN8eBAYqT8rYGmcS4e4VzUMaRvdpg0aaKOPrx+E1Rbq7KMJn9Xop7U\n2xmOX7ekHL+h9S08OGCMaQ3V1uJ2+nncOXtJZTlr797o0od/YZOx5lzd9A0Ktu1RWabmYaWWomGM\ndTY8OJAYqV9zqEmci0ckkwsi/Pbn1meoCNy9Xq3BgaFdF8qkRxN1tOZBBapul2kooraTTDvTAo5f\nt6Qcv6H1LTw4YIwxxhhjeufhjVuouqN6IGxib4suHq5aisgw8OBAYqQ66n4cOBePcC7qGNI3O0ya\npFxHpd7OcPy6pU78J1+IbrVMwKblj31wIOX3rTp4cKAlD38vReHOfai5/0Blud8P/aKliBjTX/ev\nFgEy1TdUmnazh5VnLy1FxBhjjBkGHhxoCdXUIO/fiagqvdOh7Uj5mj1N41w80tlycX7BilbL9F/z\njyaDA0O7LpRJj5TrqNTbGY5ftx5X/PevFuF2xgWVZQRjI9j07wtBJlNrH1J+36pDLwYHycnJmD9/\nPmpqahAVFYWFCxfqOiS9lVdbIenGQZM4F48YYi4eFBTj7vlspWWnDqRggJ3jowUyGax9+jyWaR3Z\n49HZ+4Nz585J9kOG1NsZjl+3Hlf82R/FtlrGfog/AnevU3sfUn7fqkPng4Oamhr89a9/xU8//QQX\nFxc89dRTmDhxInx8fHQdml66D9VzWxsSzsUjhpiLy59txuXPNistu1D9O078+0fxsf3QgLoOgQcH\nkmAI/cGdOy2fPa64fhN3z2QBoJY3IJPh7m8XNR9YG0i9neH4dUuX8ddWVaOy9A5qK6tUljO26gIT\nW6smy1W9bzsjnQ8OTp48CU9PT7i7uwMApk+fjqSkJEl1BpWld1B9777KMoJMBqqR9hubMampraxC\n5Y1bqH2oukMwsbeGsZV0v5HrLDpDf9ARtRWVyIh4V9dhMNbp3Mm4gKNDXmq13ID1H8DE1qbJ8gcF\nJSg9cQYAYOrYtdPf76bzwUFRURF69uwpPnZ1dUVaWpoOI1L28HopqLpaZZmq23eRNmluq9uimloY\ndbHsUDw3yqnD2+gsOBePcC7qNM5DeXYuUke90up6w37cjIe/31JZxti6C4y7WKjekCCDkblpm2Jl\nTel7f9ARFSW/o7aiElcyL+J+XlGzZQQjGYysLFWeONAlqbczHL9uSSH+s3/9qNnlv5XnIT35PADA\n56N5MDJrpZ2XyWDm6ACZic4/ZqtF51G35Vrg8vJyZGRkaCEa9XVNWKWV/fxTK3uRBs7FI5yLOurm\n4eJNReuFVI8d9E55ebmuQ2i3ztIfqPLn+X/DxdKW65vD159qMZr2kXo7w/HrlpTjbxj7dQDXfy9u\nfSVF818C6EJ7+wOdDw5cXFxQUFAgPi4oKICrq/J8tS+88IK2w2KMMaZl3B8wxpjuqTenkwYNHjwY\ncrkceXl5qKysRGJiIiZOnKjrsBhjjGkZ9weMMaZ7Oj9zYGxsjHXr1uGZZ55BTU0N5syZYzA3nzHG\nGHuE+wPGGNM9gYj09NYnxhhjjDHGmDbp/LIiAHjttdfg5OQEPz8/cVlpaSlCQ0PRt29fjBs3Drdv\n3xafW7lyJby8vODt7Y0DBw7oIuTHork8fPPNN+jXrx+MjIya3ITXWfMANJ+Ld955Bz4+PvD398fk\nyZOV5h02tFy8//778Pf3R0BAAMaOHat0nbah5aLeZ599BplMhtLSUnGZoeVi6dKlcHV1xcCBAzFw\n4EDs379ffE6KuWjLMSYnJ+swwpYVFBQgODgY/fr1Q//+/RETEwNAdd+mT1qKXwr5r6iowJAhQxAQ\nEABfX18sXrwYgHRy31L8Ush9QzU1NRg4cCAmTJgAQDr5r9c4fqnk393dHQMGDMDAgQMRGBgIQI3c\nkx44evQoZWRkUP/+/cVl77zzDn3yySdERLRq1SpauHAhERFduHCB/P39qbKyknJzc6lPnz5UU1Oj\nk7g1rbk8ZGVl0aVLl2j06NGUnp4uLu/MeSBqPhcHDhwQj3HhwoUGUSeIms/F3bt3xf9jYmJozpw5\nRGSYuSAiys/Pp2eeeYbc3d3p5s2bRGSYuVi6dCl99tlnTcpKNRftOUZ9U1xcTGfOnCEiorKyMurb\nty9lZma22Lfpm5bil0r+7927R0REVVVVNGTIEDp27Jhkck/UfPxSyX29zz77jF555RWaMGECEbX8\nuU5fNY5fKvlv2A/Wa2/u9eLMwciRI2Fvb6+0bN++fYiIiAAAREREYO/evQCApKQkzJgxAyYmJnB3\nd4enpydOnjyp9Zgfh+by4O3tjb59+zYp25nzADSfi9DQUMhkdVV2yJAhKCwsBGCYubC2thb/Ly8v\nR7du3QAYZi4A4K233sKnnypPAWmouaBmrhSVai7ac4z6xtnZGQEBAQAAKysr+Pj4oKioqMW+Td+0\nFD8gjfxbWtbNp19ZWYmamhrY29tLJvdA8/ED0sg9ABQWFuKHH35AVFSUGLOU8t9c/EQkmfw3jrO9\nudeLwUFzFAoFnJycAABOTk5QKOrmhb527ZrS1Haurq5ig2VIDD0PmzdvRlhYGADDzcU//vEPuLm5\nYevWreJpZ0PMRVJSElxdXTFgwACl5YaYCwD417/+BX9/f8yZM0c8ddzZctHcMeqzvLw8nDlzBkOG\nDGmxb9Nn9fEPHToUgDTyX1tbi4CAADg5OYmXR0kp983FD0gj9wCwYMECrF69WvxCD2j5c50+ai5+\nQRAkkX9BEBASEoLBgwdj48aNANqfe70dHDQkCILKH8dpyw/nGAJDycPy5cthamqKV15p+ZdvDSEX\ny5cvR35+PmbPno358+e3WK4z5+L+/ftYsWIFli1bJi5T9c1OZ84FAERHRyM3Nxe//vorevTogbff\nfrvFslLNRXuOUR+Ul5djypQpWLt2rdIZP6D1vk0flJeX46WXXsLatWthZWUlmfzLZDL8+uuvKCws\nxNGjR3Ho0CGl5/U9943jP3z4sGRy/91338HR0REDBw5ssT3W5/y3FL9U8n/8+HGcOXMG+/fvx/r1\n63Hs2DGl59uSe70dHDg5OaGkpAQAUFxcDEdHRwBNfySnsLAQLi4uOolRlww1D1u3bsUPP/yAnTt3\nissMNRf1XnnlFZw6dQqA4eXi8uXLyMvLg7+/Pzw8PFBYWIg//elPUCgUBpcLAHB0dBQb/qioKPHS\noc6Ui5aOUR9VVVVhypQpmDVrFiZNmgSg5b5NH9XHP3PmTDF+KeUfAGxtbfHcc88hPT1dUrmvVx//\n6dOnJZP7EydOYN++ffDw8MCMGTPw3//+F7NmzZJM/puLPzw8XDL579GjBwCge/fuePHFF3Hy5Ml2\n515vBwcTJ05EfHw8ACA+Pl5smCZOnIiEhARUVlYiNzcXcrlcvBu7s2s4gjXEPCQnJ2P16tVISkqC\nubm5uNwQcyGXy8X/k5KSMHDgQACGlws/Pz8oFArk5uYiNzcXrq6uyMjIgJOTk8HlAqhr9Ovt2bNH\nnOWnM+WipWPUN0SEOXPmwNfXV+nMXkt9m75pKX4p5P/GjRviJR8PHjzAwYMHMXDgQMnkvqX46z/c\nAfqbewBYsWIFCgoKkJubi4SEBIwZMwbbt2+XTP6bi3/btm2SqPv3799HWVkZAODevXs4cOAA/Pz8\n2p97zd0frb7p06dTjx49yMTEhFxdXWnz5s108+ZNGjt2LHl5eVFoaCjdunVLLL98+XLq06cPPfnk\nk5ScnKzDyDWrcR7i4uJoz5495OrqSubm5uTk5ETjx48Xy3fWPBA1nwtPT09yc3OjgIAACggIoOjo\naLG8oeViypQp1L9/f/L396fJkyeTQqEQyxtCLkxNTcW2oiEPDw+lWRoMIRcN68WsWbPIz8+PBgwY\nQFdCnXUAACAASURBVC+88AKVlJSI5aWYi/Yeoz45duwYCYJA/v7+Ypu1f/9+lX2bPmku/h9++EES\n+T979iwNHDiQ/P39yc/Pjz799FMiIsnkvqX4pZD7xg4fPizO9iOV/Dd06NAhMf6ZM2fqff6vXLlC\n/v7+5O/vT/369aMVK1YQUftzzz+CxhhjjDHGGAOgx5cVMcYYY4wxxrSLBweMMcYYY4wxADw4YIwx\nxhhjjP2BBweMMcYYY4wxADw4YIwxxhhjjP2BBweMMcYYY4wxADw4YIwxxhhjjP2BBweMMcYYY4wx\nADw4YIwxxhhjjP2BBweMMcYYY4wxADw4YIwxxhhjjP2BBweMMcYYY4wxADw4YBowevRovPHGGzqN\nYfHixXBycoJMJsO2bdt0Gou+OHz4MPr37w9TU1OMGTNGrW1ERkYiNDRUw5ExxtqK21f1PM62Ky8v\nDzKZDCdOnGjXelu3boWJiYnG45HJZPjqq686vJ2lS5fCy8tLAxFpxrlz5xAYGAgLCwv07t1brW3o\n2zFJBQ8O9ExkZCRkMhlkMhlMTEzg7u6O6OholJaWamT7qampkMlkyM/P18j2AGDv3r34/PPPNba9\n9kpLS8Mnn3yCuLg4lJSUYOrUqTqLpbCwEDKZDEePHtVZDPWio6MxePBg5ObmYvfu3WptQxAECIKg\n0bg8PT2xbNkyjW6zsT179uDZZ59Fjx49IJPJsHPnzse6PyYN3L62nyba1x07dkAm0/7HDU23Xfqq\npKQEU6ZMaXP5lurpO++8g7S0NE2Hp7Z3330XdnZ2uHTpEk6dOqX2djRdD0JCQjB79myNbrOxo0eP\n4oUXXoC7uztkMhmWL1/+WPfXGA8O9NCoUaNQUlKCq1evIiYmBrt370Z4eLhG90FEHd5GZWUlAMDO\nzg5WVlYa2ZY65HI5ZDIZnn/+eTg6OsLc3LxDsWiCJvJbVVXVof3n5OQgJCQELi4usLOzU3s7mjiW\nhjTVUBMRqqurm33u3r17GDp0KDZs2KDRfTLp4/a1ffSxfW2rjr4OHcmbNjk6OsLMzKzd6zXOT5cu\nXdC1a1dNhdVhOTk5GDVqFNzc3ODg4KD2djTdh2mSqj6sf//++PTTT+Hs7Kz9PoyYXomIiKCQkBCl\nZcuXLycjIyOqqKig2tpaWr16NXl4eJCpqSn16dOH1qxZo1R+7969FBAQQJaWlmRnZ0eBgYF05swZ\nys3NJUEQlP6Cg4PF9Xbt2kX+/v5kbm5O7u7u9NZbb9G9e/fE54OCgmjOnDm0ZMkScnZ2ph49eojL\no6KixHKVlZW0cOFCcnFxIVNTU/L19aWvvvpKKUZBECgmJoZmzJhBtra2NH369BZzsnXrVvLx8SFT\nU1NydXWlJUuWUHV1tZivhscjk8la3E5ZWRnNmzePevbsSWZmZuTu7k4rVqwQny8pKaGIiAjq3r07\nWVtb0/Dhw+no0aPi84cOHSJBEOjgwYM0cuRIsrS0JF9fX9q/f7/ScTX88/DwEJ87cOAAPf3002Rh\nYUEuLi40e/Zsunnzpvh8/WsfExNDvXr1IplMRhUVFc0ey8WLFyksLIysrKzIysqKJkyYQDk5OUpx\nNvyLj49vMS8JCQk0aNAgMjc3JwcHB3r22Wfp1q1bSjE1jrGh7du3kyAI4uOCggKaPHkydevWjczN\nzal37960evVqIqqrK41ju3r1KhERyeVymjx5MtnZ2ZG9vT2NGzeOzp07J253y5YtZGxsTIcOHaKA\ngAAyNTWl5OTkFo+rniAItHPnzlbLsc6P29emNNW+bty4kby9vcnc3Jy6du1Ko0aNosLCwmbbo9mz\nZxNRXZsYFBREXbt2JVtbWwoKCqKTJ082OZbY2FiaOXMmWVtbk6urK61cuVKpzM2bN2nq1KnUpUsX\ncnJyoiVLllB4eLjSa93WfTWXt8TEROrTpw+Zm5vT008/TUlJSSQIAh0/frzFfNTW1tKSJUuoe/fu\nZGVlRdOmTaPPP/+cjI2Nlcqp6hcOHDhARkZGVFhYqLROQkICWVpaUllZmRh3wzZuzZo1FBAQQFZW\nVuTs7EzTp0+n4uJiIiKV9fSDDz4gT09PpX2pqh9Ej+rnhx9+SM7OztS1a1cKDw+n8vLyFnNDRHTt\n2jWaNm0a2dnZkYWFBY0ePZpOnz7dYozLli1rcVsHDx6kESNGkKWlpfjaXr58udljau4Yjx07ptQX\n3blzhyIjI8nZ2ZnMzMyoZ8+e9NZbbxFR0/eEIAh05MgRImr7Z4jvv/+ehg8fTubm5rRhwwaVeSIi\ncnd3p+XLl7daTpN4cKBnIiIiKDQ0VGnZZ599RoIgUHl5Oa1bt44sLCxo48aNlJOTQxs2bCBzc3OK\ni4sjIqLi4mIyMTGh1atXU15eHl28eJF27dpF586do5qaGtq3bx8JgkCnT58mhUIhfgjcsmUL2dvb\n044dOyg3N5eOHj1KAwYMoFmzZolxBAUFkbW1NUVHR1NWVhadP3+eiIhGjx5Nr7/+ulju73//Ozk4\nONC3335LcrmcVqxYQTKZjFJSUsQygiCQg4MDrV+/nq5cuSJ+sG3su+++IyMjI1q1ahXJ5XJKTEwk\ne3t7ev/994mo7k28du1aMjY2JoVCQQqFotnt1NbWUlBQEPXp04eSkpIoNzeXUlNTxbzdv3+ffHx8\n6KWXXqL09HS6fPkyLV++nMzMzCgrK4uIHr2x/f396ccff6ScnByaPXs22djYiHk8c+YMCYJAe/bs\nIYVCQTdu3CAiopSUFLK0tKR169ZRTk4OnTp1ioKDgykoKEjptbexsaHJkyfT2bNn6fz581RTU9Pk\nWO7fv09ubm4UEhJCGRkZlJ6eTsHBweTp6UmVlZVUWVlJJSUlYqeqUCjowYMHzeZl8+bNZGJiQh9/\n/LH4mq5bt06Mu/GHqcj/3969x0Vd5f8Df80AKl5AMR2MUVCBACXAC+p+vaGCRhtZuV5LzGz3K9tF\n61ci7W6ZFVjf/RZU5K6CkfYVK1OsDBUVEjMk0ERAmZD7zQsgd0fg/P5g5yPDbS4O8zkM7+fjMY8H\nn8+cmXnPmcP5zJlzW7euU/ns2Dh47LHHmK+vL/vtt99YQUEBO336NNu/fz9jjLHKyko2fvx49tpr\nrwmfV0tLCysvL2cymYwFBQWxy5cvs5ycHPbiiy+ykSNHshs3bjDG2sqoVCplM2bMYImJiSwvL0+4\nryfUOCAqVL+qM1T9+uuvvzJzc3O2d+9eVlhYyDIyMlhUVBQrLi5mSqWSffrpp0wikQjPUVNTwxhj\n7NChQ+zrr79mOTk5LCsri23YsIHZ2Nio/WgikUiYTCZju3fvZteuXROeq/37Xbp0KXNycmKnT59m\nmZmZ7Omnn2ZWVlZqn7W2r9Ux39LT05lUKmUhISEsJyeHffvtt8zBwUFj4+Cjjz5iQ4YMYV988QVT\nKBTs/fffZ9bW1szCwkJIo+m60NLSwuRyOduxY4facz/yyCNszZo1anG3r+PCw8PZyZMnWX5+Pjt3\n7hz7wx/+oPac3ZXTjl+cNZUPxtrK7fDhw9krr7zCrl69yo4fP85sbGzU0nTU2trKvL29mZeXFzt7\n9izLyMhgK1asYCNGjGA3b94Urgljx45lW7duZRUVFd02Nk6cOMHMzMzY5s2b2aVLl9jVq1fZ559/\nzq5evdrle3rzzTeZk5OT2nN0bBy8+OKLzMPDg50/f54VFRWxn3/+me3evZsx1vY/MXfuXLZy5Uqh\nPCuVSp2+Q7i4uLDvv/+e5efnd2r4dYUaB6TTl7HMzEw2YcIENmvWLMYYY3K5nG3ZskXtMZs3b2YT\nJkxgjDGWnp7OJBIJy8/P7/L5O/4TqNjb27N//etfaueSkpKYRCJh1dXVjLG2SuChhx7q9JztL171\n9fVs4MCB7LPPPlNL88QTT7AFCxYIxxKJRO3XsO7Mnj2brVixQu1ceHg4s7S0ZHfv3mWM3ftFuScJ\nCQlMIpGwtLS0Lu/fs2cPk8vlar+IMMaYj48P27RpE2Ps3j/2oUOHhPsrKiqYRCJhx48fZ4y1/Wre\n/pcElXnz5rGtW7eqnSsoKGASiYT99ttvjLG2z37EiBFqvyZ2Zffu3Wzw4MFqF7WKigpmaWnJvvji\nC+GcNl+Kx44dy1588cVu79en58DDw4O99dZb3T6no6Njp1+B3nzzTTZz5ky1c62trWq/3O7Zs4dJ\nJBKWnJzc43vqiBoHRIXqV3WGql+//fZbZm1tLXzp76hjHdGdlpYWNmLECLX/V4lEwl5++WW1dK6u\nrkJ9qlAomEQiYQkJCcL9SqWS2dnZdWoIavNaHfNtzZo1bPbs2WrnPvnkE42NAzs7O/a3v/1N7dyy\nZcvUGgfaXBeCg4PZ5MmThfvLy8uZubm5cM1Rxd1THacqt6WlpYyx7stpxy/S2pSPefPmMU9PT7U0\nGzduFP6nuqK6Hqu+NDPG2J07d9iYMWPY22+/LZzT5kvx7Nmz2WOPPdbt/fr0HDz++ONs3bp13T7n\nokWLhN4vFV2+Q+zbt6/H99SRGI0DmnPAocTERAwbNgyDBw+Gu7s7HB0d8eWXX6KmpgYlJSWYO3eu\nWvq5c+ciPz8fTU1N8PDwwOLFizF58mQ8+eSTiIiIQHFxcY+vd+PGDRQWFmLz5s0YNmyYcPP394dE\nIsHvv/8upJ06dWqPz/X7779DqVR2GWNmZqbaOW9vb415kZWV1eVzNTU1ITc3V+PjVdLS0jBixAhM\nmTKly/tTU1NRXl6O4cOHq+VBcnKy2vsHAE9PT+Hv0aNHw8zMDBUVFT2+fmpqKj788EO15540aRIk\nEgkUCoWQztXVFYMHD+7xuTIzMzFp0iS1saGjR4/GQw89hKysrB4f297169dRXFwMPz8/rR+jjU2b\nNuG9997DzJkzERwcjDNnzmh8TGpqKtLS0tTyx8rKCgUFBZ3yf/r06QaNl/QvVL/eY6j61c/PDxMm\nTMD48eOxatUq7Nq1C7du3dL4uLy8PDzzzDNwcnKCtbU1rK2tcfv27U4TZdvXuQDw4IMP4vr168J7\nAIA//OEPwv0WFhad6gltX6tjvmVnZ6s9NwD813/9V4/vq6amBqWlpV0+jrUb/67NdWHt2rXIzMzE\nhQsXAABffvklZDIZFi1a1O3rJyYmYvHixRg3bhysrKwwZ84cAEBBQUGPcXekbfnw8PBQSzNmzJge\nr4mZmZkYOXIkXFxchHMDBgzAjBkzOpVjTdLT0w1+DQsKCsI333wDd3d3bNq0CfHx8RrnLejyHUKb\n/02xmYsdAOls5syZiImJgbm5OR588EGYm7d9TDU1NRofK5VK8eOPPyI1NRUJCQk4ePAggoOD8fXX\nX+PRRx/t8jGtra0AgIiICPj4+HS6387ODkDbpM4hQ4bo+7Y6MeRz3a/W1la4urri8OHDne7r+GV9\nwIABXT6+J4wxBAcH45lnnul0n0wm6/a1eno+bc4ZmlQq7fQ6HSdOr1u3DkuWLEF8fDxOnz6NRx55\nBE888QT27t3b7fMyxrBo0SJ88sknne6ztrYW/jYzM+sy/wnRFtWvhjdkyBD8+uuvOHv2LBISErBz\n5068/vrrOHnyZLc/yAAQJjlHRkZi7NixsLCwwOzZsztNBNa3ztXntbrKt96qW7W5Lri6umLatGn4\n4osv4OXlhS+++AJPP/10txNUCwsL4e/vj8DAQLz11lt44IEHUFRUhEWLFvXKBGuJRNLp85FIJBo/\nn64wxnp94q021zA/Pz8UFhbi2LFjSExMxNNPPw13d3ecPHmy21W3dPkOwdN3n+5QzwGHBg0ahAkT\nJmDcuHHChQsArKysIJfLkZSUpJY+KSkJEyZMUFtFYvr06di6dSuSkpIwb9487NmzB8C9SralpUVI\nK5PJMHbsWFy5cgUTJkzodNNlFQRHR0cMHDiwyxjd3d21z4T/mDRpUpfPNXjwYEycOFHr55k2bRqq\nqqqQlpbW5f3Tp0/HtWvXMGzYsE7v39bWVuvX6Sp/Va9/+fLlLvNX14pi8uTJyMrKUvtlrqKiAjk5\nOZg8ebLWzzN69GjI5XIcO3ZM68fIZDKUlpaqnUtPT++UztbWFuvWrUNMTAx2796NL7/8EnV1dQDa\n8qi7/LGzs+uUP/ezSgUhHVH9eo+h6leg7UvXnDlzsG3bNqSlpWHMmDHYv38/gHv50v5L2a1bt5Cd\nnY3g4GD4+vrCxcUFAwcOFHoEetL+C6SbmxsA4OzZs8I5pVKptvTl/byWm5tbp/0M2r9WV6ysrGBn\nZ9cp3dmzZ9Vi1/a6EBgYiP379yM9PR2XLl3qcXWt1NRUNDU14aOPPsKsWbPg5OSE8vJytTTdXac6\nMmT56Pi8qs9E5c6dO0hJSdHpGga09bbpcg0bPXo0rl+/rtZ46eoaNmLECKxcuRI7d+7EDz/8gKSk\nJCHeAQMGdFplyFDfIXhBjYM+ZuvWrfj444+xe/duKBQK/Otf/8LOnTsREhICAPj555+xfft2nD9/\nHoWFhTh58iQuXbqESZMmAQDs7e0hlUrxww8/4Pr167h9+zYA4N1330VERATee+89XL58GVevXsXh\nw4fx3//938Jrs26WtWx/fvDgwXjppZfw97//Hd988w1ycnLw3nvv4ciRI0KMur7fgwcPYseOHcjJ\nycFXX32Fbdu24dVXX1W7sGuyYMECzJkzBytWrMCRI0eQl5eHs2fPIioqCgCwZs0ajB8/Ho8++ihO\nnDiB/Px8pKSkIDQ0FHFxcVq/zgMPPIChQ4fi2LFjKC8vR1VVFQDg7bffRlxcHF599VVcvHgRubm5\niI+Px4YNG3Dnzh2d8mT16tUYNWoUVqxYgQsXLiAtLQ0rV66EXC7HihUrdHquN998E//617/wzjvv\nIDs7G5mZmfjkk0+6HRKwaNEiXLlyBZGRkcjNzcWuXbvw9ddfq6V54YUX8OOPPyI3NxeZmZn49ttv\nMW7cOGE5xvHjxyM5ORlFRUW4efMmGGN44YUX0NLSgscffxzJycnIz89HcnIy3njjDZw7d06n9wQA\nVVVVuHjxIi5evAigrTv94sWLKCoq0vm5SP9B9at+9euRI0fw0UcfIS0tDYWFhTh06BCKioqEL+7j\nx48HAMTFxeHGjRuor6/HiBEjMGrUKPz73/+GQqHAuXPnsGrVKlhaWmp8vfZ54ujoiICAAPz1r39F\nYmIisrKysGHDBtTV1Qlp7ue1Nm/ejHPnzuFvf/sbcnJycOjQIa32nXj11VcRHh6Offv2QaFQ4J//\n/CdOnjyp9hn3dF1oamoS0q1atQpVVVV47rnnMHXqVCFfu+Lk5ASJRIL/+Z//QV5eHg4fPozt27er\npemunHakTfnortz2ZOHChfD29sbq1avx888/4/Lly1i7di2USiU2btwopNPmef/+97/jxx9/xObN\nm3Hp0iVcvXoVn3/+OXJycrpMv2DBAjQ0NOAf//gHcnNz8fXXXyMyMlItzRtvvIFDhw7h6tWrUCgU\n2LdvH4YNG4Zx48YBaCvPaWlpuHbtGm7evInm5maDfYdQqa+vF65hd+7cQVlZGS5evNhpiFKvMcrM\nBqK1rlaD6Ui11J6FhQWbOHEiCw8PF+7LzMxk/v7+whJc9vb27PXXXxcmDzHG2Pvvv8/s7OyYmZmZ\n2lJ7hw8fZrNmzWKDBw9mVlZWzNPTk23fvl24v+OqGd2dv3v3LgsODhaW2ps0aZKwWo2KLpNEY2Ji\nhKXUVJO82q/is2fPHrVJXt2pra1lL774IhszZgwbMGAAGz9+vNoqELdu3WIbN24U4razs2NPPvkk\nu3jxImOsbTKRVCplJSUlas9rbm6utlToF198wcaPH8/Mzc3VljI9c+YMW7RoERs2bBgbMmQIc3V1\nZZs3bxYmMGnz2atcvXq101KmqqXbVLTN4y+//JJ5eHiwgQMHspEjR7I//vGP7Pbt293G9O677zI7\nOzs2dOhQtnr1avbpp5+qLXH417/+lTk7OzNLS0vh+bKysoT7f/31VzZlyhRmaWnJpFKpMAmsoKCA\nrVmzho0aNUoou88884ww+VPbz1mVtv3yix2XUCT9E9WvnRmifv3pp5/YggUL2KhRo9igQYOYs7Nz\npxV2Nm3axEaPHq32f5iUlCQs7+ri4sIOHjzYacGCrt5Lxwmh7ZcyHTVqFAsJCem0MpW+r8VY29Kh\nEydOZAMHDmQzZ85kcXFxTCqValzKNCQkhD3wwANsyJAh7E9/+hP78MMPO+WlpuuCyhNPPMGkUimL\niIjo9Fod4/7000/Z2LFjmaWlJZszZw6Lj49nUqlUbaGMrsrpW2+91WklH03lo6ty+84776hd+7pS\nVlbGVq5cqbaUaccFQ7SdiHvs2DE2a9YsZmlpyaytrdmCBQtYXl5et+8pOjqaTZgwgVlaWjJ/f38W\nGxurdi3avn07mzx5Mhs6dCiztrZm8+fPV/usr127xubOncuGDh2qlq/6fofoSvslgNtfw9rXKb1J\nwph+g+nCw8Oxe/duMMbw/PPP4+WXX0ZlZSVWrFiBgoICODg44KuvvhI2XwoNDUV0dDTMzMwQEREh\nTCBJS0vDunXr0NTUBH9/f4SHhxuu5UMIIcQg1q9fjx9++AGjR49GRkYGABi0zr9z5w7Wrl2L9PR0\njBw5EgcOHIC9vb04b5YQQvoxvYYVXb58Gbt370Zqaip+++03fP/998jNzUVYWBh8fX2Rk5ODhQsX\nIiwsDEDbjPcDBw4gKysL8fHxCAoKErqLNm7ciKioKCgUCigUCsTHxxvu3RFCCDGIZ599tlP9bMg6\nPyoqCiNHjoRCocDmzZuxZcsW475BQgghAPRsHFy5cgUzZszAoEGDYGZmhnnz5uHgwYM4cuQIAgMD\nAbRNoFHN2o6Li8OqVatgYWEBBwcHODo6IiUlBWVlZaitrRWWdVq7dm2XM70JIYSIa86cORgxYoTa\nOUPW+e2f66mnnsLJkyeN9dYIIYS0o1fjYPLkyThz5gwqKyvR0NCAo0ePori4GBUVFcLyWzKZTFjn\ntrS0FHK5XHi8XC5HSUlJp/N2dnYoKSm5n/dDCCHESAxZ55eUlGDs2LEAAHNzc1hbW6OystJYb4UQ\nQsh/6LXPgYuLC7Zs2QI/Pz8MGTIEnp6eMDMzU0sjkUgMtl7t//3f/6mtBU8IIaRndXV1ePzxx432\neoas83tC1wNCCNGNrtcDvTdBW79+PdavXw+gbdknuVwOmUyG8vJy2NraoqysDKNHjwbQ9utQ+yUE\ni4uLIZfLYWdnp7a7ZHFxsbAhTHsymazHjVT6k6CgoE7LbvVXlBf3UF60oXy4p6u1uw3NEHW+qifB\nzs4OhYWFePDBB9Hc3Izbt2+r7QLe/jV5ux7wWO4oJu3wGBPAZ1wUk3Z4jEnX64He+xyoNg8pLCzE\nt99+i9WrVyMgIAAxMTEAgJiYGCxduhQAEBAQgNjYWCiVSuTl5UGhUMDb2xu2trawsrJCSkoKGGPY\nu3ev8BhCCCF8M0Sdr/o1q/1zffPNN1i4cKE4b4oQQvo5vXsOli1bhlu3bsHCwgKRkZGwtrZGcHAw\nli9fjqioKGFZO6Bth8Hly5fDzc0N5ubmiIyMFLqfIyMjsW7dOjQ2NsLf3x9LliwxzDszUapNOAjl\nRXuUF20oH3rPqlWrkJSUhJs3b2Ls2LF4++23DVrnP/fcc3jmmWfg5OSEkSNHIjY2VrT3qiseyx3F\npB0eYwL4jIti0g6PMelK78bBTz/91OmcjY0NEhISukwfEhLS5Q6OU6dOFdbMJprNnj1b7BC4QXlx\nD+VFG8qH3rN///4uzxuqzh84cKDQuOhreCx3FJN2eIwJ4DMuikk7PMakK70bB4SIrbTmDrb+2PNW\n4qOGWODPM+wwdCAVdUIIIYQQTegbE+FO490WRKeWorxW2WO6rN8qUDuq84TF9sZaDzRkaIQQQggh\nJk3CVNtW6ig0NBT79u2DVCqFu7s79uzZg/r6eqxYsQIFBQXC+NPhw4cL6aOjo2FmZoaIiAj4+fkB\nANLS0rBu3To0NTXB398f4eHhnV7r5MmT3K1OQdTV32lGVVOzxnS3G5uRXlLbYxoG4JuM62hqbr3v\nuMZaD0R4gDP1HJB+Jz093SQn9dL1gC/K5lYoWzTX1WZSCSwtzDSmI4QYnq7XA72+MeXn52PXrl3I\nzs7GwIEDsWLFCsTGxiIzMxO+vr54/fXXsWPHDoSFhSEsLAxZWVk4cOAAsrKyUFJSgkWLFkGhUEAi\nkWDjxo2IioqCt7c3/P39ER8fT5OS+6A6ZQv+fPAKmlv1amsSQgjpg67XKfFmwjWN6V78w1h4PjhM\nY7ry2juoaWrRmG7UEAuMGGyhVYyEEN3o1TiwsrKChYUFGhoaYGZmhoaGBjz44IMIDQ1FUlISACAw\nMBDz589HWFgY4uLisGrVKlhYWMDBwQGOjo5ISUmBvb09amtr4e3tDQBYu3YtDh8+TI2DHiQnJ5vE\nZBdDqMm9CKuJnmKHwQUqF20oH4gYeCx3xoqJASiqvqMx3aWyOqSe+xkPT5/ZY7rfbzUgJq1c4/Pt\nfsrVII0DHj87gM+4KCbt8BiTrvRqHNjY2ODVV1/FuHHjYGlpicWLF8PX1xcVFRXCzpUymQwVFRUA\ngNLSUsycea9CkMvlKCkpgYWFhbABDtC2CU5JScn9vB9CCCGEcGbfhXLU5JbCqkpzL4M2LpXXIb+q\nscc0ZlIJJsmGYLgl9TAQogu9Gge5ubn46KOPkJ+fD2tra/zpT3/Cvn371NJIJBJhXWtDCAoKEtaO\ntba2hru7u9AyS05OBoB+cTx79myu4lEdVzXcBTACQNsv+gCEX/XFPj7381lYWphxlV+9cazCSzz0\n/2H8zz85ORmFhYUAgA0bNoAYB4+/EvIYkyF7eiPOFmlMM9hCil1PufaYhsd8AviMi2LSDo8x6Uqv\nCckHDhzAiRMnsHv3bgDA3r178csvv+DUqVM4ffo0bG1tUVZWBh8fH1y5cgVhYWEAgODgYADAIpf0\nawAAIABJREFUkiVLsG3bNtjb28PHxwfZ2dkA2tbRTkpKws6dO9Vejyag8a+i9g6e/TqbuzkHNCGZ\n9Fc0IZkYQ1F1E577JlvsMLqkahyMGjpA7FAIEZWu1wOpPi/i4uKCX375BY2NjWCMISEhAW5ubnjs\nsccQExMDAIiJicHSpUsBAAEBAYiNjYVSqUReXh4UCgW8vb1ha2sLKysrpKSkgDGGvXv3Co8hXev4\nK7Ex1CmbUdvU881MarheIm2pegiIOOWCR5QPRAw8ljseY+KxzuYxnwA+46KYtMNjTLrS6+dUDw8P\nrF27FtOmTYNUKsWUKVPw5z//GbW1tVi+fDmioqKEpUwBwM3NDcuXL4ebmxvMzc0RGRkpDDmKjIzE\nunXr0NjYCH9/f5qMzKHkvGrE/na9xzQtrYy7XgNCCCH6UTa3ovaO5uWpRfhdiBDSy/Te58CYqBtZ\nXF9fqsCu86Vih6EXGlZE+itjDiuifW9Mz816Jf7fDwrU3ul5WdGWVoaGu/e/J01voGFFhLQxyrAi\nQgghBLi37016ejoyMjLQ0tKC2NhYhIWFwdfXFzk5OVi4cKEw96z9vjfx8fEICgqC6jcq1b43CoUC\nCoUC8fHxYr61fq/2TovGG68NA0KI/qhx0MeYwlg2Q9Fm/Oqthrs4V3AbCYrKHm8FVU1GiLj3ULlo\nQ/lgfO33vWlubhb2vTly5AgCAwMBtO17c/jwYQDodt+bsrKyLve96Qt4LHc8xkRzDrTHY1wUk3Z4\njElXeo21uHr1KlauXCkcX7t2Ddu3b8fTTz/dK93IhOir4W4rPvipUGO6NxY4wH7EICNERIhpoX1v\nCCHEtOjVOHjooYdw4cIFAEBrayvs7OzwxBNPCN3Ir7/+Onbs2IGwsDCEhYWpdSOXlJRg0aJFUCgU\nkEgkQjeyt7c3/P39ER8fT5OSe2AK6+caCu2OfA+VizaUD8ZH+96Y5j4jLl5tPTiG3HfGaqKn0fe5\nSTl3FsMtLbp9v6pzYud3XzjmcR8Z1Tle4uGlPlD9re++N/c9Ifn48ePYvn07zpw5AxcXFyQlJUEm\nk6G8vBzz58/HlStXEBoaCqlUii1btgBo2+fgrbfegr29PRYsWCDscxAbG4vExETa54AzfXlCsra2\n+tjDc8wwjekGDzDDQHMajUf4Z6wJybTvjWm6Wa/EX769onFCMs9oQjIhbYw+ITk2NharVq0CgB67\nkdt3F6u6kTuep25kzQw5lq3xbguqGu72eKtubOZ2iVJDjl/98EwRgg5f1XirarxrsNc0JFMY42gI\nlA/GR/ve8FnueIyJ5hxoj8e4KCbt8BiTru5rfUelUonvvvsOO3bs6HRff+hG7uvHtq5T8I9j13Ar\np22I2EhnLwDodFx4+Vc0M2a0bmBtj1UM8Xw1OqTn5fNrf5yRkcFVPHTc97qR9UX73hBCiGm5r2FF\ncXFx+Oyzz4Tl5lxcXJCYmEjdyH2E4mYD/nr4qthh9ClfrHCD7bCBYodBiEbG3OfAmOh6YBymMqxo\n9zJXPDCEhhWR/k3X68F99Rzs379fGFIEtHUXx8TEYMuWLZ26kVevXo1XXnkFJSUlQjeyRCIRupG9\nvb2xd+9evPTSS/cTEiGEEEIImppbkXitCgPNeh5BbTXIHDPGWmGQhZmRIiOEb3rPOaivr0dCQgKe\nfPJJ4VxwcDBOnDgBZ2dnnDp1SugpaN+N/Mgjj3TqRt6wYQOcnJzg6OhI3cgamMJYNkPhcfyqWKhc\ntKF8IGLgsdzxGJOx6+xWBvw7pRQf/1zc7e3dvd/j/y6Wg7epdTx+fhSTdniMSVd69xwMGTIEN2/e\nVDtnY2ODhISELtOHhIQgJCSk0/mpU6ciIyND3zAIIYQQQvTW3MLQeLcFtXeae0wnkUgwmlY+Iv3A\nfQ0rIsbXfm3f/o72ObiHykUbygciBh7LHY8x8VhnW030RNHtO3g6NlNj2nkTRiDYx6HXYwL4/Pwo\nJu3wGJOu9B5WVF1djWXLlsHV1RVubm5ISUlBZWUlfH194ezsDD8/P1RXVwvpQ0ND4eTkBBcXFxw/\nflw4n5aWBnd3dzg5OeHll1++v3dDCCGEEKKjFqbNjbOxR4T0Er0bBy+//DL8/f2RnZ2NS5cuwcXF\nRdghOScnBwsXLhRWKWq/Q3J8fDyCgoKgWiRJtUOyQqGAQqEQVj4iXTOFsWyGQnMO7qFy0YbygYiB\nx3LHY0w81tk8xgTw+flRTNrhMSZd6dU4uH37Ns6cOYP169cDAMzNzWFtbY0jR44gMDAQABAYGIjD\nhw8DaFvydNWqVbCwsICDgwMcHR2RkpKCsrIy1NbWwtu7bZv2tWvXCo8hhBBCCCGEGJdejYO8vDyM\nGjUKzz77LKZMmYLnn38e9fX1tEOyEZjCWDZD4XH8qlioXLShfCBi4LHc8RgTj3U2jzEBfH5+FJN2\neIxJV3o1Dpqbm5Geno6goCCkp6djyJAhwhAiFUPvkEwIIYQQQgjpXXqtViSXyyGXyzF9+nQAwLJl\nyxAaGgpbW1uUl5cLOySPHj0aQFuPQFFRkfD44uJiyOVy2NnZobi4WO28nZ1dl68ZFBSEcePGAQCs\nra3h7u4utM5U47v6w3H7sWz3+3wyl7ZdRlVjLlW/oPSVY9U5Y78+T+VBdZyRkYGNGzdyE49Yx4b8\n/+hrx6q/CwsLAQAbNmwAMY7k5GTufi3kMaaa3Ivc/VLPY0wAn58fxaQdHmPSlYQx/abfz507F7t3\n74azszPeeustNDQ0AABGjhyJLVu2ICwsDNXV1QgLC0NWVhZWr16N8+fPo6SkBIsWLcLvv/8OiUSC\nGTNmICIiAt7e3nj00Ufx0ksvddoI7eTJk5gyZcr9v1sTYMhCp7jZgL8evmqQ5xKDGJX6FyvcYDts\noFFfUxumUBkZAuXDPenp6Vi4cKHYYRgcj9cDHstddzHdaW7BxdI61Clbenx8cwtD+NkiNBtwdzAe\nv4jrEtO8CcPxxoLxvRxRm75UpsREMWlH1+uB3vscfPzxx1izZg2USiUmTpyIPXv2oKWlBcuXL0dU\nVBQcHBzw1VdfAVDfIdnc3LzTDsnr1q1DY2Mj/P39aYdkDXgrcGIS4yIjlUhQWX+35zRSYLilhZEi\nakPlog3lgziqq6uxYcMGZGZmQiKRYM+ePXBycsKKFStQUFAgXA+GDx8OoG1p6+joaJiZmSEiIgJ+\nfn4A2pa2XrduHZqamuDv74/w8HAx35bWeCx33cXEGPB5WhlybzUaOSI+x/fzGBPQt8qUmCim3qF3\nz4Ex8fhLkSno6z0HYhg20Axm0p7n0qx8WIYn3UcbKSJCumbMnoPAwEDMmzcP69evR3NzM+rr6/Hu\nu+/igQcewOuvv44dO3agqqpKrSc5NTVV6ElWKBSQSCTw9vbGJ598Am9vb/j7+1NPci9outuCzd8r\nRGkc9HWOIy3xvLedxt6UB4ZYYLyNpZGiIkQzXa8Heu9zQMRhCuvnGooY61PX3mlBdWNzj7fG5laj\nx0Xlog3lg/HR0tZ8ljseY+JxTwFdYvr9ViO2/Pg73jiW2+MtpfD2fcfF4+dHMWmHx5h0RY2Dfmyg\nOX38hJD7Q0tbE0KIadF7zoGDgwOsrKxgZmYGCwsLnD9/HpWVlf1mjKlYtB3LtufXUmRV1PeYRtOE\nNN7xOlZUDKYwxtEQKB+MT7W09SeffILp06dj06ZNvb60NY+r16nwsnpVd8c/nz2L61eKgVGuAIy7\n2pwYq8tpOladM+Tz55gXAZ4BAMT/vA153H5FOB7iUWk/AVjseHipD1R/67t6nd5zDsaPH4+0tDTY\n2NgI515//XUaY8qJfxzPxS+FNWKH0S8FTh2DNV62YodB+jljzTkoLy/HrFmzkJeXB6DtghQaGopr\n167h9OnTwtLWPj4+uHLlitBwCA4OBgAsWbIE27Ztg729PXx8fJCdnQ0A2L9/P5KSkrBz506116Pr\nwf2hOQe9b/20MVjpSdcAwg+jzjno2K7oT2NMxWIKY9kMhcfxq2KhctGG8sH4bG1tMXbsWOTk5AAA\nEhISMGnSJDz22GOIiYkBAMTExGDp0qUAgICAAMTGxkKpVCIvLw8KhQLe3t6wtbWFlZUVUlJSwBjD\n3r17hcfwjsdyx2NMPNbZPMYE8Pn5UUza4TEmXek9rEgikWDRokUwMzPDX/7yFzz//PM9jjGdOXOm\n8FjVGFMLCwsaY0oIIX0cLW1NCCGmQ+/GwdmzZzFmzBjcuHEDvr6+cHFxUbu/P4wx5XnMX3FmKTDM\nCYD4Yzr727Hi4nkk19v0uzGOPBzzOCa2r4wxvR8eHh5ITU3tdD4hIaHL9CEhIQgJCel0furUqcjI\nyDB4fL2Nx7kuPMbE4zwxHmMC+Pz8KCbt8BiTrgyyz8G2bdswdOhQ7Nq1C4mJiTTGlAM050A8NOeA\n8IB2SCZdoTkHvY/mHBDeGGXOQUNDA2prawEA9fX1OH78ONzd3REQENBvxpiKxRTGshkKr2NFsyvq\nkVJ4G79ouJXV3DHYa1K5aEP5QMTAY7njMSYe62weYwL4/PwoJu3wGJOu9BpWVFFRgSeeeAJA2zJ2\na9asgZ+fH6ZNm0ZjTEm/d764BueLNffafPy4M8ZgoBEiIoQQQgjRjkGGFfU26kbWHQ0r4t/Hjzvj\noVFDxA6DmCgaVkS6QsOKeh8NKyK8MepSpoQQQgjpQwy4UAghxDRR46CPOXL8NBQ3G3q8FVQ14XZT\ns9ih9jpex4qKwRTGOBoC5QMRAy/lLq24Boczb+Bw5g2E7fte+Lv97ccrN1FeqxQlPh7rbB5jAvgp\nU+1RTNrhMSZd6b2UKQC0tLRg2rRpkMvl+O6771BZWYkVK1agoKBAmHMwfPhwAEBoaCiio6NhZmaG\niIgI+Pn5AQDS0tKwbt06NDU1wd/fH+Hh4ff/rkzYzXol/nr4qthhEEII4UyCohInc6sAADW5N2DV\nVCxyRP1T/NVbWv1AN3/CCDw0moaWEv7cV89BeHg43NzchMnFYWFh8PX1RU5ODhYuXCgsYZqVlYUD\nBw4gKysL8fHxCAoKEnZX3rhxI6KioqBQKKBQKBAfH3+fb8m0eUyfJXYI3OB1fWoxmMK6yoZA+UDE\nwGO547F+7C8xldYqcfDyDY23kh5WrOOxTFFM2uExJl3p3TgoLi7G0aNHsWHDBuGL/pEjRxAYGAgA\nCAwMxOHDhwEAcXFxWLVqFSwsLODg4ABHR0ekpKSgrKwMtbW18Pb2BgCsXbtWeAwhhBBCCCHEuPRu\nHGzevBkffPABpNJ7T1FRUQGZTAYAkMlkqKioAACUlpZCLpcL6eRyOUpKSjqdt7OzQ0lJib4h9Qu/\npZ4TOwRu8DpWVAymMMbRECgfiBh4LHc81o8Uk/Z4LFMUk3Z4jElXes05+P777zF69Gh4eXkhMTGx\nyzQSiUQYbmQIQUFBGDduHADA2toa7u7uQteN6oPoL8eqykzVHdpfj1V4iUfX4wFmLgAMUz4yMjK4\nKZ90LM6x6u/CwkIAwIYNG0AIIYToSq99DkJCQrB3716Ym5ujqakJNTU1ePLJJ5GamorExETY2tqi\nrKwMPj4+uHLlijD3IDg4GACwZMkSbNu2Dfb29vDx8UF2djYAYP/+/UhKSsLOnTvVXo/Wtb4nrbgG\nW+NzxQ6DGIDLqMEYbtlz+3yCjSXWTXvQSBERU2LsfQ6MtUAFXQ+6t+N0vjAhmfAveL49FjjaiB0G\n6QeMss/Be++9h6KiIuTl5SE2NhYLFizA3r17ERAQgJiYGABATEwMli5dCgAICAhAbGwslEol8vLy\noFAo4O3tDVtbW1hZWSElJQWMMezdu1d4DCGm7sqNBvxSWNPjLauiXuwwCdEKLVBBCCGmwSD7HKgu\nBsHBwThx4gScnZ1x6tQpoafAzc0Ny5cvh5ubGx555BFERkYKj4mMjMSGDRvg5OQER0dHLFmyxBAh\nmSyac3APr2NFxWAKYxwNgfJBHP19gQoeyx2P9SPFpD0eyxTFpB0eY9LVfe1zAADz5s3DvHnzAAA2\nNjZISEjoMl1ISAhCQkI6nZ86dSoyMjLuNwxCCCEiUS1QUVNTI5zraYGKmTNnCul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+ "text": [ + "" + ] + } + ], + "prompt_number": 51 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The MCMC algorithm has proposed that the most likely centers of the two clusters are near 120 and 200 respectively. Similar inference can be applied to the standard deviation. \n", + "\n", + "We are also given the posterior distributions for the labels of the data point, which is present in `mcmc.trace(\"assignment\")`. Below is a visualization of this. The y-axis represents a subsample of the posterior labels for each data point. The x-axis are the sorted values of the data points. A red square is an assignment to cluster 1, and a blue square is an assignment to cluster 0. " + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import matplotlib as mpl\n", + "figsize(12.5, 4.5)\n", + "plt.cmap = mpl.colors.ListedColormap(colors)\n", + "plt.imshow(mcmc.trace(\"assignment\")[::400, np.argsort(data)],\n", + " cmap=plt.cmap, aspect=.4, alpha=.9)\n", + "plt.xticks(np.arange(0, data.shape[0], 40),\n", + " [\"%.2f\" % s for s in np.sort(data)[::40]])\n", + "plt.ylabel(\"posterior sample\")\n", + "plt.xlabel(\"value of $i$th data point\")\n", + "plt.title(\"Posterior labels of data points\")\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "display_data", + "png": 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+sZtpGUudn6W0u43c0UEGquvpr64nrE1EFbvSM2m58z4cjScIGE23neN9M1BG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+ "text": [ + "" + ] + } + ], + "prompt_number": 58 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Looking at the above plot, it appears that the most uncertainty is between 150 and 170. The above plot slightly misrepresents things, as the x-axis is not a true scale (it displays the value of the $i$th sorted data point.) A more clear diagram is below, where we have estimated the *frequency* of each data point belonging to the labels 0 and 1. " + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "cmap = mpl.colors.LinearSegmentedColormap.from_list(\"BMH\", colors)\n", + "assign_trace = mcmc.trace(\"assignment\")[:]\n", + "plt.scatter(data, 1 - assign_trace.mean(axis=0), cmap=cmap,\n", + " c=assign_trace.mean(axis=0), s=50)\n", + "plt.ylim(-0.05, 1.05)\n", + "plt.xlim(35, 300)\n", + "plt.title(\"Probability of data point belonging to cluster 0\")\n", + "plt.ylabel(\"probability\")\n", + "plt.xlabel(\"value of data point\")\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "pyout", + "prompt_number": 60, + "text": [ + "" + ] + }, + { + "metadata": {}, + "output_type": "display_data", + "png": 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qiipceHExyv+6AJ+pTyD3hwOovZxuWK/Kyoe+QQ3bsADwJWJcWfUNMr7YgcJ9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+ "text": [ + "" + ] + } + ], + "prompt_number": 60 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Even though we modeled the clusters using Normal distributions, we didn't get just a single Normal distribution that *best* fits the data (whatever our definition of best is), but a distribution of values for the Normal's parameters. How can we choose just a single pair of values for the mean and variance and determine a *sorta-best-fit* gaussian? \n", + "\n", + "One quick and dirty way (which has nice theoretical properties we will see in Chapter 5), is to use the *mean* of the posterior distributions. Below we overlay the Normal density functions, using the mean of the posterior distributions as the chosen parameters, with our observed data:" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "norm = stats.norm\n", + "x = np.linspace(20, 300, 500)\n", + "posterior_center_means = center_trace.mean(axis=0)\n", + "posterior_std_means = std_trace.mean(axis=0)\n", + "posterior_p_mean = mcmc.trace(\"p\")[:].mean()\n", + "\n", + "plt.hist(data, bins=20, histtype=\"step\", normed=True, color=\"k\",\n", + " lw=2, label=\"histogram of data\")\n", + "y = posterior_p_mean * norm.pdf(x, loc=posterior_center_means[0],\n", + " scale=posterior_std_means[0])\n", + "plt.plot(x, y, label=\"Cluster 0 (using posterior-mean parameters)\", lw=3)\n", + "plt.fill_between(x, y, color=colors[1], alpha=0.3)\n", + "\n", + "y = (1 - posterior_p_mean) * norm.pdf(x, loc=posterior_center_means[1],\n", + " scale=posterior_std_means[1])\n", + "plt.plot(x, y, label=\"Cluster 1 (using posterior-mean parameters)\", lw=3)\n", + "plt.fill_between(x, y, color=colors[0], alpha=0.3)\n", + "\n", + "plt.legend(loc=\"upper left\")\n", + "plt.title(\"Visualizing Clusters using posterior-mean parameters\")\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "pyout", + "prompt_number": 61, + "text": [ + "" + ] + }, + { + "metadata": {}, + "output_type": "display_data", + "png": 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Eh4d/cDmUD4OOUYo0dBvJT4y/vz+mT5/e3GI0CefOncPEiRM/uByBQPCfOqAi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\nykGtbdJB7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+ "text": [ + "" + ] + } + ], + "prompt_number": 61 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Important: Don't mix posterior samples\n", + "\n", + "In the above example, a possible (though less likely) scenario is that cluster 0 has a very large standard deviation, and cluster 1 has a small standard deviation. This would still satisfy the evidence, albeit less so than our original inference. Alternatively, it would be incredibly unlikely for *both* distributions to have a small standard deviation, as the data does not support this hypothesis at all. Thus the two standard deviations are *dependent* on each other: if one is small, the other must be large. In fact, *all* the unknowns are related in a similar manner. For example, if a standard deviation is large, the mean has a wider possible space of realizations. Conversely, a small standard deviation restricts the mean to a small area. \n", + "\n", + "During MCMC, we are returned vectors representing samples from the unknown posteriors. Elements of different vectors cannot be used together, as this would break the above logic: perhaps a sample has returned that cluster 1 has a small standard deviation, hence all the other variables in that sample would incorporate that and be adjusted accordingly. It is easy to avoid this problem though, just make sure you are indexing traces correctly. \n", + "\n", + "Another small example to illustrate the point. Suppose two variables, $x$ and $y$, are related by $x+y=10$. We model $x$ as a Normal random variable with mean 4 and explore 500 samples. " + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import pymc as pm\n", + "\n", + "x = pm.Normal(\"x\", 4, 10)\n", + "y = pm.Lambda(\"y\", lambda x=x: 10 - x, trace=True)\n", + "\n", + "ex_mcmc = pm.MCMC(pm.Model([x, y]))\n", + "ex_mcmc.sample(500)\n", + "\n", + "plt.plot(ex_mcmc.trace(\"x\")[:])\n", + "plt.plot(ex_mcmc.trace(\"y\")[:])\n", + "plt.title(\"Displaying (extreme) case of dependence between unknowns\")\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + " \r", + "[****************100%******************] 500 of 500 complete" + ] + }, + { + "metadata": {}, + "output_type": "pyout", + "prompt_number": 62, + "text": [ + "" + ] + }, + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "\n" + ] + }, + { + "metadata": {}, + "output_type": "display_data", + "png": 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AIBAIBDWMkIsIBAKBQCAQCAQqCLmIQCAQCAQCgUBwCSGMbEGdIrRwAn8RdUUQ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TRBggfJbqN97sTfXwUATY08EC/DSBZkC0ZDnFxAq92wwTxx5hgsWBJDkCTYFSvP9rfeB6JROCaN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\nyC7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+ "text": [ + "" + ] + } + ], + "prompt_number": 62 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "As you can see, the two variables are not unrelated, and it would be wrong to add the $i$th sample of $x$ to the $j$th sample of $y$, unless $i = j$." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "#### Returning to Clustering: Prediction\n", + "The above clustering can be generalized to $k$ clusters. Choosing $k=2$ allowed us to visualize the MCMC better, and examine some very interesting plots. \n", + "\n", + "What about prediction? Suppose we observe a new data point, say $x = 175$, and we wish to label it to a cluster. It is foolish to simply assign it to the *closer* cluster center, as this ignores the standard deviation of the clusters, and we have seen from the plots above that this consideration is very important. More formally: we are interested in the *probability* (as we cannot be certain about labels) of assigning $x=175$ to cluster 1. Denote the assignment of $x$ as $L_x$, which is equal to 0 or 1, and we are interested in $P(L_x = 1 \\;|\\; x = 175 )$. \n", + "\n", + "A naive method to compute this is to re-run the above MCMC with the additional data point appended. The disadvantage with this method is that it will be slow to infer for each novel data point. Alternatively, we can try a *less precise*, but much quicker method. \n", + "\n", + "We will use Bayes Theorem for this. If you recall, Bayes Theorem looks like:\n", + "\n", + "$$ P( A | X ) = \\frac{ P( X | A )P(A) }{P(X) }$$\n", + "\n", + "In our case, $A$ represents $L_x = 1$ and $X$ is the evidence we have: we observe that $x = 175$. For a particular sample set of parameters for our posterior distribution, $( \\mu_0, \\sigma_0, \\mu_1, \\sigma_1, p)$, we are interested in asking \"Is the probability that $x$ is in cluster 1 *greater* than the probability it is in cluster 0?\", where the probability is dependent on the chosen parameters.\n", + "\n", + "\\begin{align}\n", + "& P(L_x = 1| x = 175 ) \\gt P(L_x = 0| x = 175 ) \\\\\\\\[5pt]\n", + "& \\frac{ P( x=175 | L_x = 1 )P( L_x = 1 ) }{P(x = 175) } \\gt \\frac{ P( x=175 | L_x = 0 )P( L_x = 0 )}{P(x = 175) }\n", + "\\end{align}\n", + "\n", + "As the denominators are equal, they can be ignored (and good riddance, because computing the quantity $P(x = 175)$ can be difficult). \n", + "\n", + "$$ P( x=175 | L_x = 1 )P( L_x = 1 ) \\gt P( x=175 | L_x = 0 )P( L_x = 0 ) $$\n", + "\n", + "\n", + "\n", + "\n", + "\n" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "norm_pdf = stats.norm.pdf\n", + "p_trace = mcmc.trace(\"p\")[:]\n", + "x = 175\n", + "\n", + "v = p_trace * norm_pdf(x, loc=center_trace[:, 0], scale=std_trace[:, 0]) > \\\n", + " (1 - p_trace) * norm_pdf(x, loc=center_trace[:, 1], scale=std_trace[:, 1])\n", + "\n", + "print \"Probability of belonging to cluster 1:\", v.mean()\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Probability of belonging to cluster 1: 0.025\n" + ] + } + ], + "prompt_number": 63 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Giving us a probability instead of a label is a very useful thing. Instead of the naive \n", + "\n", + " L = 1 if prob > 0.5 else 0\n", + "\n", + "we can optimize our guesses using a *loss function*, which the entire fifth chapter is devoted to. \n", + "\n", + "\n", + "### Using `MAP` to improve convergence\n", + "\n", + "If you ran the above example yourself, you may have noticed that our results were not consistent: perhaps your cluster division was more scattered, or perhaps less scattered. The problem is that our traces are a function of the *starting values* of the MCMC algorithm. \n", + "\n", + "It can be mathematically shown that letting the MCMC run long enough, by performing many steps, the algorithm *should forget its initial position*. In fact, this is what it means to say the MCMC converged (in practice though we can never achieve total convergence). Hence if we observe different posterior analysis, it is likely because our MCMC has not fully converged yet, and we should not use samples from it yet (we should use a larger burn-in period ).\n", + "\n", + "In fact, poor starting values can prevent any convergence, or significantly slow it down. Ideally, we would like to have the chain start at the *peak* of our landscape, as this is exactly where the posterior distributions exist. Hence, if we started at the \"peak\", we could avoid a lengthy burn-in period and incorrect inference. Generally, we call this \"peak\" the *maximum a posterior* or, more simply, the *MAP*.\n", + "\n", + "Of course, we do not know where the MAP is. PyMC provides an object that will approximate, if not find, the MAP location. In the PyMC main namespace is the `MAP` object that accepts a PyMC `Model` instance. Calling `.fit()` from the `MAP` instance sets the variables in the model to their MAP values.\n", + "\n", + " map_ = pm.MAP( model )\n", + " map_.fit()\n", + "\n", + "The `MAP.fit()` methods has the flexibility of allowing the user to choose which optimization algorithm to use (after all, this is a optimization problem: we are looking for the values that maximize our landscape), as not all optimization algorithms are created equal. The default optimization algorithm in the call to `fit` is scipy's `fmin` algorithm (which attempts to minimize the *negative of the landscape*). An alternative algorithm that is available is Powell's Method, a favourite of PyMC blogger [Abraham Flaxman](http://healthyalgorithms.com/) [1], by calling `fit(method='fmin_powell')`. From my experience, I use the default, but if my convergence is slow or not guaranteed, I experiment with Powell's method. \n", + "\n", + "The MAP can also be used as a solution to the inference problem, as mathematically it is the *most likely* value for the unknowns. But as mentioned earlier in this chapter, this location ignores the uncertainty and doesn't return a distribution.\n", + "\n", + "Most often it is a good idea, and rarely a bad idea, to prepend your call to `mcmc` with a call to `MAP(model).fit()`. The intermediate call to `fit` is hardly computationally intensive, and will save you time later due to a shorter burn-in period. \n", + "\n", + "#### Speaking of the burn-in period\n", + "\n", + "It is still a good idea to provide a burn-in period, even if we are using `MAP` prior to calling `MCMC.sample`, just to be safe. We can have PyMC automatically discard the first $n$ samples by specifying the `burn` parameter in the call to `sample`. As one does not know when the chain has fully converged, I like to assign the first *half* of my samples to be discarded, sometimes up to 90% of my samples for longer runs. To continue the clustering example from above, my new code would look something like:\n", + "\n", + " model = pm.Model( [p, assignment, taus, centers ] )\n", + "\n", + " map_ = pm.MAP( model )\n", + " map_.fit() #stores the fitted variables' values in foo.value\n", + "\n", + " mcmc = pm.MCMC( model )\n", + " mcmc.sample( 100000, 50000 )\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Diagnosing Convergence\n", + "\n", + "### Autocorrelation\n", + "\n", + "Autocorrelation is a measure of how related a series of numbers is with itself. A measurement of 1.0 is perfect positive autocorrelation, 0 no autocorrelation, and -1 is perfect negative correlation. If you are familiar with standard *correlation*, then autocorrelation is just how correlated a series, $x_\\tau$, at time $t$ is with the series at time $t-k$:\n", + "\n", + "$$R(k) = Corr( x_t, x_{t-k} ) $$\n", + "\n", + "For example, consider the two series:\n", + "\n", + "$$x_t \\sim \\text{Normal}(0,1), \\;\\; x_0 = 0$$\n", + "$$y_t \\sim \\text{Normal}(y_{t-1}, 1 ), \\;\\; y_0 = 0$$\n", + "\n", + "which have example paths like:" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "figsize(12.5, 4)\n", + "\n", + "import pymc as pm\n", + "x_t = pm.rnormal(0, 1, 200)\n", + "x_t[0] = 0\n", + "y_t = np.zeros(200)\n", + "for i in range(1, 200):\n", + " y_t[i] = pm.rnormal(y_t[i - 1], 1)\n", + "\n", + "plt.plot(y_t, label=\"$y_t$\", lw=3)\n", + "plt.plot(x_t, label=\"$x_t$\", lw=3)\n", + "plt.xlabel(\"time, $t$\")\n", + "plt.legend()\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "display_data", + "png": 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p5KEeHgmSNsFy9eL1Bx+Pv3x946AOFpsdMiktiEwIIeGMztKE+OCadDJdLMviO+9dwdPH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\nZk8ftxzHKSZSgilHsTFuDAJKY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+ "text": [ + "" + ] + } + ], + "prompt_number": 65 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "One way to think of autocorrelation is \"If I know the position of the series at time $s$, can it help me know where I am at time $t$?\" In the series $x_t$, the answer is No. By construction, $x_t$ are random variables. If I told you that $x_2 = 0.5$, could you give me a better guess about $x_3$? No.\n", + "\n", + "On the other hand, $y_t$ is autocorrelated. By construction, if I knew that $y_2 = 10$, I can be very confident that $y_3$ will not be very far from 10. Similarly, I can even make a (less confident guess) about $y_4$: it will probably not be near 0 or 20, but a value of 5 is not too unlikely. I can make a similar argument about $y_5$, but again, I am less confident. Taking this to it's logical conclusion, we must concede that as $k$, the lag between time points, increases the autocorrelation decreases. We can visualize this:\n" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "def autocorr(x):\n", + " # from http://tinyurl.com/afz57c4\n", + " result = np.correlate(x, x, mode='full')\n", + " result = result / np.max(result)\n", + " return result[result.size / 2:]\n", + "\n", + "colors = [\"#348ABD\", \"#A60628\", \"#7A68A6\"]\n", + "\n", + "x = np.arange(1, 200)\n", + "plt.bar(x, autocorr(y_t)[1:], width=1, label=\"$y_t$\",\n", + " edgecolor=colors[0], color=colors[0])\n", + "plt.bar(x, autocorr(x_t)[1:], width=1, label=\"$x_t$\",\n", + " color=colors[1], edgecolor=colors[1])\n", + "\n", + "plt.legend(title=\"Autocorrelation\")\n", + "plt.ylabel(\"measured correlation \\nbetween $y_t$ and $y_{t-k}$.\")\n", + "plt.xlabel(\"k (lag)\")\n", + "plt.title(\"Autocorrelation plot of $y_t$ and $x_t$ for differing $k$ lags.\")\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "display_data", + "png": 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jsXXr1lLjKcrLV+p3Q0XlqlWrFi5fvoygoCDcvn0b9erVw/Dhw/Hf//5XnUZWVhbHPZBN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\naWruK5afblT6KDkVBZl3S6WvT7mlniPdz4nlJ7a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+ "text": [ + "" + ] + } + ], + "prompt_number": 66 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Notice that as $k$ increases, the autocorrelation of $y_t$ decreases from a very high point. Compare with the autocorrelation of $x_t$ which looks like noise (which it really is), hence we can conclude no autocorrelation exists in this series. \n", + "\n", + "\n", + "####How does this relate to MCMC convergence?\n", + "\n", + "By the nature of the MCMC algorithm, we will always be returned samples that exhibit autocorrelation (this is because of the step `from your current position, move to a position near you`).\n", + "\n", + "A chain that is [Isn't meandering exploring?] exploring the space well will exhibit very high autocorrelation. Visually, if the trace seems to meander like a river, and not settle down, the chain will have high autocorrelation.\n", + "\n", + "This does not imply that a converged MCMC has low autocorrelation. Hence low autocorrelation is not necessary for convergence, but it is sufficient. PyMC has a built-in autocorrelation plotting function in the `Matplot` module. " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "###Thinning\n", + "\n", + "Another issue can arise if there is high-autocorrelation between posterior samples. Many post-processing algorithms require samples to be *independent* of each other. This can be solved, or at least reduced, by only returning to the user every $n$th sample, thus removing some autocorrelation. Below we perform an autocorrelation plot for $y_t$ with differing levels of thinning:" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "max_x = 200 / 3 + 1\n", + "x = np.arange(1, max_x)\n", + "\n", + "plt.bar(x, autocorr(y_t)[1:max_x], edgecolor=colors[0],\n", + " label=\"no thinning\", color=colors[0], width=1)\n", + "plt.bar(x, autocorr(y_t[::2])[1:max_x], edgecolor=colors[1],\n", + " label=\"keeping every 2nd sample\", color=colors[1], width=1)\n", + "plt.bar(x, autocorr(y_t[::3])[1:max_x], width=1, edgecolor=colors[2],\n", + " label=\"keeping every 3rd sample\", color=colors[2])\n", + "\n", + "plt.autoscale(tight=True)\n", + "plt.legend(title=\"Autocorrelation plot for $y_t$\", loc=\"lower left\")\n", + "plt.ylabel(\"measured correlation \\nbetween $y_t$ and $y_{t-k}$.\")\n", + "plt.xlabel(\"k (lag)\")\n", + "plt.title(\"Autocorrelation of $y_t$ (no thinning vs. thinning) \\\n", + "at differing $k$ lags.\")\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "display_data", + "png": 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v3+aN9Swd612lgXmyfMyRNDBPhtM48S8ru1EqjXdTqISEBJw4cQIJCQkYMmQI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\niuosqm1L7SJld4j3+j5Ls2f6VFvOXM6TPnUqPaf6nE9DlE21LqGTRlm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+ "text": [ + "" + ] + } + ], + "prompt_number": 67 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "With more thinning, the autocorrelation drops quicker. There is a tradeoff though: higher thinning requires more MCMC iterations to achieve the same number of returned samples. For example, 10 000 samples unthinned is 100 000 with a thinning of 10 (though the latter has less autocorrelation). \n", + "\n", + "What is a good amount of thinning? The returned samples will always exhibit some autocorrelation, regardless of how much thinning is done. So long as the autocorrelation tends to zero, you are probably ok. Typically thinning of more than 10 is not necessary.\n", + "\n", + "PyMC exposes a `thinning` parameter in the call to `sample`, for example: `sample( 10000, burn = 5000, thinning = 5)`. " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### `pymc.Matplot.plot()`\n", + "\n", + "It seems silly to have to manually create histograms, autocorrelation plots and trace plots each time we perform MCMC. The authors of PyMC have included a visualization tool for just this purpose. \n", + "\n", + "As the title suggests, the `pymc.Matplot` module contains a poorly named function `plot`, which I prefer to import as `mcplot` so there is no conflict with other namespaces. `plot`, or `mcplot` as I suggest, accepts an `MCMC` object and will return posterior distributions, traces and auto-correlations for each variable (up to 10 variables). \n", + "\n", + "Below we use the tool to plot the centers of the clusters, after sampling 25 000 more times and `thinning = 10`." + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from pymc.Matplot import plot as mcplot\n", + "\n", + "mcmc.sample(25000, 0, 10)\n", + "mcplot(mcmc.trace(\"centers\", 2), common_scale=False)\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + " \r", + "[****************100%******************] 25000 of 25000 complete" + ] + }, + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Plotting centers_0\n", + "Plotting" + ] + }, + { + "output_type": "stream", + "stream": "stdout", + "text": [ + " centers_1\n", + "\n" + ] + }, + { + "metadata": {}, + "output_type": "display_data", + "png": 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CUSalZwt3/e+tkdfgWhWioMYEVfXFy1tSAWjv40InP8MPu1sa7ZBiVp5k+cRg/m/vJQpL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9KfS0X4eFCLEmXaWq4qvSQ7K8NniZYXRJiT9pPKl/G+Denb3IXnOpdcjNHUxc7kcvYEhkPoWBme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\n/tRW7o3c3FwKCgqws7Ojfv361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+ "text": [ + "" + ] + } + ], + "prompt_number": 68 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "There are really two figures here, one for each unknown in the `centers` variable. In each figure, the subfigure in the top left corner is the trace of the variable. This is useful for inspecting that possible \"meandering\" property that is a result of non-convergence." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The largest plot on the right-hand side is the histograms of the samples, plus a few extra features. The thickest vertical line represents the posterior mean, which is a good summary of posterior distribution. The interval between the two dashed vertical lines in each the posterior distributions represent the *95% credible interval*, not to be confused with a *95% confidence interval*. I won't get into the latter, but the former can be interpreted as \"there is a 95% chance the parameter of interest lies in this interval\". (Changing default parameters in the call to `mcplot` provides alternatives to 95%.) When communicating your results to others, it is incredibly important to state this interval. One of our purposes for studying Bayesian methods is to have a clear understanding of our uncertainty in unknowns. Combined with the posterior mean, the 95% credible interval provides a reliable interval to communicate the likely location of the unknown (provided by the mean) *and* the uncertainty (represented by the width of the interval)." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The plots titled `center_0_acorr` and `center_1_acorr` are the generated autocorrelation plots. They look different than the ones I have displayed above, but the only difference is that 0-lag is centered in the middle of the figure, whereas I have 0 centered to the left. \n", + "\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Useful tips for MCMC\n", + "\n", + "Bayesian inference would be the *de facto* method if it weren't for MCMC's computational difficulties. In fact, MCMC is what turns most users off practical Bayesian inference. Below I present some good heuristics to help convergence and speed up the MCMC engine:\n", + "\n", + "### Intelligent starting values\n", + "\n", + "It would be great to start the MCMC algorithm off near the posterior distribution, so that it will take little time to start sampling correctly. We can aid the algorithm by telling where we *think* the posterior distribution will be by specifying the `value` parameter in the `Stochastic` variable creation. In many cases we can produce a reasonable guess for the parameter. For example, if we have data from a Normal distribution, and we wish to estimate the $\\mu$ parameter, then a good starting value would be the *mean* of the data. \n", + "\n", + " mu = pm.Uniform( \"mu\", 0, 100, value = data.mean() )\n", + "\n", + "For most parameters in models, there is a frequentist estimate of it. These estimates are a good starting value for our MCMC algorithms. Of course, this is not always possible for some variables, but including as many appropriate initial values is always a good idea. Even if your guesses are wrong, the MCMC will still converge to the proper distribution, so there is little to lose.\n", + "\n", + "This is what using `MAP` tries to do, by giving good initial values to the MCMC. So why bother specifying user-defined values? Well, even giving `MAP` good values will help it find the maximum a-posterior. \n", + "\n", + "Also important, *bad initial values* are a source of major bugs in PyMC and can hurt convergence.\n", + "\n", + "#### Priors\n", + "\n", + "If the priors are poorly chosen, the MCMC algorithm may not converge, or at least have difficulty converging. Consider what may happen if the prior chosen does not even contain the true parameter: the prior assigns 0 probability to the unknown, hence the posterior will assign 0 probability as well. This can cause pathological results.\n", + "\n", + "For this reason, it is best to carefully choose the priors. Often, lack of covergence or evidence of samples crowding to boundaries implies something is wrong with the chosen priors (see *Folk Theorem of Statistical Computing* below). \n", + "\n", + "#### Covariance matrices and eliminating parameters\n", + "\n", + "### The Folk Theorem of Statistical Computing\n", + "\n", + "> *If you are having computational problems, probably your model is wrong.*\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Conclusion\n", + "\n", + "PyMC provides a very strong backend to performing Bayesian inference, mostly because it has abstracted the inner mechanics of MCMC from the user. Despite this, some care must be applied to ensure your inference is not being biased by the iterative nature of MCMC. " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### References\n", + "\n", + "1. Flaxman, Abraham. \"Powell's Methods for Maximization in PyMC.\" Healthy Algorithms. N.p., 9 02 2012. Web. 28 Feb 2013. ." + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from IPython.core.display import HTML\n", + "\n", + "\n", + "def css_styling():\n", + " styles = open(\"../styles/custom.css\", \"r\").read()\n", + " return HTML(styles)\n", + "css_styling()\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "html": [ + "\n", + "\n" + ], + "metadata": {}, + "output_type": "pyout", + "prompt_number": 1, + "text": [ + "" + ] + } + ], + "prompt_number": 1 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [], + "language": "python", + "metadata": {}, + "outputs": [] + } + ], + "metadata": {} + } + ] } \ No newline at end of file diff --git a/Chapter3_MCMC/README.md b/Chapter3_MCMC/README.md index 52910479..0a01c33a 100644 --- a/Chapter3_MCMC/README.md +++ b/Chapter3_MCMC/README.md @@ -1,4 +1,4 @@ -Chapter 3: Opening the black box of MCMC (Markov Chain Monte Carlo) -================================================================== - -### [Read it online here](http://nbviewer.ipython.org/urls/raw.github.com/CamDavidsonPilon/Probabilistic-Programming-and-Bayesian-Methods-for-Hackers/master/Chapter3_MCMC/IntroMCMC.ipynb) +Chapter 3: Opening the black box of MCMC (Markov Chain Monte Carlo) +================================================================== + +### [Read it online here](http://nbviewer.ipython.org/urls/raw.github.com/CamDavidsonPilon/Probabilistic-Programming-and-Bayesian-Methods-for-Hackers/master/Chapter3_MCMC/IntroMCMC.ipynb) diff --git a/Chapter3_MCMC/data/github_data.csv b/Chapter3_MCMC/data/github_data.csv index f43fc909..3d7378e4 100644 --- a/Chapter3_MCMC/data/github_data.csv +++ b/Chapter3_MCMC/data/github_data.csv @@ -1,121 +1,121 @@ -Python, Javascript, Ruby, Java, Shell, PHP, days_since_creation, has_wiki, author_following, author_followers, starred_count, forked_count -0,1,0,0,0,0,523,1,0,0,2,1 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+1,37 @@ -age,smoke_cigars_pipe,smoke_both, smoke_cigarettes, population, deaths -1,0,0,0,656,18 -2,0,0,0,359,22 -3,0,0,0,249,19 -4,0,0,0,632,55 -5,0,0,0,1067,117 -6,0,0,0,897,170 -7,0,0,0,668,179 -8,0,0,0,361,120 -9,0,0,0,274,120 -1,1,0,0,145,2 -2,1,0,0,104,4 -3,1,0,0,98,3 -4,1,0,0,372,38 -5,1,0,0,846,113 -6,1,0,0,949,173 -7,1,0,0,824,212 -8,1,0,0,667,243 -9,1,0,0,537,253 -1,0,1,0,4531,149 -2,0,1,0,3030,169 -3,0,1,0,2267,193 -4,0,1,0,4682,576 -5,0,1,0,6052,1001 -6,0,1,0,3880,901 -7,0,1,0,2033,613 -8,0,1,0,871,337 -9,0,1,0,345,189 -1,0,0,1,3410,124 -2,0,0,1,2239,140 -3,0,0,1,1851,187 -4,0,0,1,3270,514 -5,0,0,1,3791,778 -6,0,0,1,2421,689 -7,0,0,1,1195,432 -8,0,0,1,436,214 -9,0,0,1,113,63 +age,smoke_cigars_pipe,smoke_both, smoke_cigarettes, population, deaths +1,0,0,0,656,18 +2,0,0,0,359,22 +3,0,0,0,249,19 +4,0,0,0,632,55 +5,0,0,0,1067,117 +6,0,0,0,897,170 +7,0,0,0,668,179 +8,0,0,0,361,120 +9,0,0,0,274,120 +1,1,0,0,145,2 +2,1,0,0,104,4 +3,1,0,0,98,3 +4,1,0,0,372,38 +5,1,0,0,846,113 +6,1,0,0,949,173 +7,1,0,0,824,212 +8,1,0,0,667,243 +9,1,0,0,537,253 +1,0,1,0,4531,149 +2,0,1,0,3030,169 +3,0,1,0,2267,193 +4,0,1,0,4682,576 +5,0,1,0,6052,1001 +6,0,1,0,3880,901 +7,0,1,0,2033,613 +8,0,1,0,871,337 +9,0,1,0,345,189 +1,0,0,1,3410,124 +2,0,0,1,2239,140 +3,0,0,1,1851,187 +4,0,0,1,3270,514 +5,0,0,1,3791,778 +6,0,0,1,2421,689 +7,0,0,1,1195,432 +8,0,0,1,436,214 +9,0,0,1,113,63 diff --git a/Chapter3_MCMC/github_pull.py b/Chapter3_MCMC/github_pull.py index 0d596207..b3953312 100644 --- a/Chapter3_MCMC/github_pull.py +++ b/Chapter3_MCMC/github_pull.py @@ -1,83 +1,83 @@ -#github data scrapper - -""" -variables of interest: - indp. variables - - language, given as a binary variable. Need 4 positions for 5 langagues - - #number of days created ago, 1 position - - has wiki? Boolean, 1 position - - followers, 1 position - - following, 1 position - - constant - - dep. variables - -stars/watchers - -forks - -""" -from json import loads -import datetime -import numpy as np -from requests import get - - -MAX = 8000000 -today = datetime.datetime.today() -randint = np.random.randint -N = 120 #sample size. -auth = ("username", "password" ) - -language_mappings = {"Python": 0, "JavaScript": 1, "Ruby": 2, "Java":3, "Shell":4, "PHP":5} - -#define data matrix: -X = np.zeros( (N , 12), dtype = int ) - -for i in xrange(N): - is_fork = True - is_valid_language = False - - while is_fork == True or is_valid_language == False: - is_fork = True - is_valid_language = False - - params = {"since":randint(0, MAX ) } - r = get("https://api.github.com/repositories", params = params, auth=auth ) - results = loads( r.text )[0] - #im only interested in the first one, and if it is not a fork. - is_fork = results["fork"] - - r = get( results["url"], auth = auth) - - #check the language - repo_results = loads( r.text ) - try: - language_mappings[ repo_results["language" ] ] - is_valid_language = True - except: - pass - - #languages - X[ i, language_mappings[ repo_results["language" ] ] ] = 1 - - #delta time - X[ i, 6] = ( today - datetime.datetime.strptime( repo_results["created_at"][:10], "%Y-%m-%d" ) ).days - - #haswiki - X[i, 7] = repo_results["has_wiki"] - - #get user information - r = get( results["owner"]["url"] , auth = auth) - user_results = loads( r.text ) - X[i, 8] = user_results["following"] - X[i, 9] = user_results["followers"] - - #get dep. data - X[i, 10] = repo_results["watchers_count"] - X[i, 11] = repo_results["forks_count"] - print - print " -------------- " - print i, ": ", results["full_name"], repo_results["language" ], repo_results["watchers_count"], repo_results["forks_count"] - print " -------------- " - print - -np.savetxt("data/github_data.csv", X, delimiter=",", fmt="%d" ) +#github data scrapper + +""" +variables of interest: + indp. variables + - language, given as a binary variable. Need 4 positions for 5 langagues + - #number of days created ago, 1 position + - has wiki? Boolean, 1 position + - followers, 1 position + - following, 1 position + - constant + + dep. variables + -stars/watchers + -forks + +""" +from json import loads +import datetime +import numpy as np +from requests import get + + +MAX = 8000000 +today = datetime.datetime.today() +randint = np.random.randint +N = 120 #sample size. +auth = ("username", "password" ) + +language_mappings = {"Python": 0, "JavaScript": 1, "Ruby": 2, "Java":3, "Shell":4, "PHP":5} + +#define data matrix: +X = np.zeros( (N , 12), dtype = int ) + +for i in xrange(N): + is_fork = True + is_valid_language = False + + while is_fork == True or is_valid_language == False: + is_fork = True + is_valid_language = False + + params = {"since":randint(0, MAX ) } + r = get("https://api.github.com/repositories", params = params, auth=auth ) + results = loads( r.text )[0] + #im only interested in the first one, and if it is not a fork. + is_fork = results["fork"] + + r = get( results["url"], auth = auth) + + #check the language + repo_results = loads( r.text ) + try: + language_mappings[ repo_results["language" ] ] + is_valid_language = True + except: + pass + + #languages + X[ i, language_mappings[ repo_results["language" ] ] ] = 1 + + #delta time + X[ i, 6] = ( today - datetime.datetime.strptime( repo_results["created_at"][:10], "%Y-%m-%d" ) ).days + + #haswiki + X[i, 7] = repo_results["has_wiki"] + + #get user information + r = get( results["owner"]["url"] , auth = auth) + user_results = loads( r.text ) + X[i, 8] = user_results["following"] + X[i, 9] = user_results["followers"] + + #get dep. data + X[i, 10] = repo_results["watchers_count"] + X[i, 11] = repo_results["forks_count"] + print + print " -------------- " + print i, ": ", results["full_name"], repo_results["language" ], repo_results["watchers_count"], repo_results["forks_count"] + print " -------------- " + print + +np.savetxt("data/github_data.csv", X, delimiter=",", fmt="%d" ) diff --git a/Chapter4_TheGreatestTheoremNeverTold/LawOfLargeNumbers.ipynb b/Chapter4_TheGreatestTheoremNeverTold/LawOfLargeNumbers.ipynb index efea648c..09d88211 100644 --- a/Chapter4_TheGreatestTheoremNeverTold/LawOfLargeNumbers.ipynb +++ b/Chapter4_TheGreatestTheoremNeverTold/LawOfLargeNumbers.ipynb @@ -1,1205 +1,1205 @@ -{ - "metadata": { - "name": "" - }, - "nbformat": 3, - "nbformat_minor": 0, - "worksheets": [ - { - "cells": [ - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "#Chapter 4\n", - "______\n", - "\n", - "##The greatest theorem never told\n", - "\n", - "\n", - "This chapter focuses on an idea that is always bouncing around our minds, but is rarely made explicit outside books devoted to statistics. In fact, we've been using this simple idea in every example thus far. " - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "###The Law of Large Numbers\n", - "\n", - "Let $Z_i$ be $N$ independent samples from some probability distribution. According to *the Law of Large numbers*, so long as the expected value $E[Z]$ is finite, the following holds,\n", - "\n", - "$$\\frac{1}{N} \\sum_{i=1}^N Z_i \\rightarrow E[ Z ], \\;\\;\\; N \\rightarrow \\infty.$$\n", - "\n", - "In words:\n", - "\n", - "> The average of a sequence of random variables from the same distribution converges to the expected value of that distribution.\n", - "\n", - "This may seem like a boring result, but it will be the most useful tool you use." - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### Intuition \n", - "\n", - "If the above Law is somewhat surprising, it can be made more clear by examining a simple example. \n", - "\n", - "Consider a random variable $Z$ that can take only two values, $c_1$ and $c_2$. Suppose we have a large number of samples of $Z$, denoting a specific sample $Z_i$. The Law says that we can approximate the expected value of $Z$ by averaging over all samples. Consider the average:\n", - "\n", - "\n", - "$$ \\frac{1}{N} \\sum_{i=1}^N \\;Z_i $$\n", - "\n", - "\n", - "By construction, $Z_i$ can only take on $c_1$ or $c_2$, hence we can partition the sum over these two values:\n", - "\n", - "\\begin{align}\n", - "\\frac{1}{N} \\sum_{i=1}^N \\;Z_i\n", - "& =\\frac{1}{N} \\big( \\sum_{ Z_i = c_1}c_1 + \\sum_{Z_i=c_2}c_2 \\big) \\\\\\\\[5pt]\n", - "& = c_1 \\sum_{ Z_i = c_1}\\frac{1}{N} + c_2 \\sum_{ Z_i = c_2}\\frac{1}{N} \\\\\\\\[5pt]\n", - "& = c_1 \\times \\text{ (approximate frequency of $c_1$) } \\\\\\\\ \n", - "& \\;\\;\\;\\;\\;\\;\\;\\;\\; + c_2 \\times \\text{ (approximate frequency of $c_2$) } \\\\\\\\[5pt]\n", - "& \\approx c_1 \\times P(Z = c_1) + c_2 \\times P(Z = c_2 ) \\\\\\\\[5pt]\n", - "& = E[Z]\n", - "\\end{align}\n", - "\n", - "\n", - "Equality holds in the limit, but we can get closer and closer by using more and more samples in the average. This Law holds for almost *any distribution*, minus some important cases we will encounter later.\n", - "\n", - "##### Example\n", - "____\n", - "\n", - "\n", - "Below is a diagram of the Law of Large numbers in action for three different sequences of Poisson random variables. \n", - "\n", - " We sample `sample_size = 100000` Poisson random variables with parameter $\\lambda = 4.5$. (Recall the expected value of a Poisson random variable is equal to it's parameter.) We calculate the average for the first $n$ samples, for $n=1$ to `sample_size`. " - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "%matplotlib inline\n", - "import numpy as np\n", - "from IPython.core.pylabtools import figsize\n", - "import matplotlib.pyplot as plt\n", - "\n", - "figsize(12.5, 5)\n", - "import pymc as pm\n", - "\n", - "sample_size = 100000\n", - "expected_value = lambda_ = 4.5\n", - "poi = pm.rpoisson\n", - "N_samples = range(1, sample_size, 100)\n", - "\n", - "for k in range(3):\n", - "\n", - " samples = poi(lambda_, size=sample_size)\n", - "\n", - " partial_average = [samples[:i].mean() for i in N_samples]\n", - "\n", - " plt.plot(N_samples, partial_average, lw=1.5, label=\"average \\\n", - "of $n$ samples; seq. %d\" % k)\n", - "\n", - "\n", - "plt.plot(N_samples, expected_value * np.ones_like(partial_average),\n", - " ls=\"--\", label=\"true expected value\", c=\"k\")\n", - "\n", - "plt.ylim(4.35, 4.65)\n", - "plt.title(\"Convergence of the average of \\n random variables to its \\\n", - "expected value\")\n", - "plt.ylabel(\"average of $n$ samples\")\n", - "plt.xlabel(\"# of samples, $n$\")\n", - "plt.legend();" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "metadata": {}, - "output_type": "display_data", - "png": 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aNmxIgYGBtGTJEpJIJGKZiIgIjYHMREQnT54kiURC165dE+dt2bKFWrZsSTKZ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\ndp0RZxJQE/71BlaRFdhBXmAVWYG3sVUSC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- "text": [ - "" - ] - } - ], - "prompt_number": 1 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Looking at the above plot, it is clear that when the sample size is small, there is greater variation in the average (compare how *jagged and jumpy* the average is initially, then *smooths* out). All three paths *approach* the value 4.5, but just flirt with it as $N$ gets large. Mathematicians and statistician have another name for *flirting*: convergence. \n", - "\n", - "Another very relevant question we can ask is *how quickly am I converging to the expected value?* Let's plot something new. For a specific $N$, let's do the above trials thousands of times and compute how far away we are from the true expected value, on average. But wait — *compute on average*? This is simply the law of large numbers again! For example, we are interested in, for a specific $N$, the quantity:\n", - "\n", - "$$D(N) = \\sqrt{ \\;E\\left[\\;\\; \\left( \\frac{1}{N}\\sum_{i=1}^NZ_i - 4.5 \\;\\right)^2 \\;\\;\\right] \\;\\;}$$\n", - "\n", - "The above formulae is interpretable as a distance away from the true value (on average), for some $N$. (We take the square root so the dimensions of the above quantity and our random variables are the same). As the above is an expected value, it can be approximated using the law of large numbers: instead of averaging $Z_i$, we calculate the following multiple times and average them:\n", - "\n", - "$$ Y_k = \\left( \\;\\frac{1}{N}\\sum_{i=1}^NZ_i - 4.5 \\; \\right)^2 $$\n", - "\n", - "By computing the above many, $N_y$, times (remember, it is random), and averaging them:\n", - "\n", - "$$ \\frac{1}{N_Y} \\sum_{k=1}^{N_Y} Y_k \\rightarrow E[ Y_k ] = E\\;\\left[\\;\\; \\left( \\frac{1}{N}\\sum_{i=1}^NZ_i - 4.5 \\;\\right)^2 \\right]$$\n", - "\n", - "Finally, taking the square root:\n", - "\n", - "$$ \\sqrt{\\frac{1}{N_Y} \\sum_{k=1}^{N_Y} Y_k} \\approx D(N) $$ " - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "figsize(12.5, 4)\n", - "\n", - "N_Y = 250 # use this many to approximate D(N)\n", - "N_array = np.arange(1000, 50000, 2500) # use this many samples in the approx. to the variance.\n", - "D_N_results = np.zeros(len(N_array))\n", - "\n", - "lambda_ = 4.5\n", - "expected_value = lambda_ # for X ~ Poi(lambda) , E[ X ] = lambda\n", - "\n", - "\n", - "def D_N(n):\n", - " \"\"\"\n", - " This function approx. D_n, the average variance of using n samples.\n", - " \"\"\"\n", - " Z = poi(lambda_, size=(n, N_Y))\n", - " average_Z = Z.mean(axis=0)\n", - " return np.sqrt(((average_Z - expected_value) ** 2).mean())\n", - "\n", - "\n", - "for i, n in enumerate(N_array):\n", - " D_N_results[i] = D_N(n)\n", - "\n", - "\n", - "plt.xlabel(\"$N$\")\n", - "plt.ylabel(\"expected squared-distance from true value\")\n", - "plt.plot(N_array, D_N_results, lw=3,\n", - " label=\"expected distance between\\n\\\n", - "expected value and \\naverage of $N$ random variables.\")\n", - "plt.plot(N_array, np.sqrt(expected_value) / np.sqrt(N_array), lw=2, ls=\"--\",\n", - " label=r\"$\\frac{\\sqrt{\\lambda}}{\\sqrt{N}}$\")\n", - "plt.legend()\n", - "plt.title(\"How 'fast' is the sample average converging? \");" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "metadata": {}, - "output_type": "display_data", - "png": 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kSZIkSXrj5ObmEhAQQIMGDTh//jxbtmxh8eLF7Nu3DzMzMxYsWEBwcDC3bt1i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- "text": [ - "" - ] - } - ], - "prompt_number": 2 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "As expected, the expected distance between our sample average and the actual expected value shrinks as $N$ grows large. But also notice that the *rate* of convergence decreases, that is, we need only 10 000 additional samples to move from 0.020 to 0.015, a difference of 0.005, but *20 000* more samples to again decrease from 0.015 to 0.010, again only a 0.005 decrease.\n", - "\n", - "\n", - "It turns out we can measure this rate of convergence. Above I have plotted a second line, the function $\\sqrt{\\lambda}/\\sqrt{N}$. This was not chosen arbitrarily. In most cases, given a sequence of random variable distributed like $Z$, the rate of converge to $E[Z]$ of the Law of Large Numbers is \n", - "\n", - "$$ \\frac{ \\sqrt{ \\; Var(Z) \\; } }{\\sqrt{N} }$$\n", - "\n", - "This is useful to know: for a given large $N$, we know (on average) how far away we are from the estimate. On the other hand, in a Bayesian setting, this can seem like a useless result: Bayesian analysis is OK with uncertainty so what's the *statistical* point of adding extra precise digits? Though drawing samples can be so computationally cheap that having a *larger* $N$ is fine too. \n", - "\n", - "### How do we compute $Var(Z)$ though?\n", - "\n", - "The variance is simply another expected value that can be approximated! Consider the following, once we have the expected value (by using the Law of Large Numbers to estimate it, denote it $\\mu$), we can estimate the variance:\n", - "\n", - "$$ \\frac{1}{N}\\sum_{i=1}^N \\;(Z_i - \\mu)^2 \\rightarrow E[ \\;( Z - \\mu)^2 \\;] = Var( Z )$$\n", - "\n", - "### Expected values and probabilities \n", - "There is an even less explicit relationship between expected value and estimating probabilities. Define the *indicator function*\n", - "\n", - "$$\\mathbb{1}_A(x) = \n", - "\\begin{cases} 1 & x \\in A \\\\\\\\\n", - " 0 & else\n", - "\\end{cases}\n", - "$$\n", - "Then, by the law of large numbers, if we have many samples $X_i$, we can estimate the probability of an event $A$, denoted $P(A)$, by:\n", - "\n", - "$$ \\frac{1}{N} \\sum_{i=1}^N \\mathbb{1}_A(X_i) \\rightarrow E[\\mathbb{1}_A(X)] = P(A) $$\n", - "\n", - "Again, this is fairly obvious after a moments thought: the indicator function is only 1 if the event occurs, so we are summing only the times the event occurs and dividing by the total number of trials (consider how we usually approximate probabilities using frequencies). For example, suppose we wish to estimate the probability that a $Z \\sim Exp(.5)$ is greater than 10, and we have many samples from a $Exp(.5)$ distribution. \n", - "\n", - "\n", - "$$ P( Z > 10 ) = \\sum_{i=1}^N \\mathbb{1}_{z > 10 }(Z_i) $$\n" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "import pymc as pm\n", - "N = 10000\n", - "print np.mean([pm.rexponential(0.5) > 10 for i in range(N)])" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "0.0069\n" - ] - } - ], - "prompt_number": 4 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### What does this all have to do with Bayesian statistics? \n", - "\n", - "\n", - "*Point estimates*, to be introduced in the next chapter, in Bayesian inference are computed using expected values. In more analytical Bayesian inference, we would have been required to evaluate complicated expected values represented as multi-dimensional integrals. No longer. If we can sample from the posterior distribution directly, we simply need to evaluate averages. Much easier. If accuracy is a priority, plots like the ones above show how fast you are converging. And if further accuracy is desired, just take more samples from the posterior. \n", - "\n", - "When is enough enough? When can you stop drawing samples from the posterior? That is the practitioners decision, and also dependent on the variance of the samples (recall from above a high variance means the average will converge slower). \n", - "\n", - "We also should understand when the Law of Large Numbers fails. As the name implies, and comparing the graphs above for small $N$, the Law is only true for large sample sizes. Without this, the asymptotic result is not reliable. Knowing in what situations the Law fails can give us *confidence in how unconfident we should be*. The next section deals with this issue." - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## The Disorder of Small Numbers\n", - "\n", - "The Law of Large Numbers is only valid as $N$ gets *infinitely* large: never truly attainable. While the law is a powerful tool, it is foolhardy to apply it liberally. Our next example illustrates this.\n", - "\n", - "\n", - "##### Example: Aggregated geographic data\n", - "\n", - "\n", - "Often data comes in aggregated form. For instance, data may be grouped by state, county, or city level. Of course, the population numbers vary per geographic area. If the data is an average of some characteristic of each the geographic areas, we must be conscious of the Law of Large Numbers and how it can *fail* for areas with small populations.\n", - "\n", - "We will observe this on a toy dataset. Suppose there are five thousand counties in our dataset. Furthermore, population number in each state are uniformly distributed between 100 and 1500. The way the population numbers are generated is irrelevant to the discussion, so we do not justify this. We are interested in measuring the average height of individuals per county. Unbeknownst to us, height does **not** vary across county, and each individual, regardless of the county he or she is currently living in, has the same distribution of what their height may be:\n", - "\n", - "$$ \\text{height} \\sim \\text{Normal}(150, 15 ) $$\n", - "\n", - "We aggregate the individuals at the county level, so we only have data for the *average in the county*. What might our dataset look like?" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "figsize(12.5, 4)\n", - "std_height = 15\n", - "mean_height = 150\n", - "\n", - "n_counties = 5000\n", - "pop_generator = pm.rdiscrete_uniform\n", - "norm = pm.rnormal\n", - "\n", - "# generate some artificial population numbers\n", - "population = pop_generator(100, 1500, size=n_counties)\n", - "\n", - "average_across_county = np.zeros(n_counties)\n", - "for i in range(n_counties):\n", - " # generate some individuals and take the mean\n", - " average_across_county[i] = norm(mean_height, 1. / std_height ** 2,\n", - " size=population[i]).mean()\n", - "\n", - "# located the counties with the apparently most extreme average heights.\n", - "i_min = np.argmin(average_across_county)\n", - "i_max = np.argmax(average_across_county)\n", - "\n", - "# plot population size vs. recorded average\n", - "plt.scatter(population, average_across_county, alpha=0.5, c=\"#7A68A6\")\n", - "plt.scatter([population[i_min], population[i_max]],\n", - " [average_across_county[i_min], average_across_county[i_max]],\n", - " s=60, marker=\"o\", facecolors=\"none\",\n", - " edgecolors=\"#A60628\", linewidths=1.5,\n", - " label=\"extreme heights\")\n", - "\n", - "plt.xlim(100, 1500)\n", - "plt.title(\"Average height vs. County Population\")\n", - "plt.xlabel(\"County Population\")\n", - "plt.ylabel(\"Average height in county\")\n", - "plt.plot([100, 1500], [150, 150], color=\"k\", label=\"true expected \\\n", - "height\", ls=\"--\")\n", - "plt.legend(scatterpoints=1);" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "metadata": {}, - "output_type": "display_data", - "png": 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QarU4cuQIKioqUFlZiXnz5mHVqlXYsGEDcnNzsW3bNrvzP/74Y6jVamRlZWHT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htjmO9PmT+0mp0KDz/fxHVFY+76803f6tTqJZUn315iVQ1UVeH+ZzdlYZWqwcMvt4gCkRVx9nr2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FvaPbtIZRFrIXKS6c//5jCYNWfcj2wS3u3nd5+um3Eome//l2W2MWVzLcuf8yI2fK5cqb582f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- "text": [ - "" - ] - } - ], - "prompt_number": 6 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "What do we observe? *Without accounting for population sizes* we run the risk of making an enormous inference error: if we ignored population size, we would say that the county with the shortest and tallest individuals have been correctly circled. But this inference is wrong for the following reason. These two counties do *not* necessarily have the most extreme heights. The error results from the calculated average of smaller populations not being a good reflection of the true expected value of the population (which in truth should be $\\mu =150$). The sample size/population size/$N$, whatever you wish to call it, is simply too small to invoke the Law of Large Numbers effectively. \n", - "\n", - "We provide more damning evidence against this inference. Recall the population numbers were uniformly distributed over 100 to 1500. Our intuition should tell us that the counties with the most extreme population heights should also be uniformly spread over 100 to 1500, and certainly independent of the county's population. Not so. Below are the population sizes of the counties with the most extreme heights." - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "print \"Population sizes of 10 'shortest' counties: \"\n", - "print population[np.argsort(average_across_county)[:10]]\n", - "print\n", - "print \"Population sizes of 10 'tallest' counties: \"\n", - "print population[np.argsort(-average_across_county)[:10]]" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "Population sizes of 10 'shortest' counties: \n", - "[111 103 102 109 110 257 164 144 169 260]\n", - "\n", - "Population sizes of 10 'tallest' counties: \n", - "[252 107 162 141 141 256 144 112 210 342]\n" - ] - } - ], - "prompt_number": 7 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Not at all uniform over 100 to 1500. This is an absolute failure of the Law of Large Numbers. \n", - "\n", - "##### Example: Kaggle's *U.S. Census Return Rate Challenge*\n", - "\n", - "Below is data from the 2010 US census, which partitions populations beyond counties to the level of block groups (which are aggregates of city blocks or equivalents). The dataset is from a Kaggle machine learning competition some colleagues and I participated in. The objective was to predict the census letter mail-back rate of a group block, measured between 0 and 100, using census variables (median income, number of females in the block-group, number of trailer parks, average number of children etc.). Below we plot the census mail-back rate versus block group population:" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "figsize(12.5, 6.5)\n", - "data = np.genfromtxt(\"./data/census_data.csv\", skip_header=1,\n", - " delimiter=\",\")\n", - "plt.scatter(data[:, 1], data[:, 0], alpha=0.5, c=\"#7A68A6\")\n", - "plt.title(\"Census mail-back rate vs Population\")\n", - "plt.ylabel(\"Mail-back rate\")\n", - "plt.xlabel(\"population of block-group\")\n", - "plt.xlim(-100, 15e3)\n", - "plt.ylim(-5, 105)\n", - "\n", - "i_min = np.argmin(data[:, 0])\n", - "i_max = np.argmax(data[:, 0])\n", - "\n", - "plt.scatter([data[i_min, 1], data[i_max, 1]],\n", - " [data[i_min, 0], data[i_max, 0]],\n", - " s=60, marker=\"o\", facecolors=\"none\",\n", - " edgecolors=\"#A60628\", linewidths=1.5,\n", - " label=\"most extreme points\")\n", - "\n", - "plt.legend(scatterpoints=1);" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "metadata": {}, - "output_type": "display_data", - "png": 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CwsIhMQiHswOkXV1drFq1ape2bv8lYHdtqaysJJlM4na76e/vHzGew9neVwUw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- "text": [ - "" - ] - } - ], - "prompt_number": 8 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "The above is a classic phenomenon in statistics. I say *classic* referring to the \"shape\" of the scatter plot above. It follows a classic triangular form, that tightens as we increase the sample size (as the Law of Large Numbers becomes more exact). \n", - "\n", - "I am perhaps overstressing the point and maybe I should have titled the book *\"You don't have big data problems!\"*, but here again is an example of the trouble with *small datasets*, not big ones. Simply, small datasets cannot be processed using the Law of Large Numbers. Compare with applying the Law without hassle to big datasets (ex. big data). I mentioned earlier that paradoxically big data prediction problems are solved by relatively simple algorithms. The paradox is partially resolved by understanding that the Law of Large Numbers creates solutions that are *stable*, i.e. adding or subtracting a few data points will not affect the solution much. On the other hand, adding or removing data points to a small dataset can create very different results. \n", - "\n", - "For further reading on the hidden dangers of the Law of Large Numbers, I would highly recommend the excellent manuscript [The Most Dangerous Equation](http://nsm.uh.edu/~dgraur/niv/TheMostDangerousEquation.pdf). " - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "##### Example: How to order Reddit comments\n", - "\n", - "You may have disagreed with the original statement that the Law of Large numbers is known to everyone, but only implicitly in our subconscious decision making. Consider ratings on online products: how often do you trust an average 5-star rating if there is only 1 reviewer? 2 reviewers? 3 reviewers? We implicitly understand that with such few reviewers that the average rating is **not** a good reflection of the true value of the product.\n", - "\n", - "This has created flaws in how we sort items, and more generally, how we compare items. Many people have realized that sorting online search results by their rating, whether the objects be books, videos, or online comments, return poor results. Often the seemingly top videos or comments have perfect ratings only from a few enthusiastic fans, and truly more quality videos or comments are hidden in later pages with *falsely-substandard* ratings of around 4.8. How can we correct this?\n", - "\n", - "Consider the popular site Reddit (I purposefully did not link to the website as you would never come back). The site hosts links to stories or images, and a very popular part of the site are the comments associated with each link. Redditors can vote up or down on each comment (called upvotes and downvotes). Reddit, by default, will sort comments by Top, that is, the best comments.\n", - "\n", - "\n", - "\n", - "\n", - "How would you determine which comments are the best? There are a number of ways to achieve this:\n", - "\n", - "1. *Popularity*: A comment is considered good if it has many upvotes. A problem with this model is that a comment with hundreds of upvotes, but thousands of downvotes. While being very *popular*, the comment is likely more controversial than best.\n", - "2. *Difference*: Using the *difference* of upvotes and downvotes. This solves the above problem, but fails when we consider the temporal nature of comments. Comments can be posted many hours after the original link submission. The difference method will bias the *Top* comments to be the oldest comments, which have accumulated more upvotes than newer comments, but are not necessarily the best.\n", - "3. *Time adjusted*: Consider using Difference divided by the age of the comment. This creates a *rate*, something like *difference per second*, or *per minute*. An immediate counter example is, if we use per second, a 1 second old comment with 1 upvote would be better than a 100 second old comment with 99 upvotes. One can avoid this by only considering at least t second old comments. But what is a good t value? Does this mean no comment younger than t is good? We end up comparing unstable quantities with stable quantities (young vs. old comments).\n", - "3. *Ratio*: Rank comments by the ratio of upvotes to total number of votes (upvotes plus downvotes). This solves the temporal issue, such that new comments who score well can be considered Top just as likely as older comments, provided they have many upvotes to total votes. The problem here is that a comment with a single upvote (ratio = 1.0) will beat a comment with 999 upvotes and 1 downvote (ratio = 0.999), but clearly the latter comment is *more likely* to be better.\n", - "\n", - "I used the phrase *more likely* for good reason. It is possible that the former comment, with a single upvote, is in fact a better comment than the later with 999 upvotes. The hesitation to agree with this is because we have not seen the other 999 potential votes the former comment might get. Perhaps it will achieve an additional 999 upvotes and 0 downvotes and be considered better than the latter, though not likely.\n", - "\n", - "What we really want is an estimate of the *true upvote ratio*. Note that the true upvote ratio is not the same as the observed upvote ratio: the true upvote ratio is hidden, and we only observe upvotes vs. downvotes (one can think of the true upvote ratio as \"what is the underlying probability someone gives this comment a upvote, versus a downvote\"). So the 999 upvote/1 downvote comment probably has a true upvote ratio close to 1, which we can assert with confidence thanks to the Law of Large Numbers, but on the other hand we are much less certain about the true upvote ratio of the comment with only a single upvote. Sounds like a Bayesian problem to me.\n", - "\n" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "One way to determine a prior on the upvote ratio is to look at the historical distribution of upvote ratios. This can be accomplished by scraping Reddit's comments and determining a distribution. There are a few problems with this technique though:\n", - "\n", - "1. Skewed data: The vast majority of comments have very few votes, hence there will be many comments with ratios near the extremes (see the \"triangular plot\" in the above Kaggle dataset), effectively skewing our distribution to the extremes. One could try to only use comments with votes greater than some threshold. Again, problems are encountered. There is a tradeoff between number of comments available to use and a higher threshold with associated ratio precision. \n", - "2. Biased data: Reddit is composed of different subpages, called subreddits. Two examples are *r/aww*, which posts pics of cute animals, and *r/politics*. It is very likely that the user behaviour towards comments of these two subreddits are very different: visitors are likely to be more friendly and affectionate in the former, and would therefore upvote comments more, compared to the latter, where comments are likely to be controversial and disagreed upon. Therefore not all comments are the same. \n", - "\n", - "\n", - "In light of these, I think it is better to use a `Uniform` prior.\n", - "\n", - "\n", - "With our prior in place, we can find the posterior of the true upvote ratio. The Python script `comments_for_top_reddit_pic.py` will scrape the comments from the current top picture on Reddit. Below is the picture, and some comments:" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "from IPython.core.display import Image\n", - "# adding a number to the end of the %run call with get the ith top photo.\n", - "%run top_pic_comments.py 2\n", - "\n", - "Image(top_post_url)" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "Title of submission: \n", - "Frozen mining truck\n", - "http://i.imgur.com/OYsHKlH.jpg/n" - ] - }, - { - "metadata": {}, - "output_type": "pyout", - "prompt_number": 10, - "text": [ - "" - ] - } - ], - "prompt_number": 10 - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "\"\"\"\n", - "contents: an array of the text from all comments on the pic\n", - "votes: a 2d numpy array of upvotes, downvotes for each comment.\n", - "\"\"\"\n", - "n_comments = len(contents)\n", - "comments = np.random.randint(n_comments, size=4)\n", - "print \"Some Comments (out of %d total) \\n-----------\" % n_comments\n", - "for i in comments:\n", - " print '\"' + contents[i] + '\"'\n", - " print\"upvotes/downvotes: \", votes[i, :]\n", - " print" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "Some Comments (out of 77 total) \n", - "-----------\n", - "\"Do these trucks remind anyone else of Sly Cooper?\"\n", - "upvotes/downvotes: [2 0]\n", - "\n", - "\"Dammit Elsa I told you not to drink and drive.\"\n", - "upvotes/downvotes: [7 0]\n", - "\n", - "\"I've seen this picture before in a Duratray (the dump box supplier) brochure. If I recall it was either at Ekati or Diavik... In which case the truck could be either a Komatsu or a CAT... anyone care to comment?\"\n", - "upvotes/downvotes: [2 0]\n", - "\n", - "\"Actually it does not look frozen just covered in a layer of wind packed snow.\"\n", - "upvotes/downvotes: [120 18]\n", - "\n" - ] - } - ], - "prompt_number": 15 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - " For a given true upvote ratio $p$ and $N$ votes, the number of upvotes will look like a Binomial random variable with parameters $p$ and $N$. (This is because of the equivalence between upvote ratio and probability of upvoting versus downvoting, out of $N$ possible votes/trials). We create a function that performs Bayesian inference on $p$, for a particular comment's upvote/downvote pair." - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "import pymc as pm\n", - "\n", - "\n", - "def posterior_upvote_ratio(upvotes, downvotes, samples=20000):\n", - " \"\"\"\n", - " This function accepts the number of upvotes and downvotes a particular comment received, \n", - " and the number of posterior samples to return to the user. Assumes a uniform prior.\n", - " \"\"\"\n", - " N = upvotes + downvotes\n", - " upvote_ratio = pm.Uniform(\"upvote_ratio\", 0, 1)\n", - " observations = pm.Binomial(\"obs\", N, upvote_ratio, value=upvotes, observed=True)\n", - " # do the fitting; first do a MAP as it is cheap and useful.\n", - " map_ = pm.MAP([upvote_ratio, observations]).fit()\n", - " mcmc = pm.MCMC([upvote_ratio, observations])\n", - " mcmc.sample(samples, samples / 4)\n", - " return mcmc.trace(\"upvote_ratio\")[:]" - ], - "language": "python", - "metadata": {}, - "outputs": [], - "prompt_number": 16 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Below are the resulting posterior distributions." - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "figsize(11., 8)\n", - "posteriors = []\n", - "colours = [\"#348ABD\", \"#A60628\", \"#7A68A6\", \"#467821\", \"#CF4457\"]\n", - "for i in range(len(comments)):\n", - " j = comments[i]\n", - " posteriors.append(posterior_upvote_ratio(votes[j, 0], votes[j, 1]))\n", - " plt.hist(posteriors[i], bins=18, normed=True, alpha=.9,\n", - " histtype=\"step\", color=colours[i % 5], lw=3,\n", - " label='(%d up:%d down)\\n%s...' % (votes[j, 0], votes[j, 1], contents[j][:50]))\n", - " plt.hist(posteriors[i], bins=18, normed=True, alpha=.2,\n", - " histtype=\"stepfilled\", color=colours[i], lw=3, )\n", - "\n", - "plt.legend(loc=\"upper left\")\n", - "plt.xlim(0, 1)\n", - "plt.title(\"Posterior distributions of upvote ratios on different comments\");" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "output_type": "stream", - "stream": "stdout", - "text": [ - " \r", - "[****************100%******************] 20000 of 20000 complete" - ] - }, - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "\n" - ] - }, - { - "metadata": {}, - "output_type": "display_data", - "png": 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kZGVloXfv3gDqLlyKiorv/gH/X1vm1ZCVlRVycnKwdetWyMrK4ttvv0Xfvn3x8uXLdqsT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\nx4pSd7Xmp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- "text": [ - "" - ] - } - ], - "prompt_number": 17 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Some distributions are very tight, others have very long tails (relatively speaking), expressing our uncertainty with what the true upvote ratio might be.\n", - "\n", - "### Sorting!\n", - "\n", - "We have been ignoring the goal of this exercise: how do we sort the comments from *best to worst*? Of course, we cannot sort distributions, we must sort scalar numbers. There are many ways to distill a distribution down to a scalar: expressing the distribution through its expected value, or mean, is one way. Choosing the mean is a bad choice though. This is because the mean does not take into account the uncertainty of distributions.\n", - "\n", - "I suggest using the *95% least plausible value*, defined as the value such that there is only a 5% chance the true parameter is lower (think of the lower bound on the 95% credible region). Below are the posterior distributions with the 95% least-plausible value plotted:" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "N = posteriors[0].shape[0]\n", - "lower_limits = []\n", - "\n", - "for i in range(len(comments)):\n", - " j = comments[i]\n", - " plt.hist(posteriors[i], bins=20, normed=True, alpha=.9,\n", - " histtype=\"step\", color=colours[i], lw=3,\n", - " label='(%d up:%d down)\\n%s...' % (votes[j, 0], votes[j, 1], contents[j][:50]))\n", - " plt.hist(posteriors[i], bins=20, normed=True, alpha=.2,\n", - " histtype=\"stepfilled\", color=colours[i], lw=3, )\n", - " v = np.sort(posteriors[i])[int(0.05 * N)]\n", - " # plt.vlines( v, 0, 15 , color = \"k\", alpha = 1, linewidths=3 )\n", - " plt.vlines(v, 0, 10, color=colours[i], linestyles=\"--\", linewidths=3)\n", - " lower_limits.append(v)\n", - " plt.legend(loc=\"upper left\")\n", - "\n", - "plt.legend(loc=\"upper left\")\n", - "plt.title(\"Posterior distributions of upvote ratios on different comments\");\n", - "order = np.argsort(-np.array(lower_limits))\n", - "print order, lower_limits" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "[3 1 2 0] [0.36980613417267094, 0.68407203257290061, 0.37551825562169117, 0.8177566237850703]\n" - ] - }, - { - "metadata": {}, - "output_type": "display_data", - "png": 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b2+PUqVOoqamBtrY27O3tERISgqdPn8LS0rLZa25MVlYW+vbt2+r4FAqFQqFQ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\nTHZVS5y91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- "text": [ - "" - ] - } - ], - "prompt_number": 19 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "The best comments, according to our procedure, are the comments that are *most-likely* to score a high percentage of upvotes. Visually those are the comments with the 95% least plausible value close to 1.\n", - "\n", - "Why is sorting based on this quantity a good idea? By ordering by the 95% least plausible value, we are being the most conservative with what we think is best. That is, even in the worst case scenario, when we have severely overestimated the upvote ratio, we can be sure the best comments are still on top. Under this ordering, we impose the following very natural properties:\n", - "\n", - "1. given two comments with the same observed upvote ratio, we will assign the comment with more votes as better (since we are more confident it has a higher ratio).\n", - "2. given two comments with the same number of votes, we still assign the comment with more upvotes as *better*.\n", - "\n", - "### But this is too slow for real-time!\n", - "\n", - "I agree, computing the posterior of every comment takes a long time, and by the time you have computed it, likely the data has changed. I delay the mathematics to the appendix, but I suggest using the following formula to compute the lower bound very fast.\n", - "\n", - "$$ \\frac{a}{a + b} - 1.65\\sqrt{ \\frac{ab}{ (a+b)^2(a + b +1 ) } }$$\n", - "\n", - "where \n", - "\\begin{align}\n", - "& a = 1 + u \\\\\\\\\n", - "& b = 1 + d \\\\\\\\\n", - "\\end{align}\n", - "\n", - "$u$ is the number of upvotes, and $d$ is the number of downvotes. The formula is a shortcut in Bayesian inference, which will be further explained in Chapter 6 when we discuss priors in more detail.\n" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "def intervals(u, d):\n", - " a = 1. + u\n", - " b = 1. + d\n", - " mu = a / (a + b)\n", - " std_err = 1.65 * np.sqrt((a * b) / ((a + b) ** 2 * (a + b + 1.)))\n", - " return (mu, std_err)\n", - "\n", - "print \"Approximate lower bounds:\"\n", - "posterior_mean, std_err = intervals(votes[:, 0], votes[:, 1])\n", - "lb = posterior_mean - std_err\n", - "print lb\n", - "print\n", - "print \"Top 40 Sorted according to approximate lower bounds:\"\n", - "print\n", - "order = np.argsort(-lb)\n", - "ordered_contents = []\n", - "for i in order[:40]:\n", - " ordered_contents.append(contents[i])\n", - " print votes[i, 0], votes[i, 1], contents[i]\n", - " print \"-------------\"" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "Approximate lower bounds:\n", - "[ 0.83167764 0.8041293 0.8166957 0.77375237 0.72491057 0.71705212\n", - " 0.72440529 0.73158407 0.67107394 0.6931046 0.66235556 0.6530083\n", - " 0.70806405 0.60091591 0.60091591 0.66278557 0.60091591 0.60091591\n", - " 0.53055613 0.53055613 0.53055613 0.53055613 0.53055613 0.43047887\n", - " 0.43047887 0.43047887 0.43047887 0.43047887 0.43047887 0.43047887\n", - " 0.43047887 0.43047887 0.43047887 0.43047887 0.43047887 0.43047887\n", - " 0.43047887 0.43047887 0.43047887 0.47201974 0.45074913 0.35873239\n", - " 0.3726793 0.42069919 0.33529412 0.27775794 0.27775794 0.27775794\n", - " 0.27775794 0.27775794 0.27775794 0.13104878 0.13104878 0.27775794\n", - " 0.27775794 0.27775794 0.27775794 0.27775794 0.27775794 0.27775794\n", - " 0.27775794 0.27775794 0.27775794 0.27775794 0.27775794 0.27775794\n", - " 0.27775794 0.27775794 0.27775794 0.27775794 0.27775794 0.27775794\n", - " 0.27775794 0.27775794 0.27775794 0.27775794 0.27775794]\n", - "\n", - "Top 40 Sorted according to approximate lower bounds:\n", - "\n", - "327 52 Can you imagine having to start that? I've fired up much smaller equipment when its around 0\u00b0 out and its still a pain. It would probably take a crew of guys hours to get that going. Do they have built in heaters to make it easier? You'd think they would just let them idle overnight if they planned on running it the next day though.\n", - "-------------\n", - "120 18 Actually it does not look frozen just covered in a layer of wind packed snow.\n", - "-------------\n", - "70 10 That's actually just the skin of a mining truck. They shed it periodically like snakes do.\n", - "-------------\n", - "76 14 The model just hasn't been textured yet!\n", - "-------------\n", - "21 3 No worries, [this](http://imgur.com/KeSYJud) will help.\n", - "-------------\n", - "7 0 Dammit Elsa I told you not to drink and drive.\n", - "-------------\n", - "88 23 Speaking of mining...[BAGGER 288!](http://www.youtube.com/watch?v=azEvfD4C6ow)\n", - "-------------\n", - "112 32 Wonder why OP has 31,944 link karma but so few submissions? /u/zkool may have the worst case of karma addiction I'm aware of.\n", - "\n", - "title | points | age | /r/ | comnts\n", - ":--|:--|:--|:--|:--\n", - "[Frozen mining truck](http://www.reddit.com/r/pics/comments/1mrqvh/frozen_mining_truck/) | 2507 | 4^mos | pics | 164\n", - "[Frozen mining truck](http://www.reddit.com/r/pics/comments/1cutbw/frozen_mining_truck/) | 16 | 9^mos | pics | 4\n", - "[Frozen mining truck](http://www.reddit.com/r/pics/comments/vvcrv/frozen_mining_truck/) | 439 | 1^yr | pics | 21\n", - "[Meanwhile, in New Zealand...](http://www.reddit.com/r/pics/comments/ir1pl/meanwhile_in_new_zealand/) | 39 | 2^yrs | pics | 12\n", - "[Blizzardy day](http://www.reddit.com/r/pics/comments/1uiu3y/blizzardy_day/) | 7 | 19^dys | pics | 3\n", - "\n", - "*[Source: karmadecay](http://karmadecay.com/r/pics/comments/1w454i/frozen_mining_truck/)*\n", - "-------------\n", - "11 1 This is what it's typically like, living in Alberta.\n", - "-------------\n", - "6 0 That'd be a haul truck. Looks like a CAT 793. We run em at the site I work at, 240ton carrying capacity. \n", - "-------------\n", - "22 5 Taken in Fort Mcmurray Ab!\n", - "-------------\n", - "9 1 \"EXCLUSIVE: First look at \"Hoth\" from the upcoming 'Star Wars: Episode VII'\"\n", - "-------------\n", - "32 9 This is the most fun thing to drive in GTA V.\n", - "-------------\n", - "5 0 it reminds me of the movie \"moon\" with sam rockwell.\n", - "-------------\n", - "4 0 Also frozen drill rig.\n", - "-------------\n", - "4 0 There's just something awesome about a land vehicle so huge that it warrants a set of stairs on the front of it. I find myself wishing I were licensed to drive it.\n", - "-------------\n", - "4 0 Heaters all over the components needing heat: \n", - "http://www.arctic-fox.com/fuel-fluid-warming-products/diesel-fired-coolant-pre-heaters/n", - "-------------\n", - "4 0 Or it is just an amazing snow sculpture!\n", - "-------------\n", - "3 0 I have to tell people about these awful conditions... Too bad I'm Snowden.\n", - "-------------\n", - "3 0 Someone let it go\n", - "-------------\n", - "3 0 Elsa, you can't do that to people's trucks.\n", - "-------------\n", - "3 0 woo Alberta represent\n", - "-------------\n", - "3 0 Just thaw it with love\n", - "-------------\n", - "6 2 Looks like the drill next to it is an IR DM30 or DM45. Good rigs. \n", - "-------------\n", - "4 1 That's the best snow sculpture I've ever seen. \n", - "-------------\n", - "2 0 [These](http://i.imgur.com/xYuwk5I.jpg) are used for removing the ice.\n", - "-------------\n", - "2 0 Nigger\n", - "-------------\n", - "2 0 Please someone post frozen Bagger 288\n", - "-------------\n", - "2 0 It's kind of cool there are trucks so big they need both a ladder and a staircase to get into them.\n", - "-------------\n", - "2 0 Eight miners are just out of frame hiding inside a tauntaun.\n", - "-------------\n", - "2 0 http://imgur.com/gallery/Fxv3Oh7\n", - "-------------\n", - "2 0 BRAZZERS.\n", - "-------------\n", - "2 0 It would take a god damn week just to warm that thing up.\n", - "-------------\n", - "2 0 Maybe /r/Bitcoin can use some of their mining equipment to heat this guy up!\n", - "-------------\n", - "2 0 Checkmate Jackie Chan\n", - "-------------\n", - "2 0 I've seen this picture before in a Duratray (the dump box supplier) brochure. If I recall it was either at Ekati or Diavik... In which case the truck could be either a Komatsu or a CAT... anyone care to comment?\n", - "-------------\n", - "2 0 The Texas snow has really hit hard!\n", - "-------------\n", - "2 0 I'm going to take a wild guess and say the diesel is gelled.\n", - "-------------\n", - "2 0 Do these trucks remind anyone else of Sly Cooper?\n", - "-------------\n", - "2 0 cool\n", - "-------------\n" - ] - } - ], - "prompt_number": 20 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "We can view the ordering visually by plotting the posterior mean and bounds, and sorting by the lower bound. In the plot below, notice that the left error-bar is sorted (as we suggested this is the best way to determine an ordering), so the means, indicated by dots, do not follow any strong pattern. " - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "r_order = order[::-1][-40:]\n", - "plt.errorbar(posterior_mean[r_order], np.arange(len(r_order)),\n", - " xerr=std_err[r_order], xuplims=True, capsize=0, fmt=\"o\",\n", - " color=\"#7A68A6\")\n", - "plt.xlim(0.3, 1)\n", - "plt.yticks(np.arange(len(r_order) - 1, -1, -1), map(lambda x: x[:30].replace(\"\\n\", \"\"), ordered_contents));" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "metadata": {}, - "output_type": "display_data", - "png": 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FcePGUVBQQHFxMbt37y43mb9Ro0Z88cUXHDhwgAYNGrBv3z7ef/99FAoF48aN486dO+jp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/xz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\nnRwcHDhz5ky5Nffq1QsAJycntm7dCkB8fLzUGOjSpQvm5ublnrt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- "text": [ - "" - ] - } - ], - "prompt_number": 23 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "In the graphic above, you can see why sorting by mean would be sub-optimal." - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### Extension to Starred rating systems\n", - "\n", - "The above procedure works well for upvote-downvotes schemes, but what about systems that use star ratings, e.g. 5 star rating systems. Similar problems apply with simply taking the average: an item with two perfect ratings would beat an item with thousands of perfect ratings, but a single sub-perfect rating. \n", - "\n", - "\n", - "We can consider the upvote-downvote problem above as binary: 0 is a downvote, 1 if an upvote. A $N$-star rating system can be seen as a more continuous version of above, and we can set $n$ stars rewarded is equivalent to rewarding $\\frac{n}{N}$. For example, in a 5-star system, a 2 star rating corresponds to 0.4. A perfect rating is a 1. We can use the same formula as before, but with $a,b$ defined differently:\n", - "\n", - "\n", - "$$ \\frac{a}{a + b} - 1.65\\sqrt{ \\frac{ab}{ (a+b)^2(a + b +1 ) } }$$\n", - "\n", - "where \n", - "\n", - "\\begin{align}\n", - "& a = 1 + S \\\\\\\\\n", - "& b = 1 + N - S \\\\\\\\\n", - "\\end{align}\n", - "\n", - "where $N$ is the number of users who rated, and $S$ is the sum of all the ratings, under the equivalence scheme mentioned above. " - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "##### Example: Counting Github stars\n", - "\n", - "What is the average number of stars a Github repository has? How would you calculate this? There are over 6 million respositories, so there is more than enough data to invoke the Law of Large numbers. Let's start pulling some data. TODO" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### Conclusion\n", - "\n", - "While the Law of Large Numbers is cool, it is only true so much as its name implies: with large sample sizes only. We have seen how our inference can be affected by not considering *how the data is shaped*. \n", - "\n", - "1. By (cheaply) drawing many samples from the posterior distributions, we can ensure that the Law of Large Number applies as we approximate expected values (which we will do in the next chapter).\n", - "\n", - "2. Bayesian inference understands that with small sample sizes, we can observe wild randomness. Our posterior distribution will reflect this by being more spread rather than tightly concentrated. Thus, our inference should be correctable.\n", - "\n", - "3. There are major implications of not considering the sample size, and trying to sort objects that are unstable leads to pathological orderings. The method provided above solves this problem.\n" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### Appendix\n", - "\n", - "##### Derivation of sorting comments formula\n", - "\n", - "Basically what we are doing is using a Beta prior (with parameters $a=1, b=1$, which is a uniform distribution), and using a Binomial likelihood with observations $u, N = u+d$. This means our posterior is a Beta distribution with parameters $a' = 1 + u, b' = 1 + (N - u) = 1+d$. We then need to find the value, $x$, such that 0.05 probability is less than $x$. This is usually done by inverting the CDF ([Cumulative Distribution Function](http://en.wikipedia.org/wiki/Cumulative_Distribution_Function)), but the CDF of the beta, for integer parameters, is known but is a large sum [3]. \n", - "\n", - "We instead use a Normal approximation. The mean of the Beta is $\\mu = a'/(a'+b')$ and the variance is \n", - "\n", - "$$\\sigma^2 = \\frac{a'b'}{ (a' + b')^2(a'+b'+1) }$$\n", - "\n", - "Hence we solve the following equation for $x$ and have an approximate lower bound. \n", - "\n", - "$$ 0.05 = \\Phi\\left( \\frac{(x - \\mu)}{\\sigma}\\right) $$ \n", - "\n", - "$\\Phi$ being the [cumulative distribution for the normal distribution](http://en.wikipedia.org/wiki/Normal_distribution#Cumulative_distribution)\n", - "\n", - "\n", - "\n", - "\n" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "##### Exercises\n", - "\n", - "1\\. How would you estimate the quantity $E\\left[ \\cos{X} \\right]$, where $X \\sim \\text{Exp}(4)$? What about $E\\left[ \\cos{X} | X \\lt 1\\right]$, i.e. the expected value *given* we know $X$ is less than 1? Would you need more samples than the original samples size to be equally accurate?" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "# Enter code here\n", - "import scipy.stats as stats\n", - "exp = stats.expon(scale=4)\n", - "N = 1e5\n", - "X = exp.rvs(N)\n", - "# ..." - ], - "language": "python", - "metadata": {}, - "outputs": [], - "prompt_number": 14 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "2\\. The following table was located in the paper \"Going for Three: Predicting the Likelihood of Field Goal Success with Logistic Regression\" [2]. The table ranks football field-goal kickers by their percent of non-misses. What mistake have the researchers made?\n", - "\n", - "-----\n", - "\n", - "#### Kicker Careers Ranked by Make Percentage\n", - "
Rank Kicker Make % Number of Kicks
1 Garrett Hartley 87.7 57
2 Matt Stover 86.8 335
3 Robbie Gould 86.2 224
4 Rob Bironas 86.1 223
5 Shayne Graham 85.4 254
\u2026 \u2026 \u2026
51 Dave Rayner 72.2 90
52 Nick Novak 71.9 64
53 Tim Seder 71.0 62
54 Jose Cortez 70.7 75
55 Wade Richey 66.1 56
" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "In August 2013, [a popular post](http://bpodgursky.wordpress.com/2013/08/21/average-income-per-programming-language/) on the average income per programmer of different languages was trending. Here's the summary chart: (reproduced without permission, cause when you lie with stats, you gunna get the hammer). What do you notice about the extremes?\n", - "\n", - "------\n", - "\n", - "#### Average household income by programming language\n", - "\n", - "\n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - "
LanguageAverage Household Income ($)Data Points
Puppet87,589.29112
Haskell89,973.82191
PHP94,031.19978
CoffeeScript94,890.80435
VimL94,967.11532
Shell96,930.54979
Lua96,930.69101
Erlang97,306.55168
Clojure97,500.00269
Python97,578.872314
JavaScript97,598.753443
Emacs Lisp97,774.65355
C#97,823.31665
Ruby98,238.743242
C++99,147.93845
CSS99,881.40527
Perl100,295.45990
C100,766.512120
Go101,158.01231
Scala101,460.91243
ColdFusion101,536.70109
Objective-C101,801.60562
Groovy102,650.86116
Java103,179.391402
XSLT106,199.19123
ActionScript108,119.47113
" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### References\n", - "\n", - "1. Wainer, Howard. *The Most Dangerous Equation*. American Scientist, Volume 95.\n", - "2. Clarck, Torin K., Aaron W. Johnson, and Alexander J. Stimpson. \"Going for Three: Predicting the Likelihood of Field Goal Success with Logistic Regression.\" (2013): n. page. [Web](http://www.sloansportsconference.com/wp-content/uploads/2013/Going%20for%20Three%20Predicting%20the%20Likelihood%20of%20Field%20Goal%20Success%20with%20Logistic%20Regression.pdf). 20 Feb. 2013.\n", - "3. http://en.wikipedia.org/wiki/Beta_function#Incomplete_beta_function" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "from IPython.core.display import HTML\n", - "\n", - "\n", - "def css_styling():\n", - " styles = open(\"../styles/custom.css\", \"r\").read()\n", - " return HTML(styles)\n", - "css_styling()" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "html": [ - "\n", - "\n" - ], - "metadata": {}, - "output_type": "pyout", - "prompt_number": 1, - "text": [ - "" - ] - } - ], - "prompt_number": 1 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "" - ] - } - ], - "metadata": {} - } - ] -} +{ + "metadata": { + "name": "" + }, + "nbformat": 3, + "nbformat_minor": 0, + "worksheets": [ + { + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "#Chapter 4\n", + "______\n", + "\n", + "##The greatest theorem never told\n", + "\n", + "\n", + "This chapter focuses on an idea that is always bouncing around our minds, but is rarely made explicit outside books devoted to statistics. In fact, we've been using this simple idea in every example thus far. " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "###The Law of Large Numbers\n", + "\n", + "Let $Z_i$ be $N$ independent samples from some probability distribution. According to *the Law of Large numbers*, so long as the expected value $E[Z]$ is finite, the following holds,\n", + "\n", + "$$\\frac{1}{N} \\sum_{i=1}^N Z_i \\rightarrow E[ Z ], \\;\\;\\; N \\rightarrow \\infty.$$\n", + "\n", + "In words:\n", + "\n", + "> The average of a sequence of random variables from the same distribution converges to the expected value of that distribution.\n", + "\n", + "This may seem like a boring result, but it will be the most useful tool you use." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Intuition \n", + "\n", + "If the above Law is somewhat surprising, it can be made more clear by examining a simple example. \n", + "\n", + "Consider a random variable $Z$ that can take only two values, $c_1$ and $c_2$. Suppose we have a large number of samples of $Z$, denoting a specific sample $Z_i$. The Law says that we can approximate the expected value of $Z$ by averaging over all samples. Consider the average:\n", + "\n", + "\n", + "$$ \\frac{1}{N} \\sum_{i=1}^N \\;Z_i $$\n", + "\n", + "\n", + "By construction, $Z_i$ can only take on $c_1$ or $c_2$, hence we can partition the sum over these two values:\n", + "\n", + "\\begin{align}\n", + "\\frac{1}{N} \\sum_{i=1}^N \\;Z_i\n", + "& =\\frac{1}{N} \\big( \\sum_{ Z_i = c_1}c_1 + \\sum_{Z_i=c_2}c_2 \\big) \\\\\\\\[5pt]\n", + "& = c_1 \\sum_{ Z_i = c_1}\\frac{1}{N} + c_2 \\sum_{ Z_i = c_2}\\frac{1}{N} \\\\\\\\[5pt]\n", + "& = c_1 \\times \\text{ (approximate frequency of $c_1$) } \\\\\\\\ \n", + "& \\;\\;\\;\\;\\;\\;\\;\\;\\; + c_2 \\times \\text{ (approximate frequency of $c_2$) } \\\\\\\\[5pt]\n", + "& \\approx c_1 \\times P(Z = c_1) + c_2 \\times P(Z = c_2 ) \\\\\\\\[5pt]\n", + "& = E[Z]\n", + "\\end{align}\n", + "\n", + "\n", + "Equality holds in the limit, but we can get closer and closer by using more and more samples in the average. This Law holds for almost *any distribution*, minus some important cases we will encounter later.\n", + "\n", + "##### Example\n", + "____\n", + "\n", + "\n", + "Below is a diagram of the Law of Large numbers in action for three different sequences of Poisson random variables. \n", + "\n", + " We sample `sample_size = 100000` Poisson random variables with parameter $\\lambda = 4.5$. (Recall the expected value of a Poisson random variable is equal to it's parameter.) We calculate the average for the first $n$ samples, for $n=1$ to `sample_size`. " + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "%matplotlib inline\n", + "import numpy as np\n", + "from IPython.core.pylabtools import figsize\n", + "import matplotlib.pyplot as plt\n", + "\n", + "figsize(12.5, 5)\n", + "import pymc as pm\n", + "\n", + "sample_size = 100000\n", + "expected_value = lambda_ = 4.5\n", + "poi = pm.rpoisson\n", + "N_samples = range(1, sample_size, 100)\n", + "\n", + "for k in range(3):\n", + "\n", + " samples = poi(lambda_, size=sample_size)\n", + "\n", + " partial_average = [samples[:i].mean() for i in N_samples]\n", + "\n", + " plt.plot(N_samples, partial_average, lw=1.5, label=\"average \\\n", + "of $n$ samples; seq. %d\" % k)\n", + "\n", + "\n", + "plt.plot(N_samples, expected_value * np.ones_like(partial_average),\n", + " ls=\"--\", label=\"true expected value\", c=\"k\")\n", + "\n", + "plt.ylim(4.35, 4.65)\n", + "plt.title(\"Convergence of the average of \\n random variables to its \\\n", + "expected value\")\n", + "plt.ylabel(\"average of $n$ samples\")\n", + "plt.xlabel(\"# of samples, $n$\")\n", + "plt.legend();" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "display_data", + "png": 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G/g3ubsQYq1J5N4ZNmzbhzTffhLm5OT799FMAQGhoKFxcXGBmZoaWLVti1qxZKC4uFteN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\ndp0RZxJQE/71BlaRFdhBXmAVWYG3sVUSC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+ "text": [ + "" + ] + } + ], + "prompt_number": 1 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Looking at the above plot, it is clear that when the sample size is small, there is greater variation in the average (compare how *jagged and jumpy* the average is initially, then *smooths* out). All three paths *approach* the value 4.5, but just flirt with it as $N$ gets large. Mathematicians and statistician have another name for *flirting*: convergence. \n", + "\n", + "Another very relevant question we can ask is *how quickly am I converging to the expected value?* Let's plot something new. For a specific $N$, let's do the above trials thousands of times and compute how far away we are from the true expected value, on average. But wait — *compute on average*? This is simply the law of large numbers again! For example, we are interested in, for a specific $N$, the quantity:\n", + "\n", + "$$D(N) = \\sqrt{ \\;E\\left[\\;\\; \\left( \\frac{1}{N}\\sum_{i=1}^NZ_i - 4.5 \\;\\right)^2 \\;\\;\\right] \\;\\;}$$\n", + "\n", + "The above formulae is interpretable as a distance away from the true value (on average), for some $N$. (We take the square root so the dimensions of the above quantity and our random variables are the same). As the above is an expected value, it can be approximated using the law of large numbers: instead of averaging $Z_i$, we calculate the following multiple times and average them:\n", + "\n", + "$$ Y_k = \\left( \\;\\frac{1}{N}\\sum_{i=1}^NZ_i - 4.5 \\; \\right)^2 $$\n", + "\n", + "By computing the above many, $N_y$, times (remember, it is random), and averaging them:\n", + "\n", + "$$ \\frac{1}{N_Y} \\sum_{k=1}^{N_Y} Y_k \\rightarrow E[ Y_k ] = E\\;\\left[\\;\\; \\left( \\frac{1}{N}\\sum_{i=1}^NZ_i - 4.5 \\;\\right)^2 \\right]$$\n", + "\n", + "Finally, taking the square root:\n", + "\n", + "$$ \\sqrt{\\frac{1}{N_Y} \\sum_{k=1}^{N_Y} Y_k} \\approx D(N) $$ " + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "figsize(12.5, 4)\n", + "\n", + "N_Y = 250 # use this many to approximate D(N)\n", + "N_array = np.arange(1000, 50000, 2500) # use this many samples in the approx. to the variance.\n", + "D_N_results = np.zeros(len(N_array))\n", + "\n", + "lambda_ = 4.5\n", + "expected_value = lambda_ # for X ~ Poi(lambda) , E[ X ] = lambda\n", + "\n", + "\n", + "def D_N(n):\n", + " \"\"\"\n", + " This function approx. D_n, the average variance of using n samples.\n", + " \"\"\"\n", + " Z = poi(lambda_, size=(n, N_Y))\n", + " average_Z = Z.mean(axis=0)\n", + " return np.sqrt(((average_Z - expected_value) ** 2).mean())\n", + "\n", + "\n", + "for i, n in enumerate(N_array):\n", + " D_N_results[i] = D_N(n)\n", + "\n", + "\n", + "plt.xlabel(\"$N$\")\n", + "plt.ylabel(\"expected squared-distance from true value\")\n", + "plt.plot(N_array, D_N_results, lw=3,\n", + " label=\"expected distance between\\n\\\n", + "expected value and \\naverage of $N$ random variables.\")\n", + "plt.plot(N_array, np.sqrt(expected_value) / np.sqrt(N_array), lw=2, ls=\"--\",\n", + " label=r\"$\\frac{\\sqrt{\\lambda}}{\\sqrt{N}}$\")\n", + "plt.legend()\n", + "plt.title(\"How 'fast' is the sample average converging? \");" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "display_data", + "png": 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kSZIkSXrj5ObmEhAQQIMGDTh//jxbtmxh8eLF7Nu3DzMzMxYsWEBwcDC3bt1i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+ "text": [ + "" + ] + } + ], + "prompt_number": 2 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "As expected, the expected distance between our sample average and the actual expected value shrinks as $N$ grows large. But also notice that the *rate* of convergence decreases, that is, we need only 10 000 additional samples to move from 0.020 to 0.015, a difference of 0.005, but *20 000* more samples to again decrease from 0.015 to 0.010, again only a 0.005 decrease.\n", + "\n", + "\n", + "It turns out we can measure this rate of convergence. Above I have plotted a second line, the function $\\sqrt{\\lambda}/\\sqrt{N}$. This was not chosen arbitrarily. In most cases, given a sequence of random variable distributed like $Z$, the rate of converge to $E[Z]$ of the Law of Large Numbers is \n", + "\n", + "$$ \\frac{ \\sqrt{ \\; Var(Z) \\; } }{\\sqrt{N} }$$\n", + "\n", + "This is useful to know: for a given large $N$, we know (on average) how far away we are from the estimate. On the other hand, in a Bayesian setting, this can seem like a useless result: Bayesian analysis is OK with uncertainty so what's the *statistical* point of adding extra precise digits? Though drawing samples can be so computationally cheap that having a *larger* $N$ is fine too. \n", + "\n", + "### How do we compute $Var(Z)$ though?\n", + "\n", + "The variance is simply another expected value that can be approximated! Consider the following, once we have the expected value (by using the Law of Large Numbers to estimate it, denote it $\\mu$), we can estimate the variance:\n", + "\n", + "$$ \\frac{1}{N}\\sum_{i=1}^N \\;(Z_i - \\mu)^2 \\rightarrow E[ \\;( Z - \\mu)^2 \\;] = Var( Z )$$\n", + "\n", + "### Expected values and probabilities \n", + "There is an even less explicit relationship between expected value and estimating probabilities. Define the *indicator function*\n", + "\n", + "$$\\mathbb{1}_A(x) = \n", + "\\begin{cases} 1 & x \\in A \\\\\\\\\n", + " 0 & else\n", + "\\end{cases}\n", + "$$\n", + "Then, by the law of large numbers, if we have many samples $X_i$, we can estimate the probability of an event $A$, denoted $P(A)$, by:\n", + "\n", + "$$ \\frac{1}{N} \\sum_{i=1}^N \\mathbb{1}_A(X_i) \\rightarrow E[\\mathbb{1}_A(X)] = P(A) $$\n", + "\n", + "Again, this is fairly obvious after a moments thought: the indicator function is only 1 if the event occurs, so we are summing only the times the event occurs and dividing by the total number of trials (consider how we usually approximate probabilities using frequencies). For example, suppose we wish to estimate the probability that a $Z \\sim Exp(.5)$ is greater than 10, and we have many samples from a $Exp(.5)$ distribution. \n", + "\n", + "\n", + "$$ P( Z > 10 ) = \\sum_{i=1}^N \\mathbb{1}_{z > 10 }(Z_i) $$\n" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import pymc as pm\n", + "N = 10000\n", + "print np.mean([pm.rexponential(0.5) > 10 for i in range(N)])" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "0.0069\n" + ] + } + ], + "prompt_number": 4 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### What does this all have to do with Bayesian statistics? \n", + "\n", + "\n", + "*Point estimates*, to be introduced in the next chapter, in Bayesian inference are computed using expected values. In more analytical Bayesian inference, we would have been required to evaluate complicated expected values represented as multi-dimensional integrals. No longer. If we can sample from the posterior distribution directly, we simply need to evaluate averages. Much easier. If accuracy is a priority, plots like the ones above show how fast you are converging. And if further accuracy is desired, just take more samples from the posterior. \n", + "\n", + "When is enough enough? When can you stop drawing samples from the posterior? That is the practitioners decision, and also dependent on the variance of the samples (recall from above a high variance means the average will converge slower). \n", + "\n", + "We also should understand when the Law of Large Numbers fails. As the name implies, and comparing the graphs above for small $N$, the Law is only true for large sample sizes. Without this, the asymptotic result is not reliable. Knowing in what situations the Law fails can give us *confidence in how unconfident we should be*. The next section deals with this issue." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## The Disorder of Small Numbers\n", + "\n", + "The Law of Large Numbers is only valid as $N$ gets *infinitely* large: never truly attainable. While the law is a powerful tool, it is foolhardy to apply it liberally. Our next example illustrates this.\n", + "\n", + "\n", + "##### Example: Aggregated geographic data\n", + "\n", + "\n", + "Often data comes in aggregated form. For instance, data may be grouped by state, county, or city level. Of course, the population numbers vary per geographic area. If the data is an average of some characteristic of each the geographic areas, we must be conscious of the Law of Large Numbers and how it can *fail* for areas with small populations.\n", + "\n", + "We will observe this on a toy dataset. Suppose there are five thousand counties in our dataset. Furthermore, population number in each state are uniformly distributed between 100 and 1500. The way the population numbers are generated is irrelevant to the discussion, so we do not justify this. We are interested in measuring the average height of individuals per county. Unbeknownst to us, height does **not** vary across county, and each individual, regardless of the county he or she is currently living in, has the same distribution of what their height may be:\n", + "\n", + "$$ \\text{height} \\sim \\text{Normal}(150, 15 ) $$\n", + "\n", + "We aggregate the individuals at the county level, so we only have data for the *average in the county*. What might our dataset look like?" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "figsize(12.5, 4)\n", + "std_height = 15\n", + "mean_height = 150\n", + "\n", + "n_counties = 5000\n", + "pop_generator = pm.rdiscrete_uniform\n", + "norm = pm.rnormal\n", + "\n", + "# generate some artificial population numbers\n", + "population = pop_generator(100, 1500, size=n_counties)\n", + "\n", + "average_across_county = np.zeros(n_counties)\n", + "for i in range(n_counties):\n", + " # generate some individuals and take the mean\n", + " average_across_county[i] = norm(mean_height, 1. / std_height ** 2,\n", + " size=population[i]).mean()\n", + "\n", + "# located the counties with the apparently most extreme average heights.\n", + "i_min = np.argmin(average_across_county)\n", + "i_max = np.argmax(average_across_county)\n", + "\n", + "# plot population size vs. recorded average\n", + "plt.scatter(population, average_across_county, alpha=0.5, c=\"#7A68A6\")\n", + "plt.scatter([population[i_min], population[i_max]],\n", + " [average_across_county[i_min], average_across_county[i_max]],\n", + " s=60, marker=\"o\", facecolors=\"none\",\n", + " edgecolors=\"#A60628\", linewidths=1.5,\n", + " label=\"extreme heights\")\n", + "\n", + "plt.xlim(100, 1500)\n", + "plt.title(\"Average height vs. County Population\")\n", + "plt.xlabel(\"County Population\")\n", + "plt.ylabel(\"Average height in county\")\n", + "plt.plot([100, 1500], [150, 150], color=\"k\", label=\"true expected \\\n", + "height\", ls=\"--\")\n", + "plt.legend(scatterpoints=1);" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "display_data", + "png": 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QarU4cuQIKioqUFlZiXnz5mHVqlXYsGEDcnNzsW3bNrvzP/74Y6jVamRlZWHT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htjmO9PmT+0mp0KDz/fxHVFY+76803f6tTqJZUn315iVQ1UVeH+ZzdlYZWqwcMvt4gCkRVx9nr2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FvaPbtIZRFrIXKS6c//5jCYNWfcj2wS3u3nd5+um3Eome//l2W2MWVzLcuf8yI2fK5cqb582f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+ "text": [ + "" + ] + } + ], + "prompt_number": 6 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "What do we observe? *Without accounting for population sizes* we run the risk of making an enormous inference error: if we ignored population size, we would say that the county with the shortest and tallest individuals have been correctly circled. But this inference is wrong for the following reason. These two counties do *not* necessarily have the most extreme heights. The error results from the calculated average of smaller populations not being a good reflection of the true expected value of the population (which in truth should be $\\mu =150$). The sample size/population size/$N$, whatever you wish to call it, is simply too small to invoke the Law of Large Numbers effectively. \n", + "\n", + "We provide more damning evidence against this inference. Recall the population numbers were uniformly distributed over 100 to 1500. Our intuition should tell us that the counties with the most extreme population heights should also be uniformly spread over 100 to 1500, and certainly independent of the county's population. Not so. Below are the population sizes of the counties with the most extreme heights." + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "print \"Population sizes of 10 'shortest' counties: \"\n", + "print population[np.argsort(average_across_county)[:10]]\n", + "print\n", + "print \"Population sizes of 10 'tallest' counties: \"\n", + "print population[np.argsort(-average_across_county)[:10]]" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Population sizes of 10 'shortest' counties: \n", + "[111 103 102 109 110 257 164 144 169 260]\n", + "\n", + "Population sizes of 10 'tallest' counties: \n", + "[252 107 162 141 141 256 144 112 210 342]\n" + ] + } + ], + "prompt_number": 7 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Not at all uniform over 100 to 1500. This is an absolute failure of the Law of Large Numbers. \n", + "\n", + "##### Example: Kaggle's *U.S. Census Return Rate Challenge*\n", + "\n", + "Below is data from the 2010 US census, which partitions populations beyond counties to the level of block groups (which are aggregates of city blocks or equivalents). The dataset is from a Kaggle machine learning competition some colleagues and I participated in. The objective was to predict the census letter mail-back rate of a group block, measured between 0 and 100, using census variables (median income, number of females in the block-group, number of trailer parks, average number of children etc.). Below we plot the census mail-back rate versus block group population:" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "figsize(12.5, 6.5)\n", + "data = np.genfromtxt(\"./data/census_data.csv\", skip_header=1,\n", + " delimiter=\",\")\n", + "plt.scatter(data[:, 1], data[:, 0], alpha=0.5, c=\"#7A68A6\")\n", + "plt.title(\"Census mail-back rate vs Population\")\n", + "plt.ylabel(\"Mail-back rate\")\n", + "plt.xlabel(\"population of block-group\")\n", + "plt.xlim(-100, 15e3)\n", + "plt.ylim(-5, 105)\n", + "\n", + "i_min = np.argmin(data[:, 0])\n", + "i_max = np.argmax(data[:, 0])\n", + "\n", + "plt.scatter([data[i_min, 1], data[i_max, 1]],\n", + " [data[i_min, 0], data[i_max, 0]],\n", + " s=60, marker=\"o\", facecolors=\"none\",\n", + " edgecolors=\"#A60628\", linewidths=1.5,\n", + " label=\"most extreme points\")\n", + "\n", + "plt.legend(scatterpoints=1);" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "display_data", + "png": 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CwsIhMQiHswOkXV1drFq1ape2bv8lYHdtqaysJJlM4na76e/vHzGew9neVwUw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+ "text": [ + "" + ] + } + ], + "prompt_number": 8 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The above is a classic phenomenon in statistics. I say *classic* referring to the \"shape\" of the scatter plot above. It follows a classic triangular form, that tightens as we increase the sample size (as the Law of Large Numbers becomes more exact). \n", + "\n", + "I am perhaps overstressing the point and maybe I should have titled the book *\"You don't have big data problems!\"*, but here again is an example of the trouble with *small datasets*, not big ones. Simply, small datasets cannot be processed using the Law of Large Numbers. Compare with applying the Law without hassle to big datasets (ex. big data). I mentioned earlier that paradoxically big data prediction problems are solved by relatively simple algorithms. The paradox is partially resolved by understanding that the Law of Large Numbers creates solutions that are *stable*, i.e. adding or subtracting a few data points will not affect the solution much. On the other hand, adding or removing data points to a small dataset can create very different results. \n", + "\n", + "For further reading on the hidden dangers of the Law of Large Numbers, I would highly recommend the excellent manuscript [The Most Dangerous Equation](http://nsm.uh.edu/~dgraur/niv/TheMostDangerousEquation.pdf). " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "##### Example: How to order Reddit comments\n", + "\n", + "You may have disagreed with the original statement that the Law of Large numbers is known to everyone, but only implicitly in our subconscious decision making. Consider ratings on online products: how often do you trust an average 5-star rating if there is only 1 reviewer? 2 reviewers? 3 reviewers? We implicitly understand that with such few reviewers that the average rating is **not** a good reflection of the true value of the product.\n", + "\n", + "This has created flaws in how we sort items, and more generally, how we compare items. Many people have realized that sorting online search results by their rating, whether the objects be books, videos, or online comments, return poor results. Often the seemingly top videos or comments have perfect ratings only from a few enthusiastic fans, and truly more quality videos or comments are hidden in later pages with *falsely-substandard* ratings of around 4.8. How can we correct this?\n", + "\n", + "Consider the popular site Reddit (I purposefully did not link to the website as you would never come back). The site hosts links to stories or images, and a very popular part of the site are the comments associated with each link. Redditors can vote up or down on each comment (called upvotes and downvotes). Reddit, by default, will sort comments by Top, that is, the best comments.\n", + "\n", + "\n", + "\n", + "\n", + "How would you determine which comments are the best? There are a number of ways to achieve this:\n", + "\n", + "1. *Popularity*: A comment is considered good if it has many upvotes. A problem with this model is that a comment with hundreds of upvotes, but thousands of downvotes. While being very *popular*, the comment is likely more controversial than best.\n", + "2. *Difference*: Using the *difference* of upvotes and downvotes. This solves the above problem, but fails when we consider the temporal nature of comments. Comments can be posted many hours after the original link submission. The difference method will bias the *Top* comments to be the oldest comments, which have accumulated more upvotes than newer comments, but are not necessarily the best.\n", + "3. *Time adjusted*: Consider using Difference divided by the age of the comment. This creates a *rate*, something like *difference per second*, or *per minute*. An immediate counter example is, if we use per second, a 1 second old comment with 1 upvote would be better than a 100 second old comment with 99 upvotes. One can avoid this by only considering at least t second old comments. But what is a good t value? Does this mean no comment younger than t is good? We end up comparing unstable quantities with stable quantities (young vs. old comments).\n", + "3. *Ratio*: Rank comments by the ratio of upvotes to total number of votes (upvotes plus downvotes). This solves the temporal issue, such that new comments who score well can be considered Top just as likely as older comments, provided they have many upvotes to total votes. The problem here is that a comment with a single upvote (ratio = 1.0) will beat a comment with 999 upvotes and 1 downvote (ratio = 0.999), but clearly the latter comment is *more likely* to be better.\n", + "\n", + "I used the phrase *more likely* for good reason. It is possible that the former comment, with a single upvote, is in fact a better comment than the later with 999 upvotes. The hesitation to agree with this is because we have not seen the other 999 potential votes the former comment might get. Perhaps it will achieve an additional 999 upvotes and 0 downvotes and be considered better than the latter, though not likely.\n", + "\n", + "What we really want is an estimate of the *true upvote ratio*. Note that the true upvote ratio is not the same as the observed upvote ratio: the true upvote ratio is hidden, and we only observe upvotes vs. downvotes (one can think of the true upvote ratio as \"what is the underlying probability someone gives this comment a upvote, versus a downvote\"). So the 999 upvote/1 downvote comment probably has a true upvote ratio close to 1, which we can assert with confidence thanks to the Law of Large Numbers, but on the other hand we are much less certain about the true upvote ratio of the comment with only a single upvote. Sounds like a Bayesian problem to me.\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "One way to determine a prior on the upvote ratio is to look at the historical distribution of upvote ratios. This can be accomplished by scraping Reddit's comments and determining a distribution. There are a few problems with this technique though:\n", + "\n", + "1. Skewed data: The vast majority of comments have very few votes, hence there will be many comments with ratios near the extremes (see the \"triangular plot\" in the above Kaggle dataset), effectively skewing our distribution to the extremes. One could try to only use comments with votes greater than some threshold. Again, problems are encountered. There is a tradeoff between number of comments available to use and a higher threshold with associated ratio precision. \n", + "2. Biased data: Reddit is composed of different subpages, called subreddits. Two examples are *r/aww*, which posts pics of cute animals, and *r/politics*. It is very likely that the user behaviour towards comments of these two subreddits are very different: visitors are likely to be more friendly and affectionate in the former, and would therefore upvote comments more, compared to the latter, where comments are likely to be controversial and disagreed upon. Therefore not all comments are the same. \n", + "\n", + "\n", + "In light of these, I think it is better to use a `Uniform` prior.\n", + "\n", + "\n", + "With our prior in place, we can find the posterior of the true upvote ratio. The Python script `comments_for_top_reddit_pic.py` will scrape the comments from the current top picture on Reddit. Below is the picture, and some comments:" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from IPython.core.display import Image\n", + "# adding a number to the end of the %run call with get the ith top photo.\n", + "%run top_pic_comments.py 2\n", + "\n", + "Image(top_post_url)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Title of submission: \n", + "Frozen mining truck\n", + "http://i.imgur.com/OYsHKlH.jpg/n" + ] + }, + { + "metadata": {}, + "output_type": "pyout", + "prompt_number": 10, + "text": [ + "" + ] + } + ], + "prompt_number": 10 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\"\"\"\n", + "contents: an array of the text from all comments on the pic\n", + "votes: a 2d numpy array of upvotes, downvotes for each comment.\n", + "\"\"\"\n", + "n_comments = len(contents)\n", + "comments = np.random.randint(n_comments, size=4)\n", + "print \"Some Comments (out of %d total) \\n-----------\" % n_comments\n", + "for i in comments:\n", + " print '\"' + contents[i] + '\"'\n", + " print\"upvotes/downvotes: \", votes[i, :]\n", + " print" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Some Comments (out of 77 total) \n", + "-----------\n", + "\"Do these trucks remind anyone else of Sly Cooper?\"\n", + "upvotes/downvotes: [2 0]\n", + "\n", + "\"Dammit Elsa I told you not to drink and drive.\"\n", + "upvotes/downvotes: [7 0]\n", + "\n", + "\"I've seen this picture before in a Duratray (the dump box supplier) brochure. If I recall it was either at Ekati or Diavik... In which case the truck could be either a Komatsu or a CAT... anyone care to comment?\"\n", + "upvotes/downvotes: [2 0]\n", + "\n", + "\"Actually it does not look frozen just covered in a layer of wind packed snow.\"\n", + "upvotes/downvotes: [120 18]\n", + "\n" + ] + } + ], + "prompt_number": 15 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + " For a given true upvote ratio $p$ and $N$ votes, the number of upvotes will look like a Binomial random variable with parameters $p$ and $N$. (This is because of the equivalence between upvote ratio and probability of upvoting versus downvoting, out of $N$ possible votes/trials). We create a function that performs Bayesian inference on $p$, for a particular comment's upvote/downvote pair." + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import pymc as pm\n", + "\n", + "\n", + "def posterior_upvote_ratio(upvotes, downvotes, samples=20000):\n", + " \"\"\"\n", + " This function accepts the number of upvotes and downvotes a particular comment received, \n", + " and the number of posterior samples to return to the user. Assumes a uniform prior.\n", + " \"\"\"\n", + " N = upvotes + downvotes\n", + " upvote_ratio = pm.Uniform(\"upvote_ratio\", 0, 1)\n", + " observations = pm.Binomial(\"obs\", N, upvote_ratio, value=upvotes, observed=True)\n", + " # do the fitting; first do a MAP as it is cheap and useful.\n", + " map_ = pm.MAP([upvote_ratio, observations]).fit()\n", + " mcmc = pm.MCMC([upvote_ratio, observations])\n", + " mcmc.sample(samples, samples / 4)\n", + " return mcmc.trace(\"upvote_ratio\")[:]" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 16 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Below are the resulting posterior distributions." + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "figsize(11., 8)\n", + "posteriors = []\n", + "colours = [\"#348ABD\", \"#A60628\", \"#7A68A6\", \"#467821\", \"#CF4457\"]\n", + "for i in range(len(comments)):\n", + " j = comments[i]\n", + " posteriors.append(posterior_upvote_ratio(votes[j, 0], votes[j, 1]))\n", + " plt.hist(posteriors[i], bins=18, normed=True, alpha=.9,\n", + " histtype=\"step\", color=colours[i % 5], lw=3,\n", + " label='(%d up:%d down)\\n%s...' % (votes[j, 0], votes[j, 1], contents[j][:50]))\n", + " plt.hist(posteriors[i], bins=18, normed=True, alpha=.2,\n", + " histtype=\"stepfilled\", color=colours[i], lw=3, )\n", + "\n", + "plt.legend(loc=\"upper left\")\n", + "plt.xlim(0, 1)\n", + "plt.title(\"Posterior distributions of upvote ratios on different comments\");" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + " \r", + "[****************100%******************] 20000 of 20000 complete" + ] + }, + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "\n" + ] + }, + { + "metadata": {}, + "output_type": "display_data", + "png": 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kZGVloXfv3gDqLlyKiorv/gH/X1vm1ZCVlRVycnKwdetWyMrK4ttvv0Xfvn3x8uXLdqsT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\nx4pSd7Xmp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+ "text": [ + "" + ] + } + ], + "prompt_number": 17 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Some distributions are very tight, others have very long tails (relatively speaking), expressing our uncertainty with what the true upvote ratio might be.\n", + "\n", + "### Sorting!\n", + "\n", + "We have been ignoring the goal of this exercise: how do we sort the comments from *best to worst*? Of course, we cannot sort distributions, we must sort scalar numbers. There are many ways to distill a distribution down to a scalar: expressing the distribution through its expected value, or mean, is one way. Choosing the mean is a bad choice though. This is because the mean does not take into account the uncertainty of distributions.\n", + "\n", + "I suggest using the *95% least plausible value*, defined as the value such that there is only a 5% chance the true parameter is lower (think of the lower bound on the 95% credible region). Below are the posterior distributions with the 95% least-plausible value plotted:" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "N = posteriors[0].shape[0]\n", + "lower_limits = []\n", + "\n", + "for i in range(len(comments)):\n", + " j = comments[i]\n", + " plt.hist(posteriors[i], bins=20, normed=True, alpha=.9,\n", + " histtype=\"step\", color=colours[i], lw=3,\n", + " label='(%d up:%d down)\\n%s...' % (votes[j, 0], votes[j, 1], contents[j][:50]))\n", + " plt.hist(posteriors[i], bins=20, normed=True, alpha=.2,\n", + " histtype=\"stepfilled\", color=colours[i], lw=3, )\n", + " v = np.sort(posteriors[i])[int(0.05 * N)]\n", + " # plt.vlines( v, 0, 15 , color = \"k\", alpha = 1, linewidths=3 )\n", + " plt.vlines(v, 0, 10, color=colours[i], linestyles=\"--\", linewidths=3)\n", + " lower_limits.append(v)\n", + " plt.legend(loc=\"upper left\")\n", + "\n", + "plt.legend(loc=\"upper left\")\n", + "plt.title(\"Posterior distributions of upvote ratios on different comments\");\n", + "order = np.argsort(-np.array(lower_limits))\n", + "print order, lower_limits" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "[3 1 2 0] [0.36980613417267094, 0.68407203257290061, 0.37551825562169117, 0.8177566237850703]\n" + ] + }, + { + "metadata": {}, + "output_type": "display_data", + "png": 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b2+PUqVOoqamBtrY27O3tERISgqdPn8LS0rLZa25MVlYW+vbt2+r4FAqFQqFQ\nui5UUWzC6NGjGXs9oH5xx4QJEzB79mx4e3u3mN7S0hKRkZGoqanB9evXcebMGRE7xW3btuHFixdI\nT09HSEgIJk6cKDYvDw8PHD16FJmZmXj69Cm2bt0KLy8vsXE//vhjZGRk4OzZs6ipqcH+/ftZSqqb\nmxv27dsHoVCI8vJyrFu3Dm5ubszooJ2dHQ4cOIAhQ4YAqLdbaXC3ZYud2NhYODk5tTo+hULpetBZ\ngQ+HrmqjWPKsEAUP74j+HuWitq6ms8X7oJDubAHOpj9CRGoJXtbUvrUy5KWlMNlSA5+a9Wgxrqen\nJxwcHPDy5UvIy8vjyJEjyMvLw+bNm7F582YmnlAoFJt+1apVmD17NgwNDWFnZ4fJkyeLLD6xs7OD\njY0N6urqsHDhQowYMQIAEB8fDw8PDyZvR0dHLFq0CBMmTMCLFy8wfvx4fPPNN2LL7d69O4KCguDn\n54eFCxfCw8ODNUU+ffp0FBUVYdy4cXj16hUcHR2xadMmlkwVFRWMPeLgwYPx8uVLRnFsoDmlsaio\nCFlZWRg3bpzEOBQKhUKhNMfJ+F+QkZ8kMVyJp4Yvx66BrLRcB0r14cIh4lZbtAMXLlyAtbW1iH9h\nYSHLls47/PZbVRIbkJeWwq/u5q2Ku379evTo0YPZ1qa9EAqFGDBgAB4+fMiy83tfWLNmDQwNDZnN\nyikUyrtJenp6s7s7UN4fYmJiutyo4saIxaitrRG7GJQDgMvlws1uDkx1rTpeuHeY5ORkODo6tjld\np48odoSS2NZyvv3227coyfvLunXrOlsECoVCobzjkLpagNTb2ivzVNEwj1X5shy1pH7aubaOngDW\nUXS6otiYUK/WL5poLZ7Bqe2e55vQkUfqUSgUyutAbRQ/HLraaGJTXAbNYN6b0clheFQmfpcQytuj\nSymK7zt8Ph+PHj3qbDEoFAqFQqFQWsX7ZyhHoVAolDeC7qP44UD3UaS0BFUUOwEXFxccOXKks8V4\na8TExHT5vRQLCgrA5/PFGku3hqZnen9IdPS1v3jxAlOnToWBgQFmzZrV5vTq6uq4d+9e+wtGoVAo\nHwBUUWyClZUVdHR0wOfzIRAIMHbsWPz666+vrVBs3LhRZPV00/OgOxqhUAh1dXXU1dV1mgydja6u\nLoRC4Wvfh86+h51JR1/76dOn8fDhQ9y9exe//PKLSPizZ8+wcOFCmJmZgc/nY9CgQdi1a1e7lJ2U\nlAR3d3caZgS2AAAgAElEQVQIBAIYGRnByckJwcHB7ZJ3e1FbW4sVK1bA0tISAoEAX3zxBV6+fPlG\neVIbxQ+Hrm6jSOl8upSNYldYeMLhcBASEgIHBwc8f/4csbGx8PPzQ2JiIvbs2dPZ4rUrzSm/tbW1\nkJKS6kBpmqempgbS0l2quVI6iPz8fBgbG0vcUmrVqlV4+fIlEhISoKKiguzsbKSnp79xuf/++y8m\nT56M5cuXY//+/VBTU8PNmzfh7+8vceP7joYQglevXkFVVRX//e9/ISMjg8mTJ+Pnn3/G4sWLO1s8\nCoXyHtDpI4ry0h2jjLxOOcrKyhg7diwOHTqE0NBQ5uVTVlaGefPmoXfv3rCyssK2bdvEKl1///03\ndu7ciZMnT4LP52P48OFMmFAoxCeffAI+n49Jkybh8ePHTNi1a9cwZswYCAQCODg4sE6KCQ4OhrW1\nNfh8PgYMGICIiAgm7OjRo7C1tYWhoSEmT57MOiqwMQ0bYgsEAvD5fFy7dg3BwcEYO3YsVq9eDWNj\nY2zcuFFkNLTpSOSTJ0+wYMECWFhYwNDQEJ999pnY8vbv348hQ4bgwYMHKC0thaenJzNCM27cOIkK\nq7q6Og4dOgQbGxsMGjQIAHD+/Hk4ODgwo723b99m4ltZWWH37t0YOnQo+Hw+Fi1ahJKSEkyZMgX6\n+vqYOHEiY3vV9FpcXFzw448/SrwnYWFh6NevH4yNjbF9+3ax8jYQHR2N4cOHQ19fH5aWlqyNzRvK\nDQ0NRb9+/WBiYsLkV1xcDF1dXTx58oSJf/PmTfTu3Ru1tbWoq6vD1q1bYWVlBVNTU8yfP585/7u5\nfIF6hWLnzp346KOPYGxsjFmzZolsBN+Y5uq5MUlJSRg1ahT09fXRp08f1tZSzbXjpmRmZsLFxQUC\ngQB2dnb4888/AQA//fQTtm7dyjxDx44dE0l748YNTJo0CSoqKgAAExMTjB8/XiRecnIy+vTpw2pv\nZ86cgYODg1iZvv/+e0ydOhWLFy+GmpoagPo2dujQISbO4cOHYWNjAyMjI0ybNo11bntCQgIcHR1h\nYGAAJycn/Pvvv0yYi4sL1q5dCycnJ+jr62P69Oms+9Fc3bm4uGDDhg0YO3YsdHV1UVJSgtWrV0Nd\nXR0qKiqwsLB440Vz1Ebxw4HaKFJaotMVxcmWGm9dWWw4meV1sba2Rq9evZCQkAAAWLlyJcrLy3H9\n+nWcPXsWYWFhYl9gTk5OWLp0Kdzc3CAUChm7LkIITpw4gYCAAGRlZaG6upoZrSwsLMTUqVOxYsUK\n5ObmYu3atZg5cyYeP36MiooK+Pn54fjx4xAKhTh//jxjC/jHH39g586dOHLkCHJycjBkyBDMnj1b\n7PX88ccfAIB79+5BKBRi4MCBAOpfpAKBAFlZWfj6669bnF6cO3cuXr16hfj4eGRlZWH+/PkicTZv\n3oywsDD8/vvv0NbWRkBAAHR0dJCTk4OsrCysWbOm2XL++OMPXLhwAfHx8UhJScHixYuxc+dO3L17\nF97e3vDy8kJ1df1+WhwOB2fPnkVUVBQSEhIQHR0Nd3d3fP/998jKygIhBPv375dYVmRkpNh7kpGR\ngRUrVuDnn3/G7du38fjxYxQWFkrMR1FREYGBgcjLy0NYWBiCgoKYOm8gISEB165dQ1RUFLZs2YLs\n7GxoamrC3t4eUVFRTLywsDC4ublBSkoKwcHBCA0NxZkzZ5CcnIzy8nKsXLmyxXyBemX93LlzOHv2\nLNLT06GqqooVK1aIlb+lem6Mn58f5s2bh7y8PCQnJ8PV1RWA5HZcWloqkkd1dTW8vLzg6OiI7Oxs\nbNq0CXPmzEFOTg78/PxYz9C0adNE0tvY2GD9+vUIDg7GnTt3JN4Xa2trqKmp4cKFC4xfeHg4PD09\nReJWVlYiMTFRrMLZwJUrV7B+/XoEBQUhPT0denp6zDP35MkTeHp6Yu7cubh79y7mzZsHT09PljIY\nFhaGPXv2ID09HVJSUsypS831AY3l3rVrF/Lz86Grq8v4JyQkIDIyEpMnT5YoN4VCobSFTp/L+9Ss\nR6uO1utstLS08OTJE9TW1uLkyZO4cuUKFBUVoaioiPnz5yM8PBzTp08XSUcIERkx43A4mDZtGgwN\nDQEArq6uOHfuHADg+PHjGD16NHNe8ogRI9C/f39ER0dj/Pjx4HK5uH37Nnr16gUNDQ1oaNQrwEFB\nQViyZAlMTEwAAEuXLsWOHTtQUFDAepE0yCTpGhtedPLy8s1OTRcVFeHChQu4e/cuM5LT+Lg/QghW\nr16NGzdu4NSpU1BWVgYAyMjIoLi4GEKhEAKBgHXMoDiWLl3K2EsdPnwYM2fOZE788fT0xI4dO5CY\nmMiUPWfOHPToUd+ebG1toaGhwSjT48aNw5UrV8SWw+Fw4OXlJfaenD59GmPGjGFkXbVqFQ4ePChR\nZnt7e+a/ubk5Jk6ciNjYWDg7OzP+vr6+kJOTg4WFBSwsLJCWlgYTExN4eHjgwIED8PHxYdpag01c\nREQEFixYAD6fDwD47rvvYG9vj4CAgBbzDQoKwpYtW6Ctrc3Es7Kywv79+0WmdFtTzw3Iysrizp07\nKC0thbq6OmxsbABIbsd//fWXiGKWmJiIyspKLFmyBAAwbNgwjBkzBidOnMDKlSvFPkON2bRpE/bt\n24eDBw9i6dKl0NPTw8aNG8WeOe7p6Ynjx4/DyckJT548waVLl7Bt2zaReE+fPkVdXR00NTUllnv8\n+HFMnz4dlpb1+782nEyUn5+PuLg4GBsbY8qUKQCASZMm4eeff8a5c+cwdepUcDgceHp6ok+fPgDq\n29Tw4cOxd+/eZvsAT09PcDgcTJ06FaampgDA3L87d+5g2rRp2LNnD/r16ydR7tZAbRQ/HKiNIqUl\nOn1E8V2hsLAQampqKC0tRXV1NfT09JgwXV1dPHjwoE35NSh4QL1SVlFRAaDeHuvUqVMQCATM799/\n/0VJSQl4PB4OHTqEoKAgmJubw9PTkxkxys/Px6pVq5g0RkZGANAmuXR0dFod9/79+1BTU2OUxKaU\nlZXhyJEjWLJkCaMkAsCiRYsgEAgwadIkWFtbt7jooLFM+fn52Lt3L6tuCgsLWdfYs2dP5r+CggLL\nLScnh/LycollSbonRUVFrGMneTweunfvLjGfhpGo3r17w8DAAIcPH2ZNJwNgKSA8Ho8py9nZGZmZ\nmRAKhbh06RJUVFQwYMAARo7GSr+uri5qampQUlLSYr4FBQX47LPPmHobMmQIpKWlWWkbaE09N+Dv\n7487d+7A1tYWTk5OiI6OZvKQ1I6b8uDBA5G2p6en1+q2Ky8vj6VLl+LixYvIycmBq6srZs2aJXb6\ndPLkyfjzzz9RWVmJqKgoDBkyhHXfG1BVVQWXy0VxcbHEcouLi1n9gKKiIrp3747CwkLGjKDpNTWe\nmm58zbq6uqiurkZpaWmr6k7csxocHAxnZ2e4uLhIlJlCoVDaSqePKL4LJCcno6ioCIMHD4a6ujpk\nZGQgFAqZL/qCggKWItGYtp7prKurC3d3d+zcuVNs+KhRozBq1Ci8evUK69evx5IlS/D7779DV1cX\nK1aswKRJk1osQ9JUb1N/RUVFVFZWMu7GL00dHR08efIEZWVlYpXFbt264eeff4aPjw9+++03DB48\nGACgpKSEdevWYd26dUhPT4erqysGDBgg0U6ssUy6urpYtmwZli1b1uI1NtAeR5lraWkhKyuLcVdW\nVrKmAZsyZ84czJkzBxEREZCVlcWqVauajd8YeXl5TJgwAeHh4cjOzoaHhwcTpq2tjfz8fMZdUFAA\naWlpaGhoSLRHbUBXVxe7d+9mbD1bitvaejY0NMSBAwcA1I+8ent7Iycnp8V23BhtbW3cv38fhBDm\nfufn5zOj421BWVkZS5YswY4dO5CXlycysqajowMbGxucPXsW4eHh+Pzzz8Xmw+PxMHDgQJw+fZo1\nQtwYLS0tCIVCxl1RUYHHjx9DR0cHWlparHvVcE2NRzkb37OCggLIyMigR48erao7cc9wcXGxxH6o\nrTx79qzd8qJ0bbriWc+UrgUdURRDg3JRVlaG8+fP44svvoCHhwfMzMwgJSUFV1dXbNiwAeXl5cjP\nz8e+ffuYKaamaGhoQCgUiigskhSYKVOm4Pz587h48SJqa2vx8uVLxMTEoLCwEA8fPsQff/yBiooK\nyMjIgMfjMSuTfXx8sH37dmRkZDCyN7Z1a4y6ujq4XC5yc3ObrQdLS0vEx8ejoKAAZWVlrBeXlpYW\nnJycsHz5cjx79gzV1dWIi4tjpbezs8P+/fsxc+ZMJCcnA6hf6HH37t36MzyVlSElJdXq1dUzZsxA\nUFAQkpKSQAhBRUUFoqOjmx0lbAuS7omLiwuio6Nx9epVVFVV4aeffmp2a6GKigqoqqpCVlYWSUlJ\nOHHiRIv2no3L9vDwQHBwMM6dOwd3d3fG383NDfv27YNQKER5eTnWrVsHNze3Vn2MeHt7Y/369Yxy\n8ujRI2ZqvSltqefw8HBm4YSKigo4HA6kpKSabcdNsbGxgYKCAvz9/VFdXY2YmBicP38ebm5uLV4X\nAGzZsgXXr19HVVUVXr58if3790NVVRXGxsZi43t6emLXrl1IT0/Hp59+KjHf//znPwgJCcHu3bsZ\nRT8tLY0xz5g0aRKCg4ORlpaGV69eYd26dbCxsYGuri6cnJxw584dnDhxAjU1NYiMjER2djbGjBkD\noP5+h4eHIzMzE5WVlfjpp58wYcIEcDicVtWduLb6448/4quvvmpVnVEoFEproYqiGLy8vMDn89Gv\nXz/s2LEDCxYsYG2Ns2nTJvB4PFhbW8PZ2RlTpkwRa2QPABMmTAAAGBkZYdSoUYx/Y8Wh8b50Ojo6\nOHr0KHbs2IHevXujX79+CAgIACEEdXV12LdvHywsLGBkZISrV69i69atAOrt77766ivMnj0b+vr6\nsLe3x8WLF8XKxOPxsGzZMnzyyScwNDREYmKi2L3xRowYgYkTJ2LYsGFwdHTEmDFjWHECAwMhIyOD\nwYMHw9TUlLVQpCHeiBEjsHv3bnh5eSElJQV37tyBm5sb+Hw+xo4di88//1ziiE1Tefr374+dO3di\n5cqVMDQ0xMCBAxEaGtqsEiapnsXlLymumZkZNm/ejDlz5sDc3BxqamrNTtNv2bIFP/30E/h8PrZu\n3YqJEyc2e11N/WxtbcHlctG/f3/W9OX06dPh7u6OcePGwdraGjwej7Wiurl6mDt3LsaOHYtJkyaB\nz+djzJgxjPLelLbU88WLF2Fvbw8+n4/Vq1fj4MGDkJOTk9iOxSnYMjIyCA4Oxt9//w0TExP4+voi\nMDCQUfRa2reRy+Vi4cKFMDExgYWFBa5cuYLQ0FDweDyx9fLpp5+ioKAA48aNg7y8vMR8Bw0ahKio\nKPzzzz+wtraGkZERli5dio8//hgAMHz4cKxatQozZ86Eubk5hEIhY7vavXt3hISEICAgAMbGxggI\nCEBISAizeprD4cDDwwMLFiyAmZkZqqursXHjRgDN9wENiKuPH374Afv27WP5xcfHMzatALB9+3bW\nx4ekkUtqo/jhQEcTKS3BIe0xNyeGCxcuMMbwjSksLKRTGhRKC0ycOBGTJk0Su0CK8ubY2Nhg+/bt\nEk0e3jbjx4+Hu7t7l72/tJ+mdCY/hS9AXR1BHamD14jFzIdRdHIYHpUVQYorhQm2PjDn23SypO8W\nycnJcHR0bHM6OqJIoXQxkpOTcfPmTZGRSEr7cObMGXA4nE5TEht4S9/o7QLdR/HDge6jSGkJupiF\nQulCzJ8/H3/88Qc2btwIRUXFzhbnvcPFxQXZ2dkiU7SdwYd6BCSFQnm3oIoihdKF2Lt3b2eL8F5z\n5syZzhYBQP0K8a4MtVH8cKA2ipSWoFPPFAqFQqFQKBSxUEWRQqFQKCyojeKHA7VRpLQEVRQpFAqF\nQqFQKGKhiiKFQqFQWFAbxQ8HaqNIaQmqKFIoFAqFQqFQxEIVRTGsXbsWgYGBnS3GG+Pi4oIjR450\nWHlr1qxBUFBQh5VHoVDeDtRG8cOB2ihSWoIqik149OgRwsLC4OPjAwA4fvw4+Hw+89PV1YW6ujpS\nUlI6RJ69e/fCzMwM+vr6WLRoEaqqqlqdtqWjz9qbhQsXYvv27aiuru6wMikUCoVCobw9qKLYhODg\nYHz88ceQk5MDAEyZMgVCoZD5bdmyBQKBAP369Xvrsly4cAH+/v6IiopCSkoK8vLymPNguyKampow\nMTHBuXPnOlsUCoXyBlAbxQ8HaqNIaQmqKDbh4sWLsLe3lxgeEhICDw8PieFWVla4fPky4964cSPm\nzp0LABAKhVBXV8fhw4dhYWEBc3Nz7NmzR2JeoaGh+Oyzz2Bqaopu3bphxYoVCAkJkRj/0qVLGDx4\nMAwMDLBy5UoQQphjwggh2Lp1K6ysrGBqaor58+ejrKwMQP1pIAEBAQDqz3hVV1fHoUOHAAC5ubkw\nMjICUD9FYWFhgYCAAJiamsLc3BzBwcEsGYYOHYro6GiJMlIoFAqFQnl3oIpiE27fvg1jY2OxYfn5\n+YiPj4enp6fE9E2ne8VN/cbGxiIxMRERERHw9/dnFMurV69CIBAw8TIzM2FhYcG4LSwsUFJSgqdP\nn4rkWVpaipkzZ+Lbb7/FnTt3YGBggISEBKb8Y8eOITQ0FGfOnEFycjLKy8uxcuVKAIC9vT1iY2MB\nAHFxcTAwMEBcXBwjq52dHVPOw4cP8fz5c9y+fRu7du2Cr68vo3ACgImJCW7duiWxfigUSteH2ih+\nOFAbRUpLUEWxCc+ePYOSkpLYsNDQUNjZ2UFPT6/V+TWM6DXG19cXCgoKMDc3h5eXF06cOAEAsLW1\nRW5uLhOvoqICKioqjFtZWRkAUF5eLpLnX3/9BTMzM7i4uEBKSgrz5s2DhoYGEx4REYEFCxaAz+dD\nUVER3333HSIjI1FXVwc7OztcvXoVhBDEx8dj0aJFSEhIAFCvODZWFGVkZODr6wspKSmMHj0aioqK\nyM7OZsKVlJToS4ZCoVAolPeEZhXFWbNmQVNTE5aWliJh27ZtA5fLxePHj9+acJ2BqqqqWEUMAMLC\nwpodTWwtOjo6zH9dXV0UFRWJjaeoqIjnz58z7oaRO3GKbFFREXr16iWxnKKiIujq6rLKrampQUlJ\nCQQCAXg8HlJTUxEfH48xY8ZAS0sLOTk5iIuLY03Fq6mpgcv9X7NRUFBARUUF4y4vL6f2TRTKOw59\nhj8cqI0ipSWaVRR9fHzw559/ivjn5+fjr7/+gr6+/lsTrLMwNzdHTk6OiP/Vq1dRXFyM8ePHN5ue\nx+OhsrKScZeUlIjEKSgoYP3X1tYWm1efPn2QlpbGuNPS0qChoQFVVVWRuFpaWrh//z7jJoSw3Nra\n2sjPz2eVKy0tzYw62tvb49SpU6ipqYG2tjbs7e0REhKCp0+fiv1QkERWVhb69u3b6vgUCoVCoVC6\nLs0qisOGDYOampqI/7Jly7B58+a3JlRnMnr0aMZerzGhoaEYP348FBUVm01vaWmJyMhI1NTU4Pr1\n6zhz5oyIneK2bdvw4sULpKenIyQkBBMnThSbl4eHB44ePYrMzEw8ffoUW7duhZeXl9i4H3/8MTIy\nMnD27FnU1NRg//79LCXVzc0N+/btg1AoRHl5OdatWwc3NzdmdNDOzg4HDhzAkCFDANR/ZTa427LF\nTmxsLJycnFodn0KhdD2o+ciHA7VRpLSEdFsTnDp1Crq6uu22PYzw8EncCwxBbeXLdslPHFI8eRjM\nnQr+TPEKWWM8PT3h4OCAly9fQl5eHgDw8uVLnDp1Cr/99luL6VetWoXZs2fD0NAQdnZ2mDx5ssji\nEzs7O9jY2KCurg4LFy7EiBEjAADx8fHw8PCAUCgEADg6OmLRokWYMGECXrx4gfHjx+Obb74RW273\n7t0RFBQEPz8/LFy4EB4eHrC1tWXCp0+fjqKiIowbNw6vXr2Co6MjNm3axJKpoqKCsUccPHgwXr58\nySiODTSnNBYVFSErKwvjxo1rsZ4oFAqFQqF0fThE3GqLRty7dw8uLi5ITU1FZWUlRo4cib/++gsq\nKioQCARITEyEurq6SLoLFy7g4MGD4PP5AOptXiwtLWFoaMiypbsyxP2tKokNSPHk4RAf3qq469ev\nR48ePZhtbdoLoVCIAQMG4OHDhyw7v/eFNWvWwNDQkNmsnEKhvJukp6ejtLSUsV9rGHWiburuCPe8\ndZNBCIGOSU94jViMpGvXAQCPpbPxqKwI97Mfwd78E0yf9HmXkLeruhv+Nww+zZ49G46OjmgrbVIU\nU1NT4eTkBB6PB6Dezk1HRwf//vsva4UtUK8oWltbi+RXWFjIUhQvWTVv89eejLx5usPKEsf7rihS\nKJT3g6b9NIXSkfwUvgB1dQR1pA5eIxYzM1nRyWF4VFYEKa4UJtj6wJxv08mSvlskJye/lqLYpqln\nS0tLFBcXM26BQICkpCR07969zQWL420och2piLaGjjxSj0KhUF6HZ8+eUUXxAyEmJoaufKY0S7PD\nWlOnToWdnR2ysrKgp6eHoKAgVjhVetoGn8/Ho0eP6GgihUKhUCiUd4JmRxSbOy4OAO7evduuwlAo\nFAql86H7KH440NFESkvQoa13jK+//hpbt25tl7wazp6uq6trl/zeBgsWLMCGDRskhqurq+PevXsd\nJ9A7TkxMTIv7XNrZ2TFHOLZE07PNO4qW2kVjWtPO3d3dERYW1l7iUSgUynsDVRSbYGVlBR0dHfD5\nfAgEAowdOxa//vqr2KP4OoNt27Zh+fLlAFr30l+wYAG0tLTA5/OZ3/Dhw9+qjM0pb215wTfwPps4\ntKToBgcHw9nZueMEguixjc3R9GzzjqQ9yw0PD4eHh0e75feuQ/dR/HCg+yhSWqLN+yi+TbrCwhMO\nh4OQkBA4ODjg+fPniI2NhZ+fHxITE7Fnz57OFu+1WLx4MVatWtXZYrw2XUVJf1t0leurqamBtHSX\n6hKapT3qrSGP9/ljhEKhUN6ETh9RlOLJd9lylJWVMXbsWBw6dAihoaFIT08HAERHR2P48OHQ19eH\npaUla+Pqhmmu4OBgWFpawsjICEFBQUhOTsbQoUMhEAiwcuVKJn5wcDDGjh2L1atXQyAQ4KOPPkJC\nQgKOHTsGS0tLmJqaIjQ0lInfMCJXWVkJd3d3FBUVMSOFjVekvw7BwcGwtrYGn8/HgAEDEBERAQDI\nzc3FhAkTYGxsDBMTE3z55ZfMudNt4ddff0VERAR2794NPp+PadOmAQAyMzPh4uICgUAAOzs7scdG\nNuDv7w9zc3NYWFjg6NGjEuNFRUVh1KhRLL+AgABMnz4dQP252fPmzUPv3r1hZWWFbdu2MUrDxo0b\nWXtotjR1aWVlhT179mDYsGEwMDDA559/jlevXjHhhw8fho2NDYyMjDBt2jTmbO+GjckdHBzA5/MR\nFRXFyjczMxPLly/HtWvXwOfzYWho2KLsTXnx4gUWLFgAQ0NDDBkyBMnJySKy+/v7Y+jQoeDz+ait\nrYWVlRWuXLnC1IWPjw/mz58PPp8POzs73LhxQ2xZmZmZGDBgACIjI8WGf/PNN7C0tIS+vj5GjRqF\nq1evMmEtlZOSkoIRI0aAz+eL1G9T6urqsGbNGpiYmMDa2hrR0dGscBcXF2zYsAFjx46Fnp4eswXY\nkSNH8OrVKxgYGDDPOgA8evQIOjo6KC0tBQCcP38eDg4OzIzD7du3JcryrkJtFD8cqI0ipSU6XVE0\nmDv1rSuLDSezvC7W1tbo1asXEhISAACKiooIDAxEXl4ewsLCEBQUhD/++IOVJjk5GUlJSTh48CD8\n/PywY8cOnDp1CnFxcYiKimLZgCUnJ6Nv3764e/cu3NzcMGvWLKSkpCA5ORmBgYHw9fVlnR/N4XDA\n4/Fw/PhxaGlpQSgUQigUQlNTU6z8rRl5qaiogJ+fH44fPw6hUIjz58+zprWXLVuG9PR0XL16Fffv\n38fGjRvbVIcA4O3tjcmTJ2Px4sUQCoU4duwYqqur4eXlBUdHR2RnZ2PTpk2YM2cO67zthtGev//+\nG3v37kVkZCSuXbvWrG2cs7Mz8vLykJWVxfiFh4fD09MTALBy5UqUl5fj+vXrOHv2LMLCwnDs2DFW\nea2Fw+Hg1KlTiIiIwI0bN3Dr1i1mIdiVK1ewfv16BAUFIT09HXp6epg9ezYA4PfffwcA/PPPPxAK\nhXB1dWXla2pqim3btmHgwIEQCoXM4rHmZG/K5s2bkZeXh+vXryMiIgKhoaEi1xcZGYnw8HDk5uZC\nSkpKJPz8+fNwc3NDXl4ePvnkE/j6+oqUc/PmTUyZMgWbN2+Gm5ubWFk++ugj/PPPP8jNzcWkSZPg\n4+ODqqqqFsupqqrC9OnT4enpyXy0iDsas4HDhw8jOjoaly9fxsWLF3H69GmRuOHh4di1axeEQiH0\n9PSYKXQ5OTm4uLiwlN2oqCjY29tDXV0dKSkpWLx4MXbu3Im7d+/C29sbXl5erOugUCiU94lOn2fi\nz5zYqqP1OhstLS08efIEAGBvb8/4m5ubY+LEiYiNjWXZki1fvhyysrIYOXIklJSUMGnSJOYEG1tb\nW6SkpDB2YPr6+pg6tV6RnThxIrZv344VK1ZARkYGI0eOhKysLHJzc2FhYQHgf4pfa6feAgICcPDg\nQcbt7OyMgIAAkXhcLhe3b99Gr169oKGhwWyiLhAIIBAIANTb1M2bNw9btmxpVdniaCx3YmIiKisr\nsWTJEgD154uPGTMGJ06cYI28AvUv7GnTpqFPnz4A6keoJI1eycrKwtXVFcePH8fq1auRnp6O/Px8\njBkzBrW1tTh58iSuXLkCRUVFKCoqYv78+QgPD8f06dNfa0rzyy+/ZBT1sWPHIjU1FQBw/PhxTJ8+\nHZaWlgD+d3pNQUEBdHV1W8y3qSwtyd6UU6dOYevWrejWrRu6deuGL7/8knXvOBwO5syZ0+yeeba2\ntjH1UJ0AACAASURBVMz53VOmTEFgYCArPDY2FseOHcPPP//crG3jlClTmP8LFizAtm3bkJOTA3Nz\n82bLSUxMRG1tLTPKO378eOzdu1diOVFRUZg3bx5zTUuXLmWd387hcDB16lSYmpoCgMh2VZMnT8ay\nZcuwevVqAEBERARmzZoFoF4JnTlzJnOYgKenJ3bs2IHExMRW23W+C9B9FD8c6D6KlJbo9BHFd4UH\nDx5ATU0NQP2La/z48ejduzcMDAxw+PBhRolsoPFJNfLy8iy3goICa4SwZ8+erLgA0KNHD5ZfeXn5\na8u+cOFC5ObmMj9xSqKioiIOHTqEoKAgmJubw9PTE9nZ2QCAkpISfP7557CwsIC+vj7mzZuHx48f\nv7Y8jXnw4AF0dHRYfnp6esz0bGOKi4tZcVtStDw9PZnp8/DwcEycOBEyMjIoLS1FdXU19PT0WHk9\nePDgta+j6f1uuL/FxcWschQVFdG9e3cUFha+Vjltlb2oqKjFOmta/01pfG08Hg8vX75kpuEJITh8\n+DAGDx7coqK0e/du2NrawsDAAAKBAGVlZcx0bnPlPHjwANra2qy89PT0JCr0b3rNQ4cOxYsXL5CU\nlAShUIhbt24xZgL5+fnYu3cv8/EkEAhQWFgotr1SKBTK+wBVFFtBcnIyHjx4gMGDBwMA5syZA2dn\nZ6SlpeHevXvw9vbu0C1mGqbR2tsAf9SoUYiMjERGRgZMTEyYUb5169ZBSkoKcXFxyMvLw759+177\nepvKrK2tjfv377Ne+vn5+SKKAQBoamqioKCAcTf+L46BAwdCVlYWcXFxOHHiBNzd3QHUj4rKyMgw\n51825NUwgsLj8ViK/JvYfjaYBjRQUVGBx48ft3q0pml9tSR7U1pTZ2/SjjgcDrZv3478/HxmBE4c\n8fHx2LNnD4KCgnDv3j3k5uZCRUWlVaO3WlpaIopwfn6+RLm1tLRw//59xt3Wa5aSksKECRNw4sQJ\nnDhxAmPGjIGioiKAeqVz2bJlrA+v/Px8idPt7yrURvHDgY4mUlqCKopiaHh5lZWV4fz58/jiiy/g\n4eEBMzMzAPUve1VVVcjKyiIpKQknTpxo88v2TVZsNqTt2bMnnjx50uLCktaU9fDhQ/zxxx+oqKiA\njIwMeDwepKSkANRfL4/Hg7KyMgoLC7F79+7Xll1DQwN5eXmM28bGBgoKCvD390d1dTViYmIYW7Wm\n8ru6uiIkJASZmZmorKzE5s2bWyzP3d0dvr6+kJWVZRR9KSkpuLq6YsOGDSgvL0d+fj727dvHTI32\n69cP8fHxKCgoQFlZGXbu3Nnm62yQedKkSQgODkZaWhpevXqFdevWwcbGhhnl0tDQQG5ursR8NDQ0\nUFhYiOrq6lbJ3hRXV1fs3LkTz549w/3793HgwIE2X0tLKCkpISIiAvHx8Vi7dq3YOOXl5ZCWloa6\nujqqqqqwefNmPH/+vFX5Dxw4EFJSUti/fz+qq6tx5swZXL9+XWJ8V1dX7N+/H4WFhXj69Cl27dol\nEkfcM9HYb/LkyTh58iQiIiIwefJkxn/GjBkICgpCUlISCCGoqKhAdHT0G434UygUSleGKopi8PLy\nAp/PR79+/bBjxw4sWLCAtTXOli1b8NNPP4HP52Pr1q2YOJFtY9kapbHxqGDT+C2lbwjv3bs33Nzc\nYG1tDUNDQ4kjXw2rjBt+vXv3Fsmrrq4O+/btg4WFBYyMjHD16lVmY29fX1+kpKTAwMAAXl5ecHFx\naVbG5sKmT5+OzMxMCAQCzJgxAzIyMggODsbff/8NExMT+Pr6IjAwEMbGxiL5OTk5Ye7cuXB1dcXA\ngQPh4ODQYl15eHggIyNDRJHatGkTeDwerK2t4ezsjClTpjCrsEeMGIGJEydi2LBhcHR0xJgxY9r0\nIdD4ng4fPhyrVq3CzJkzYW5uDqFQyLIXXblyJRYsWACBQIBTp/6PvTsPi6p8/wf+HjZlUTFUMGFY\nBEEQEdwAK0vEfUXFPbWfH1MxW1Q0y66yTLI0s0yzsiwFF0TKrXLp4wpumKmAC6IDIrgrqywzvz/4\ncj4MDBxgWIY579d1cV2cOdtz5h7g5jnPee7fyh3rpZdegpubG9zc3IS4Vdb2skJDQ2FnZ4cuXbpg\nzJgxGDt2bI2vpfRrZTVv3hxRUVE4ePAgli9fXm59QEAA+vTpg+7du6NLly5o2rSp2i3hys5jYmKC\nX375BREREWjfvj2io6MxdOjQCtv86quvok+fPnjppZfQp08fjZ9XTddQ+rWuXbvC3NwcGRkZwrhJ\nAOjSpQtWr16NhQsXwsnJCd27d1d7QCg4OFjtHwu5XC483R0TEwO5XC6sW7VqldDLrWs4j6J0cB5F\nEiNT1dEkbocOHRIGfJeWlpbGQdJUb3Jzc+Hq6oojR44ID+QQUeUSEhKEOyik33TxYZbl20OgVKqg\nVCkx4eW5wj9if8Vtw/2n6TA0MMRw32lwl3dr4JY2LnFxcQgICKj2fuxRJL22ceNGdO3alUkiUTVw\njKJ06FqSSLqnwafHIaorXl5ekMlklU7MTURERBVjokh668KFCw3dBKJGifMoSocu3nquioeZ95By\n77raa1bNbWDWxKKBWqS/mCgSERFRo3Ls8h4cu6z+mqGhMca8MBOO1m4N0yg9xTGKRESkhmMUpaMx\n9SY2NTGHSgUUKZUavwoLC5CgONfQzdQ77FEkIiIindfJvjvyC58h95n6vKX5hc+Ql58LyIBCZVED\ntU5/MVEkIiI1HKMoHY1pjOJzzazRt8uocq//mxyLizdPNUCLpIG3nomIiIhIIyaKGixduhTr169v\n6GZobejQofj111/r7XxLlizBTz/9VG/nI6K6wTGK0tFYehOp4TBRLOP+/fvYtm0bpk2bBgA4c+YM\nRo4cifbt26NDhw6YNm1ahaXy6sK3336Ljh07wt7eHm+88Qby8/OrvK+msmh1ac6cOVi1apVQl5iI\niIgaNyaKZYSHh6Nfv35o0qQJgOKxOtOmTcOFCxdw4cIFWFhYYM6cOfXSlkOHDmHNmjWIjo7Gv//+\ni1u3biEsLKxezl0T1tbWcHFxwf79+xu6KUSkBdZ6lg7WeiYxTBTLOHz4MHr16iUs9+3bF8OGDYOF\nhQVMTU0xffp0nDpV8aBZLy8vHDlyRFgOCwvDzJkzAQAKhQJWVlbYtGkTPDw84O7ujm+++abCY23d\nuhWTJ0+Gq6srWrRogQULFiAiIqLC7f/++2/07NkTDg4OWLhwIVQqFUpKeatUKnzxxRfw8vKCq6sr\nZs+ejadPnwIAZs+ejbVr1wIorsVtZWWFH3/8EQCQnJyM9u3bAyj+heLh4YG1a9fC1dUV7u7uCA8P\nV2vDCy+8gL/++qvCNhIREVHjwUSxjPj4eDg7O1e4/uTJk+jYsWOF68ve7tV06/fEiRM4e/YsIiMj\nsWbNGiGxjI2NVatJfOXKFXh4eAjLHh4euHv3Lh4/flzumA8ePMCUKVPw/vvvIykpCQ4ODjh16pRw\n/i1btmDr1q3YvXs34uLikJWVhYULFwIAevXqhRMnTgjX5+DggJMnTwpt9ff3F85z7949ZGZmIj4+\nHl999RVCQ0OFhBMAXFxccPlymVlQiahR4RhF6eAYRRLDRLGMJ0+ewMJCcwmgy5cv44svvsBHH31U\n5eOV9OiVFhoaClNTU7i7u2PChAnYuXMnAMDX1xfJycnCdtnZ2WjevLmw3KxZMwBAVpb6HFIAcODA\nAXTs2BFDhw6FoaEhZs2ahTZt2gjrIyMjERISArlcDnNzc3zwwQeIioqCUqmEv78/YmNjoVKpEBMT\ngzfeeEPoNT158qRaomhsbIzQ0FAYGhoiMDAQ5ubmuHbtmrDewsKCt62IiIj0BBPFMiwtLTUmYjdu\n3EBwcDDCwsLg6+ur1TnatWsnfG9ra4v09HSN25mbmyMzM1NYLum505TIpqenl5v3rPR50tPTYWtr\nq3bewsJC3L17F46OjjAzM8PFixcRExOD/v37w8bGBtevX8fJkyfVbsW3bNkSBgb/+9iYmpoiOztb\nWM7KymJvBFEjx3/2pINjFEkME8Uy3N3dcf26eqHxlJQUBAUFYcGCBRgzZkyl+5uZmSEnJ0dYvnv3\nbrltUlNT1b5v27atxmO5ubnh0qVLwvKlS5fQpk0bWFpaltvWxsYGt2/fFpZVKpXactu2bZGSkqJ2\nXiMjI6HXsVevXvjtt99QWFiItm3bolevXoiIiMDjx4/h6elZ6TWXdvXqVXTq1KnK2xMREZHuYqJY\nRmBgoDBeDyh+uGP48OGYPn06pk6dKrq/p6cnoqKiUFhYiPPnz2P37t3lximuXLkSubm5SEhIQERE\nBEaOHKnxWGPHjsXmzZtx5coVPH78GF988QUmTJigcdt+/fohMTERe/bsQWFhIb777ju1JDUoKAjr\n1q2DQqFAVlYWPv74YwQFBQm9g/7+/vj+++/h5+cHoHjcSslydabYOXHiBPr27Vvl7YlI9/CugHRw\njCKJafASfv+cUuDs8ZsoyK+7+ozGJobo9oIDuvSUi247btw4vPTSS8jLy0PTpk3x66+/4tatW1ix\nYgVWrFghbKdQKDTuv3jxYkyfPh1OTk7w9/fH6NGjyz184u/vj27dukGpVGLOnDl4+eWXAQAxMTEY\nO3ascOyAgAC88cYbGD58OHJzczFs2DAsWrRI43mfe+45/PTTT3j33XcxZ84cjB07Vu0W+aRJk5Ce\nno7Bgwfj2bNnCAgIwGeffabWpuzsbGE8Ys+ePZGXlyckjiUqSxrT09Nx9epVDB48uMJtiIiIqPGQ\nqTQ9bVELDh06BB8fn3Kvp6WlqY2l+2Hl0TpNEksYmxhi+ryXqrTtJ598glatWgnT2tQWhUIBb29v\n3Lt3T22cn75YsmQJnJychMnKiahxSkhIqHR2B9Ifuljrefn2ECiVKihVSkx4ea7oXa2SWs+GBobo\n5NATw3q+Wk8tbVzi4uIQEBBQ7f0avEexPpLE6p7n/fffr8OW6K+PP/64oZtAREREtajBE8XSZr37\nSq0fc93yv2v9mNqoz5J6REQ1wTGK0qFrvYmke3QqUdR3crkc9+/fb+hmEBEREVWJ/g2UIyIirXAe\nRengPIokhokiAQDCw8MxaNCgCtcHBwdj27ZttXrOL7/8Em+++WatHrM2HD9+XKu5IDdu3AhXV1fI\n5XKN5RZrU13EReqWLl2K9evXV7i+dP322ib2c0hEVN+YKJbh5eWFo0ePAij+pR0SEtLALap9CoUC\nVlZWUCqVVd5n+/btGDt2bK224+2338ZXX30lul1ISAiWLVtWq+euKwUFBViyZAl27doFhUKhcXL0\n2lQXcdEkLCwMbdq0gVwuh1wuR48ePbBw4UJkZGTU2Tlr8jnV1v3797Ft2zbhyX1N/zRIYZwxxyhK\nB8cokhidGqOoCw+eSOGPQIk6mhlJ5xQWFsLIqH4+6hkZGcjLy4Orq2u19y2Jhy5+BmUyGUaNGoV1\n69ahqKgI165dQ1hYGPr06YPDhw/D2tq62sdUKpVVmiaqss9pUVERDA0Nq33uioSHh6Nfv35o0qRJ\njdpDRKRvGrxH0dik9n7J1/Z5ZDKZ8Ed7zJgx+OGHH9TWv/jii9i7dy+A4tJ1I0eORPv27dGzZ09E\nR0dXeNzw8HD4+PhALpfD29sbkZGRwrrNmzfD19cXTk5OGD16tFq5v8rOERISggULFmDcuHGQy+UI\nDAzEzZs3NZ6/ZEJsR0dHyOVynDlzRrjODz74AE5OTvD29sbBgweFfYYOHYpff/0VQHHd6yFDhsDB\nwQEuLi74f//v/2k8T0mP0KZNm+Dh4QF3d3d88803wvqyt/BiY2PRv39/ODo6wtPTExEREdi0aRMi\nIyPx9ddfQy6XY+LEiQAAKysrtesr3et4/PhxeHh4YM2aNejYsSPmzp0LlUqF1atXo2vXrnB2dsZr\nr70melv4yy+/hIuLC7p06aIWo2fPnmHJkiXo3Lkz3NzcMG/ePOTl5eH69evCBOWOjo5CxZ1Tp04h\nICAADg4O6Nu3L06fPq32vi5btgwDBgyAra0tbt26Va3PUum4hIeHY+DAgRXGsKyS90Mul8PPz0/4\nLGuiUqmEBMnQ0BBubm7YuHEjrKyssHbtWuH8ZW+blo5TSEgI5s2bh+DgYNjZ2eH48eP466+/0Lt3\nb9jb28PT01NtEnhNn9Pw8HAMGDAA7733HpydnfHZZ5/h5s2bGD58OJydneHi4oLXX39dqIu+Zs0a\nTJkyRa1NixYtwrvvvqvxOg8fPizUNs/OzkZwcDDS09OFntT09HTIZDLk5+dj9uzZkMvl8Pf3xz//\n/CMc486dO3j11VfRoUMHeHt7Y8OGDRW+rw8fPsSECRNgb2+Pvn37Ijk5ucJt6xPHKEoHxyiSmAZP\nFLu94FDnyWJJZZbqGj9+vJDYjB49Gjt37hTWJSYmIjU1Ff369UN2djaCgoIQHByMa9eu4YcffsCC\nBQtw5cqVcsfMzs7Gu+++ix07dkChUODPP/8Ubm3t27cPq1evxq+//iokHdOnTxf2EzvHrl27sHDh\nQiQnJ8PJyQmffPKJxuvat28fAODmzZtQKBTo3r07VCoVzp07BxcXFyQlJWHu3Llq4wdLJ82ffvop\nAgICcPPmTVy+fBkzZsyo9H08ceIEzp49i8jISKxZswZHjhwRjlkiJSUFwcHBeP3113H9+nUcPXoU\nnp6emDJlCkaPHo25c+dCoVBgy5YtFZ6n9PHu3buHx48f499//8WqVavw3XffYf/+/dizZw8SEhJg\naWmJBQsWVHisu3fv4uHDh4iPj8e3336Lt99+W6gB/tFHHyE5ORnHjh3D2bNncefOHXz++edwdnbG\nyZMnhfd2165dePToEcaNG4eZM2fixo0bmDVrFsaNG6eWpG7fvh1fffUVUlJS8Nxzz1X5s1Q2LkDx\nhKoVxbAsR0dH7Nu3DwqFAqGhoZg5c2a1biUbGBhg4MCBiImJqfI+O3fuxPz585GSkoKePXvC3Nwc\n69evx61bt7Bt2zb89NNPwudT0+e05BodHR1x9epVvPPOO1CpVHjnnXeQkJCA2NhY3L59G2FhYQCK\ny2AePnxYSBwLCwuxa9cujB8/XmP74uPj4ezsDAAwNzfHjh07YGNjA4VCAYVCARsbG6hUKvzxxx8I\nCgrCrVu3MHDgQISGhgIo7iWdMGECOnfujPj4eERHR2P9+vU4fPiwxvMtWLAApqamSExMxNdff43w\n8HCd7FEmIulq8FvPXXrKq1Rar6ENGjQI8+fPR2pqKmxtbREZGYmhQ4fC2NgYu3fvhr29vfDHx9PT\nE0OGDMFvv/0m/AEpzcDAAPHx8Xj++efRpk0btGnTBgDw008/4a233oKLiwuA4jF8X375JVJTU3H6\n9GnRcwwZMgTe3t4AihPbiiYOr+jWmZ2dHSZPngyg+A/s/Pnzce/ePbRu3VptOxMTEygUCqHKTs+e\nPSt970JDQ2Fqagp3d3dMmDABO3fuRO/evdXaERkZiZdffhlBQUEAgJYtW6Jly5aiba7ougwMDLBo\n0SIYGxvD2NgYP//8M1asWIG2bdsKbfLy8sJ3331X4e3PxYsXw9jYGP7+/ggMDER0dDTmzZuHX3/9\nFceOHRPGcb311lt4/fXXsWTJknLt/Ouvv+Ds7IwxY8YAAEaNGoUNGzZg//79GD9+PGQyGcaPHy/c\nqj548GC1PktlVTWGADB8+HDh+5EjR2L16tWIi4vDwIEDRc9TwsbGploP7AwePBg9evQAADRp0kTo\nvQMAd3d3jBw5EidOnMCgQYMqjLmNjY3wD1TTpk3h6OgIR0dHAMU9mLNmzcLnn38OALC2toavry+i\no6Px6quv4tChQ7CyskLnzp01HvvJkyewsLAQlitqg6+vr1DTfMyYMcLDL3FxcXjw4AHmz58PALC3\nt8fkyZMRFRWFPn36qB2jqKgIe/bswYkTJ2BqaoqOHTti/Pjxwj8bDYljFKWDYxRJTIMnio1Fs2bN\nEBgYiKioKMydOxdRUVHCgxipqak4d+6c8McKKP4joOkhA3Nzc/z444/45ptvMHfuXPTs2RMff/wx\nXFxckJKSgsWLF2PJkiVq+6SlpVXpHKWTAVNTU2RnZ1frGksSVgAwMzMDUNyTWTbJ+PDDD/Hpp58i\nMDAQLVq0QEhIiHBLWJN27doJ39va2iI+Pr7cNrdv34aDg0O12lsZKysrmJiYCMspKSmYPHmyWlJo\nZGSEu3fvwsbGptz+lpaWMDU1FZbt7OyQkZGBBw8eICcnB6+88r/J4VUqVYUPXKSnp8PW1lbtNTs7\nO6SnpwvLpd+f6nyWNKlqDAFg69atWLdunVBbPDs7Gw8fPqzSeUqkpaWpJfRiSpfvBICzZ89i6dKl\nSExMRH5+PvLz8zFixIhKj1H6/QKKe3/fffddxMbGIisrCyqVSu0honHjxuHnn3/Gq6++Kvrwj6Wl\nJbKyskSvo+z7nJeXB6VSiZSUFKSnp5eLX0kN9dLu37+PwsLCcj8fRFKhUqnwJOchVKr6e2CNqo+J\nYjWMGjUKK1asgK+vL549e4YXX3wRQPEfLn9/f0RFRVXpOH369EGfPn3w7NkzfPLJJ3jrrbewd+9e\n2NraYsGCBRg1alS5fVJSUqp1jspoe2urTZs2WL16NYDicYVBQUHo1atXhYleamqq0Euampoq9OqV\nZmtri7i4uCq318zMDDk5OcJyRkaG2h/csvvY2tri66+/FnqzxDx+/Bg5OTlCspWSkgIPDw9YWVnB\n1NQUMTExGhPMstq2bYvdu3ervZaSkiL0RpVta3U/SzWVkpKCt99+G9HR0ejRowdkMlm5Xt7SNMVA\nqVTizz//FJJmMzMz5ObmCuurcht7xowZmDFjBiIjI2FiYoLFixcLyWpFn9Oyr3/88ccwNDTEyZMn\n0aJFC+zduxcLFy4U1g8aNAgLFixAfHw8Dhw4gKVLl1bYHnd3d1y/fh1dunSpsA2V/fy0a9cO9vb2\nOHPmTMUX/X9atWoFIyOjcj8fuuDJkyflknrSTw1V67lIWYiNBz7D/Sdp9X5uqp4GH6PYmAQGBiIl\nJQVhYWHCgwoA0L9/fyQlJWH79u0oKChAQUEB4uLicPXq1XLHuHfvHvbt24fs7GwYGxvDzMxMeGpz\n2rRpWLVqFRITEwEAT58+FR5kqM45xFhZWcHAwKDGA+ejo6Nx+/ZtAMW3qGQyWaVPr65cuRK5ublI\nSEhARESE2ntXYvTo0fjvf/+L6OhoFBYW4uHDh7h06RKA4sT01q1batt36tQJkZGRKCoqwsGDB0XH\nyU2dOhWffPKJ8If4/v372L9/f6X7hIWFoaCgADExMThw4ACGDx8OmUyGyZMnY/HixUKVnbS0tArH\noAUGBiIpKQk7d+5EYWEhoqKicO3aNfTv31/YpnRyVptxrkx2djZkMpkw/cyWLVuQkJBQ4fal21hY\nWIgrV65g+vTpuH//PmbPng2gOCaJiYm4dOkS8vLy1B5MqawdlpaWMDExwblz57Bz504hEavq5zQ7\nOxtmZmZo1qwZ0tLS8PXXX6utNzU1xdChQzFjxgx07dq1XI9kaYGBgThx4oSw3Lp1azx69EgY41j2\nvSira9eusLCwwJo1a5Cbm4uioiLEx8fj/Pnz5bY1NDTEkCFD8NlnnyE3NxeJiYmIiIjgGEWShOSM\nK7j/JA1KpQpFSmW5LxWUMDYyET8Q1TkmitVgYmKCIUOG4OjRoxg9erTwuoWFBXbu3ImoqCh4eHig\nY8eO+Pjjj1FQUFDuGEqlEuvWrYOHhwfat2+P2NhYfPHFFwCKx2+9+eabmD59Ouzt7dGrVy8hAanK\nOcr+ganoD46ZmRneeecdDBw4EE5OTjh79my5hyIq2/+ff/5Bv379IJfLMWnSJCxfvhxyecXjTP39\n/dGtWzcEBQVhzpw5ePnll4Xjl5zD1tYW27dvx9q1a9G+fXv07t0bly9fBgBMmjQJV65cgaOjI159\n9VUAwPLly/HHH3/A0dERO3fuFJ6QrajtM2fOxIABAzBq1CjI5XL079+/0h5Ma2trWFpawt3dHTNn\nzsSqVauEhxw+/PBDODk5oV+/frC3t0dQUBCSkpI0nrtly5aIiIjA2rVr4ezsjLVr1yIiIkLtdm3p\n7avzWdLU7qrG0M3NDSEhIejfvz/c3NyQkJAAX1/fSo+9a9cuyOVyODo6YtKkSWjVqpXa1DjOzs5Y\nsGABRo4ciR49esDPz0+0PZ9//rnw+fniiy/U/omo6uc0NDQU//77LxwcHDBhwgQMHTq03Dbjx49H\nQkICgoODK7xGoPg29YEDB5CXlwcA6NChA4KCguDj4wMnJyfhqeeKrsvQ0BARERG4ePEifHx84OLi\ngrfffhuZmZkaz7dixQpkZ2fDzc0Nb7zxRrkhHP7+/sJDdKmpqZDL5cI/aTt27NB4S7s2cIyidDTU\nGMXCwnwAgApKyGQymBg1Ufsya9oMnR16Vvsfpxvp8fjp4Aq1r63H1iL1vm7MKNAYyVR1NCnYoUOH\n4OPjU+71kgcgSP8pFAp4e3vj3r17VZovj6iupKamwtfXF4mJiWoPq2jyySefoFWrVnVWfaUx4O9p\nqmuJKeexK+YHFCmL8FxzGwzwqXnhgIs3T+Hf5FgYGhgA0JxYtmvliCkB82t8Dn0QFxeHgICAau/H\nv95EpNeUSiXWrl2LoKAg0SQRAN5//31JJ4kA51GUEn2YR9G2VXsYGBr+323ronJfKqiQlfdU/ECk\nER9moTrF8VbUkEpu68rlcuzYsaOhm0NEdaClRSuM8J2G+0/vqL2elZuJuOtHG6hV+kM0UXzttdew\nd+9etGnTBhcvXgRQPEnsnj17YGJigvbt2+Onn37imBYqRy6XCw98EDUEc3NzpKSkNHQzGh3+PpcO\nfZlH0dTEHHatnNVee5h5t4Fao19Ebz1PmzYNf/zxh9pr/fr1w+XLl3HhwgV06NABy5cvr7MG6qZm\n/wAAIABJREFUEhEREVHDEE0UX3zxxXIT6gYGBgoPJ/Ts2VNn5v4iIiLtcYyidOjDGEWqW1o/zLJx\n40YMGjSoNtpCRERERDpEq4dZli1bBhMTE0yYMEHj+tmzZwvz67Vo0QKenp5wcnLS5pRERFQPSlfs\nKOl14rL+Lb/wwgsNcn7F3WsocSM+FWcL49CtR/GUemdPF89xq+2yU8fikpgpVzPwyDQP+L/pdnXp\n/a/L5ZLvS8q0Tp8+HTVRpXkUb968iaFDhwoPswDAzz//jO+//x6HDh1C06ZNy+3DeRSJiBon/p6m\nulab8yhW5GHmXew/GwEDAwNYWrRCyOCKy3dKQb3Oo/jHH3/g888/x2+//aYxSWzsli5divXr1zd0\nM3Sal5cXjhw5Um/nmzJlCg4ePFhv5yOSMo5RlA6OUSQxooni+PHj4e/vjytXrsDOzg4bN27EG2+8\ngaysLAQGBsLb21uo9aoP7t+/j23btmHatGkAgIKCAkyZMgVdunSBlZWVWh1YAFizZg169eoFuVwO\nb2/vcnVmFQoFhg0bBltbW/Ts2bPekiuxdhcWFmLhwoXo2LEj2rdvjwkTJuDOnTsVHK08TWXM6tKb\nb76JTz/9tN7OR0RERFVIFCMiIpCWlob8/HykpKTgtddew7Vr13Dr1i2cP38e58+fx7ffflsfba0X\n4eHh6NevH5o0aSK85u/vj/Xr18Pa2lpjcrR+/XrcvHkTO3bswA8//ICoqChh3fTp0+Hl5YWkpCS8\n//77mDp1Kh48eFAv11JZu3/88UfExMTg2LFjiI+Ph6WlJRYuXFgv7aoJHx8fZGZm4p9//mnophDp\nPc6jKB36Mo8i1R2W8Cvj8OHD6NWrl7BsbGyM119/Hb6+vhrrFc+dOxeenp4wMDCAs7MzBg4ciNOn\nTwMArl+/josXL2LRokVo0qQJhg4dCg8PD+zevVvjuUNCQrBs2TJh+fjx4+jUqZOw7OXlhdWrV8PP\nzw9OTk6YM2cOnj17pvFYYu1OTExEnz590KpVKzRp0gQjRozAlStXKnxftm3bhs6dO8PZ2RmrVq1S\nW/fs2TO8++678PDwgIeHBxYvXoz8/OKC70OGDBGuNzY2FlZWVjhw4AAA4MiRI+jduzeA4gR94MCB\n+OCDD+Dk5ARvb+9yt5p79eqFv/76q8I2EhERUe1iolhGfHw8nJ2dxTfUQKVSISYmBm5ubgCKkzF7\ne3uYm5sL23Tq1AmJiYkVHkPsdm5kZCR27tyJuLg4JCUl4YsvvhDWOTo64tSpU1Vq6yuvvIKDBw8i\nPT0dOTk52LFjB/r27atx28TERCxYsAAbNmxAfHw8Hj58iLS0NGH9ypUrERcXh6NHj+Lo0aOIi4sT\n2tWrVy/htvfJkyfh4OCAkydPAgBOnDihlpTHxcXBxcUFSUlJmDt3Lt588021dnTo0AGXLl2q0vUR\nUc1xjKJ0cIwiiWGiWMaTJ09gYWFRo33DwsIAABMnTgRQXGe2efPmats0a9YMmZmZFR6jsofQZTIZ\npk+fjueffx6WlpZ455131G5zJycno2fPnlVq67Bhw9C5c2d4eHjAwcEB169fx4IFCzRu+/vvv6N/\n//7w9fWFiYkJFi9erNZLuXPnTixYsABWVlawsrJCaGgotm/fDqD49ndJohgTE4O33npLLXEsnSja\n2dlh8uTJkMlkGDt2LNLT03Hv3j1hvbm5OZ4+ZWF3IiKi+sJEsQxLS0tkZWVVe7/vv/8eO3bswNat\nW2FsbAygOLEpmxQ+efIEzZo1q3H72rVrJ3xva2uL9PT0Gh1nyZIlyMrKwo0bN5CamorBgwdjzJgx\nGrfNyMhQmyrDzMwMzz33nLCcnp4OOzs7je3q3r07kpKScO/ePVy6dAnjxo3D7du38fDhQ5w/fx7+\n/v7Cfm3atFE7B1CcbJfIysoql3gTUe3jGEXp4BhFEsNEsQx3d3dcv369Wvts3rwZa9asQXR0NNq2\nbSu87ubmhlu3bqklnpcuXRJuTZdlbm6O3NxcYTkjI6PcNrdv3xa+T01NhY2NTbXaWuLQoUOYMGEC\nWrRoARMTE/znP/9BXFwcHj16VG5ba2trtfPm5OTg4cOHwrKNjY0woWfZdpmZmcHLywvr169Hx44d\nYWxsjB49emDt2rVwdHQsVx6yMlevXoWnp2dNLpeIiIhqgIliGYGBgeWmknn27Bny8vLKfQ8AO3bs\nwLJly7Bz506hCk0JZ2dndOrUCStWrEBeXh52796NhIQEDBs2TOO5O3XqhAMHDuDx48fIyMgoN5ej\nSqXCjz/+iLS0NDx69AirVq1CUFBQhddSWbs9PDwQERGBp0+foqCgAD/++CPatm2rMXEbNmwY/vrr\nL8TGxiI/Px/Lly+HUqkU1gcFBWHlypV48OABHjx4gM8//xzBwcHC+l69euGHH34QbjO/8MIL+P77\n79VuO1dFTExMheMoiaj2cIyidHCMIonRqoRfbThwPhJ7z2zGs4Jc8Y1rqImxKQZ3n4RA79Gi244b\nNw4vvfQS8vLyhMnEe/TogdTUVMhkMowePRoymQz//PMPbG1t8emnn+LRo0dqCUxwcLDwMMePP/6I\nkJAQtG/fHra2tti0aZPabdvSxo4diyNHjsDLywv29vYYP3682tRDJecfNWoU0tPTMWjQIMybN09Y\nL5fLsX37dvj6+oq2e9myZVi4cCG6du2KwsJCuLu749dff9XYLjc3N6xYsQIzZsxATk4OZs+erXYL\nfP78+cjMzMSLL74IABg+fDjmz58vrPf398fq1auF28x+fn7IycmBn5+f2rWVfZCn9HJcXBwsLCzg\n7e2tsY1ERERU+6pUwq8mqlrC760NI+o0SSzRxNgUq2dEV2nbTz75BK1atcLMmTPruFXV06VLF6xZ\nswYvvfRSQzel3k2ZMgWTJ09mjyJRPWAJP6prLOFX/2pawq/BexTrI0ms7nnef//9OmwJ1cSmTZsa\nuglERESS0+CJYmnrQv6s9WPOWtu/1o9JRKTPnjx5wh5FiTh+/DiffKZK6VSiSJVj+ToiIiKqT3zq\nmYiI1HAeRelgbyKJYaKoo8LCwoSHaRQKBaysrNSmpKmq4OBgbNu2rVbaoQ+GDh1a4dPd1eHl5YUj\nR45UadvY2Fh069YNcrkc+/fv1/rcdWHevHlq5SDpf6ysrHDz5k2N67T9+SIi0nVMFCswdOhQODk5\nIT8/v0rbh4eHY9CgQbV2frGaz1W1fft2jB1b/DRZTdpYW+2oD1W5Pk3T8NREdY4TFhaGGTNmQKFQ\nYODAgVqfuy6sXLlSbUqjmjh+/Dg6depUSy1qHEr/fOkTzqMoHZxHkcTo1BhFXXnwRKFQIC4uDra2\ntti/fz+GDx9e722oo1mLqAGkpqbC1dVV47qSODemhLwxKyoqgqGhYUM3g4io0WjwHsUmxqY6d56t\nW7eid+/eCA4OxtatW9XWpaam4tVXX0WHDh3g7OyMhQsX4urVq5g3bx7OnDkDuVwOJycnAOVvc5bt\n8Vq0aBE8PT1hb2+PPn36IDY2VrRt0dHR6NOnj9pra9euxaRJkzRuX9KGitpY1q1btzBkyBDI5XIE\nBQWpleoDgP3798PPzw+Ojo4YNmwYrl69Kqy7c+eO8N54e3tjw4YNwrpz586hT58+sLe3h5ubW4VT\nEB0/fhweHh5Yu3YtXF1d4e7ujvDwcGH906dPMWvWLHTo0AFeXl5YuXIlVCoVrly5gvnz54teX2kq\nlQpffPEFvLy84OrqitmzZ+Pp06dVutbSrly5Am9vb0RFRZVb5+Pjg5s3b2LChAmQy+XIz8/H0KFD\nsWzZMgwYMAC2tra4desWTp06hYCAADg4OKBv3744ffo0AOD06dOQy+XCV9u2bdGlSxcAgFKpxOrV\nq9G1a1c4Ozvjtddew+PHjwH8b7jC1q1b0blzZ7i4uGDVqlUVvhchISFYtmwZAM09s6Vvvx44cAB+\nfn6Qy+VCrHJychAcHIz09HShrZpKUObm5uL999+Hl5cXHBwcMGjQIKFiUEXv91dffYWpU6eqHWfR\nokVYtGgRgOLPxBtvvAF3d3d4eHhg2bJlwjCN8PBwDBgwAO+99x6cnZ3x2WefIT8/H0uWLEHnzp3h\n5uaGefPmqVUtWrNmjXCszZs3V/ieAeo/4+Hh4Rg4cCA++OADODk5wdvbGwcPHqxw35LYyeVy+Pn5\nYe/evZWeqz5xjKJ0cIwiiWnwRHFw90l1niyWVGapqm3btmHkyJEYMWIEDh8+jHv37gEo7o0YP348\n5HI5Lly4gMuXLyMoKAgdOnTAqlWr0L17dygUCty4cQOA+O3Jrl274tixY0hOTsaoUaMwbdo00Vvd\nAwcOxK1bt9SSlu3bt2PcuHEaty9pQ0VtLOs///kPvL29kZSUhAULFiAiIkK4huvXr2PGjBkICwvD\n9evX0bdvX0yYMAGFhYVQKpWYMGECOnfujPj4eERHR2P9+vU4fPgwAODdd9/FrFmzcOvWLcTFxWHE\niBEVXuO9e/eQmZmJ+Ph4fPXVVwgNDRUSuIULFyIrKwvnz5/Hnj17sG3bNmzZsgWurq5YuXKl6PWV\ntmXLFmzduhW7d+9GXFwcsrKysHDhQtFrLe3ChQsYM2YMVqxYobGcYknPdEREBBQKBUxMTAAUx+yr\nr75CSkoKzMzMMG7cOMycORM3btzArFmzMG7cODx69Ag9evSAQqEQrqlbt24YPbq4wtCGDRuwf/9+\n7NmzBwkJCbC0tMSCBQvUzn/q1CmcOXMG0dHR+PzzzytMdoGq92rOnTsXX375JRQKBWJiYvDiiy/C\nzMwMO3bsEOp+KxQKWFtbl9v3gw8+wMWLF/Hnn3/ixo0b+Oijj2BgYFDp+x0UFISDBw8KNdOLiorw\n+++/Y8yYMQCKk1wTExOcO3cOR44cwd9//41ffvlFLQaOjo64evUq3nnnHXz44YdITk7GsWPHcPbs\nWdy5cweff/45AODgwYP49ttvERUVhTNnzoiOQy37Mx4XFwcXFxckJSVh7ty5ePPNNyvc19HREfv2\n7YNCoUBoaChmzpypMbkmImpIDX7rOdB7dJVK69WX2NhY3LlzBwMGDECzZs3g6uqKyMhIzJo1C+fO\nnUNGRgaWLl0KA4PiHLtnz54AanaruOQPHVD8x27lypW4fv063N3dK9ynSZMmGDFiBHbs2IH33nsP\nCQkJSElJQf/+4rftxdqYmpqKf/75B7/99huMjY3h5+eHAQMGCOt37dqFfv36oXfv3gCAN954A999\n9x1OnTqFJk2a4MGDB8I4N3t7e0yePBlRUVHo06cPTExMkJSUhAcPHsDKygrdunWrsB3GxsYIDQ2F\ngYEBAgMDYW5ujmvXrqFLly7YtWsXjh49CnNzc5ibm2P27NnYvn07Jk2aVO0YREZGIiQkRKjR/cEH\nH6BXr1745ptvKrzW06dPC6UIT5w4gS1btmDDhg3Ca1Uhk8kwfvx44Xb033//DWdnZ+HzMGrUKGzY\nsAF//PEHxo8fL+y3cOFCNGvWTOiN/fnnn7FixQq0bdsWABAaGgovLy989913wj6hoaFo0qQJPDw8\n4OHhgUuXLqFDhw7Vep/KMjY2RmJiItzd3dG8eXN07twZgPjnS6lUIjw8HAcOHICNjQ0AoHv37gAq\n/myVvN+dO3fG3r17MXbsWBw9ehSmpqbo2rUr7t69i4MHDyI5ORlNmzaFqakpZs2ahV9++UXohbSx\nscH06dMBFP/8/Prrrzh27JjQa/bWW2/h9ddfx5IlSxAdHY2JEyfCzc0NQHHPpaae4orY2dlh8uTJ\nAIpLcs6fPx/37t1D69aty21bekjLyJEjsXr1asTFxenEOFbOoygdnEeRxDR4j6KuiYiIwCuvvIJm\nzZoBKP5lXnL7+fbt27CzsxOSRG19/fXX8PX1hYODAxwdHfH06VM8ePBAdL9x48YhMjISQHHP1MiR\nI2FsbKx1e+7cuQNLS0uYmv6vh9fOzk74Pj09Hba2tsKyTCZDu3btcOfOHaSmpiI9PR2Ojo7C15df\nfon79+8DKL6dl5SUBF9fX/Tt2xd//fVXhe1o2bKl2ntsamqK7OxsPHjwAAUFBWptsrW1xZ07d2p0\nvWWvx9bWFoWFhbh79y4yMjIqvFagOCnatGkTevbsWa0ksUTpWtll2wEUv++lr+vnn3/GyZMn1W7n\np6SkYPLkycL77efnByMjI9y9e1fYpnSvnpmZGXJycqrd1rI2bdqEgwcPokuXLhg6dCjOnDlTpf0e\nPHiAvLw8ODg4lFsn9n6PHj0aO3fuBFCc4Jf0qqakpKCgoAAdO3YU3od33nlH+NwB6u/1/fv3kZOT\ng1deeUXYPjg4WPi5y8jIUNu+bFzEtGnTRvjezMwMAJCdna1x25IhLiXtSEhIKDfUg4iooTV4j6Iu\nyc3NRXR0NFQqFTp27AgAePbsGZ48eYLLly+jXbt2SE1N1TggXtNtu7J/mEv/AY+JicE333yD6Oho\n4VxOTk5V6hXr3r07TExMcPLkSezcuRPff/99la5P7NaijY0NHj9+jJycHOGPXEpKinCtbdu2RXx8\nvLC9SqXC7du38fzzz8PY2Bj29vYVJg1OTk5CO3///XdMnToVSUlJakmpGCsrKxgbG0OhUAi9camp\nqULPR3UfCGnbti1SUlKE5dTUVBgZGcHa2ho2NjYar7Wk904mk2HVqlVYvXo13nvvPWF8X1WVbmvb\ntm2xe/dutfUpKSlCXeuYmBgsX74c+/fvh4WFhbCNra0tvv76a/To0aPc8RUKRbXaU5qZmRlyc/9X\n8rLs7VBvb29s3rwZRUVF2LBhA1577TVcvHhR9P23srJC06ZNkZycDA8PD7V1Yu/3sGHDsGTJEqSl\npWHfvn3CPxrt2rVDkyZNkJSUVOE/cKXbZWVlBVNTU8TExAi9mqVZW1sjNTVVWC79fW1KSUnB22+/\njejoaPTo0QMymQy9e/fWmYfYOEZROtibSGLYo1jKvn37YGRkhJiYGBw9ehRHjx5FbGws/Pz8sHXr\nVnTr1g3W1tb46KOPkJOTg7y8PJw6dQoA0Lp1a6SlpaGgoEA4nqenJ/bs2YPc3FzcuHEDmzdvFv5o\nZWVlwcjICFZWVsjPz8eKFSuQmZlZ5bYGBwcjNDQUJiYmwu1vMZraWJqdnR26dOmCsLAwFBQUIDY2\nFn/++b+yisOHD8eBAwdw9OhRFBQU4JtvvkHTpk3Ro0cP+Pj4wMLCAmvWrEFubi6KiooQHx+P8+fP\nAyju+Szp5WnevDlkMlm1e2YNDQ0xYsQILFu2DFlZWUhJScG6deuEW7Zi11dWUFAQ1q1bB4VCgays\nLHz88ccICgqCgYFBpddawsLCApGRkYiJicHSpdUrNl86IQgMDERSUhJ27tyJwsJCREVF4dq1a+jf\nvz9SU1Px2muvYd26deUe0Jk6dSo++eQTIZm5f/++6DyNlSUiJes6deqExMREXLp0CXl5efjss8+E\nbQoKCrBjxw48ffoUhoaGsLCwEP6RaN26NR49eqT2QFBpBgYGmDhxIt5//32kp6ejqKgIp0+fRn5+\nPkaMGFHp+92qVSv06tULISEhcHBwgIuLC4DiBPOVV17Be++9h8zMTCiVSiQnJ+PkyZMVtmHy5MlY\nvHix8HlMS0sTxtKOGDECERERuHLlCnJycrBixYpK38+ays7OhkwmE+ZH3bJlCxISEurkXERE2mCi\nWMrWrVsxceJEtGvXDq1bt0br1q3Rpk0bTJ8+XbjtFR4ejuTkZHTu3Bmenp6Ijo4GAPTu3Rtubm5w\nc3MTxoDNmjULxsbGcHV1xZw5c9TGJAYEBKBPnz7o3r07unTpgqZNm5a79Va6J6Rsb83YsWORmJio\ndkwxmtpY1vfff49z586hffv2WLFihdoYORcXF6xfvx4LFy6Ei4sLDhw4gPDwcBgZGcHQ0BARERG4\nePEifHx84OLigrfffltIfg8fPoxevXpBLpfjvffeww8//IAmTZpobENlPVOfffYZzMzM4OPjg0GD\nBmHMmDGYOHFila+vtEmTJiE4OBiDBw+Gj48PzMzMhKSosmstrXnz5oiKisLBgwexfPly0XNqusaW\nLVsiIiICa9euhbOzM9auXYuIiAi0bNkSR48exb179zB16lThaeJevXoBAGbOnIkBAwZg1KhRkMvl\n6N+/P+Li4ip9H6vS6+rs7IwFCxZg5MiR6NGjB/z8/NT22759O7p06QJ7e3ts2rRJGBPZoUMHBAUF\nwcfHB05OThofzFi6dCk6duyIgIAAtG/fHh9//DGUSiWcnZ1F3+/Ro0fj6NGjGDVqlNoxv/32WxQU\nFMDPzw9OTk6YNm2acG5ND5R9+OGHcHJyQr9+/WBvb4+goCAkJSUBAPr27YuZM2dixIgR6N69O156\n6aUq91RrOldF+7q5uSEkJAT9+/eHm5sbEhIS4OvrK6yPiYkRxs4CwKpVqxAcHCwsBwcHY/Xq1VVq\nV01wHkXp4DyKJEamqqN7HYcOHYKPj0+519PS0jhIuhbk5ubC1dUVR44cgaOjY0M3hxq52bNnw8nJ\nSetJt0k/JCQkCENiSL811MMsiSnnsSvmBxQpi/BccxsM8Kn9iesfZt7F/rMRMDAwgKVFK4QMrt6d\nH30TFxeHgICAau/HHsVGauPGjejatSuTRNJaYWEhrl27Bnt7+4ZuCukIjlGUDo5RJDF8mKUR8vLy\ngkwmE50MmKgq3Nzc4O3tjaFDhzZ0U4iISMcwUWyELly40NBNID1y/fr1hm4C6RjOoygdnEeRxPDW\nMxERERFpxESRiIjUcIyidLA3kcTUe6JYUupNVyaWJSKi/8nJySlXUICIpKvexyhaWVkhKysLaWlp\n1a6kQbrpyZMn7IGQCMZa/xkaGuLatWtq5R9Jf3GMIolpkIdZLCws1EqRUeN248YNzrkmEYy1NFy7\ndq2hm0BEOoJjFElr/G9UOhhraWCcpYOxJjFMFImIiIhIIyaKpDXWCpUOxloaGGfpYKxJDBNFIiIi\nItKIiSJpjWNcpIOxlgbGWToYaxLDRJGIiIiINGKiSFrjGBfpYKylgXGWDsaaxDBRJCIiIiKNmCiS\n1jjGRToYa2lgnKWDsSYxTBSJiIiISCMmiqQ1jnGRDsZaGhhn6WCsSQwTRSIiIiLSiIkiaY1jXKSD\nsZYGxlk6GGsSY9TQDSAiIiL99KwgF8cu78f9p3fUXs95ltlALaLqYo8iaY1jXKSDsZYGxlk66jrW\nZ68dwZmrh3DjTrzaV/rDFKhUxdvI6rQFpC32KBIREVGdeJR1HyoVUKQsqnAbm5byemwRVVelieJr\nr72GvXv3ok2bNrh48SIA4OHDhxg7dixu3boFBwcHbN++HZaWlvXSWNJNHOMiHYy1NDDO0lGfsW7X\nyhHtnnNQe62ZqSWsW9rVWxuo+iq99Txt2jT88ccfaq+FhYUhMDAQV69eRUBAAMLCwuq0gURERNT4\ntbRoBZd2ndW+bJ6TQybjzWddVmmi+OKLL6Jly5Zqr/3++++YMmUKAGDKlCmIjo6uu9ZRo8DxTNLB\nWEsD4ywdjDWJqfYYxYyMDFhbWwMArK2tkZGRUeuNIiLtZT0rRFpmPgDA3NgQTfIKUFhYPE7IqrUF\njE0MG7J5RHXu2b2HyEu7CwAwsbKEqa1NA7eoccrMfYx7T4qfWrZo2hxtLNs1cIuoPmn1MItMJqu0\ny3j27NmQy4sHqbZo0QKenp7CeIiS/2K43PiXX3jhBZ1qD5eLly+lZyHqcfE/dXZZ1/C84iFaNHUA\nALj2kKFlK3Odai+XdWe55DVdaU9Nl+2uZiBh8UrEK7PRZsBLmPTL1zrVPl1Yrsrv7193/oDomI14\nzt4UL7gPRBfLAdU6n+JqBpRKJTo5AABw9nQcAKBbD586XXbqaAsASLmagUemecBgNPj7XZ/LJd8r\nFAoAwPTp01ETMpWq5AF1zW7evImhQ4cKD7O4ubnhv//9L2xsbHDnzh288sorSExMLLffoUOH4OPj\nU6NGEZH2Ttx8jI8OJgMA/OxboH3iHdy9Uzx32eQ5/rB+vnlDNo+ozt3auBMJi1cCAORTg+AeNr+B\nW9Q4Hbu8D2v3LgEAvOA+EHOGfFLlffec3ox/k2NQpCxCJ4fu8HL0r6tmlvMw8y72n42AgYEBLC1a\nIWTw0no7ty6Ki4tDQEBAtfer9jyKw4YNw6ZNmwAAmzZtwogRI6p9UtIvpf97Id1hbmIIZytTOFuZ\n4vlmJniutQWsn28O6+ebw8ioZlOoMtbSoC9xNrGyRPPOrmje2RVN27Vp6ObopKrE2qJpczhau8HR\n2g2tWzxfD60iXWJU2crx48fjyJEjuH//Puzs7LB06VIsWrQIwcHB+PHHH4XpcYhI93R5vhm+Hen2\nvxd8bRuuMUQNoO3wALQdXv0eFFLn3f4FeLd/QXxD0kuVJooREREaXz948GCdNIYap9Ljmki/MdbS\nwDhLB2NNYljCj4iIiIg0YqJIWtOX8UwkjrGWBsZZOhhrEsNEkYiIiIg0qnSMIlFVcIyLbqqLCbcZ\na2nQlzhzwm1xVYk1J9yWNiaKRHrqwp0szqNIkpa++2/Oo1gL/rlxssbzKFLjx1vPpDWOcZEOxloa\nGGfpYKxJDBNFIiIiItKIiSJpTV/GM5E4xloaGGfpYKxJDBNFIiIiItKIiSJpjWNcdBNrPVNN6Uuc\nWetZHGs9kxg+9Uykp1jrmaSOtZ5rB2s9Sxt7FElrHOMiHYy1NDDO0sFYkxgmikRERESkERNF0pq+\njGcicYy1NDDO0sFYkxgmikRERESkER9mIa1xjItuYq1nqil9iTNrPYtjrWcSw0SRSE+x1jNJHWs9\n1w7WepY23nomrXGMi3Qw1tLAOEsHY01imCgSERERkUZMFElr+jKeicQx1tLAOEsHY01imCgSERER\nkUZMFElrHOOim1jrmWpKX+LMWs/iWOuZxPCpZyI9xVrPJHWs9Vw7WOtZ2tijSFrjGBcWAsx0AAAg\nAElEQVTpYKylgXGWDsaaxDBRJCIiIiKNmCiS1vRlPBOJY6ylgXGWDsaaxDBRJCIiIiKN+DALaY1j\nXHQTaz1TTelLnFnrWRxrPZMYJopEeoq1nknqWOu5drDWs7Tx1jNpjWNcpIOxlgbGWToYaxLDRJGI\niIiINGKiSFrTl/FMJI6xlgbGWToYaxLDRJGIiIiINGKiSFrjGBfdxFrPVFP6EmfWehbHWs8khk89\nE+kp1nomqWOt59rBWs/SxkSRtMYxLtLBWEsD4ywdtRnr+0/TkZX7RO217GdPa+341DCYKBIREZFW\n/v73N8Qm/tXQzaA6wDGKpDV9Gc9E4hhraWCcpaO2Yp2Y+g9UKqBIqSz3pVQpAQBmJha1ci6qX+xR\nJCIiIq0olUVQQQWVSoVmZs1hYKCeXlhZtIGjTccGah1pg4kiaY3jmXQTaz1TTelLnFnrWVxd1Hr2\ndx+EVs2sa6V91PCYKBLpKdZ6JqljrefawVrP0sYxiqQ1jmeSDsZaGhhn6WCsSQwTRSIiIiLSiIki\naU1fxjOROMZaGhhn6WCsSQwTRSIiIiLSiIkiaY1jXHQTaz1TTelLnFnrWRxrPZOYGj/1vHz5cmze\nvBkGBgbw9PTETz/9hCZNmtRm24hIC6z1TFLHWs+1g7Wepa1G3Qo3b97E999/j7i4OFy8eBFFRUXY\nunVrbbeNGgmOcZEOxloaGGfpYKxJTI16FJs3bw5jY2Pk5OTA0NAQOTk5aNeu8gk4iYiIiKhxqVGP\n4nPPPYd58+ZBLpfj+eefh6WlJfr27VvbbaNGQl/GM5E4xloaGGfpYKxJTI0SxaSkJKxevRo3b95E\nWloasrKysGXLltpuGxERERE1oBrdej579iz8/f1hZWUFAAgKCsLJkycxceJEte1mz54NuVwOAGjR\nogU8PT2F8RAl/8VwufEvv/DCCzrVHi4XL+cWFMHeszsAIP7cKRjnF6KrTw8AQOLVCzAyNtCp9nJZ\nd5ZLXtOV9tR0uburO/LS7iL2nzgYNbdAwMhhOtU+XViuyu/vvw79gcfZD9Cthw8smjbH1UvJ5bZP\nTkhFS3lTAMCFc5fQwuw2uvXwAQCcPR0HAPW+7NSx+AG+lKsZeGSaBwxGg7/f9blc8r1CoQAATJ8+\nHTUhU6lUqurudOHCBUycOBFnzpxB06ZNMXXqVPTo0QMhISHCNocOHYKPj0+NGkVE2jtx8zFrPZOk\n3dq4k7Wea8Gxy/tEaz2v3fMBHmffh1KpRP9u49CqmXV9N7Och5l3sf9sBAwMDGBp0Qohg5c2dJMa\nVFxcHAICqj8LQI1uPXt5eeHVV19Ft27d0LlzZwDAjBkzanIo0gOl/3sh/cZYSwPjLB2MNYkxqumO\noaGhCA0Nrc22EBEREZEOYWUW0lrpcU2k3xhraWCcpYOxJjFMFImIiIhIIyaKpDWOcdFNrPVMNaUv\ncWatZ3FViTVrPUtbjccoEpFuY61nkjrWeq4drPUsbexRJK1xjIt0MNbSwDhLB2NNYpgoEhEREZFG\nTBRJa/oynonEMdbSwDhLB2NNYpgoEhEREZFGfJiFtMYxLrop61kh0jLzAQDmxoZokleAwsIiAIBV\nawsYmxhW+5iMtTToS5yf3XuIvLS7AIqfgDa1tWngFumeqsQ6M/cx7j25A6D4Ceg2lu3qulm17kn2\nQ3y+82211wwMjdDZvicCvUc3UKsaByaKRHrqwp0s1nomSUvf/TdrPdeCf26cFK31rIuMDY0BACqV\nCoAS+YXP1NbLCp/h7LX/ws8tEBamLRqghY0Dbz2T1jjGRToYa2lgnKVDn2PdzKwl2rVyhAoqKJXK\n8l8qFQAV8gpyG7qpOo09ikRERKSXXvYchvzCPKiUKrXX95zdjGf5TBCrgokiaU1fxjOROMZaGhhn\n6ZBCrE2MmpZ7TdYA7WiseOuZiIiIiDRiokha0+cxLo0Zaz1TTelLnFnrWRxrPZMY3nom0lOs9UxS\nx1rPtYO1nqWNPYqkNSmMcaFijLU0MM7SwViTGCaKRERERKQRE0XSmr6MZyJxjLU0MM7SwViTGCaK\nRERERKQRH2YhrXGMi25irWeqKX2JM2s9i5NKrWeqOSaKRHqKtZ5J6ljruXY01lrPVDt465m0xjEu\n0sFYSwPjLB2MNYlhokhEREREGvHWM2lNX8YzkTjGWhoYZ+lgrHWTSqnEozMXkXc7o3YOKJMB9lY1\n2pWJIhEREZEOufPbIdzetq/2Dmggg+H8STXbtfZaQVLFMS66ibWeqab0Jc6s9SyOtZ51U9aVZECl\ngqqwqNa+aoo9ikR6irWeSepY67l2sNZzw2rarg1MWtZ8lgoDExPImhgjs4b7M1EkrXGMi3Qw1tLA\nOEsHY637WnR2hWU3zxrvLzMygszECJmZD2u0P289ExEREZFGTBRJa/oynonEMdbSwDhLB2NNYpgo\nEhEREZFGHKNIWuMYF93EWs9UU/oSZ9Z6FsdazySGiSKRnmKtZ5I61nquHaz1LG289Uxa4xgX6WCs\npYFxlg7GmsQwUSQiIiIijZgoktb0ZTwTiWOspYFxlg7GmsQwUSQiIiIijZgoktY4xkU3sdYz1ZS+\nxJm1nsWx1jOJ4VPPRHqKtZ5J6ljruXaw1rO0sUeRtMYxLtLBWEsD4ywdjDWJYaJIRERERBoxUSSt\n6ct4JhLHWEsD4ywdjDWJYaJIRERERBrxYRbSGse46CbWeqaa0pc4s9azONZ6JjFMFIn0FGs9k9Sx\n1nPtYK1naeOtZ9Iax7hIB2MtDYyzdDDWJKbGieLjx48xevRodOzYEe7u7oiNja3NdhERERFRA6vx\nrec333wTgwYNQmRkJAoLC5GdnV2b7aJGRF/GM5E4xloaGGfpYKxJTI0SxSdPnuDYsWPYtGlT8UGM\njNCiRYtabRgRERERNawa3XpOTk5G69atMW3aNPj4+OA///kPcnJyartt1EhwjItuYq1nqil9iTNr\nPYtjrefapSwoRGF2jtZfqqKihr4UQY16FAsLCxEXF4dvvvkG3bt3x1tvvYWwsDAsXbpUbbvZs2dD\nLpcDAFq0aAFPT0+hm7vkw8llLnO57pa/HVlq2RYYMq7U8tXqH6+Erlwfl+tm+eLFizrVnhov/1+t\n5+PHjyMNgBOgW+1rJMvZd4DB7WdVun1yQipaypsCAC6cu4QWZrfRrYcPAODs6TgA0KnlW4l3YO1k\nCQA4FXMaLcyf0/r9ci0wQsqmXYhLUwAAvJ4rno7pwsP0mi23tC5ub9IVWBgVwLdLcftj/ym+HrHl\nku9TMzIAAxlmvfMWakKmUqlU1d0pPT0dfn5+SE4unnrj+PHjCAsLw549e4RtDh06BB8fnxo1ioiI\niBqPtXs+wOPs+1AqlejfbRxaNbNu6CZVKurk98jLz4WhgQH+M2AJWjXXfo7N+HdXIvtGClD9tKpC\nKqUKbYP6orlHhxofQ2ZkBJmJEa5lPkRAQEC196/R/ScbGxvY2dnh6tWrAICDBw/Cw8OjJociIiIi\navSU+QUAVFApVYBMBpmBgXZfhgYwc7JFM9f2DXpdNbr1DABff/01Jk6ciPz8fLRv3x4//fRTbbaL\nGpHjx4/zyTmJYKylgXGWDsa6bthOGAIzB9uGbkatqHGi6OXlhTNnztRmW4iIiIhIh9Q4USQqwf9G\ndRNrPVNN6UucWetZXFVizVrP0sZEkUhPsdYzSR1rPdcO1nqWNtZ6Jq2VnTqF9BdjLQ2Ms3Qw1iSG\niSIRERERacREkbSmL+OZSBxjLQ2Ms3Qw1iSGiSIRERERacREkbTGMS66ibWeqab0Jc6s9SyuKrFm\nrWdp41PPRHqqy/PN8O1It/+94Ksfk78SVVXb/6v1TNrxbv8CvNvzFrVUsUeRtMYxLtLBWEsD4ywd\njDWJYaJIRERERBoxUSSt6ct4JhLHWEsD4ywdjDWJYaJIRERERBrxYRbSGse46CbWeqaa0pc4s9az\nONZ6JjFMFIn0FGs9k9Sx1nPtYK1naeOtZ9Iax7hIB2MtDYyzdDDWJIaJIhERERFpxESRtKYv45lI\nHGMtDYyzdDDWJIaJIhERERFpxESRtMYxLrqJtZ6ppvQlzqz1LI61nkkMn3om0lOs9UxSx1rPtYO1\nnqWNPYqkNY5xkQ7GWhoYZ+lgrEkME0UiIiIi0oiJImlNX8YzkTjGWhoYZ+lgrEkME0UiIiIi0ogP\ns5DWOMZFN7HWM9WUvsSZtZ7FsdYzsPFAWLnX2raUY+yLs2Fi3LQBWqRbmCgS6SnWeiapY63n2qGP\ntZ4NZEYAVFCqVFAW5pdbn3o/CZcVZ/m0N3jrmWoBx7hIB2MtDYyzdEg11q62XjA0MIZSqSz/pVIC\nAHLzsxu4lbqBPYpEREQkKR3tfNChXWcUFRWiMDMbRXnPAABn02KQlpkClVKFgkeZyE1Nr/IxlUVF\nddXcBsVEkbSmL+OZSBxjLQ2Ms3RUN9bZeZnYfeqX/9/enQbHVZ57Av+/Z+lF3Vot2ZJsy6vwgncM\nNiFcIAwTIAlUBeYWuVOTVEJIKlSKIfdLUvAhN/lAtpqkGFKVm2GyFBAmqSxT5CbgO4EbIDaxDdjY\nxgbhRbYly5a1S61ezznvfGhJSHZL3X3O6fX8f1UGn9bpc177saRH73ne94EpjTmvx5IRN4dVFKqi\nYeClv2F43yFApl+b6EzCXCIgpUDf//0L3u3ZV9pBlgEmikRERJSTcwMnYZpG9hMrxNihE4CUM4ki\npAQgpn5vAZaV1/Xk1HXUUI1rYyw11iiSY16tcSl37PVMdlVLnNnrObt8ej0vb14LTdFgSQumZV71\ny7Is+HwBNIYWFWHk7pBTj4ulJSH8Pgh1ajcIASg+DWpNIK9fWm0NGm/YDH9LUwn/VO7ijCJRlWKv\nZ/I69np2x3Sv5+GJAfz0pX+BaVnQNB3Xduycc54qVHQs7oSqVGZq0f7p/4xLkSMYj/dBURQ033Yj\n1iy+odTDKrnKjCaVFdYzeQdj7Q2Ms3fYjbWmaNi0gkmUF/DRMxERERFlxESRHKuWeibKjrH2BsbZ\nOxhryoaJIhERERFlxBpFcoz1TOWJvZ7JrmqJM3s9Z5dPr+fx6AgSqTg01VeEkVG5YKJIVKXY65m8\njr2e3TG713NDqBnLFq0u8YiomPjomRxjjYt3MNbewDh7B2NN2TBRJCIiIqKMmCiSY9VSz0TZMdbe\nwDh7B2NN2TBRJCIiIqKMmCiSY6xxKU/s9Ux2VUuc2es5u3x7Pfs0fxFGReWEq56JqhR7PZPXsdez\nOzL1eibv4IwiOcYaF+9grL2BcfYOxpqyYaJIRERERBkxUSTHqqWeibJjrL2BcfYOxpqycZQomqaJ\n7du341Of+pRb4yEiIiKiMuFoMcuTTz6JjRs3YmJiwq3xUAVijUt5Yq9nsqta4sxez9mx1zNlYztR\n7O3txYsvvojHH38cP/zhD90cExG5gL2eyevY69kd7PXsbbYfPX/ta1/DD37wAygKyxy9jjUu3sFY\newPj7B2MNWVja0bxT3/6ExYvXozt27fj1Vdfnfe8hx9+GB0dHQCA+vp6bN68eWaae/ofJ495zOPC\nHL97KQJgCQCg9/hbsM4Poz6wEgBw8ODf0dgcyvv608rhz8fjwh0fO3asrMZj93g50k5YkxjsO4eN\nU8flMr5KOT52+ASGz8XQtCIIAOj54DJ0zQfclP77fOvgIQDAzht2VOTxe4MDkKbE9E6zPScvQxEK\ndjenj/e/kz5/97YdFXU8/fve/n5AEfjKPz8KO4SUUub7psceewzPPvssNE1DPB7H+Pg47rvvPjzz\nzDMz57zyyivYsWOHrUERkXP7zo7y0TN52rmf/56Pnl3wt+MvXvXo2a8HcN9NXyrxyJx7/1/+J6xE\nMp0o/tdP4VDkCPrifVAUBbubP4Kdi28o9RAdE5oG4dNwcmIYt9+e/wb0tp4bP/HEE+jp6UF3dzd+\n/etf42Mf+9icJJGIiIiIKp8rBYZCCDcuQxWKNS7lib2eya5qiTN7PWeXS6zZ69nbbK96nnbLLbfg\nlltucWMsROQi9nomr2OvZ3ew17O3cckyOVYte65Rdoy1NzDO3sFYUzZMFImIiIgoIyaK5Fi11DNR\ndoy1NzDO3sFYUzZMFImIiIgoI8eLWYhY41Ke2OuZ7KqWOLPXc3bs9UzZMFEkqlLs9Uxex17P7mCv\nZ2/jo2dyjDUu3sFYewPj7B2MNWXDRJGIiIiIMmKiSI5VSz0TZcdYewPj7B2MNWXDRJGIiIiIMmKi\nSI6xxqU8sdcz2VUtcWav5+zY65my4apnoirFXs/kdez17A72evY2ziiSY6xx8Q7G2hsYZ+9grCkb\nzigSERFRxUiNTWD8yHswU4bja0mz+LOjFycSeKtnHDGjOPeuCfpQG/Jj2RJ772eiSI7t3buXP5V6\nBGPtDYyzd1RarKWUOPvTXyM1Ml7qodj2t+5R9EcSRbtf2AKSQsEy6Lbez0SRiIiIKoIxMZlOEqWE\ntKRr11WDPigBHxBx7ZLziiZNSABwb/gLkhKO/q6YKJJjlfTTqJew1zPZVS1xZq/n7Cq517NQBUKr\nXVikp2oIr18NIYq/bGPTkjCCNr4W5yMU9CFc44OEvVlMJopEVYq9nsnr2OvZHWXb61lTseiW3aUe\nhSMtIR31QXuPhHPlD+jw+3QMSXuJIlc9k2PVsucaZcdYewPj7B2MNWXDRJGIiIiIMmKiSI5VSz0T\nZcdYewPj7B2MNWXDRJGIiIiIMmKiSI6xxqU8sdcz2VUtcWav5+zmi3U8GcPpSydw+tIJTMRG0d60\nEq0Ny9nr2YO46pmoSrHXM3kdez3bMxoZxNP//gQM88NVsi11H24txF7P3sJEkRxjjYt3MNbewDh7\nR6ZYf9B3FIaZmDchlJAI+GoKPbSiMSwLlyaSsCQwkTRgTm3mPRBJ4qSIun4/s0gbbbuFiSIRERHN\nsCxz6ncSuuZDyD93z1Wf7semFTcUf2AFYEFiT9cQoqn0n9n0J6H4LAghcGJgEqcvDbp7QynhlyqC\nUAEJRCImrIRw9x5X0H0SwYAE6u29n4kiOVZpvULJPsbaGxhn78gW69bGDtx87Scc38eMxRHp6oZ0\n+NjairvbI3k0aiCaMjHd4W7OZJ8EXOwSCABYIoMIiKnUSwAjQxKjIuXuTa6SQm2thbZ6ewkpE0Ui\nIiIqGCuZwqn/8XOYk7FSD2VBigA0VYElBBQhEPSpqBXudU2RlkQwoc1ko4oAINO9mAvNMi0A9loF\nMlEkxzjzUJ7Y65nsqpY4s9dzdrnEOhqfwMhk+hFs0BdCU21+K8ij5/vSSaKUkG5lRRLQg0F3rjXF\npyloDOkYSgmoAuhcVIN19Y2uXd8wLHSdTkwlhhI+vbCPnKfpPg2hkA7A3mwuE0WiKsVez+R17PXs\njq6+I/jt3n8FAGxb9RH8480P53mFD5/rCk2Fr7nJ8ZgUn4a6zeuzn1imBASWNBcnBattqEFNyI8J\njNt6PxNFcoz1TN7BWHsD4+wdxY61Fq5B6yduLdr9yDluuE1EREREGXFGkRzjzIN3MNbewDh7h1dj\nbZgW3j8Xw0TMwmIZgASgpIDxCQuWDkgBXLqcgtkfL/VQS46JIhEREXnK4GgKkZgFS0oIKSAACAFI\nKSEhIQBYUsJye38cIF2rWUHPc5kokmOsZypP072eAcz0ehYivcrOSa9nxrr6VUucp3s9A2Cv53nk\nEusaXxjtTSsBAA3hloKMI2mYSKaK17Iklsi0ceIVZJaP2yWAcE1xVjy7gYkiUZVir2fyOvZ6dse6\nZduwbtm2gl2/bzCBnsvJouwnmEnUSmHcTMKnKagNKEhBQAFQX69gqd/e3oMLEQIzP7RXAiaK5Fg1\nzDxQbhhrb2CcvaMcYj04asCyZEEm73JhSUxnbxBTm2BDAIoQUJTKSegKhYkiERERldCHKaKmFHe2\nTQggmih0C73KxkSRHKuWeibKjrH2BsbZO8ot1u2LfAgFi7fSYzxu4MwkClOLWCWYKBIREVFGhiVx\nqHcck0nT9jXUvghClgQsE/GkicN9czuERJMS1lR3uXMjUWgRBXV+Fa21vvSUH5UUE0VyrJx+GqUP\nsdcz2VUtcWav5+yyxfrSeALHRvtgpEYAAIoahKbn14KvbiiKay0JWBKxlIWTg9E5H2+0/PBN9f8Y\nnEwiNTW9JxFGW50/r3uR+5goElUp9nomr2OvZ+dihoVYvAtj/b8FAATC29Cw5B/zusbMVoQSkHLW\ncQZSTq0lEcB4wkSbvWGTi5gokmPlVuNChcNYewPj7B35xjrsU7CqMZDXPXwxHxQhAFXArwm01/vm\nnhARwNSj54CmIGXYf8xN7mOiSERERDlpDOrYmufTiFRiDFEVkKYCn66hqTk05+M9iWR6s22ZThQn\nmCiWlQpqIkPlijMP3sFYewPj7B2MNWXDGUUiIiLKSJgWFMOYOZaWBSsez+8iqaTLo6JiYqJIjrGe\nqTyx1zPZVS1xZq/n7OaLtQRgxOKo7zuNlgsxnFgShADgP3YeE//xv4s+Tiod24liT08PPvvZz+Ly\n5csQQuBLX/oSHnnkETfHRkQOsNczeR17PdtnpYyZ5clt42G0ja2FriiAAGw325MSUuf8VKWxHTFd\n1/GjH/0I27ZtQyQSwXXXXYc77rgDGzZscHN8VAGqYeaBcsNYewPjXB5GhiYxdDlS0Hu0LurEqff6\n57w2Ohyd06lEWoClCKhCQHGwskEEAlDXr4WUVyaa0w2WqRzZThRbW1vR2prevDQcDmPDhg3o6+tj\nokhEROTQpd5R/O0vJ0ty7wEMIKUClqYj0bwIAzdshqVq0FQBx31STADnWLNYSVxZ9Xz27FkcPnwY\nu3btcuNyVGH27t1b6iFQkTDW3sA4l96l3nSbO2nKgv56/4N3rn79isk9OfUfKdMPnQvxawZb9pUd\nx8UCkUgE999/P5588kmEw+E5H3v44YfR0dEBAKivr8fmzZtnHmlMfyHiMY95XDnH08plPDwuzPGx\nY8fKajxePD51oh8hvQMSwNne4wgEdVy7fgcA4Pj7hwDAleO6oSAuDn0wczw0EEH3qdMYUS+jfe0i\nAED32VOQQsHaNdcAAM50p89fvcrNY4n116xHAhIXzp6CEEDHts0AgHffex8AsGnD+oIcXzh7ClIC\nq9amx9N7cgCKEFh9LQAAx947AgDYvGFrRR0DwLH3j2JkfBCqpuKfv/412CHk1cUCOUulUvjkJz+J\nu+66C48++uicj73yyivYsWOH3UsTkUOF6PVMVEkqudfzO/vP4+R7/bBMiaUrGrF2Y/FWbR/peR0H\nT/4JRjKOmssK/Jea0NvRghWNAdT7wwjrDQW7d89oDJcjqXSi2BDEupaagt0LAMbjBg70jEFKwKcp\nqGs6hVHZD0UoWO3biVWBbQW9fzHUNtSgJuTHhBjH7bfnv7jL9oyilBIPPvggNm7ceFWSSESlx17P\n5HXs9eyOkcAges1X0TsIdISuxe6We4py30jSQO94oqD3iCfZBSYb24nivn378Nxzz2HLli3Yvn07\nAOA73/kO7rzzTtcGR5WhWvZco+wYa29gnL3j4Jv7ccP1u0s9jIyGoykMR1OlHobn2U4UP/rRj8Ky\nLDfHQkRERB7m11QAqasW1BTl3ioX0mTCnS/JMc48eAdj7Q2Ms3eU22xic0iHYUpMpoo7EaUpQFut\nH/3czvEqTBSJiIiqgWlh9NBxxHovObrMuHYG0m+4NKj8KEKgvd5fknsDALjF41WYKJJjrGcqT+z1\nTHZVS5y91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+ "text": [ + "" + ] + } + ], + "prompt_number": 19 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The best comments, according to our procedure, are the comments that are *most-likely* to score a high percentage of upvotes. Visually those are the comments with the 95% least plausible value close to 1.\n", + "\n", + "Why is sorting based on this quantity a good idea? By ordering by the 95% least plausible value, we are being the most conservative with what we think is best. That is, even in the worst case scenario, when we have severely overestimated the upvote ratio, we can be sure the best comments are still on top. Under this ordering, we impose the following very natural properties:\n", + "\n", + "1. given two comments with the same observed upvote ratio, we will assign the comment with more votes as better (since we are more confident it has a higher ratio).\n", + "2. given two comments with the same number of votes, we still assign the comment with more upvotes as *better*.\n", + "\n", + "### But this is too slow for real-time!\n", + "\n", + "I agree, computing the posterior of every comment takes a long time, and by the time you have computed it, likely the data has changed. I delay the mathematics to the appendix, but I suggest using the following formula to compute the lower bound very fast.\n", + "\n", + "$$ \\frac{a}{a + b} - 1.65\\sqrt{ \\frac{ab}{ (a+b)^2(a + b +1 ) } }$$\n", + "\n", + "where \n", + "\\begin{align}\n", + "& a = 1 + u \\\\\\\\\n", + "& b = 1 + d \\\\\\\\\n", + "\\end{align}\n", + "\n", + "$u$ is the number of upvotes, and $d$ is the number of downvotes. The formula is a shortcut in Bayesian inference, which will be further explained in Chapter 6 when we discuss priors in more detail.\n" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "def intervals(u, d):\n", + " a = 1. + u\n", + " b = 1. + d\n", + " mu = a / (a + b)\n", + " std_err = 1.65 * np.sqrt((a * b) / ((a + b) ** 2 * (a + b + 1.)))\n", + " return (mu, std_err)\n", + "\n", + "print \"Approximate lower bounds:\"\n", + "posterior_mean, std_err = intervals(votes[:, 0], votes[:, 1])\n", + "lb = posterior_mean - std_err\n", + "print lb\n", + "print\n", + "print \"Top 40 Sorted according to approximate lower bounds:\"\n", + "print\n", + "order = np.argsort(-lb)\n", + "ordered_contents = []\n", + "for i in order[:40]:\n", + " ordered_contents.append(contents[i])\n", + " print votes[i, 0], votes[i, 1], contents[i]\n", + " print \"-------------\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Approximate lower bounds:\n", + "[ 0.83167764 0.8041293 0.8166957 0.77375237 0.72491057 0.71705212\n", + " 0.72440529 0.73158407 0.67107394 0.6931046 0.66235556 0.6530083\n", + " 0.70806405 0.60091591 0.60091591 0.66278557 0.60091591 0.60091591\n", + " 0.53055613 0.53055613 0.53055613 0.53055613 0.53055613 0.43047887\n", + " 0.43047887 0.43047887 0.43047887 0.43047887 0.43047887 0.43047887\n", + " 0.43047887 0.43047887 0.43047887 0.43047887 0.43047887 0.43047887\n", + " 0.43047887 0.43047887 0.43047887 0.47201974 0.45074913 0.35873239\n", + " 0.3726793 0.42069919 0.33529412 0.27775794 0.27775794 0.27775794\n", + " 0.27775794 0.27775794 0.27775794 0.13104878 0.13104878 0.27775794\n", + " 0.27775794 0.27775794 0.27775794 0.27775794 0.27775794 0.27775794\n", + " 0.27775794 0.27775794 0.27775794 0.27775794 0.27775794 0.27775794\n", + " 0.27775794 0.27775794 0.27775794 0.27775794 0.27775794 0.27775794\n", + " 0.27775794 0.27775794 0.27775794 0.27775794 0.27775794]\n", + "\n", + "Top 40 Sorted according to approximate lower bounds:\n", + "\n", + "327 52 Can you imagine having to start that? I've fired up much smaller equipment when its around 0\u00b0 out and its still a pain. It would probably take a crew of guys hours to get that going. Do they have built in heaters to make it easier? You'd think they would just let them idle overnight if they planned on running it the next day though.\n", + "-------------\n", + "120 18 Actually it does not look frozen just covered in a layer of wind packed snow.\n", + "-------------\n", + "70 10 That's actually just the skin of a mining truck. They shed it periodically like snakes do.\n", + "-------------\n", + "76 14 The model just hasn't been textured yet!\n", + "-------------\n", + "21 3 No worries, [this](http://imgur.com/KeSYJud) will help.\n", + "-------------\n", + "7 0 Dammit Elsa I told you not to drink and drive.\n", + "-------------\n", + "88 23 Speaking of mining...[BAGGER 288!](http://www.youtube.com/watch?v=azEvfD4C6ow)\n", + "-------------\n", + "112 32 Wonder why OP has 31,944 link karma but so few submissions? /u/zkool may have the worst case of karma addiction I'm aware of.\n", + "\n", + "title | points | age | /r/ | comnts\n", + ":--|:--|:--|:--|:--\n", + "[Frozen mining truck](http://www.reddit.com/r/pics/comments/1mrqvh/frozen_mining_truck/) | 2507 | 4^mos | pics | 164\n", + "[Frozen mining truck](http://www.reddit.com/r/pics/comments/1cutbw/frozen_mining_truck/) | 16 | 9^mos | pics | 4\n", + "[Frozen mining truck](http://www.reddit.com/r/pics/comments/vvcrv/frozen_mining_truck/) | 439 | 1^yr | pics | 21\n", + "[Meanwhile, in New Zealand...](http://www.reddit.com/r/pics/comments/ir1pl/meanwhile_in_new_zealand/) | 39 | 2^yrs | pics | 12\n", + "[Blizzardy day](http://www.reddit.com/r/pics/comments/1uiu3y/blizzardy_day/) | 7 | 19^dys | pics | 3\n", + "\n", + "*[Source: karmadecay](http://karmadecay.com/r/pics/comments/1w454i/frozen_mining_truck/)*\n", + "-------------\n", + "11 1 This is what it's typically like, living in Alberta.\n", + "-------------\n", + "6 0 That'd be a haul truck. Looks like a CAT 793. We run em at the site I work at, 240ton carrying capacity. \n", + "-------------\n", + "22 5 Taken in Fort Mcmurray Ab!\n", + "-------------\n", + "9 1 \"EXCLUSIVE: First look at \"Hoth\" from the upcoming 'Star Wars: Episode VII'\"\n", + "-------------\n", + "32 9 This is the most fun thing to drive in GTA V.\n", + "-------------\n", + "5 0 it reminds me of the movie \"moon\" with sam rockwell.\n", + "-------------\n", + "4 0 Also frozen drill rig.\n", + "-------------\n", + "4 0 There's just something awesome about a land vehicle so huge that it warrants a set of stairs on the front of it. I find myself wishing I were licensed to drive it.\n", + "-------------\n", + "4 0 Heaters all over the components needing heat: \n", + "http://www.arctic-fox.com/fuel-fluid-warming-products/diesel-fired-coolant-pre-heaters/n", + "-------------\n", + "4 0 Or it is just an amazing snow sculpture!\n", + "-------------\n", + "3 0 I have to tell people about these awful conditions... Too bad I'm Snowden.\n", + "-------------\n", + "3 0 Someone let it go\n", + "-------------\n", + "3 0 Elsa, you can't do that to people's trucks.\n", + "-------------\n", + "3 0 woo Alberta represent\n", + "-------------\n", + "3 0 Just thaw it with love\n", + "-------------\n", + "6 2 Looks like the drill next to it is an IR DM30 or DM45. Good rigs. \n", + "-------------\n", + "4 1 That's the best snow sculpture I've ever seen. \n", + "-------------\n", + "2 0 [These](http://i.imgur.com/xYuwk5I.jpg) are used for removing the ice.\n", + "-------------\n", + "2 0 Nigger\n", + "-------------\n", + "2 0 Please someone post frozen Bagger 288\n", + "-------------\n", + "2 0 It's kind of cool there are trucks so big they need both a ladder and a staircase to get into them.\n", + "-------------\n", + "2 0 Eight miners are just out of frame hiding inside a tauntaun.\n", + "-------------\n", + "2 0 http://imgur.com/gallery/Fxv3Oh7\n", + "-------------\n", + "2 0 BRAZZERS.\n", + "-------------\n", + "2 0 It would take a god damn week just to warm that thing up.\n", + "-------------\n", + "2 0 Maybe /r/Bitcoin can use some of their mining equipment to heat this guy up!\n", + "-------------\n", + "2 0 Checkmate Jackie Chan\n", + "-------------\n", + "2 0 I've seen this picture before in a Duratray (the dump box supplier) brochure. If I recall it was either at Ekati or Diavik... In which case the truck could be either a Komatsu or a CAT... anyone care to comment?\n", + "-------------\n", + "2 0 The Texas snow has really hit hard!\n", + "-------------\n", + "2 0 I'm going to take a wild guess and say the diesel is gelled.\n", + "-------------\n", + "2 0 Do these trucks remind anyone else of Sly Cooper?\n", + "-------------\n", + "2 0 cool\n", + "-------------\n" + ] + } + ], + "prompt_number": 20 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We can view the ordering visually by plotting the posterior mean and bounds, and sorting by the lower bound. In the plot below, notice that the left error-bar is sorted (as we suggested this is the best way to determine an ordering), so the means, indicated by dots, do not follow any strong pattern. " + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "r_order = order[::-1][-40:]\n", + "plt.errorbar(posterior_mean[r_order], np.arange(len(r_order)),\n", + " xerr=std_err[r_order], xuplims=True, capsize=0, fmt=\"o\",\n", + " color=\"#7A68A6\")\n", + "plt.xlim(0.3, 1)\n", + "plt.yticks(np.arange(len(r_order) - 1, -1, -1), map(lambda x: x[:30].replace(\"\\n\", \"\"), ordered_contents));" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "display_data", + "png": 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FcePGUVBQQHFxMbt37y43mb9Ro0Z88cUXHDhwgAYNGrBv3z7ef/99FAoF48aN486dO+jp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/xz\nHBwc8PT05Pz58wWOm5SUROvWrXF2dqZt27ZcvnyZ48ePExQUxNatW6WK4/k5cuQIHh4eqFQq3N3d\nefDgARkZGQwZMgSlUinVPgEKbS+Ix48f88knnxAaGoparWbDhg0AnDlzpsD7W716Ne7u7qjVakaM\nGCFlNKtQoQLjx49HpVJx8ODBQs/Lz8yZM3Fzc0OhUDB8+HCp3cvLi7Fjx9KkSRPmz5+PVqvFy8sL\nV1dXOnbsyLVr1/TGOXDgANu3b2fChAm4uLhw8eJFgzEELw+xt9a4CH2Nh9DWuJiDvtFR+/lxcSh1\n7Vpj/1pr6tq15sfFoURH7S9p156KOehrrghtTROTXBnR8fXXX+sVKwSktMBz5sxh0aJFNGvWjIcP\nH1K2bNkCxzh//jz9+/dn5cqVKBQKgxf6hIQEoqKiSEtLw8HBgcDAQI4fP05oaCgnTpwgMzMTFxcX\nqZp6fkaPHs2QIUN45513WLFiBWPGjCE8PJxPP/0UrVZr8PL8+PFj+vXrx4YNG9BoNKSnp2Ntbc13\n332HXC7n5MmTnD9/nvbt25OQkMDChQsLbC8IKysrZs6cqXfd4OBgzp07R3R0tN79JSQksGHDBg4c\nOIBcLicwMJA1a9bwzjvv8PDhQ5o2bcrs2bM5e/YsX3/9dYHn5WfUqFFMmzYNyCs0uWPHDnx8fJDJ\nZGRmZnLkyBGysrJo2bIl27dvp3LlyoSGhvLxxx+zbNkyaZzmzZvTtWtXfH19pQrz+ccQlE6u/nWP\n0KWHS9qNl07SX6c5uudhSbtRKhHaGhdz0DfywHpaNemj16aq78u3X6zkeHRGIb1MA3PQ11wR2hqX\nlt1eK1Y/k56MFJV12MPDg7FjxzJgwAD8/PyoWbOmwTk3btyge/fuhIeH07BhQ4PjMpmMLl26YGlp\nSeXKlalatSrXrl0jJiYGPz8/rK2tsba2pmvXrgX6cujQIbZs2QLAwIEDmThxouR3QeefP3+e119/\nXdompouNiY2NZcyYMUBeMcI6deqQkJBQaHtReuW/rkwmw8fHx+D+IiMj0Wq10gTr0aNHVK9eHQC5\nXC5VUy/qvPzs3buXWbNm8fDhQ+7cuYOTkxM+PnmFpfr27QvkFTo8ffo0bdu2BfK2XNWoUaPQ+8iP\nboyCCAwMlOq3VKxYEYVCIe0J1X0DIuzi2bo2Y1+vXh0nsjJzSL5yBoA6NRsDlHo7OyuXP5J+Nxl/\nSpNdq1oj/kj63WT8KW22Oeh77/5tkq+cMTgOMpP/vDEHfc3ZNvXnb042QHLKGe7dzyvy3bLbdIqD\nSU9GiiIoKAgfHx927tyJh4cHv/zyCw4ODnrnVKpUiTp16hATE1PgZATyVhR0yOVysrKykMlkei/E\nRU2KXlSZlsLGebK9qDiQgo4VdH8AgwcP5osvvjA439raWm+cws7TkZGRwfvvv49Wq6VmzZrMmDFD\nb2uajY2NdB+Ojo4cOHCg0LEKuw/dGAWxaNGiQo89GagmbNO0c3Jy+SC4HdAOfYQtbGELu3j2pduR\n1KncWLJ1L1G55a6KzxthC/uF23mc+v1Ege1Pw6QnI7a2tty/f7/AY3/88QeOjo44Ojpy5MgRzp8/\nbzAZsbKyYvPmzXTo0IEKFSpIgfA6CpoAyGQyWrZsib+/P5MnTyYzM5MdO3YwYsQIg3ObN2/O+vXr\nGThwIGvWrKFly6ID4xwcHLh69SpHjx7F1dWV+/fvU758eTw9PVmzZg3e3t4kJCTw559/0rBhwwLb\nHRwcuHXr1nPrlf/+2rRpQ7du3Rg7dixVqlThzp07pKenG1SIf5bzdBOPypUrk56eTlhYGH36/LM0\nrtPYwcGBmzdvcujQIZo2bUpmZiYXLlygcePGete0tbUlLS2tyHsQvBzyr4oYEwsLGRZW/73EBC9L\n3/8iQlvjYg769u7ny4+LQ1HV/yfzZHziNgJG9sPSxD9vzEFfc0Voa5qY5GRE9824s7MzcrkclUrF\nkCFD9FLyzps3j6ioKCwsLHBycpIySD05Tvny5dmxYwft2rXD1tYWW1tbaXyZTFbgaoJaraZv3744\nOztTtWpV3NzcCvRzwYIFDBkyhFmzZlG1alVWrFhR5LhWVlaEhoYyevRoHj16RPny5fn1118JDAxk\n5MiRKJVKypQpw8qVK7G0tCy0vbDxvb29+eqrr1Cr1UyePFlPy/w0atSIzz77jPbt25OTk4OlpSWL\nFi2idu3aeucXdZ6OSpUqERAQgJOTE9WrV8fd3d3gGejufePGjYwZM4Z79+6RlZXF2LFjDSYj/fr1\nIyAggAULFhAWFlag7gKBQCAQFIUua9amsB3kZIFFGQgY2U9k0xIITBBZ7ovaZyQQvGQiIyNxcXEp\naTcEAoFAIBAI/vMcO3aMNm3aPHc/k07tKxAIBAKBQCAQCEovYjIiEAgKRORjNy5CX+MhtDUuQl/j\nIvQ1HkJb06REJiNyuVwqWKhWq/nmm28ACAgI4OzZs0X29ff3Z9OmTQbtycnJrFu37l/59f3337Nq\n1ap/NUZJsX37dr7++uti9S0qW9bzsnXr1qc+wye5efMm7u7uaDQaYmNj9Y7FxMTg6OiIi4uLQQFJ\ngUAgEAgEAoF5UyIxI8+S9akwhgwZgo+Pj1QLQ0d0dDRz5szRK5BYUmRlZVGmzIvJDZCdnY1cbtzM\nH//meTyJv78/vr6+Bs+nKNavX09kZCRLly41ODZixAg8PT0ZMGCAwTERMyIQCASCwoiO2s/GDTvI\nzQaZHHr18REB7AKBESkVMSNeXl5otVoAli1bhoODA+7u7gQEBDB69GjpvP379+Ph4UG9evWkVZJJ\nkyYRExODWq1m3rx5euNGR0fTqlUrunfvTr169Zg0aRKrVq3Czc0NpVLJxYsXgbyK5XPmzJF8mTRp\nEu7u7jg4OEhLe9nZ2UyYMAE3NzecnZ354YcfpGt4enrSrVs3nJycePjwIV26dEGlUqFQKNiwYYPB\n/S5duhQ3NzdUKhW9evXi0aNHQN4L/YgRI2jatClBQUH88ccfdOrUCVdXV1q2bMn58+cNxgoJCZE0\nenL1SFdc8erVq7Rs2RK1Wo1CoeC3335j0qRJPHr0CLVabVBZHWDdunUolUoUCgWTJk0yGBNg48aN\nDBkyhIMHD7J9+3YmTJiAWq2WdNWRlJRE69atcXZ2pm3btly+fJnjx48TFBTE1q1bUavVeqsfP/74\nI2FhYUybNo2BAwca+CYQCAQCQUFER+3nx8Wh1LVrjf1rralr15ofF4cSHbW/pF0TCARPUCKpfXUv\nvzqmTJlC7969pZS1KSkpfPbZZ8THx1OhQgVat26NSqUC8upWXLt2jdjYWM6ePUvXrl3p2bMnX3/9\nNbNnzy50ZeTkyZOcO3cOOzs77O3tCQgIIC4ujvnz57NgwQLmzp2rlzJXJpORnZ3N4cOH2bVrFzNm\nzGDPnj0sW7aMSpUqERcXx99//02LFi1o3749APHx8Zw+fZo6deqwadMmatasyc6dOwEKrJ3Rs2dP\nAgICAJg2bRrLli1j1KhRAKSkpHDw4EGpLsj3339P/fr1OXz4MIGBgURGRuqNlT8l75PpfHX22rVr\n6dixI1OmTCEnJ4eHDx/SokULFi5cSHx8vIF/KSkpTJo0iWPHjlGpUiXat2/P1q1b6datW4HXa9as\nGV27dsXX1xc/Pz+D8UaPHs2QIUN45513WLFiBWPGjCE8PJxPP/0UrVbL/Pnz9c4fOnQosbGxhY4n\nMC4vKx/7zWv32b3xlNGvY2pcuHSSt+yVJe1GqURoa1zMQd8tu1bTzFn/3w1VfV8WzF7N5dMmWdVA\nwhz0NVeEtsbFsbl1sfqVyP+R5cqVK/DlF/ImG3FxcbRq1YpKlSoB0Lt3bxISEoC8F9/u3bsDeXUw\nrl+/LvUriiZNmlCtWjUA6tevT4cOHQBwcnIiKiqqwD66F2AXFxeSkpIAiIiI4NSpU2zcuBHIm2Qk\nJiZSpkwZ3NzcqFOnDgBKpZLx48czadIkfHx8CnypO3XqFFOnTuXevXukp6fTsWNH6R51k7P09HQO\nHjxI7969pX6PHz8u8l4Lw83NjXfffZfMzEy6d++Os7NzkecfOXIEb29vKleuDMCAAQPYv38/3bp1\nK7JfYc/i0KFDbNmyBYCBAwcyceJE6fziVrkPDAyU6p5UrFgRhUIhaa1bzRJ28exTp069lOvVq+PE\n9ZQ0kq+cAf6plFza7XPnznD31kOT8ac02XdvPSTu1iGT8ae02eag783b10m+csbgeObjHJP/vDEH\nfc3VBrhe1rSfvznZAMkpZ7h3/yYAc5tPpziY5NcDT36z/+TLqJWVVaHHCqNs2bLS7xYWFpJtYWFB\nVlZWkX3kcrneOf/73/9o166d3rnR0dHY2NhI9ltvvUV8fDw7d+5k6tSptGnThmnTpun18ff3Z9u2\nbSgUClauXEl0dLR0rHz58gDk5ORQqVKlQidvBVGmTBlycnKk/rrJi6enJzExMezYsQN/f3/GjRtX\n4NYsHTKZTE/f3NxcvZUjHbrtZfn7FcaLDlFatGhRoceenAAK+/nskSNHvpTrPX6cxcD3mwHN0Kd0\n2wNNzJ/SZT95rKT9KW226eubcPUX6rz+T1Fd3UvUY/lfZvB5Y/r6ClvYBZFy/Y8C25+GyU1GZDIZ\nTZo04cMPPyQ1NZUKFSqwadOmp36L/yKCsJ/2DT1Ahw4dWLRoEd7e3pQpU4aEhARq1aplcN7Vq1ex\ns7NjwIABVKxYkWXLlhmck56eTvXq1cnMzGT16tW88cYbBue88sor2Nvbs3HjRnr16kVubi6nTp1C\nqSx8mbFu3bpotVp69+7Ntm3byMzMBODPP/+kZs2aDB06lIyMDOLj43nnnXewtLQsMOi+SZMmjBkz\nhtu3b1OpUiXWr1/PmDFjAKhWrRrnzp2jQYMGhIeHU7FiRSDvORS0JQ2gefPmrF+/noEDB7JmzRpa\nthSBhAKwsipD9ZoVS9oNgUBQinh7UA9+XByKqr6v1BafuI2Akf3E541AYCRSrhevX4kEsOtiRnQ/\nU6ZM0Tteo0YNpkyZgpubGy1atMDe3l562YWC4yOcnZ2Ry+WoVCqDAPb8sSBP8mScSFHnQV4cQ+PG\njXFxcUGhUDBy5EiysrIM+p46dQp3d3fUajUzZ840WBUBmDlzJu7u7rRo0YJGjRoVeD2ANWvWsGzZ\nMlQqFU5OTmzbtq1IHwMCAti3bx8qlYpDhw5JweZRUVGoVCpcXFwICwvjgw8+AGDYsGEolUqDVZLX\nX3+dr776Cm9vb1QqFa6urvj65n2wf/XVV/j4+ODh4UGNGjWkPv369WPWrFloNBqDAPYFCxawYsUK\nnJ2dWbNmjfScitL9SS0ELw+Rj924CH2Nh9DWuJiDvl7eLRk6si/JqXu5dGsvyal7CRjZzyyyaZmD\nvuaK0NY0KZHUvs/CgwcPsLGxISsrCz8/P957772nxir8l5kzZw7p6elMn168/XrmiEjta1xeVgD7\nfxWhr/EQ2hoXoa9xEfoaD6GtcSlual+TnYxMmDCBX3/9lYyMDDp06MB3331X0i6ZLEuWLGHx4sVs\n3ryZevXqlbQ7Lw0xGREIBAKBQCAwDUrdZEQgeBpiMiIQCAQCgUBgGpRo0cOkpCQUCoVB+8qVK7l6\n9apkf/fddwaZl56FzMxMNBqNZI8YMYIDBw4wffp0g3obpYH169fzxRdfFKtv3bp1uXPnDqBfmPBF\noNPd39+fN998U4r5+d///vfcYyUnJ6PRaFCr1Tg6OurF+Tx+/JgPP/yQt956iwYNGtC9e3euXLny\nIm9F8AyIvbXGRehrPIS2xkXoa1yEvsZDaGuaGDWbVkhICE5OTrz++usAzJs3j3feeYdy5co91zhP\n7vE7fPgwixcvpnnz5i/U36dRUMYpY7B7924puPx5Kar4YVHoFsiK6nP48GEWLVrE0qVLmT179r8q\nRFijRg0OHTqEpaUlDx48wNHRkZ49e1KrVi2mTJnC5ikzuAAAIABJREFUgwcPSEhIQCaTERISgp+f\nH4cPHy729QQCgUDw3yI6aj8bN+wgNxtkcujVx8csAtgFgv8aLyybVnZ2NsOGDcPJyYkOHTqwevVq\njh49yoABA1Cr1cyfP5+UlBS8vb2lJZwKFSowbtw4nJycaNu2Lbdu3Spw7N27d9OpUycAzp49i4OD\nAzKZDH9/fzZt2gTkrQhMmTIFtVqNq6srx44do3379tSvX5/vv/8eyKu5ERgYSKNGjWjfvj1dunTR\n669bUTh69Cje3t4ABAcH884779CiRQsGDx5s4JdGo0GlUtG2bVsA7ty5IxUUbNasmVQ4Ljg4mMGD\nB9OyZUvq1q3L5s2bGT9+PEqlkk6dOkl1THJzczl+/DhqtZqbN2/Srl07nJycCAgI0POxR48euLq6\n4uTkxNKlS5/6fGbNmoWbmxvOzs4EBwcDeStaDg4ODB48GIVCwcyZMxk7dqzUZ+nSpYwbN05PdwsL\nC8nP/CQnJ9OgQQNu375NTk4Onp6e7Nmzh8mTJ+vVAgkODmbOnDlYWlpiaWkJ5GVXs7S0pHz58jx8\n+JCQkBDmzp0rTYz8/f0pW7Yse/fufep9Cl4cIsjPuAh9jYfQ1riYg77RUfv5cXEode1aY/9aa+ra\ntebHxaFER+0vadeeijnoa64IbU2TF/Y1/4ULF1i/fj0//PADffv2RSaT4erqypw5c6R9/XPnziU6\nOppXX30VgIcPH9KkSRO+/fZbZs6cyYwZM1iwYIE0eRg+fDiQV1BwxowZAOzatUuvUnn+tLx16tQh\nPj6ecePG4e/vz8GDB3n06BFOTk4MHz6czZs3k5yczNmzZ7l+/TqNGjXivffek/oXxrlz5/jtt9/0\nCifevHmTYcOGERMTQ506dUhNTQVg+vTpaDQatmzZQlRUFIMGDZIKFl66dImoqChOnz5N06ZNCQ8P\nl1YYdu7cSbdu3YiPj0elUgEwY8YM2rZtS1BQEL/88oterZLly5djZ2fHo0ePcHNzo1evXtjZ2RXo\nf0REBImJicTFxZGTk0O3bt2IiYnhjTfeIDExkVWrVuHm5saDBw9wdnZm9uzZyOVyQkJC+OGHHwx0\nz83NZcKECXz22WcArF69GkdHR4KCghg5ciRNmjTBycmJdu3aUaVKFT788EMCAwMBCAsLIyIiAoC/\n/vqLzp07k5iYyOzZs3n11Vc5efIktWvXNthi5urqyunTp2ndunWhz0lgnty9/YADkYkl7YZAIChF\nrFq3DtdG+hk4VfV9WTJ/HQ9uijojAoExeL1+8fq9sMmIvb29VIhPo9GQlJQEFF1x28LCgr59+wIw\ncOBAaduPbhICcOXKFV599VWsra2BvBfrkJCQAsfr2rUrAAqFQkoNbGNjQ9myZbl37x6xsbH06dMH\nyCvap1v9KAqZTEbXrl31JiIAhw4dolWrVtSpUweASpUqARAbG8vmzZsB8Pb25vbt29y/fx+ZTEan\nTp2Qy+U4OTmRk5NDhw4dJH91euVfBYqNjWXLli1AXrHF/JONefPmSccuX77MhQsXcHNzK/AeIiIi\niIiIQK1WA3lpkxMTE3njjTeoU6eO1M/GxobWrVuzfft2GjZsSGZmJo6Ojga6y2SyArdpvffee2zY\nsIHvv/+eEydOAKBSqbhx4wZXr17lxo0b2NnZUbNmTQBq1arFyZMnuXr1Kq1ataJ9+/ZPfRZPEhgY\nSO3atQGoWLEiCoVC+uZDtzdU2MWzFy9e/FL0rFfHibPHr5J85QzwT6Xk0m7HnfiZaq/VNRl/SpOt\n+91U/Clttjnom3I1heRXzhgcf5ieafKfN+agr7naujZT8cfcbYDklDPcu38TgLmLilde4oVNRvK/\nrMvlcilQ/VnjFnJzcws8d/fu3dI38g8fPiQ1NZXq1asX6YOFhQVWVlZSu4WFhd42qPzX1FGmTBly\ncnIAyMjI0Bu3fPnyBteSyWSFTrQKa9f5ZGFhIW1R0tnZ2dkA7Nmzh5EjRxY5VnR0NJGRkRw6dAhr\na2u8vb0NfH6SyZMnM2zYML22pKQkbGxs9NqGDh3K559/TqNGjXj33XeBgnUvyK+HDx/y119/IZPJ\nuH//vjR279692bhxI9euXaNfv34G/V5//XU8PT05ceIEnTp14s8//yQ9PV1vdUSr1UoFF/OTfwvY\nkzy5HCvs57PzT0SMeb2HDx7TubcSUKJP6barv5WBi8qt0OPCLr597PiT2pqWf+Zum4O+p5PrSC9O\n8M9LVHp2ssl/3piDvuZqHzseh4vKtJ+/edp5ZOReK7D9aRg1GtvW1pa0tDQDW7dNKycnh7CwMPr2\n7cvatWvx9PQ0GOOXX36RtgNFRUU90zadgl6UZTIZHh4erFy5ksGDB3Pjxg327dvHwIEDgbyYkaNH\nj9KxY0cpjqSwsQDc3d0JDAwkKSlJiuV49dVX8fT0ZM2aNUydOpXo6GiqVKmCra1tkStEuuukpaWR\nlZUlrYB4eHiwYcMGJk6cSEREBHfv3gUgLS0NOzs7rK2tOXfuHIcOHSpy7A4dOjBt2jQGDBiAjY0N\nV65c0Zus5cfNzY2//vqL+Ph4Kd7lWXUPCgrinXfeoXbt2gQEBLB9+3YA+vbty9ChQ7l9+zb79+ft\n19WteJUrV467d+8SGxtLUFAQ5cuXZ/DgwYwbN44lS5ZgYWHBTz/9xKNHj55pJUvw4nhZe2vL21jR\nWF3jpVzLlGis7l7SLpRahLbGxRz0HTy0Fz8uDkVV/58vseITtxEwsp/Jf96Yg77mitDWuBw7VsKT\nkSdXNXQB5iNGjKB8+fIcOHCAYcOG0bFjR2rWrElkZCQ2NjbExcXx2WefUa1aNUJDQwGkmJGhQ4eS\nmJhIgwYNgLy4Bd02q6f5UlBWqZ49exIZGUnjxo154403cHFxoWLFvL2j06dP57333uOVV17By8tL\nLxYl/1hqtZr4+HiqVKnCDz/8gJ+fHzk5OVSrVo1ffvmF4OBg3n33XZydnbGxsWHlypVF+pTfjoiI\noF27dlLb9OnT6d+/P6tWraJZs2ZUr14dW1tbOnbsyJIlS2jcuDEODg40a9asyGfSrl07zp49K51n\na2vL6tWrDXzS0adPH06cOCFpU5DuT/bbt28fWq2W+fPnI5PJ2LRpEyEhIfj7+9O4cWPS09OpVasW\n1apVA/IC4j/66CPJhylTpkjP+csvv2T8+PE0aNAACwsLGjVqRHh4eIH3KBAIBALBk+iyZm0K20FO\nFliUgYCR/UQ2LYHABCnRooe2trbcv3+/0OOxsbGsWbNG2oqj0WiIi4tDLpcX+5q6WJLbt2/j7u7O\ngQMHqFq1arHHe5EEBAQQEBAgxXA8fvwYuVyOXC7n4MGDvP/++xw7dszofvj6+jJu3DhpJeJF6G4M\nRNFD4/JkSm3Bi0XoazyEtsZF6GtchL7GQ2hrXIpb9ND4RTOK4GnxJB4eHnh4eEi2Vqv919f08fEh\nNTWVx48f88knn5jMRAQwSNH7559/0qdPH3JycrCysnqmFL7/htTUVNzd3VGpVHpbol6E7gKBQCAQ\nCAQCwZOU6MqIQPBvECsjAoFAIBAIBKZBcVdGXljRQ4HpIJfLUavVqFQqNBoNBw8eBPKyZ5UrVw61\nWo2TkxNDhw6VMohBXoX5KlWqMHnyZKnt8uXLqNVqvZ9XXnmFyZMnExcXZ3CsXLlyUsyPzg/dzzff\nfAOAl5cXDRs2RKVS0axZM86c+SdF3PLly1EqlTg7O6NQKNi2bdvLkEwgEAgEAoFAUAKIyUgppHz5\n8sTHx3P8+HG+/PJLvclF/fr1iY+P5+TJk1y6dEkvMHzPnj1oNBq9bGJvvPEG8fHx0s9PP/2EnZ0d\nY8eOxc3NTe/YV199xZtvvilVqtf5ofuZOHEikLc9b+3atRw/fpzhw4cTFBQE5BVB/OKLL4iNjeXE\niRMcPnxYql0jePno6oAIjIPQ13gIbY2L0Ne4CH2Nh9DWNBGTkVLOvXv3pFTK+bGwsMDNzY0//vhD\nalu/fj0jR47kzTfflFZT8pORkcHbb7/NwoULDWJtbt26xfDhw1m9erVUoPJZaNq0qeTDjRs3sLW1\nleqTlC9fnrp16z7zWAKBQCAQ6IiO2s+okRN5f9hERo2cSHTU/pJ2SSAQFECJBrALjMOjR49Qq9Vk\nZGRw9epV9u7da3BORkYG+/btY+rUqZK9d+9eli5dyu3bt1m3bp1ByuCJEyfSsmVLfHx8DMZ77733\neP/996Uq7/n90DFlyhR69+4N/FO/Zffu3Tg5OQF51dqrVauGvb09bdq0wc/Pr8BrCV4OLyvjyP17\nGZw+duWlXMuUKMPrHIr64+knCp4boa1xMQd9j588yq+/RtJU4Se1/e/b1Zw7eRWV0rUEPXs65qCv\nuSK0NS5WFYvXT0xGSiHlypUjPj4egEOHDjFo0CB+//13AP744w/UajWXLl2iTZs2dO7cGYAdO3bg\n5eWFlZUV3bt3Jzg4mHnz5kkZz3bt2kVkZGSBqYWXLFlCeno6EyZMKNSP/OTm5jJgwAAeP37M3bt3\npeKKFhYW7N69myNHjhAZGcnYsWPRarVMnz79xYkjMDnS0zL4bc+FknZDIBCUIqLjfsHLTb8+VlOF\nHzu3byD9ejHfmAQCQZG07lW8DLViMlLKadq0Kbdu3eLWrVsA1KtXj/j4eG7fvk3Lli05evQorq6u\nrFu3jtjYWOzt7QG4c+cOkZGRtG3blhs3bjBixAi2bdtG2bJl9cY/d+4cn3/+OYcPH35mn3QxIy4u\nLkyYMIFZs2Yxb9486XiTJk1o0qQJ7dq1Y8iQIUVORgIDA6lduzYAFStWRKFQSN/o6/aGCrt49uLF\ni1+KnkonDe5eb3LqdF4KaYWjBqDU21t3ruPNug1Mxp/SZOt+NxV/SpttDvpGxt0n+coZ6tRsDEDy\nlbxEKRXtypv854056Guutq7NVPwxdxvg9zPHuH7zKgCtGUdxEKl9SyH5i0meO3cOT09Pbty4QXJy\nMr6+vtJKxJYtW1i0aBEbN27krbfe4q+//sLS0hKAkJAQYmJiWLZsGT4+Pnh5eTF+/Hi96zx+/Jim\nTZvy8ccf07NnzyL9yI+3tzezZ89Go9GQkZGBg4MDMTExWFpacvXqVSld748//si2bdsKzaglUvsa\nF1EcyrgIfY2H0Na4mIO+o0ZOpK5da4P25NS9LFj0TQl49OyYg77mitDWuBQ3ta+YjJRCypQpg0Kh\nAPK2RH355Zd06tSJpKQkunbtysmTJ6VzVSoVfn5+nDt3jrVr10rtd+7coVGjRoSFheHl5YVSqdQr\nUtmuXTtcXFwYNGgQjo6Oetf39/fngw8+0PMDoFOnTnzxxRd4e3szZ84caSLx7bffkpCQwJQpUxgy\nZAgpKSlYW1tTtWpVlixZgr29vZQuePjw4dJ4YjIiEAgEgoKIjtrPj4tDUdX3ldriE7cRMLIfXt4t\nS9AzgaD0IiYjgv8cYjIiEAgEgsKIjtrPprAd5GSBRRno2dtHTEQEAiMiih4KBIIXisjHblyEvsZD\naGtczEVfL++WLFj0DQt/+IYFi74xm4mIuehrjghtTRMxGREIBAKBQCAQCAQlwr+ejFSoUAGA5ORk\n1q1b968delb8/f31KoXriI6OxtfX16D9xIkT7Nq166njhoSEMHr06BfiozEIDg5mzpw5Tz1P91zM\nlcKer+DlIYL8jIvQ13gIbY2L0Ne4CH2Nh9DWNPnXkxFdUPOlS5f0AqCNjUwm0wuofhrx8fH8/PPP\nzzSuKfOs/pn6fTwNc/dfIBAIBAKBQPB0Xtg2rUmTJhETE4NardarGQEwatQotm/fDkCPHj147733\nAFi+fLlUAfzbb79FoVCgUCik/klJSXrZmGbPns2MGTMkO38V70aNGqHRaAgPDzfw7fHjx3zyySeE\nhoaiVqvZsGEDR44coXnz5ri4uODh4UFCQoJBv507d9K8eXNu375NREQEzZs3R6PR0KdPHx48eGBw\n/tKlS3Fzc0OlUtGrVy8ePXpkcM7Nmzdp164dTk5OBAQEULduXe7cuVOoBgCff/45Dg4OeHp6cv78\n+YLk59KlSzRr1gylUilpCpCenk7btm3RaDQolUopTW5SUhINGzZkyJAhODg4MGDAACIiIvDw8KBB\ngwYcOXIEyFuJeffdd/H29qZevXosWLDA4NphYWF89NFHAMybN4969eoBcPHiRelbCK1Wi5eXF66u\nrnTs2JFr164BeUUYO3XqhKurKy1bttS7P92EZNq0aQwZMoScnJwC711gHMTeWuMi9DUeQlvjYi76\nRkftZ9TIibw/bCKjRk4kOmp/Sbv0TJiLvuaI0NY0eWFFD7/++mtmz54tTTry4+npSUxMDL6+vly5\ncoXr168DEBMTw9tvv41WqyUkJIS4uDhycnJwd3enVatWVKpUSW+cJ1dDZDIZGRkZDBs2jKioKOrV\nq0ffvn0NvlW3srJi5syZaLVa5s+fD8D9+/eJiYlBLpfz66+/MmXKFDZu3ChNcMLDw5k7dy67du0i\nMzOTzz//nMjISMqVK8fXX3/Nt99+y7Rp0/Su07NnTwICAoC8F+hly5YxatQovXNmzJhB27ZtCQoK\n4pdffmHZsmUAhWqQnZ1NaGgoJ06cIDMzExcXF1xdXQ00/uCDD3j//fcZOHAgixYtktrLlStHeHg4\ntra23Lp1i2bNmtG1a1cgbyKwadMmGjduTJMmTQgNDSU2NpZt27bxxRdfSBO7hIQEoqKiSEtLw8HB\ngcDAQORyuXSNli1bMmvWLOmZvvbaa6SkpBATE0OrVq3Iyspi9OjRbN++ncqVKxMaGsrHH3/MsmXL\nGDZsGN9//z3169fn8OHDBAYGEhkZCeRNNidMmMCDBw9YsWKFwT0LSgePHj7m8sU7Je3GS+fypTsk\nVLpW0m6USoS2xsUc9I07eojtW3bTpHF3qW3xvLX8lXwHN9emJejZ0zEHfc0Voa1p8sImI0VlCPb0\n9OS7777j7NmzODo6kpqayrVr1zh06BD/+9//+PHHH/Hz86NcuXIA+Pn5ERMTI700F3ad3Nxczp07\nh729vfRt/MCBA/nhhx8K7Je/b2pqKoMGDSIxMRGZTEZWVpZ0bO/evRw9epQ9e/ZQoUIFduzYwZkz\nZ2jevDmQt9Ki+z0/p06dYurUqdy7d4/09HQ6dOhgcE5sbCxbtmwBoEOHDtjZ2ZGbm8tvv/1WoAY5\nOTn4+flhbW2NtbU1Xbt2LVDrAwcOSJOHgQMHEhQUBEBOTg6TJ08mJiYGCwsLUlJSuHHjBgD29vZS\njRBHR0fatm0LgJOTE0lJSUDehK9Lly5YWlpSuXJlqlatyvXr16lRo4Z07WrVqpGenk56ejp//fUX\nb7/9Nvv37+e3336jZ8+enDt3jtOnT0vjZ2dnU6NGDR48eMCBAwfo3bu3NNbjx4+l5zVz5kzc3d2l\nGiOCl8vL2lubevsh29YefynXMi2suHL2v3jfLwOhrXExfX2j47bh5dZHr61J4+6Ert7AtQTrEvLq\nWTF9fc0Xoa0xad2rarH6vbDJSFHUqFGD1NRUdu/eTcuWLblz5w6hoaHY2tpiY2ODTCYzmGTIZDLK\nlCmjtzXn0aNHBqseT9qFTYqePG/atGm0adOG8PBwkpOT8fLyks6rV68ely5d4vz582g0GiCvyN/T\nYmL8/f3Ztm0bCoWClStXEh0dXeB5BflYkAZP+/1ZWLNmDbdu3eLYsWPI5XLs7e3JyMgAoGzZstJ5\nFhYWWFlZSb/nn5zp2gHkcrneMR3NmzdnxYoVODg40KJFC5YtW8bBgwf59ttvSUpKwtHRkQMHDuj1\nSUtLw87Ojvj4eIPxZDIZTZo0QavVcvfuXezs7Aq8v8DAQGrXrg1AxYoVUSgU0ku0bjlW2KZtN26o\n5q3G1Th3Ie8fiIZvqQCELWxhC7vY9i+x90i+coY6NRsDkHzlDADlbazF542whf2C7LzfT3DrTt5q\nU+teEykO/7rooa2tLffv30er1fLRRx8V+gI+ZMgQ9u7dS1RUFLdu3aJnz5706dOHOXPmEB8fj7+/\nP4cOHSInJ4emTZuyevVqGjduTI0aNTh//jw2Nja0atWKzp0788knnzBkyBB8fX3p0qULDRo0ICoq\nijfffJP+/fuTnp5usF1s8+bNbNu2jZCQECBv5WHgwIH4+fkRHBzMypUruXTpEiEhIWi1WkaNGoWf\nnx9hYWFUqVIFV1dX9u7dS7169Xjw4AEpKSm89dZbeteoUqUKZ86coVKlSnTu3JlatWoZbC8aNWoU\ntWvXZuLEiURERNCxY0du3bpFcnJygRrk5OTg7+/P4cOHyczMRKPRMGLECMaNG6c3brdu3ejTpw8D\nBgxg8eLFTJw4kfv37zN//nwSExOZP38+UVFRtGnThqSkJHJycvD19eXUqVPS8/Hx8aFnz54kJSVJ\nx4KDg7G1tZViQhQKBTt37pQmADpWrlzJtGnTCA4Oxt/fH0dHR2xsbDh69CiPHz/G0dGRVatW0bRp\nUzIzM7lw4QKNGzfGw8ODsWPH0qtXL3Jzczl16hRKpVLyJzc3l2+//ZaIiAiDDGGi6KFx+e2330Tm\nESMi9DUeQlvjYg76jho5kbp2rQ3ak1P3smDRNyXg0bNjDvqaK0Jb41JiRQ91Kw7Ozs7I5XJUKpVB\nADvkbdXKzs7mzTffRK1Wc/fuXTw9PQFQq9X4+/vj5uZG06ZNCQgIwNnZGUtLSz755BPc3Nxo3749\njRs3Nhi3bNmy/PDDD3Tp0gWNRkO1atUKzMTk7e3NmTNnpAD2iRMnMnnyZFxcXMjOzpb66OJSHBwc\nWLNmDb179yY9PZ2QkBD69++Ps7MzzZs3LzCQXLetqEWLFjRq1KhAP6ZPn05ERAQKhYKNGzdSvXp1\nbG1tC9VArVbTt29fnJ2d6dy5M25ubgU+h3nz5rFw4UKUSiUpKSnStQcMGMDRo0dRKpWsWrWKRo0a\nGTy7guwn9XgaLVq04MqVK7Rs2RILCwtq164t/Q9vZWXFxo0bCQoKQqVSoVarOXjwIJC3crNs2TJU\nKhVOTk5SgL3u2r169SIgIICuXbvy999/P9UPgUAgEAh69fHheKL+l5Lxidvo2dunhDwSCASF8a9X\nRgTPx+PHj5HL5cjlcg4ePMj777/PsWPHStots0SsjAgEAoGgMKKj9rMpbAc5WWBRBnr29jGbKuwC\ngTlS3JWRlxIzIviHP//8kz59+pCTk4OVlRVLly4taZcEAoFAICh1eHm3FJMPgcAMeGF1RgTPRv36\n9Tl27BjHjx8nLi5OCpAXCEwNkY/duAh9jYfQ1rgIfY2L0Nd4CG1NEzEZEQgEAoFAIBAIBCXCC52M\nWFhY8M4770h2VlYWVapUwdfXt1jjBQcHM2fOnH/l01dffVVoSl5ddirIS1mrVqtRqVRoNBopwDol\nJUWqg3HixAl27dpVbF+6dOlCWlpasfsLBC8TkXHEuAh9jYfQ1rgIfY2L0Nd4CG1NkxcaM2JjY8Pp\n06fJyMjA2tqaPXv2UKtWrWfKxlQQxe2Xn4iICMLCwvTasrOzkcvleineypcvL9W7iIiIYPLkyURH\nR1OjRg2pf3x8PFqtlk6dOhXLl507d/6LOxEIBAKBQPCsREftZ+OGHeRmg0yel2FLxJAIBKbHCw9g\n79y5Mzt37qRnz56sW7eO/v37ExMTA0BcXBwffvghGRkZlCtXjhUrVtCgQQNatWrF/PnzcXZ2BvJm\nrosWLQLyViOaN2/OrVu3mDhxIkOHDgVg1qxZhIWF8ffff9OjRw+Cg4MNfElLS+Px48dUrlwZf39/\nrK2tOX78OC1atGD27Nns3r27wInFvXv3ePXVVwGkmhvHjh3jk08+ISMjg99++40pU6bQqVMnRo8e\njVarRSaTERwcTI8ePVi3bh1ffvklubm5dOnSha+++gqAunXrcuzYMdLS0ujUqROenp4cOHCAmjVr\nsnXrVqyt9avCXr9+nREjRnDp0iUAlixZQtOmTenRoweXL18mIyODDz74gICAAAAqVKjAhx9+yI4d\nOyhXrhxbt26lalX9aphP1g1xcnLi559/pnLlyvTp04crV66QnZ3NtGnT6NOnj1Q/Jj09nddee42Q\nkBCqV6+uN2ZYWBiffvopcrmcihUrsm/fPjIyMhg5ciRarZYyZcrw7bff4uXlRUhICFu2bOHhw4dc\nuHCBjz76iIyMDNauXUvZsmX5+eefsbOz448//mDUqFHcvHmT8uXLs3TpUhwcHJ7xr1DwInhZ+dgz\nM7NJu/vI6NcxNQ4fPoi7e7OSdqNUIrQ1Luagb2zsAdatDkfj0E1q+/5/60hLzcDDo3kJevZ0zEFf\nc0Voa5q88MlI3759+fTTT/Hx8eHUqVO899570mSkUaNGxMTEIJfL+fXXX5kyZQobN27kvffeIyQk\nhLlz55KQkMDff/+NUqlk8+bNnDx5ksOHD5Oeno5araZLly6cOnWKxMRE4uLiyMnJoVu3bsTExEh1\nS3T8+uuvtG3bVrJTUlI4ePCgtOISHR3NjBkzgLzq7mq1moyMDK5evcrevXv1xrK0tGTmzJlotVrm\nz58PQFBQEHZ2dpw8eRKA1NRUUlJSmDRpEseOHaNSpUq0b9+erVu30q1bN72VnsTEREJDQ/nhhx/o\n27cvmzZtYsCAAXrXHDNmDN7e3oSHh5OTk0N6ejoAy5cvx87OjkePHuHm5kavXr2ws7Pj4cOHNGvW\njM8++4ygoCCWLl3Kxx9/rDdmQbVFcnNz2b17NzVr1pRWb9LS0sjMzGT06NFs376dypUrExoayscf\nf8yyZcv0xpg5cyYRERG8/vrr0ja0hQsXIpfLOXnyJOfPn6d9+/YkJCQAcPr0aY4fP86jR4+oV68e\ns2bN4tixY4wbN46ffvqJDz74gGHDhvH9999Tv359Dh8+TGBgIJGRkYX81QnMmVvX7rNm8aGSduOl\nk3zlDGcOZpe0G6USoa1xMQd9o+M24OXWR69dAhOvAAAgAElEQVRN49CNpQvXk3Akp4S8ejbMQV9z\nRWhrXFr3qvr0kwrghU9GFAoFSUlJrFu3ji5duugdS01NZdCgQSQmJiKTycjMzASgV69ezJw5k1mz\nZrF8+XKGDBkC5L0od+/enbJly1K2bFm8vb2Ji4sjJiaGiIgI1Go1AA8ePCAxMdFgMvLLL7/w7rvv\nSmP17t1behm/cuUKr776qrQaUa5cOWmb1qFDhxg0aBC///673ni5ubnkL8sSGRlJaGioZFeqVIl9\n+/bh7e1N5cqVgbyig/v376dbt256Y9nb26NUKgHQaDQkJSUZaBkVFcXq1auBvHicV155BcgrcLhl\nyxYALl++zIULF3Bzc8PKykrSXKPRsGfPHoMxC0Imk6FUKhk/fjyTJk3Cx8eHFi1a8Pvvv3P69Glp\nQpednU2NGjUM+nt4eDB48GD69OmDn58fALGxsYwZMwYABwcH6tSpQ0JCAjKZDG9vb2xsbLCxsaFS\npUpSTJFCoeDkyZM8ePCAAwcOSLE6kFefpSACAwOlavAVK1ZEoVBI3+brsmYIu3i2rs3Y12tQT8mr\nVWxITDoFQP26CoBSb995YM2dBxdNxp/SZL9apYlJ+VPabHPQ98GjuyRfOUOdmnnFkpOvnAHA0srS\n5D9vzEFfc7XVqiYm5Y+52wB/JP/OndTrALTupf8F+LNilDojXbt2Zfz48ezbt4+bN29K7dOmTaNN\nmzaEh4eTnJyMl5cXkBev0a5dO7Zs2UJYWFiRRQB1k4nJkyczbNiwIv2Ii4tjyZIlkl2+fHnp9927\nd9OxY8cC+zVt2pRbt25x69atp97rkzUjdSsN+Y8XFPtStmxZ6Xe5XM6jRwVvU3ly/OjoaCIjIzl0\n6BDW1tZ4e3uTkZEB5K3e6LCwsCArK8tgvDJlypCT88+3Qrq+b731FvHx8ezcuZOpU6fSpk0bevTo\ngaOjIwcOHCj0/gEWL15MXFwcO3fuRKPRoNVqC/S9oHu3sLCQbJ3POTk52NnZSZPDotBt5yuIJ7cY\nCdt07XfHegL6XyYIW9jCFnZx7WMJ26lj11iydZMSbK6JzxthC/uF23kUt4i3UVL7vvvuuwQHB+Po\n6KjXnpaWJn2zvmLFCr1jQ4cOZcyYMbi5uVGxYkUg72V269at/P3339y+fZvo6Gjc3Nzo0KEDy5cv\n58GDB0DeKkf+SQ/kbQVq2LBhoUHwv/zyS6GB6OfOnSM7O1ta3dDxyiuvcP/+fclu164dCxculOzU\n1FTc3NzYt28ft2/fJjs7m/Xr19OqVatCtSqKNm3asHjxYiBvVSItLY20tDTs7Oywtrbm3LlzHDr0\nfNtbdHErkPdHo4tHuXr1KtbW1gwYMIDx48cTHx+Pg4MDN2/elK6RmZnJmTNnDMb8448/cHNzY8aM\nGVSpUoXLly/j6enJmjVrAEhISODPP/+kYcOGhU5Q4J/Ji62tLfb29mzcuFFq122FE7w8RD524yL0\nNR5CW+NiDvr26uPD8cTtem3xidvo2dunhDx6dsxBX3NFaGuavNDJiO7Fv2bNmowaNUpq07VPnDiR\nyZMn4+LiQnZ2tt5EwcXFhYoVK0pbtHR9lUol3t7eNGvWjE8++YTq1avTrl073n77bZo1a4ZSqaRP\nnz5SPIWOXbt2GUw2dNfLzs4mMTGRBg0aSMd0MSNqtZp+/frx008/Sefr/uvt7c2ZM2dQq9WEhYUx\ndepU7t69i0KhQKVSER0dTfXq1fnqq6/w9vZGpVLh6uoqbUPKf78FxW48ybx584iKikKpVOLq6srZ\ns2fp2LEjWVlZNG7cmMmTJ9OsWbMCx8ive3569uzJnTt3cHJyYuHChVJQ+KlTp3B3d0etVvPpp58y\ndepULC0t2bhxI0FBQahUKtRqtZTyOD8TJ05EqVSiUCjw8PDA2dmZwMBAcnJyUCqV9OvXj5UrV2Jp\naWngV2E+r1mzhmXLlqFSqXBycmLbtm0G1xUIBAKBoCC8vFsydGRfklP3cunWXpJT9xIwsp/IpiUQ\nmCCy3KK+qn6JpKSk4O3tzfnz51/IeO3bt2fVqlVUq1bN4FhsbCxr1qwpcouPwPSJjIzExcWlpN0Q\nCAQCgUAg+M9z7Ngx2rRp89z9jBIz8rz89NNPTJ06lblz576wMSMiIgo95uHhgYeHxwu7lkAgEAgE\nAoFAIHh+jBIz8rwMGjSIP//8k549e5a0KwKB4P8Re2uNi9DXeAhtjYvQ17gIfY2H0NY0MYnJiDG5\ndu0a/fr1o379+ri6utKlSxcuXLhAdHS0FMvxb3hR4zzJypUruXr16nP1CQ4OZs6cOc99raSkJBQK\nhUG7Vqvlgw8+eK6xEhIS6Ny5Mw0aNECj0dC3b19u3LhBSEgIo0ePfm7fBAKBQCAQCASlF5PYpmUs\ncnNz6dGjB0OGDGH9+vUAnDx5kuvXrxeaZctUCAkJwcnJiddff/2Z+7zoe9JoNGg0mmc+PyMjAx8f\nH+bOnSvVO9GldzZ1vQWGvIzq6/9lhL7GQ2hrXMxF3+io/WzcsIPcbJDJ8zJsmUMAu7noa44IbU2T\nUr0yEhUVhZWVlV49EqVSKf0xpqen07t3bxo1asTAgQOlc7RaLV5eXri6utKxY0euXbsG5FVNb9u2\nLSqVCo1Gw8WLF/Wud+TIEVxcXLh48SLBwcEMHjyYli1bUrduXTZv3sz48eNRKpV06tRJqgEyc+ZM\n3NzcUCgUDB8+HICNGzdy9OhRBgwYgIuLCxkZGYX6VBhLly7Fzc0NlUpFr169pDom169fp0ePHqhU\nKlQqlUFq4IsXL+Li4oJWq9Vb9Xnw4AHvvvsu7u7uuLi4FJjdau3atTRv3lyv2GWrVq2kFM8pKSl0\n6tSJBg0aEBQUJJ0TGBhIkyZNcHJyIjg4WGqvW7cuwcHBaDQalErlC0tuIBAIBILSTXTUfn5cHEpd\nu9bYv9aaunat+XFxKNFR+0vaNYFA8ASlemXk999/L/Sb/dzcXOLj4zlz5gyvv/46Hh4exMbG4ubm\nxujRo9m+fTuVK1cmNDSUjz/+mGXLljFgwACmTJlCt27dePz4MdnZ2fz5558AHDhwgDFjxrBt2zZq\n1aoFwKVLl4iKiuL06dM0bdqU8PBwZs+ejZ+fHzt37qRbt26MGjWKadOmAXmxMzt27KBXr14sXLiQ\nOXPm4OLiQmZmZqE+FUbPnj0JCAgA8opNLlu2jFGjRjFmzBi8vb0JDw8nJyeH9PR07ty5A8D58+fp\n378/K1euRKFQEB0dLY33+eef06ZNG5YvX05qairu7u60bdtWr5Dk6dOni9T7+PHjHD9+HCsrKxwc\nHBgzZgw1a9bk888/x87OjuzsbNq2bcvvv/+Ok5MTMpmMKlWqoNVqWbx4MbNnz2bp0qXP+PQF/5b8\n1deNydXLqaxZ/Hz1ckoD+atDC14sQlvjYg76RsdtwMutj16bqr4vcz4P4eiehyXj1DNiDvqaK0Jb\n49K6V9Vi9SvVk5GnbQ1yc3OTijCqVCqSkpKoWLEip0+fpm3btkBeTZIaNWqQnp5OSkoK3bp1A8DK\nykoa5+zZswwfPpw9e/ZQvXp16dqdOnVCLpfj5ORETk4OHTp0AEChUJCUlATA3r17mTVrFg8fPpTq\nf/j45BVl0mVdPn/+fIE+FcWpU6eYOnUq9+7dIz09Xao2HxUVxerVq4G8iuevvPIKd+7c4caNG3Tv\n3p3w8HAaNmxoMF5ERATbt29n9uzZAPz9999cvnxZqlOio7BM0TKZjDZt2mBrawtA48aNSU5OpmbN\nmoSGhrJ06VKysrK4evUqZ86cwcnJCQA/Pz8grw7N5s2bDcYNDAykdu3aAFSsWBGFQiG9QOsC1YRd\nPPvUqVMv5Xr16uQ96+QreQU1df9QlHb7+q0kk/JH2MIuTXZa+m29F0/dcZnMwiT8E3bJ2DpMxR9z\ntwGSU85w735e4fHWvaZTHEymzogx2Lt3LzNmzGDfvn0Gx6Kjo5kzZw7bt+dVaB09ejSurq5oNBqG\nDRvGgQMH9M6/f/8+jRs35vLly3rt+/btY+rUqfz9998EBwfTuXNnAGbMmEGFChX46KOPgLyq4rrq\n7TNmzMDW1pb333+fOnXqoNVqqVmzJjNmzEAmk/HJJ5/g7e0trYycOnWK4cOHG/j0JLpxx40bh729\nPdu2bUOhULBy5Ur27dvH8uXLqVq1Kn/99ZfeZCopKYkOHTpgb2+vt6KSXyNXV1fWrVvHW2+9Vej1\nly9fzr59+1i5cqXBsZUrV3L06FEWLFgAgK+vLxMmTOCNN96gffv2HD16VCp66e3tzaBBg7C3t0er\n1fLqq69y9OhRJkyYQFRUlDSmqDMiEAgEgoIYNXIide1aG7Qnp+5lwaJvSsAjgaD0U9w6I6U6ZqR1\n69b8/fffelt7Tp48yW+//VbgqolMJsPBwYGbN29KsRSZmZmcOXMGW1tbatWqxdatW4G8lYFHjx6R\nm5tLpUqV2LFjB5MnTy5w4lMQubm5ZGRkAFC5cmXS09MJCwuTjtva2pKWlgZQqE9FkZ6eTvXq1cnM\nzJRWQgDatGnD4sWLgbwVFt01rKys2Lx5Mz/99BPr1q0zGK9Dhw7Mnz9fsuPj4w3Oefvttzlw4AA/\n//yz1LZ//35Onz5dqAb379/HxsaGV155hevXr7Nr164i70sgEAgEgqfRq48PxxO367XFJ26jZ2+f\nEvJIIBAURqmejACEh4fz66+/Ur9+fZycnPj444+lDFUFTUgsLS3ZuHEjQUFBqFQq1Go1Bw8eBGDV\nqlXMnz8fZ2dnWrRowbVr15DJZMhkMqpWrcqOHTt4//33iYuLMxj/yWvJZDIqVqxIQEAATk5OdOzY\nEXd3d+m4v78/I0aMwMXFhZycnEJ9yk9WVhZly5YF8gLj3d3dadGiBY0aNZLOmTdvHlFRUSiVSlxd\nXTl79qzkT/ny5dmxYwdz585lx44d0r1BXtxJZmYmSqUSJycnpk83XIqztrZmx44dLFiwgAYNGuDo\n6MiSJUuoUqVKoRoolUrUajUNGzZkwIABhcYo5PdF8HIQ+diNi9DXeAhtjYs56Ovl3ZKhI/uSnLqX\nS7f2kpy6l4CR/cwim5Y56GuuCG1Nk1K9Teu/hp+fH8OGDZPiQ0o7YpuWcXlZAez/VYS+xkNoa1yE\nvsZF6Gs8hLbGpbjbtMRkpJSgVCpxcHAgNDQUC4tSv+AFiMmIQCAQCAQCgalQ3MlIqc6m9V/i5MmT\nJe2CQCAQCAQCgUDwXJjMV+gVKlQA8jI7eXt7l7A3z0dycrJe0HdISAijR48u8NwuXbpIQePFZfv2\n7Xz99deFHr93754UpG4MvLy80Gq1z9Wnf//+ODs7M2/ePCN5JXjRiL21xkXoazyEtsZF6GtchL7G\nQ2hrmpjMyog5BydfunSJtWvX0r9/f6Doe9m5c+e/vp6vr69UGb0g7t69y6JFixg5cuRzjZuTk/NM\nW7ye91ldu3aNo0ePcuHChWfuk52djVwuf67r/F97dx9Q8/3/f/x+lMbSKlf7TDO1WHRxTqdU1Irk\nIpSraK6J8ZlcNJdrzGSbbchcjhlTGCPXi20YpVyToq+wmJLrSEWxSuf3R7/eH0fFmTl1Tnvd/vJ+\nn/f7fZ7ncc7OzqvX+/V6CYIgCEKp2Jg4NkftRPUYZAYlM2zpwwB2Qfi30ZmekVIGBgbUq1cPgFat\nWqlNYdu2bVtOnTpFXl4ew4YNw83NDScnJ37++ecy17lx4wZeXl4olUocHByk1vCePXtwd3fH2dmZ\nwMBA8vLyAEhISKBt27a0bNkSX19fbt68KT1naGgobm5u2NjYlNuqDg0NJT4+HqVSyYIFCwC4fv06\nnTt35p133uGjjz6SjrW0tCQrK4u8vDy6du2Ko6MjDg4OREVFlblu27Zt+fDDD6XXcOLECUC95+XW\nrVv07NkTR0dHHB0dOXLkCKGhoVy6dAmlUsmUKVM4cOCAWuNlzJgx0loglpaWhIaG4uzszKZNmyrM\n52lr164tU1dF70vHjh25du0aSqWSgwcPkpSURKtWrVAoFPTq1Yvs7Gzp9Y4fPx4XFxcWLVpU4Xsi\nVA4xyE+7RL7aI7LVLn3INzYmjpXLNmJp3g6r+u2wNG/HymUbiY2Jq+rSnksf8tVXIlvdpDM9I6Ua\nN27M5s2bAejbty9RUVGEhYVx48YNbt68iZOTE1OnTsXHx4dVq1aRnZ2Nm5sb7du359VXX5Wu89NP\nP+Hr68vUqVMpLi4mPz+fO3fuMGvWLPbt20ft2rWZPXs233zzDR9//DFjx44lOjqaevXqsXHjRqZN\nm8YPP/yATCbj8ePHHDt2jF9//ZWZM2eyd+9etZpnz55NeHi4tIBiZGQkSUlJJCUlYWRkhI2NDePG\njcPCwkLqVfjtt9+wsLCQekrKu3VLJpPx8OFDEhMTiY+PZ9iwYdKq2KXGjRuHt7c327Zto7i4mAcP\nHjB79mzOnj0rrQUSGxtb5rqldchkMurXr09CQgJ37twhICCgTD7Tp08vU1t5dc2aNavM+9KhQwei\no6Px8/OT6pHL5Xz77bd4enoyY8YMZs6cyfz585HJZBQWFnLixAmKiorw8vIq9z0RqpfbN3LZueF0\nVZchCEI1Er13LR6OAWr7HJv6s2juWv5M0t87MQRBlzm2MX6h83SuMfKkwMBAOnbsSFhYGFFRUfTp\n0wco6d2Ijo4mPDwcKFmAMCMjAxsbG+lcFxcXhg0bRmFhIT169EChUBAbG0tKSgru7u4AFBQU4O7u\nzoULFzh79izt27cHSm4RatSokXStXr16AeDk5ERaWlqZOp+ekEwmk+Hj44OJiQkAtra2pKenY2Fh\nIR0jl8uZNGkSoaGh+Pn5VdhaL731y9PTk9zcXHJyctQej4mJkRY1rFGjBq+99hpZWVnPirWM9957\nD4CjR4+Wm4+mdZX3vly5ckVa+wRKxrPk5OTg6ekJwJAhQ6T39clazp8//8z3pFRwcDBvvfUWAKam\npjg4OEhZlvZiie0X2162bFml5GndxJ6szDzSr5X0gjaxsAWo9tvHT//C6/Utdaae6rRd+m9dqae6\nbetDvnezbpN+LaXM40WFKp3/vtGHfPV1u3SfrtSj79sA6ddTyLmfCYBjm7Jr0GlCpxsjjRo1ol69\neiQnJxMVFcXy5culx7Zu3UqzZs0qPNfT05P4+Hh27tzJ0KFDmTBhAubm5nTo0IH169erHZucnIyd\nnR2HDx8u91qlP6YNDAwoKirSqPYnf4CXd16zZs1ITExk165dfPLJJ/j4+JTbA/G08sZ0PG92ZkND\nQ4qLi6Xthw8fqj1ubPy/lmx5+WiitKelvPelvAZcqadrL61FpVI98z0ptXTp0gofe7qBJ7b/3vaT\nDRFtPl9h4WOCPnwXeLpBXr23bY8Z4ObWWmfqqU7bx8pkq1v16fu2PuSbemsPTV63lbZLf0QVGl7T\n+e8bfchXX7ePHTvy/7PVjXqqz3aJ9Kt/lLv/eXS6MQIlfymfPXs2ubm52NvbA9CpUycWLVrE4sWL\nAUhMTESpVKqdd+XKFSwsLHj//ff566+/SExMZOrUqYwePZpLly5hbW1NXl4e169fp3nz5mRmZnL0\n6FFatWpFYWEhqamp2NralqmnPK+99hr379+XtjVZuuXGjRuYm5szYMAATE1NK7z9aOPGjbRt25aD\nBw9iZmYm9baU8vHxYdmyZYSEhPD48WPy8vIwMTFRq6dJkyakpKRQUFBAfn4++/fvx8ur7CA+Nze3\ncvN5unGhUqnK1PXaa69p9L6Ymppibm4uLTy0du1a2rZtWyY7Gxubf/SeCP9cZd1bW7OmAfUa1qmU\n59IlXfw7VHUJ1ZbIVrv0Id9+A3uwctlGHJv+b7xk4sWfGTGqr85/3+hDvvpKZKtd6Vdf7DydaYxU\nNENT7969CQkJ4dNPP5X2TZ8+nQ8//BC5XE5xcTFvv/12mUHssbGxzJ07l5o1a2JiYsKaNWuoX78+\nkZGR9OvXj7/++guAWbNm0axZMzZv3sy4cePIycmhqKiI8ePHl/vDt7w65XI5BgYGODo6MnToUMzN\nzSt8PaX7k5OTmTx5MjVq1MDIyKjCqXhr1aqFk5MTRUVFrFq1SrpG6XUWLlzIyJEj+eGHHzAwMOC7\n777Dzc0NDw8PHBwc6NKlC7NnzyYwMBB7e3usrKwqXCiwQYMGFebz9Gsor65nvS9P5rF69Wo++OAD\n8vPzsba2JiIiokw+RkZGGr8ngiAIgvCk0lmztmzaSXER1DCEEaP6itm0BEEHiRXYdZi3tzfz5s0T\nq4xXQKzArl2lvVeCdoh8tUdkq10iX+0S+WqPyFa7XnQFdp2b2lcQBEEQBEEQhH8H0TMi6C3RMyII\ngiAIgqAbdLpn5O7duyiVSpRKJW+88QZvvvkmSqUSc3Nz7OzsXuiaERER0jWNjIyQy+UolUqmTp36\nkqvXHXXq6N6gu9JFHOHv1RcbG1vhKvIjRozg/PnzAHz55Zf/vEhBEARBEARBJ1VKY6RevXokJiaS\nmJjIBx98wIQJE0hMTCQpKancqWo1ERQUJF3TwsKC2NhYEhMTq/WP14oGxb8MKpVKo1nAnvZkTS+r\nvhUrVtC8eXMAvvrqq5dyTeHvK10HRNAOka/2iGy1S1/yjY2JY8yoKYweOYUxo6boxerroD/56iOR\nrW6qkjEjpT96VSoVjx8/ZuTIkdjb29OpUycePXoEwKVLl+jcuTMtW7bEy8uLCxcuaHTtuXPn4urq\nikKhICwsDIBt27ZJi+fduHEDGxsbbt++TVpaGl5eXjg7O+Ps7MyRI0ekY7y8vFAqlTg4OJT74Q0N\nDcXOzg6FQsGUKVMAGDp0KCEhIXh4eGBtbc2WLVuk1zl58mQcHByQy+VERUUBMHr0aGnV9p49ezJ8\n+HAAVq1axSeffFLu6/vkk09wdHSkdevW3L59G4Do6GhatWqFk5MTHTp0kPYfOHBA6j1ycnLiwYMH\natdKS0vDxsaGIUOG4ODgQEZGRrn5ldbXsmVL7O3tWbFixTPfg8GDB7Njxw5pe8CAAWVmO5PJZDx4\n8IA+ffrQokULBg4cKD3Wtm1bEhISCA0N5eHDhyiVSgYNGvTM5xQEQRCEUrExcaxcthFL83ZY1W+H\npXk7Vi7bqDcNEkH4N6nyqX1TU1PZsGED33//Pe+99x5btmxhwIABjBw5kuXLl9O0aVOOHTtGcHAw\n+/bte+a19uzZw8WLFzl+/DjFxcV0796d+Ph4evbsydatW1myZAm7d+/ms88+o2HDhjx8+JC9e/fy\nyiuvkJqaSv/+/Tlx4gTr16/H19eXqVOnolKpyMvLU3ueu3fvsn37dulWotzcXKDkB/bNmzc5dOgQ\n586do1u3bgQEBLB161ZOnz7NmTNnyMzMxMXFBS8vL7y8vIiPj8ff359r165x69YtAOLj4+nfv3+Z\n15eXl0fr1q354osv+Oijj1ixYgXTpk3D09OTo0ePArBy5UrmzJlDeHg48+bNY+nSpbRu3Zr8/Hy1\nhRhLXbx4kbVr1+Lq6lphfp6enqxatQpzc3MePnyIq6srvXv3xtzcvNz34f3332f+/Pl0796dnJwc\njhw5wtq1a9WOUalUJCYmkpKSwhtvvIGHhweHDx/G3d1dmrr466+/5ttvvyUxMfGZ77ugHZU140jW\nnTzif3uxhZL0mzE70sRnWztEttql+/mu37QeF7seavscm/qzbOFP5FwzqeAsXaH7+eovka02NX7B\n1ReqvDFiZWWFXC4HwNnZmbS0NPLy8jh8+DB9+vSRjisoKHjmdVQqFXv27GHPnj3SQnt5eXlcvHgR\nT09PFi9ejJ2dHe7u7rz33nvSNceMGcPp06cxMDAgNTUVAFdXV4YNG0ZhYSE9evRAoVCoPZeZmRm1\natVi+PDh+Pn54efnJz3Wo0fJl1+LFi2kxsXBgwfp378/MpmMhg0b0qZNG06cOIGnpycLFizg3Llz\n2NnZkZ2dzc2bNzl69ChLliwp8xqNjIzo2rWrlNXevXsByMjIIDAwkJs3b1JQUMDbb78NgIeHB+PH\nj2fAgAH06tULCwuLMtds0qQJrq6uAM/Mb+HChWzfvl16vtTUVOm8p3l5eREcHMydO3fYvHkzvXv3\nLvd2PFdXVxo1agSAo6MjaWlpuLu7l3vNigQHB/PWW28BJQsqPrlqeGmPltjW7W3rJvakptwi/VoK\n8L+VksW22BbbYvtFt2/cukG6WUqZxx/mFYrvG7Ettl/SNkD69RRy7mcCMH/pDF5Epc+mNXPmTOrU\nqcPEiRNJS0vD39+f5ORkAObNm0deXh7jx4/HxsaG69eva3RNKysrTp48yVdffcU777zDyJEjyxyT\nnJxM165dsbS05MCBA8hkMsLCwsjPz2fOnDk8fvyYWrVqUVhYCMDNmzfZuXMn3377LRMmTChzm1BB\nQQH79u1j8+bNpKWlsW/fPoKCgvDz8yMgIABAWgl9woQJODg4EBQUBMCgQYN477338PPzo0WLFowc\nORIzMzOysrIwNDTkxx9/5MSJE2Vew5Mrq2/evJldu3YRERFB27ZtmTRpEn5+fhw4cICwsDBiYmIA\nOHv2LLt27WLp0qXs3r0bGxsb6XpP5z9p0qRy84uNjWX69Ons3buXWrVq4e3tzcyZM/Hy8sLKyoqE\nhATq1q2rVt+cOXOoWbMmGzduJDIyUhoD8uQ1582bJ92mNnbsWFxcXBg8eLDa+ipPryb/JDGblnZV\n1nzsD/MLyPgzS+vPo2sSEo/jrCy/QS/8MyJb7dKHfL/++its3+pcZv+5jN/46KPQKqhIc/qQr74S\n2WrXg4LrLzSbVpX3jDxNpVJhYmKClZWV9Fd1lUpFcnKy1INSHplMRqdOnZg+fToDBgzA2NiYa9eu\nYWRkhLm5OcOHD2fDhg1ERkbyzTffMHHiRHJzc3nzzTcBWLNmDY8fPwbgypUrWFhY8P777/PXX3+R\nmJio1hjJy8sjLy+Pzp074+7ujrW19RHt4fMAACAASURBVDNfk6enJ8uXL2fIkCHcvXuX+Ph45s2b\nB0CrVq1YsGABMTEx3Llzh4CAAAIDA/9WZrm5uVIPQ2RkpLT/0qVL2NnZYWdnx4kTJ7hw4YJaY+Rp\nFeWXm5uLubk5tWrV4vz589ItYc8ydOhQXFxcaNSoUZmGyN9Rs2ZNioqKMDTUuY+q8JLUftWId+z/\nU9VlVLrb2XX/la+7MohstUsf8h08PICVyzbi2PR/szYmXvyZEaP66nzt+pCvvhLZatepU5p1Ijyt\nSn7hPWsGptLtdevWMWrUKL744gsKCwvp169fhY2R0nM6dOjAuXPnaN26NVDSk7B27Vq+++47vLy8\ncHd3Ry6X4+Ligp+fH8HBwQQEBLBmzRp8fX2lqWljYmIIDw+nZs2amJiYsGbNGrXnu3//Pt27d+fR\no0eoVCrmz5//zNfWs2dPjhw5gkKhQCaTMXfuXBo2bAiUNFT27t3L22+/TePGjbl37x6enp4a5Va6\nHRYWRp8+fTA3N6ddu3akp6cDsHDhQmJiYqhRowb29vZ07lz2r0RPXrO8/H788Ud8fX357rvvsLW1\nxcbGRnr8Wddq2LAhtra29OzZs8JjNZl9a+TIkcjlcpydncuMOxG0S6xSq10iX+0R2WqXPuTb1tsL\ngC2bdlJcBDUMYcSovtJ+XaYP+eorka1uEoseClqRn5+PXC4nMTERExPtDBYUt2kJgiAIgiDoBp1e\n9FD4d/n999+xtbVl3LhxWmuICNon5mPXLpGv9ohstUvkq10iX+0R2eomcSO+8NK1b9+etLS0qi5D\nEARBEARB0HFa7xkpHYeRlpaGt7e3tp9Ocv36dbWpgf+JAwcOSAsivuxzwsLCpMHsVSE6OprZs2c/\ns5a0tDQcHBwquzShiol7a7VL5Ks9IlvtEvlql8hXe0S2uknrPSOaDFLWhkaNGrFp06aXcq2YmBhM\nTEwqHLj9T86pqnxK+fv74+/vrxO1CIIgCMLLEhsTx+aonageg8wAegf66cUAdkH4t6m0MSMGBgbU\nq1cPKJl+tkePHnTs2BErKyuWLFlCeHg4Tk5OtG7dmnv37pU5/9KlS7Rq1Qq5XM4nn3wijUVQqVRM\nnjwZBwcH5HI5UVFRgPpf8yMjI+nVqxedO3fmnXfe4aOPPpKu+8MPP2BjY4ObmxsjRoxg7Nixas+b\nlpbG8uXLmT9/PkqlkkOHDpGWlka7du1QKBS0b9+ejIyMZ55z8OBBdu7cSatWrXBycqJDhw7cvn1b\nOr60EbBixQq6dOnCo0eP+PHHH3Fzc0OpVPLBBx9QXFxcJpPPP/8cV1dXHBwc+O9//1vm8cePH0sL\nIGZnZ2NgYCDdL+nl5cXFixeJjIws85oBEhISUCgUODo6snTp0jKPl2YfHBxMixYt6NixI127dmXL\nli0AWFpakpVVsnbEyZMnpV6xvLw8hg0bhpubG05OTvz8889AyXoopa9XoVBw6dIl8vLy6Nq1K46O\njjg4OEjvrVA5xL212iXy1R6RrXbpQ76xMXGsXLYRS/N2WNVvh6V5O1Yu20hsTFxVl/Zc+pCvvhLZ\n6qZKGzPSuHFjNm/eLG2fPXuWpKQkHj58iLW1NXPnzuXUqVNMmDCBNWvWEBISonZ+SEgI48eP5733\n3mP58uXS/q1bt3L69GnOnDlDZmYmLi4utGnTpszznz59mqSkJIyMjLCxsWHcuHHIZDK++OILEhMT\nqVOnDu3atcPR0VHtPEtLSz744ANMTEyYMGECUNKbEBQUxKBBg4iIiGDcuHFs27btmedkZ2dL63Os\nXLmSOXPmEB4eDpT8qF+yZAn79u1jx44dXLx4kaioKA4fPoyBgQHBwcGsW7euzMKLY8aMYfr06QAM\nHjyYnTt3qq0Gb2BggI2NDSkpKfz55584OzsTFxeHi4sLV69epWnTpmX+wyxtGAUFBbF06VLeffdd\npkyZUu57umXLFtLT0zl37hy3bt2iRYsWDB8+XO06T5s1axY+Pj6sWrWK7Oxs3NzcaN++PcuXLyck\nJIT+/ftTVFREUVERu3btwsLCgl27dgEl66kI1U9u9kNOH894/oHVTPLZDFT5f1R1GdWSyFa79CHf\nFSs2omzmr7bPsak/K5dFYVCo2+tM6EO++kpkq13G9V/svCpbZ8Tb2xtjY2OMjY0xMzOTbhVycHDg\nzJkzZc45evSo9Ff0fv36MWnSJKCkldu/f39kMhkNGzakTZs2HD9+vMwYBx8fH6k3xdbWlrS0NDIz\nM2nTpg1mZmYA9OnThz/+KP9D+uQMyEePHmX79u0ADBw4sMIf60+ek5GRQWBgIDdv3qSgoEDqsVCp\nVKxZs4bGjRuzY8cODAwM2LdvHwkJCbRs2RKAhw8f8p//lP3y3L9/P3PnziU/P5+srCzs7OzUGiNQ\nso5JXFwcly9f5uOPP2bFihW0adMGFxeXcmsGyMnJIScnR7q3ctCgQfz6669ljjt06JC0QOPrr7+u\n0ZigPXv2EB0dLTXE/vrrL65cuULr1q2ZNWsWV69epVevXjRt2hS5XM6kSZMIDQ3Fz8+v3Hs9g4OD\neeuttwAwNTXFwcFBOq60oSW2X2y7dJ+2n8+6iT3HYv8k/VoKAE0sbAH+Bds3OJe0U4fqqU7b5kSt\n26lD9VS3bd3PNyPjKnVfTSnzeO69R3rwfaP7+erztu6///qzDZB+PYWc+5kAzF86gxeh9XVGTExM\nuH//vtq+1atXc/LkSRYvXgyAlZUVCQkJ1K1bt8xjperXr8/t27epUaMGubm5WFhYcP/+fSZMmICD\ngwNBQUFASQ9BYGAg9vb2+Pv7k5ycTGRkJAkJCdI1/f39mTRpEtnZ2Wzbtk1atXzRokWkpqaWee6Z\nM2dSp04dJk6cCECDBg24ceMGhoaGFBYW0qhRIzIzM595Ttu2bZk0aRJ+fn4cOHCAsLAwYmJimDlz\nJqmpqZw+fZro6GgsLS1ZsmQJ169f58svv6ww10ePHmFpaUlCQgIWFhbMnDkTgBkz1D8IBw8eZOnS\npdy4cYPffvsNb29vunbtipmZGaNHj1bLZubMmZiYmDB8+HDkcrm0eOKZM2cYMGAAycnJatceP348\nCoWCoUOHAtCrVy8GDhxIr169aNasGUeOHKF+/focPHiQ6dOnExMTQ8uWLfnpp59o1qxZmdd0+fJl\ndu7cyeLFi1m+fDne3t5kZ2eza9cuVqxYgY+Pj9QTBGKdkerifs4jzp66VtVlCIJQjXz73XwU1n5l\n9p+5tIvgDz6sgooEofozMs15oXVGqqRn5Fntn4oea9WqFZs3byYwMJANGzZI+z09PVm+fDlDhgzh\n7t27xMXFER4eTn5+/jNrkMlkuLi48OGHH5KdnU2dOnXYsmULCoWizLEmJiZqtwi5u7uzYcMGBg4c\nyLp16/DyKjsg7ulzcnNzadSoEYDU+Cl9vUqlklGjRtGtWzd2796Nj48P3bt3Z/z48TRo0ICsrCwe\nPHgg9QBASWMEoF69ejx48IBNmzZJvRRPcnV1ZeDAgTRt2pRXXnkFhULB8uXLpVufnqRSqVCpVJia\nmmJmZsahQ4fw8PBg3bp15Wbo4eHB6tWrGTJkCLdv3+bAgQMMHDgQKLlV7eTJk/j6+krjSAA6derE\nokWLpAZfYmIiSqWSy5cvY2VlxdixY7ly5QpnzpyhefPmmJubM2DAAExNTfnhhx/KrUPQjid7RbTJ\nxLQWrbyttf48uqay8v03Etlqlz7k+4hAVi7biGPT/92qlXjxZ0aM6qvz3zf6kK++Etlq16lTp17o\nPK0PYC9v7IBMJlPb//S/yztnwYIFfPPNNzg6OnLp0iVMTU0B6NmzJ3K5HIVCgY+PD3PnzqVhw4Zq\n163omo0aNWLq1Km4urry7rvvYmVlxWuvvVbmOH9/f7Zt2yYNYF+8eDEREREoFArWrVvHwoULn3nO\nwYMHCQsLo0+fPrRs2ZIGDRqUqc3Dw4Pw8HC6du1Kw4YN+eKLL+jYsSMKhYKOHTty8+ZNteubmZkx\nYsQI7O3t8fX1xc3NrWz4gJGREW+99RatWrUCSgauP3jwQLqN7clsnvx3REQEo0ePRqlUlnmPSgUE\nBPDmm29ia2vLoEGDcHJykt6XGTNmEBISgouLC4aGhtL506dPp7CwELlcjr29vdSTExUVhb29PUql\nkrNnzzJkyBCSk5OlQe2ff/65Wq+IIAiCIFSkrbcX7496j/Ts/Vy+s5/07P2MGNVXzKYlCDpI67dp\nvSwPHz6kdu3aAGzYsIGNGzeqDRp/UXl5eRgbG1NUVESvXr0YPnw43bt3/8fX/bcoze/u3bu4ublx\n+PBhqTGobeI2LUEQBEEQBN1w6tQp/blN60UkJCQwZswYVCoV5ubmrFq16qVcNywsjN9//51Hjx7R\nqVMn0RD5m/z8/MjOzqagoIBPP/200hoigiAIgiAIgv7Tm54RQXia6BnRLnFvrXaJfLVHZKtdIl/t\nEvlqj8hWu160Z+QfjxkxMDBAqVRib2+Po6Mj33zzzTMHqD8tPT2dn376SdquaBE+bTh9+nS5U9a+\nqLCwMObNm/fSrveiZsyYwb59+/7WOU8uUigIgiAIgiAIleEfN0ZeffVVEhMT+b//+z/27t3Lr7/+\nKk0zq4nLly+zfv16abuixfK0ITExkV9++aXcx4qKiv729V5G7S/yvE+bOXPm326ZVmbugn4Qfz3S\nLpGv9ohstUvkq10iX+0R2eqmlzqbVoMGDfj+++9ZsmQJUDL9bFBQEHK5HCcnJ2JjY8ucExoaSnx8\nPEqlkgULFgBw/fp1OnfuzDvvvMNHH30kHbtnzx7c3d1xdnYmMDCQvLw86Rp2dnYoFAomT54MQGZm\nJr1798bV1RVXV1cOHz6s9rylYxw2btyIUqkkKiqKsLAwBg0axLvvvsvgwYNZvXq1Wi9N6RohAL/9\n9hvOzs44OjrSoUMH6ZjSH/UrVqygS5cuPHr0iEWLFkn19evXr0wGkZGRdOvWDR8fHzp06EB+fj7D\nhg3Dzc0NJycnabHHyMhIevToQceOHbGysmLJkiWEh4fj5ORE69atuXfvHgBDhw6VptO1tLQkLCwM\nZ2dn5HI5Fy5cAODu3bt07NgRe3t7RowYUWFvVnBwMC4uLtjb2xMWFibtL++6xcXFvPPOO9y5cweA\n4uJimjVrxt27d0lLS6Ndu3YoFArat29PRkaGVGtISAgeHh5YW1urTQM8d+5cXF1dUSgUas8tCIIg\nCM8TGxPHmFFTGD1yCmNGTSE2Jq6qSxIEoRwvfQC7lZUVjx8/5vbt26xduxYDAwPOnDnDhQsX6Nix\nI6mpqRgZGUnHz549m/DwcKKjo4GSH9xJSUkkJSVhZGSEjY0N48aN45VXXmHWrFns27eP2rVrM3v2\nbL755htGjx7N9u3bOX/+PIC0tkdISAjjx4/Hw8ODK1eu4OvrS0rK/1aMNDIy4vPPPychIYFFixYB\nJbdZnT9/noMHD/LKK6+wevVqtddWOvVtZmYmI0eOJD4+niZNmpCdnS0do1KpWLJkCfv27WPHjh3U\nrFmT2bNnk5aWRs2aNdXWHnlSYmIiycnJmJmZMXXqVHx8fFi1ahXZ2dm4ubnRvn17AM6ePUtSUhIP\nHz7E2tqauXPncurUKSZMmMCaNWsICQkpM11vgwYNSEhIYNmyZYSHh7NixQpmzpyJl5cXn3zyCb/8\n8kuFa3jMmjULc3NzHj9+TPv27fm///s/7O3tK7xu6dorISEh/P777zg6OlKvXj2GDh1KUFAQgwYN\nIiIignHjxkmzod28eZNDhw5x7tw5unXrRkBAAHv27OHixYscP36c4uJiunfvTnx8PJ6enhp+EoV/\nqrLurc3PKyDtjztafx5dcyrpOE6OrlVdRrUkstUufcj3ZMIxdkb/hqtdT2nf0gXruHLpLi2dy58K\nX1foQ776SmSrm7Q6m9ahQ4cYN24cADY2NjRp0oQLFy5Ia1xA2UUOZTIZPj4+mJiYAGBra0taWhr3\n7t0jJSUFd3d3oKRnw93dHVNTU2rVqsXw4cPx8/PDz69kxdXff/+dc+fOSde9f/8++fn5vPrqq2rP\n/eTzy2QyunXrxiuvvFLha1KpVBw9ehQvLy+aNGkClKz5UfrYmjVraNy4MTt27MDAwAAAuVxO//79\n6dGjBz169ChzTZlMRocOHaTr7Nmzh+joaMLDwwH466+/uHLlCjKZDG9vb4yNjTE2NsbMzAx//5IF\nnRwcHDhz5ky5Nffq1QsAJycntm7dCkB8fLzUGOjSpQvm5ublnrt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AAElFTkSuQmCC\n", + "text": [ + "" + ] + } + ], + "prompt_number": 23 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "In the graphic above, you can see why sorting by mean would be sub-optimal." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Extension to Starred rating systems\n", + "\n", + "The above procedure works well for upvote-downvotes schemes, but what about systems that use star ratings, e.g. 5 star rating systems. Similar problems apply with simply taking the average: an item with two perfect ratings would beat an item with thousands of perfect ratings, but a single sub-perfect rating. \n", + "\n", + "\n", + "We can consider the upvote-downvote problem above as binary: 0 is a downvote, 1 if an upvote. A $N$-star rating system can be seen as a more continuous version of above, and we can set $n$ stars rewarded is equivalent to rewarding $\\frac{n}{N}$. For example, in a 5-star system, a 2 star rating corresponds to 0.4. A perfect rating is a 1. We can use the same formula as before, but with $a,b$ defined differently:\n", + "\n", + "\n", + "$$ \\frac{a}{a + b} - 1.65\\sqrt{ \\frac{ab}{ (a+b)^2(a + b +1 ) } }$$\n", + "\n", + "where \n", + "\n", + "\\begin{align}\n", + "& a = 1 + S \\\\\\\\\n", + "& b = 1 + N - S \\\\\\\\\n", + "\\end{align}\n", + "\n", + "where $N$ is the number of users who rated, and $S$ is the sum of all the ratings, under the equivalence scheme mentioned above. " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "##### Example: Counting Github stars\n", + "\n", + "What is the average number of stars a Github repository has? How would you calculate this? There are over 6 million respositories, so there is more than enough data to invoke the Law of Large numbers. Let's start pulling some data. TODO" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Conclusion\n", + "\n", + "While the Law of Large Numbers is cool, it is only true so much as its name implies: with large sample sizes only. We have seen how our inference can be affected by not considering *how the data is shaped*. \n", + "\n", + "1. By (cheaply) drawing many samples from the posterior distributions, we can ensure that the Law of Large Number applies as we approximate expected values (which we will do in the next chapter).\n", + "\n", + "2. Bayesian inference understands that with small sample sizes, we can observe wild randomness. Our posterior distribution will reflect this by being more spread rather than tightly concentrated. Thus, our inference should be correctable.\n", + "\n", + "3. There are major implications of not considering the sample size, and trying to sort objects that are unstable leads to pathological orderings. The method provided above solves this problem.\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Appendix\n", + "\n", + "##### Derivation of sorting comments formula\n", + "\n", + "Basically what we are doing is using a Beta prior (with parameters $a=1, b=1$, which is a uniform distribution), and using a Binomial likelihood with observations $u, N = u+d$. This means our posterior is a Beta distribution with parameters $a' = 1 + u, b' = 1 + (N - u) = 1+d$. We then need to find the value, $x$, such that 0.05 probability is less than $x$. This is usually done by inverting the CDF ([Cumulative Distribution Function](http://en.wikipedia.org/wiki/Cumulative_Distribution_Function)), but the CDF of the beta, for integer parameters, is known but is a large sum [3]. \n", + "\n", + "We instead use a Normal approximation. The mean of the Beta is $\\mu = a'/(a'+b')$ and the variance is \n", + "\n", + "$$\\sigma^2 = \\frac{a'b'}{ (a' + b')^2(a'+b'+1) }$$\n", + "\n", + "Hence we solve the following equation for $x$ and have an approximate lower bound. \n", + "\n", + "$$ 0.05 = \\Phi\\left( \\frac{(x - \\mu)}{\\sigma}\\right) $$ \n", + "\n", + "$\\Phi$ being the [cumulative distribution for the normal distribution](http://en.wikipedia.org/wiki/Normal_distribution#Cumulative_distribution)\n", + "\n", + "\n", + "\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "##### Exercises\n", + "\n", + "1\\. How would you estimate the quantity $E\\left[ \\cos{X} \\right]$, where $X \\sim \\text{Exp}(4)$? What about $E\\left[ \\cos{X} | X \\lt 1\\right]$, i.e. the expected value *given* we know $X$ is less than 1? Would you need more samples than the original samples size to be equally accurate?" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# Enter code here\n", + "import scipy.stats as stats\n", + "exp = stats.expon(scale=4)\n", + "N = 1e5\n", + "X = exp.rvs(N)\n", + "# ..." + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 14 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "2\\. The following table was located in the paper \"Going for Three: Predicting the Likelihood of Field Goal Success with Logistic Regression\" [2]. The table ranks football field-goal kickers by their percent of non-misses. What mistake have the researchers made?\n", + "\n", + "-----\n", + "\n", + "#### Kicker Careers Ranked by Make Percentage\n", + "
Rank Kicker Make % Number of Kicks
1 Garrett Hartley 87.7 57
2 Matt Stover 86.8 335
3 Robbie Gould 86.2 224
4 Rob Bironas 86.1 223
5 Shayne Graham 85.4 254
\u2026 \u2026 \u2026
51 Dave Rayner 72.2 90
52 Nick Novak 71.9 64
53 Tim Seder 71.0 62
54 Jose Cortez 70.7 75
55 Wade Richey 66.1 56
" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "In August 2013, [a popular post](http://bpodgursky.wordpress.com/2013/08/21/average-income-per-programming-language/) on the average income per programmer of different languages was trending. Here's the summary chart: (reproduced without permission, cause when you lie with stats, you gunna get the hammer). What do you notice about the extremes?\n", + "\n", + "------\n", + "\n", + "#### Average household income by programming language\n", + "\n", + "\n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + "
LanguageAverage Household Income ($)Data Points
Puppet87,589.29112
Haskell89,973.82191
PHP94,031.19978
CoffeeScript94,890.80435
VimL94,967.11532
Shell96,930.54979
Lua96,930.69101
Erlang97,306.55168
Clojure97,500.00269
Python97,578.872314
JavaScript97,598.753443
Emacs Lisp97,774.65355
C#97,823.31665
Ruby98,238.743242
C++99,147.93845
CSS99,881.40527
Perl100,295.45990
C100,766.512120
Go101,158.01231
Scala101,460.91243
ColdFusion101,536.70109
Objective-C101,801.60562
Groovy102,650.86116
Java103,179.391402
XSLT106,199.19123
ActionScript108,119.47113
" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### References\n", + "\n", + "1. Wainer, Howard. *The Most Dangerous Equation*. American Scientist, Volume 95.\n", + "2. Clarck, Torin K., Aaron W. Johnson, and Alexander J. Stimpson. \"Going for Three: Predicting the Likelihood of Field Goal Success with Logistic Regression.\" (2013): n. page. [Web](http://www.sloansportsconference.com/wp-content/uploads/2013/Going%20for%20Three%20Predicting%20the%20Likelihood%20of%20Field%20Goal%20Success%20with%20Logistic%20Regression.pdf). 20 Feb. 2013.\n", + "3. http://en.wikipedia.org/wiki/Beta_function#Incomplete_beta_function" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from IPython.core.display import HTML\n", + "\n", + "\n", + "def css_styling():\n", + " styles = open(\"../styles/custom.css\", \"r\").read()\n", + " return HTML(styles)\n", + "css_styling()" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "html": [ + "\n", + "\n" + ], + "metadata": {}, + "output_type": "pyout", + "prompt_number": 1, + "text": [ + "" + ] + } + ], + "prompt_number": 1 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "" + ] + } + ], + "metadata": {} + } + ] +} diff --git a/Chapter4_TheGreatestTheoremNeverTold/README.md b/Chapter4_TheGreatestTheoremNeverTold/README.md index 74bff691..93752488 100644 --- a/Chapter4_TheGreatestTheoremNeverTold/README.md +++ b/Chapter4_TheGreatestTheoremNeverTold/README.md @@ -1,3 +1,3 @@ -Chapter 4: The Greatest Theorem Never Told -==== -### [Read it online here](http://nbviewer.ipython.org/urls/raw.github.com/CamDavidsonPilon/Probabilistic-Programming-and-Bayesian-Methods-for-Hackers/master/Chapter4_TheGreatestTheoremNeverTold/LawOfLargeNumbers.ipynb) +Chapter 4: The Greatest Theorem Never Told +==== +### [Read it online here](http://nbviewer.ipython.org/urls/raw.github.com/CamDavidsonPilon/Probabilistic-Programming-and-Bayesian-Methods-for-Hackers/master/Chapter4_TheGreatestTheoremNeverTold/LawOfLargeNumbers.ipynb) diff --git a/Chapter4_TheGreatestTheoremNeverTold/data/census_data.csv b/Chapter4_TheGreatestTheoremNeverTold/data/census_data.csv index 0f5e9a2e..61827fb5 100644 --- a/Chapter4_TheGreatestTheoremNeverTold/data/census_data.csv +++ b/Chapter4_TheGreatestTheoremNeverTold/data/census_data.csv @@ -1,20002 +1,20002 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+77.099999999999994,987 +88.200000000000003,954 +89.599999999999994,1165 +78.700000000000003,93 +77.900000000000006,1726 +81.099999999999994,821 +83.400000000000006,1141 +81.400000000000006,569 diff --git a/Chapter4_TheGreatestTheoremNeverTold/top_pic_comments.py b/Chapter4_TheGreatestTheoremNeverTold/top_pic_comments.py index 9f0eeffe..9be379b4 100644 --- a/Chapter4_TheGreatestTheoremNeverTold/top_pic_comments.py +++ b/Chapter4_TheGreatestTheoremNeverTold/top_pic_comments.py @@ -1,63 +1,63 @@ -import sys - -import numpy as np -from IPython.core.display import Image - -import praw - - -reddit = praw.Reddit("BayesianMethodsForHackers") -subreddit = reddit.get_subreddit( "pics" ) - -top_submissions = subreddit.get_top() - - -n_pic = int( sys.argv[1] ) if sys.argv[1] else 1 - -i = 0 -while i < n_pic: - top_submission = top_submissions.next() - while "i.imgur.com" not in top_submission.url: - #make sure it is linking to an image, not a webpage. - top_submission = top_submissions.next() - i+=1 - -print "Title of submission: \n", top_submission.title -top_post_url = top_submission.url -#top_submission.replace_more_comments(limit=5, threshold=0) -print top_post_url - -upvotes = [] -downvotes = [] -contents = [] -_all_comments = top_submission.comments -all_comments=[] -for comment in _all_comments: - try: - upvotes.append( comment.ups ) - downvotes.append( comment.downs ) - contents.append( comment.body ) - except Exception as e: - continue - -votes = np.array( [ upvotes, downvotes] ).T - - - - - - - - - - - - - - - - - - - - +import sys + +import numpy as np +from IPython.core.display import Image + +import praw + + +reddit = praw.Reddit("BayesianMethodsForHackers") +subreddit = reddit.get_subreddit( "pics" ) + +top_submissions = subreddit.get_top() + + +n_pic = int( sys.argv[1] ) if sys.argv[1] else 1 + +i = 0 +while i < n_pic: + top_submission = top_submissions.next() + while "i.imgur.com" not in top_submission.url: + #make sure it is linking to an image, not a webpage. + top_submission = top_submissions.next() + i+=1 + +print "Title of submission: \n", top_submission.title +top_post_url = top_submission.url +#top_submission.replace_more_comments(limit=5, threshold=0) +print top_post_url + +upvotes = [] +downvotes = [] +contents = [] +_all_comments = top_submission.comments +all_comments=[] +for comment in _all_comments: + try: + upvotes.append( comment.ups ) + downvotes.append( comment.downs ) + contents.append( comment.body ) + except Exception as e: + continue + +votes = np.array( [ upvotes, downvotes] ).T + + + + + + + + + + + + + + + + + + + + diff --git a/Chapter5_LossFunctions/DarkWorldsMetric.py b/Chapter5_LossFunctions/DarkWorldsMetric.py index 0b59edf4..530c3145 100644 --- a/Chapter5_LossFunctions/DarkWorldsMetric.py +++ b/Chapter5_LossFunctions/DarkWorldsMetric.py @@ -1,433 +1,433 @@ -""" DarkWorldsMetricMountianOsteric.py -Custom evaluation metric for the 'Observing Dark Worlds' competition. - -[Description of metric, or reference to documentation.] - -Update: Made for the training set only so users can check there results from the training c - -@Author: David Harvey -Created: 22 August 2012 -""" - -import numpy as np -import math as mt -import itertools as it -import csv as c -import getopt as gt -import sys as sys -import argparse as ap -import string as st -import random as rd - -def calc_delta_r(x_predicted,y_predicted,x_true,y_true): - """ Compute the scalar distance between predicted halo centers - and the true halo centers. Predictions are matched to the closest - halo center. - Notes: It takes in the predicted and true positions, and then loops over each possible configuration and finds the most optimal one. - Arguments: - x_predicted, y_predicted: vector for predicted x- and y-positions (1 to 3 elements) - x_true, y_true: vector for known x- and y-positions (1 to 3 elements) - Returns: - radial_distance: vector containing the scalar distances between the predicted halo centres and the true halo centres (1 to 3 elements) - true_halo_idexes: vector containing indexes of the input true halos which matches the predicted halo indexes (1 to 3 elements) - measured_halo_indexes: vector containing indexes of the predicted halo position with the reference to the true halo position. - e.g if true_halo_indexes=[0,1] and measured_halo_indexes=[1,0] then the first x,y coordinates of the true halo position matches the second input of the predicted x,y coordinates. - """ - - num_halos=len(x_true) #Only works for number of halos > 1 - num_configurations=mt.factorial(num_halos) #The number of possible different comb - configurations=np.zeros([num_halos,num_configurations],int) #The array of combinations - #I will pass back - distances = np.zeros([num_configurations],float) #The array of the distances - #for all possible combinations - - radial_distance=[] #The vector of distances - #I will pass back - - #Pick a combination of true and predicted - a=['01','012'] #Input for the permutatiosn, 01 number halos or 012 - count=0 #For the index of the distances array - true_halo_indexes=[] #The tuples which will show the order of halos picked - predicted_halo_indexes=[] - distances_perm=np.zeros([num_configurations,num_halos],float) #The distance between each - #true and predicted - #halo for every comb - true_halo_indexes_perm=[] #log of all the permutations of true halos used - predicted_halo_indexes_perm=[] #log of all the predicted permutations - - for perm in it.permutations(a[num_halos-2],num_halos): - which_true_halos=[] - which_predicted_halos=[] - for j in xrange(num_halos): #loop through all the true halos with the - - distances_perm[count,j]=np.sqrt((x_true[j]-x_predicted[int(perm[j])])**2\ - +(y_true[j]-y_predicted[int(perm[j])])**2) - #This array logs the distance between true and - #predicted halo for ALL configurations - - which_true_halos.append(j) #log the order in which I try each true halo - which_predicted_halos.append(int(perm[j])) #log the order in which I true - #each predicted halo - true_halo_indexes_perm.append(which_true_halos) #this is a tuple of tuples of - #all of thifferent config - #true halo indexes - predicted_halo_indexes_perm.append(which_predicted_halos) - - distances[count]=sum(distances_perm[count,0::]) #Find what the total distances - #are for each configuration - count=count+1 - - config = np.where(distances == min(distances))[0][0] #The configuration used is the one - #which has the smallest distance - radial_distance.append(distances_perm[config,0::]) #Find the tuple of distances that - #correspond to this smallest distance - true_halo_indexes=true_halo_indexes_perm[config] #Find the tuple of the index which refers - #to the smallest distance - predicted_halo_indexes=predicted_halo_indexes_perm[config] - - return radial_distance,true_halo_indexes,predicted_halo_indexes - - -def calc_theta(x_predicted, y_predicted, x_true, y_true, x_ref, y_ref): - """ Calculate the angle the predicted position and the true position, where the zero degree corresponds to the line joing the true halo position and the reference point given. - Arguments: - x_predicted, y_predicted: vector for predicted x- and y-positions (1 to 3 elements) - x_true, y_true: vector for known x- and y-positions (1 to 3 elements) - Note that the input of these are matched up so that the first elements of each - vector are associated with one another - x_ref, y_ref: scalars of the x,y coordinate of reference point - Returns: - Theta: A vector containing the angles of the predicted halo w.r.t the true halo - with the vector joining the reference point and the halo as the zero line. - """ - - num_halos=len(x_predicted) - theta=np.zeros([num_halos+1],float) #Set up the array which will pass back the values - phi = np.zeros([num_halos],float) - - psi = np.arctan( (y_true-y_ref)/(x_true-x_ref) ) - - - # Angle at which the halo is at - #with respect to the reference point - phi[x_true != x_ref] = np.arctan((y_predicted[x_true != x_predicted]-\ - y_true[x_true != x_predicted])\ - /(x_predicted[x_true != x_predicted]-\ - x_true[x_true != x_predicted])) # Angle of the estimate - #wrt true halo centre - - #Before finding the angle with the zero line as the line joiing the halo and the reference - #point I need to convert the angle produced by Python to an angle between 0 and 2pi - phi =convert_to_360(phi, x_predicted-x_true,\ - y_predicted-y_true) - psi = convert_to_360(psi, x_true-x_ref,\ - y_true-y_ref) - theta = phi-psi #The angle with the baseline as the line joing the ref and the halo - - - theta[theta< 0.0]=theta[theta< 0.0]+2.0*mt.pi #If the angle of the true pos wrt the ref is - #greater than the angle of predicted pos - #and the true pos then add 2pi - return theta - - -def convert_to_360(angle, x_in, y_in): - """ Convert the given angle to the true angle in the range 0:2pi - Arguments: - angle: - x_in, y_in: the x and y coordinates used to determine the quartile - the coordinate lies in so to add of pi or 2pi - Returns: - theta: the angle in the range 0:2pi - """ - n = len(x_in) - for i in xrange(n): - if x_in[i] < 0 and y_in[i] > 0: - angle[i] = angle[i]+mt.pi - elif x_in[i] < 0 and y_in[i] < 0: - angle[i] = angle[i]+mt.pi - elif x_in[i] > 0 and y_in[i] < 0: - angle[i] = angle[i]+2.0*mt.pi - elif x_in[i] == 0 and y_in[i] == 0: - angle[i] = 0 - elif x_in[i] == 0 and y_in[i] > 0: - angle[i] = mt.pi/2. - elif x_in[i] < 0 and y_in[i] == 0: - angle[i] = mt.pi - elif x_in[i] == 0 and y_in[i] < 0: - angle[i] = 3.*mt.pi/2. - - - - return angle - -def get_ref(x_halo,y_halo,weight): - """ Gets the reference point of the system of halos by weighted averaging the x and y - coordinates. - Arguments: - x_halo, y_halo: Vector num_halos referring to the coordinates of the halos - weight: the weight which will be assigned to the position of the halo - num_halos: number of halos in the system - Returns: - x_ref, y_ref: The coordinates of the reference point for the metric - """ - - - #Find the weighted average of the x and y coordinates - x_ref = np.sum([x_halo*weight])/np.sum([weight]) - y_ref = np.sum([y_halo*weight])/np.sum([weight]) - - - return x_ref,y_ref - - -def main_score( nhalo_all, x_true_all, y_true_all, x_ref_all, y_ref_all, sky_prediction): - """abstracts the score from the old command-line interface. - sky_prediction is a dx2 array of predicted x,y positions - - -camdp""" - - r=np.array([],dtype=float) # The array which I will log all the calculated radial distances - angle=np.array([],dtype=float) #The array which I will log all the calculated angles - #Load in the sky_ids from the true - num_halos_total=0 #Keep track of how many halos are input into the metric - - - - for selectskyinsolutions, sky in enumerate(sky_prediction): #Loop through each line in result.csv and analyse each one - - - nhalo=int(nhalo_all[selectskyinsolutions])#How many halos in the - #selected sky? - x_true=x_true_all[selectskyinsolutions][0:nhalo] - y_true=y_true_all[selectskyinsolutions][0:nhalo] - - x_predicted=np.array([],dtype=float) - y_predicted=np.array([],dtype=float) - for i in xrange(nhalo): - x_predicted=np.append(x_predicted,float(sky[0])) #get the predicted values - y_predicted=np.append(y_predicted,float(sky[1])) - #The solution file for the test data provides masses - #to calculate the centre of mass where as the Training_halo.csv - #direct provides x_ref y_ref. So in the case of test data - #we need to calculate the ref point from the masses using - #Get_ref() - - x_ref=x_ref_all[selectskyinsolutions] - y_ref=y_ref_all[selectskyinsolutions] - - num_halos_total=num_halos_total+nhalo - - - #Single halo case, this needs to be separately calculated since - #x_ref = x_true - if nhalo == 1: - #What is the radial distance between the true and predicted position - r=np.append(r,np.sqrt( (x_predicted-x_true)**2 \ - + (y_predicted-y_true)**2)) - #What is the angle between the predicted position and true halo position - if (x_predicted-x_true) != 0: - psi = np.arctan((y_predicted-y_true)/(x_predicted-x_true)) - else: psi=0. - theta = convert_to_360([psi], [x_predicted-x_true], [y_predicted-y_true]) - angle=np.append(angle,theta) - - - else: - #r_index_index, contains the radial distances of the predicted to - #true positions. These are found by matching up the true halos to - #the predicted halos such that the average of all the radial distances - #is optimal. it also contains indexes of the halos used which are used to - #show which halo has been mathced to which. - - r_index_index = calc_delta_r(x_predicted, y_predicted, x_true, \ - y_true) - - r=np.append(r,r_index_index[0][0]) - halo_index= r_index_index[1] #The true halos indexes matched with the - predicted_index=r_index_index[2] #predicted halo index - - angle=np.append(angle,calc_theta\ - (x_predicted[predicted_index],\ - y_predicted[predicted_index],\ - x_true[halo_index],\ - y_true[halo_index],x_ref,\ - y_ref)) # Find the angles of the predicted - #position wrt to the halo and - # add to the vector angle - - - # Find what the average distance the estimate is from the halo position - av_r=sum(r)/len(r) - - #In order to quantify the orientation invariance we will express each angle - # as a vector and find the average vector - #R_bar^2=(1/N Sum^Ncos(theta))^2+(1/N Sum^Nsin(theta))**2 - - N = float(num_halos_total) - angle_vec = np.sqrt(( 1.0/N * sum(np.cos(angle)) )**2 + \ - ( 1.0/N * sum(np.sin(angle)) )**2) - - W1=1./1000. #Weight the av_r such that < 1 is a good score > 1 is not so good. - W2=1. - metric = W1*av_r + W2*angle_vec #Weighted metric, weights TBD - print 'Your average distance in pixels you are away from the true halo is', av_r - print 'Your average angular vector is', angle_vec - print 'Your score for the training data is', metric - return metric - - -def main(user_fname, fname): - """ Script to compute the evaluation metric for the Observing Dark Worlds competition. You can run it on your training data to understand how well you have done with the training data. - """ - - r=np.array([],dtype=float) # The array which I will log all the calculated radial distances - angle=np.array([],dtype=float) #The array which I will log all the calculated angles - #Load in the sky_ids from the true - - true_sky_id=[] - sky_loader = c.reader(open(fname, 'rb')) #Load in the sky_ids from the solution file - for row in sky_loader: - true_sky_id.append(row[0]) - - #Load in the true values from the solution file - - nhalo_all=np.loadtxt(fname,usecols=(1,),delimiter=',',skiprows=1) - x_true_all=np.loadtxt(fname,usecols=(4,6,8),delimiter=',',skiprows=1) - y_true_all=np.loadtxt(fname,usecols=(5,7,9),delimiter=',',skiprows=1) - x_ref_all=np.loadtxt(fname,usecols=(2,),delimiter=',',skiprows=1) - y_ref_all=np.loadtxt(fname,usecols=(3,),delimiter=',',skiprows=1) - - - for row in sky_loader: - true_sky_id.append(row[1]) - - - - num_halos_total=0 #Keep track of how many halos are input into the metric - - - sky_prediction = c.reader(open(user_fname, 'rb')) #Open the result.csv - - try: #See if the input file from user has a header on it - #with open('JoyceTest/trivialUnitTest_Pred.txt', 'r') as f: - with open(user_fname, 'r') as f: - header = float((f.readline()).split(',')[1]) #try and make where the - #first input would be - #a float, if succeed it - #is not a header - print 'THE INPUT FILE DOES NOT APPEAR TO HAVE A HEADER' - except : - print 'THE INPUT FILE APPEARS TO HAVE A HEADER, SKIPPING THE FIRST LINE' - - skip_header = sky_prediction.next() - - - for sky in sky_prediction: #Loop through each line in result.csv and analyse each one - sky_id = str(sky[0]) #Get the sky_id of the input - does_it_exist=true_sky_id.count(sky_id) #Is the input sky_id - #from user a real one? - - if does_it_exist > 0: #If it does then find the matching solutions to the sky_id - selectskyinsolutions=true_sky_id.index(sky_id)-1 - else: #Otherwise exit - print 'Sky_id does not exist, formatting problem: ',sky_id - sys.exit(2) - - - nhalo=int(nhalo_all[selectskyinsolutions])#How many halos in the - #selected sky? - x_true=x_true_all[selectskyinsolutions][0:nhalo] - y_true=y_true_all[selectskyinsolutions][0:nhalo] - - x_predicted=np.array([],dtype=float) - y_predicted=np.array([],dtype=float) - for i in xrange(nhalo): - x_predicted=np.append(x_predicted,float(sky[2*i+1])) #get the predicted values - y_predicted=np.append(y_predicted,float(sky[2*i+2])) - #The solution file for the test data provides masses - #to calculate the centre of mass where as the Training_halo.csv - #direct provides x_ref y_ref. So in the case of test data - #we need to calculae the ref point from the masses using - #Get_ref() - - x_ref=x_ref_all[selectskyinsolutions] - y_ref=y_ref_all[selectskyinsolutions] - - num_halos_total=num_halos_total+nhalo - - - #Single halo case, this needs to be separately calculated since - #x_ref = x_true - if nhalo == 1: - #What is the radial distance between the true and predicted position - r=np.append(r,np.sqrt( (x_predicted-x_true)**2 \ - + (y_predicted-y_true)**2)) - #What is the angle between the predicted position and true halo position - if (x_predicted-x_true) != 0: - psi = np.arctan((y_predicted-y_true)/(x_predicted-x_true)) - else: psi=0. - theta = convert_to_360([psi], [x_predicted-x_true], [y_predicted-y_true]) - angle=np.append(angle,theta) - - - else: - #r_index_index, contains the radial distances of the predicted to - #true positions. These are found by matching up the true halos to - #the predicted halos such that the average of all the radial distances - #is optimal. it also contains indexes of the halos used which are used to - #show which halo has been mathced to which. - - r_index_index = calc_delta_r(x_predicted, y_predicted, x_true, \ - y_true) - - r=np.append(r,r_index_index[0][0]) - halo_index= r_index_index[1] #The true halos indexes matched with the - predicted_index=r_index_index[2] #predicted halo index - - angle=np.append(angle,calc_theta\ - (x_predicted[predicted_index],\ - y_predicted[predicted_index],\ - x_true[halo_index],\ - y_true[halo_index],x_ref,\ - y_ref)) # Find the angles of the predicted - #position wrt to the halo and - # add to the vector angle - - - # Find what the average distance the estimate is from the halo position - av_r=sum(r)/len(r) - - #In order to quantify the orientation invariance we will express each angle - # as a vector and find the average vector - #R_bar^2=(1/N Sum^Ncos(theta))^2+(1/N Sum^Nsin(theta))**2 - - N = float(num_halos_total) - angle_vec = np.sqrt(( 1.0/N * sum(np.cos(angle)) )**2 + \ - ( 1.0/N * sum(np.sin(angle)) )**2) - - W1=1./1000. #Weight the av_r such that < 1 is a good score > 1 is not so good. - W2=1. - metric = W1*av_r + W2*angle_vec #Weighted metric, weights TBD - print 'Your average distance in pixels you are away from the true halo is', av_r - print 'Your average angular vector is', angle_vec - print 'Your score for the training data is', metric - - -if __name__ == "__main__": - #For help just typed 'python DarkWorldsMetric.py -h' - - parser = ap.ArgumentParser(description='Work out the Metric for your input file') - parser.add_argument('inputfile',type=str,nargs=1,help='Input file of halo positions. Needs to be in the format SkyId,halo_x1,haloy1,halox_2,halo_y2,halox3,halo_y3 ') - parser.add_argument('reffile',type=str,nargs=1,help='This should point to Training_halos.csv') - args = parser.parse_args() - - user_fname=args.inputfile[0] - filename = (args.reffile[0]).count('Training_halos.csv') - if filename == 0: - fname=args.reffile[0]+str('Training_halos.csv') - else: - fname=args.reffile[0] - - main(user_fname, fname) - +""" DarkWorldsMetricMountianOsteric.py +Custom evaluation metric for the 'Observing Dark Worlds' competition. + +[Description of metric, or reference to documentation.] + +Update: Made for the training set only so users can check there results from the training c + +@Author: David Harvey +Created: 22 August 2012 +""" + +import numpy as np +import math as mt +import itertools as it +import csv as c +import getopt as gt +import sys as sys +import argparse as ap +import string as st +import random as rd + +def calc_delta_r(x_predicted,y_predicted,x_true,y_true): + """ Compute the scalar distance between predicted halo centers + and the true halo centers. Predictions are matched to the closest + halo center. + Notes: It takes in the predicted and true positions, and then loops over each possible configuration and finds the most optimal one. + Arguments: + x_predicted, y_predicted: vector for predicted x- and y-positions (1 to 3 elements) + x_true, y_true: vector for known x- and y-positions (1 to 3 elements) + Returns: + radial_distance: vector containing the scalar distances between the predicted halo centres and the true halo centres (1 to 3 elements) + true_halo_idexes: vector containing indexes of the input true halos which matches the predicted halo indexes (1 to 3 elements) + measured_halo_indexes: vector containing indexes of the predicted halo position with the reference to the true halo position. + e.g if true_halo_indexes=[0,1] and measured_halo_indexes=[1,0] then the first x,y coordinates of the true halo position matches the second input of the predicted x,y coordinates. + """ + + num_halos=len(x_true) #Only works for number of halos > 1 + num_configurations=mt.factorial(num_halos) #The number of possible different comb + configurations=np.zeros([num_halos,num_configurations],int) #The array of combinations + #I will pass back + distances = np.zeros([num_configurations],float) #The array of the distances + #for all possible combinations + + radial_distance=[] #The vector of distances + #I will pass back + + #Pick a combination of true and predicted + a=['01','012'] #Input for the permutatiosn, 01 number halos or 012 + count=0 #For the index of the distances array + true_halo_indexes=[] #The tuples which will show the order of halos picked + predicted_halo_indexes=[] + distances_perm=np.zeros([num_configurations,num_halos],float) #The distance between each + #true and predicted + #halo for every comb + true_halo_indexes_perm=[] #log of all the permutations of true halos used + predicted_halo_indexes_perm=[] #log of all the predicted permutations + + for perm in it.permutations(a[num_halos-2],num_halos): + which_true_halos=[] + which_predicted_halos=[] + for j in xrange(num_halos): #loop through all the true halos with the + + distances_perm[count,j]=np.sqrt((x_true[j]-x_predicted[int(perm[j])])**2\ + +(y_true[j]-y_predicted[int(perm[j])])**2) + #This array logs the distance between true and + #predicted halo for ALL configurations + + which_true_halos.append(j) #log the order in which I try each true halo + which_predicted_halos.append(int(perm[j])) #log the order in which I true + #each predicted halo + true_halo_indexes_perm.append(which_true_halos) #this is a tuple of tuples of + #all of thifferent config + #true halo indexes + predicted_halo_indexes_perm.append(which_predicted_halos) + + distances[count]=sum(distances_perm[count,0::]) #Find what the total distances + #are for each configuration + count=count+1 + + config = np.where(distances == min(distances))[0][0] #The configuration used is the one + #which has the smallest distance + radial_distance.append(distances_perm[config,0::]) #Find the tuple of distances that + #correspond to this smallest distance + true_halo_indexes=true_halo_indexes_perm[config] #Find the tuple of the index which refers + #to the smallest distance + predicted_halo_indexes=predicted_halo_indexes_perm[config] + + return radial_distance,true_halo_indexes,predicted_halo_indexes + + +def calc_theta(x_predicted, y_predicted, x_true, y_true, x_ref, y_ref): + """ Calculate the angle the predicted position and the true position, where the zero degree corresponds to the line joing the true halo position and the reference point given. + Arguments: + x_predicted, y_predicted: vector for predicted x- and y-positions (1 to 3 elements) + x_true, y_true: vector for known x- and y-positions (1 to 3 elements) + Note that the input of these are matched up so that the first elements of each + vector are associated with one another + x_ref, y_ref: scalars of the x,y coordinate of reference point + Returns: + Theta: A vector containing the angles of the predicted halo w.r.t the true halo + with the vector joining the reference point and the halo as the zero line. + """ + + num_halos=len(x_predicted) + theta=np.zeros([num_halos+1],float) #Set up the array which will pass back the values + phi = np.zeros([num_halos],float) + + psi = np.arctan( (y_true-y_ref)/(x_true-x_ref) ) + + + # Angle at which the halo is at + #with respect to the reference point + phi[x_true != x_ref] = np.arctan((y_predicted[x_true != x_predicted]-\ + y_true[x_true != x_predicted])\ + /(x_predicted[x_true != x_predicted]-\ + x_true[x_true != x_predicted])) # Angle of the estimate + #wrt true halo centre + + #Before finding the angle with the zero line as the line joiing the halo and the reference + #point I need to convert the angle produced by Python to an angle between 0 and 2pi + phi =convert_to_360(phi, x_predicted-x_true,\ + y_predicted-y_true) + psi = convert_to_360(psi, x_true-x_ref,\ + y_true-y_ref) + theta = phi-psi #The angle with the baseline as the line joing the ref and the halo + + + theta[theta< 0.0]=theta[theta< 0.0]+2.0*mt.pi #If the angle of the true pos wrt the ref is + #greater than the angle of predicted pos + #and the true pos then add 2pi + return theta + + +def convert_to_360(angle, x_in, y_in): + """ Convert the given angle to the true angle in the range 0:2pi + Arguments: + angle: + x_in, y_in: the x and y coordinates used to determine the quartile + the coordinate lies in so to add of pi or 2pi + Returns: + theta: the angle in the range 0:2pi + """ + n = len(x_in) + for i in xrange(n): + if x_in[i] < 0 and y_in[i] > 0: + angle[i] = angle[i]+mt.pi + elif x_in[i] < 0 and y_in[i] < 0: + angle[i] = angle[i]+mt.pi + elif x_in[i] > 0 and y_in[i] < 0: + angle[i] = angle[i]+2.0*mt.pi + elif x_in[i] == 0 and y_in[i] == 0: + angle[i] = 0 + elif x_in[i] == 0 and y_in[i] > 0: + angle[i] = mt.pi/2. + elif x_in[i] < 0 and y_in[i] == 0: + angle[i] = mt.pi + elif x_in[i] == 0 and y_in[i] < 0: + angle[i] = 3.*mt.pi/2. + + + + return angle + +def get_ref(x_halo,y_halo,weight): + """ Gets the reference point of the system of halos by weighted averaging the x and y + coordinates. + Arguments: + x_halo, y_halo: Vector num_halos referring to the coordinates of the halos + weight: the weight which will be assigned to the position of the halo + num_halos: number of halos in the system + Returns: + x_ref, y_ref: The coordinates of the reference point for the metric + """ + + + #Find the weighted average of the x and y coordinates + x_ref = np.sum([x_halo*weight])/np.sum([weight]) + y_ref = np.sum([y_halo*weight])/np.sum([weight]) + + + return x_ref,y_ref + + +def main_score( nhalo_all, x_true_all, y_true_all, x_ref_all, y_ref_all, sky_prediction): + """abstracts the score from the old command-line interface. + sky_prediction is a dx2 array of predicted x,y positions + + -camdp""" + + r=np.array([],dtype=float) # The array which I will log all the calculated radial distances + angle=np.array([],dtype=float) #The array which I will log all the calculated angles + #Load in the sky_ids from the true + num_halos_total=0 #Keep track of how many halos are input into the metric + + + + for selectskyinsolutions, sky in enumerate(sky_prediction): #Loop through each line in result.csv and analyse each one + + + nhalo=int(nhalo_all[selectskyinsolutions])#How many halos in the + #selected sky? + x_true=x_true_all[selectskyinsolutions][0:nhalo] + y_true=y_true_all[selectskyinsolutions][0:nhalo] + + x_predicted=np.array([],dtype=float) + y_predicted=np.array([],dtype=float) + for i in xrange(nhalo): + x_predicted=np.append(x_predicted,float(sky[0])) #get the predicted values + y_predicted=np.append(y_predicted,float(sky[1])) + #The solution file for the test data provides masses + #to calculate the centre of mass where as the Training_halo.csv + #direct provides x_ref y_ref. So in the case of test data + #we need to calculate the ref point from the masses using + #Get_ref() + + x_ref=x_ref_all[selectskyinsolutions] + y_ref=y_ref_all[selectskyinsolutions] + + num_halos_total=num_halos_total+nhalo + + + #Single halo case, this needs to be separately calculated since + #x_ref = x_true + if nhalo == 1: + #What is the radial distance between the true and predicted position + r=np.append(r,np.sqrt( (x_predicted-x_true)**2 \ + + (y_predicted-y_true)**2)) + #What is the angle between the predicted position and true halo position + if (x_predicted-x_true) != 0: + psi = np.arctan((y_predicted-y_true)/(x_predicted-x_true)) + else: psi=0. + theta = convert_to_360([psi], [x_predicted-x_true], [y_predicted-y_true]) + angle=np.append(angle,theta) + + + else: + #r_index_index, contains the radial distances of the predicted to + #true positions. These are found by matching up the true halos to + #the predicted halos such that the average of all the radial distances + #is optimal. it also contains indexes of the halos used which are used to + #show which halo has been mathced to which. + + r_index_index = calc_delta_r(x_predicted, y_predicted, x_true, \ + y_true) + + r=np.append(r,r_index_index[0][0]) + halo_index= r_index_index[1] #The true halos indexes matched with the + predicted_index=r_index_index[2] #predicted halo index + + angle=np.append(angle,calc_theta\ + (x_predicted[predicted_index],\ + y_predicted[predicted_index],\ + x_true[halo_index],\ + y_true[halo_index],x_ref,\ + y_ref)) # Find the angles of the predicted + #position wrt to the halo and + # add to the vector angle + + + # Find what the average distance the estimate is from the halo position + av_r=sum(r)/len(r) + + #In order to quantify the orientation invariance we will express each angle + # as a vector and find the average vector + #R_bar^2=(1/N Sum^Ncos(theta))^2+(1/N Sum^Nsin(theta))**2 + + N = float(num_halos_total) + angle_vec = np.sqrt(( 1.0/N * sum(np.cos(angle)) )**2 + \ + ( 1.0/N * sum(np.sin(angle)) )**2) + + W1=1./1000. #Weight the av_r such that < 1 is a good score > 1 is not so good. + W2=1. + metric = W1*av_r + W2*angle_vec #Weighted metric, weights TBD + print 'Your average distance in pixels you are away from the true halo is', av_r + print 'Your average angular vector is', angle_vec + print 'Your score for the training data is', metric + return metric + + +def main(user_fname, fname): + """ Script to compute the evaluation metric for the Observing Dark Worlds competition. You can run it on your training data to understand how well you have done with the training data. + """ + + r=np.array([],dtype=float) # The array which I will log all the calculated radial distances + angle=np.array([],dtype=float) #The array which I will log all the calculated angles + #Load in the sky_ids from the true + + true_sky_id=[] + sky_loader = c.reader(open(fname, 'rb')) #Load in the sky_ids from the solution file + for row in sky_loader: + true_sky_id.append(row[0]) + + #Load in the true values from the solution file + + nhalo_all=np.loadtxt(fname,usecols=(1,),delimiter=',',skiprows=1) + x_true_all=np.loadtxt(fname,usecols=(4,6,8),delimiter=',',skiprows=1) + y_true_all=np.loadtxt(fname,usecols=(5,7,9),delimiter=',',skiprows=1) + x_ref_all=np.loadtxt(fname,usecols=(2,),delimiter=',',skiprows=1) + y_ref_all=np.loadtxt(fname,usecols=(3,),delimiter=',',skiprows=1) + + + for row in sky_loader: + true_sky_id.append(row[1]) + + + + num_halos_total=0 #Keep track of how many halos are input into the metric + + + sky_prediction = c.reader(open(user_fname, 'rb')) #Open the result.csv + + try: #See if the input file from user has a header on it + #with open('JoyceTest/trivialUnitTest_Pred.txt', 'r') as f: + with open(user_fname, 'r') as f: + header = float((f.readline()).split(',')[1]) #try and make where the + #first input would be + #a float, if succeed it + #is not a header + print 'THE INPUT FILE DOES NOT APPEAR TO HAVE A HEADER' + except : + print 'THE INPUT FILE APPEARS TO HAVE A HEADER, SKIPPING THE FIRST LINE' + + skip_header = sky_prediction.next() + + + for sky in sky_prediction: #Loop through each line in result.csv and analyse each one + sky_id = str(sky[0]) #Get the sky_id of the input + does_it_exist=true_sky_id.count(sky_id) #Is the input sky_id + #from user a real one? + + if does_it_exist > 0: #If it does then find the matching solutions to the sky_id + selectskyinsolutions=true_sky_id.index(sky_id)-1 + else: #Otherwise exit + print 'Sky_id does not exist, formatting problem: ',sky_id + sys.exit(2) + + + nhalo=int(nhalo_all[selectskyinsolutions])#How many halos in the + #selected sky? + x_true=x_true_all[selectskyinsolutions][0:nhalo] + y_true=y_true_all[selectskyinsolutions][0:nhalo] + + x_predicted=np.array([],dtype=float) + y_predicted=np.array([],dtype=float) + for i in xrange(nhalo): + x_predicted=np.append(x_predicted,float(sky[2*i+1])) #get the predicted values + y_predicted=np.append(y_predicted,float(sky[2*i+2])) + #The solution file for the test data provides masses + #to calculate the centre of mass where as the Training_halo.csv + #direct provides x_ref y_ref. So in the case of test data + #we need to calculae the ref point from the masses using + #Get_ref() + + x_ref=x_ref_all[selectskyinsolutions] + y_ref=y_ref_all[selectskyinsolutions] + + num_halos_total=num_halos_total+nhalo + + + #Single halo case, this needs to be separately calculated since + #x_ref = x_true + if nhalo == 1: + #What is the radial distance between the true and predicted position + r=np.append(r,np.sqrt( (x_predicted-x_true)**2 \ + + (y_predicted-y_true)**2)) + #What is the angle between the predicted position and true halo position + if (x_predicted-x_true) != 0: + psi = np.arctan((y_predicted-y_true)/(x_predicted-x_true)) + else: psi=0. + theta = convert_to_360([psi], [x_predicted-x_true], [y_predicted-y_true]) + angle=np.append(angle,theta) + + + else: + #r_index_index, contains the radial distances of the predicted to + #true positions. These are found by matching up the true halos to + #the predicted halos such that the average of all the radial distances + #is optimal. it also contains indexes of the halos used which are used to + #show which halo has been mathced to which. + + r_index_index = calc_delta_r(x_predicted, y_predicted, x_true, \ + y_true) + + r=np.append(r,r_index_index[0][0]) + halo_index= r_index_index[1] #The true halos indexes matched with the + predicted_index=r_index_index[2] #predicted halo index + + angle=np.append(angle,calc_theta\ + (x_predicted[predicted_index],\ + y_predicted[predicted_index],\ + x_true[halo_index],\ + y_true[halo_index],x_ref,\ + y_ref)) # Find the angles of the predicted + #position wrt to the halo and + # add to the vector angle + + + # Find what the average distance the estimate is from the halo position + av_r=sum(r)/len(r) + + #In order to quantify the orientation invariance we will express each angle + # as a vector and find the average vector + #R_bar^2=(1/N Sum^Ncos(theta))^2+(1/N Sum^Nsin(theta))**2 + + N = float(num_halos_total) + angle_vec = np.sqrt(( 1.0/N * sum(np.cos(angle)) )**2 + \ + ( 1.0/N * sum(np.sin(angle)) )**2) + + W1=1./1000. #Weight the av_r such that < 1 is a good score > 1 is not so good. + W2=1. + metric = W1*av_r + W2*angle_vec #Weighted metric, weights TBD + print 'Your average distance in pixels you are away from the true halo is', av_r + print 'Your average angular vector is', angle_vec + print 'Your score for the training data is', metric + + +if __name__ == "__main__": + #For help just typed 'python DarkWorldsMetric.py -h' + + parser = ap.ArgumentParser(description='Work out the Metric for your input file') + parser.add_argument('inputfile',type=str,nargs=1,help='Input file of halo positions. Needs to be in the format SkyId,halo_x1,haloy1,halox_2,halo_y2,halox3,halo_y3 ') + parser.add_argument('reffile',type=str,nargs=1,help='This should point to Training_halos.csv') + args = parser.parse_args() + + user_fname=args.inputfile[0] + filename = (args.reffile[0]).count('Training_halos.csv') + if filename == 0: + fname=args.reffile[0]+str('Training_halos.csv') + else: + fname=args.reffile[0] + + main(user_fname, fname) + diff --git a/Chapter5_LossFunctions/LossFunctions.ipynb b/Chapter5_LossFunctions/LossFunctions.ipynb index 41f4a2db..366a3143 100644 --- a/Chapter5_LossFunctions/LossFunctions.ipynb +++ b/Chapter5_LossFunctions/LossFunctions.ipynb @@ -1,1651 +1,1651 @@ -{ - "metadata": { - "name": "" - }, - "nbformat": 3, - "nbformat_minor": 0, - "worksheets": [ - { - "cells": [ - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "# Chapter 5\n", - "____\n", - "### Would you rather lose an arm or a leg?" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Statisticians can be a sour bunch. Instead of considering their winnings, they only measure how much they have lost. In fact, they consider their wins as *negative losses*. But what's interesting is *how they measure their losses.*\n", - "\n", - "For example, consider the following example:\n", - "\n", - "> A meteorologist is predicting the probability of a possible hurricane striking his city. He estimates, with 95% confidence, that the probability of it *not* striking is between 99% - 100%. He is very happy with his precision and advises the city that a major evacuation is unnecessary. Unfortunately, the hurricane does strike and the city is flooded. \n", - "\n", - "This stylized example shows the flaw in using a pure accuracy metric to measure outcomes. Using a measure that emphasizes estimation accuracy, while an appealing and *objective* thing to do, misses the point of why you are even performing the statistical inference in the first place: results of inference. The author Nassim Taleb of *The Black Swan* and *Antifragility* stresses the importance of the *payoffs* of decisions, *not the accuracy*. Taleb distills this quite succinctly: \"I would rather be vaguely right than very wrong.\" " - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Loss Functions\n", - "\n", - "We introduce what statisticians and decision theorists call *loss functions*. A loss function is a function of the true parameter, and an estimate of that parameter\n", - "\n", - "$$ L( \\theta, \\hat{\\theta} ) = f( \\theta, \\hat{\\theta} )$$\n", - "\n", - "The important point of loss functions is that it measures how *bad* our current estimate is: the larger the loss, the worse the estimate is according to the loss function. A simple, and very common, example of a loss function is the *squared-error loss*:\n", - "\n", - "$$ L( \\theta, \\hat{\\theta} ) = ( \\theta - \\hat{\\theta} )^2$$\n", - "\n", - "The squared-error loss function is used in estimators like linear regression, UMVUEs and many areas of machine learning. We can also consider an asymmetric squared-error loss function, something like:\n", - "\n", - "$$ L( \\theta, \\hat{\\theta} ) = \\begin{cases} ( \\theta - \\hat{\\theta} )^2 & \\hat{\\theta} \\lt \\theta \\\\\\\\ c( \\theta - \\hat{\\theta} )^2 & \\hat{\\theta} \\ge \\theta, \\;\\; 0\\lt c \\lt 1 \\end{cases}$$\n", - "\n", - "\n", - "which represents that estimating a value larger than the true estimate is preferable to estimating a value below. A situation where this might be useful is in estimating web traffic for the next month, where an over-estimated outlook is preferred so as to avoid an underallocation of server resources. \n", - "\n", - "A negative property about the squared-error loss is that it puts a disproportionate emphasis on large outliers. This is because the loss increases quadratically, and not linearly, as the estimate moves away. That is, the penalty of being three units away is much less than being five units away, but the penalty is not much greater than being one unit away, though in both cases the magnitude of difference is the same:\n", - "\n", - "$$ \\frac{1^2}{3^2} \\lt \\frac{3^2}{5^2}, \\;\\; \\text{although} \\;\\; 3-1 = 5-3 $$\n", - "\n", - "This loss function imposes that large errors are *very* bad. A more *robust* loss function that increases linearly with the difference is the *absolute-loss*\n", - "\n", - "$$ L( \\theta, \\hat{\\theta} ) = | \\theta - \\hat{\\theta} | $$\n", - "\n", - "Other popular loss functions include:\n", - "\n", - "- $ L( \\theta, \\hat{\\theta} ) = \\mathbb{1}_{ \\hat{\\theta} \\neq \\theta } $ is the zero-one loss often used in machine learning classification algorithms.\n", - "- $ L( \\theta, \\hat{\\theta} ) = -\\hat{\\theta}\\log( \\theta ) - (1-\\hat{ \\theta})\\log( 1 - \\theta ), \\; \\; \\hat{\\theta} \\in {0,1}, \\; \\theta \\in [0,1]$, called the *log-loss*, also used in machine learning. \n", - "\n", - "Historically, loss functions have been motivated from 1) mathematical convenience, and 2) they are robust to application, i.e., they are objective measures of loss. The first reason has really held back the full breadth of loss functions. With computers being agnostic to mathematical convenience, we are free to design our own loss functions, which we take full advantage of later in this Chapter.\n", - "\n", - "With respect to the second point, the above loss functions are indeed objective, in that they are most often a function of the difference between estimate and true parameter, independent of signage or payoff of choosing that estimate. This last point, its independence of payoff, causes quite pathological results though. Consider our hurricane example above: the statistician equivalently predicted that the probability of the hurricane striking was between 0% to 1%. But if he had ignored being precise and instead focused on outcomes (99% chance of no flood, 1% chance of flood), he might have advised differently. \n", - "\n", - "By shifting our focus from trying to be incredibly precise about parameter estimation to focusing on the outcomes of our parameter estimation, we can customize our estimates to be optimized for our application. This requires us to design new loss functions that reflect our goals and outcomes. Some examples of more interesting loss functions:\n", - "\n", - "\n", - "- $ L( \\theta, \\hat{\\theta} ) = \\frac{ | \\theta - \\hat{\\theta} | }{ \\theta(1-\\theta) }, \\; \\; \\hat{\\theta}, \\theta \\in [0,1] $ emphasizes an estimate closer to 0 or 1 since if the true value $\\theta$ is near 0 or 1, the loss will be *very* large unless $\\hat{\\theta}$ is similarly close to 0 or 1. \n", - "This loss function might be used by a political pundit who's job requires him or her to give confident \"Yes/No\" answers. This loss reflects that if the true parameter is close to 1 (for example, if a political outcome is very likely to occur), he or she would want to strongly agree as to not look like a skeptic. \n", - "\n", - "- $L( \\theta, \\hat{\\theta} ) = 1 - \\exp \\left( -(\\theta - \\hat{\\theta} )^2 \\right) $ is bounded between 0 and 1 and reflects that the user is indifferent to sufficiently-far-away estimates. It is similar to the zero-one loss above, but not quite as penalizing to estimates that are close to the true parameter. \n", - "- Complicated non-linear loss functions can programmed: \n", - "\n", - " def loss(true_value, estimate):\n", - " if estimate*true_value > 0:\n", - " return abs(estimate - true_value)\n", - " else:\n", - " return abs(estimate)*(estimate - true_value)**2\n", - " \n", - "\n", - "\n", - "- Another example is from the book *The Signal and The Noise*. Weather forecasters have a interesting loss function for their predictions. [2]\n", - "\n", - "\n", - "> People notice one type of mistake — the failure to predict rain — more than other, false alarms. If it rains when it isn't supposed to, they curse the weatherman for ruining their picnic, whereas an unexpectedly sunny day is taken as a serendipitous bonus.\n", - "\n", - "> [The Weather Channel's bias] is limited to slightly exaggerating the probability of rain when it is unlikely to occur — saying there is a 20 percent change when they know it is really a 5 or 10 percent chance — covering their butts in the case of an unexpected sprinkle.\n", - "\n", - "\n", - "As you can see, loss functions can be used for good and evil: with great power, comes great — well you know.\n" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Loss functions in the real world\n", - "\n", - "So far we have been under the unrealistic assumption that we know the true parameter. Of course if we knew the true parameter, bothering to guess an estimate is pointless. Hence a loss function is really only practical when the true parameter is unknown. \n", - "\n", - "In Bayesian inference, we have a mindset that the unknown parameters are really random variables with prior and posterior distributions. Concerning the posterior distribution, a value drawn from it is a *possible* realization of what the true parameter could be. Given that realization, we can compute a loss associated with an estimate. As we have a whole distribution of what the unknown parameter could be (the posterior), we should be more interested in computing the *expected loss* given an estimate. This expected loss is a better estimate of the true loss than comparing the given loss from only a single sample from the posterior.\n", - "\n", - "First it will be useful to explain a *Bayesian point estimate*. The systems and machinery present in the modern world are not built to accept posterior distributions as input. It is also rude to hand someone over a distribution when all the asked for was an estimate. In the course of an individual's day, when faced with uncertainty we still act by distilling our uncertainty down to a single action. Similarly, we need to distill our posterior distribution down to a single value (or vector in the multivariate case). If the value is chosen intelligently, we can avoid the flaw of frequentist methodologies that mask the uncertainty and provide a more informative result.The value chosen, if from a Bayesian posterior, is a Bayesian point estimate. \n", - "\n", - "Suppose $P(\\theta | X)$ is the posterior distribution of $\\theta$ after observing data $X$, then the following function is understandable as the *expected loss of choosing estimate $\\hat{\\theta}$ to estimate $\\theta$*:\n", - "\n", - "$$ l(\\hat{\\theta} ) = E_{\\theta}\\left[ \\; L(\\theta, \\hat{\\theta}) \\; \\right] $$\n", - "\n", - "This is also known as the *risk* of estimate $\\hat{\\theta}$. The subscript $\\theta$ under the expectation symbol is used to denote that $\\theta$ is the unknown (random) variable in the expectation, something that at first can be difficult to consider.\n", - "\n", - "We spent all of last chapter discussing how to approximate expected values. Given $N$ samples $\\theta_i,\\; i=1,...,N$ from the posterior distribution, and a loss function $L$, we can approximate the expected loss of using estimate $\\hat{\\theta}$ by the Law of Large Numbers:\n", - "\n", - "$$\\frac{1}{N} \\sum_{i=1}^N \\;L(\\theta_i, \\hat{\\theta} ) \\approx E_{\\theta}\\left[ \\; L(\\theta, \\hat{\\theta}) \\; \\right] = l(\\hat{\\theta} ) $$\n", - "\n", - "Notice that measuring your loss via an *expected value* uses more information from the distribution than the MAP estimate which, if you recall, will only find the maximum value of the distribution and ignore the shape of the distribution. Ignoring information can over-expose yourself to tail risks, like the unlikely hurricane, and leaves your estimate ignorant of how ignorant you really are about the parameter.\n", - "\n", - "Similarly, compare this with frequentist methods, that traditionally only aim to minimize the error, and do not consider the *loss associated with the result of that error*. Compound this with the fact that frequentist methods are almost guaranteed to never be absolutely accurate. Bayesian point estimates fix this by planning ahead: your estimate is going to be wrong, you might as well err on the right side of wrong." - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "##### Example: Optimizing for the *Showcase* on *The Price is Right*\n", - "\n", - "Bless you if you are ever chosen as a contestant on the Price is Right, for here we will show you how to optimize your final price on the *Showcase*. For those who forget the rules:\n", - "\n", - "\n", - "1. Two contestants compete in *The Showcase*. \n", - "2. Each contestant is shown a unique suite of prizes.\n", - "3. After the viewing, the contestants are asked to bid on the price for their unique suite of prizes.\n", - "4. If a bid price is over the actual price, the bid's owner is disqualified from winning.\n", - "5. If a bid price is under the true price by less than $250, the winner is awarded both prizes.\n", - "\n", - "The difficulty in the game is balancing your uncertainty in the prices, keeping your bid low enough so as to not bid over, and trying to bid close to the price.\n", - "\n", - "Suppose we have recorded the *Showcases* from previous *The Price is Right* episodes and have *prior* beliefs about what distribution the true price follows. For simplicity, suppose it follows a Normal:\n", - "\n", - "\n", - "$$\\text{True Price} \\sim \\text{Normal}(\\mu_p, \\sigma_p )$$\n", - "\n", - "\n", - "In a later chapter, we will actually use *real Price is Right Showcase data* to form the historical prior, but this requires some advanced PyMC use so we will not use it here. For now, we will assume $\\mu_p = 35 000$ and $\\sigma_p = 7500$.\n", - "\n", - "We need a model of how we should be playing the *Showcase*. For each prize in the prize suite, we have an idea of what it might cost, but this guess could differ significantly from the true price. (Couple this with increased pressure being onstage and you can see why some bids are so wildly off). Let's suppose your beliefs about the prices of prizes also follow Normal distributions:\n", - "\n", - "$$ \\text{Prize}_i \\sim \\text{Normal}(\\mu_i, \\sigma_i ),\\;\\; i=1,2$$\n", - "\n", - "This is really why Bayesian analysis is great: we can specify what we think a fair price is through the $\\mu_i$ parameter, and express uncertainty of our guess in the $\\sigma_i$ parameter. \n", - "\n", - "We'll assume two prizes per suite for brevity, but this can be extended to any number. \n", - "The true price of the prize suite is then given by $\\text{Prize}_1 + \\text{Prize}_2 + \\epsilon$, \n", - "where $\\epsilon$ is some error term.\n", - "\n", - "We are interested in the updated $\\text{True Price}$ given we have observed both prizes and have belief distributions about them. We can perform this using PyMC. \n", - "\n", - "Lets make some values concrete. Suppose there are two prizes in the observed prize suite: \n", - "\n", - "1. A trip to wonderful Toronto, Canada! \n", - "2. A lovely new snowblower!\n", - "\n", - "We have some guesses about the true prices of these objects, but we are also pretty uncertain about them. I can express this uncertainty through the parameters of the Normals:\n", - "\n", - "\n", - "\\begin{align}\n", - "& \\text{snowblower} \\sim \\text{Normal}(3 000, 500 )\\\\\\\\\n", - "& \\text{Toronto} \\sim \\text{Normal}(12 000, 3000 )\\\\\\\\\n", - "\\end{align}\n", - "\n", - "For example, I believe that the true price of the trip to Toronto is 12 000 dollars, and that there is a 68.2% chance the price falls 1 standard deviation away from this, i.e. my confidence is that there is a 68.2% chance the trip is in [9 000, 15 000].\n", - "\n", - "We can create some PyMC code to perform inference on the true price of the suite." - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "%matplotlib inline\n", - "import scipy.stats as stats\n", - "from IPython.core.pylabtools import figsize\n", - "import numpy as np\n", - "import matplotlib.pyplot as plt\n", - "\n", - "figsize(12.5, 9)\n", - "\n", - "norm_pdf = stats.norm.pdf\n", - "\n", - "plt.subplot(311)\n", - "x = np.linspace(0, 60000, 200)\n", - "sp1 = plt.fill_between(x, 0, norm_pdf(x, 35000, 7500),\n", - " color=\"#348ABD\", lw=3, alpha=0.6,\n", - " label=\"historical total prices\")\n", - "p1 = plt.Rectangle((0, 0), 1, 1, fc=sp1.get_facecolor()[0])\n", - "plt.legend([p1], [sp1.get_label()])\n", - "\n", - "plt.subplot(312)\n", - "x = np.linspace(0, 10000, 200)\n", - "sp2 = plt.fill_between(x, 0, norm_pdf(x, 3000, 500),\n", - " color=\"#A60628\", lw=3, alpha=0.6,\n", - " label=\"snowblower price guess\")\n", - "\n", - "p2 = plt.Rectangle((0, 0), 1, 1, fc=sp2.get_facecolor()[0])\n", - "plt.legend([p2], [sp2.get_label()])\n", - "\n", - "plt.subplot(313)\n", - "x = np.linspace(0, 25000, 200)\n", - "sp3 = plt.fill_between(x, 0, norm_pdf(x, 12000, 3000),\n", - " color=\"#7A68A6\", lw=3, alpha=0.6,\n", - " label=\"Trip price guess\")\n", - "plt.autoscale(tight=True)\n", - "p3 = plt.Rectangle((0, 0), 1, 1, fc=sp3.get_facecolor()[0])\n", - "plt.legend([p3], [sp3.get_label()]);" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "metadata": {}, - "output_type": "display_data", - "png": 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Lt1/lhQ9dtHvDNHtCdPtVcuxmHDk2TAaFpr3vjXUTxQhq2vseaVYjZ+baMRkV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\nM8j4fFsvx/7fOS59MUgikVtBgRDZdMNqx6k+kExlu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- "text": [ - "" - ] - } - ], - "prompt_number": 7 - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "import pymc as pm\n", - "\n", - "data_mu = [3e3, 12e3]\n", - "\n", - "data_std = [5e2, 3e3]\n", - "\n", - "mu_prior = 35e3\n", - "std_prior = 75e2\n", - "\n", - "true_price = pm.Normal(\"true_price\", mu_prior, 1.0 / std_prior ** 2)\n", - "\n", - "\n", - "prize_1 = pm.Normal(\"first_prize\", data_mu[0], 1.0 / data_std[0] ** 2)\n", - "prize_2 = pm.Normal(\"second_prize\", data_mu[1], 1.0 / data_std[1] ** 2)\n", - "price_estimate = prize_1 + prize_2\n", - "\n", - "\n", - "@pm.potential\n", - "def error(true_price=true_price, price_estimate=price_estimate):\n", - " return pm.normal_like(true_price, price_estimate, 1 / (3e3) ** 2)\n", - "\n", - "\n", - "mcmc = pm.MCMC([true_price, prize_1, prize_2, price_estimate, error])\n", - "mcmc.sample(50000, 10000)\n", - "\n", - "price_trace = mcmc.trace(\"true_price\")[:]" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "output_type": "stream", - "stream": "stdout", - "text": [ - " \r", - "[****************100%******************] 50000 of 50000 complete" - ] - }, - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "\n" - ] - } - ], - "prompt_number": 8 - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "figsize(12.5, 4)\n", - "\n", - "import scipy.stats as stats\n", - "\n", - "x = np.linspace(5000, 40000)\n", - "plt.plot(x, stats.norm.pdf(x, 35000, 7500), c=\"k\", lw=2,\n", - " label=\"prior dist. of suite price\")\n", - "\n", - "_hist = plt.hist(price_trace, bins=35, normed=True, histtype=\"stepfilled\")\n", - "plt.title(\"Posterior of the true price estimate\")\n", - "plt.vlines(mu_prior, 0, 1.1 * np.max(_hist[0]), label=\"prior's mean\",\n", - " linestyles=\"--\")\n", - "plt.vlines(price_trace.mean(), 0, 1.1 * np.max(_hist[0]),\n", - " label=\"posterior's mean\", linestyles=\"-.\")\n", - "plt.legend(loc=\"upper left\")" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "metadata": {}, - "output_type": "pyout", - "prompt_number": 9, - "text": [ - "" - ] - }, - { - "metadata": {}, - "output_type": "display_data", - "png": 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qR8vK6NixY/D19a12PjMzs86529rm4+OD9evXY8CAAdoOhRpAGw8tq0lTv7+J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\nysql9u9bXyuxoZz4vEC8uF4zcT0mhmvGlveaieGYuF4zEtCLBn9P9Kf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- "text": [ - "" - ] - } - ], - "prompt_number": 9 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Notice that because of our two observed prizes and subsequent guesses (including uncertainty about those guesses), we shifted our mean price estimate down about $15 000 dollars from the previous mean price.\n", - "\n", - "A frequentist, seeing the two prizes and having the same beliefs about their prices, would bid $\\mu_1 + \\mu_2 = 35000$, regardless of any uncertainty. Meanwhile, the *naive Bayesian* would simply pick the mean of the posterior distribution. But we have more information about our eventual outcomes; we should incorporate this into our bid. We will use the loss function above to find the *best* bid (*best* according to our loss).\n", - "\n", - "What might a contestant's loss function look like? I would think it would look something like:\n", - "\n", - " def showcase_loss(guess, true_price, risk=80000):\n", - " if true_price < guess:\n", - " return risk\n", - " elif abs(true_price - guess) <= 250:\n", - " return -2*np.abs(true_price)\n", - " else:\n", - " return np.abs(true_price - guess - 250)\n", - "\n", - "where `risk` is a parameter that defines of how bad it is if your guess is over the true price. A lower `risk` means that you are more comfortable with the idea of going over. If we do bid under and the difference is less than $250, we receive both prizes (modeled here as receiving twice the original prize). Otherwise, when we bid under the `true_price` we want to be as close as possible, hence the `else` loss is a increasing function of the distance between the guess and true price." - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "For every possible bid, we calculate the *expected loss* associated with that bid. We vary the `risk` parameter to see how it affects our loss:" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "figsize(12.5, 7)\n", - "# numpy friendly showdown_loss\n", - "\n", - "\n", - "def showdown_loss(guess, true_price, risk=80000):\n", - " loss = np.zeros_like(true_price)\n", - " ix = true_price < guess\n", - " loss[~ix] = np.abs(guess - true_price[~ix])\n", - " close_mask = [abs(true_price - guess) <= 250]\n", - " loss[close_mask] = -2 * true_price[close_mask]\n", - " loss[ix] = risk\n", - " return loss\n", - "\n", - "\n", - "guesses = np.linspace(5000, 50000, 70)\n", - "risks = np.linspace(30000, 150000, 6)\n", - "expected_loss = lambda guess, risk: \\\n", - " showdown_loss(guess, price_trace, risk).mean()\n", - "\n", - "for _p in risks:\n", - " results = [expected_loss(_g, _p) for _g in guesses]\n", - " plt.plot(guesses, results, label=\"%d\" % _p)\n", - "\n", - "plt.title(\"Expected loss of different guesses, \\nvarious risk-levels of \\\n", - "overestimating\")\n", - "plt.legend(loc=\"upper left\", title=\"Risk parameter\")\n", - "plt.xlabel(\"price bid\")\n", - "plt.ylabel(\"expected loss\")\n", - "plt.xlim(5000, 30000);" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "metadata": {}, - "output_type": "display_data", - "png": 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EBQUhIiJC4VfFdu/eHf7+/ujfvz+WL18ODw8PPHz4EKdPn4aOjg5Gjx4NAFBX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\nGNFTBlwVBUTj2SwavngDY8YmFEs9AOqQKAIG/5KAIXfz1dF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ibKOnUql4+OGH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\nxe23387jjz8OQDqd5qGHHmLnzp0Eg0GeffZZ6usnt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Xk5nwuNaQmaBpI0dsc50BPn/feb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\noDlSqGo/arYdEkchsh8l24YihhurjvoLqhpayTSU4lrMwkpSvmLi7gLCT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- "text": [ - "" - ] - } - ], - "prompt_number": 11 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### Minimizing our losses\n", - "\n", - "It would be wise to choose the estimate that minimizes our expected loss. This corresponds to the minimum point on each of the curves above. More formally, we would like to minimize our expected loss by finding the solution to\n", - "\n", - "$$ \\text{arg} \\min_{\\hat{\\theta}} \\;\\;E_{\\theta}\\left[ \\; L(\\theta, \\hat{\\theta}) \\; \\right] $$\n", - "\n", - "The minimum of the expected loss is called the *Bayes action*. We can solve for the Bayes action using Scipy's optimization routines. The function in `fmin` in `scipy.optimize` module uses an intelligent search to find a minimum (not necessarily a *global* minimum) of any uni- or multivariate function. For most purposes, `fmin` will provide you with a good answer. \n", - "\n", - "We'll compute the minimum loss for the *Showcase* example above:\n" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "import scipy.optimize as sop\n", - "\n", - "ax = plt.subplot(111)\n", - "\n", - "\n", - "for _p in risks:\n", - " _color = ax._get_lines.color_cycle.next()\n", - " _min_results = sop.fmin(expected_loss, 15000, args=(_p,), disp=False)\n", - " _results = [expected_loss(_g, _p) for _g in guesses]\n", - " plt.plot(guesses, _results, color=_color)\n", - " plt.scatter(_min_results, 0, s=60,\n", - " color=_color, label=\"%d\" % _p)\n", - " plt.vlines(_min_results, 0, 120000, color=_color, linestyles=\"--\")\n", - " print \"minimum at risk %d: %.2f\" % (_p, _min_results)\n", - "\n", - "plt.title(\"Expected loss & Bayes actions of different guesses, \\n \\\n", - "various risk-levels of overestimating\")\n", - "plt.legend(loc=\"upper left\", scatterpoints=1, title=\"Bayes action at risk:\")\n", - "plt.xlabel(\"price guess\")\n", - "plt.ylabel(\"expected loss\")\n", - "plt.xlim(7000, 30000)\n", - "plt.ylim(-1000, 80000)" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "minimum at risk 30000: 13945.51\n", - "minimum at risk 54000: 12716.02" - ] - }, - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "\n", - "minimum at risk 78000: 12063.18" - ] - }, - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "\n", - "minimum at risk 102000: 11369.82" - ] - }, - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "\n", - "minimum at risk 126000: 11273.77" - ] - }, - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "\n", - "minimum at risk 150000: 11273.77" - ] - }, - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "\n" - ] - }, - { - "metadata": {}, - "output_type": "pyout", - "prompt_number": 13, - "text": [ - "(-1000, 80000)" - ] - }, - { - "metadata": {}, - "output_type": "display_data", - "png": 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h5+eH/Pz8Wvf5RdTVtkDF+x/PnleVv1fuf7du3ZCamoqzZ88iMDAQCxYswOLFi3Ht2rUq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3HwRz9Id5zenFVroGa9ma+Lb0AnRXBqYyaX3yNprTh+hrew3ftj/T2ttAS08d3b6xAQaApukU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\nD/8nA4ER+2N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- "text": [ - "" - ] - } - ], - "prompt_number": 13 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "As intuition suggests, as we decrease the risk threshold (care about overbidding less), we increase our bid, willing to edge closer to the true price. It is interesting how far away our optimized loss is from the posterior mean, which was about 20 000. \n", - "\n", - "Suffice to say, in higher dimensions being able to eyeball the minimum expected loss is impossible. Hence why we require use of Scipy's `fmin` function.\n", - "\n" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "______\n", - "\n", - "### Shortcuts\n", - "\n", - "For some loss functions, the Bayes action is known in closed form. We list some of them below:\n", - "\n", - "- If using the mean-squared loss, the Bayes action is the mean of the posterior distribution, i.e. the value \n", - "$$ E_{\\theta}\\left[ \\theta \\right] $$\n", - "\n", - "> minimizes $E_{\\theta}\\left[ \\; (\\theta - \\hat{\\theta})^2 \\; \\right]$. Computationally this requires us to calculate the average of the posterior samples [See chapter 4 on The Law of Large Numbers]\n", - "\n", - "- Whereas the *median* of the posterior distribution minimizes the expected absolute-loss. The sample median of the posterior samples is an appropriate and very accurate approximation to the true median.\n", - "\n", - "- In fact, it is possible to show that the MAP estimate is the solution to using a loss function that shrinks to the zero-one loss.\n", - "\n", - "\n", - "Maybe it is clear now why the first-introduced loss functions are used most often in the mathematics of Bayesian inference: no complicated optimizations are necessary. Luckily, we have machines to do the complications for us. \n", - "\n", - "## Machine Learning via Bayesian Methods\n", - "\n", - "Whereas frequentist methods strive to achieve the best precision about all possible parameters, machine learning cares to achieve the best *prediction* among all possible parameters. Of course, one way to achieve accurate predictions is to aim for accurate predictions, but often your prediction measure and what frequentist methods are optimizing for are very different. \n", - "\n", - "For example, least-squares linear regression is the most simple active machine learning algorithm. I say active as it engages in some learning, whereas predicting the sample mean is technically *simpler*, but is learning very little if anything. The loss that determines the coefficients of the regressors is a squared-error loss. On the other hand, if your prediction loss function (or score function, which is the negative loss) is not a squared-error, like AUC, ROC, precision, etc., your least-squares line will not be optimal for the prediction loss function. This can lead to prediction results that are suboptimal. \n", - "\n", - "Finding Bayes actions is equivalent to finding parameters that optimize *not parameter accuracy* but an arbitrary performance measure, however we wish to define performance (loss functions, AUC, ROC, precision/recall etc.).\n", - "\n", - "The next two examples demonstrate these ideas. The first example is a linear model where we can choose to predict using the least-squares loss or a novel, outcome-sensitive loss. \n", - "\n", - "The second example is adapted from a Kaggle data science project. The loss function associated with our predictions is incredibly complicated. \n", - "\n" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "\n", - "##### Example: Financial prediction\n", - "\n", - "\n", - "Suppose the future return of a stock price is very small, say 0.01 (or 1%). We have a model that predicts the stock's future price, and our profit and loss is directly tied to us acting on the prediction. How should we measure the loss associated with the model's predictions, and subsequent future predictions? A squared-error loss is agnostic to the signage and would penalize a prediction of -0.01 equally as bad a prediction of 0.03:\n", - "\n", - "$$ (0.01 - (-0.01))^2 = (0.01 - 0.03)^2 = 0.004$$\n", - "\n", - "If you had made a bet based on your model's prediction, you would have earned money with a prediction of 0.03, and lost money with a prediction of -0.01, yet our loss did not capture this. We need a better loss that takes into account the *sign* of the prediction and true value. We design a new loss that is better for financial applications below:" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "figsize(12.5, 4)\n", - "\n", - "\n", - "def stock_loss(true_return, yhat, alpha=100.):\n", - " if true_return * yhat < 0:\n", - " # opposite signs, not good\n", - " return alpha * yhat ** 2 - np.sign(true_return) * yhat \\\n", - " + abs(true_return)\n", - " else:\n", - " return abs(true_return - yhat)\n", - "\n", - "\n", - "true_value = .05\n", - "pred = np.linspace(-.04, .12, 75)\n", - "\n", - "plt.plot(pred, [stock_loss(true_value, _p) for _p in pred],\n", - " label=\"Loss associated with\\n prediction if true value = 0.05\", lw=3)\n", - "plt.vlines(0, 0, .25, linestyles=\"--\")\n", - "\n", - "plt.xlabel(\"prediction\")\n", - "plt.ylabel(\"loss\")\n", - "plt.xlim(-0.04, .12)\n", - "plt.ylim(0, 0.25)\n", - "\n", - "true_value = -.02\n", - "plt.plot(pred, [stock_loss(true_value, _p) for _p in pred], alpha=0.6,\n", - " label=\"Loss associated with\\n prediction if true value = -0.02\", lw=3)\n", - "plt.legend()\n", - "plt.title(\"Stock returns loss if true value = 0.05, -0.02\");" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "metadata": {}, - "output_type": "display_data", - "png": 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0dOLj41GpVDRr1gxr68IX1NVqNadPn+bu3bvUq1cPT09PANauXcuoUaNwdHTE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\nmhf1KAeSPyPF1tnZg4aXt8FjswMAJPFK5K6/DdIk1bDnktHRecsfii1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vrKyETqeDyWTC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- "text": [ - "" - ] - } - ], - "prompt_number": 15 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Note the change in the shape of the loss as the prediction crosses zero. This loss reflects that the user really does not want to guess the wrong sign, especially be wrong *and* a large magnitude. \n", - "\n", - "Why would the user care about the magnitude? Why is the loss not 0 for predicting the correct sign? Surely, if the return is 0.01 and we bet millions we will still be (very) happy.\n", - "\n", - "Financial institutions treat downside risk, as in predicting a lot on the wrong side, and upside risk, as in predicting a lot on the right side, similarly. Both are seen as risky behaviour and discouraged. Hence why we have an increasing loss as we move further away from the true price. (With less extreme loss in the direction of the correct sign.)\n", - "\n", - "We will perform a regression on a trading signal that we believe predicts future returns well. Our dataset is artificial, as most financial data is not even close to linear. Below, we plot the data along with the least-squares line." - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "# Code to create artificial data\n", - "N = 100\n", - "X = 0.025 * np.random.randn(N)\n", - "Y = 0.5 * X + 0.01 * np.random.randn(N)\n", - "\n", - "ls_coef_ = np.cov(X, Y)[0, 1] / np.var(X)\n", - "ls_intercept = Y.mean() - ls_coef_ * X.mean()\n", - "\n", - "plt.scatter(X, Y, c=\"k\")\n", - "plt.xlabel(\"trading signal\")\n", - "plt.ylabel(\"returns\")\n", - "plt.title(\"Empirical returns vs trading signal\")\n", - "plt.plot(X, ls_coef_ * X + ls_intercept, label=\"Least-squares line\")\n", - "plt.xlim(X.min(), X.max())\n", - "plt.ylim(Y.min(), Y.max())\n", - "plt.legend(loc=\"upper left\");" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "metadata": {}, - "output_type": "display_data", - "png": 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OVreTk5Px8vIqs09KSgqenp4afZycnHj++ec5evQoHTt2fOg4I0aMwMfHR923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\n3NxcuLi4wMPDo4VR6hd9z3VOTg5mzpyJ+/drpjGdO3cuPvvsM0gkEh1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- "text": [ - "" - ] - } - ], - "prompt_number": 17 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "We perform a simple Bayesian linear regression on this dataset. We look for a model like:\n", - "\n", - "$$ R = \\alpha + \\beta x + \\epsilon$$\n", - "\n", - "where $\\alpha, \\beta$ are our unknown parameters and $\\epsilon \\sim \\text{Normal}(0, 1/\\tau)$. The most common priors on $\\beta$ and $\\alpha$ are Normal priors. We will also assign a prior on $\\tau$, so that $\\sigma = 1/\\sqrt{\\tau}$ is uniform over 0 to 100 (equivalently then $\\tau = 1/\\text{Uniform}(0, 100)^2$)." - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "import pymc as pm\n", - "from pymc.Matplot import plot as mcplot\n", - "\n", - "std = pm.Uniform(\"std\", 0, 100, trace=False) # this needs to be explained.\n", - "\n", - "\n", - "@pm.deterministic\n", - "def prec(U=std):\n", - " return 1.0 / (U) ** 2\n", - "\n", - "beta = pm.Normal(\"beta\", 0, 0.0001)\n", - "alpha = pm.Normal(\"alpha\", 0, 0.0001)\n", - "\n", - "\n", - "@pm.deterministic\n", - "def mean(X=X, alpha=alpha, beta=beta):\n", - " return alpha + beta * X\n", - "\n", - "obs = pm.Normal(\"obs\", mean, prec, value=Y, observed=True)\n", - "mcmc = pm.MCMC([obs, beta, alpha, std, prec])\n", - "\n", - "mcmc.sample(100000, 80000)\n", - "mcplot(mcmc)" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "output_type": "stream", - "stream": "stdout", - "text": [ - " \r", - "[****************100%******************] 100000 of 100000 complete" - ] - }, - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "Plotting prec\n", - "Plotting" - ] - }, - { - "output_type": "stream", - "stream": "stdout", - "text": [ - " beta\n", - "Plotting" - ] - }, - { - "output_type": "stream", - "stream": "stdout", - "text": [ - " alpha\n", - "\n" - ] - }, - { - "metadata": {}, - "output_type": "display_data", - "png": 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tqKiIwMBAGhoaqKysxNdXd/LvC1vewLNXc5LrTl270y0wTPVBUzps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sDAzDoEuXLsjIyEBYWBi++eYbo9qY7du3G7VHt4fX1tuaL3I+rq96iQvFHnPr\nJ/VGi+bVUK+05j7d422tvfhuHyFu6+67cOECrIXV+dL9IiwsLNTSQACAv78/evToAVdXV7i6uuKZ\nZ57BxYsXIZFITOZVoXpwNabeQqNOKAjVjc7obAPAfy7fQYFbILr0f3yNinq9H4Y52xERMuQ/XjhZ\nta2i+wDZ45AAJUbzqziWVw6gB7r0f6IDMNqw17IAQMvRBIDwMU+jS4EXgBadlm5+Yz/8w1fv4cCV\nu5B4+qG4sh49OjdrlUe1PqYqf1ZxFf704028NmogdmXIoepr0T3/gGFhSG96sqi0ufWrcr5lYWPQ\n5dqTXpSIiAitYS1T5QsZHo6Igd210t+8Xwdcv2a0PjRF1WwPymalEoNHhGvZ15r7R/f8VfVNwLUc\nveOllfWImBOBxvxyIDtZzx5T9uoeX7r/GmJCghGtUT+q40WV9Rjk466uj4d1jfBydUFERAQOV91A\nyeNeZc3zKZXs5cstq9G4f6rxxnfXWNr/ybavrzsiIqQQX9PsTbNd11hJSQkWL16M5uZmNDc3Y+HC\nhZg4cSIWLVqE7OxsMAyDvn37YufOnQCAkJAQzJ07FyEhIRCJRNi+fbv6/t2+fTteeeUV1NXVYerU\nqZgyZYrN7OYK3XuGb8gedoRmDyA8m4RmDxewOl8jR45EXl4eCgoK4Ofnh6SkJCQmJmqlmTlzJpYv\nXw6FQoH6+npkZGRgzZo1GDBggMm8KiofNaFLJ5HJ2Yu6fHGuRGv7wBW2mWCte9gbipzPJZovrzvV\nDfjrqSehIRbsuYy/TZNC4tnRZE9iS9iDluFRQHsIyBDrH4c52PZLEWs6a7hUUoW1399Qbzc1K5Hy\n231s/7UIm6L76/2gDBVRs9XuVDcg5bf7+CeLKP/Y9fv4JL0Q70/pjyG+HlrHYvddxWujfPFUnxbn\n9o/HbiKT40Webz98hNh9Vw0fVBeQUbd7blkNQloxxAcA+ffr8PHp2xjUqzM8XUXw7PTk5/zhz7cR\nKe0GJ4bBF+dKsPdiGdaN64NJ0m6tHhJcdcj83wKfw46hoaEGv0y//vpro3k2bNiADRs26O0fMWIE\ncnK4X/uSIIj2DavgXiQSYdu2bZg8eTJCQkIwb948BAcHY+fOneqvxqCgIEyZMgVDhgxBeHg4Xn/9\ndfUXpKG8htiaruoh43baWYmZwvu0goeQmwiTYGsSs0vxt59+xyWNWZ7ldU1Ysu8qtv/K3wyrw1ct\nmaH25I3FZmYbAAAgAElEQVRbVd+ktTYnAGxIuYGPTt/Go6ZmbNZwMlXo6tSAFgfu+8ez5Dak5LM6\nXgDwwc+30aBQGoxvdvvhI7z745PYa6Ycr9Y4EN+zzOgTOTG4ca8WSReflGHVoevqnkDNjw/V//dr\nG/Gfy3eMxmADgNjvrhpcHPunmw9w4kY59j7WJT6pO8MFE4hMi7ASvmMiUZwvy+DbHorzxQ8mlxeK\njo5WByNUERcXp7W9du1arF271qy8hjC0mLO11DUq1OJ7U/z5uO2CoRrirsZMQZWQ84tzJfDx6GAw\nfXLuXYzt64Uhvu5a+w/m3sW0oB5wNiOiaWuF/HeNxC4zdUW/Lh319mnGvFIqW35QprqTU288QOqN\nBwju2VndqydkqliCoDIA4g/8BkBbwPvr7xV4OsDLYJ63j9zA7w8e4eb9Oqwd18ciWzad1HdAlUol\nsoqNxEPj0PsiR679QjGjHAtqL34QWIR77h7ZC/Zc1j5zK07dYEXAVTY+NxAlH2CPCr/WQJyZbb8U\n4ZBFPVPcwdUyNyrqGhWsPZUP6iwPYGtvGpqaUcqypJSxOvvT8VvYf1m7l1B1u/7+ePg4p5UBZHUx\ntuQR0XYQmj6G7GFHaPYAwrNJaPZwgaAW1k4rqODsXOYsiWOMqvomXCqpRspv1sXaMoZmdHhtwTK7\nR2Mo/lL+ffvEqNKFgXYPnqHjptD8Qb3yba5WkFZHZPqXF81OqytU33FGjlmPF4y3HUqteG/6R20D\n1446QRCEoyOYni9LxfYWn9+CtJ/+UoQ/Hb+FDI7F2CqM9WKYCtq3/PGQlSZHr5cbXD9QE0PLCXHB\nimRtAbY1TWjK8apoxZqGxhauvl/baJYekOs7sqqePdaa5vW2phdy/psormQPrmss/hfhWPCtjyHN\nl2XwbQ9pvvhBMD1fu4wMxan4WScEhaXk32df21GTExwOzdwqr8MP1+5h4XBf3K9tRFW9QmupJE3t\njyluGCnD/54oYM23+nAeFgz1Ntdk82AYvZf1mdtPei4LK+rh0dH47VVW3WCW5ktFggGBvikMLVwN\n6A9JG8OW3wOm2v3o9XLMDLGsJ+ybCyUm01izdqkl2PpjihAupCFyLKi9+EEwzte+nDumE1nBzgx+\nZgyq1r6rqldw6tRZCleaIRUnb+gvwq276DPbEJetaQvv/gaFxuxHM9J/c8H0uphHr5u3eLq1KNpA\n/TsqQtPHkD3sCM0eQHg2Cc0eLhCE89UeJCFyI0OK9lrj73IZt44QFy/XiIgIlFbVs4ZRaC3GZmla\nhu08CEPtruswni16MuzNxXqc9uS0lT3VBGENdY0Ki58rTfTFQNgRQThfdzh5UQqbttATYwsWJeXy\nbYJRuHHgWs+/dGKa/ftSmZGUwuc/l23bs008wZLhfFug0g+phrP4sKe8thErjATIfpCXha5Smd7+\nOismaVmD0NoL4N8mXYRmDxcIwvmyRc+H0DAmGLdE89XWOH7yZwAeJtPxhSmBvDW0pt1N6SKFCgPg\nH0YWLyfaHkLREBn7/dY2NkNkw9+2oyGU9mpvCGa2Y1unjCX+U3vl0FW25aCItkIz9fraFaH1EAjN\nHqF97AqtfgDh2SQ0e7iAnC+eEdqDwJ7UeofwbQJvtKd2v0MfHgRBEFqQ80Xwxu8mFv9ub1i2jqbj\n0EhCZrvCd0wkocf5qszP5tsELfiuH4rzxQ+C0Hy1Z9qz5ovKrl32T38t4ska23KPgre2K0hD5FhQ\ne/GDyZ6vlJQUBAUFQSqVYvPmzXrHT506BU9PT8hkMshkMrz33nvqYwEBARgyZAhkMhnCwsK4tZwg\nCILQQ2j6GKHZI7QPPqHVDyA8m4RmDxew9nwpFAosX74cx48fh1gsxqhRoxATE4Pg4GCtdOPGjcPB\ngwf18jMMg1OnTqFbt27cWt2GENqDwJ5Q2QmCIIj2CGvPV2ZmJgIDAxEQEAAXFxfMnz8fycnJeunY\nlhKhZUYIgiDsB9/6GNJ8WQbf9UOaL35g7fmSy+Xw9/dXb0skEmRkZGilYRgGv/zyC4YOHQqxWIwP\nPvgAISEh6mOTJk2Cs7Mz4uLi8Prrr9ugCI4N6Z6o7ATRlmgvGqK7NQ24WV4HhQWxVLw6idDTvYMN\nrbKc9tJeQoPV+WIY0wv/DB8+HIWFhXBzc8ORI0cwa9YsXL/eElk4PT0dvr6+uHv3LiIjIxEUFISx\nY8dyYzlBEAShh9D0MUKzh6uPnpP5D3Ey37JltP4+Q6rnfAmtfgDh2SQ0e7iA1fkSi8UoLCxUbxcW\nFkIikWil8fB4EqE8Ojoa8fHxKC8vR7du3eDr6wsA6NmzJ2bPno3MzEyDztfNpM3o2NUHAODs2hlu\nfoHqH4iqi7itbqv2CcUee2536T9MUPbQtu22AaAq/yLqHzxeMmn4OhAEQbRXGCWLKKupqQkDBw5E\namoq/Pz8EBYWhsTERC3BfVlZGXr16gWGYZCZmYm5c+eioKAAtbW1UCgU8PDwQE1NDaKiorBx40ZE\nRUVpXSM1NRVvX2gPS2sTBKEiYbgSEydO5NsMTkhNTcXw4cP5NkMN3+vgCWFtR3nFI7z676sGj1ky\n5H9uXcs9OvKvqZzY9fcZUoR4u2vtE1p7AfzbpIvQ7Llw4YLVzy/Wni+RSIRt27Zh8uTJUCgUWLJk\nCYKDg7Fz504AQFxcHPbt24cdO3ZAJBLBzc0Ne/fuBQCUlpbiueeeA9DixL300kt6jhfRvrU/VPb2\nWXaibUMaIseC2osfTAZZjY6ORnR0tNa+uLg49f/Lli3DsmXL9PL169cP2dnZevsJgiAI2yGkHgJA\nePYI7aNHaPUDCM8modnDBbS8EM8I7UFgT6jsBEEQRHuEnC+CIIg2BN8xkSjOl2XwXT8U54sfaG1H\nnmnP2h8qe/ssO9G2IQ2RY0HtxQ/U80UQBNGGEJo+Rmj2CO2jR2j1AwjPJqHZwwXkfPGM0B4E9oTK\nThAEQbRHyPkiCIJoQ/CtjyHNl2XwXT+k+eIH0nzxTHvW/lDZ22fZibYNaYgcC2ovfqCeL4IgiDaE\n0PQxQrNHaB89QqsfQHg2Cc0eLiDni2eE9iCwJ1R2giAIoj1CzhdBEEQbgm99DGm+LIPv+iHNFz+Q\n88UzQnsQ2BMqO2ELHj16hPDwcAwbNgwhISF45513AADl5eWIjIzEgAEDEBUVhYcPH6rzbNq0CVKp\nFEFBQTh27Jh6//nz5xEaGgqpVIqVK1favSyOyIoVK0hH5EBQe/EDOV8EQbQpOnXqhJMnTyI7OxuX\nLl3CyZMnkZaWhoSEBERGRuL69euYOHEiEhISAAC5ublISkpCbm4uUlJSEB8fD6VSCQBYunQpdu/e\njby8POTl5SElJYXPopmF0PQxQrNHaEP+QqsfQHg2Cc0eLiDni2eE9iCwJ1R2wla4ubkBABoaGqBQ\nKNC1a1ccPHgQixcvBgAsXrwYBw4cAAAkJydjwYIFcHFxQUBAAAIDA5GRkYGSkhJUVVUhLCwMALBo\n0SJ1HoIgCGsw6XylpKQgKCgIUqkUmzdv1jt+6tQpeHp6QiaTQSaT4S9/+YvZeQmCIGxBc3Mzhg0b\nBm9vb0yYMAGDBg1CWVkZvL29AQDe3t4oKysDABQXF0MikajzSiQSyOVyvf1isRhyudy+BWkFfOtj\nSPNlGXzXD2m++IE1zpdCocDy5ctx/PhxiMVijBo1CjExMQgODtZKN27cOBw8eLBVeds77TneE5W9\nfZbdHjg5OSE7OxsVFRWYPHkyTp48qXWcYRgwDMOTdW0b0g85FtRe/MDqfGVmZiIwMBABAQEAgPnz\n5yM5OVnPgVLpI1qTlyAIwlZ4enpi2rRpOH/+PLy9vVFaWgofHx+UlJSgV69eAFp6tAoLC9V5ioqK\nIJFIIBaLUVRUpLVfLBYbvE58fDx69+6tvmZoaKhap6L6arfXtmofX9cXgj33ahoAdAXwpKdL82NH\n8+NH97i16U1tC6F+zNnWtK2925OTk4OKigoAwO3btxEbGwtrYZSGPKfH7Nu3D0ePHsWuXbsAAP/8\n5z+RkZGBrVu3qtP89NNPeO6559QPqw8++AAhISFm5QWA1NRUvH2BvkAJoj2RMFyJiRMn2uTc9+7d\ng0gkgpeXF+rq6jB58mRs3LgRR48eRffu3bF+/XokJCTg4cOHSEhIQG5uLl588UVkZmZCLpdj0qRJ\nuHHjBhiGQXh4OD755BOEhYVh2rRpWLFiBaZMmaJ1vdTUVAwfPtwmZSFah7ziEV7991Wrz3NuXcs9\nOvKvqVafCwD+PkOKEG93Ts5F8MeFCxesfn6xar7M6ZYfPnw4CgsLcfHiRbz55puYNWuWVQYRBEFY\nQ0lJCZ599lkMGzYM4eHhmDFjBiZOnIi3334bP/74IwYMGIATJ07g7bffBgCEhIRg7ty5CAkJQXR0\nNLZv365+9m3fvh2xsbGQSqUIDAzUc7yECN/6GNJ8WQbf9UOaL35gHXbU7Y4vLCzUEqACgIeHh/r/\n6OhoxMfHo7y8HBKJxGReFTeTNqNjVx8AgLNrZ7j5BXLWxSv07dLT+9pVeTW3NR+CQrDHntu6dcC3\nPfYob1X+RdQ/KG3ZGL4OtiI0NBQXLlzQ29+tWzccP37cYJ4NGzZgw4YNevtHjBiBnJwczm1sy5CG\nyLGg9uIH1mHHpqYmDBw4EKmpqfDz80NYWBgSExO1dFtlZWXo1asXGIZBZmYm5s6di4KCArPyAjTs\n2J6F11T29ll2wLbDjvaGhh2FBw07EraEi2FH1p4vkUiEbdu2YfLkyVAoFFiyZAmCg4Oxc+dOAEBc\nXBz27duHHTt2QCQSwc3NDXv37mXNS2jTnl/AVHaCIAiiPcLqfAEtQ4nR0dFa++Li4tT/L1u2DMuW\nLTM7L0EQBGE7NGfO8YFKP6QazuLbHl2E1uvMd/3othfAv026CM0eLjDpfBG2RWgPAntCZW+fZSfa\nNqQhciyovfiBlhciCIJoQwith0Bo9gjto0do9QMIzyah2cMF5HzxjNAeBPaEyk4QBEG0R8j5IgiC\naEPwHROJ4nxZBt/1Q3G++IE0XzzTnrU/fJR9VYQ//p5WaDqhjWnP7U60bUhD5FhQe/ED9XwR7QqR\nU/uNKUe0D4SmjxGaPUL76BFa/QDCs0lo9nABOV88I7QHgT3ho+wMAwz27mxW2tfD/GxmR3tud4Ig\niPYOOV9Eu4IBg81TA02mWxnhjxeGeNvBIoLgFr71MaT5sgy+64c0X/xAmi+eac/aHz7K7uwEuDjz\n/80hxHafMqA7Uq7f59sMwsEhDZFjQe3FD/y/hQjCjjAwT/Pl16WjjS0RHr292l+Z2yJC08cIzR6h\nffQIrX4A4dkkNHu4gJwvnhHag8Ce8FF2JzPv+IE93GxqR3tud4IgiPYOOV8ELzgzwP+9YPuF1gO7\nu2ptm9vzpWJMb08uzbEZri7W/5SVHNhB8A/f+hjSfFkG3/VDmi9+IM0XzwhR+2MPYkJ6oiDnHADz\nZh62FjcXZ61tSwNNdHXj7ify5lMSbP2lCAD37R4l7Y7k3LtWnYOcL4ILSEPkWFB78YPJz+WUlBQE\nBQVBKpVi8+bNRtOdPXsWIpEI3333nXpfQEAAhgwZAplMhrCwMG4sJtoGHITb6ihqRW8Pj2G+Arq5\nmk7USjxd6TuKaEFo+hih2SO0j12h1Q8gPJuEZg8XsL69FAoFli9fjpSUFOTm5iIxMRFXr141mG79\n+vWYMmWK1n6GYXDq1ClkZWUhMzOTW8vbCEJ7ENiLHm4urf5B9evWCV+8EAKPjs6mE+tgru/F2NhJ\n47rdO3ARPNZE19czfb2svwZBEATB7nxlZmYiMDAQAQEBcHFxwfz585GcnKyXbuvWrXj++efRs2dP\nvWNKpTAHM75bGMq3CTbBr0sHvk0wyQixB2YO0r9XzGX9+ACIPc2bmddaJ8r5cUYufTBLzmVpO9rj\nVybMXzKhC9/6GNJ8WQbf9UOaL35gdb7kcjn8/f3V2xKJBHK5XC9NcnIyli5dCqClt0sFwzCYNGkS\nRo4ciV27dnFpt9V4dBTGMA33DwLhL5+zfnwfdHB2QlpaGvp07WRx/ns1jTawShtnGy9DZKrdnSz0\nGpUcuEamztCa76idzwW1yhbCcVmxYgXpiBwIai9+YHW+GDNeAKtWrUJCQgIYhoFSqdTq6UpPT0dW\nVhaOHDmCTz/9FKdPn7beYjuxbIwEPdxc+DbDIsb388K8odxGZR/Xz7yhplUR/qYTPUbzvpo6sLvF\nNqmyd3C2nYNkju+1dLTYZtfvZIGe7aPp0lY5RrqYduAsv0hfG+rcCMMITR8jNHuEJvUQWv0AwrNJ\naPZwAesTXiwWo7CwUL1dWFgIiUSileb8+fOYP38++vbti++++w7x8fE4ePAgAMDX1xcA0LNnT8ye\nPduo7utm0mbIj30F+bGvUHp6n1avQGV+ttZ2hEuhenv12N56x7nanjmoJ/61YJDNzq+JJekbfr9k\n9Piyp/zhcfcq3uzzUL2AtLX2uZVdNSv95AHdMW+ot1nnv5DxC4CWH9S1rAyL7bt49lcAwP+b2Bdu\nZbmY3/2O0fQlV89rbV86d0arC9vY9VQOYkHOWaP2iJwYi+qTATDa6bbWTEdj6VU9X7rHPe7qt8fD\nG7a7PzW3lUrL86elpan3yY99hZtJm3EzyfjEHYIgiPYA69jbyJEjkZeXh4KCAvj5+SEpKQmJiYla\naW7evKn+/9VXX8WMGTMQExOD2tpaKBQKeHh4oKamBseOHcPGjRsNXqffvPVGbdD9Shn/zFikNRYA\nADw6Ousd53KbYRi9431DR+F+baPB9PbYXrNgKrY9DlegZy+efCHsS7qCkqoGq683eGQ4jtTcNpne\n2YnByzIfJF1kP9+Yp57GhHED1NtBsnCcrJcbTW9oe+io/gCA/t3dcOB/XgIAfLs7C81K/fS+wSNw\np6RavR06cjQiAryAa1lmXS8gdBSuuNw3eNy3S0eL6/PPr82E+EwRvrt8lzW9qndP97g4ZASq7tZq\npY+IkGFPVqlZ12fbVhqoP83tUF93pFt4/oiICHS51tnAMVKQ2Yq0tDReewpU+iHVUBbf9ugitPA+\nfNePbnsB/Nuki9Ds4QLWni+RSIRt27Zh8uTJCAkJwbx58xAcHIydO3di586drCcuLS3F2LFjMWzY\nMISHh2P69OmIioqy3mKen9nrxvXBu5F9zU6/deYA1uOWar66sQyFauqU3ovqb9F5jWFpUFJTvBfV\nT/2/MRFlRxPDiYaG2AZ7u5tnAIf3zwixh2UZNIplqt2N1YAx89mKxZV8bVzfrur/N03h5v4i2h6k\nIXIsqL34waTqPDo6GtHR0Vr74uLiDKb94osv1P/369cP2dnCmlXCxr8WDMIHP91GVnEVa7pOLk6Q\niT3g2UmEikdNrGlDfdwxsKdtg4hq4qYR5bx3104I9XFHTmk1Sw5uMecd764z0cGQrvDD6QOwPPk3\njqzSxlLfi835NEcTaQl/mxqI//7hxuNzW5bXWLlekvlg8Qhf1DYoMOvrS1bZp2mTWwfzw3wM6OGG\n6/dqsWlKf7yTkm+VDYRphNZDIDR7hNTrBQivfgDh2SQ0e7jAsZcX4qgXIy5cjJ6dO2Dd+D4Y08cT\nH06XcnJec8TqbA+C8WaK3V+W+eDLuSGcOwO2xtgPakBP69ZV9HZ/EqbBWJVsnTkA882YnMDFLEJD\nGGr3ThrOs6U9jj7uhkNTqCbA6DpLM0N6GEjLfo3W3l1bYgbgPwtD0bOz8MOgEARB2APBOV/zh3oj\npJf9eosAqIN1dndzwZ8i+yHUx/gQluoFNFJi4ZBTK5g9uBcOvjJUe6eBF6S/Vyf4dTEv7pWlWDRk\nxYHvt+Jpw7Mmpwx4MivSkEOkueeDaVL069YJ70zoYyBdS8qBPTtjpKSLdcZaiCUOlWa975rzJFyD\n2Eg7T+jf1eB+QyRE98crI/3MTq/GwvbdMXsggJbhcPeOIrjYcHYq8QS+YyJRnC/L4Lt+KM4XPwjG\n+erZ2QVHXhuG10b5WbRUirmhEAzxbmRfTA3qjomB3czOo3rJv/mUP1aaCK/Qo7PpUBVsDwIGLSEH\nBvRg7wky9krj4lXX28t4HK7VOuXXvd6i4T7ozqJRS0tL08szPbilR2bpaLFWz1Q/jQWyu7my16u3\nRwf847lgTOjP3q6DvDubdPQHmaslsxBD7e4qetI7NaZPy4Legd1d0UujV8vYb8PZicFLMh+zrt2z\ncwe9evfo6IxoC8N+DDTRQ9lLpzfO10YfCISwIA2RY0HtxQ+CcL7mDemFD6ZLnwjGWYY/fDy0H+Be\nnZ68jNaN0+/pYOOpPl5YFdG7VQE13To4Y1qQ/tCNiiWj/DCmt6fF59XE4JCZgX1uHbhtRs0YU2wj\nmcHe7I7Ly8N98fnzwaxpjJ1/9uBeeG2Udu/MB9OkWBXhj0ADzmhrHE1nJwZ/j9GfECHRiJ7/bKD5\nPUqmUJXV2PBwb42As327uWLPgkH4ZOZAs89v7moSIgP3+76XQ9HVRFw7tjo2d4icsD1C08cIzR7S\nfJlGaDYJzR4uEITztSRMDF8Pw1/FL4T20trW1QP10wjiOElqvKcjzJ+bISZzX/LzhnqbpcHyDhqu\n/v+1Ub4612rJL3s8q663Vyc9x3R6cA9Oh8/emRCg1aNnSfBOSzVnlv6ghvi6Y6oRh9eYmXoWmSjP\n/kVDsGvOE4fR3EjzpnpBdTH1AmAA9OjcwaCjZAnhGh8AsaP8MD24h8EeKFXbPft4+PKpPvofDrrt\nq6mtiw0TI6BrJ6wfb9kHEEEQRHtEEM6XLs8Nbln3b2pQd7weLmbVYEUN6I4VT/vj/15g72FZONwH\nLq14kS0e4Yv+3W0XpdtdQwg9f6j2sFFHUYu9C2U+WPtMb/xtWqBe/hVP+1u8FA3QoilaONwHATrL\n+3RwNl+ZxOaY/WFigMU2GWLKgO5wZqwbXjaFaqgTADp3cG5VT2gXC5arMjWMDFi+vJAh3p/SH8Ea\nw6pzh3qrNXXGTr9mbG9smtIf//NsAL54IVhraFk3y/DHHwXd3VzQy70DPpsTbNEQPmEb+NbHkObL\nMviuH9J88YMwFjjUYaifB/6zMBSdzZjO7uzEaL08jeHeoXVFfUnmg5dkPoj6PIs13dpneuODn2+z\nptFk2RgJbj2oQ87ZM4CH4dmVfbq2OH0dRE6IGmD5MjymWDjcF11dXfBJeqHWfmMv5n0vh+Lg1Xv4\n+nyJweOa2Z7u46W3T5e0tDSgG/uw2ppnemNlhD9nay0a8heXjPLD4av3rD73SIkHzhWxhyoBWhzJ\ntz83EeiRg+K2ZhJGB5ETRjzuSRV7dkJ+eZ3RtFMGdodHRxEGmRh+JtoXpB9yLKi9+EGQPV9ASzwo\nLkIneHYSYcXT/hB7ciP21TVJNVPS0i/+mYN6YlVEb6Mv2Ykcao0MYVSkz2gf1Sxvl04izBncE0/1\n8cQfJ5ofaNZauFzkujVrIG6bNVCvh9AQq8f2RvwYicl05tzXjjAv0IlhMLavF2vgX8L+CE0fIzR7\nSPNlGqHZJDR7uECwzhcbvdxbHvYSL32HavEIbd3UCLHHk54xG7zR9r44GIdfGWqWg6AKE6A5K00y\naKRF1+N7URZXF2e8G9kPEX3ZhwGfiMuNp4mIiEBXEzMXrcf6Rh/Qw82socKenTtg1qCeWvumGOmx\nNEfzZSnWxkczhaOEkSssLMSECRMwaNAgDB48WD2k8u6770IikUAmk0Emk+HIkSPqPJs2bYJUKkVQ\nUBCOHTum3n/+/HmEhoZCKpVi5cqVdi8LQRBtE4dwvlS9Dir/ZnN0IN6f0h8BXfW1WLrT7bVeGDbw\nXFycndBBZF41PtXHE/sXDdFyEPl6n22MbFnmRzMqPtAi8vfxsE0wzM1T9TVrTwdYNyPUUgzdAp3M\nbD9z+WpeCN6L6oeUJcOw5pnerTqHMUdn2kDjQ+xjenvi/3HdI6lRYebeq0/38cQQH3ctPaM9cXFx\nwccff4wrV67gzJkz+PTTT3H16lUwDIM1a9YgKysLWVlZ6pU7cnNzkZSUhNzcXKSkpCA+Pl49c3Tp\n0qXYvXs38vLykJeXh5SUFF7KZAl862OEoPli+xgmzZc2pPniB0FqvnRZMsoPHh2d8ezjoT2xZyeI\nPU0PAwHA8zqzJa3FmrUOO7k46enYiq6cA9z1NV/mXMWcOGKGeD60F0Y/ngX3VIAXArqWoeDBI/Xx\n4F6dsfaZ3uhjYqhNdyaepsNgyH6Zn3ZgWtViqevG9cFff/rdskJwiLMTg6SXBsOZpWvHkl4fX4+O\nRmfvqtBd3DdGJ+I8WziKQ68MRcpv9/Hpr0V6ecaa6JG0BoZpccxLqxrQhyX+28bIflAqlbytuODj\n4wMfn5aPMHd3dwQHB0Mub1m83VA4juTkZCxYsAAuLi4ICAhAYGAgMjIy0KdPH1RVVSEsLAwAsGjR\nIhw4cABTpkyxX2EcEFtoiM7crsBFE0u/aVLdoODchrYKab74wSGcL7cOzq2LyA2gf3eNoRg7vQtc\ndXqT3h7fB0evl+O5wdY7gppBSz9q5TJIb4SL1f93EjnhsznBehMKVAL//Pu1Rs8j8eyIaUHdDToa\nqhevWfomDtrF2CnEXTqaXK8TgMXDn7qhS8wpgqE0swf3xJQB3fWC2bKdr6PIyaxOXLZzaLYL22xi\n3ZP83wshaFQ0w9WFvVdLKEtdFRQUICsrC6NHj0Z6ejq2bt2Kr7/+GiNHjsSHH34ILy8vFBcXY/To\n0eo8EokEcrkcLi4ukEieaPjEYrHaiRMyQtPHcGHP5dJqfHf5LgfWkObLHIRmk9Ds4QKHGHZ0NHRf\nO88GdsPmqYEGZ2/6W6j5CvHujPgxEnwwLVAv4Kw5vGxmFHRzYBgGKyN6Y+7jSPRmxoRVw+UP6s2n\nJejR2UUv0O6SMD/M1tJhWT/2vG5cH7wzIcCqc6heAAxaAqrqDpOYcl3MmQBgLpaEBRE5MSYdL6FQ\nXV+q2RkAACAASURBVF2N559/Hlu2bIG7uzuWLl2KW7duITs7G76+vnjrrbf4NpEgiHaKSecrJSUF\nQUFBkEql2Lx5s9F0Z8+ehUgkwnfffWdxXoeC5a34v5P7o5ubCH+O6t/q06tmTw5m6Y2YNagnhvia\nXlvSUOfDIp0JCVzCMAxiQnpoDaGZMxFhxON4UTK/1i/l06erK/YsGKwXaLdzB2csNWMGoiVMknYz\nKwyKORitHRPVNszPA3+c2BdfmIhvZw6enVg6wDV8VWsDvtqTxsZGzJkzBy+//DJmzZoFAOjVqxcY\nhgHDMIiNjUVmZiaAlh6twsIn4VaKioogkUggFotRVFSktV8sFsMQ8fHxSEhIQEJCAnbs2KGlUUlL\nS7PrNt/XX716NVavXs2pPfkXz6q3K/OztXRblm6Xnt5nUXrVPq6uL/T2SktLw44dO3izx9A23/bs\n2LFD/fuOj48HF7AOOyoUCixfvhzHjx+HWCzGqFGjEBMTg+DgYL1069ev19JCmJvXntj61THKvwv2\nvhhqUR5dzddnc4JxpbQaTwc45nIty5/SjvQucmLwwTQpnA24+SrNl5erCw69MhQd7LDwcmtCTXCF\npjOsq/nSxZwgq6ZmnLLaYuR/NjpyMDFBpRmzJUqlEkuWLEFISAhWrVql3l9SUgJf35aPj/379yM0\ntOW3GhMTgxdffBFr1qyBXC5HXl4ewsLCwDAMunTpgoyMDISFheGbb74xqo/Zvn27UXt0e3htvR0a\nGqq1z97X//jjjzm351oHOc5fugNAf9jQ0m03v0CtfabS6+6z9vpCby97X98RtnX3XbhwAdbC6nxl\nZmYiMDAQAQEBAID58+cjOTlZz4HaunUrnn/+eZw9e9bivLagh5sL7tU26u235r0bKe2G/Pt16N/N\ndtHugRZN1zP9bBvjy94M8TXdo8XFi90c+A7VYS4dNbzVDoY8V3MQYEfVrjnBeFDXiOK8Kza7Rnp6\nOv75z39iyJAhkMlkAID3338fiYmJyM7OBsMw6Nu3L3bu3AkACAkJwdy5cxESEgKRSITt27erNWvb\nt2/HK6+8grq6OkydOtUhxPZC08cIzR7SfJlGaDYJzR4uYHW+5HI5/P2f9GRIJBJkZGTopUlOTsaJ\nEydw9uxZ9UPLnLy2Yt5Qb72ZYNby3+P62GQGV0DoKPx+6yGn51QxXOyBiyXVFuXRLZ41sztN0aZ+\nUGZUk2ZdGnsBrI7wx+2Hj9C32xNNl7MTg11zgjhZcsigXXYUx3cUOcHHoyOKbXiNiIgINDc36+1X\nhZYwxIYNG7Bhwwa9/SNGjEBOTg6n9hEEQbA6X+Y8lFetWoWEhAQwDAOlUqmeym3JAz0+Ph69e7fE\nQ/L09NTqhlWNvVqyraxpBOAFiWdHveNPxt5lFp+fYZhW2cO2PURRgDOlcqyYF83J+TS3XxjijfLr\nWcgprcZNt0DW9EDLEjGXzp5B0+3O6uPnMtJRmV+odha4Lr+9tlXlu3zuDDqWdmlF/pYPicr8bKSl\n1ejfT5P6Gs1fmZ+nV38qe+oKLiGtqUCd3uPeNQwCwDCSVpfX0PV004eNfspgeXTT55w7g8r8Uqvb\nX/X/7dstS3DFxsaCsA2q4Xy+UMWMUg3R8m2PLqaG/O0N3/Wj214A/zbpIjR7uIBRGgp885gzZ87g\n3XffVQcW3LRpE5ycnLB+/Xp1mn79+qkdrnv37sHNzQ27du1Cr169TOYFgNTUVAwfPpzzgt2vbUSX\njs5w0Riymf5FNhoULbYei5Vxfs3WYI+b6tNfCpGc27J2obFyq0JN/DmqnzoGGNASamLp/t9Y87YW\ne/6gVOVbN66PnijfHD78+XccvV4OQLseVOd9f0p/jJR0MZhXlWbbzIHqKPQHjp5Ep4AhiBrQjfMe\nLdX1vpoXYjTeWH1TM2Z8eREAe7v+fPMB/nKiwGQ6S7lw4QImTpzI2fn4xFbPsNYitBcVF/Z8ninH\nt481X9ZiifN1bl3LPTryr6mcXHvbzIHw66IdxPrXX9Ix5qmnjebp3MHZ7qFb2uI9xCVcPL9Ye75G\njhyJvLw8FBQUwM/PD0lJSUhMTNRKc/PmTfX/r776KmbMmIGYmBg0NTWZzGtLutN6c4QdWDO2N66U\nVWO42PTsU82hyR6dXRAxkPvF0oGW2YsVj5roN9BOEdJLChCePXz2ev3xx3wDM6V7Yu+h6wbT9+/m\nhv8e1xsudpiMpInQ2kxo9nABq/MlEomwbds2TJ48GQqFAkuWLEFwcLBaqBoXF2dxXj4Z5N0ZWcXV\nZq3TZy/scVNZIjK350+cjx+Ue8fWhYgY5O2Oo9fL9ZZjmjKwO6a0womyZdn3LBiEpmZl64X6BEHY\nhPLaJpTXNpmdnq8lugjbYzLCfXR0tJ5Q1ZjT9cUXX5jMyydvTwjA99fuI9pGPQ5tEVsK7u3Jxkl9\nkVNarReZ3lyiBnSDm4sTBnlbHotsZkhP3Cy3/UxZFS7OTnCQOKiEDeB7iIY0X5bBtz2k+eIHh1he\niCu6urpwGuGdC+xxU1kS28qe0gJ7/qCeDvCyKnaaE8O0OgTIsqf0g7y2xYcJQQC0VqCjQe3FDzQu\nQRCEUTq50CPC0RCaUy80e4TU6wUIzx5AeG0mNHu4gJ6sPGOPm2qYX4sYvKursDo62+IPylwcpewj\nxF0wSdoNq8f25tsUgiCINgM5X+2AiABPbI4OxGdzTE946O3F3YLNhOPj7MRg3bg+pJN0IDRjq/HB\nJ598otYRAfzbo4vuuo18w7c9uu0FCK/NhGYPFwirK6QdYg/tD8MwkJkIhZD44mA8qG2Ej05cKFtq\nwNqz7qk9l51o25CGyLGg9uIHcr4IAC1x0SguVPvBqW1MYiUMIDSnXmj2CE1jJTR7AOG1mdDs4QJy\nvnimLd5U5kJl5w8XZye8+ZQEIvLCCIIg7A5pvgiinTIjpCeig3rwbQbBMXzrY0jzZRl820OaL36g\nni+eEbr2p6PIdv650MtuS9pz2Ym2DWmIHAtqL34g54tgxa9LR7wk80Ev9w6mExMEwTtCc+qFZo/Q\nNFZCswcQXpsJzR4uIOeLZxzhplo8wtcm53WEstuK9lx2giCI9g5pvgiCINoQfOtjSPNlGXzbQ5ov\nfjDpfKWkpCAoKAhSqRSbN2/WO56cnIyhQ4dCJpNhxIgROHHihPpYQEAAhgwZAplMhrCwMG4tbyO0\nxZvKXKjsBNH2WLFiBemIHAhqL35gdb4UCgWWL1+OlJQU5ObmIjExEVevXtVKM2nSJFy8eBFZWVn4\n8ssv8cYbb6iPMQyDU6dOISsrC5mZmbYpgYOTk5PDtwm8QWUnCO4R2pC20OwRmsZKaPYAwmszodnD\nBazOV2ZmJgIDAxEQEAAXFxfMnz8fycnJWmk6d+6s/r+6uho9emhPXVcqlRya2/aoqKjg2wTeoLIT\nBEEQ7RFW50sul8Pf31+9LZFIIJfL9dIdOHAAwcHBiI6O1ho7ZhgGkyZNwsiRI7Fr1y4OzSYIgiAM\nwfeQNmm+LINve0jzxQ+ssx0ZMxf2mzVrFmbNmoXTp09j4cKF+O233wAA6enp8PX1xd27dxEZGYmg\noCCMHTvWeqvbELdv3+bbBN6gshPmsGjRIixYsADR0dF8m0KYAemHHAtqL35gdb7EYjEKCwvV24WF\nhZBIJEbTjx07Fk1NTbh//z66d+8OX9+WEAU9e/bE7NmzkZmZqed8VVdX48KFC9aUwaGJjY1tt+Wn\nsrfPsgMtv3tz2bVrF5KSkjBv3jw89dRTiI2N1ZI7ENoITR8jNHuEprESmj2A8NpMaPZwAavzNXLk\nSOTl5aGgoAB+fn5ISkpCYmKiVpr8/Hz069cPDMOoXybdu3dHbW0tFAoFPDw8UFNTg2PHjmHjxo16\n15g5cyaHxSEIoq1x//593Lx5E56envD29sZrr72GpKQkvs0iCIJoNazOl0gkwrZt2zB58mQoFAos\nWbIEwcHB2LlzJwAgLi4O3333Hb7++mu4uLjA3d0de/fuBQCUlpbiueeeAwA0NTXhpZdeQlRUlI2L\nQxBEW+PDDz9EfHw8+vfvDwBaOlRCH76XrlLph1TDWXzbo0tlfragepv4tke3vQDhtZnQ7OECkxHu\no6Oj9bQWcXFx6v/XrVuHdevW6eXr168fsrOFJWwkCMLxGD9+vNrx+v777zFt2jSeLSLYIA2RY0Ht\nxQ+8Rrg3FcDVUTEUXLa8vByRkZEYMGAAoqKi8PDhQ3X6TZs2QSqVIigoCMeOHVPvP3/+PEJDQyGV\nSrFy5Uq7l8McXnvtNXh7eyM0NFS9j8uy1tfXY968eZBKpRg9ejR+//13+xTMDAyV/d1334VEIoFM\nJoNMJsORI0fUx9pS2YEWDeiECRMwaNAgDB48WP0FzXX7r127Vl0Hhw8ftl8BHRSh9RAIzR4h9XoB\nwrMHEF6bCc0eLuDN+TIngKujYii4bEJCAiIjI3H9+nVMnDgRCQkJAIDc3FwkJSUhNzcXKSkpiI+P\nV8dGW7p0KXbv3o28vDzk5eUhJSWFtzIZ49VXX9Wzi8uy7t69G927d0deXh5Wr16N9evX27eALBgq\nO8MwWLNmDbKyspCVlaXuNW5rZQcAFxcXfPzxx7hy5QrOnDmDTz/9FFevXuW8/QHgH//4ByIjIwX5\nGyAIgrAU3pwvcwK4OjK6wWUPHjyIxYsXAwAWL16MAwcOAGhZnmnBggVwcXFBQEAAAgMDkZGRgZKS\nElRVVal7zhYtWqTOIyTGjh2Lrl27au3jsqya55ozZw5SU1PtVTSTGCo7YDiwcFsrOwD4+Phg2LCW\nr3Z3d3cEBwdDLpdz3v7bt2/H9evX0atXL1RWVvJQUseC75hIFOfLMvi2h+J88QNvzpe5AVwdEUPB\nZcvKyuDt7Q0A8Pb2RllZGQCguLhYK3yHqh5094vFYoepHy7LqnmfiEQieHp6ory83F5FaRVbt27F\n0KFDsWTJEvWQW1sve0FBAbKyshAeHs55+wMtKwKUl5dDqVQKtg6IFmitQMeC2osfeHO+zA3g6oik\np6cjKysLR44cwaefforTp09rHWcYpk2XX5P2VFagZfjs1q1byM7Ohq+vL9566y2+TbI51dXVmDNn\nDrZs2QIPDw+tY1y0/2effYbp06dj/vz5cHd3t+pc7QGh6WOEZo/QNFZCswcQXpsJzR4u4M35sjSA\nqyNhKList7c3SktLAQAlJSXo1asXAP16KCoqgkQigVgsRlFRkdZ+sVhsx1K0Hi7KqroXxGKxOhp8\nU1MTKioq0K1bN3sVxWJ69eqldjhiY2PVmr+2WvbGxkbMmTMHCxcuxKxZswBw3/7e3t4YPHgw+vfv\nj7q6OsHVAUEQhKXw5nxpBnBtaGhAUlISYmJi+DKHM2pra1FVVQUA6uCy/7+9e4+rqsr/x/86XDK7\nYd5QOCgqRwFFwgitSX8a3sBg6mOhNKWWqF/IzK826sceM2mfMbEZp19JlpPWZz41EpaT4CfFC4qF\nJqhokmhh6XBRSES8QSiH/f2D2OPh4rlwzlnrbF7Px4NH7H325b33Wh5Wa7332iEhIYiNjcXf//53\nAMDf//539Q9VbGwsPv30U9y4cQNnzpxBUVERIiIi0KtXL9x3333Izc2Foij4+OOP1X1kZ49rbZp8\n99Zjff7554iMjBRzURY6f/68+vsXX3yhPgmpxWtXFAUzZ85EcHAw5s+fr663d/mnp6cjJiYGjz76\nKO68807nX6iLEZ0fw5wv64iOhzlfYpid58thJ25jAldXV1FRgSeffBKA6eSy4eHhiIuLw4YNG+Dv\n749NmzYBAIKDgxEXF4fg4GB4eHhg7dq16jDN2rVrMWPGDNTW1iI6OhoTJ04Udl1tiY+Px759+1BZ\nWQk/Pz+8/vrrWLJkid2udebMmXjuuedgMBjQrVs3dRJfGTS/9uXLlyM7OxvHjh2DTqdDv3791AmJ\ntXbtQOPw+ieffKJOqwI0TiVh7/LfvXs3Dh06BF9fX/VYt1NSUoJp06bh559/hk6nw+zZszFv3jxU\nVVVhypQp+Ne//qXG1aVLFzXuDz/8EO7u7njnnXfUCaGPHDmCGTNm4JdffkF0dDTefvttu99HrWH+\nkGtheYmhU1p7NIuISBKzZs3CHXfcgXfffRdJSUlYu3btbbcvLy9HeXk5HnjgAVy7dg0PPvggtmzZ\ngo8++gjdu3fHokWLsGrVKly6dAnJyckoLCzEM888g0OHDqGsrAxjx45FUVERdDodIiIikJKSgoiI\nCERHR2PevHkt/icoKysLw4YNc+Qt6PDW55Vh0/GfnX7ew4sae5vD3xTzpHFQz7vwl0kGeLoLnZKT\nmsnPz2/3SARLlIikds8996hPT3bu3Nns9s6YAoOIqD3Y+CIiqXXv3h0HDhzAwoUL4eZm3VeWo6bA\nkJno/BjmfFlHdDzM+RJDWM4XEZElXn31VZw6dQoNDQ0IDg62eD9HT4Fxq6SkJPTp0wcA4OXlhZCQ\nEPXx+KY/HM5aLigocOr5mi83H4K1Rzw/nqwEdH0B/Lux0jRFg7XLNedOW7V90zpbz9feePbvz4GH\nm5vTyisnJwcFBQXC6k9ry6LjKSgowOXLlwEAxcXFSEhIQHsx54uIpBYfHw8AqK2tBQCLhv5u3ryJ\nxx9/HFFRUeqTmIGBgcjOzkavXr1w/vx5jBkzBqdOnVJff7RkyRIAwMSJE7F8+XL07dsXY8aMUV97\nlpqain379uH99983ORdzvhyPOV8cpJIJc76ISPNSU1ORmpqKL774AqNGjTK7vSOnwHCV6V6ISG5s\nfBGR1E6cOIHCwkIcP34cJ06cMLt90xQYe/fuRVhYGMLCwpCZmYklS5Zg165dGDhwIPbs2aP2dN06\nBUZUVFSLKTASEhJgMBgQEBAg5XQvzYnOj2HOl3VEx8OcLzGY80VEUvv8888BAJ06dbJoTqJHH30U\nDQ0NrX62e/fuVtcvXboUS5cubbH+wQcfVHOWyDKcN8q1sLzEYOOLiKQWHh6u/l5aWorS0lJMmjRJ\nYERyk+09eLLFI9u7FGWLB5CvzGSLxx7Y+CIiqa1fvx6/+c1voNPpkJOTw7wrInJ5zPkiIqkFBgbi\nlVdewcKFCzFo0CB1olRqnej8GOZ8WUd0PMz5EoM9X0QkvZkzZ0Kn06mTpJK8mEPkWlheYrDxRURS\nW7FiBUpLS9GlSxd06tRJdDjSky0/RrZ4ZMuxki0eQL4yky0ee+CwIxFJbf78+Vi+fDnuu+8+vPTS\nS6LDISJqNza+iEhqbm5u6Nu38dUyXbp0ERyN/ETnxzDnyzqi42HOlxgcdiQiqXXq1AmFhYVYs2YN\nLl26JDocMoM5RK6F5SUGG19EJC1FUfDUU0+hsrISiqIgKSlJdEjSky0/RrZ4ZMuxki0eQL4yky0e\ne2Dji4ikpdPpsHfvXixatEh0KEREdsOcLyKSVnp6OtLT0xEZGYmnn34aTz/9tOiQpCc6P4Y5X9YR\nHQ9zvsQQ3vO1c+dOuLu7iw6DiJwsMjLS7DaZmZnYv38/EhMT8d577zkhKmov5hC5FpaXGMIbX+7u\n7hg2bJjoMIRJTk7GkiVLRIchBK+9Y147AOTn51u0XXFxMb788ksUFxdj27ZtAIDo6GhHhubyZMuP\nkS0e2XKsZIsHkK/MZIvHHoQ3voiI2vL000+jsrIScXFxuHDhguhwiIjsgo0vwYqLi0WHIAyvncyZ\nMWOG6BBcTk5OjtCegqb8oabhLNHxNHflx2NS9TaJjqd5eQHylZls8dgDG1+ChYSEiA5BGF47kfYw\nh8i1sLzE4NOOgiUmJooOQRheO5H9ydZDIFs8MvV6AfLFA8hXZrLFYw9sfBERERE5kc2NrxdeeAHe\n3t63HT6ZN28eDAYDQkNDcfToUVtPpWlanL/EUrx2IvsTXbc4z5d1RMfDeb7EsDnn6/nnn8dLL72E\nadOmtfr5tm3bcPr0aRQVFSE3NxeJiYk4ePCgzYESEZH8mEPkWlheYtjc8zVy5Ejcf//9bX6ekZGB\n6dOnAwCGDx+O6upqVFRU2Ho6zdLiWLaleO1E9idb3ZItHtlyrGSLB5CvzGSLxx4clvNVVlYGPz8/\ndVmv16O0tNRRpyMiIiJyCQ5NuFcUxWRZp9M58nQuSYtj2ZbitRPZn+i6xZwv64iOhzlfYjhsni9f\nX1+UlJSoy6WlpfD19W1126SkJPTp0wcA4OXlhZCQELWbsemma3W5oKBAqnictfz+++/jwoULWLp0\nKdzd3YXH4+zlJrLE44zrzcnJUSeXTUhIAGkTc4hcC8tLDJ3SvHvKCmfPnkVMTIzagLjVtm3bkJKS\ngm3btuHgwYOYP39+qwn3WVlZHfrdjh1Vz549UV9fj4qKCnh6eooOh5wsPz/fohdruwJ+hzne+rwy\nbDr+s9PPe3hRYx0NfzPL6ecGgKCed+EvkwzwdOesUDKxx/eXzT1f8fHx2LdvHyorK+Hn54fly5fj\n5s2bAIA5c+YgOjoa27ZtQ0BAAO6++2589NFH7QqUiIiISAtsbnylpqaa3SYlJcXWw3cYWnxnFZnH\ncidHEV23+G5H64iOh+92FEP6dztu3LgRNTU1FuWIpKam4qmnnuIwFhGRIMwhci0sLzGkH0i25gnJ\n1NRU3Lhxw4HRmGpoaDBZtiV9TmutebIMy50cRba6JVs8MvV6AfLFA8hXZrLFYw/S93wBwL59+7Br\n1y5cu3YN69evR+/evbFx40b84x//gNFoxKuvvopOnTqhoKAAcXFxmDRpEoKDg7F69WrU1tYiJiYG\nL7/8sskx16xZg127duHq1at47bXXMHr0aPz0009YsGABGhoa8MADD+D111/Hu+++i4yMDLi7uyM5\nORlDhw7F6NGj8fDDD6Oqqgr9+/dHcXExKisr8Yc//AFDhgwRdJeIiIjIFUjf86UoCu666y6kpaVh\nwYIFePvtt3Hp0iV88cUX+PLLL7F582b8+c9/RkREBEJCQvDZZ58hKSkJw4cPx9atW7Fz505s3boV\ndXV1JsdNSEhARkYGNm3ahNWrVwMAli1bhtdffx0ZGRlYvnw5KioqsH37duzYsQPr1q3DsmXLAACX\nL1/GnDlzsG7dOgCNE8impaXZ1PDS4vwlZB7LnRxFdN3iPF/WER0P5/kSQ/qeL51Oh6FDhwIAwsLC\nsG7dOpw5cwanTp1CbGwsAODixYst9jt27BjefPNN1NfXo7i4GBcuXIBer1c/T0tLw+effw43Nzf8\n/HPjI8znzp1Tz6XT6VBSUqI2qPz8/HDlyhUAQJcuXeDv768ei4+ZExE1Yg6Ra2F5ieESPV9N84gd\nPXoU/fv3h7+/PwYPHoyMjAxkZGRg3759AAAPDw/U19cDaBxWfOutt5Ceno7evXu3OO4HH3yArVu3\nYv369Wrulo+PD44fP66et0+fPigoKICiKCguLoaXlxcAwM3N9La1Z+Z+LY5lk3ksd8d54YUX4O3t\njZCQEHXdsmXLoNfrERYWhrCwMGzfvl39bOXKlTAYDAgMDMTOnTvV9UeOHEFISAgMBkOLtAWZyVa3\nZItHthwr2eIB5Csz2eKxB5fo+bpx4waefvpp1NTU4IMPPkDXrl3xH//xH3j88cfh7u6OoKAgJCcn\nIyoqCi+88AJiYmIQExODZ599FsHBwbj33ntbHHfEiBGYOHEiwsPDcc899wAAli9fjvnz50NRFDXn\nKyoqChMmTICbmxvefPPNNmMkIjk8//zzeOmllzBt2jR1nU6nw4IFC7BgwQKTbQsLC5GWlobCwkKU\nlZVh7NixKCoqgk6nQ2JiIjZs2ICIiAhER0cjMzMTEydOdPblEJEGSd/4io+PR3x8fIv1cXFxiIuL\nM1k3a9YszJo1y2TftjTled2qX79+SE9PN1k3d+5czJ0712RdVta/ZztevHjx7S/ADC3OX0Lmsdwd\nZ+TIkTh79myL9a09jZyeno74+Hh4enrC398fAQEByM3NRd++fXH16lVEREQAAKZNm4YtW7a4RONL\ndN3iPF/WER0P5/kSQ/rGFxGRPaxZswb/8z//g/DwcKxevRpdunTBuXPnMGLECHUbvV6PsrIyeHp6\nmuSI+vr6oqysTETYLoc5RK6F5SWG9DlfWqe11jxZhuXuXImJiThz5gyOHTuG3r17Y+HChaJDchjZ\n6pZs8cjU6wXIFw8gX5nJFo89sOeLiDSvZ8+e6u8JCQmIiYkB0NijVVJSon5WWloKvV4PX19flJaW\nmqz39fVt8/hJSUno06cPAMDLywshISHqH4ymx+S5bPvyjycrAV1fAP+emqGp0eLo5aZ1zjpf8+X9\n+3Pg4eYmVXl0tOWCggJcvnwZAFBcXGzRG3fM0Sm2TMtuR1lZWR16qgYtjmVbomfPnqivr0dFRUWH\nfB1URy33Jvn5+YiMjHTY8c+ePYuYmBj1Senz58+rTz2/9dZbOHToEDZu3IjCwkI888wzyMvLUxPu\nT58+DZ1Oh+HDh+Odd95BREQEJk2ahHnz5rWa8yXbd5jouuWInK/1eWXYdPzndscGWJdjdXhRYx0N\nfzPLzJaOiSeo5134yyQDPN0dN0jFnC/r2eP7iz1fRKQp8fHx2LdvHyorK+Hn54fly5cjOzsbx44d\ng06nQ79+/dQJkoODgxEXF4fg4GB4eHhg7dq16tPLa9euxYwZM1BbW4vo6GiXSLaXAXOIXAvLSwz2\nfJEQHb3nq6NzdM+XM/E7zPHs2fNlDWf0fN2OM3q+yHr2+P5iiRIRERE5ERtfgmnxnVVkHsudHEV0\n3eK7Ha0jOh6+21EM5nwREZHdmMshKrv8C85U/WLx8XQ6oLDienvDckn1RgVX64y4aay3eJ87PHS4\nv7PlqRzM+RKjXY2vzMxMzJ8/H0ajEQkJCS1me6+srMSzzz6L8vJy1NfX45VXXsGMGTPac0rNkekJ\nDnIeljs5imx1q3k8l38x4vWsM4KikW9erdvFU3SxFs99esKq4/1hbD+M6OPVrphkr0NaYPOwuspq\neQAAIABJREFUo9FoxNy5c5GZmYnCwkKkpqbi5MmTJtukpKQgLCwMx44dQ3Z2NhYuXKi++JqIiIhu\n72aDYtWP2EfoyFI2N77y8vIQEBAAf39/eHp6YurUqS3ei9i7d29cuXIFAHDlyhV069YNHh4c6byV\nFseyyTyWOzmK6LrFnC/riI6HOV9i2NwSKisrg5+fn7qs1+uRm5trss2sWbPw2GOPwcfHB1evXsWm\nTZtsj5SIiKTHHCLXwvISw+aer6aJCG/njTfewAMPPIBz587h2LFjePHFF3H16lVbT6lJWhzLJvNY\n7uQostUt2eJxpZwvUWQrM9nisQebe76avxOtpKQEer3eZJsDBw7g1VdfBQAMGDAA/fr1w/fff4/w\n8HCT7fhetI633GT//v3w8PAQHg+XHV/eOTk5KC4uBgC7vBuNiMhV2TzDfX19PQYNGoSsrCz4+Pgg\nIiICqampCAoKUrdZsGABvLy88Nprr6GiogIPPvggjh8/jq5du6rbdPTZoWV7Z5WzdPQZ7jtquTfh\nDPeOI7pumXu3Y2HFdczf+oOQ2ADXerejLZaP64+H+1r+tCPf7Wg9oe929PDwQEpKCiZMmACj0YiZ\nM2ciKChIfWfanDlzsHTpUjz//PMIDQ1FQ0MD3nzzTZOGFxERaQtziFwLy0uMdj16GBUVhaioKJN1\nc+bMUX/v3r07tm7d2p5TaJ5MrXlyHpY7OYpsdUu2eGTLsZItHkC+MpMtHnvg64WIiIiInIiNL8G0\nOH8JmcdyJ0cRXbc4z5d1RMfDeb7E4IynRERkN8whci0sLzHY8yWYFseyyTyWOzmKbHVLtnhky7GS\nLR5AvjKTLR57YOOLiIiIyInY+BJMi2PZZB7LnRxFdN1izpd1RMfDnC8xmPNFTvWvf/0Ln3zyCRoa\nGgAAycnJiI+PR0BAgODIiMgemEPkWlheYrDnSzAtjmXfTklJCVavXo2mFyu89dZbOHPmjOConK+j\nlTs5j2x1S7Z4ZMuxki0eQL4yky0ee2Dji4iIiMiJ2PgSTItj2WQey50cRXTdYs6XdUTHw5wvMZjz\nRUREdsMcItfC8hKDPV+CaXEsm8xjuZOjyFa3ZItHthwr2eIB5Csz2eKxBza+iIiIiJyIjS/BtDiW\nTeax3MlRRNct5nxZR3Q8zPkSgzlfRERkN8whci0sLzHY8yWYFseyyTyWOzmKbHVLtnhky7GSLR5A\nvjKTLR57sLnxlZmZicDAQBgMBqxatarVbbKzsxEWFoYhQ4Zg9OjRtp6KiIiISDNsanwZjUbMnTsX\nmZmZKCwsRGpqKk6ePGmyTXV1NV588UVs3boV3333HT7//HO7BKw1WhzLJvNY7uQoousWc76sIzoe\n5nyJYVPOV15eHgICAuDv7w8AmDp1KtLT0xEUFKRus3HjRkyePBl6vR4A0L179/ZHS0REUmMOkWth\neYlhU89XWVkZ/Pz81GW9Xo+ysjKTbYqKilBVVYUxY8YgPDwcH3/8cfsi1SgtjmWTeSx3chTZ6pZs\n8ciWYyVbPIB8ZSZbPPZgU8+XTqczu83NmzeRn5+PrKws1NTU4OGHH8aIESNgMBhsOSURERGRJtjU\n8+Xr64uSkhJ1uaSkRB1ebOLn54fx48ejc+fO6NatG0aNGoVvv/221eMlJSUhOTkZycnJeO+990zG\nd3NycjS93NGut6CgAM2dOHFCmvictdy0TpZ4nHG9ycnJSEpKQlJSEhzphRdegLe3N0JCQtR1VVVV\nGDduHAYOHIjx48ejurpa/WzlypUwGAwIDAzEzp071fVHjhxBSEgIDAYDXn75ZYfGbE+i82OY82Ud\n0fEw50sMnaIoirU71dfXY9CgQcjKyoKPjw8iIiKQmppqkvN16tQpzJ07Fzt27EBdXR2GDx+OtLQ0\nBAcHmxwrKysLw4YNa/+VuKicnBxNdqm2JScnB7GxsdDpdGiqemlpaRg3bpzgyJyro5V7c/n5+YiM\njHTIsb/++mvcc889mDZtmtrYX7RoEbp3745FixZh1apVuHTpEpKTk1FYWIhnnnkGhw4dQllZGcaO\nHYuioiLodDpEREQgJSUFERERiI6Oxrx58zBx4sQW55PtO0y2utU8nsKK65i/9Qdh8Vz58ZjFQ32H\nFzXW0fA3s6SIxxLLx/XHw3292nUM2euQaPb4/rKp58vDwwMpKSmYMGECgoODMWXKFAQFBWHdunVY\nt24dACAwMBATJ07E0KFDMXz4cMyaNatFw4u0OZZN5rHcHWfkyJG4//77TdZlZGRg+vTpAIDp06dj\ny5YtAID09HTEx8fD09MT/v7+CAgIQG5uLs6fP4+rV68iIiICADBt2jR1H9nJVrdki0e2HCvZ4gHk\nKzPZ4rEHm2e4j4qKQlRUlMm6OXPmmCy/8soreOWVV2w9BRGRXVRUVMDb2xsA4O3tjYqKCgDAuXPn\nMGLECHW7poeHPD09TVIpfH19WzxURERkK85wL5gWx7LJPJa7ODqdzqKHhlyV6LrFnC/riI6HOV9i\n8N2ORKR53t7eKC8vR69evXD+/Hn07NkTQMuHh0pLS6HX6+Hr64vS0lKT9b6+vm0ePykpCX369AEA\neHl5ISQkRB0qafrD4azlpjw3Uedvnv/WPJ78vG9w5ccSdbitqfHhrOWac6et2r5pnSzxmFs+fvgg\njCV321xeOTk5KCgoEFZ/WlsWHU9BQQEuX74MACguLkZCQgLay6aEe3uSLVmVHIsJ9wQ4NuEeAM6e\nPYuYmBiThPtu3bph8eLFSE5ORnV1tUnCfV5enppwf/r0aeh0OgwfPhzvvPMOIiIiMGnSJJdJuJed\n6IR7azgj4d7e7JFwT7dnj+8v9nwRkabEx8dj3759qKyshJ+fH15//XUsWbIEcXFx2LBhA/z9/bFp\n0yYAQHBwMOLi4hAcHAwPDw+sXbtWHZJcu3YtZsyYgdraWkRHR7fa8CIisgUbX4LJ9ggtOQfL3XFS\nU1NbXb979+5W1y9duhRLly5tsf7BBx9sdV462YmuW035Q02vrREdT3P2ntqhvUTH07y8APnKTLZ4\n7IGNLyIishu+K9C1sLzE4NOOgmmtNU+WYbmTo8hWt2SLR6ZeL0C+eAD5yky2eOyBPV/kNJmZmfjk\nk09arP/www9RW1uL2NhYAVERERE5F3u+BNPi/CVtOXz4MLZt29Zi/Y4dO5CbmysgInE6UrmTc4mu\nW5znyzqi4+E8X2Kw54uIiOyGOUSuheUlBnu+BNPiWDaZx3InR5GtbskWj2w5VrLFA8hXZrLFYw9s\nfBERERE5ERtfgmlxLJvMY7mTo4iuW8z5so7oeJjzJQZzvoiIyG6YQ+RaWF5isOdLMC2OZZN5LHdy\nFNnqlmzxyJZjJVs8gHxlJls89sDGFxEREZETsfElmBbHssk8ljs5iui6xZwv64iOhzlfYtjc+MrM\nzERgYCAMBgNWrVrV5naHDh2Ch4cH/vnPf9p6KiIichHz5s1jHpELYXmJYVPjy2g0Yu7cucjMzERh\nYSFSU1Nx8uTJVrdbvHgxJk6cCEVR2h2sFmlxLJvMY7mTo8hWt2SLR7YcK9niAeQrM9nisQebGl95\neXkICAiAv78/PD09MXXqVKSnp7fYbs2aNXjqqafQo0ePdgdKREREpAU2Nb7Kysrg5+enLuv1epSV\nlbXYJj09HYmJiQAAnU7XjjC1S4tj2WQey50cRXTdYs6XdUTHw5wvMWya58uShtT8+fORnJwMnU4H\nRVFuO+yYlJSEPn36AAC8vLwQEhKidjM23XStLhcUFEgVj6OXzREdn7OWO+L15uTkoLi4GACQkJAA\n0ibmD7kWlpcYOsWGZKyDBw9i2bJlyMzMBACsXLkSbm5uWLx4sbpN//791QZXZWUl7rrrLnzwwQeI\njY01OVZWVhaGDRvWnmsgF/GnP/0Jf/3rXwFAbZQ3SUxMxIoVK0SFRk6Wn5+PyMhI0WHYBb/DrFNY\ncR3zt/4gOgyLHF7UWEfD38wSHInllo/rj4f7eokOQ9Ps8f1lU89XeHg4ioqKcPbsWfj4+CAtLQ2p\nqakm2/z000/q788//zxiYmJaNLyIiIiIOhqbcr48PDyQkpKCCRMmIDg4GFOmTEFQUBDWrVuHdevW\n2TtGTdPiWDaZx3InRxFdt5jzZR3R8TDnSwyb3+0YFRWFqKgok3Vz5sxpdduPPvrI1tMQEZELYQ6R\na2F5icEZ7gXT4vwlrZk0aRLefvvtNj//29/+hscee8yJEYnVUcqdnE+2uiVbPLLNqyVbPIB8ZSZb\nPPbAxhc5RV1dHYxGY5ufG41G1NXVOTEiIiIiMdj4EkyLY9lkHsudHEV03WLOl3VEx8OcLzFszvki\nIqKOTVEUXKsz7dF+fnYSAODqL/UAgJobRvV3APB044TbMmHOlxhsfAmmxbFsMo/lTo7izLplbFDw\nzoESFFXW3marHtiY8e95vWpvtp1+4Ayy5VjJFg8g3/eTbPHYAxtfRERkswvXbuLcFeZrElmDOV+C\naXEsm8xjuZOjiK5bj9d8jcdrvlaXRec0Ncd4TDHnSwz2fBERkd38710jRYdAVmDOlxjs+RJMi2PZ\nZB7LnRxFtrolW04T4zFPtjokWzz2wJ4vIiIiDblYc8Oq7e+9wwN3eLAvxpnY+BIsJydHk616uj2W\nOzmK6LrVlO/VNPx45cdjUvXuaD2eN/acQWdPd4u3f7RqLwDT4UfRdag52eKxBza+iIjIbpjzJVad\nUUGdsd78hr/K7jIaf5sc6MCIqDXsZxRMa615sgzLXQx/f38MHToUYWFhiIiIAABUVVVh3LhxGDhw\nIMaPH4/q6mp1+5UrV8JgMCAwMBA7d+4UFbZVZKtbMvUyAYzHErLVIdnisQc2vsih6uvrkZubi+vX\nr5vdtra2Frm5ubhxw7p8BSJL6XQ6ZGdn4+jRo8jLywMAJCcnY9y4cfjhhx8QGRmJ5ORkAEBhYSHS\n0tJQWFiIzMxMJCUloaGhQWT4RKQRbHwJpsX5S25VU1ODqKgoFBUVmd22pKQEUVFRJj0PWqX1cpeZ\noigmyxkZGZg+fToAYPr06diyZQsAID09HfHx8fD09IS/vz8CAgLUBpvMRNctzvNlHdHxjK7OxsYN\n75usE12HmpMtHntg44uIOgydToexY8ciPDwcH3zwAQCgoqIC3t7eAABvb29UVFQAAM6dOwe9Xq/u\nq9frUVZW5vygXcz/3jWSeV8uJLvLaDwz8/+IDqPDaVfjKzMzE4GBgTAYDFi1alWLz//xj38gNDQU\nQ4cOxW9+8xscP368PafTJC2OZZN5LHcx9u/fj6NHj2L79u1499138fXXX5t8rtPpoNO1/eLn230m\nC9nqlmw5TYzHPNnqkGzx2IPNTzsajUbMnTsXu3fvhq+vLx566CHExsYiKChI3aZ///746quv4OXl\nhczMTMyePRsHDx60S+BERNbq3bs3AKBHjx548sknkZeXB29vb5SXl6NXr144f/48evbsCQDw9fVF\nSUmJum9paSl8fX1bPW5SUhL69OkDAPDy8kJISIj6B6NpyESry+Unj+BK9S9qI6JpGE0ry03rZInH\n3suXio4i95uLmDR2DADx9UnG5YKCAly+fBkAUFxcjISEBLSXTmmeAGGhb775BsuXL0dmZiYAqEmq\nS5YsaXX7S5cuISQkBKWlpSbrs7KyMGzYMFtC0AQtzl9yqytXrsDf3x9ubm4myco6na5F7o27uzuM\nRiNOnTql/gHUKq2Xuzn5+fmIjIx06jlrampgNBpx77334vr16xg/fjxee+017N69G926dcPixYuR\nnJyM6upqJCcno7CwEM888wzy8vJQVlaGsWPH4vTp0y16v2T7DnNm3ao3NuCVL0+j8Od/P1CjpXm+\nDi9qrKPhb2ZJEY8jNJUX5/mynD2+v2zu+SorK4Ofn5+6rNfrkZub2+b2GzZsQHR0tK2nIyJql4qK\nCjz55JMAGp/C/d3vfofx48cjPDwccXFx2LBhA/z9/bFp0yYAQHBwMOLi4hAcHAwPDw+sXbvWJYYd\nRWO+l2vhPF9i2Nz4suZLaO/evfjwww+xf/9+W0+nWTK15sl5WO7O169fPxw71vL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wNPoze+NXuC3thuso+ba4uABPZjejzTdMa//Xf7IXTdduadXv/bwqNJUX4+2p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- "text": [ - "" - ] - } - ], - "prompt_number": 18 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "It appears the MCMC has converged so we may continue.\n", - "\n", - "For a specific trading signal, call it $x$, the distribution of possible returns has the form:\n", - "\n", - "$$R_i(x) = \\alpha_i + \\beta_ix + \\epsilon $$\n", - "\n", - "where $\\epsilon \\sim \\text{Normal}(0, 1/\\tau_i) $ and $i$ indexes our posterior samples. We wish to find the solution to \n", - "\n", - "$$ \\arg \\min_{r} \\;\\;E_{R(x)}\\left[ \\; L(R(x), r) \\; \\right] $$\n", - "\n", - "according to the loss given above. This $r$ is our Bayes action for trading signal $x$. Below we plot the Bayes action over different trading signals. What do you notice?\n" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "figsize(12.5, 6)\n", - "from scipy.optimize import fmin\n", - "\n", - "\n", - "def stock_loss(price, pred, coef=500):\n", - " \"\"\"vectorized for numpy\"\"\"\n", - " sol = np.zeros_like(price)\n", - " ix = price * pred < 0\n", - " sol[ix] = coef * pred ** 2 - np.sign(price[ix]) * pred + abs(price[ix])\n", - " sol[~ix] = abs(price[~ix] - pred)\n", - " return sol\n", - "\n", - "tau_samples = mcmc.trace(\"prec\")[:]\n", - "alpha_samples = mcmc.trace(\"alpha\")[:]\n", - "beta_samples = mcmc.trace(\"beta\")[:]\n", - "\n", - "N = tau_samples.shape[0]\n", - "\n", - "noise = 1. / np.sqrt(tau_samples) * np.random.randn(N)\n", - "\n", - "possible_outcomes = lambda signal: alpha_samples + beta_samples * signal \\\n", - " + noise\n", - "\n", - "\n", - "opt_predictions = np.zeros(50)\n", - "trading_signals = np.linspace(X.min(), X.max(), 50)\n", - "for i, _signal in enumerate(trading_signals):\n", - " _possible_outcomes = possible_outcomes(_signal)\n", - " tomin = lambda pred: stock_loss(_possible_outcomes, pred).mean()\n", - " opt_predictions[i] = fmin(tomin, 0, disp=False)\n", - "\n", - "\n", - "plt.xlabel(\"trading signal\")\n", - "plt.ylabel(\"prediction\")\n", - "plt.title(\"Least-squares prediction vs. Bayes action prediction\")\n", - "plt.plot(X, ls_coef_ * X + ls_intercept, label=\"Least-squares prediction\")\n", - "plt.xlim(X.min(), X.max())\n", - "plt.plot(trading_signals, opt_predictions, label=\"Bayes action prediction\")\n", - "plt.legend(loc=\"upper left\");" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "metadata": {}, - "output_type": "display_data", - "png": 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HmzZtknrM6Oho5OTkYOnSpeDzS79vlz2oW1kcDhw4gOHDh6Np06YAgIULF8LW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- "text": [ - "" - ] - } - ], - "prompt_number": 19 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "What is interesting about the above graph is that when the signal is near 0, and many of the possible returns outcomes are possibly both positive and negative, our best (with respect to our loss) prediction is to predict close to 0, hence *take on no position*. Only when we are very confident do we enter into a position. I call this style of model a *sparse prediction*, where we feel uncomfortable with our uncertainty so choose not to act. (Compare with the least-squares prediction which will rarely, if ever, predict zero). \n", - "\n", - "A good sanity check that our model is still reasonable: as the signal becomes more and more extreme, and we feel more and more confident about the positive/negativeness of returns, our position converges with that of the least-squares line. \n", - "\n", - "The sparse-prediction model is not trying to *fit* the data the best (according to a *squared-error loss* definition of *fit*). That honor would go to the least-squares model. The sparse-prediction model is trying to find the best prediction *with respect to our `stock_loss`-defined loss*. We can turn this reasoning around: the least-squares model is not trying to *predict* the best (according to a *`stock-loss`* definition of *predict*). That honor would go the *sparse prediction* model. The least-squares model is trying to find the best fit of the data *with respect to the squared-error loss*.\n" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "##### Example: Kaggle contest on *Observing Dark World*\n", - "\n", - "\n", - "A personal motivation for learning Bayesian methods was trying to piece together the winning solution to Kaggle's [*Observing Dark Worlds*](http://www.kaggle.com/c/DarkWorlds) contest. From the contest's website:\n", - "\n", - "\n", - "\n", - ">There is more to the Universe than meets the eye. Out in the cosmos exists a form of matter that outnumbers the stuff we can see by almost 7 to 1, and we don\u2019t know what it is. What we do know is that it does not emit or absorb light, so we call it Dark Matter. Such a vast amount of aggregated matter does not go unnoticed. In fact we observe that this stuff aggregates and forms massive structures called Dark Matter Halos. Although dark, it warps and bends spacetime such that any light from a background galaxy which passes close to the Dark Matter will have its path altered and changed. This bending causes the galaxy to appear as an ellipse in the sky.\n", - "\n", - "\n", - "\n", - "\n", - "The contest required predictions about where dark matter was likely to be. The winner, [Tim Salimans](http://timsalimans.com/), used Bayesian inference to find the best locations for the halos (interestingly, the second-place winner also used Bayesian inference). With Tim's permission, we provided his solution [1] here:\n", - "\n", - "1. Construct a prior distribution for the halo positions $p(x)$, i.e. formulate our expectations about the halo positions before looking at the data.\n", - "2. Construct a probabilistic model for the data (observed ellipticities of the galaxies) given the positions of the dark matter halos: $p(e | x)$.\n", - "3. Use Bayes\u2019 rule to get the posterior distribution of the halo positions, i.e. use to the data to guess where the dark matter halos might be.\n", - "4. Minimize the expected loss with respect to the posterior distribution over the predictions for the halo positions: $ \\hat{x} = \\arg \\min_{\\text{prediction} } E_{p(x|e)}[ L( \\text{prediction}, x) ]$ , i.e. tune our predictions to be as good as possible for the given error metric.\n", - "\n" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "The loss function in this problem is very complicated. For the very determined, the loss function is contained in the file DarkWorldsMetric.py in the parent folder. Though I suggest not reading it all, suffice to say the loss function is about 160 lines of code — not something that can be written down in a single mathematical line. The loss function attempts to measure the accuracy of prediction, in a Euclidean distance sense, such that no shift-bias is present. More details can be found on the metric's [main page](http://www.kaggle.com/c/DarkWorlds/details/evaluation). \n", - "\n", - "We will attempt to implement Tim's winning solution using PyMC and our knowledge of loss functions." - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### The Data\n", - "\n", - "The dataset is actually 300 separate files, each representing a sky. In each file, or sky, are between 300 and 720 galaxies. Each galaxy has an $x$ and $y$ position associated with it, ranging from 0 to 4200, and measures of ellipticity: $e_1$ and $e_2$. Information about what these measures mean can be found [here](https://www.kaggle.com/c/DarkWorlds/details/an-introduction-to-ellipticity), but for our purposes it does not matter besides for visualization purposes. Thus a typical sky might look like the following:" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "from draw_sky2 import draw_sky\n", - "\n", - "n_sky = 3 # choose a file/sky to examine.\n", - "data = np.genfromtxt(\"data/Train_Skies/Train_Skies/\\\n", - "Training_Sky%d.csv\" % (n_sky),\n", - " dtype=None,\n", - " skip_header=1,\n", - " delimiter=\",\",\n", - " usecols=[1, 2, 3, 4])\n", - "print \"Data on galaxies in sky %d.\" % n_sky\n", - "print \"position_x, position_y, e_1, e_2 \"\n", - "print data[:3]\n", - "\n", - "fig = draw_sky(data)\n", - "plt.title(\"Galaxy positions and ellipcities of sky %d.\" % n_sky)\n", - "plt.xlabel(\"x-position\")\n", - "plt.ylabel(\"y-position\");" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "Data on galaxies in sky 3.\n", - "position_x, position_y, e_1, e_2 \n", - "[[ 1.62690000e+02 1.60006000e+03 1.14664000e-01 -1.90326000e-01]\n", - " [ 2.27228000e+03 5.40040000e+02 6.23555000e-01 2.14979000e-01]\n", - " [ 3.55364000e+03 2.69771000e+03 2.83527000e-01 -3.01870000e-01]]\n" - ] - }, - { - "metadata": {}, - "output_type": "display_data", - "png": 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6CAgQqiVWxePQ6SiwvqpKyQkIgIAA9Z6WhPR0iIvTEhTkIDq6/EsYQhUo9bRx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3n5mVKw1IWnBTI4wJewdNqy0omaSmqurOVyPLhdsti9sWmjWT+PJLOz17egutf3TsmMgrr1w9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\nq50iTiecOKESGiq8mgPK6YQVK9ynMe+5p5TERO3H17mzi5dfLsHlqrpV2Rs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- "text": [ - "" - ] - } - ], - "prompt_number": 20 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### Priors\n", - "\n", - "Each sky has one, two or three dark matter halos in it. Tim's solution details that his prior distribution of halo positions was uniform, i.e.\n", - "\n", - "\\begin{align}\n", - "& x_i \\sim \\text{Uniform}( 0, 4200)\\\\\\\\\n", - "& y_i \\sim \\text{Uniform}( 0, 4200), \\;\\; i=1,2,3\\\\\\\\\n", - "\\end{align}\n", - "\n", - "Tim and other competitors noted that most skies had one large halo and other halos, if present, were much smaller. Larger halos, having more mass, will influence the surrounding galaxies more. He decided that the large halos would have a mass distributed as a *log*-uniform random variable between 40 and 180 i.e.\n", - "\n", - "$$ m_{\\text{large} } = \\log \\text{Uniform}( 40, 180 ) $$\n", - "\n", - "and in PyMC, \n", - "\n", - " exp_mass_large = pm.Uniform(\"exp_mass_large\", 40, 180)\n", - " @pm.deterministic\n", - " def mass_large(u = exp_mass_large):\n", - " return np.log(u)\n", - "\n", - "(This is what we mean when we say *log*-uniform.) For smaller galaxies, Tim set the mass to be the logarithm of 20. Why did Tim not create a prior for the smaller mass, nor treat it as a unknown? I believe this decision was made to speed up convergence of the algorithm. This is not too restrictive, as by construction the smaller halos have less influence on the galaxies.\n", - "\n", - "Tim logically assumed that the ellipticity of each galaxy is dependent on the position of the halos, the distance between the galaxy and halo, and the mass of the halos. Thus the vector of ellipticity of each galaxy, $\\mathbf{e}_i$, are *children* variables of the vector of halo positions $(\\mathbf{x},\\mathbf{y})$, distance (which we will formalize), and halo masses.\n", - "\n", - "Tim conceived a relationship to connect positions and ellipticity by reading literature and forum posts. He supposed the following was a reasonable relationship:\n", - "\n", - "$$ e_i | ( \\mathbf{x}, \\mathbf{y} ) \\sim \\text{Normal}( \\sum_{j = \\text{halo positions} }d_{i,j} m_j f( r_{i,j} ), \\sigma^2 ) $$\n", - "\n", - "where $d_{i,j}$ is the *tangential direction* (the direction in which halo $j$ bends the light of galaxy $i$), $m_j$ is the mass of halo $j$, $f(r_{i,j})$ is a *decreasing function* of the Euclidean distance between halo $j$ and galaxy $i$. \n", - "\n", - "Tim's function $f$ was defined:\n", - "\n", - "$$ f( r_{i,j} ) = \\frac{1}{\\min( r_{i,j}, 240 ) } $$\n", - "\n", - "for large halos, and for small halos\n", - "\n", - "$$ f( r_{i,j} ) = \\frac{1}{\\min( r_{i,j}, 70 ) } $$\n", - "\n", - "This fully bridges our observations and unknown. This model is incredibly simple, and Tim mentions this simplicity was purposefully designed: it prevents the model from overfitting. \n", - "\n", - "\n", - "### Training & PyMC implementation\n", - "\n", - "For each sky, we run our Bayesian model to find the posteriors for the halo positions — we ignore the (known) halo position. This is slightly different than perhaps traditional approaches to Kaggle competitions, where this model uses no data from other skies nor the known halo location. That does not mean other data are not necessary — in fact, the model was created by comparing different skies. \n" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "def euclidean_distance(x, y):\n", - " return np.sqrt(((x - y) ** 2).sum(axis=1))\n", - "\n", - "\n", - "def f_distance(gxy_pos, halo_pos, c):\n", - " # foo_position should be a 2-d numpy array\n", - " return np.maximum(euclidean_distance(gxy_pos, halo_pos), c)[:, None]\n", - "\n", - "\n", - "def tangential_distance(glxy_position, halo_position):\n", - " # foo_position should be a 2-d numpy array\n", - " delta = glxy_position - halo_position\n", - " t = (2 * np.arctan(delta[:, 1] / delta[:, 0]))[:, None]\n", - " return np.concatenate([-np.cos(t), -np.sin(t)], axis=1)\n", - "\n", - "import pymc as pm\n", - "\n", - "# set the size of the halo's mass\n", - "mass_large = pm.Uniform(\"mass_large\", 40, 180, trace=False)\n", - "\n", - "# set the initial prior position of the halos, it's a 2-d Uniform dist.\n", - "halo_position = pm.Uniform(\"halo_position\", 0, 4200, size=(1, 2))\n", - "\n", - "\n", - "@pm.deterministic\n", - "def mean(mass=mass_large, h_pos=halo_position, glx_pos=data[:, :2]):\n", - " return mass / f_distance(glx_pos, h_pos, 240) *\\\n", - " tangential_distance(glx_pos, h_pos)" - ], - "language": "python", - "metadata": {}, - "outputs": [], - "prompt_number": 20 - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "ellpty = pm.Normal(\"ellipcity\", mean, 1. / 0.05, observed=True,\n", - " value=data[:, 2:])\n", - "mcmc = pm.MCMC([ellpty, mean, halo_position, mass_large])\n", - "map_ = pm.MAP([ellpty, mean, halo_position, mass_large])\n", - "map_.fit()\n", - "mcmc.sample(200000, 140000, 3)" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "output_type": "stream", - "stream": "stdout", - "text": [ - " \r", - "[****************100%******************] 200000 of 200000 complete" - ] - }, - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "\n" - ] - } - ], - "prompt_number": 21 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Below we plot a \"heatmap\" of the posterior distribution. (Which is just a scatter plot of the posterior, but we can visualize it as a heatmap.)" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "t = mcmc.trace(\"halo_position\")[:].reshape(20000, 2)\n", - "\n", - "fig = draw_sky(data)\n", - "plt.title(\"Galaxy positions and ellipcities of sky %d.\" % n_sky)\n", - "plt.xlabel(\"x-position\")\n", - "plt.ylabel(\"y-position\")\n", - "scatter(t[:, 0], t[:, 1], alpha=0.015, c=\"r\")\n", - "plt.xlim(0, 4200)\n", - "plt.ylim(0, 4200);" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "metadata": {}, - "output_type": "display_data", - "png": 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ixAm2bdvGkCFDspiTMiphwcHBGI1GPvnkE06dOsWaNWt49tln3VZr0pSu/v3789BDDzFn\nzhxiYmKYMGGC23XbtWtHvXr1ePHFFxkyZEiePuy+vr488sgj7N69m127djFixAiaNGniiuKbOHEi\nixcvdpk0Fy5cyOuvv87zzz+PXq/n5MmTvPTSS2zZsoVz586xbds2Nm3adMMP5m233cbatWuJiooi\nJiYm22Oeeuop4uLiePjhhzl8+DCbN29m+PDhdOjQIc+O2qBFcP76668cP36cEydO8P333+Pv70/N\nmjWzPf7222/nypUrzJkzh9OnT/Ptt9/eUGnIiTFjxnDlyhVGjx7N0aNHWbNmDZMmTcr1vDfeeIMl\nS5bw/PPPs2/fPk6dOsXq1asZOXLkLadveP/991m1ahVHjx5lzJgxXL16lSeffBLQTMROp5O+ffuy\ndetWzpw5w/Lly1m9enW21woODkZVVVasWMHly5e5fv36TT1PYmIiY8eOZd26dZw5c4a9e/eyevXq\nG/afF198kT179jB+/HiOHTvG6tWrefrppxk2bFi2QQM5sW3bNt58803+/vtvzp8/z5o1azhw4EC2\n937++ed599136du3L6tWrXLtt1gsDBs2jOeff55atWrRsWPHG95zw4YNfP755+zfv5/z58+zZcsW\nBg4ciE6ncwuw6Nq1K6+88kqen0UicVH0bnESiWcQExMjXnrpJVG/fn1hNpuF2WwWDRo0EOPHj3dz\nqN6wYYNo3LixMJlM4vbbbxeLFy8WderUEa+//rrrmMzBBIsWLRKhoaHCZDKJpk2big0bNrg53D/x\nxBOidu3aIj4+3nXOpk2bhMFgECtXrnRr57Rp04SiKGLXrl25PlOa4/cPP/wgQkJChMlkEnfddVcW\n5+p58+aJ+vXrCx8fH1GtWjUxefJkl5N8VFSUGDBggKhevbowGo2iatWqYvTo0SIuLs51fmYH+tWr\nV7uup6qqEEJz3FZV1c35e/v27aJDhw7CbDaLMmXKiKFDh4orV664/v7aa6+J0NBQt7Zu2rRJqKrq\n+k3efPNN0bBhQ+Hn5ycCAwNFp06dxJYtW24olylTpoigoCBhsVhEr169xI8//uh2zW+++UYYDAa3\ncy5cuCBUVRUbNmxw7VuzZo0IDw8XRqNRhIeHi7Vr1+YaTJD2DHfddZfw9/cXFotF1K9fX4wbN07Y\n7fZsnztzezLLMs0pftmyZaJZs2bCaDSKsLAw8ddff7ndNyIiQvTv318EBgYKX19fcccdd4hVq1Zl\ne00hhPjggw9EtWrVhE6nE507d862bbk9T0pKinjwwQfFbbfdJkwmk6hUqZIYPHiwiIyMvKGMVq5c\n6XqWihUriieffNItECK79mbm8OHD4p577hGVK1cWRqNRBAcHiwkTJrgCWLK7xueffy5MJpNYunSp\na19akMtHH310wzYLoQWddOrUSZQvX951z+HDh4ujR4+6HRcSEiIeeeSRXK8nkWRGEaIQnBgkEkmB\nMWHCBNasWcPu3btzPfa1117jhx9+kPmbvJz169fTpUsXIiMjqVq1anE3x+tYuXIlAwYMIDIykgoV\nKhR3cySlnKzJZSQSiUdw/fp1IiIimDVrFp9++mlxN0ci8XqSk5O5dOkSr732GsOGDZNKmsQjkD5q\nEomH0rdvXzp27MiAAQMYNmxYns4pbTVHSzPydy543n//fUJDQ/Hx8eH9998v7uZIJABI06dEIpFI\nJBKJhyJX1CQSiUQikUg8FK/1UVuzZk1xN0EikUgkEokkz3Tt2jXLPq9V1ACaNm1a3E0oEs6cUfno\nIxMLF/pQu7aDDz9Mpn17O4oCY8eOZcaMGQV+zxUrDDz2mAWrVfOTCQx08sEHSXTvbiMgoMBvd0MO\nH1YZONCfS5fSF4h79LAya1YiaWnHCksOJZGSKIukJK3PPf+8BZsN5s9PoHNne7bHjh7ty6JFRrd9\nAwem8sknSZhM6fvyKoeYGIUVKwy8846ZK1dUjEbB228nMXiwlRzq1Jc4SmKfKAykHNLJiyySkuCB\nB/zYssXg2lenjoPVq+MpV847vKqKsk/s2bMn2/3S9FnCcThgxgwjP/5oxOFQiIjQM2SIHydOFO5P\n2727jY0b41i6NI7ly+PYsCGe++8veiXtxAmVQYP83JQ0VRWMH5/CLSZ9l3gQ69YZePxxCwkJCqmp\nCq+9ZiZDOVY3KlTI+oFYvtyHmJj8O98nJsIHH5gYN87ClStaH0tNVXjhBV/On5fDZ25cvKhw+rSK\nTNDvnfj6wtNPuydtPnlSx/nzMtClIJEjTQnn8mWFxYvdayMmJSmcOqX9tDlla79V9HqoW9dJ+/YO\n2rZ1ULNm9nUWCxOHA37+2YeoKJ1rn6IIvv46kUaN3L8MhSWHkkhJk0VUlKYYQfrgn5qqYM9+QY0H\nH7Ti5+eurNWt68Bicd+XFzmcOqXy9dfGLPv9/cHX1ztWDKBw+kRcHLz0kpn27QNYtsyQ4+/lSZS0\nd6MwyassWra088gj7spaUpL3KGqe0CekolbCMZkElSplVZLSVpPyU5qnpBEVpTBzZroty9dXMH9+\nAvfcYyNTXW+vlkN+KWmyiIpS3VZMAe66y0ZgYPbHN2zoYPnyeAYNSqVaNSc9e1r5/PNEMtfVzosc\nFEX7lxEfH8HXXydQs6b3KGq5ySKP5ULduHRJZcUKH1JSFEaNsrBrly7XcxwOOH5c5erV4vnQl7R3\nozDJqyzKlIEJE1J46aVkDAZBnTp2goOLfuJeWHhCn/BqH7XSQNmy8OabyQwZ4ocQ2uDWpo2NevW8\n39ZgNEJ4uJ3Tp3UMH55Kv35WGjb0ngFCopE5gZDRKLj/fmv2B/9Ho0YOZs5MIjZWwWIRZCrNmmfq\n1XPy888JfPSRicREhdat7QwZYs2yYuuNXL0KW7caWLHCwPHjOoKDnbRpY6dBAwe33+6gYsUbK6pW\nK6StgjocCu++a+b77xPw98/5nL//1tGvnz/Nm9v5/PNEr1KGvZmgIM3dZPBgKz4+gipV5O9WkEhF\nzQvo2NHOypXx7Nmjp3JlJy1a2AkK8v4XpWJFwY8/JpCSohAUJLKsfEi8g5AQJ5062Vi/3kBAgJN5\n87KatrNDVbP3V8sPPj7QpYudtm0TcDrxmuCBvPD33wZGjPBzbe/fD0uXakvVLVrY+OijRMLDBUlJ\nmjLt4wOGdJ9yAgIE/v6C+Hjtxdy0Sc/p0yqNG2c/mbLZYPp0EzabwrZtBhYsMDJuXIrbNSWei8GA\nV62kAdjtmh/05csGAgIEDRo4qFq16L+tXpvwds2aNaUm6lMi8XaiohQiI1XKlxfUquVdHwNPJSJC\npU8ffy5fTjc7V63qpF8/K2XLCoQQXL6ssmuXHrsdzGbo1s1G//5WatVy4nDA00/7smBBuo/fnDkJ\n9Otny/Z+Fy8qtG0bQFycdj+LRbBly3W5qlZAOJ1w9qxKTIyCj48gJMRJmTLF3SrP5o8/9Awd6ofD\noU02wsPtzJ2byG23Fc4YtGfPntKXnkMikXgHVaoIqlTxfnOjJ1G3rpMVK+L59lsfFi/2YfhwKwkJ\nCj/+6ENsbPbuzYcO6bj7bk0R0+lgyBCrm6J27VrOy946HZhMWhACQGKiwqVLKjVryt/9Vrl2DX77\nzYfJk31djv4DB6byxhvJVK4sFeHsSEiAt94yu5Q0gIMH9fz0kw8vv5xygzMLHhlM4OVs3ry5uJvg\nEZRUOfz7Lxw6pLJzp46dO3UcOKBy+fKt2XhLqiwKGimHdHKSRe3aTiZPTmHGjCS+/NLIjBmmHJW0\n9u1tLF0aT3h4umIVFmZn0KBU13bmaNyMBAYKatd2V8oSEorWn8Fb+8SaNQbGj7e4RWMuWmTkyJGc\nAzy8VRb5QVUFsN5t386duQfFFDRyRU0i8UASE2HtWgPvvGPi+HH317RGDQcvvJBCr15WypUrpgZK\nSg3JyfDhhyauXcusoAlq13Zy//1W2rWzExZmz2JKK1cOJk1KxsdHsH694Ya+hSYT9OtnZdu2dKc0\nHx+52nOrOBwwf75Ptn/zphQzBY2fH7zySgqDB7vL6J57sjfdFybSR00i8UA2b9bTp48fGXOHZWb+\n/Hh69CgByakkJZ7oaC03Y3Kylr/O319QsaKgYkVnlrQn2ZGaCtevK1SqdOPPzalTKt27+xMbq+Lv\nL9i4Mc7rHNSLg6lTjbz1lnskzOOPp/Dyy8k5prmRQEoKbNmi57PPjFy5ovLww6n07WvLNeL5ZpE+\nakXMgQMqs2YZ8fOj1ITzSwqOatWcNGliZ+/e7EPeqld3yA+YpMioXFlQufLNj2FGI7kqaaCZWhcu\nTOCDD0yMHp1aLIm0vZFhw6xUqCBYvtxA+fKC/v2ttGpll0paLphM0LWrnY4d7SQnc8PUMoWJXFHL\nhvPnFQ4f1nH4sJ74eGjTxkHr1rY8R8jExCjce6+fy2RlNgsWL46ndeuiV9Y2b95M+/bti/y+nkZJ\nlMPlywoREToOHtQRFaXgcGgfu/BwLY/VzYaJl0RZFAZSDul4miwcDi24oKjxNDkUJ1IWGkUpB7mi\nlgeEgO3bdYwcaXErS/Tpp/DVVwkMHJg323R8PBw/nn5+crLC449b+OOPeI/KbxYdrXDypEpMjOZ7\n0rChgzp15AzWU6hUSVCpkp327aV5My/Y7VppM0nJpziUNInkRhw4oGP2bB8GDLDRooW9SHMqyhW1\nDBw+rNKtWwDJyVn9gvKjqMXFQa9e/hw+7P7VWL06jpYti98EGh2tsHGjnjff9OWff9IdhN96K4kn\nn0y9wZkSiecQGalw9qzKqVM6du/WceKEnuBgB3feaadDBxs1anjl0JYtQsD169qk0GZT0OkEZrPA\nz48s5dQkEkn++eUXAyNH+gGCl19O4dFHU285oXZm5IpaHrhwQc1WSWvTxkarVnlf1QgIgEmTUnjw\nQT+3/baiDxbJwoEDKk88YeHYMfef3mAQ+XpGiaS4iI2FjRsNvPSSL1euuEci7tihZ+FCI1OnJvLw\nwzcuM+Ut7NypY84cI7t367lyRSEuTsHPD8qXd1KlipNmzew0bOikenUHISHOYsmsLpGUdCpWTLM2\nKbz3nhlfX8GoUakYjTc8rUCQedQyUL++k3vvTUVRtIGsZk0H06YlMnt2Yr5n5+3a2fj000QMBu28\n5s1thIYWvVkxYy6cw4d1DBjgn0VJ0+sFP/yQQJMmxb/aV1jInEDplGRZ2Gwwd66RRx/1y6KkpREe\nnjdzcUmWQ0bOn1dZtMiHkyd1XL+uIoRCfLzC2bM6tm0z8NlnZp54wkLv3gF06hTAhx+aOHHCXXbe\nIotbRcohHSkLjTQ53Habk7Jl07/h//d/ZnbtKhobvVxRy0BwsJMZM5KYMiUFVdUSMJYvf3OzT39/\neOABK82b24mLU6hWzZmnqKecOHJE5cIFlcaNHTeVSdpqhffey5qssls3KxMnptCwoQNVqu0SD8dm\ng1Onsg6OiiIID7czdmwqd95pL1XZ1vv2tREWdp0DB/TMnGniwAEdOaV1iYlRefddMz/+6MOyZfFU\nq1Z65CSR3ArVqwvefTeJJ57QLGVCKDzzjC9LliRQvXrhvkfSR60EcP063H+/H7t2GejdO5WPP07O\ndx6XpCT47DMTX39tpHx5wZ132hg40Eq9eg4Zoi0pUfz7L5w4oePaNQWrFcqU0XJ6Va3qLLbw+eLk\n7FmVX34x4HQqtGljo3x5wb//KsTGKly/rhIdrRIVpRAQoMmoUiVBvXpa4JCcnLlz8qTKsWM69HpB\nWJijVPk5SnLnyhWFkSMtbNqUnjZp7twE+vQpGL+mnHzUpKJWAoiMVGjRIpDUVG2W/OGHiTz2WP79\nbxwOLXWI2SwICCjoVkokkpshNhZ27tSMG2FhjnzPzv/4Q8/gweka6uOPp/D00ynSFy2fnDih0rev\nP9HRmvbaqJGdOXMSqVVLRsJL0omIUOnVy5+rV7V+0ru3lTlzEgsk4jwnRU3Op0oIGdXp994zc+FC\n3mrgZfQz0OkgKKh0KmnS3yIdKQsNT5HDsWM6hgzxZ8gQf3r0CGD79vz5vWir6+kDxJdfmpgwwZeo\nqLzXyfQUWRQnW7fqiY7e6No+cEDPypXZJ5wuDcg+oZFZDnXrOlm8OJ5atTQ/2CNHdMTF3fgaNhv/\nBfrcXBuqnMbFAAAgAElEQVSkolYCqFDBPSLz6lU1Wz8dicSTiYuDfft0LFtm4Pff9fzzT9EW3PZU\nlAxiuHhR5f77/dmzJ+/vd926Du67z32FfeVKH77/3ohTLgblGWs2RoqNG6UbtyQrjRo5Wbw4kRkz\nEnnlleQbJsM/eVJl7FhfOnUKoHv3AGbN8sn32FekiprD4aBJkybce++9AMTGxnL33XdTt25dunXr\nxrVr11zHvvvuu4SGhnL77bfzxx9/uPbv3r2b8PBwQkNDefbZZwusbSdOqHz/vQ/Llhk4edKz9FeT\nCR580H0U2bcvbwN5ac0sHRsLf/+t46+/9GzcqKNKlQ4ekR7FEyiOPnHkiMro0Ra6dAlgxAg/hgzx\nZ+ZMU5G3IyOe8m6EhDgzhP5DYqLCY49ZOHs2b+OQxaIVPm/SxD3S9X//M3H6dN6u4SmyKE4aNnQC\nHd32NW/uvZHwueHtfSIhARYtMrBqlYHLl3NWnHKSQ3CwkyFDrAwYYMvR19NqhTfeMLNokZGoKJXj\nx3W89JKFRx+1cPFi3pW1ItVIpk+fToMGDVD+m0K+99573H333URERNC1a1fee+89AI4cOcJPP/3E\nkSNHWL16NU8++SRprnRjxoxh9uzZnDhxghMnTrB69eoCaduaNQaeecbCiBF+dOoUwKpVepKTC+TS\nBUKTJnZMpnTzRmysXI3IiWvXYPJkX3r0CGDQIH/69QugXbsA3n8/7x8uScFx4IBKnz7+/PGHe+ZV\nvV76UAFUqSKYPj2JjObLc+e0JL55JSREMHt2Iv36pSesTklR+PdfOU7klUaN7Hz2WRJGo/Y7NG1q\nY9AgmQDcW7l2TeG55ywMHerHqFEWIiIK/tugqlogX2Z27jSwf3/e3+8i+2pFRkaycuVKRo4c6VK6\nli5dyogRIwAYMWIEv/32GwBLlixhyJAhGAwGQkJCqFOnDjt27CAqKor4+HhatmwJwEMPPeQ651Yp\nXz59RpuUpDB0qB9LlhiyXQ4vDurUcfLZZ4mkDeZVquTtI1ca/QwSExVWr3b3LbFaNzB1qpkhQyyc\nO1e6lbWi7BOXLys88YQlS1oYf3/B/fcX78vlSe/GnXfaePVV95nhkiU+5CfUKyTEyYcfJrFsWRyT\nJiUzbVoiwcF5s316kiyKC4sFqldfy+bNcWzYcJ0FCxIJCSm9kwlv7xNlygjCwrRV6E2bDDzwgB+n\nT2ed2NyKHPR6GDcuJdtJqdOZ90lUkRngx40bx4cffkhcBm+6S5cuERQUBEBQUBCXLl0C4OLFi7Ru\n3dp1XPXq1fnnn38wGAxUr17dtb9atWr8888/Od5z7Nix1KxZE4CAgADCw8Ndy5hpwk/bFmI9ZrOF\n5OTO/529gSefFISENKN1a0eW44t6e+vWzQQEwOzZnfnqKyMBAevYvNmZ6/lpFHf7i3K7WjXBqFG/\n8+GHJiDt99wHwIkTnTh2TOXChY0e015v3vbz6/BfguX1aHSiShUnL7ywimvXnEDxte/gwYPFLp+0\n7b17N1O/PnzySRcmTzYTF7cRH59UFKVlvq/Xrp0DITYAUKlS3u5/8ODBYn1+T9lWVahd28nmzZu5\nfr3421Oc2570fhTW9qhRndm50wCs59w5eOmldsycmcjx45sK7H6tWzt4772V/PijD0eO3IWqwj33\n/IHTaWPzZsGWLVs4f/48AI899hjZUSTpOZYvX86qVauYMWMG69ev5+OPP2bZsmWULVuWf//913Vc\nuXLliI2N5emnn6Z169YMHToUgJEjR9KzZ09CQkJ4+eWX+fPPPwHYtGkTH3zwAcuWLctyz5tJz7Fp\nk5777/fDak3XdPv0sfLll4lFUiYir6SkaH5rkpxJTYX9+3V89JGJtWsNrtnLHXfY+fLLxGKpElGa\nOHtW5ccffYiMVClb1smqVT5Urepk+HArrVrZ87zSUxo5c0bl8mWF6tWdMiGtJFeuXtUqURiNWj7B\ngkgTUVq4cEGhXz8/zpxJF9r06YkMG2Z1C/IpCFJStPRYiqJlX8judyrWWp9bt25l6dKlrFy5kpSU\nFOLi4hg+fDhBQUFER0dTuXJloqKiqFSpEqCtlF24cMF1fmRkJNWrV6datWpERka67a9WrVqBtbNd\nOzu//BLP8OF+/PuvZqrZtUtPXJyS7wSzhYlU0nLHaISWLR3MnZvIP/+oJCRohaqrVhUFXkhX4s7F\ni1pSyD17tOElJMRBq1Z2nnsumXr1pOxz47bbnNx2W3G3QuLJJCTA3r1a+pBVqwxcuKBStqzg3nut\nPPtsKiEhciKUF2rUEMyYkUTv3v6uyfyECb60amWnbt2ClaHJxE1XMCgSZ5133nmHCxcucObMGRYs\nWECXLl347rvv6NOnD/PmzQNg3rx59OvXD4A+ffqwYMECrFYrZ86c4cSJE7Rs2ZLKlSsTEBDAjh07\nEELw3Xffuc4pCFQV2rZ1sHp1PJ99lsh991l5990kypQpuR8Xb/czyA1fXwgNdZKYuIFGjZxFqqRd\nuqTw1196li41cPy45/jFFXaf2LFD71LSAM6e1fHTT0YSEjxHBiDfjYxIWWiUBDlcuqTw1ltm+vb1\n58svTZw/r0MIhdhYlXnz0kqI3TolQRYFQbNmDqZNS/f4T01VOHw4XYaeIIdiWSRNi/p8+eWXGTRo\nELNnzyYkJISFCxcC0KBBAwYNGkSDBg3Q6/XMnDnTdc7MmTN5+OGHSU5O5p577qFHjx4F3r7QUCeh\nodYsKTEyY7VqS5lVqogCXyaVlGyiohRefNGXlSu1SMeKFZ0sXRpPvXrZz9ISErQgiAoVBLoSniLv\n0qWsClnbtjY5y5dICoDdu/V89VX2ZpWqVR3Ur196U4rcDAYD9O1rJTFRYdIkM06nwl9/Gejf33Py\nOckSUjeJzQY//eTDq6+aeffdJPr2tUmTpMTFr78aeOwxP7d9n3yi+T5kZu9eHZMnmzl1SsegQamM\nGGGldu2Sq9Ts2qWjd29/l69ns2Y2Zs5Mkn6BEkkBsGuXjv79/UlMTF8dsFgEDz6YyuOPp1Crlld+\n0gsdmw1279bx6acmeva0ZTtWFzbF6qPmjZw8qTJ+vC92u8KTT1qoXTu+VCdHlLjz999ZXy1HNt3j\n6lXNn+vMGW0Z7bPPzKxda+DnnxPynILF02ja1MHatXGcO6dSpoygTh2nR/l4SiQlmebNtfcrMlIl\nOVlLM1G1qqB6dacMJLgFDAZo3dpBixaJ2Y7VxYlnOY2UIKKiVOx2bUYjRNa8XZ6CJ9jXPYGilkNQ\nUObVI0Hdulnf/mvXtCi/jBw5oufQocKzfxa2LFQVGjRw0rOnnTZtHB6rpMl3Ix0pC42SIofQUCed\nO9u55x47bds6CAkpeCWtpMiioNHpwCdDbm5PkINU1G6SlBT37dWrDSQkFE9bJJ7HPffYqFZNU8wU\nRfDee0k0apRVUStfXtC6tT3L/rg46fQokUgkEumjdtNs26ayfLkRHx/47DMj1ao5WbMmnvLlvVKc\nkpvg3DmV8+cVAgMFdes6c/Rh3LtXR//+fsTFafMmk0nw++9xhIdLny6JRCK5EbGxWgWAgIDibsmt\nI33UCpDYWDh9WsfPP/vQtq2dsDAHfn6CgACppJUG7HY4flwlMlJFCK04b926zizRmsHBToKDc79e\nkyYO/vgjnj179MTHQ4sWjv8KREskEknRYbdDfDyULVvcLckbCQnw3ntmKlYUjB2bgq9vcbeocJCm\nz3xy9qzK2LEWnn7aj5gYlaAgJ5cuqQwbZsXggW5qnmBf9wQKUg5//aWnc+cAhgzx58EH/encOYA5\nc3yIj7/5a9at62TwYCujRlm54w5HoaZ7yU0Wp0+r/O9/Rr7/3ofLl73XBCvfjXSkLDRKuxz++ktP\nz54BrFmjZ+NGz5fF6dMqX39t5L33TJw4UTh+vZ7QJ6Silg8uXFB4+mlffv9d8zTU6QRdu9oYPz6Z\nLl08J+eKpPD491949VVfVyAJgNWq8NJLFvbvL/kL1NeuwYsv+vLmm74884yFBQvyVxhcIpGUTFJS\nYOpUExEROh580M+jknTnxMWLKqAghMLBgyU8AeUN8PxfwkO4ckXhlVfMbNmSvmz2+OOpdOpkZ9Qo\nK5UqeebXLK1IbGmnoOTg7w9Nm2Z1/gctY3hJ4EayOHdOZd269D7+yScmoqJKxnPlF/lupCNloVGa\n5WC1Qny8phLYbApz53YnNtaz3/1//klXYX75xVAoaTU8oU9IRS0PpKTA99/7sGJFemX2Bg3sPP54\nilsYr8T70evhhRdSaNPGfQW1dm07TZpkr8CVJK5ccR8SYmNVYmI8e7CWSCS3jtEIlSun+8YeParn\n2DHPVhEyWjbOn9cRF1eMjSlEPPtX8BAOHtTx5ptm13bZsk6+/DKRGjU8cxUtI55gX/cEClIOdeo4\n+e67BJYvj2PevAQWL47n118TijQj+IEDOqZPN/Lll0YiI/OnSN1IFln9LIVH+l4WBPLdSEfKQqM0\ny8FohPvuy5iNfz27dnm2O4denz7mXrmikpxc8JNKT+gTnv0reABJSTBzphHQOoC/v2DRogTCwmRU\nXmmmXDlo29YBFH0K64MHVXr1Si8hc/q0yltvJReIQlWjhhOTSZCSol27dm1nNsl7JRKJN9K4sR1V\nFTid2vu/YoUPTzyRekuWo3/+UTh1SqVCBUGDBgU7lgQGpitqVis4vXSokitquXD+vMrSpVovrV/f\nztKlcTRpUvz1JVJTyZNJyhPs656At8ghOVkLR89Y52/BAiNXruR9JnkjWYSEOPnggyQURWAwCN5/\nP4ly5W6pyR6Lp/aJ5GTYulXPX3/pi8w/0FNlUdR4uxycTq1/5URoqJOhQ1P/2+qEENxSBPrp0yoP\nPOBHv34B9OgRwL59Bevwb7GkK2pOJ4US+OQJfUKuqOWCqkKrVnYGDLDSs6eNatWK39wZFaUwc6aR\nJUt8mDQpmd69bVgsxd0qzyI5WfMt9PfHq+rfXb2qsHat+9KZ0ShQb2LKZbVqARCpqQqVKjkJCND6\n+8CBVho0cGAwFPwMWJI7q1YZGDnSAih06mRj5sxEKlcu/nGnJJKYCDEx6n++Swp6vaB8eeGxwV+F\nycGDKlOnmjl3TqVJEzsDBtho0sTulnvMZILx41PZs0fP4cN62ra13fRKvcMB333nw5Ej2gCckKDw\n228G7rij4BY6qlYVgAAUgoOd+Pl55+/q1Stq0dEKSUm3do26dZ389lsCI0daPUJJA1izxsCMGWYi\nI3WMGXPjtBCeYF8vKoSAQ4dUpk0z0ru3P127BvD44xaOHVO9Sg6ZlbL77rPmq57m+vWb2blTx+jR\nFtq0CaRly0Aee8yPCxe0qbPJpBVWDw/PmsTXm/DEPhEbq/DWW2bSXC3WrzewZ0/hzzQ8URY3g80G\nEREqf/6p5+23TfTs6U+rVgF07BhIx44BtGsXSPfufhw5kv2nz1vkkJmrVxUeftiPJUt82LdPzzff\nmLj3Xj9mzjRx/br7scHBTr77LpGJE1cxfLg1+wvmgagohTlz3MuxnDpVsANKzZoO6tfXFL9OnWyF\nkqjXE/qEVytqHToE8Ntvtx6W6UmRncnJ8MMPGRuksHKll3p754PUVC08++67A3jjDV/27tVz9qyO\nX3/1YerUHGo3lUCCggRPPJFeaLZ6dQejRqXmWaFKSYGNG/X07OnP0qU+JCVpCsGaNQYiI716OCgR\nxMcrnD/v/jv88YcXLQkXEg6HFvT12msm2rcP4IEH/Pn4YzOHDumxWjPa7gS9etndohtLA3q9wGzO\nPJlTeOcdc7YTgZAQJ23a2Kld++blpKX7cLebNmxYsG5DZcvClCnJgKBv35tXKj0drx4BYmJUXn3V\nTOfONqpU8YzVsFslORkuX3YfyA8cyPkr7Qn29aLgwAFthUiIrA4VnTvbvUYOBgOMGpXKHXc4EEIb\n+GrVyvtgqkWL9sgip6pVHVSvXro+Xp7YJ8xmzSwXHZ3++6SmFr6fmifKIq/Y7bB8uYHHH7dgs+Uk\nK8G991oZMyaV8HBHjq4iJVkONyIwEN57L5mBA/0yKa5atZ3suFVZWCxQtarzv6S0oKqCbt0KPjH8\nnXfa+euveNfKWkHjCX3C66fQ3pYHKiAga8JVb8jfdatcuaJko6QJxo1LpmtXz6oaYbNpJtozZ27u\n9atcWXDvvTb69LHlS0kDiIjQZZFTUJCT+fMTSkS6GW+nUiXBM8+kuO1r316+3zciMRF27HBfczAa\nBY0a2XnmmWTmz49n8+Y4Zs5MonXrnJU0b6dtWzsrVsTTrp0Nza8L6tSx06pV4fSvoCDB9OmJ6PUC\nHx/BjBmJBb6iBppC2LSpA7M592NLKl69opaGN4Xs6vUwYkQqixf7oPmxCLp3z1kR2bx5s0fMCAqb\nZs0cfPBBIj/+aMTHB9q3t9Gtm43wcAcmk2fJYe1aPcOH+1G3roOff04o0tXeO+6wU7PmGs6f70Jw\nsJNhw6z062e9JRNHScWT+kRGeve2snu3jsWLfeja1c6ddxb+RMNTZZEXAgPh9deTGTMmldT/AhaN\nRqhQwZnvIt0lWQ65oaraODl/fgKXLqkkJ2sTg6Cg7MefgpBFp052Nm+OQ6+HmjWdJTKwyxP6RAkU\nW/5QFIG/v3etFDRr5mDBggTmzTMydKjVI9KFFDdBQYKRI60MHWrFYCi4SM/r1zU/C7MZype/9X50\n8qTKmDEW7HaFI0f0nDqlUqVK0f1+DRs6eeedZOrXv05AQME8kyTvnDqlcvq0SpUqTurVc2YbUVe9\numDatCQmTEihfHmn16ZHKUh8fDRFIL9cuKAQG6tQqZLwGveY3PD3B3//opmY6XRaQJ7k1lCE8M6S\ny2vWrOGuu7pSr56D1avjCAws7hZJShLXrmkRdx9/bOLkSR1Vqjj59NNE2rW7NaVq2TIDI0b4ubZn\nz06gf3/PMs1KspKaqkVk+vjcvHJrt8OoURaWLPFBrxdMmJDMI49YpbJcTOzbpxUfj45WqVxZM/8X\nZOoIiSS/7Nmzh65du2bZ7/U+ag88kCqVNEm+SEyEzz4z8eijfhw+rCc1VeHsWR2PPebHsWMqZ84o\nXL6s3FQB4L//dg/8MBrlR9rTOXVK5fnnfWnfPoC77vLn99/1WG8iwMxux5XA1m5XeOcdX2bMMJKQ\nUMANluTKtWswbpwv0dHaJzA6WmXkSF+3IA6JxFPwakUtIMBJr16le7XCE3LAeAL5kUNEhC7blB5+\nfoLPPjPRrFkgnTsH8MILZvbt0+VZYUtLIZCRMmWKXlHLLAshYPt2HRMnmpk718eVT83byUufuHJF\n4cknfZk/38i//6qcO6etwhw+nP98UCaTlkw4I9Ommdm8ufjT65S2ceL6dTXLu3j6tJ5Vq7YUU4s8\nj9LWJ3LCE+Tg1Yra4sUJhIZK+7g3Eh2tcPVq4Vw7JQXSEo6modcLRo1KZdkyLYgjKkpl3jwT3bv7\nZ1klywmtxEn6dc1m4RFJlI8eVbnvPn++/NLE+PEWnn3WUmSlizydc+dUdu50V6SEUG565aVzZzsV\nK7qPSW+9ZeLatZtuouQmsFhENulohEflzJRI0vBqRa1ZM+lvUNzRKoXB2bMqQ4b48eGH5jybjfIj\nh3r1HLzySjJms8BoFHToYOPdd5P44gtjlgSONpvCoUN5U9QMBujRI32Fd9KkZGrUKPqJRGZZnD+v\nkpyc/lzr1xvYts3r44zy1Cd8fNJK1GQk50i53Khd28m33yZgMqWff+SIjkuXinco9sZx4kZUqCD4\n8EOtpm0aw4en0rdv22JslWdR2vpETniCHLx/NJYUORs26PHzE9xxh6NQShCtWaNn/349+/frGDo0\nlfDwglV2ypWDZ59N4YEHUv/bFpw5o3DqlI6VK+HCBRUhFKpVczJyZAq9e+fdvN65s42qVZ20a2ej\nXz/rTdXoLGjKlNGKrwPMmWPk+HEd69YZGDCgdLsNgKZYTZyYwrvvakmaVFXwv/8l3VJyzZYtHfz6\nazzjx/ty9KieihWF19Yo9GQ6dLCzcmU8+/frqVxZy8Tv55f7eRLJtWtw+LCO48d1VKwoaNbM/l/d\n0cLBq6M+mzZtWtzNKHaKOgdMZKRC+/YBJCcrLF0aT6tWBbuqefmyQpcuAa5s1/Pnx9OjR+4JGwtC\nDkJokX8JCVoggZ/fzRV3jo5W8PMTxfZRyCyLDRt0DBjgD8BbbyUzaZKZwYOtzJx5i4VyPZy89omE\nBDh6VEdcnFa8vl49Z4GYyK5c0cpFBQSIYnfR8IRcUZ6AlEM6abJwOLQAK5tNwd+/9JmHM/eJmBiF\nd94xMXduuh/z0KGpfPRREkbjrd0rp6hPuaImKVCsVoiL05Soxx+3sGRJAsHBBfcRunpVcSlpkH6v\nokBRtNQMt5pOoXJlz5kbORywdKmPy3du3ToDd95p46GHUou5ZZ6Dnx+0aFHwbhQVKwoqVpTuGYXN\nuXMqW7bo2bBBT4UKgh49bNxxhx1//+JumWeSmqq5Q+zZo2P7dhMbNuiJiVFJSoJGjRy8+mpyjhOL\nuDhITlYoX16UyOS2eWHjRr2bkgawYoWBV15RCi0Xn5eKUpJGUc8O9XoFnU7gcCicP69j2zY9wcEF\nVyz3+nV3HzFVzduLIWfJ6aTJIikJ/vlHYe3adGf5LVv0rFwZR/363h+EkyaHf/+FhAQt6emtzohL\nKt76fkRHKzz6qIW9e9M/dZ9/buKNN5J44onULMqEt8ohL1y4oHDwoJ7583344w8Ddvs9WY5p1sye\nbaS6ELBrl46XXjJz8aKOESNSGT06hfLli6LlhUvGPuFwwHffZV1SbNTIQWBg4U3APcBDRlKSsNm0\nj3tSDlaxMmWc1KuXvkowdaqRq1cLLoIwc9Fls7lgXg67HU6cUAu0rZ7IxYsKW7fqmDHDSN++fnz1\nlYmUlPRnTk7WTLulxbyxZ4+OXr38ad48kK+/Nv4X8SvxFs6fV92UtDTeftvM+fPy8wcQG6sVte/Z\nM4Bhw/xYudIHu919HCxf3snEiUlUruwkISHrGHnokI6+ff3Zt8/A5csqH35oZtu24k87U9DodBAW\n5j6J9fUV/N//Jee7XFl+kD3VyynIHDCRkQqTJ5tp2zaQCRN8OXdO6z7JyXDggMrixQbeesvs5lx/\n8qSes2cLrptldqnM6ywmNzmsW6enbdsAHnzQctPF0j2ZCxcUvv/eh06dAujdew9Tpviye7eB2Fg1\niwwLc2boSXz//Vb69/fn2DE9NpvClClmTpzwvt8+L3hCrqjCoEoVZ5Z0KKAF0GSMvE3DW+WQE1FR\nChMn+vLQQ35uLiUa62jb1sasWQnMnZvA55+b+OILMwsX+mDLFGe0fbvObcIHsHNnIUSSFQOZ+8Qj\nj6Ty0EMp3Habg0ceSWHlyvhCL+MoTZ+SPPPTT0ZmzdJs8/PnG6lSxcnAgVY++8zEDz+kFYmH995L\ndDsvIkJXYKlSKlZMS5egEBDgpHr1W1cqLl1SePZZCw6Hws6dBubP9+GVV1JQvGRxbe9eHcOHW7h4\nMevAeeGCSu3aDiIitL8FBDiLJQlvcbBpkz5TuhWFxEQv+dG9hKQkiIlRSUnRioqXKaP5iOb13axR\nQ7BoUTyvvebLunXa5+722x189llSoUbplRQiIlQiIlT8/bXI43LlnLRvb+fOO23ExibRv38CFgv8\n8ouBa9c0RW7qVBP33WelTp10BTirkgf16nmn+0Tt2k4+/DCZ+PhkAgMplMwGmZGKmpdTUD4XUVEK\nn3/u7sCzcKEPV64o/PBD+n5/f0HbtnYaN7azf7/WvQ4c0DFkSIE0gypVnDRs6ODQIT1jx6YSEpK3\nweBGcoiNVVylZAC++srEQw+lUqNGyR/IExPhgw9MmZS0jtSu7aBrVxudO1tRFIVVqzRb50MPpXpE\nEt7CJjERjh1zj64yGAQVKnj/s2eHJ/pmnT+v8MYbZpYuTTPFaUlq27e307Onjbp1HdSt68xVaQsP\ndzJvXgIXL6o4nVCpUs6F7j1RDoVFUhK8/76Z4GBB27aphIfb6d7dRtmyaUek55QLCnLy8svJgJYQ\n/OJFhTp10q/VqZOd6dO1CTRAlSoOWrbMPRq/JJBdnzAYyLEPFQZSUZPkCbudLL4JDodCxgz+Zco4\n+emnBBo2dPL668n06+cHKAXq91WmDPzvf0ksXOjjynN2q2Rexo+P19rsDYqaxQIzZiRx4UIyNpuC\nXq/5VFSs6HQNyNeuwYQJyaxdq2f4cKvXrCTeCJ2OLLnLxo9PybPiLyl8FEXzIUz3l1KIjNSxYIGO\nBQuMmEyCSZOS6dfPmuvkws8P6taVv21GUlLg0iWV7du1SZyiCNaujadsWXfrx8mTKi++6MuxY5q6\nUK6ckwYNHDgc6Xkymze3M3duIvPn+1CnjpPhw1PdVtwkt0bpdMgoRRSUz0WlSoKOHd01mm7dbGza\npL28Q4em8vvv8a40Bs2b23nhBc0zu2bNgn1hmzVz8P77ydSsmXdF6kZyKFMma1BCcWcXLMj7lysn\naNzYSfPmDu64w8HlyxszzJq153/uuRR++qn0lFwzmaBXrz9dlQdGjUrh4YezRgGWFjzRN6tGDcGC\nBYk8/HAKWatDQEqKwpQpvrz0ki+xsQVzT0+UQ2Hh7w9hYelKmRAKW7akvwBpspg/38elpAHExqqM\nHWvh2LF09cFigT59bCxYkMhbbyV7ldnTE/pEKR2WJPnFaITJk5M5elRHZKSOpk3tBAU5KV/eySef\nJNKokcMtL5GvL4wenUrjxg5q1fLsXFHVqjkZNizV5X9nNArKlCmethw9qjJvnpErV1ReeSWZ2rWL\nZsAzmbR/pYnwcAebNsXhcGiTicKM2pLcHHXrOnn77WSGDbNy6JCOhQt92L9f7/IlVBRBQIBwmUYl\necdggPvvt7J8eXqI98KFBh56KNUtGbczmyHIZtPqHYeFOXE64dgxlfPnVYKCtIo0sbFw7JgOm02r\n4Aq8egYAACAASURBVFKrlrNIfLm8FVmZQJJnEhO16MiYGJWKFQXlyjmoW/fWE8B6AkePqvTp48/V\nqyqTJiXxzDOp7N+v4+effQgJcdKtm5XatQv3OSMitDZcvqzNVF98MZmJE2W+CIkkjZQUraLD9esK\niqJgNguCgpxYLMXdspLJuXMqXbr48++/2phTt66D33+PIzAw/ZgDB1R69w5wc30JCnKyYkU8gYFO\nfvvNh0mTfLFaFYxGwdatcRw9qmPYME3bMxi09BX9+1sLLSGstyArE0huGYsFevf2DgfRzNSv7+T3\n3+OIjNQRHm7nyBEd997rT2qqNjjNn+/D/PkJhea3lpKiRVOlKWmgBWFIJJJ0TCbNJJrdeygErFql\n55tvjPToYaNHD1upCIy5FYKDncyencigQX7Y7QphYY4sSm+jRtrYuHq1gZ079dSo4aRXLxuVKjmZ\nPt3Exx+bXcdarZrPb8blH5tNYfJkX9auNfDRR0nSD/QmkD5qXo4n2Nc9gbzIoVYtQYcOdsqWhePH\nVZeSBnD4sJ7duwtvXnPhgsqiRe5ZZnNKaSIEnDql8vffOi5cyL/nv+wTGlIO6XiDLCIjFcaM8WPN\nGh9efNHCU09Z8v1+eIMc8sudd9pZsSKeKVOSePHFZJefZkZZ1K/vZNy4VObMSWTYsFQaNrSzZ4/e\nTUkDzW+5alUnjRrZqVbNffxau9bA9OlGkpI0U+nx4yVD/fCEPlEyJCWRFDHZRT6ePl14K1wxMQpO\nZ8abCtq3t2U57to1mDfPhw4dAujRI4CePf05fVq+xhKJw6GQmCGF44YNBubMMWItuAp2XolOp9Wy\nHTculdtvv/Fql8mkpTsxmeDDD92dWo1Gwcsvp+Dnp616fvttIhUquF9v3jwjERE6pk0z0a1bALt2\nSatBXpAjvJdTmvIC3Yj8yiE01Ile7242qVGj8IIiLJa0RL4aY8em0LCh+/2cTvj5Zx/Gj7eQnKwp\ndRcv6vJd+UH2CQ0ph3S8QRZBQU66dHGf3MycacrX++ENcigobiSLuDiFY8fSlSyzWfD99wk0apQ+\nZjVp4mDZsnh69XJPo2SzwblzOuLjFUaMsHj8RNMT+oRnS0giKSbCwx3MmpWI0agpT+3a2WjVqvD8\n8+rUcfLaa8ncdpuDKVOSGDvWPfIKtGCD//u/zKGJWtSbxHNwOODQIZUvvzQyerQvu3fLVYOiwGyG\nZ591T+VhsylERsrPXEFTvrzg6adTqFHDwYMPpvLHH3F06WLPYomoV8/Jp58m8ddfcXz3XTzLl8fT\noIGDBg20sTQqSseXXxqz5LKUuCN7sJfjCfZ1TyC/ctDp4N57bWzaFMeff8Yxe3ZivvK25RdfXxgz\nJpW//orjuedSqVw5670uXlSz1NPr2dNGvXr5W+mTfUKjMOSQkACLFhno0iWAiRN9WbTI6Mo16Ml4\nS59o1szB1KlJZFTWMudIvBHeIoeC4EayMBi08Wrt2nimTUsiLCznChFlykDTpg569bLTtq0WrJDR\n/3bOHGOR+qtdvapw6pTC8eMqFy8queas9IQ+4fkjiOSWcTohOlqhXDlR6nJl3QqqSpFm1zYYcEtE\nm5kKFZyoqnD5sjVrZuPNN5Pd8tdJio/ERPj2WyOTJ7uvejZu7Nl5BL0JkwkGD7YSGupg6VIfQkMd\n+Z7ISPKGwcBNp2bSEu1qJaccDoV16ww0bFgwlWZywmqFtWv1TJzoy7lzKmn1oocNszJ4sDWLq4kn\nIfOoeTkpKfDrrwZeecWXhx9OZezY1FJbz7CkY7XCrl06Dh3SExzsoEkTB5Uqyd/SU1i50sCwYRYy\nllVr2lTL1i7fOc/B4YDr18Hp1PJ+yYlO0RMfD/ff78fffxsAqFzZydq1cdlaEgqKgwdVOnUKQIis\nS38Wi2DlynjCw4tXWZN51EopR47oeOopC0IoTJ9uplkzB717S4eAkoiPD7Rt66BtW8+d+ZVWLl5U\nmDDBl4xKWkiInS++SJJKmocQEaGycaOeZct8uHBBxW7X6lYOHWqjUydbqSmf5gn4+2u1dQcP1hS1\n6GiV06dVKlcuvLGtUiVB/foOjhzJqvYkJiqcOKEWu6KWE9JHzctZtmyr2wzixx99SqXjpif4GXgK\nUhYaBSmHf/5RuXgxfTht29bGwoWJJaYwtbf3id27ddx1VwATJljYtMnA2bNaKbwDBwy89JIvgwb5\n8c8/isfLISpKYe1aPcuX6ws9WrKwZdG4sYPatdMDtK5eLdznCQoSfPddIpMmJVOunPZe+vgI6tSx\nM2FCEm3bZv9h9IQ+IVfUvJyYGPdl3hMndCQmUmy1LCUSb6RCBUH37lbsdnjkEStNmtj/n73zDm+q\nXh/455yMpm3askttAaHMUqZQAVGQPRRwABeRoQxFFPUirutC7xVcF0EUUeEqgqAiIlNAlhZliPID\nZMgoexRoaZM285zz++PQpqEFOtIkbc/neXwwaZLzzZvveM87tXY5QcTevTqvFkhX06CBHNTxu5IE\n27freOKJMI4eVY/twYMdzJqVHeCRFZ/oaIVZs7Lp0ycCt1ttC1ba1K0rM3GinSFDHFy4IHDwoI6d\nO/WcPy/y6acmWrWSqFVLok4dOajOSE1RK+d06NCRBQs8j6Ojg3tDKi2CoRZOsKDJQsWXcqhbV2b+\n/CxkWQ2yLmuU9znRq5cLScpi9mwThw6pgeRhYao15YknHLRv76ZqVYUWLTqyebOePXt0yDIkJko0\naCCVWuu4wvLbb3ruvdd8pfm8itUqIEmUWrNzf8yJVq0kPv44i0cfDScqyn8yvukmhcuXBSZMCMfp\nvFpBVEhIkHj8cQd33OG6oRwOHBBJTRVp0cLt1SPVl2iKWjmncWMJQVBy3Z+DBjkrpKKmoVHa6HSl\nd2hqlIzoaIWHH3Zyzz1O0tPVvdBohKgo72SC//s/Pffc451dUKOGzJtvZtOjhytfbUN/kJIiMmpU\nuJeSBvDQQ44yP990OujXz0XDhplUqeJfZbhxY5kvv7Qydmw4GRl53a4C+/bpeewxPfHxbmbPzqZ1\n64Jj106eFBg0yMypUzreey+Lhx4qnTYYWoxaOSc9fTPTpmWj16uumc6dK2CAGsERZxAsaLJQ0eTg\noaLIonJltadvvXoKcXH5Mz5TUn7GYPBWGFJTRUaPNrNwoTEg7aj27dNx4YL3UT16tJ22bUuvADf4\nb07o9ZCYKHPTTf5V1EQRund3s3atheees1G1av540iNH9AwY8DspKQWrSkeOqLGOAK+9FsaRI6Wj\nUmkWtXKO0QgPPODk9tvdVKokX7dOl4aGhkZFpk4dmf/9z8qIEWYkyduC9eKLYXTu7PZ7dmjeAlo6\nncKzz9oZMcKhlRXxEQ0ayDz3nJ0HH3Rw7JjI0aM6NmwwkJ6udrto1MiJ2VywEnn2rGeOWCwCx46J\nxMf7fn5oddQ0NDQ0NDSu4HbDnj065s83smhRSG5f3ebN3Xz5pdXv8Wpnzwps26bH4RBo0kSiSROp\nTMZBlke+/trAuHEef/js2VYGDiy+10qro3YD7HbVxLx/v46zZ0Xi4mQaN5Zo2lRbFP7k0iW1ns1f\nf+k4eFCHy6VaBNu2Dc76NhoaGuULvV4Ncm/WzMbjj6vZgXo9xMXJASkwHROjMGBAxQxZCXbCwrzn\nQ3Z26WSuajFqqKnP33xjpHv3CJ54Ipw33wzlscfC6dYtgpUry7aWVlZiT86dE1ixwkDv3mb69Ilk\n0qRwPvvMxBdfmFi/vuS/QVmRgz/QZKGiycGDJguVvHLQ69Vs3qQkidatK14XEG1OqFxLDi4X1Ksn\nU7Omx9VZWol6mkUNOHVK5JlnwvK1lpBlgX/9K4z27TOJjq5Yi9SfHDgg8sgj4ezZk386JiS4GTgw\nABG8GhoaGgHk+HGRgwdFzGZo1cpNaGigR3Rt0tPVWLoqVQI9ktLn0iX47rsQvvvOiMGgcN99TqpX\nl/n1V71XAd9jx0RSU9Ue2yUtfK3FqKH2fXv88TBWrgzJ97enn7bx7LN2QvL/ScMHHDgg0r9/RL6s\nJlAYNMjJCy/YqVPHd8GZaWkCZ88KpKUJpKeLZGYKnDunLqhq1RRiY2Vq1JBp0kQiLq5cLg2NUkAN\nQhYJD1dITJQIDw/0iDTKMr//rmPYMDPnz4uAwsaNmbRoEXxdLtLSYNUqI++/r5qSJk6006uXs1wn\nre3fL3LbbZHkbRcHCl26uHjlFRuJiTJr1ugZO9ZMVpZAeLjCJ59Y6dXLjXADz6gWo3YdoqJgyhQb\n3bu7WbjQyLlzIvXrSzz4oJMOHdyaklaKrF9v8FLSjEaFgQOdDB/uICHBNwee06nGH27dqmfOnBCO\nHLlx8aG+fZ3Mnp1FWFjJr1/RycpS5b95s4F9+3Tcf7+DLl3c5aae3+7dIoMGRZCaqh6qn3ySxf33\nlyymKC0N1qwx8Pvvelq2lEhMlKhaVcZmE4iNlQNSz0vDP+zeLTJgQESeeCeBzMzSr9pfHDZtMjBh\ngmeTHj8+nLlzy3dMXa1aMqNGOZgzJ+8GJrBhg5Fdu/R8+aWVhx8243Cov1lWlsCYMWa2bMksttHB\nL4qa3W6nU6dOOBwOnE4n/fv3Z8qUKbz22mt89tlnVK9eHYA333yT3r17AzBlyhTmzp2LTqdjxowZ\n9OjRA4CdO3cycuRI7HY7ffr0Yfr06T4ZY1ycwvDhTgYOdGKzQXg45UJBS05ODuqq4z17uoiLsyJJ\nEBmpUKeOTN26MnofzUxFUeMPJ0zYDtx5w9fXrCnz2GN27r7bVW6VNH/OiVOnBGbMMPHZZyHk3IH+\n8IOB33/PoG7dwFosfSGHc+cERo8Ov6KkAQhMnRpKly6uErmBUlNFxo/3aGOiqDB4sJPatWVSUwUm\nTbJTs6bv5Bfs+4S/CLQcMjLgpZfCvILSw8MVv9cYgxvLQpLgf//Lf0jOnRvCXXe5fLaHB5qr5WA2\nw6RJdsLCFGbONHmFTKWliezapc9V0nLIzhawWIo/Br+I0mQysXHjRsLCwnC73XTs2JHk5GQEQeCf\n//wn//znP71ev2/fPr7++mv27dvH6dOn6datG4cOHUIQBMaNG8ecOXNISkqiT58+/Pjjj/Tq1ctn\nYw0NJahjAcob9evLpdq4WhDU7gw9erg4cUIiNVXg8mWByEiFKlUUYmJk2rRx06SJTO3aEnXrylo8\noo9ITRV4+eVQfvjBezOvV08qNxah48dFDh/23kZFkRu6OG5EdLRMp04uNm9WE2lkWWDhwhDi4iTG\nj3ewfLmBMWO02M3yxqFDOpKTvZOnnn7aRr16wef2FEVo0kRiyxbv8davL5UbJe1a1Kih8MILdgYM\ncPHDDwbmzQvh8mURQVAKLJzbooW7RDdWfhNn2BXzhNPpRJIkKl9xYhcUIvfDDz8wZMgQDAYDN998\nM/Xr12fbtm3UqVMHi8VCUlISAMOHD2fp0qU+VdTKG9pdMrRpI7FoUVsyMzPJzhZwuQT0egWTScFs\nLpu9GUuCv+bEtm36fEqawaAwY0Y21asHXhn2hRwcjvzP3XdfyWN0KleGKVOy6dcvgosXPaEBp07p\nmDcvhJ49nZw7J/jMqqbtEyqBlsOFC94aftu2LgYPdpZY8S8ON5KFIMDw4U6WLDGSlqbO0cqVZR5+\nuHzdQFxLDiaTWsalVSuJMWMcZGUJCIIqg5deyubNN0ORZYGGDd3MnJlFtWrFX6t+K88hyzItW7Yk\nOjqaO++8k6ZNmwLwwQcf0KJFC0aNGsXly5cBOHPmDHFxcbnvjYuL4/Tp0/mej42N5fTp0/76Chpl\nnMhIqFlToVYtmZgYhcqVK56S5k+2b/eOBYyIUFi40Mqtt5afmnh166qW2BxatXIzaJBvDqrGjWVW\nrLDQq5f35+3fryM0VMHlCs64JY3iExurYDQqCILCyJF25szJIjY28Dc11yIxUWLtWgvz5lmZP9/C\n2rWZJCaWn/VdWGJjFRo2lGnQQKZaNXj8cQc//5zJxo0ZLF9upWnTkllE/WZRE0WRXbt2kZGRQc+e\nPdm0aRPjxo3jlVdeAeDll19m4sSJzJkzx2fXHD9+PLVr1wYgMjKSZs2a5WrHObVRyvvjnOeCZTyB\nejxr1qwK+fsX9PjquVFa16tXT+S223qQnS3Qrt1PJCZKdOnSIeDfP+fxnj17GDduXIk/b9EiK99+\n+yshIfCPf7Sndm2lRJ/ndMIvvyQTEqI+/uijLD75ZD3r1hk4daoLUVEKGRk/s3evi1q1yv/6sNth\n+fIt6HRw7723Ffj69euTOXVKxOXqzJEjOpo2Xc/NN8tlbr/s0KEjmzdn8vvvydSsKRMX55/rb9qU\nzOHDIuHhnbl0SSA7ezMWy/8xadIjREZe//316smcOfMzAPHxgZ8vvn5cnP1y+/bCz7ctW7Zw4sQJ\nAEaNGkVBBKQ8xxtvvEFoaCjPPPNM7nPHjh3j7rvvZs+ePUydOhWA559/HoBevXoxefJk6tSpw513\n3sn+/fsBWLhwIZs3b+bjjz/Odw2thZRKoINjgwVNDh78KQubTf03EHGfqakCKSkiiqJmal1tmQi2\nOXH8uMCyZUZWrDDgcgn07euib18njRvLZGTA6tUGdu7U43LBsGEObrnFd3FLwSaLHM6fF3j/fROf\nfhpCZKTCvHlWWrSQvPpcnj4tMHduCNOmmchJWJk/30KfPu4iXy9Y5VDabN6s5957zVfVEt3I3Xd3\n4JVX7Ln9K2VZXVcOh4AoKsTEKOU+Hs2fc+Ja5Tn8oqhdvHgRvV5PpUqVsNls9OzZk1dffZWmTZtS\ns2ZNAKZNm8aOHTv46quv2LdvHw888ADbt2/PTSY4fPgwgiBw6623MmPGDJKSkujbty8TJkwoMEZN\nU9Q0NCouBw+qRZR371ZPkbg4iUWLrCQkXFu5cblgyRID//d/ejp0cNOokeTTDOTrkZUFTz4ZxpIl\n3jF9kZEyy5ZZad5cwuWCM2dERFHxe7/JQCBJ8N//mpgyxaPlN27spnt3FwkJarJFVhaMGxfO7797\nYhgiI2XWrbP4vXl6WWblSgPDhhWc4dO0qZsvvrCSkqJj5UoDy5YZSU8XMBjg1VdtjB3rQHfjikca\nhSCgddTOnj3LiBEjkGUZWZYZNmwYXbt2Zfjw4ezatQtBEKhbty6zZ88GICEhgUGDBpGQkIBer+ej\njz5CuBJN+dFHHzFy5EhsNht9+vTREgmKgd0Ov/2mZ/VqA48/bqd27fK/6WtUHJxOmDIlNFdJAzUI\nf8qUUObMycJoLPh9BgP83//p+fhjEx9/DCEhCs89Z+O++5ylrhjZ7QI7d+bfjjMzRZYtM9C8udpz\n2JfFn4OdkyfFK1YyD6dP65BlN+PGhdOunYvevV1eShrAtGnZmpJWRJKS3EyYYGPGDI9VMof9+3Ws\nXm3k5Ze96xU5nepZImqNKEsdrTNBOacgs+2aNXqGDDEDAnPmWLnnnvJbnDCHiurSKIjyLovz5wU6\nd468UtXdQ/PmLlassOaWBilIDgcPitx1VwSXLnneW6uWxOzZWbRpU7plB5YuNfDww+FcfVB+/LGV\nQYNKd40G45zYt0+kY8cor+datnRTq5bM8uWqtj1qlJ01awycOqUDFN5/P5v77nMWu1B2MMrBX2Rl\nwe7danmQtWv1nDjxC61adaRrVzeffRbCoUPeZrNRo+z88592YmLKpQqRSzC4PjVduIJx9KjI2LGq\nkgbkO8w0NMo6VaooDBqUv27GmDHOG9Zva9RIZuFCK2FhnsPn5Ekdd98dwYIFRqzWwo9DUWDvXpFV\nq/Rs26YjLe36r+/Vy8WqVRYGD3bQsKFEhw4uPv7YSrdu5f9GqiAqVVKoXt1jGRMEtejv2rUeC9qx\nYzri4mSiomS+/trKoEHFV9IqOuHh0L69xKRJdpYvtzJxoo3Ll0VeeinUS0lr3tzNwoVWXn7ZVu6V\ntOJgt6thFL5Es6hVMNS7ds9p9fbbWYweXb7q3mhonDolMH9+CN98YyQkBP75Txtduxa+W8Du3SLj\nxoWzf7+3CW3mzCwGDnQWqqzLgQMiXbpEYrerN0W33OLivfeyad78+m45RYHMTAgLK3n5GEVRLYyZ\nmQI2m4AkqcV0g7nkQ162b9cxYUI4ggAvvpiN0Qjz5oVw/LhIfLxEp05uHA648043jRtr7k5Qg/3/\n+ENHfLxcIhfw/v0i770XytGjIpGRMj17umnd2k2DBlKFaL5eHNLTYfr0UGrXlhgyxFnkJKqAJhME\nAk1Ry4+aLRbO2rWeIJ0lSyx07lz07CgNjbJAWpoaQ1OpUtHfe/Kk2g3g7bdNyLKqbAmCwqpVlkLV\ngvvjDx3dukV6PRcRobByZSaJiaWnVDgcaseEQ4d0/PSTnpUrjV5Fc+PjJVassJSZDhzp6epvGHXF\nC6ooqpvOblcfV6sWuLEFG3Y7vPWWienTQxkwwMnHH187JrMwSJIai2YylbzbRkVgyxYdd98diSAo\nbNyYecObsqvRXJ8VlLz1Ws6fF/jlF+/sqLp1K8ZdaF45VHQqkiyqVLm2knYjOdSqpfD003bWrrXw\n8MNqbz9FEfjhh8KdfLVry7Ru7e0DsVgEnnsujIyMQn1EkbBa1YNi7NhwOnaMZNgwM198YfJS0qKi\nZKZPz8qnpAXznKhc2aOkgaowmM2qguZrJS2Y5VAY/vpLdyUhAH76yZCv00FRSE5ORqdTS+tUZCWt\nKHMiJyFIUQSvZKaSUs4roGjkRZYFr5Y348c7/JZFlp4OR4/qOHFCJCVFR0yMTOPGEs2bS1pqt0bQ\nYjBA69YSLVrYGD/eQWqqQJUqhbNEVaumtsvq3987OeG33/RcuCASFeW7tXfggMhbb5nytezKQadT\neOopO4MGObWMSD+gKGrNMX/vbRs3GnJroVmtAllZAlA6ltPjx0X27RPZvVtPRoZAbKxMx45uWrSo\neJ0JQP29163zGELWrDHw4IO+CSvSFLVyTt5sldBQtUDh6dMCjRq5+cc/CmhUWArs2SPy1FNh/Pmn\nd8CNXq+wYoWFpCTfLGyHQzXVh4Xl/1tFzeQqCE0WKkWRg06ntouqW7do10hIUNtAzZxp4uuvjbjd\nAm3buomM9N3heeiQyIABEaSmejtIBEEhKcnNww87SUx0U7++XGDMm8UCJlMnFi3SceyYSPXq6oHb\nqFHFU+hKsjZcLtWitW2bnnXr9GRnC9xyi5vOnd20bClRtWrpupozM9UY5ByMRoXQ0OJf81qycDph\nwwY9jz8entvjMweTSeHHH4vu8gtmCjsnnE6w2Tymx3PnRBwOCCn43qlIaIpaBaJ6dYUPP8zip58M\nDBvm8EvRzL/+Ernrrkgslvy2c0nyXa/NEydEJk8O5dgxkaeestOli0vL/tIICho1knnvvWyeeMJO\nVpZAXJzs06b0oghPPWXnwAGRqlUVbrpJpk4d+Uo3Bvm6ma6HD4u8/baJxYu9T5O4OImffrJQo0bZ\niGMLBpKT9QwaZEaSPHvd1q0GPvwQHnrIzmuv2bw6Kviay5dFDh/2mPDq1pWJivL977d3r46hQ6/u\nYqDidlPuOxUUluxsAafTN4qaFqNWzrnav37HHW5ef93mN/dHSoquQCUtLEzhyy+tNG3qG2vaypUG\nvv/eyJ9/6hkxIpwNG7w1wLIee+JLNFmo+FMORiM0bCjTqpXkUyUNID5e5tFHHbz/vo2XX7YzapST\nbt1Ui9j1lLSTJwUeeCD8ipK2yetvsbGyV4mSikJJ5sS6dQYvJS0vX38dwuXLpXvcZmeD0+m5fv/+\nTiIjr/OGG3AtWeRkMV9N5coyX31lpWHD8mNNg8LPCZMJr3IyISG+a6+l6b4apcott7h5441svvnG\nyKVLIomJbgYMcNGihZsmTXy3oLdtyzuVBZ5+OoyWLTMrRKsdDY3icPiwjsOH8x8BcXES77yTfcOa\ncxrePPSQgx07dOzc6X2TWKmSzGefZVGrVukqMKGhYDAouFxqXFqnTqVTf69NGzfLl1tYtcrAuXM6\nqleX6dDBTbNmEjffXL6UtKLSsqXEmjXq/9etK/vEmgYVrDxHSopYYbIcg43sbNUUXLmyUioBtm++\naeLdd72L1qxZk0nbthUzsFVD40YcOaLGjm7ZoiprsbEK48fb6dPHRe3a2j5ZHC5dEjh2TOT8eQG3\nW6BqVdUF7Y82fVlZMHCgma1bDQwd6mDq1Gwt/MPP/PyzngEDVP/2Z59ZuffeoinLAe31GQxs367j\ntddCWbzYWmCwuUbpEhZGqbpSunZ18e673n3qpDKmo8my1jdPw3/Ex8vMm2clNVVEp4OoKMXnbtmK\nRtWqClWrBmbjCQ+Ht9/OZutWPT17ajG6gaBxY4nWrd0cOybSrJnv5kGFOBZOnBAYNSqcM2dEr6yM\nikBFiUdq0ULiP/+xkZOK3rCh28sqEMxysFjggw9CuOeecF5/3cTKlXoOHRKRS8moEcyy8CeaHNQa\nZY0ayZw797OmpFH250Rioszo0U6fhHyUdVn4iqLIoUYNhU8+yeKHHyw+jQOvEBa19esNnD6to0MH\nFxER2mZUHjGZYPhwBy1buklNFWnSROKmm8rGb20ywcmTIr/8YuSXX9TnwsJUN1T//k6aNJErdMFJ\nDQ0NjbJCvXq+v8Mu9zFqR48KdO0aSUaGyLPP2nj+eXugh6ahkY8TJ0SefDKMzZu9A5FNJoWXXrLR\nv7+zzPRn1NDQKJ+cPq3G4KlZzJJXxwiNklNhW0j9/LOBjAz1ayYklLGgJY0KQ+3aMh9+mMUjj9jJ\nW0ncbhd46aUwHnssnJQUzaymoaHhf7KzYfVqPT17RnL33ZH07BnJ+vU+KoKpcUPKtaJ24YLA9Omm\n3McxMaWXyXT4sNpOIy+ZmbBzp46NG/WkpARG1FqcgUpZkMNNNym8/LKNNWss3H67d7bQL78YGDnS\nzOnTHmXtwgWB337Tce5c0RS4siALf6DJwYMmCxVNDh5yZCHLsHy5gaFDzZw54znH/vqrYvT+ZLDN\n3gAAIABJREFUC4Y5Ua4VtcOHRY4fVyfTTTfJpZZyvn+/SO/eEfTtG8H+/apI9+4VGTbMTPfukdx3\nXwT33x9OaqpmEdG4PmFh0LatxLx5Vn78MZPhw+1Uq6bO2z179F6Vx5csMdC3bySjR4dz5ow2t4qC\n2w2XLwtkZQV6JBoaHi5dgvnzjYwdG8b8+cYi34SVBn/9JfLkk+HkzagH6NjRHZgBVUDKdTLBmjUe\n0+ywYQ6io30f4+NywYIFxtymy7t363C7ydc26eRJ3ZWMU//GGWl9HVWKIofz5wUMBoUqVUpxQDcg\nKgqSkiTatFHjKi9eVOdSbKyqtGVkwOefq9biX381sGiRkaefdhQq6aAiz4n0dPjjDz2ffhrC3r19\nqFdP4t13s8tMNXWnU7VknDwpEh0tk5Ag+aQtUUWeE3kJtBx++cXAhAlqXY3Fi0MYMMDBO+9kU7Vq\n8T7v6FGRPXt0XLyo1rBs1EiicWO5ULUsc2Sxb5/eq+MBwIgRdm65pWIoaoGeE1DOFbUvv/SUBe7Q\noXQm1ZkzIp995nGvXr4s8MQT4fnaJg0e7KRmzbJxGFRkjh4VGDPGzMMPOxg61Bno4SCKULOmQs2a\n3gp+Vpbg5YaYMcPEwIG+Scsvrxw5IvLaayZWrvTsC2fOiJw+LZYZRW3jRj0PPJDTZ1HhkUccPPus\njcqVAz0yDV+wapV33NfSpSEMH+6kc+ein19Hjojcd5+ZEyc8WpnRqPDmm9kMHuwsdJ21vP1C9XqF\np5+289BDjmK3p3I61X1N6wlaeMq16zM9Xf16NWrIxMeXTiJBWpp3f7WwMNi923sGxsVJPPWU3Wft\nJIpCMPjXg4HCyMFuh48+MvHnn3q+/dZQanXMfEFEhEJcnGeAmZkiJ04UbjlXxDmR09cyr5IGm4iJ\nkUolnb40SE+HV14Jy9MMW2D2bBN795b8xKuIc6IgAi2Hxo3zz8XixjefOyd4KWmgnlXPPBPG7t03\nNqnlyCIpycWSJRa++MLKhg2ZPPOMPd+NY2HIzFTDNR56KJxlywy8+24IX35p5MCB4FZDAj0noJwr\najmMG2cvtZpaWVneljOzWSEkJOdaCnfd5eS776zEx5eNwyBQWK1w8KDIjh06DhwQcQfAqv7XXzr+\n9z/1IM/O9ozhwgWBXbt0OANvYMslIgJ69fIeUGpqhVjOxWLlSiOHDnkrNCaTwpw5WdSpUzbWpssl\n5NtvAI4fL9nvfv68QFpa4GOhSkp6Opw6Vba/x513utDrvc+qqlWLd3bVqyeTmFjQRiqQnl54OVWp\nAp07u7n7bheJiTKGYiR7qiFCIYwebaZlS4nx48N5880wnnwynK5dI9mwQTOvXY8KsbPffnvpnfpX\nW130eoW1azP56isLP/1kYdasLJ9WKC4qweBfvx5uN+zYoWPoUDPt26tp33fcEcny5b5N/S6MHNas\nMeRaK3Q61Txvs8G0aSa6do1g06bg2kyK4w6B4J8TpcHWrd6/3R13uFi7tjXt2pWdkj01aiiMHZu/\nDmRey2pROXhQpGvXSJ55pg8LFhjJyCjJCAPHgQMiAwZE0KlTJLt3F/9YC/TaaNZM4ptvrLkJRJ07\nu2jTpnjrPCZG4fPPs3jmGRtms6rs6fUKjz5qp3XrG897X8ri4EGRV15RezErCjgcHkXRZhMYOdIc\ntJa1QM8JKOcxaqD2gKxfv/Q24xo1FNQEAQFRVKhdW6FZM5lmzcrGXXphcDrh779F9uzRs2ePjkqV\nFAYMcPokrmfNGj0jR5qRJM/CdbsF5s830q+fq1QauBfE+fMCX33lcYt17OhCr1c3mNmzQ1AUgVde\nCaVtW0vQxAM1a+Zm4EAH336rjrt69fIz53zNs8/aaNfOTWioQny8TNOmbs6eFXA6wWgM9OgKz8CB\nTi5fFpg504ROBxMm2GnevPg3ovv26XJjHZ94Ipzz5wUefdRRpvohX7wo8Nhj4ezZox5n//tfCP/9\nry1ounkcPChy8KCOKlUUbrnFTWjotV+r16s3YJs2ZWKxCNSoIZdov6lXT+bZZ+0MG+bAahUwmdQK\nCP4OwzlxQszd4+12qFpVzk3AA7BaBfbs0RXo+tUo94qawqRJtmIHPRaGuDiZbt1c/PSTkbFjHTRu\nXDylcPt2HZIEiYm+yeLKITk5uUR3BIcOicydG8Jnn4V4KVNNmkglVtSOHxd55BFvJS2Hhx92+lRJ\nu5Eczp4VvYLzmzdXf8cjR3S5Vra//9Zz7JiOypWDwwpTqRK8+KKd6tUVdDpo2rRw4yrpnCiLJCTI\nJCQ4ch//9puOe+/dyc8/tw6oxbuoxMQovPCCnQcfdCII6v5THFdUDp73bgI68+9/h9K+vZv27YNj\njheGv/7SsWuX5yjbs0eP00mxlBFfr40//tBxzz0RV5LLFFatshTKiquG6vgmXEev50qSUdE+z5ey\ncLs9e/zcuSG88IKNf/0rDFn2PO+vm/KiEgz7ZblW1Pr1c5Z6NwKzGaZOtXHwoJPWrd3F2hyys2HS\npDD27NHz2GM2Hn/cUaxgTV+zY4eOQYPMuZ0dcqheXS62QpoXh0ONXchLSIjCjBlZdOrkKvhNpYR3\nHTKFm29Wv192trcSabX6cVCFoE4dmcmTbUDwbnTBxsWLakC1wyGQmirQoEGgR1Q0DAbf9ROMj5fQ\n6RSk3OUssHixkVtvtSEGpycqH7t2eU98k0kJirGfOiUwfLg5TwUAge3b9WXK3e4rEhIkqlWTuXhR\nxO0WaNpUYsUKC++/b2L7dj1durgK5Y6tqJRrRW3SJDtmc+lfp149uUQbp8EA0dEye/bARx+Fcu6c\nyNtvZ/ukjldx7wQOHBAZPDi/khYVJbNwodUnVoj4eJmVKy2sXm3A6YQWLSQSEyUaNfJ9E/IbyeH0\nac/3TEiQcosjX53U4HIVf2AXLwpcvChgt6sKfmysfF03SGEpqoIW6LvDQLN/v479+/VAZxTFEujh\nBJT69WUmTbIzdWrn3OfWrzeQnm4vdhC7vzl3znuP6tnTVWwro2/jsnReVnqAatXKhkzBt7KoX19m\nxQoLZ86IxMTINGyo7vFz52aRkSFQpYoSkKoIhSEY9styrag1bVo2XBoGA9x3n+o+BViyJIROndwM\nHeoM2J3hH3/ouXzZc3FRVHjoIQdjxzp85irS6aBNG4k2bQJ/J5VXAXvySXtus+GwMO+N1Wgs+kbr\ndsOGDXqefTYsN11ep1O47TY3zz9vo00bSasp5CecTvjiC09Q2tUZdhUNg0EtBn7ypMiCBepJ2aCB\nRGho2ZFLjRqe/UinU+jc2b/W+GuRU6Tag0LDhoHf6wJFw4ZyvnCZsLD8e2xeUlMFTp0SiY2VS6Vg\nfVkhCAzEGgAtW7oJD/dMxEmTwvL1Di0Oxa0B06KFm6FD7Qwc6OCdd7LYsMHCv/9tK1PxPHm5kRxy\nNot69dxerVHyHgKCoBTLyrB/v8jQod6FJyVJ4OefDfTrF8Hevf71WQZDXaBAcfasyOrVOYraJkym\nirv55xATo9C791q++cbCtGlZvP66rUwlE3Tq5L5yA6XwzjvZJQpI9+XauHqvmDjRXuqhOL4k0PtE\nSorIAw+Y6dYtkscfDw9YO61AywHKuUWtLNGokczrr2czcaJaLtrpFPjwQxPvvptd6ArSvqRpU5kP\nPrD5/8IBonFjiapVZT79NJuYGM8G26CBTGyszOnTIl26uIpVcysqSiE6WimwH6fbnb8WX1nC4VBd\niUePikRFKbRp4861RgYjp08LV1q5qdbRsuLeK20iI8tu78aWLSVWr7agKOo6LklyhS9p1UpiwgQb\nv/xiYNgwB3fd5SpTCnAgkSRYuNDIH3+oKsr69Qb279dRs2bZnKMlRVAUpVzuVOvXr6d169aBHkaR\nOHdOYPjwcH7/Xd1pBEEhOTmTJk3KphXLV1y6JHDmjIDTqcYyxMbKPi+pYLOp14mLy78cduzQ8eqr\nobzzTnax3ekHD4rMnx/CwoVG0tJEBEGhfn2ZF1+00a2bKyDKeEk5c0bgk09CmDnTlJu9tXSphTvu\nCN7NdMECI088oQq7dWsXy5dbfRInqKFREG63+p/JdOPXang4cUKgQ4cor2SuTz6xcv/9weHWLi3+\n+OMPunbtmu95zaIWRNSsqTBtmo277tKRkSGiKAIpKWKFVdQkCTZv1vPMM2EcO6a6B0NCFEaOdPDY\nY3af9rUMDaVAJQ2gbVuJ774r2YHeqJHMG2/YeOwxOxaLgF4PlSuXrEZSIElPh9deC2XxYu8IYIfj\nGm8IEpKTPVtejx7Xr2mVw7FjIseOiTidqjsrPl6iUqVSHKRG0HLsmMgPPxjYs0dPbKxE167uKxmN\nBe8den3Z6GmZlaW6Gq1WgdhYOeA9gy0WIV/GfVmqd+hrtBi1IKNpU4llyyzUrataJUrqFgsG/3px\n2b9fZMgQc66SBmpF69mzTXz3XdFWbUnl4CurS0yMQsOGapZwoJQ0X8yJrVsN+ZS06Gg5qGMY09Nh\n+3bPqRkSsvGG79m7V0f37hHce28E//hHBN27RzJ6tJn9+wu3dV6+rJZpSEsr9rD9QlneJ0qK3a7W\nO/vuOwNvvbWVvXvFa/b5/f13HZMnh7FkiZEPPghlwIAIhg4N588/y25tnAsXBF5/PZROnSLp0yeS\nrl0j+fVXXUDnhMmkIAgeZVEUFerWDUx8XzCsDU1RC0KaNZNZsiSLBQsstGhRdoJPfY3TKVyz52dJ\nymRolAxJgnnzvBVlvV7hk0+yuPnm4FXUMjNVyxioYQXVq9/YapCcrPeqoA6wYYOBBx9Uq/hfj4MH\n1bZGbdtG0aNHJB9/HMLhw9qWG0xYrfDxxyF07x7BmDFm3norlO7dI9m+vWDFq3Zt2UuBANixw8A9\n95jZs6ds/rZ//KHj009NuYW9L14UGT3azKVLgdtja9ZU6NfP08t4wgS7TzrhlFXK5syqANSpI9O7\nt7vEkzMYasAUl4QEiY8+ysrtUwfqATtwoIOBA4vWIb0sy8HXlFQWOh3UrOmZl7VqSSxZYqFDh+CN\nTQM1VijnMOrZ00X//h1u+J4WLdz5DmaAlBT9DRW1ixcFdu/W43AIHD2q48UXw+jRI4JVqwzYgixP\np6KujwMHdLz+emjuvIDOOBwCH3xgoqDo7ZYtJWbMyObqKv+ZmSIzZoQW+J5gJyUlv1J67pxI/fq3\nB2A0KuHhMHmynTffzGbuXCuPPuoIWJ21YFgbZcB7rlFRMZlg0CAX7dplcvasgMsF1asr1Koll8ng\n+/LEU0/Z6dHDRUiImmmntrwJbqQ8xumxYx2FmkOtW6tNsp98MjxP8VLlSozk9W+iGjaU6djRRXKy\nJw3x8mWRBx8MZ9EiKz16BLdiWxHIzBSA/Ap3QoJUYNFtoxHuvddJgwYSb78dyoYN+tz3R0TIuN0E\nTdZpYVG9Nmq/6hyaN3cHvDtO7doyjz4a5EGvfkKzqJVzgsG/XhIEQbUutmsncfvtEo0bF09JK+ty\n8CW+kEWdOgq9e7vp0sVdJpQ0UA9ZnU4hMdFN06ZSoeQQEgJdu7pZuzaT1asz+f57Cxs2WHj+efsN\nYwyrV1f473+zadXqaoVMYNy4cE6fDh73fUVdHwkJErffnjeTcBPNmrkZPPjaFvvQUEhKkvjiCyub\nNqlzYsWKTP71L3uZU9JAtRr/739Z3HSTjCgqdOvmZNasLPbv/yXQQwsKgmFtlGuL2q5dIoIAsbFK\nmWrdoaGh4Xtq1pQZMcLBiBEOqldXOHiw8O+96SaFm24qerxo/foyX31lZcMGA5Mnh5Kaqt4bu91q\nuRlfNd7WKB41ayrMnp3FX3/pSE8XOHMmm8GDrYWqgh8eDs2by0DZjp2y2QQ6dXKxYUMmNptA9eoy\nYWEQBPqJxhXKdR21bt3UeiQNGriZOTObtm0rbmC+P3C54NAhkexsgYYNJSIjAz0ijbKE3Q6nTomc\nP6/Wy2vc2Pc9X7OyCJjb/NQpgdOnRbKyBOLi8rfT0SgdzpwRsNlUpUwLmfBm504dY8aEYzTCxIk2\n7rzTrRk1Asi16qhVCNfnoUN67rsvgj17ym4KdbCTmQlz5oRwxx2R9OgRydq1ZdAHoBEwDhwQmTQp\njA4dIrn77ki6d4/k1Cnfb0+BPKjj4hRuvVWiS5eSJwlpFI7Dh0W6dIkkKSmK++83s369Hqs10KMK\nHrZu1XPsmI6//9bxyCNmnn02lLNng8clr6FSIRQ1AKtVYM2aiqc8+MO/riiwYoWRF18My61Qv3hx\ncFUnDIY4g2AhmGThcMD69Xp69oxkwYIQ3G51/kRHl35j8GCSQ6Apr7Kw29XG3ooisG2bgYEDzbz9\ntonU1IKVEX/J4Vp12vzN1QkxS5eGMG9eCC5X+Z0TRSUY5FBhFDXA524UDZWjR0Wee867iV0w19PS\nCB42btQzaJAZiyXv4lT4739tmgtGo8TUqSPTt2/exACBmTNDee21UDIyAjOm337TMWhQOM89F8qP\nP+oDasFq2dLtVWoH4N13TRw4UKFUg6CnXP8ab72VRY0a6iRMSnJx111Fq71VHvBHDZijR8V8HRS6\ndw+unmzBUAvHn5w+LbBxo56ff9Zx6JDoVd8pWGTx998ijzxizlPDSs3K/PDDbJKSSr90RbDIIRgo\nr7KIiIAXXrATHe2tjCxaFJLb8Dsv15LD8eOCV3mXkrBvn44NG4x8+qmJBx6IoH9/M1u26ALSfq12\nbYU5c6yEhHg2CEkSOHFCLLdzoqgEgxzKtaI2erSTzZsz2b49g4ULrTRqpFl5SoOMDG8l7bbbXBW6\no0KgURR4441Q7rsvggEDIuncOZKZM0M4dSq4TMqHD4telrT4eDfLl1sYONCpNUrX8BkJCTLff2+h\neXNv5b8o4Rl79+rZvFnvk4K2t93mJirKcxYdPqynX78IZs8O4dKlkn9+UWnXTmLlSgvNmqnyKWzX\nDg3/Ua4VNUGA6GiF+vXLbvPrkuIP/7rq5lQXdtu2LmbMyAo6t1UwxBn4C0HAK77LZhN49dUwhgwx\n8/ffopcsUlJEFiwwcuiQ/7eCevVkHnrIziOP2FmwwMLSpVbatZP81sS6Is2JG1HeZdG4sczChVY+\n+CCLFi1cVK4sc9tt+a2215JD7doSQ4ea2bGj+AlpR46IfP+9gdRUkW+/tRIa6lHWFEXgtdfCWLw4\nBKefHT+CoBZ2XrzYytq1mWzalEmrVoWrM1gRCAY5lOs6ahr+oVkziTVrLNjtajX2wtQg0ihdRo1y\n8s03IdhsHovVX3/pef75MEaPVp87d07g0UfD2LHDwIQJNl57ze7XMTZuLPPee0HWS0mj3BITozB0\nqJO773aSlSXk3kxeuCDw998iR4/q2LLFyLJloRgMCi1ayDRqJNGwoUTt2jKJiW4efjic5cst1K1b\n9D1u1SoDr76qxvImJblYtszK44+HcvCgJ8ntxRdDSUpy06qV/z0S1asrVK+ueUKCkXJdR61169aB\nHkZQc/q0wBdfhHD//c4yUS7gzBmBY8dETp7Uce6cgCzD7be7adNG21wK4tdfdYwcaebiRW9r2erV\nmdx6q8TcuUaeeUatV9G2rZsVKyxlsrJ6XtLT4Y8/9CxebCQqSmHMGDvx8eVyi9PwAXv2iIweHc6h\nQ9eyWSjMnJnNAw84WbnSwLBhZoYNc/Dvf2cTEVHwOyQJ9u7VoSjQoIGUWxJm5swQXnnFk3TVsKGb\nuXOz+O03PW+9FZq7Tr/6ykKvXlp7sYrIteqoaRa1CorTCZ99FsL06aE0aSIFraLmcsHBgyLr1xv4\n8ENTPqVj+HA7LVva/OYuK0t06CCxapWFJUuMfPihCYtFrTpuNiucOyfw3nueQDCHQ5V1WVbUTp4U\neOmlUJYv93RvTkpyEx8fXIktGsHDxx+brqOkAQhcuqRaoJs3d1O9usyXX4bQp4+Tnj0LVqaSk/UM\nHGjG7Ya33spmxAgnRiO0aeP9+r//1jNjhom3386mTx8Xp0+LuN0QHx+ce7FG4CjXMWoa1/avHzig\n44MPTED+ZIBg4dw5gVmzQujcOZLJk8PyKWmtW7t5/HFHoZS0YIgzCAT168tMnGjn118z2LIlgw0b\nMklP/5ljx0TOnvXIMynJTVjYdT4oyElPJ5+SBmA2e1vTJEm1JJ89K1TYOVEQFVUWzzxjY+JEGzEx\nOcrRJgDCwhT69nWyeLGFBx9U0zFr1VJ48UXVVT9+fDiHD+c/Pq1WeP1105V6gAIvvBDG33+rr0tI\nkBg1yju84JtvjBw9qiMmRqFNG4l27SSiohSOHBE5elQMSCZoDhV1TlxNMMhBs0NUUL791phbnDYY\n68udOyfw5JPhrFuX38RjMilMnGjngQccxMRobi2AfftEDh7UUbu2zC23eLuCdTq1321srCqrlBTy\nVf3v2LFsu1r++EOfT0lr0EBtvp7Dvn0iCxaE8OWXIRiNCuPH6wiCzHuNAFK3rsK//mVn9GgH6ekC\nO3dm0bZtBuHhClWrKphM3q/v2NGF2ayQliYybZqJKVOyvVrlXb4scOCA51iVZYH9+3UkJspERsKE\nCXaOHtWxcWPOviZw/LhIy5bqPHW5YPbsEF5/XbV29+zpYsIEO61aSWXa2q1RMjSLWjmnoBowZ84I\nLFrkSU2/2uoQDBw8qLtKSVNo1crFhx9msXlzJk89ZS+SkhYMtXBKi99+09GjRySjRpm5/34zKSnX\nX9YdO3YkJcWTvSaKCg0blu04v1WrvE+xiAiFjz/OzlVOt2/X0bt3JLNmmbBaBdLSRH75pZtPyi2U\nB8rz+igM0dFqb9mhQzvQsKFMbGx+JQ2gXj2Fp59WrWoLF4awbZu3rUOvV28k83L+vGc91qqlMG1a\nFi+8YMNkUhAEJbfWJ6gWuXnzQpAkAUkSWLXKSJ8+EfzwgwGXnz34FX1O5BAMctAUtQrIyZMily55\nfvqrK1MHA4mJblauzGTRIgtLl2by88+ZLF1qZcgQJw0ayOi0tq2AWjR2yBAz2dmqWTQjQ8yNqbke\nlSp5fvOHH3ZQp07wzYGi0KiRR9Hs3NnFihWW3My5I0dEHnzw6u4H0LGjFJTWZI3gRRCgVy8XRqOq\njE2cGMbJk55JVLWqQr9+3vU1ctyqLpcaR5mVJdC9u5PlyzNZvTqTyEg5t/9oeLjqjo2Pl8gpeSTL\nAo8+Gs4ff2ibXkVFU9T8TGam2oDa5qeqBDn+dbdbzXCaOjWEP//0LHi9XqFmzeAzK1StCu3bS/To\n4eaOOyQSE+VrZlkVhmCIMygN1q0zkJnpWcaiqBAVdf3fMzk5mXr11MOjdm2JcePsZb7A7D33uFi5\nMpN16zKZO9dKs2Yexe2vv3T54htr1ZKoVWu9v4cZtJTX9VFUCiOHhg1lnn1WjTU7dUrH6tXGXMus\nwQAjRzpzrWomk0JCgpu//hIZMyacDh2iuO22KLp3j+Txx80sWmTip5+MzJtnYOlSAw8+GM4HH5jo\n0MHNlCk2qlRR16ksC/z4o399n9qcUAkGOWgxan7k/HmBF18M5fvvjcydm8WAAf6xZbvdsGaNgYce\nCqduXZkWLTzxSLfd5iY2tmxbUyoqFgt8+6335t21q6tQv2fLlm4WLrRQv75UrJpQwcb1akBdbX1t\n0cLNRx9lcelS2f/eGqWPoqjlNg4fFomPl2jWTKZ/fyczZoSQmSkyeXIot9/uokkTdd01b65mW2/d\nqicpyU3dugr33hvO1q2etSpJAgcP6jh4UEdoqMJHH2Xx6KPhOByqdW7fPj0REaqb9fXX1SwfrX9y\nxUWro+ZH5s0z8tRTalGduDiJDRssfqngv2WLjgEDIpAkgS5dXFgsAjt2qDr6Rx9l8Y9/VLweqGUJ\nWYYTJ0TOnhVwOAQqV1aoX18iO1ugc+fI3OxNo1Fh1SoLrVuX7XgzX5OaKrB1q56zZ0UaN5Zo0kSi\nRo1yue1plAK7dul46KFw+vd3YTbLNGokExMjk5oq8OCDqpl/xAg7//mP7ZqZ05s36xkyxIzdXrCv\n/f77Hezbp2PfPm/byZw5VqpUUQgNVeNIK1Xy6VfTCDK0OmoB5tIlgWnTPNGpp07puHhRKHVF7dgx\nkdGjzUiSukGIIrnNhcPDFW65pWxn+5Vn7Ha1jMq33xqZPz8kT4yVwnffWenY0c199zmYOTOUsDCF\nzz+35maPaXioUUOhXz+tllp5xWKB7dv1HDqkIyFBonVrN2az7z7/wAGR++938tlnIWRkeFzogwY5\nGDHCzhdfmPjiixAGD3bSrl3B6++OO9ysX5/JqlVGVq3Sc/iwHqtV7ZbQrZuT9u3dfPedd+/R0FDl\nyo2FZkmr6Ggxan7iwgU1DTsvBkPp39UvXbrFK+vI6VQIC1Ov++KLNurXrxibQDDEGRSFixcFpk83\n0bVrBLNmmbwC4Y1GqFZNxmCAceMcLF+eyYYNmXTr5kYsxIoua7IoLTQ5eCjLsti5U8/AgRG8+GIY\nAwZE8N57Ji5fLt5nXS2H7Gz49VcD770X6qWkAXz/vZH77su5ARB49dXQaybyCAI0aaLWNFy+3Mpv\nv2WwY0cm331nYfRoBw0aSDz9tJ3oaDm3htuyZZaAKmlleU74kmCQg2ZR8xPqQetZxDExJQuOLyyn\nT+fdXBT+8Q8nTqdAWJianaRlvQUfWVkwbZqJWbPy1wcID1eYP99K06bqBh4ToxATUzGtaJcuCRw9\nKnL4sI4DB0RSU0WysgSaNnUTG6uwebOeli0levRw0qCB5uosr+ze7R2EOH16KB06uOneveTegjNn\nRL76yljg355+2k7Dhm5uucXFzp0GduwwsHOnjh49rn/dsDCu3Cx7z8nWre2MGePA7abAGm7lGYdD\nrUZQvbpMVFSgRxN8aDFqfmLPHpFOnTwzcOxYO1Onln7q56+/6hg+3EzduhL/+pedtm3d2O2gKKXv\ndtUoHgcPinToEImieLRovV5hzBgHQ4Y4SEysGFbQ63HggMijj4aze3f+e81XX81m8mSBZdDCAAAg\nAElEQVRPsFB0tMzixZZc5VajfLFsmYGRI719nXfd5WTu3KwSt5ZLS4OXXgpj0SJPMeXoaJk33sjm\nzjtdVK0K27bp6N07AhCoW9fN8uVWbrpJ21sLS2YmfPppCFOnhvL++9kMHRrcMdMpKSL794sYjWrn\nF18meQQ0Rs1ut9OpUyccDgdOp5P+/fszZcoU0tLSGDx4MMePH+fmm2/mm2++odKVaMkpU6Ywd+5c\ndDodM2bMoEePHgDs3LmTkSNHYrfb6dOnD9OnT/fHVygxsbEyjRq5OXhQT3i4wvDh/ukN0q6dxC+/\nZBIeruRW0FabBAduI8nOhsOHRS5cENHpoFYtmXr1ZM26d4WYGJkFC6z8/rses1mhXj2ZRo0k6tWT\nterkV7DZBI4dK9jPe3XA9vnzIq+/HsqcOVk+jV3SCA6aNZOoUUMmNdUzH1JTBSSJEitqVarAG29k\nc889Tvbv1xEertC+vZuEBM/h3KyZxEMPOfjf/0ykpOhJTjYwaFBwKxsFoSiq3CIjlVIp13PkiMCu\nXXoURe1n2qiRRFgYrFhh5D//UW+s5s0LYeBAtTdqMHLkiMjdd0dw7pw616pUkfnySyvt25euV8Mv\nMWomk4mNGzeya9cudu/ezcaNG0lOTmbq1Kl0796dv//+m65duzJ16lQA9u3bx9dff82+ffv48ccf\neeyxx8gx/I0bN445c+Zw6NAhDh06xI8//uiPr1BiqlSBTz7JYtQoO0uXWrwWemny66/JxMQoXm1O\nAonForr1OneOZODACO69N4I774xk/nxjbtHH0iAY4gwKS2Qk9Orl5qWX7Dz1lIN+/Vw0auQ7Ja0s\nyeJatGolsX59Jl99ZWHiRBvduztp395Fu3YuateWEEXvG5F16wycOOG93ZUHOfiKsiyLunVlvvnG\nws0357gcFZ54wkFIyHXfViAFyaFqVeje3c2wYQ4GD3bm27vDwmD0aEee2N/QG3YHCTYuXYIPP1T7\nKv/nP6Gkp/t2TqSlwUMPmRkzxszYsWa6do3gzTdN7Nsn8sILHuu3w6GWkwom8srh+HExV0kDSEsT\neeABc24/19LCbzFqYVfylp1OJ5IkUblyZZYtW8bmzZsBGDFiBJ07d2bq1Kn88MMPDBkyBIPBwM03\n30z9+vXZtm0bderUwWKxkJSUBMDw4cNZunQpvXr18tfXKBHNmsm8846fKt0GKQcP6njvPe/bNatV\n7esZHy/RoUPFjLfSKDrx8Qrx8W569VJ3dllWrQIuFxw/bufttz3zTKcruXVFI3hp3lxm+XIrKSki\nYWHQpInv95HKla/9t8aNZSZPzmbSpHDS0kTWrTMwdmwAO6oXAUVRrVqvvKKe0R99ZKJ3b99aBG02\n4aobJYFZs0zUry97JUo1ayYFdWyeWkxcIW+8eUaGyIEDOho2LD3ji9+2LlmWad26NUeOHGHcuHE0\nbdqU8+fPEx0dDUB0dDTnz58H4MyZM7Rr1y73vXFxcZw+fRqDwUBcXFzu87GxsZw+ffqa1xw/fjy1\na9cGIDIykmbNmuX27crRkrXH/n0cE3MHZrOC1aoq6ND5yr+b+O23bDp0aF8q1895LtDfPxged+zY\nMajG4+vHOh00b/4TTzxhYOHCHtjtAv/4xxpOnXLRsKH363MIlvHHx9/O5csCf/6ZTLVqMj16+Of6\nOc8F+vuX1cdbtiRTpYpA3bq9SEnR8+9/b6VKFRv3398hKMZ3vccpKSLPP78dVfnoDMDWrcnceiu5\nlPR6hw//Qq9eRr75pueVT9xE/foSP/10e+5jgD59bkEUg0s+effL1q078vTTdqZN23Zl3Kq8jh79\nmeRkqcifD7BlyxZOnDgBwKhRoygIvycTZGRk0LNnT6ZMmcK9995Lenp67t+qVKlCWloaTzzxBO3a\ntWPo0KEAjB49mt69e3PzzTfz/PPPs27dOgB++eUX3n77bZYvX57vOsGWTKDhYetWHU8+GcahQzn3\nCQqDBjl57TVbULaz0ii7nDsn4HarTbeDOb7vyBGRb7818umnIaSni+SsicmTbURHa2uirPDbbzru\nuisCRRGYNSuLwYN9H6uWkiLy++86YmJkWrWSrsQcF5/Nm/Xcc493CYIlSyx07uxbH+SZMwL//GcY\na9eqAWj33utk714df/+tZu1GRsps2mQJ+g4MFy8KrFtn4IMPQkhNFRk1ysGoUQ6fFNG+VjKB3x3p\nUVFR9O3bl507dxIdHc25c+cAOHv2LDVq1ABUS9nJkydz33Pq1Cni4uKIjY3l1KlTXs/Hxsb69wuU\nMYIx9qRdO4mVK62sXZvJ0qWZbN6cyTvvZJeqkhaMcggUFUkWNWsqxMUVrKQFixx27dLRp08Eb78d\nekVJAxD45hsj6en+ybAJBlmkpIisX6/n22/VvpeHDvk/zqukcmjVSmLSJLUP6BtvhHL2rG9/vzNn\nBIYNC+eRR8z06xfBxo0lv/twXOWhjYhQqFNH9vmcuOkmhQ8+yGb+fCu9ezuJjpa8aom+8YYtKJW0\nq+VQrZrCkCFOVq2ykJycyaRJ9lLvdOKXlXDx4kUuX6lAaLPZWLduHa1ataJfv3588cUXAHzxxRcM\nGDAAgH79+rFo0SKcTicpKSkcOnSIpKQkatasSWRkJNu2bUNRFL788svc92iULapVU2jTRuKOO9Te\nef6oKVdaZGfD/v0imzbp+eknPTt26Dh/Xkth1bgxFy8KPPJIGBcu5N+KBw50Bl0fXrdbLd5t82Go\nbVoafP21MTfB6JFHzDz8sJm+fSOumdkbrJhMMHSog3r13Jw5I7Jrl+7GbyoCBw/mbTMl8O9/m8jj\nlCoWapkmj6Lx3ntZ1K1bOvOuenWFPn1cfP55Fi+9ZL+SHaswcaKNu+8uW5mylSqpN4L+iH31i+tz\nz549jBgxAlmWkWWZYcOGMWnSJNLS0hg0aBAnTpzIV57jzTffZO7cuej1eqZPn07PnqpvO6c8h81m\no0+fPsyYMaPAa2quTw1/cO6cwDvvmPj88xCvumcxMTLvv5/FnXe6tSB2jWty/LjIbbdFkp2dV7FX\nePJJO6NHO4iNDR6356lTAp9+GsLixSE0aiTx1FN2br3VXazsyhwcDpg508R//pO/HkRoqEJycmap\nKQ2lybZtOvr2jaBlSzeLF1t91qNz4UIj48d7+zq3bs0oUSC7zQaLFxtZsMDImDEOevRw+e3G+cIF\ngQsXBOrUkUvswi0PXMv1qRW81dAoAWvW6BkypOBdTa9XWL8+k2bNyt5BUx5xueC33/QsWWKgcWOZ\nrl1dNGgQ2N9GUeDPP3WsXGnAYhFo3lwiMVGiUSOpVGpZlYRFi4w89pjnNBUEhUWLrCXqAHD0qEj7\n9pG4XN4WaFFU+OSTLAYMcBWqLVqw4XTCJ5+E8MorYaxencmtt/omC3XJEgOjR3uKAYqiwrZtmcTH\nl3weZ2TAnj16fv1Vz99/64iPl2jWTJ2LgV4nFQWtKXsFJW8mV0WmtORQr56cr9hmDhERSomsDaVF\nRZ0Tx46JDBxozlUKzOYNLF3ahtatA1cSRhCgdWspoGOAws2Jq2PGFEXgqafC2bAhs9gJD5GRCj16\nOFm5MmehKHTo4OaVV2y0bCn5XUnz1dowGlXXdXKynp079T5T1OrVk8lbHiIpyU3Nmr5RorZv1zN4\nsBlP6YlNQGeiomRmz86ia1c3Ot96cssEwbBflsF7FY1rcf68wNGjAllZgR5JxaFBA5mVKy28/34W\nHTq4qFNHonlzN5Mm2Vi2zFKqtXU0ikZ2Nl6WG6tVZMQIM6dPa/GEhaFTJ1e+51JThavctkWjWjWF\n6dOzWbcuk5UrM9myJZOFC60kJUlBW52+sERHK7zzTjYpKSKZmb75zMaNJd54w4YgKFSqJPPGGzaf\nuQwdDu9+1DlkZIgMH24OSHKHhorm+iwnnDwp0L+/mRMndPTo4eL55+00ayaV+7ZMdjv89ZeOY8fE\n3NYkjRsHxm1kt6vKgMmkVivXCC4uXFDXyIED3o6ERYssN2ykrQFWK8yaZWLKFBM5B/o99ziYPj1b\na811HU6eFIiK8l13GLtdbcEXFpZjYfMNly7BokUhTJ4citvtfXDExUksXWr12fVOnBA4fFhHlSoK\nCQllXyn3FZrrs5xz8aLIsWPqz/njj0Y2bjTw9ddW7rij/B5Asqw2ZH700XByDg5BUHjpJRtjxjj8\nfniYTAR1Ve2KTvXqCu++m03//hFIkucgKolFqCJhNsNjj9np3NnF0aMiUVEKLVpImpJ2A2rV8q0t\nxGSCxETfW+qrVoVHHnHQqZOL48dFjh/XcemSQIsWEk2bSj5T0i5fhhdeCGP1aiOCoPDf/2YzeLBT\n2zuvg2bLLCdUry5TpYpnITkcAg88YGbBgl8DOKrS5fx5gRdfDCOvuV5RBN54IzS3iGIOwVAnKlio\nyLJISpL44QcL9eq5gU1Uq6Y2h67oFHZOhIdD27YSgwe76NXLTUxM+XLIVOS1AWqbtcREmb593TRv\nvp6XX7bTr5/ruskKWVkwa1YIr71mIjlZT1ra9a9x7pzI6tWqCU1RBJ5+OoydO4M3+C0Y5oSmqJUT\n4uIU3nor2+u57GyBH380IJXTcygiQjWb50fAbvf7cDTKAHo9dOggsWqVlenTs9iwIZMmTbQ4Qg2N\n4iII8N13BmbMCKVfvwjuvz+C3buvrVqo5YryKvgCn3xiCrpm7MGEFqNWjkhPh//+18SHH3oCtGrU\nkNm8ufhZWb7G4VBrR6WlCdjtAjVqyNSvLxc7RmHfPpGxY8PzFIFUePRRB889ZyMqSo0ZS09XFbfI\nSNX9paGhoaHhO3780cADD3h84KGhCnPmWOnSxZ1vb8/MhPvvN/P7756uCjExMhs3ZpZ6hf9gR4tR\nqwBUrgxPP22nRQuJSZPCyMgQadbMTURE4Cf/xYsCe/bo+PzzEFavNuQGq+p0Cps3Z5KQUDyrxv+z\nd97hTZVtA/+dk9kVoAVaSsss0NICZYgyypahgIqAMhRR1FdRUVFxvCDg4lNREfdWVARBQVFUtoC+\nqICy9yq07JY2e5zz/XFsQyiFjrRN0vO7Li9pmqRP7jzjfu7ZsqXEokVm9uwRsVgEateWadjQw5Ej\nIps2afnsMz379mnJzxdITPSwaFE+jRtXvTxUgpv9+0W2b9fw118aXC6B9HQl2zc5WQr5BB4VlQvp\n3NnFTTc5mDdPKbNiswmMGhXJm29aGDzY5ZNcZTLBtGk2Bg/WFsaKmkwyBoO6LxeHqqiFGNHRMHSo\ni44d8zhzRuDIkbWEh3epsvHIMmzapOH++8OLZNsBdOtW/jpAtWvL1K7twWqFrVs1PPpoOIsW6X06\nBcBqunXrVO1vbBAYdYECgbLK4Z9/RG68MYqzZ33dO+HhMkuW5JGeHnyuVHVOKKhy8FIaWZhM8NRT\nNux2WLxYUdZkWeDeeyOIjTXTs6evX/OKKzx89ZWZBx6I4Nw5gRdesFKjht8/gl8IhDmhKmohSoMG\nMg0ayFgsVauYrFypZfToyH9r9PgydKiD//7XRnR0+f9OVpbARx8ZeOUVb+kALzI33eTgqaf8V3NI\nJTQ4fVrgwAGRgwc1OBxwzTWuf3sfFs8bbxiLKGmgxIRu26YlPT24ehaqqPiDhASZF16w0bChxOuv\nF+zDAvfcE8FPP+X7NFzXaqF3bzcrV+bhchFQrdICkWoTo2a1wqZNWnbs0BAeLpOUpKQcB3Mz8EDn\n6FGBHj1MRQ61Dh1cTJpkJz3dTUxM+f/OiRMC48dHsHKlrsjvMjJcPPqojXbtPGptM5VC9u4VWbtW\nyxtvGDl0SMk4e/JJGxMm2NEVnUY+LFmi49ZbvSVhCmjUyM38+RaSkoLPoqai4i8sFlizRsejj4aT\nna3s/V9+mU///mq2wOWo9jFqK1boGDPGd3O9/XY7EyfaQy7FPFAID5eZPNnGTz/piI2VSEvz0Lat\nhyZNPNSqdenXOp1w5IjIkSMiBw+KnD6t1G1q2dJDerrbp3jkvn0aVq70TuWYGIlx4xz07OkiOdnj\nt0KTKsHPoUMiP/+s47nnwjCbvXvBuHF2brnFcVklDaB3bxc//5zPX39p2bxZQ0yMTEaGi7Q0Dw0a\nqHuJSvUmIkKxTKen57F9u4bDh0UaNFAvL+Wh2ihqf/yh4cIb8EcfGUlJ8XDHHaHrqqhK/3p0NIwZ\n42TMmJLL1+mELVs0vPGGkZ9+0uF0FnWZrliRR9u23rIcrVq5Wb06D5tNwGSSqVlTLqJ8B0KcQXGc\nOwdLl+pYvlxPr14uund3VagrIJBlUVGcPQvr1umYODGcM2cKLLyrEYTuvPSSlSFDnNSsWbL3CgtT\nYmyuuCJ06t5UxzlxMVQ5eCmvLOLjZeLjg9+KFghzotooav37u3jzzaLxS8uW6bj9dqeaqRUA5OXB\np58qLUwk6eJfyAMP2EhK8j0gTSZo3Tp4b2y7d2u4914ltf2bb/SkpLj59FPVhVZWcnNh/34NJ04I\n1KsnIYoCTz8dxq+/+prL6tf38O67+XTooLawUVFRCVyqTYya3Q6//qpl/PiIwhu1Xi8zf35ot1kK\nJn7/XcO1117cT9m8uZvnn7fRsaM75FrWrFmj4YYbfD93//5O3n3XosZQlpIDB0SefDKMX37Rk5bm\n5uabnbzwQhgWi1fxDwuTmT7dyoABLuLjQ3L7U1FRCUKqfYya0Qh9+ypZJpmZIk6nQFycRIsWqtUi\nUKhfX+L5560sW6bFbBZp2tRDjx5ukpI8NGrk8Ut2aCDSuLFE7doSp097ky5++knH7t0aOnQIHfda\nRXP8uMC994bzxx86OnZ0062bi8mTwwrLtGi1MhMm2Bk61Enz5mq9MxUVleCg2rWQSkyU6dxZUQCq\nQ3HKQOhTVlIaNFC6CixcaGHJknzeesvK8OFO2rUrv5IWyHJo0EDm1VetXNhWJTe3YiZnIMuiPOza\npeGPP3SEh8sMGuTk5ZeNyLJAfLzE9OlWVq7MY9IkOy1aKOs+VOVQFipSFm634o62Wi//3KpGnRNe\n/CGLU6cEtm4Vyc4O3oM2EOZEtbGoqQQXJcm+CyV693Yxd66Z++5TXPMxMRING6rW3rIQEyNRs6bM\npEl2YmMlMjJcNG2qujirgvx8mDnTyI8/6gkLk0lO9tCxo5v69SVq15aJj5eoV08O+QtzdWXdOi13\n3BFJfLzEtGlWund3X7ZOoUpRqk2MmopKMJCZKXDihEjt2rJPgUiVy3PqlMAXX+j59FMD8fESY8c6\nyMhwB0yf2+rKsWMCc+camDnTWKTwda1aEgMGuOjb10Xjxh4SE6USZ98GOmfOwJYtWmQZGjVSLl4a\nTene4/RpAY+HoJ3D332n47bbvEHFI0c6eOIJm1rgthiKi1FTFbVqRm4u7N2rwWwW0Ghk6taVSUyU\n1Ir9KiGBJClz3GhELXB8EfbtEzl1SqB1a0+lrnmPB/bsEfn1Vx0zZxp94jG9yKSkeBg71kGbNh4a\nNZKoUyd4j6dff9Vw/fVKklBYmFJT8oYbnCVSulwu+O03LRMmhNO4scTnn5uDco8+cECkT58ocnO9\n3/d11zmYMcMWtMpnRVKcolbtYtSqGxf61xcv1tOvn4kbb4zi+utNdOli4rrrIvn6az379oXudAiE\nOINAIZRlIYpK/b6SKGmhLIeL8fffGvr0ieLaa6PYts3XtFPRstBoICVF4u67HaxYkceXX+YzaJAT\nvd43LnPnTi2PPRZBv34m+vSJYs4cPXv2iHgqKafGn3KoVUtGFJXPZ7MJPPlkOPfcE8GhQ5f280oS\nfP+9jiFDIjlyRMPGjdoKi1e9FP6QRZMmEjNn+sbfLl5s4JNPDLhc5X77SiEQ9onQPZlVLkrr1h7C\nwryLRpYFNm3ScffdEfTqZeK773Tk51fhAAMYi0UpnDxrloHZsw3s3Bn6y+fkSYHc3KoeReVgtcK2\nbSJr12r4/XcNp0+HTuDU4cMio0dHkJcnAgJHjpRu7prNylyw28s/lsREmf793bz/voX16/OYNy+f\n226zU6uWr6s/M1PDhAkR9OhhYto0I1u3aoLmcAdo0ULioYd8BbZ6tY6xYyPJyip+bm3dKnLvvRGF\n2cqpqW6ioyvH+nTwoMiaNVo2btRgNvvnPfv2dTF9us3nsZkzjezeHfr7p79QXZ/VkL//Frn//gi2\nb794LsnLL1sYO1YtAnw+Z84ozbhnzfIWTW7Vys3ixfkhE1NzIb//ruHOOyOJjpaYMcNKp06ekJwT\nNhts26bh1VeN/PyzrvCAHDfOzowZNsQQOE8WLNBx113eWKF33jEzfHjJtJ4dO0Qefjicw4c11K8v\nMXSok4wMF82bS35L+pFlyMoSyMoS2b9fw6JFOv74Q+vjMtNoZJ55xsbQoc6gCUg/elRgypQwFi0y\n+Dz+yisWbrutaMeWnBy49dZI1q/XXfa5/ubvvzUMHx5Z6JYePFhxUcbFlV/W+fmwYIGeiRPDKdg/\n33jDwsiRodsVqCxU+zpqKl7S0yW+/trM9u0a5swx8MsvOux27wn8zjtGBg1yBXV8iL/56Sc9s2aF\n+Tx29KiIzSZQs2boySkvDyZNCicrSyQrS2TIkCi++y6fjh1Dq66b2Qwff2zg6afDuLBrSXi4HBJK\nWn4+vP22r6JQmsPXZhP44w8toCS6bNqkRaNRatKNGOHwS0atIED9+jL16yutuYYMcXLmjFKi5swZ\ngZwcAatVQK+H3FyhXIqaxQJbt2rYvl3D6dMi11zjpFWrikncSUiQeeEFG2lpEs89Zyy8BLz3npEh\nQ5xF+hBv2aL1UdKioyW6d6/4guwuFzz/vG/s4HffGeje3c3YseVXpqKiYMQIJ61aeXjvPQOrVumI\niVGTpUqKqqiFOMX1KYuLk4mLc5OR4ebYMZGsLAG7XUAUlQKsoaakladf24kTAs8+G1bk8TvucARl\nQGxJZGG3C+f1xASnU+CJJ8JYsMBMrVoVPcLKYd26dZw715Onny4a0NaggYfRo0Pjtn/smMjff3u3\n+qgouUjpl0vNieRkD1On2pg61Ssnj0fglVfCWLBAz1dfmUlO9u+hq9dDvXpFe/aWl0OHlHF//rme\nAsV8/36R995TirxVRF/H2FiZ++6zk5HhYvlyHcuX6xg2zHnRtmWrV/seya+9ZqVx44pXaBwOyMq6\n8Fayml9/7ewXRQ2UBJ8OHTy0amUlJ0egRo3g2DvVXp8qVY5eryhmjRtX9UgCF1lWinaeT4cOLkaP\ndoSExeVixMTIdOzoZvFi72myebOWEyfEIrFEwYos8++B7UWvl/nvf61ccYWHvDyBzEyBxMTgOFCK\nw2YTCi05AA88YC9Vjb6ICBg71kHNmjJPPBGOzeZ9ryNHNNx6awTffWf2i4usItmzR4nT27fP99jr\n1KniLVZ6PVxxhWItfPBBO2FF733YbPj0o73rLjvdulVOUF5kJIwb5+Dhh31lc+WV/peNwVA6i66K\nqqiFPFV9E6hsZFkJiLVaFWUjLk4pplkeOcTGyrz3noUpU5Rm8ffcY6dnT1fQ1gIqiSw0GiVGa/Fi\nHV6XoH+CyQOFjIyuhIXZkWWw2WRuvtlFWBjMmmVkyhRla6xbV+Kbb/Jp2TJwlVOzWenKcO6cQKNG\nEk2b+o7VYJBRsu4EmjRxc8MNjiLvcbk5ERUFt9zipGNHN0uW6HnjDcO/iQmwb5+GEydE4uKKd4vv\n2iXy4YcGMjNFhgxxcdVVLho0qLz1k5cHzz1nLKKkNW7spk8frzJUGfvlxZQ0UBSYtDQ327ZpmD7d\nxrBhjiKu0Ypk4EAXp0/beO01I3Y7jBlzFddeG0ILvowEwhmqJhOohBSrVmm55ZZIrFaBmBil6Omw\nYU6aNSv/QZuXp/y/MjfPqsRmUwKAH3wwHFkWSE93M2+eOeTc4pKkFGV98MEIVq0qGh2/fHke7doF\nZmyeLMP77+t5/HGlyFaNGhKffGLxiWuyWGDGjDD27BGZNs3mFzfl4cNKWyCzWSAmRuk4UJwCIklw\nyy0RLF3qtV4mJbn5/HMLzZtXjgL8zz8iPXvW8HmsQwcXb75p9dkbTpwQ2L9fRKtVMuSNxkoZXiEF\nISgNGkhoq8CM4vEoY3C7BWJjJbUW4WXIz/dekmJjJZo1k8o1Z9Q6atWUQKgBU5ls3KjFalUsQGfO\niLz8chiDBkXxySe/lfu9TabQUNJKOifCwmD4cCcrVuQzd24+H3xgCSklrUAOVquiyFxMSbvzTjvN\nmgWmkgZKVuH06d7T9Nw5kdGjI31qIkZEwJNP2vj4Y0uxSlpp94mGDSWuuspDnz5u2rYtXkkDJWwg\nP983UWPfPi2TJoWTk1OqP1tmDAYwmZTPHhsr8dJLFj791FKopFks8OOPOrp128TAgSb694/i8OHK\nPx7j42WaNKkaJQ0US3piokzjxhKbNlWvs6M4ilsbZjO89ZaRfv1MDB8eRc+eJubM0WOx+H8MqqKm\nElL06OFCo/FVJk6eFJk+PYxDh9TpXloMBkhP99Cvn5smTQLX/VcesrNF5s71jVUTRZkJE2w8+KCd\nqKgqGlgJkGUB6YKvxWIRihSvDguruk4Nej3cf7+d84ueAqxZoyt1Pbeykpws8euveaxde47Vq/O4\n4w5nYaLCmTOKu3v06AhOnVLGEx0tExER3JcSiwV++EHL+PHhLFyoC6m6gIHA/v0i//d/XvOZJAlM\nmhTO1q2l7BNWAtSTK8QJBP96ZdKmjYe5c80Yjb6bbG5uL1VR+5fqNieKo0AOMTESjz5qJz5eIinJ\nw4QJNpYty+eJJ+x+zzr0N/XrS9x+e9GYM4PhIk++BBU9Jzp1cv9b9NQrT41GLvU4y0ODBjKpqZJP\npnZODrz+upGXXy4oz9IDgGeesZGQENjf/eXYsEEJA5k718Cdd0by8ceGUsWYqvuEQnFy8HgELizp\nAwLHj/v/nFGTCVRCCp0Oevd2s2xZHgsX6pk/30BWlkCXLm4SE0PTIlQcDofyn6lwJPwAACAASURB\nVF5PpcfaBBPR0fDYY3bGjXOg08mYTARNNq9Go2QHZmcLfPutovX06OEiJSWw3LUFWYVXXulmzRod\n2dkCN97oJCmpatfkhg1aZs/29dvecIODnj2DqAVCMSxbdn4iEMyYYeSaa5ykppZO5mfOCBw7JqDR\ngMkkEx8vl7q5fCjSsKFE164u1q3zhkwIgkx8vP/ntKqohTiBUAOmshEESE2VSE2185//OLDZBHbt\n+pWmTUNfDlYr7N2rYcsWDQsW6Dl5UsRkknj4YTu9e7vRaqvnnLgY58tBoyFo4+8aNJB57TUr993n\nwOOBRo2kUheErYw5YTR6S1QEAqdOCfz3v75KWs+ey3j22StCsnyELAucPCmWWFFbt24dbdt25f77\nw/npJyU0IDxcZuRIBzfc4CQ11RMSMbuXo7i1ERMjM3u2lQ8/1LNokZ7wcJg2zUrr1v6f36qipgIo\n2U47dij93bRaxaWSmCgFfXHTunWV0gSZmVU9kopn/36R554zsnix3qduFmiYPl3gyitDt91VdScq\nCtq2DQwFKFgwm+HAAcU0ZDJJPP20jbi4wHd3l5Q+fVy8+66vKf38Ps8lITwc2rd3FypqVqvABx8Y\n+eADIw8+aOO665y0aVO9PBXn07ChxNSpdh54wIFGI1fYeamW51AB4KGHwvj0U99FnZzs5sEHHWRk\nuEJm8wpVdu8WGTo0kmPHivokDAaZefPMdOtW8YU9VVSqAqtV6df6v/9pyc4WGTDASceOly6vYbPB\npk1abDZISpJo1Ci0FI7cXHj22TA++kgRwjXXOHntNWupra3Z2QIzZxoL3wcgI8NFYqLEDz/oeOcd\nC/36qXuLPyiuPIeqqKkA8M03OsaNi7zo7y5Wb0glsHj3XQNPPFE0ra99exf/93822rYN/obqDgfs\n2yeya5dyINtsAh06uLn66uAtPqxSfsxm+OgjA1Onnt+vVebnn/MDxs1aVeTmwo4dGmw2gZYtPWW+\ncOfkwLp1OiZPDuPIEQ1PPWXjueeMgEB0tMSiRfmkpannQ3lR66hVU0paH6lPHxdvv21Gry+6kP/6\nS8ekSeHk5/t7dJVHqNeT697dxdixdjp2dJOR4eLFFy38/HMeCxaYadfOV0kLRlns2CEycWI43bub\nuPPOSD780MiXXxp4+OEI9u0rW2RzMMqhoghmWfzxh/bfPqTn30QEzp0r/c0kmOVwMWrWhM6dPfTu\n7S61kna+LGrVgkGDXCxdms/ChfnUqCFRIO+zZ0V27gzd7IJAmBNqjJoKoBRyHTbMRVpaHhs2aPn4\nYwM7dmj+jXWSadTIQ2jaXkOD5GSJmTNthT1Jq6pgZkXwxx8abropknPnit4r27Vzk5RUva0m1R0l\nu9GX6GgpZOv+VSX16snUq+fGbvfdYDZu1DJsWPBnygYqqutT5aLk5SmFQB0OAYNBJiFBIiLCP+/t\ndoPdrqTsq6hciuPHBfr0MZGVdaGSJnPjjU4mT7bToIF6IJ+Px6OsscqsUVaVfPKJnocf9m5OtWpJ\nzJtnpkMHVYGvKNat0zB4sDflMyPDxbffmoOmrE2gUpzrM4Tu3Sr+RGmXVDEH4IYNGv7v/8J47jkr\nrVqph6zKpUlLc5OVpWSd1a4tMWKEg4EDlVphqrLvy4kTAk8+Gc6JEwK33OLkiiuCt6PEmTNw6JCG\nJk08l8ymu/ZaF3XqmNm2TUOLFh5atXLTtGlI2h8ChthYGUGQC7PLXS7lcqDXX+aFKmVC1X9DnEDw\nr1/Ili1a1q3TMXRoFHv3Vs4UDEQ5VBXBJIu4OJn33rOwYcM5/vc/pf3PtGl2rrii/EpaIMvBZlOs\n2qXF4RBYskTHb7/puOeeCAYMiOL33zW4LuOVCjRZSBLMmWPg6qtNPPFEOGfPFv/cOnVkrr3WxaRJ\ndq6/3lUuJS3Q5FCVXEoWiYkS48Z5O2IMGOAKWSUtEOaEqqipVDomk7KRnjol8sQT4eTmVvGAVAIa\nkwmaNZNo3lwiPj70LSV//qnh5psj6d/fxOuvG0rV+qxePYl77/X2CTp1SmTw4CiWLtXhdFbEaCuG\nrCyBV19VitHOn29g/fqicWgqVYfRCHfe6aBFCzc1a0r06qXGp1UkaoyaSqXz889aRozwdrpesiSf\nzp3VOjwqKpmZAhkZJvLyvMpZaqqbuXPNJe49uX+/yKBBUT49BwVBZuFCMz16BMc627JFpEePGoU/\nd+rkYsECM2Fhl3iRSqWTnS1gswlB614PNNTyHCoBQ6NGElqt99B5773SNQtWUQlVzGbBR0kD2L5d\ny9q1JbcoNW0qsXBhPgkJ3mB6WRa4//5wMjODo5jehYkQf/2l5eRJ9bgKNOrVk1UlrRJQZ36IEwj+\n9Qtp1Ehi4ECvH+aHH3Slcu+UhUCUQ1WhykIhEOUQGytx1VVF3UiHD5dufaSkSHz7rZn+/b3r7Ngx\nDfv3X7zeVaDJomZNmTp1vAqAyyVUSh3HQJNDVRJKsnA6lWzoshAIclAVtYuwb5/I0qVaPvtMz/r1\nWiyWqh5RaGEwwB13eA8Qj0dgz57QLZioolJSoqNh5kwrDRt6TxVBkOnatfQxQE2bSsyebWXRonxG\njFBawcXEBEekS926ss9lDuSQqg2oUvEcPy6wfLmWhx4KY+DAKCZMCK+05DV/o8aonYfbDStWaLnr\nrkjy872tSBYvNpORERyxHcFCbi6MGhXJ778rLp1nn7Vy772Oy7xKRaV6kJkpsHOnhtxcgaQkidRU\nT7nqokkSyDJogug+tHWrhr59o3A4BJo3d7N0aX6FNb1WCR0sFti4UcPEieHs3++r3X/7bT7duwfu\nWa7WUSsBf/yhYfToSDwe31Ykwdw6KVCpWRNefNHKNdeYyM8XOHLk4jed/Hyl5EBpGwlXBw4fFrFY\nIC5OIjq6qkdTFKsVTp8WyM8XcblkTCaIj5cu2ShbRSExUSYx0X8Hir8KkTqdSs/VyEgqvHdsaqqH\nBQvMvPiikaeesqlKmsplsdth4UI9Dz54YUsxuPJKF82bB2cR5OC0A1YAdju89FLYBUqa0oqkRYvg\n/HIhMPzrxZGaKvHVV/nUrSuRnu4r4xMnBL79VsfAgVH07h3FTz+V704RyHIoLadPC7z/vp5u3Ux0\n7VqDUaMiOXy45KdmRcsiJweWL9cybFgkV11Vg4wME7161aBzZxN33hnBvn2Bse2E0pwoL5eTxeHD\nIq+/bmDgwCj69TPxn/+Es2qV9pL1zcqLKEKXLm4WLDDTsWPl7MHqnPBSHlmcOCHwzTc6pk0zsnlz\n5ZlxN2/WXFRJa9vWzZtvWsvUlD4Q5oRqUfsXWVZuiucTHa20IlGrXFccnTp5WLYszyft/tAhkUce\nCWflSm+m28cfG+jfP3BN1pWFxwNffqn/twm1woYNOnbu1NCwYdXLx2qF114zMnt20ToKTqfADz/o\nadfOzUMPqW7usuJywa5dIjabQNu2HnQVXGLM6YRnngnjm2+8FU137dLw9dcGhg938Oyztgq1eFf0\n51PxL1YrzJxp5IMPFNP5++8bWbYsj5SUis8O3bJFy/lKWlycxNNP2+jRw0VsbPCe49VKUbNaITdX\noE4ducjiDwuDl16y8cEHHrKzRQYPdnHllW6aNg3u1OOuXbtW9RAuS2KidwHl5MD06UYfJQ0od1xB\nMMihJOzfL/Lcc+UrJlWRsjh3TmDevOKDqZKT3Vx7bWAUxwzGOSFJ8MsvOsaMiUAQ4Kef8mnfvvzW\npkvJQolivvghN3++gdGjHXTtGrxeh/MJxjlRUZRVFjt3avjgA+8eYLUK7N2rqRRFrW9fF3FxZtxu\niImRadbMQ/365VPQAmFOVBtFbfdukcmTw9iwQcejj9q49VYHJpPvc1JTPbz6qq1qBqgCwD//aFm0\nyPegr1dPYsCAICqrXoHk5Qm4XL5m/bg4Jdg8EKhXT+abb/JZskTPt9/qsdmUUgsdO7rp2dNF27Ye\n4uKC92Zb1WzdquH22yOQJGUObN+uKbGitnu3yM6dGvR6mbQ0Dw0alOx7MBjg0Uft7N2rYetW3yMj\nOlpS40dVfMjOFrjQ9Xi5Fmb+onFjicaNg9u4cjGqhaJ28qRS7PGvvxQrzZQp4bRr56Zz58o/3Fwu\nZXM9d04gPd1NjRqXf015WLduXUDcCErKgQO+8Uu1a0t88YWZxo3LdxgEmxyKo359iaQkN/v2KUs3\nLk7i88/NPlbJy1HRsmjZUqJlSzv/+Y8dl0sgLEwmPPzyr6tsgnFOrFyp9VHUS1oE9vffNQwbFoXV\nqrw2NdXN/Pnmwpidy8miRQuJBQvM7NihYdcuZf9q1MhDmzYeWrQInYMxGOdERVFWWRTNTpZJSAje\nORIIc6JaKGq7domFSloB2dkiULyi5nQq/5W38fOF/PablhtvjESSBKZMsXL//Y6gSpmvaNLSPNSu\nLeF2w7hxDoYNc9KsWfAucn9Tr57MvHkWdu0S0WggJcVTKiWtMlEs1qUbm8WixCjm5opoNDJ168ok\nJkpqnBJKWMDcub6nYEmy2E6cEBg/PrxQSQOl28GePRrq1St5SEGdOjLdu7sDuryBStWTlCRRt65U\neIkYM8ZBWlpgWPyDlWpRR+3773WMGeOrcX36qZlBgy5ujz1wQGTSpDBOnhQZPdpJ795OmjQpv5hy\ncmDw4Ci2b1f0Y71e5vff80LSVFtWZFk5WGQZYmNlv5UVUAl8zp2DWbOMvPaakQLXiU4nc9ttDm67\nzVEpMS6BzKFDAu3a1aBANqIos2ZNHqmpl5bLhX0zC1i8OI+MDPUAVfE/O3eKrF6tIzFR4oor3EEd\nyF+ZVOs6aiaT7ySJiJAveRPNyhJYsULJcJo0SUt8vIE5cyy0bVu+Te3YMbFQSQMlC+70aYHGjcv1\ntiGFIKDGMFVTzp4VePNNr5IGSuug9983snChnh9+yA86N9uZMwIGg+wXy7zBoMT75eYq8rn5ZmeJ\nkp1q1ZKpWVMiN9d760lJcdO8eXDJUiV4SEmRSElRM7v9RbWwVyQne+jbVwlG1+tl3n3XfMkNv149\nmchIr7KQlaXhhhsi+fvv8vkobbbKb4gcCDVgAgFVDl4CVRYJCTL//e/Fk3nOnlUC4f1JRckhLw9+\n/VXLI4+E0adPFIMHR7J7t+9Wm5kpsHq1lp9/1rJ1q1iiYOs6dRTrIkCHDi4ee8xeouLBiYkyH35o\nIT5eQhBkrr/ewccfW3ysHIE6JyobVQ5eVFkoBIIcKk1Ry8zMpGfPnqSmppKWlsbrr78OwNSpU0lI\nSKBt27a0bduWpUuXFr7mhRdeoFmzZiQnJ/PLL78UPr5x40ZatWpFs2bNmDBhwmX/dmyszGuvWVmy\nJI/Vq/Po1+/SMRZNmkg8/bTV57G8PMUdmpNTmk/tS82aMufH7ERFKTE4KioqSr2ssWMdfPttPhkZ\nLkSxYG3I9OzponXrwHfT7dwpcvfdEVx/fRQffWTk8GEN//yjxXle0vKePSLXXGNiyJAoRoyIomdP\nE2+8Ybhs8VitFu6+28FPP+Xx2WcWGjQouUWsZ083K1fmsXFjHm+8YVWtaX5EkpRkjTvvjODhh8NY\nvVpLbm5Vj0ollKi0GLXjx49z/Phx0tPTMZvNtG/fnkWLFjF//nyioqJ4+OGHfZ6/Y8cORo4cyZ9/\n/smxY8fo06cPe/fuRRAEOnbsyBtvvEHHjh255ppreOCBB+jfv7/P68vS6/N8cnPhrbeMvPyyb82q\nX37Jo0OHsh0YZjPcdVcEP/2kuFUff9zGI4/Y1TgsFZULsFjgxAkRq1VAr5epV08iKqqqR3Vp1q3T\nMmrU+X2CFR591MZDD3mtX++8Y+DJJ4umwc6bl8/VV6uB+sHGvn0iXbuacDq93/ttt9l56ikbMTFV\nODCVoKO4GLVKUxHi4uJIT08HIDIykpSUFI4dOwbAxXTFxYsXM2LECHQ6HY0aNSIpKYkNGzaQnZ1N\nfn4+HTt2BODWW29l0aJFfh9vzZpw//12PvjATJ06yu1TFIsWyi0NkZHwzDM2xo61M326lVtucahK\nmorKRYiIUCzbaWkemjcPfCVt2zYNI0cWVdKGDXNw++0OHxdlXNzFrVk7dqjp38FIQYWA8/nkEyPL\nl6upyir+oUrUhEOHDrF582auuuoqAGbPnk2bNm244447yP3XZpyVlUVCQkLhaxISEjh27FiRx+vX\nr1+o8PmbqCgYMsTFqlV5/PBDHitX5pGSUj73S9OmEjNn2rjvPkeZ+o6VlkDwrwcCqhy8qLJQ8Jcc\nZBnefNOA2exV0qKiZN56y8KMGdYiGW8dO7qLFHA2GmUyMqrOmqbOCYWyyCEhQWLgQCdNmniYOtXK\n44/bmDLFyqJFeqzWy78+UFHnhEIgyKHSsz7NZjNDhw5l1qxZREZGcs899zBlyhQAJk+ezMSJE/nw\nww/98rfGjx9PgwYNADCZTLRq1aqwcF2B8Evyc3y8zIEDa8jLA72+9K+vyp8LCJTxVNXPW7duDajx\nqD9X/c9bt271y/s5neBwrMZo1JOUlMFNNzmJiVlFQoJErVoX309Gj/6Zq67SYDR2JyoKnM7VWCwS\nUPT5O3aIfPPNbxiNcNNNnUhMlNX1EUD7pckEgwYto3FjLc880w+PR0CnW8W99zowGq8MqM9XFetD\n/fnS8239+vUcOXIEgDvuuIOLUal11FwuFwMHDmTAgAE8+OCDRX5/6NAhBg0axNatW5kxYwYAjz/+\nOAD9+/dn2rRpNGzYkJ49e7Jz504A5s6dy5o1a3jnnXd83qu8MWoqKioqJcVmU8qLmEyyX920WVkC\nvXubOHFCcX7Ex0t88UU+bdqoyQCBhMsFI0ZEsHKlt3F9dLTEypV5JW7VpaJS5TFqsixzxx130LJl\nSx8lLTs7u/Df3377La1atQJg8ODBfPXVVzidTg4ePMjevXvp2LEjcXFxmEwmNmzYgCzLzJkzh+uv\nv76yPkal43Ipm/WJE5Vf2kNFRaVkhIVB/fr+VdJAqcNWoKQBZGWJjBwZxZEj6n4QSMiyUhngfM6e\nFTl6VA1CVik/lTaL1q9fz+eff86qVat8SnFMmjSJ1q1b06ZNG9asWcOrr74KQMuWLRk+fDgtW7Zk\nwIABvPXWWwiCsjm99dZbjBs3jmbNmpGUlFQk4zNUyMwUmDIljM6do+jVK4ovvtBz7lzp3iMQ/OuB\ngCoHL6osFIJBDnXqyMTH+1rPsrNFtmzR+vXvBIMsKoOyykGvh2uucV7+iUGEOicU/CmH3Fz47TcN\ny5dri/S1vhT+Xe2XoGvXrkhSUXP9gAEDin3Nk08+yZNPPlnk8fbt2xfGVIQqkgSffWbgr7+0PPaY\ng3PnhMINuiqDjlVUQh2PB6xWMBqp8h6jcXEyr7xi4eabIzm/Y8PZs6pFLdC47joXX37pZt8+5VhN\nS3Or7QFVCnE64eOPDTzzjFKap04dia+/zqd168vPkWrR6zMYOXNGoE+fKG64wcn77xuxWJSNOSJC\nZsoUGwMGOElICMmvTkWl0rHbYetWDevXa1m1Ssfp0yING3q46SYnXbu6qrQels0Gq1drmTAhgtOn\nRSIiZL7/Pp/09MAvAFzdOHRIZPNmDTabwFVXuWnSRFXUVBT27xfp1MmE2+29ZKWkuFm82Ezt2spZ\nXlyMmqqoBShuN4wbF8GBAyLt2nn47DODz+9btHDz1lvWcvcfDSbOnYMDBzTIskzNmjLLluk5fFjk\nnnvsJCaG5DQOGGRZ6cMaipjN8M47Rl54wYgsF/2Qr75qYcyYqndrZWYq8WrR0bKqAKioBBn79ol0\n7GjifMs4wNq150hNVdZzlScTqJQOrVapaH7unEBYmEyHDr7uzt27tVx3XRT//HPprzAU4gxkGTZu\nVPqt9u5tYu5cA+PHR/DEE+G8846RP/+8vAc/FOTgL0oqC7sd/vxTw/PPGxk+PIL//a/8BVntdti9\nW+TPPzXs2iXiqMK+zQVy2LNH+YwXU9JAqYkWCCQmynTo4KkQJU1dHwqqHLxUlizMZsjJUfb5QMRf\ncqhbV6JLlwvDluQSFb1XFbUAJjVVYsmSfPr2dfLMMxYmTLBxfq9Qs1lg3LgIjh8PUVPHv6xZo2XQ\noCj+/ltHXJxEZCRs2OANHlIzq/zPmTPwwQcG+veP4uWXw1ixQs/SpeUL2Dp0SOmX26WLiX79THTt\nauKLL/RVqqwBxMZK9O1btCu6ySTxzjtmevYsQcd0FRWVUvPPPxoGD46kb18Tt98eweef69m5UyzS\n6SEUMJngxRetJCR4vWD33WenYUM1Rq2qh+FXrFYljubZZ8NYv15LgQl15cq8kI1X+ftvkWuvNWGz\nKZ91/Hg7c+fqOXvWq5x98IGZIUPUw9Rf5OTA668bmTXLt8/tnDlmrr22bHI+eVLg1lsj+OMPX2VP\no5H544+8Kg+6PntWcatnZ4totTK1asnEx8ulanyuoqJSOnbuFOnd24Td7jU2aLUyo0c7GDvWSXKy\np8oTevzN4cMie/eKGAzQsqXbJ/61ONdnpWV9qpSf8HC48koPc+aYOXpUJDtbJDxcpkmT0FTSHA4l\ndqhASQOIipJ8lDSQy3TIW62wa5eG7ds1HDok0qGDh06dXNSs6YeBBzlr1+qKKGnNm7tp2tTNkSMi\nsbESBkMxLy6Gw4fFIkoaKAVcIyOr/q4YHQ3R0R4gNNeSikpZyM1VMp8jIirm/ZOTJebNMzNqVGRh\nCza3W+CTT4zMmWNg8mQbo0Y5Qqq5fcOGUomsaOej+oyCkJo1IS1N4uqr3XTp4sFkKv65wRxzceqU\nwHffeSt9i6JM/fq+E3zECCfNm1/+cD1fDllZAtOnh9GnTxQTJkTw6qthjBoVydat1ePecqk5cfq0\nwLRpRp/HEhI8PPKIne7dTXToYOKhh8LZv790W0dUlExYmK9CVqOGxPvvW6hTp2oUtWBeG/5GlYWC\nKgcv3323nkcfDWfOHAPuCqoIJQiQkeFmyZI8unTxtdZ7PAJTp4YzdWo4J09WXXhPIMyJ6nEyVTOc\nTjh2TOTMGYHMTBGPBzTljwOvdCIiZHr0cLF8uY5OndwMHOjCbBbR62WcToGkJDePPGIr1W3v9GmB\nRx8NZ+lS/QW/KapIVEfMZoFDh7yTpVcvF3ffbeeWWyJxuZTN8quvDPz1l4ZvvjGXuERMcrISbzl3\nrp6cHJEOHdx07+4iOVl1LaqoBCK7dmlYuNDAkiUy/fq5KjQ8oXVric8+M7Nli5bZs42sXOkN7fni\nCwP9+7vKHHYRCqgxaiHG7t0iH3xg4PPPDTgcAnq9zJw5Zq6+OjiL5ObkwMmTIrNmGZg/30DDhhL3\n3OPg7Fno399VomKB57N6tZYhQ4r2+bnvPhuPPWYnMtJfIw9ObDb4/Xcthw+LpKR4aNbMw5w5eqZP\nL6oNL1yYT8+ewTmvVFRUiicvD4YOjeSvv5RwhR9/zOOqqyonLMBqVTKxjxwR2b9fxOMRGDDAWVjC\nIpRRY9SqAdu2iQwdGsXJk163lNMp8M8/2qBV1GrVglq1JEaPdvL11wYOHtQwaVIYgqAoaqXFdcFL\ndDqZyZNtjBzpqPZKGig9K3v18p0rvXp5mDlTLiy6XIBeHzp3PItFSdQ5dkykZk2ZtDQPsbHFf75g\ntVJXFVar0vrq2DEBs1nAZhNwOITC+nwRETIxMRJxcTKJiaWPgVTxL8ePi/z1l1c9yM2tPNdjeDik\np3tCNkGuLKiKWohw+rTAvfdG+ChpCqvIyGhfJWPyJx07eli0KJ+77ookO1ukfXsX9euXXFFYt24d\nXbt2pV07N199lc+ePRoSEyWaNfPQvLmEthqthAJZlJTWrT0sWZLHs8+GsXatDqNR5r//tZGWVjkb\n6alTAtu2adBqITXVTXS0f963QA75+TBrlpFXXjFS4G7p3dvFm29aqFvXd44dPCjy4486fvlFS/v2\nHoYPd4aE+7a0c6Kk5ObC+vU63nhDaYfn8Vz6wNdqZf7zHzvjxzsuqShXFBUlh2AjJ0cA1gA9AKrV\n/nghgTAnqrH4Q4uzZwW2bfP9OrVamYkT7SFxM9FqoUsXD8uW5XH6tEDt2jIxMaXfyGNioG9fN337\nBqeFsapo00bi008tnD0rIAgQHy9XSqeC06cFHn44jB9+UEwsY8faefpp2yUTaErL7t0aXnnFN8t1\nxQodW7dq6N3bO0/OnoWHHgrn118Vd9DatfD55wZ++CGfZs2CX1mrCA4c0HDXXRE+mduXwmhUCvuG\nkrU2GCnIwCxA/T6qFlVRCxFiYyWmTLHy+utGwsNh8GAnN93kJDX1qpC6DcXHK/WtSktV34hKQm4u\nnD4tkpOjuIf0eqUcSYMGkl/LhpRVFuHhEB5euRv2zp2aQiUN4OOPjYwc6aR9+/JfPgrkcO5cyZSI\nQ4c0hUpaAadPi+zcqQl6Ra2i1kfbth6WL89j3z4NO3YovVQLlACNBmrXlkhIkEhN9dC0qYcGDRTX\nZ0mqtZcUux1EEfQX5g9dhKraJ9zuwLJaOZ0CBdY0gJo1q6+iFghnRwBNDZXyUKMG3H+/g5tucqLV\nUmUlD0KV06eVxAx/WnJACdrdsUPDL7/oWLJEz759Ihf2grv6aidvvGGtlt9pdnZRJerYMdEviloB\nTZtKJCR4OHrUG3TWooW7SNmXiAgZUZSRJN8x+VOpCDUEAVJSJFJSJAYNcuF2e+NERZEKj0XbvFnD\n1KlhSBI89JCdjAx3QBVQPXRI5Msv9fz+u5YHH7TTrZt/xpeZKeDxCCQmSmWKpdRqvXtNRIRSAFql\n6lC3mBBCo4F69WSfAz0QasAEAmWVw9mz8O67Bnr3juL66yP55x//RZDv2iUydmwk11xj4rXXwti3\nT8OFShrIZGS4iYjw30ZZEXMiK0vg/fcNTJ1qZM8e/20rF+uz6a/emwVyaNRIYv58M489ZqNnTyfP\nPGNl7lwLiYm+f6dRI4np033buLVu7aZt2+B3oxfIoqJrAGi1SsJKWFjFDHu9lAAAIABJREFUK2kH\nD4rceGMka9fqWL9ex/DhkWzefOn1W5n7ZX4+PPlkGC+/HMb69Tpuusk/+8uOHSJ9+pjo0sXEggU6\n7PbSv0edOhKwGoAxY+yligcONQLhDFUtaioql2DFCh1PPBEOQGamhpEjNfzyS165N67cXBg/PpzN\nmy9+fRYEmWuvdTJ+vINWrTyEh5frz1Uobje8/76hsJvBihU6Fiww+yUYPDlZIiZG4swZRfmrV89D\nUpL/Yy6TkyUef9xemIV4MQwGuO02Bx06uDlwQEONGhKtWnlC4hBzOODTT/V8842OoUNd9OvnKpJI\nEWwcOyaQm+u9NEiSwIcfGrjiCmulxFdejr17Nfz0k3f9S5LAP/9o6NChfPP7xx/1nDqlfO57742g\nSZN8rriidO9Zr55M3boSp0/L3HCDS7UaVzGqohbiBIJ/PRAoixzOnaNIkHl2tsiJEyL165dvM61R\nA155xcaaNS5279Zw/LhAUpJEWpqHhASJ+HgldqciWrf4e05kZoq89563m8H27VoOHRKJjS2/QtW4\nscQ335h55x0Doihzzz2OIpausnIxOVzuAA8PVzKQO3YM/gSd86lRozvDhoUDAmvX6rn7bjuPP26j\nRo2qHlnZuZjL78gRDW43xboXK3O/VGIjfSdcTk75NSIlfEJBlgXefttI27aWUsXAxcbKzJvXAbPZ\nTOvWoTXXS0sgnKGqoqaiUgwul4DFcuGjMjpd+RUFQYA2bTy0aRP8m+DZs0KRrL7Tp/1nsmjVysOb\nb1r99n4qRVHKMXi/s3ffNXLNNS4yMgLfret0KmEEhw9rcLkgOdlDy5YSjRtLJCe72bXLe8z17OkK\nmBi1mBgJxY3ulXu7duWXd0KCb2LLmjVaTp0SqFevdPtWKOxNoYJq0AxxAsG/HgiURQ61askMHOhb\nIff6652lbqgbaPh7ThiNMufHbQEB7aotQF0bXo4e/bXIY8uXB/49PicH3nzTQK9eJsaMiWTcuEj6\n9TOxdatIXJzMe+9ZSEtzAzK9e7sYNsx5yferzDnRtKnE+PGOwp8HDlTCHMpLt26+yp7TKSCVYctS\n14dCIMgh8FeiikoVodHA3Xc7yM8XWL5cR9++TiZMcPg98zPYqVdPidUqaGpvMkkV2hdQxf/UqyfR\npYuL9eu95qYtWzSXjNkLBL7/Xs8zz/jeCiwWgePHRVq1kkhLk1i0KJ/cXIHoaNmvZW7KS0QETJxo\no29fF7IMKSkev2R2t2njZtAgB99/r2RrdOrkIjo6uOMNqztqr88LyM9XmtFu364hLAyuvNJNo0bq\noVOdcTiUFioxMXJA1ToKJP7+W8Po0RFYrQIffWShR4/Ad5mp+LJrl5IlmZ2tBHf93/9ZuPPOS1ug\nqpL8fBgwIIodO3wXZUSEzPLlebRoUX337cxMgUWL9GzapOXxx23VWhZVzZkzArt3K7HNogiNG3tI\nS7t4rcBy9fo8cOAATz31FH///Tdms7nwcUEQOHLkSNk/QYBx5IjASy+F8cUX3rzxhx6yMXly6fOb\nA/0mqlJyDAaqpJ1NMJGe7mHZsnzcbvwW7K9SuSQnSyxaZGbjRg2yLNC9e+l76VYmej2kpnp8FLWo\nKJm5c/OrvWKSmChz//0OZNmhnkNVyK5dIg89FM6GDV5LtU4ns2hRPp06ldzNXSJFbeTIkSQlJfHK\nK68QFhZ2+RcEITk58NxzYXz9teGCx0s/y3ftEnn7bQPt2nkYOtRZIZl7JSUQ+pQFAqocvFSULEob\nrFzVqHPCy7p169DruzNjhpHrrnMycKCTmJiqHtWlMRhg8mQbvXq52L9fQ0qKh7Q0T7m6RITanCiP\nkhZqsigrZZXDyZMCY8ZEsHevr5rlcgn89pvO/4rajh07WL9+PZqylDgOErZt0xZR0gRBZvjw0pn+\nMzMFxo6NYPduLXPmyKSlefxaRV1FRUXF32RliTz6aBT5+QKrV+sxGCzcfHPguj0LSEiQuekmFxDY\n1j+V6seZMwJ79xbVmbRaudTW6hJlfXbr1o3NmzeX6o2DjaLlBGReftlK27alU7L+9z8tu3cX6L8C\nx45VbWKteiNSUOXgxZ+yCOYI19LKISdHKVQcikRHdyM/37sHzphh9FuJlbNnYdkyLQ8/HMbo0RF8\n/rmekycD0x+n7hNeVFkolFUOCQkSTz1lRxS9m2SbNm6+/z6/1HpFiSxqDRs2pH///gwZMoTY2NjC\nxwVBYPr06aX6g4FKcrKHFi3c7NunoUsXNxMn2mjf3lOqNidOJ3z9tW/n32A+yFRUimP3bpGff9ax\ncqWW3r3dXHedkwYNgm+ynzghsHevSFaWhvx8MJlkatRQqrI3bixRo4bS1HvVKi2TJ4cTGyvx/vsW\n4uOLftZjxwQOHdLg+LfiQliYTGSk0h82PFymZk05YGp4XUhBo/QCjhzRcPasQO3a5ftOjx8XmDYt\njHnzvBvpjz/qmTrVygMPOC7xyuqN2QxHj4q43UrrssjIqh6RSmmJioLx4+1cc40Ts1nAaJSpX18i\nOrr071UiRc1isTBw4ECcTidHjx4FQJZlhBCKUkxJkfjxx3zy80Wio8u2MHJyBDZv9hWpUtSw6lDj\nDBSCUQ7nzsH27Ro2bdKyb59ImzYe+vRxlTtYv7yy2L1bZODAqMK2Tr/+qufQIZH/+z9bUGXFLl68\nnnff7cf//ndx7emqq1w89ZQNlwtGjYoEBA4cUDLC4+OLZrXq9coe8N//hnHkiNflodHIxMbKNGjg\noW1bD+3auYmNlYiNlYmJKdvG7W8yM38Frin8WRT9k+H8119aHyWtgIMHA7OEZ0XuEzYb/POP0hkh\nJcVTbAzgkSMCzzwTxsKFyqV/+HAnkyfbKr1VWTDumRVBeeRgNCq6RXkp0VL85JNPyv2HgoFataBW\nrbIL1e0Gh8OrvEZFyTRoUL2zj1TKRmamwIsv+mYgg9IgeeZMW5X23vv0U0OhklbAihU6zp2zExMT\nPFY1jUZRrorjf//Tcd11Wl54wcr51eM9xXgt6tRRCiR36OBmzx4NS5fqmD9fT06OSFaWQFaW6KMU\nCoJMw4YSXbq46dbNTUKCh7g4mbg4icrO2apfX6ZmTamwN2Z6upvatcu/d2VmFp2ogiBftvBsKLJ0\nqY5x4yIAgZEjHUyfbi2ipMsyfPWVgYULvet+/nwDffq4GDpUjcOrrpT4zrRnzx7mzp1LVlYW9evX\n5+abb6Z58+YVObagIScHrFbFTdChg5vVq5XN+OmnrSQkVO3Bpd6IFIJJDk4nvPWWsYiSBkoWV3mV\ntPLIwu2GbduKBsh26uSmRo3gUdIABg7sQnq6hTVrdDz/fBjZ2UUF26iRB5fL13NwuVItirLlJiPD\nzX332Tl8WGTTJi2ffWb4tw+j8n6yrLhKDx3SFH7Xer1Merqba691kZrqoWFDiQYNpAp3mQ4Z0pno\naAtjx0YgCDBjhs0vhZ179HDRuLGbgweVoyYx0cPs2dZyNx6vKCpqnzh9WmDq1DAKvvsvvzRw441O\nevb0tczm5MC8eUVvD//8o6l0Rc1o7M66dVC3rkxCghQU3UYqgkA4O0qkqH3//feMGjWKgQMH0rBh\nQ3bt2kWHDh2YM2cO1113XUWPMaDZtUtkwoRwdu3SMmOGhccft3HwoMjo0Q6uu85ZpZYPleDkzBmB\n+fOLbtY1a0rcfnvVWiK0Wrj5Zifr1nk1h/h4Dw89ZC+Rqyw7W2D3bg0xMRLJyRWvgFyOhASZUaOc\nXH21i5MnBc6cEbDbRWRZpk4dmaNHRe66y1tfp3NnF40bl0zJEATFUlW/vofOnT2MGuUgO1skK0tk\nzx4NS5bo2LxZ62OFdzoF/vhDxx9/KIIxGGT69XMxZIiTZs0Uxa2iDswePdysXp0P4Lc2aSkpEkuW\nmDl2TESrlYmPl6lbN7gUen9gsSgW1fP5+WddEUXNZIIWLTwcPOh7GerSpfIVW4tF4MYblRigjAw3\nY8Y4SEnx0KiRVKrYbZXyU6LOBGlpacyePZuePXsWPrZ69Wruu+8+tm3bVqEDLCtl7UxQGqxWGDMm\nghUrCg5VmWXL8mjUSKZWLTkglLQL/euHDols2aKhRw9XtWqFFEzxFg4HvPeegaefVm7gGo3M9dc7\nmTjRTnJy+Q/Q8soiNxc2btSyaZOWpk09pKd7aNKkZON6/XUDU6eGo9HIvPCClZtuchIVVeahlIuS\nyGHWLAPTpimaUUSEzA8/5NG6tX+UGLsdjh8XOX5c4ORJZV2uWqVlxw5f5a0AQZDJyHBz550OOnRw\n+7UIczCtj4qkouRw6pRAz54mH2Xt+uudfPSRpchzt2wRGTUqkmPHNIDMf/7j4JFHbD5uUo9Hcd1X\nJKtXr8Pj6cHtt0cWZgRrtTIjRji59VYHycmeKq0RWllU5tooV2eCY8eOkZGR4fNYly5dChMLqivZ\n2QKrVp1vEhBYs0ZP+/al72RQGWRnC4wbF8GmTRpWr/bfgaPiXwwGuPNOB717u7BaBWrUkElMlDAa\nq3pkCjVrQu/ebnr3Ln2bqFWrlC3H4xF47LEIjEYYNcoZsNXTe/Vy8/bbEnXqSMycafXrmjEalYy+\nRo0APAwe7OLhh+HUKZHTpwVycgTy8hRLzPbtGvbt05CZKTJpUjjt27uYMsVO06bqGg4G6tSRmTDB\nzqRJXnNox44XXz+tWyuJbZmZIiaTTOPGEhERygVp82YtS5boOHxYZOJEe6mKppYWrVaxsv70Ux5P\nPx3O8uU63G6BOXMMzJmjZ9AgJ+PHO0hNrR4KW1VSIotajx496N+/P48//jigZHy++OKLLF26lNWr\nV1f0GMtEZVjUdu0S6dy5hs9j48bZefFFW4X+3bIgy/DRR3oefVRZUYsW5dGtW2DGiaiELi+/bOT5\n572R8kajzMqVeX6xFFYUx48LGAwytWpV7TgcDrBYFCU3LEwmPLz88YoqlcexYwJPPBHGkiV6mjf3\n8PnnFpKSSjbvjxwRef55I/Pne32Oo0fbef31yjlrzpwR+PlnHU88Ee5Tbw8Ua//99zto2bJ05awq\nA4sFJIkqs9qXlnJZ1N5++20GDRrErFmzSExMJDMzk/DwcL7//nu/DzSYiI2VaN7czZ49XjEWd0uq\narZtE5kyxXub27VLS1qaJyBKA6hUH7p3d/H880YKgqrtdoGtW7UkJwduFmBcXGDEVBkM/HsQBsZ4\nLmTrVg3r12s5ckQkPFwmNlapQxcVJVGnjkzt2ko5kmA5NP1N/foys2dbeewxO7VqySUut3H4sMhd\nd4Xz55++AZ3dulXeWRMTIzNypJMrrnCzaJGemTONOJ0CILBokYHvvtMzbpyD22930Lx5YFy67HZ4\n4YUw1q3T8OyzNjp18lS4u7iiKNF9LCUlhZ07dzJ//nwmTpzI/Pnz2blzJy1btqzo8QU0tWrB88/b\nCisPN2rkrtB2UcePCxw9KiCVYh2sW7cOiwV+/12LzaYcjhqNTE6OcNEst1Bl3bp1VT2EgKEqZZGa\n6uGBB3xDA/7+u2rmoTonvPhDFhEREtu3a3jnHQOvvBLGpEkR/Oc/EYwaFUXfviauvNLEgAFRTJ1q\n5IcftPzzj8iJE0JAFQWv6DlRowakpUklVtIkCb75RldESWvWzE2nThWrqF1MFs2aSTz8sJ0VK/K4\n9147Wq387zgF3nvPyIABUfz8sxazuUKHViKOHxd45x0DW7boGDIkitWry1YYMBD2iRKPXKfTFYlT\nU4GuXd0sX55PdrZAy5aS37KlLiQ3F269NYIdO7Q88oiNG290lrjw6cGDIgsWeLMI27b1sGOHhptv\nrpChqqgUS3g43HOPA4tF4MMPlaC7li0D4wauUj6aNJGZMcPKHXc4+PVXLe++a/S5DLpcAjt2KMkS\nBdStK3HzzQ6uvtpFUpLk1wSJUCA7W+C113yL6rVu7eaDDyyVXgC3AI0GUlMlnn7axogRDn74Qc9r\nrxmx2wVyckRGjIhi3Dg7999vL3dx7vKg1Sp1Eu12cLsF7r47gl9+yaNJk+CbY8XGqCUnJ7Nr1y4A\nEhMTL/5iQeDIkSMVN7pycLkYNZcLDhwQcTiUnlyB7gLMyhLo3NlEXp63IOXHH5tp2PDyk27lSg3D\nh0chSYpF7aGHbNSpI3H33YEbxK0S2uTlwY4dGvLyBFq18lCvXvBtniqX5vhxgX37RLZt0/L99zo2\nbtT+6y67OPXqSTz4oJ3evV0lziIOdU6eFBgwIJKDB7VERcncd5+dkSMdVaakXQxJ4t/vWcNHHxn4\n7TctINCxo4sPPrBUWS1RsxmGD4/0KTI9Y4aVu+4K3NZlxcWoFauorV27ttCCVlzCgCAIdO/e3X+j\n9COXUtROnhR47z0Ds2YZ8XgEMjJczJ5tCehehW43PPBAOF995Y3WvPpqF2++ablsP75vv9Vxxx0F\nPbFk3njDQs+ebvVwVFFRqRTsdsjOFsnOFjhxQmTzZg1r1ujYvVtTRHmLi5P4+ut8UlNLr6xlZgqY\nzQJJSVVfo89fHD0qcOqUSO3aiss0kBNIzGalBNSBAxoOHhTp1s1d6gbk/mTpUi2jRnmDIuvUkVi9\nOi9gz75SJxOc7+Y8deoUw4YNK/KcBQsW+Gl4lcsPP+h45RWvOXntWuW216BB4Lbo0Grh1lsdzJun\nR5aVjW3ZMh3ff69j7NjiA7HXrVuH3e6tf9exo5tevVzExVX4kAMKtU6UF1UWCqocvFS0LIxGaNxY\nonFjAA833ODCYrGTkyNgswnYbEpiiSRBzZpKG63ScuKEwF13RbBxo5a33rIwZIir1EpNIM6JhASZ\nhAT/KTt5ebBzpwabTaB1a3ex3qSyyCIyUonBS0sLDIto+/YeWrd2s2WLouqcOiWSmyuUSlELhDlR\noml8++23X/TxO++806+DqQzOnoXZs4sWpDp7NvB9gOnpHp54wjcQ+9lnwzh69NJjt1gKfi/z9NO2\naqekqaiEElarUq4hM1MgL6+qR1N2IiIUJaRZM4nWrSU6dvRw1VUekpMlatYs/fsdPCiyYYNS6+u+\n+yLYujVIU/wqEKdT6dU7YICJIUOimDkzDKu1qkdVcdStK/Paa1Zq1ixQHGUcgev5LJZLJhMcOHAA\nWZaRZZkDBw74/G7//v2EVXbnYD8gCFzEJC7TqlXg1xQzGhWr2r59YmE9nZwckcOHxWJvXF27duXQ\nIeXf99xjp02bwP+cFUFV34gCCVUWCsEoh717RSZPDmPlSh2iCM2aebj7bgc9ergKY4G2bxf55Rcd\nDodA+/Zu2rTxXLZtUzDK4kLOv2w7nQLr12tLvd+Fghwuxd69ItOne8/tt982MGKE46IWsFCRRXq6\nh+++M/PSS0bCwmS+/16PyeQocVJBIMjhkopaUlLSRf8NEBsby9SpUytkUBVJrVpKs/RbbolElgW0\nWpnnn7eSmhocCkzduopVLD3dw7RpYTgcSmbLpUhPdzNlipXhw53VtrFuRZGTo7ilq2ttKJXKZeNG\nDb/84l3w27dreeABLQ0buvnySwsRERLXXRfF2bNeZ0nnzi7efNNaYRnpgcKFnTsWLtRx220Odc87\nj0OHRDye8z0wAmf+n73zDo+q2vrwe86UZDKZ0CH03ov0ogEBpUlHiohS9QooApZrL/DZQBQpcm1I\nVWkqoJQglyIBhCuCSBERAoQAoYVkej3fH0cyGVJIyEwyMznv8/A8zGQyObNm733WXnut37omAuE9\nNpo0cdOxo5O1a7WsWhXBvn1qvvzSHDJ9Z3M9+vR4PHg8HuLi4jL+f/PfxYsXeeKJJwrrOv3K/fe7\n2LYtnW++MbJtWzqjRjlCqgVGxYoS//qXnZ9/Tmf79vRcncyEhASaNPEwZYqdSpVCY1AGgkBo4Rw5\nItK/v4EhQ6I5dCh0jlmCQRcoGAhFOzRs6CEyMus8PntWzdtv63A6hSxpHHv2aHj//UhsuXS2C0Vb\n3Er58h4yiwH//beaGzfyl9IS6na4dg2++krL8OF6PvggksTE23/+7MYThL4tbuWXXzTs2SMfp+3Z\no+Ho0byt2cFghzzlqP3888+Bvo5CRauFu+7y0KOHiyZNQrM6SD728HDXXR5lx1gEpKXBc89FceSI\nmv37NQwfHk1SUvDnOSqENs2auVm/3kjTplnFTt1uKFFConv3rEVR336r5erV8B6fVap4aNjQu2nV\n6YK7QjIQbN2qZdIkPfHxWt5+W8ewYdGcO+f93mVZD69jVru2q9hIoTRr5jtnVq3S5ks8vijJUZ6j\nR48exMfHA+QodCsIQtA6cYHo9ZmeLiesms0C5ctL1K7tUXTIiimJiSKtW8dkVOACfP21kZ49g7OF\nmEJ4cfmywF9/iSQlqbhxQ6ByZQ8tW7qoUkXizBmBSZP07N7t3YG2bevkm29MRd6vNNDs3q2ib18D\nIDB4sJ3//McSsm2D8ovbDQMHRpOQ4Bt5WLzYRL9+svNus8GyZVpeeimKChUkli41BbSbTjCRkKCi\nX7+YjMelSnlISAguqY58y3OMHDky4//jxo3L9jVCMfJSzp8XmDFDx1dfyUn8Op08yO+7T7kxF0fc\nbrK0vjl9WgUo40HBl2vXYO9eDV9/raVRIzcPP+wocBSjfHmJ8uXdQNabbI0aEosWmTl6VMWZMyIG\ng0Tr1u6wd9IAWrd2s3KliaVLI3jmGVuxcdJA7hhQr547i6N29qw3rBgZCaNGObj3XhfR0VKxSodp\n2NC3N3d2a3iwkqOjNmLEiIz/jx49ujCuJaj54QdthpMGYLUKPPaYnoSE9KBSib6VYNCACQb8bYcy\nZeRjluPHvVOoZMngHQeZUcaETGHYIT0dZs3S8emncqb75s1w7ZrAzJnWgKZclC0rce+9LvKqRx4u\nYyIiArp1c9Gt251tmELdDg895GDJkgifgoFbFQ20WvLUOD3UbXErZcpILFhgoX9/A2azQKNGbkqU\nuP2aHQx2yNMJ/tdff82xY8cAOHHiBJ06daJLly4ZLabCHbcbNm/O6tPabAIul8CFCwKLFmkZMULP\nkCF63n03kq1b1T47GYXwQq4etmZ6RqJeveJxhKCQd44dU2U4aTfZtk1DWlrxOY1QKDxkKQoj7ds7\nqVfPzaxZZlq0UKL8N2nZ0s2PPxqZNs3C++9bQqaIMMcctczUqlWLvXv3UqFCBfr06UODBg3Q6/Xs\n2rWLbdu2FcZ15ht/56gtWqTl2Wd9v9VJk6y8/LKNP/5Q0b17TJbfiYnxMHmyjaFDHUEddVO4M8xm\n+PlnNYsXRzBqlIOuXZ1ZJAIUijcrVmiYODHa57mhQ+3Mn29Bnas4ksylSwInT4oYDHDXXW4lJ1Yh\nT1gscj/rEiWK+kryx9GjKn7/XSQuzhXULR0DRb5z1DJz9epVKlSogNVqZffu3Xz77bdoNBrKlCnj\n9wsNVvr2dWK3W1i6NAJJgieesPHAA04iIuS8gClTrHz0ka8AcHq6yP/9XxTffadl4UJznsLNCqGD\nXg+9erno1Ss0dqweD8WuCq6oufVoRauVePxx+22dNLcbfvlFxZQpUZw6paZSJQ/btqWHjO6TQvb8\n8ouK//5Xg0olV6lWr+6hRg03VapIfnXCQ1EJ4MwZkQEDorl2TWTgQDvz5llC8nMEgjwt2+XKlePk\nyZNs2rSJNm3aEBERgdVqJQ/BuLChbFmJ8ePtbN6czubN6Ywe7chYNGNiYOpUG0uXmqhcOaszdvSo\nmiVLIrI8XxgEgwZMUeBwwJUrAs5/lAqKqx1AlhJZu1bDsmWyUGpxtkVmCsMOzZu7efRRG9HREs2b\nO1m/3ujTpDq7JdTjge3b1QwcaODUKdmj0+slNJrArbfKmJAJpB3cbli3TssHH+iYOVPH00/r6d/f\nQKdOMcyYEcnvv6ty1borbAp7TBw4oPpHfBfWrtVy+nRw7CqDYW7kyRKvvfYarVu3Zty4cTz33HMA\nbN26lebNmwf04oKRmJjsw8kGA/Tp42Tr1nTWrjXy6qtWmjd30aCBm06dnPTrl3PjdAX/YbPB3r0q\nJk6MokuXGNatC0GRPD9iMsHnn0cydmw0e/bkKYCu4EcqVpSYMcPK3r1prF1rom1bd0ZU8/BhkUcf\n1fPSSzr27lVhNsvPHzqk4pFHonG5vCGWp56yFYuqzXBGpYLHH5fbfWUmLU1k5kwdXboYmDUrkuTk\n4nm+/b//edcnSRJISQkORy0YyFOOGoDZbEYQBKL+iUVevnwZj8dDbJB2+A6Ejlp+sVjkXVRExO3b\nPCkUnPR0WLlSywsvRAHyYvfIIzbmzrXm/othitMp2+Ppp+Xcyo8+MjNypLJhCBbmzo3gzTdvnu1I\nvPqqjUGD7AwZEp0RSQNZlHT1ajM1aiipE+HAlSsC69drmD49CqMxq1PWooWLL780h33Lr1sZOVLP\njz96b5TffGOkR4/QSCuRJNi3T0VCgoZ69dy0besiNjb/EfAC5agBOBwO1q9fz4ULF6hcuTJ9+vSh\ndOnS+b6Q4oRyvl54WK3wzTcRvPSSr9HzO9EliUJJ2D56VKRMGemOJnNeOXJExdSpXnuESj/bcCUl\nRSAlRSA6GipV8tyipSbw1ls6zGaoVEni1Cn5WYNB4osvFCctnChXTmLcOAf33efi999VLFoUQUKC\nGo9HXngOHlTz22+qgDlqqalw+bLIlSsCggC1a3sCug7llZgY32vIqbVVMJKYKDJkiCz7AdCxo5O5\nc/3XXzdPscW9e/dSu3ZtPv30Uw4fPswnn3xCnTp12LNnj18uQiFwBMP5emFw6JCKl17yLeZo2NCV\nUZp+OztcvSqwcqWW/v2jWbxYiyOAgacTJ0R69zbw73/ruH49MH/j6lWBV1/VZegp1a3ryrjZF5cx\ncTsK0w7Hjon07h1N584laNcuhuefj6J6dTexsb4L+ezZOrp1cwISJUt6WLPGyF13Bd5JU8aETGHa\noUYND/37O/n6axMJCemsX5/OihVG1q410r69/yNJp0+LrF6tpXeavzofAAAgAElEQVRvAx06xNCv\nXwx9+8Zw7Fj2qsCFPSY6dPB+5ogIKWg6BuTFDjduCBlOGsCuXRr+858Iv91H8hRRmzx5MgsWLOCh\nhx7KeG7lypVMnjyZ//3vf/65EgWFO8ThgC++iODmcSdAbKyHL78050l5+/JlOZqxfLlc8PHLL2ri\n4lzUqROYG+TJkyrS00V+/DGCxx930LGj/xflI0dU9O7tJDlZ5Nw5FdOnWylTJjgWvuLIzp0aTp++\nqYgu8NVXERw+LLJokYmJE/X07OkkKkpi3z41v/8u8vHHZtq2dVG7tvKdhTtRUdCgQeCc8bNnRX76\nSc3//V/Wo9auXZ00ahQckfbWrV0YDBJGo8CkSTZq1w6dKHK5ch5KlfKQmuqNfS1aFMHYsXa/qD3k\nKUetZMmSXL9+HTFTbb/L5aJs2bLcuHGjwBcRCIIhR02hcLh2TeD++w2cPSvvDFu0cPGf/+RdDiWr\nRp7EL7+kB0xO5cMPI3nrLTn6N2SInQUL/NuP8NdfVQwaZMBuh1dftbJmjZZvvzVRtmzOU/3iRYHD\nh1XUq+ehZs3QWSBDhe++0/DYY9FZnl+6NB2tVuCpp/SkpQnExbkYNMjBwIEOJXVCocAcPKhi1Cg9\n589nXWDGjrXxzDO2oGojdfiwinPnRNq0cVGhQvBcV15YuFDL88/7aq1u2GD0iRTejpxy1PJ09Fm3\nbl2++eYbn+dWr15NnTp18nwBSUlJdOnShcaNG9OkSRPmzp0LwPXr1+nWrRv16tWje/fuPo7fu+++\nS926dWnQoAFbtmzJeP7AgQM0bdqUunXrMnny5Dxfg0J4UrKkxIcfWnj5ZSvffmvkm29MeXaykpIE\npk/3PTK95x5XtjIr/uLaNe//ExI0XLvmv6S41FR46y0dJpOA0ylgsQjMmGHO1UlLTYU33tAxfLiB\nr79Wql4CQbt2Ljp1cmZ53uMR+OEHLVevijidAtu3a5g0KYrPPovAaCyCC1UIG375RW5Qf6uTVr++\ni9WrZWWCYHLSAJo1c9OnjzPknDSA/v2dTJliBeRrNxgkKlQoxBy1OXPm8NRTT9G+fXuGDh1Ku3bt\nmDhxInPmzMnzH9JoNMyePZujR4/yyy+/8PHHH3P8+HHee+89unXrxl9//cV9993He++9B8CxY8dY\nuXIlx44dY/PmzUycODFDt23ChAksXLiQkydPcvLkSTZv3nwHH714UBxyT1Qq6NLFxXPP2ejSxZWt\nKGhOdjh7ViQtLfM0kHjuOVtAW4tkvr6LFwW/thNKTBT5+WevJInJRJYcp1ttkZCgYc0a+dh32zZN\nUGk5BZLCnBuVK0vMm2dm2jQLVau6Uasl+vWz07SpO4tcAwhMnx7F9u0Fk5ZJThY4cULEZLr9a4vD\nOpEXwsUOV68KPPVUFBbLzbVFoksXJ6tWGVm71sR997koWTL39yhsW5w7J7Bpk5oPP4zk88+17Nyp\nJjW1UC8hW/Jqh7JlJZ591sbGjUa+/NLE+vXGWwqG7pw85ajdfffdnDp1ig0bNnDx4kX69etHr169\n8tWZIDY2NkPKIzo6moYNG5KcnMz69evZuXMnAKNGjaJz58689957rFu3juHDh6PRaKhRowZ16tRh\n3759VK9eHaPRSNu2bQEYOXIka9eupWfPnvn97AoKWSo8p02z0rp1YEvCfaN1QqbFtOAkJvrunmvW\n9KDT5fBiZDHcmTO9fa/MZgG7HaUVVgCoWlVi0iQ7w4c7sFqhdGkJvR70ehdDhthZvdpXFHvOnAju\nv9+Z7yNQl0tubTZhgp4rVwRee83KpEm374agED7o9RJz5li5ckWgZEk5slO1qoforKfvQcHhwyJD\nhxq4fNk3dvTKK1aeftqGJkTkMPV6aN/eDfg37y/PU7d06dJ06dIlQ56jIO2jzpw5w8GDB2nXrh0p\nKSlUqFABgAoVKpCSkgLAhQsXaN++fcbvVKlSheTkZDQaDVWqVMl4vnLlyiQnJ9/xtYQ7cXFxRX0J\nQUFOdqhTx8OoUTZOnVIxcaKdjh2dAW/Ue+sxpD8rTJOSfBe67I5wM9vi7FmRo0e9zl3Dhm4MBv9d\nTzBTVHPj1u+/fHmJN9+00qSJm3ff1WGzyY571apSnlp+Wa384/jJj/ftUzFsWHRGxe977+l48EEn\n1arlvLtX1gmZcLGDTiencBSEwrKFxQL/93+6LE4awJdfRvDII/YiPQoNhjGRJ0ft3LlzjBgxgr17\n91K6dGmuX79Ohw4dWL58OdWrV8/XHzSZTDz44IPMmTMHwy13BEEQEPwoYvXkk09SrVo1AGJiYmja\ntGmG0W+GM5XHyuP337eSkJCAWg16feD/XtWqHnS67VitAnAvBoPkt/e/fv1+ZHYAElWrtsz19enp\nnZGrZXcA0K1bG0QxuL6f4vD41Kld3HUX7NrViXPnRI4c2UW1ah4iI+/J9febN4/j5Zej2Lp1Nx07\nOhk3rgMLFkTgdsunFNAZrRZ+/XUX585JQfN5lcfK45uPRRHM5p2ABuiMzA4Ann66DRUq+G99DLbH\nALt37+bcuXMAjBs3juzIU9Vn586dad68OW+//TZ6vR6TycRrr73GwYMH2bFjx+1+PQOn00mfPn3o\n1asXU6ZMAaBBgwbs2LGD2NhYLl68SJcuXfjzzz8zctVefPFFAHr27Mm0adOoXr06Xbp04fjx4wB8\n88037Ny5k08++cTnbylVnzIJCQlBsSMoaoLJDpIEs2ZF8u67OqpWdfPf/xpzTfbPD6tWaRk/Xg4J\nDhtm5/33LVmOOzLb4vPPtbzwgjeEuHVrOi1bBke5fqAJpjFxp5jN0LdvNIcOyWdDKpXExIl2LlwQ\n+fZbuTBkyBA7H39syfXoMxxs4Q8UO3gpTFucOiXy8ccRbNigJT1doEkTF888Y6dDB+dtc+kCTWHa\noUBVn7/99hszZ85E/8+ZUHR0NDNmzODAgQN5vgBJkhg3bhyNGjXKcNIA+vXrx5IlSwBYsmQJAwYM\nyHh+xYoVOBwOEhMTOXnyJG3btiU2NpaYmBj27duHJEksW7Ys43cUFEIBQYAhQxzcf7+Dt9+2+s1J\nA/noMjJSolw5D5Mn226bk5I5/6ljRycVKxYPJ+0mqamwbp2Gzz7TcvCgCneIfXy9Hp5/3p7x2O0W\nmDcvErtdll+IjJQdNyU/Lbhwu8GjqOBkULu2h5kzrezcmc7//pfG99+b6NWr6J20YCFPEbXu3bvz\n+uuv+3iVu3fvZtq0aT6yGbmRkJBAp06daNasWcbx5rvvvkvbtm0ZOnQo586do0aNGqxatYqS/3w7\n77zzDl9++SVqtZo5c+bQo0cPQJbnGD16NFarlQceeCBD6iMzSkRNIdhJS5MdJX8mykoS/P67ipgY\nKU8VR1u3qhk61IBeL/HKK1Z0Og+jRmWVkQhXfv5ZzYABcgqGWi3x2Wdmevd2hkzyMsjO5osvRmUp\nRhg82M748TZatPAUSlu0osTp9O888jepqXD0qJpfflFz4ICKGzdEypb1MGCAgzZtXFSrFnpyFAr+\nJ6eIWp4ctfHjx/P111/Tp08fqlSpQlJSEhs3buThhx+mbNmy8hsJAtOnT/f/ld8hiqOmoHB7LlwQ\nWLVKi04HH3wQScmSEvHx6ZQqVdRXVjh8/72GceO8YUeVSmLTJiOtW4dWaO3SJYGZM3UsXpzZWZP4\n4Qcj99wTWp8lP5w5I7JihZadOzV07Ohk4EAHDRsGV6gqKUlg6lQ927Zl70m2auXkq6/M2coKKQQf\nkiTLKun1EiVK+Pe9C3T0abPZGDRoEFqtlitXrhAREcHAgQOx2WycP3+epKQkkpKS/HvFCn4hc9Ji\ncUaxg5fMtrhxQ+CjjyJ56SUdV6+KnDsnYjKFefjlHxISErJUxbrdAsuXa/16BOpywV9/iezfr8q3\nLtTZsyJbtqj57jsNW7aoOX5cxGrN+rrYWInXXrMwb54ZrfbmDV8gPj5vYaZQnB9mM7zyio6ZM3Xs\n26dm1iwd/foZ+PPPPN3WsiUQdjhyRJWjkwYQEYFfO5P4i1AcE4HgVjscOqQiLi6GYcOiOXhQVShH\n2HnKXFi8eHGAL0NBQaEoOHdOJD3de2OrVs2DwVB8dvZ16riJi3OSkOC9kW7apOXFF23ExhbcDidP\niqxapWXevEgcDoENG9KpUsVDmTLSbfXRUlIEhgzR8/ff3mVaECR69XIydaqNFi3cPvIdpUrB8OEO\nWrVyceiQmn37VHTr5irwZwhWUlMFduzwdYCuXRNZu1b+/oKFZs3cjB1rY/nyCBwO7yYoOlpi6lQr\nAwY4lT68IcTZsyI3bojs3y/Sq5ea774zcvfdgY1a53vrMXHixEBch0KAUCqYZBQ7eMlsi0uXfJeA\n3r0dxSaBNy4ujtKlYeZMCzVqeB2aSpU86HQFu3FKktxztU8fAx98oMPhEDAYJH7/XUXr1iUYMSKa\nP/7IffmNjJSy3MAlSWDjRi0PPGAgPj7rPlsU5QbfDz3kYPZsKx075s1RC8X5UaKERNOmWT/f1at3\nHhEOhB0qV5Z45x0re/aks2FDOhs3prNzZxp79qQxZYo9aHvrhuKYCAS32qFECe+cdDgExo6N5vTp\nwJ5C5NtRW7ZsWSCuQ0FBoQjIvOiARM+exaeQ4CYNGnhYs8bMW29ZGDnSxuzZlgLlnkgS7Nqlpl8/\nA1eueJfYJ5+08dFHOpxOgZ07NQwdauDs2ZyX4BIlYM4cCy1aZHVGnE6BiRP1nD9fPI6ps8NgkJ3s\nUqW8jo5aLdG/vx8VpP2EVgu1anno0MFN+/Zumjb1UKWKFPZFHuFI9eoeSpTwjrnLl0XWrInAFcDg\n9Z0f5iuEBEqegUyw2+HSJYH4eDX//reOV1/VcepU4KZmZlvUru3JyGl64w0rd90Vvonnt5LZDrVq\neZg40c5HH1lp3rxgNti/X8VDD0VndBgA6NHDwfnzoo/6ekqKyIkTuX/P9ep5WLrUxNKlJjp1cmZ8\nV4IgMWyYg6go34jbnj0qZs2KZMcONdeu5d0LCPb5kRPNmnmIjzeyeLGJOXPMxMcb6dDhzr+/ULVD\nIFBsIXOrHWrV8vDuu76JovPmRXLxYuC87jzlqE2ZMoVRo0bRokULXn755YBdjIJCceTYMZEpU6L4\n9Vdvvk1cnJPatQN/JNK0qZsffjBiswk0bepSenwWkKQkgccf1/s4aV27OnnjDSt9+2btzZUXe1eu\nLFG5spP773dy4YKIxQJRURKxsVnz3BITVbzzjtzctUkTFzNmWGjd2h3U0hUFpU4dD3XqBOfxoUJ4\ncv/9Tnr1crBpkywqbTYLXLsmULWqd+N0+bKA2w0VKxY8/zBP23aPx0PPnj1p0qQJoihy/vz5Av9h\nhcJByTOQCVY7HDqkol8/g4+TplZLVKkSuBtPZlsIArRp46ZjR1exyU27SSDGxPbtGs6f95bwjR5t\nZ84cMw0aePj008wVmXDvvU7q1ct79CcyUt7NN2nioVat7IsR2rRxZRzLHDmipm9fA0uXam9bbRqs\n86OwUezgRbGFTHZ2KFtWzjscNUoWm9ZqpQxx8YsXBZYs0dK1awydOsVw8GDBS3rzpKMG4HK52Lx5\nM8uXL2fDhg20a9eORx99lAcffJDo28mfFwGKjppCsHPhgkDfvtEkJvoGtl95xcLkyYqafGaSkgRO\nnlRx+rRIgwYeOnRwBaWkwfDheuLjtVSu7OHtty107OjM0KTzeOD4cZHTp1VERUk0aeIOSLPp+Hg1\nw4dHI/dwlZk40crkyXbKlVOqCxWKN4cOqfjhBw0tWrhp0cJF5cp3PieMRvjrLxWiKFf3Xrok8MIL\nUWzcqM14zaJFJvr3z1vub4F01ADUajV9+vRhxYoV7N27l8uXLzNmzBgqVKjAY489RnJycl7fSqEQ\nUfIMZILRDocPq7I4aZMnWxk1yhFQJy0YbZETdjskJKjo2TOGwYMN/PvfeiZM0HP9esHzQQJhh5df\ntvHDD+nEx6fTr5/TRzhYFKFxYw99+zq57z5XQJw0gLg4F/PmWRAE7/svWKBj5sxI0tOz/51QGhOB\nRLGDl3C1xblzIrNn6xg5Mpru3WPYvl2N3Z7z63Ozg8EArVq5adHCjdEIH3yg83HSAJ9ilzslz45a\nWloaX3zxBZ07d6ZTp060a9eOn3/+mT///JPo6Gh69uxZ4ItRUChOuN1eZ6NMGTlpfOpUm197f4Yy\nZjOsXq2lf38DFy96l6r77nPcUq0aPDRt6uaee9xUqlR016fXw+DBDpYuNRMR4b2OhQsjs+iOKSgU\nNxo0cGdoRV68KDJ4cDRLl2pz3MTklT/+UN/SGQTuuUfOKy0oeTr6HDx4MJs3b6Zjx46MGjWK/v37\no9PpMn7u8XiIiYnBZDIV+IL8hXL0qRDsXLki8NdfIqIoC80WJAQfjvz4o4aRI33TKqKiJLZsSadR\nIyV5HORq4cuXBUwmAY0GDAaJEiUkypeXEEX5mOeJJ6IyRHNLlfKwfXu60ltSoVizapWG8eN915bX\nX7cwdqydmJg7e88334xk7lyvX1S1qpuxY+2sWKElPt6Yp/fN6egzTwcs7dq1Y/78+cTGxmb7c1EU\nSUlJyctbhSwOB5w/L6LTSX6p4lBQKFdOoly54iOHkR/OnhWZOtU3Wz4mxsOKFaag6+VYFFitsiP7\n6qtRPlptIDtjI0bYefBBJ02auFm71sSvv6p5//1IEhNV3LghKI6aQrGme3cnL7xgZcYMr2M1fXoU\n1ap5GDTozrQkM7eda9bMydChTqZP1+FyyR0zYmLufN3KU0zu+eefz9FJu4ler7/jiwh20tNhwYII\nOnSI4YEHDLfVPgomAplnkJgosn27mvh4dUB1v/xBdnZIShL44w+Rc+eEgIoVBhuhkHty4YLAtWve\nMXX33U42bjTSvr3bbyKhoWCHnDAaBWbMiMzipAGkporMn6/j/vsN7NmjplIliX79nPzwg5Fffkmj\nQYOsN4xQtoU/UezgJZxtUbIkPPGEjWnTLIB30/LMM1GcPOk7p/Jqh1GjHCxcaGLdOiOjRzt44w25\nI4nHI2Tbnzc/KHVleeDAATXTp8u7+7NnVSxbFsFbbxXQ8iGMywU7d6oZN06f0SeyTBkP339vpEmT\n0Ih2HDigYtiwaK5fF4mOlhg0yM64cQ6aNPGfI6Bw51Sr5uG998yYzQKtW7tp0MCtVCxmonx5iWXL\nzMycGcn69VokKeugdbshLc37fMmSULKkYkMFBZDnw2OP2alTx82kSXquX5f7Hh8/rqJu3fzfxzLr\n+V25ovHJQS4oeZbnCDX8laPmcsGjj8ol9zdp1crFjz8aiYjI5RfDmN9+U9GzpwGXy3cgfvaZicGD\nQ6MF0dq1GsaO9c1R0Okkli410aWLy6fZtYJCsGK1yo3fk5NFLl0SuXpVxGqFxo3d1KjhoXFjtyJi\nHMZcuiSg10sYsmopK+SDs2dFfv1Vxc8/q3n0UQetWxcsJeXUKZGuXWMwGgXKlvXw88/pxMbe3tUq\nUI5acSY9Hf7801ewSa+XglLDqbA4ckSVxUkDQqpasVEjNyVKeEhL83pkVqvAiBHRbNlipFkzJXcs\n1ElJEUhKEtFoJCpUkPK0UIYaOp3cRqlZs9CIZGfGbJZvkJIEMTGSj6p7sJKWJvftzFRLV2QcOSIy\naJCBWrXcvPGGlRYtFKf8Tqle3UP16h4efNA/gYbatT3MmWPmscf0TJ5sK7AUjxI3uA06nXysl5mH\nHgqszpU/CUSeQXYO2YQJVpo1C95Er1vtUK+eh+++M1G+vO9363AI/PlneE+LcM49ucmpUyLDhsk6\nSV26lOD++2PYvFmNxeJ9TXGwQ14pbFtYrfDOOzri4mLo2LEEnTrF8N57kRw7JuIJoM9pscDRoyJb\nt6rZulXNvn0qzp3zbjpvZ4e9e9U89FA0CQmqAucdFZTr1wWuXhXZv19D794G1qzR5qoHll+U+SFz\np3bo3dvJjh3pPPSQvcDpNOF9R/IDOh1MnOgd/Y0bu4iLC43jvUDRoYOThQtN3Hefg5EjbaxaZeTZ\nZ22ULl3UV5Y/WrRws3FjOu+8Y/mnlY9E3bouGjZUommhzokTIocPe3dTFy6IPPxwNBs2KDpid4rR\nKNv10CGRAwdUHD6s4swZ0afaLa8IghyZv9k9IS1NZOZMHfffH8PatRocDv9eO8gR1tde09GpUwxD\nhxoYOtRAr14xdO0aw5o1mjzpaJUtK7Frl5p+/QzMmxfJpUveO7DRCOfPCz6bgUBSubJEZOTNTbPA\n5MlR7NwZIhGEYoBGA02aeChTJvufW63w668q/vvf2xfjKTlqecBkgv371aSlCbRs6aZ69dA7ZggE\nkkTYJN6npkJ6uoheL4XUEa5C9hw4oKJ7d0OWJPsKFTzs2JEesK4A4Uh6OuzYoWHOnAgOHlSTuTVV\nVJTEoEEOHnvMnu90gQMHVPTvb8Bi8f2OBEHi229NdO7s3wj9zp1qBg7MOZnru++Mt/2bRiM8/XQU\n69bJCcr33utk7lwzbjc895yePXvUdOzoZPp0K/XrB/Y+4XLBtGk6Pv7Ye95pMEhs3pyuSNiEAFu2\nyNFZEChVShY81+n+V7AWUsWZ6Gjo2tXFwIHOsHLSnE7Yu1fFlCk63norkrNn8zccwsVJAyhVSs5T\nUJy08KBJEzfz55sRRd/vU6ORwmrcFgb796sZPTqagwc1ZHbSACwWgeXLI+jfPzrf60erVm6+/95I\ngwa+zpEkCXz6acQdRepyo25dN23bZn8aIgiSTxeHnDAY4NlnbRmv3blTw5Qpek6dUrFtmwabTeCn\nn7QMHGjg9OnA3l7Vahg3zk7Vql5DGY0C69Zpc/kthWDhyy8juDmfUlNFhg/PeROhOGphTm7n64cO\nqejb18DSpZF8+KGOl17SEUTNJfyKkm/hJdxt4XaDSgWDBzuJjzfy739b6dzZwZgxNlasMFG+vHyT\nDXc75IfcbFG7tpvOnXNO99BqJV5+2ZollzcvtGnj5vvvTaxcaaR/fwcNGrhp3tzJk0/a/V6wVamS\nxOLFZpYsMTF0qJ2mTeU0hzFjbPz4o5FWrdx5GhONGnmYNct7vrl9u4ZPP41g9GhvisylSyK//BL4\nY8gaNeRITGYx1cWLI0hJCc5euKFIoOxQqZLvfDGZcv7OlAPtYorDAR98EInH4x0cmzdrSEkRiI5W\nokrFHatV1uAKpUrJkydF9u9X8+23GiIi5MhH69ZuWrVy4/FQaJIrHo98XGi1CjidAnJ2iSyjUKZM\n6EX0ataUWLTIRGKiisREEaNRwGoVMBgkypTxULu2hxo1PHdcYFWhgkS3bi66dHFhschOdqD002Nj\nJfr2ddK3rxOLRXbq9fr8jQ1RhD59HPz5p8jHH8vln1u3ahk+3M599zn573/lPMhdu9Q8/HAAku1u\n4a67PKxbZ2TyZD2HD6uxWIpGwLsw51g4MGiQ45/eoLdfEJQctWLKlSsCXbrE3NIwVmLfvvQ7EvtT\nCB8SEwXeekvHrl0aVq82cdddwV1c4fHIN8XRo/U+ciutW7tYv95YKJIFN27A33+rOHFCxfr1Gs6e\nVZGSImA0ysrkgiBRpYqHli3dDBjgoF07V0g5wQpZuXRJ4Nlno9i0yXvU+MILVpYvjyA5WWTGDDOP\nPx54R+0mKSkCf/6pIjJSolUrd6EqE5jNMGdOJF26OOnQIbjXi2DBbIYlSyJ49VUdsrMmsXXrNkVH\nLSdsNvjf/1Skpoo0auTOUBcOZ/R6ierV3T6O2r33uoiNDY/PfnNnXlxFie+UpCSB0aOj+eMPeWn4\n9VdV0DtqN7tMOBy+O9M2bVyF8v2fPi3y4otRbN2ac0WpJAkkJalISlKxbp2GtWuNxMYGt10Vcic2\nVuK99yzYbALbt8vf/dy5kbz1loXff1fRo0fhqgNUqCBRoYJvKC0pSWDrVg1RURAX56Ry5cBsDv7+\nW2TWrEgWLoxg61YjNWuGx30kkOj1MHasndatXSQmirn2EFcClcCJEyoGDDAwenQ0PXoYOHAgfNRs\nczpfj4qCV1+1ZpR3lyvn4f/+zxIWCte//aZi0KBohg6NZu9eFR6Pkm+RmdxssXWrJsNJCwUcDpg1\nKzKLk1a9upvRo3PXL/LXmJAk0Os9WQoXbqV8eQ9PPGFj40YjbdsGl5OmzA+Z/NqhalWJ2bMtGTl8\nVqvA3r1qpk+3Fnnje7MZ3nxTx7PP6pkwQc+0abo8SZDcJD+2kPvyCqSmivz6q3/XDzmlQcWVK0WT\nMxDIuREZCW3buhk2zEmnTjmfV4fOihxArl0TMsr4U1NFhgyJZvNmI/XqhfeuoH17N1u2pHPtmki1\nap6w2AWdPSsydKjcwxPkirWffjIW8VWFBufPC7zzjq/kepUqwT0m3G4wm30X8K5dnbz9tqXQjvBr\n1/Ywf76Fl1+2cfWqwPXr8nGnKMqJ9lFREtHR4dsdIRRITZUd6kBoPVar5mHBAjPLl0fwzjuRrFmj\nZfx4Oy1bFq0znpws8v333mPZNWu0PP64nTZt/H9dmbXj5s+PoEcPBzExBX/fs2dFBgwwcPGiSPv2\nTj7+2EzNmsVvDimOGnI0CeSEX4AbN0TWr9fy3HO2Ir0ufxAXF5fjzwSBf5qoB/fNOD9cuCBkOGkA\ndrvApk0ann8+ZzsUN3IaE6dPq/7ZGcsYDFKRb1ZOnRKYNy+SlBSRsWPtdOzo8sk50+ngww8tGbv4\n2rXd1K/vpmTJ2793bnMjv+j1ULeuh7p1/faWhYo/bRFsHDqk4l//kqsTJk2ycf/9zhyPme7UDrGx\nEk89ZePuu53Mnx9JWlrRV4wYjQK+ieoC586JeXbU8mOLzBW6x46puHpV9KlEvVMSE0UuXpTXpF9+\n0fDyy1F8/LG5UMXVg2FuhP3Rp7zjzv01NWp4uO8+37DjokURXL5c9JNNIX9kV3V07Fj4HGUHklvn\nyRtvWIo0yipJ8NlnkSxdGkl8vJZhw+TOAreWP9Wr5+Hhh6qFOmUAACAASURBVB08/LCDdu3y5qQp\nFB+OHFHx99/yv8mT9YwZo+fMGf+v7ZGRcPfdbhYvNtO2bdG30ytRQkKt9p0sgao4Nhi8f8ftFvwi\nDwKy7mFm4uO1HDlS/OJLYe2onTghMmVKFA88YGDWrEhOnMj+4xoM8k0p82C7fFnAbg99R6245Z5U\nr+6hdm3fRbJlS1exs0Nu5Ja3eJM+fez07Fm0rdIsFrm3oheBp5/Wc/Kkf5atcBgTFy4IfP+9hmXL\ntOzbp8pXDlJmwsEWOVGhgu9mY/9+DS+9FEVqatbX3s4OZ86IxMermTs3gtWrNSQnZ71HaLWBkxfJ\nD9WrexgzJnPzTylfqQz5GROlSvk6VP6KKMbGSuh0vu/9+++Fu/EOhrkR1o7aq6/q+OqrCP74Q807\n7+jo08eQY8PtJk08rF1rzLjJP/yw/Z8jUYVQIjZW4tNPLRnimw0auOjVq3j3Zs0rjRu7ef11CwsW\nmJgxw0qlSkWbC6LXk6UtkdUqkJQU1stWvjhwQM24cdFMnqynV68Yxo/X8/ffin0yc9ddblq18l0D\n4uO1/P573iMzTids26ame3cDw4cbePPNKJ54Ipo9e4I3uqPRwIQJdnr1cqDRSEyfbqVRo8DkzZUp\nI3H33U5eecXKCy9Ycfppya1Z08Ozz1p9nvvrr7w5anv3qnjySZ3fNnZFSVjrqD32WGfOnPH9UocM\nsTN/vgVNDpX0KSkCV66IVKjgoVy5sDRNseDcOYHLl0UqVvQErCRdIbCkpcHatVqeeSbKp2fnihVG\nuncv+qOlYCA+Xp2l9Uzt2i5WrzZRo4Yy7m9y7JjIgw8aSEnx3rRfftma5zzkn35SM3x4tI9AOMCS\nJSb69g3ujaDFAlevyve0QMnVeDywfLmWqVOj0Ghg5kwLw4c7crzP5oeLFwUmT9ZnyN988omJoUNz\nt/n16wLduhlITFTRpYuThQtNIZES8dtvvxW/Xp8jR9qzPLd/v5r09JzDshUqSDRp4lactBCnWjWJ\n1q3dipMWwpjNAsuWaXn9da+MTK1actsfBZnGjd1ZemWeOqVm/vxIHIWntRr0NGokq/ePGGFHEOSx\n1Lhx3pz9c+cExo/XZ3HSWrRw0aJF8G8YoqLkytRAagqaTPD55xFIkoDDIQsB++uIsmJFiblzzXz9\ntZGFC025yljc5PJlgcRE2b3Zvj20JIeyI6wdtaFDHfTo4bta9enjpGTJ4nPzDobz9WBAsYOXULGF\nxwN//KFm4cIIpk618cEHZr77zkTVqv6Zv6Fih9yoUkXiiy/MVKzo67wuX56/fo/hYIvbUa+eh/fe\ns5CQkM7PP6fRsWPWG352dkhPl/XBMtO5s5PPPzdRpUrh30tMJllKJ9DkZ0xcvSrw8MMO2rSRbep2\nCyxZEoHbT3uq2FiJnj1dDBzozJPEjSzZ47XRoUN37jQGw9wIbTfzNlSqJDF/voUjR+ycOiUr/7Zs\n6fJ7s18FhXDDbIbdu9XYbAL168vdOgp73pQsKVG/vpsjR9S8+66Or782FrmIaDDSqJGH9etNLF2q\n5bPPIrHbBRo3dvkUh4QrFoucXC5J0LChm1Klcn+9Xg8NG+Yv97haNQ//+Y+J5csjaNDAzQMPOGnW\nzE2ZMkUzFn/9Vc2YMXo+/NBCr17OQmmRlhs3bsC0aTp++EHLiy/auHBBJDlZZPduNWlpgdGuux1R\nUb7fzU8/aRg/3u6Xo9jbcfiwisOHVbhcssZi8+auAgvJh3WOmtLrM3+YTHJV09WrIg6HrI0TFSVR\nrZqS51XcuHRJ4N57Y7hyRSQiQmLSJBsjR9oLPYLw2WdaXnxRT5Mmct5VhQrKOMwJt1sWCE1LE6hU\nyVMsbLVvn4pevQyAwIABdt5+25prK56CIEmBk7fID2vXahg7NhpBkFiyxEyvXs4iDT7I34Gsbmsw\nSDzxhI1Zs3TUqOFm69b0InHULlwQiIuL4cYNORJas6abn34K/LUcPKiib18DFot3oIwbZ+OFF2yU\nLXv7cZlTjlpYR9QU8s4ff4i8/HIUu3er8RVJhNKlPTz/vJUhQxxFMukUCp9y5SRGjrTzwQc67HaB\nWbN0bNmi4ZNPzDRoUHjV0H37Oild2kSLFu5i4XgUBJUKatUqXpXq58/LrYsA1q6NoEwZiTfftAZE\nHiMYnDSQ12OQ+8eOG6fnp5+MWaqjC5O///Z6iUajkNEM/vHH7UV2vyhfXuKee1xs2CB3ZnC5+CfH\nMLBryB9/qHycNICFCyPp1s1ZoAKosM5RU8jb+brFAs8+q2f3bg23OmkA16+LvPSSnt9+C12/Phjy\nDIKFvNhCpZIlasqX9974Dx9W8+CD0Rw5UnjLRsWKEoMHO6ld2/8OiDImvISqLW7NN164MIKjR0M7\nH+l2VKzoFbJ1OgVmz47AGIAueXm1xY0bvveMqlXdrFhhZMiQoqtmUatlR/EmrVvf+VF1fsZE1arZ\nr1OXLhVszVQcNQWiomDGDEuOVVAqlcSoUTal2q6YUbOmxNdfmyhZ0rv4XLyoYtgwA2fOKEtHIEhJ\nEdi7V8W6dRo++iiCV16J5M03I3n77Ug+/1zLt99q+OknNcePi6SlFfXVFj01aniIjs58AxbYty90\nN5R5oUYND6NGeZ2QdesiOH686M4+b1Zk30Sng+7dXXk66gskzZu7GDfOBsinA4GKiJrNZKyHLVu6\neO01C5kjd2XKeGjdumDVwUqOmkIG169DYqKKy5cFbDa5qbROJ1G9uofq1T1FnrSqUDQcPizy6KPR\nJCV5bwbPPWfl3/+2ZRxzKBSc06cFHn00muPH82JUicaN3TzzjI1OnZyUKRPwywtaFi3S8uyz3rPO\nbt0crFx5m76BIc6BAyq6dZNz8wCGD7fz4YeWgEpw5MT69RpGj47OeBxMOoc3bsDZsyrq1XOj0/n/\n/a9fh1mzdCxbFsGGDfIRtM0mty1MShJRqSTq1/dQt27eTgSKpY6aQv4oXRpatXLTq5dcBt2/v3yu\nXr++4qQVZ5o1k7t2DB5s5+ZOcd68SC5eDJKknTChbFmJl1+2Ua+ei9vn0ggcParm6af1nD1bvMvY\n+/VzMH68V70+r03HQ5lGjdyMG+eNqq1apSU52T+388uXBf7+W8zz/G7QwJ0RVYuMlAKSpnCnlCwp\nd6YIhJMGsG+fhk8+icRsFtixQ95gRUZCy5Zu+vd30qePK89OWm4oEbUwJyEhgbi4OK5fh6QkuaKz\nalUP9eoFz2QqDG7aQeHObWE2w4kTKnbtUuNywSOPOEI6wT9Yx0Rqqpwkn5QkcuWKyIUL8v/tdgGH\nA6KjJVq3dlG5sodatfwzl4PVFnklLQ0OHVJz9apAy5Zuata8M5tktsPZswK//aamcmUPzZq5g26z\n+uefIr16GUhLkx20H39M5+6779xJNRph40YNb70VRXKySIkS23jllXYMGODM9RjT44E1azQ8+aSe\nuXPNDBvmRAyjEFBOc+P6dXjggZiMllZdu8qR3IJU4CpVn8UUSZLF/l56Sce+fbKITO3abjZvNhaZ\nDpBCaKLXyzvFli3DP2JRlJQqBaVKeWjatHhtpvLL6dMiRqNAvXpuSpSAe+/173Hb/v1qnngiGpB4\n/XUro0bZb6vTVpg0aODhm29MDBpkwGYTMBoLFuE+dEjFhAneI8y0NJF//1tPTIyZoUNzLgwQRRg4\n0EmbNmlUqiSFvJNmMkFqqly9mpu4bkqKyF9/eT9sIOVbQtykCrnhcIDF0plevQwZThrI2mgaTeCd\ntKNHRa5dC47jsVCOFvgbxRYyih28hKItTp0S6drVwMcfR/ptnclsB6/MgsD06VFs3aoh2M6f2rVz\ns369kd69HVSpUjDHPnMOqkxnALZsub1KrEYjFx8VRY6cPzlxQmTEiGhatixBx44xzJ8fQZ06HbN9\n7ZUrvt0PmjRxB8xJVRy1MObQIRUPPxyN3e67iL3+upWYmMD+7dRUGDkymqeeiuLCheBw1hSKnsRE\nkf375YIVBYWCULashCQJvPOOjpkzI/+5cfqPSpV8HZ+pU/U+EZRgQBBk6YkvvzTTuHHBHLVmzVzo\n9bd6ohLDh2ftmR2OWCzw4otR7Nqlwe0WuH5d5I03opg5MxJzNrUpJpPveGvVKnAnDcE16hT8htEI\n06frkKSdmZ6VmD7dktGPLZBYLAKXL4vEx2tZujQCmy3gfzJXQkEfqbAoCluYzfDDDxruu89Az54x\nbNtWCL1cboMyJryEoi1q1nTTpo0TgM8/j+STTyKwWAr2npnt0LCh28dZs1gENm0q+nGbHf5ojdSk\niYcNG4xMmWKlVSsXXbv+xLp1Ru6+OzgqOAON05m93tnixXu5eDHr85kLFNRqiVq1FEetyDh1SiA+\nXs2OHWpOnxaDLvSdEyaTwLFj3lB2qVIevv7axJgx9oBH00BOeK5cWV7k3n8/skBNcRVCG7cbNm/W\nMGqUPqOli6wor6Bw55QsCU8/7Y32zJ4dya5d/ku7rlJF4v33fT2/deu0BXYGg5lmzdy8/rqNH380\nMnmyjY4dA1cxGWyUKAFPPpk1oqDTZe8Ix8Z6EEXZIXj+eVtAO7YoVZ+5kJgo0qOHgatX5ZtKVJTE\nG29YGDgw9yqYYMDthv37VRw5oqJaNQ916ngKvWx6/PgoVq2SkxZ69HDwxRfmgLR2UcgZi0VOci1K\nu//+u0j37jE4nd6jgm++MdKjR/HYqSsEjpQUgYceiub332UHzWCQ2LIlnfr1/bPWGY3w7rs6PvlE\nLvmsVMnD9u3plCsX3Ou/wp1x44bcwP2NN6K4dEmkalU3CxaYuftud5ZCAYcDfvxRQ2KiiuHD7VSq\nVPAxkVPVp+Ko5cLRoyIdO8Zwa1ulCROsvPCCrVAiU6HMhg0aHn30ZhWRxNatRqVisBBJSFDz+us6\nQOK55+zExTkLfcyaTDB6dLTPUWeVKm5+/NFItWphufQoFDK//qqiZ0/DP70cYdgwOzNnWjAY/PP+\nqakQH6/hgw90jB1rZ/z4wKncKwQHKSkCVquAXi8VqlOuCN7eAdWqeejXL2tZ8n/+o+PIkdA4yivK\n3JP69d1otTcHucDOnUWnBhOKOTgFITlZbth86JCaQ4c0PPJINGvWaHG5vLZITYWrVwN7xzl/XmT7\ndu/3LggSH39sDgonrbiNidwIZVs0a+bmlVe8grcrV0Zw4MCdrTXZ2aFUKXjoISdbtqQzenTxcdJC\neUwUlAoVJGrU8FCunBQUdlActVwwGOD//s9Kt27OLD9LSysms7UAVK/u4dFHvTkkn32mqNkXFiaT\nwJUrvtP75ZejSEyUnzt+XKR/fwNduxpYulRLaqr3dVeuCBw4oMp4bUFISxOQpJvfucRHH1lo316J\nqir4D60WHn7Ywd13e9fp2bMjMZn8+3dKlaLY5GspBBfK0WceuHZN4LffVKxfr+XIERU9ejh55BE7\nVaqEpen8yq+/quje3duTLj4+vVi0eClqUlOhb18Dx475Rha+/dZIly4u3norkg8/9N51nn3WytSp\nNpKTRcaM0XPsmJoSJTwsXmwukJDo+fMCkybpEUWJ556z0aJF8Cm8K4QHJ06IPPhgNBcuqFBSLRRC\nkWJ59JmcLPilSrNMGYlu3VzMnWth40YjL75oU5y0PFK/vpsHH/QeH1+/rkTUCoNSpeC99ywZVUky\nEiVLyo9v3PD9Hj74IJK//xZZuDAiw7lLSxP517/0BdLBq1JF4quvTHz9tZkOHRQnTSFw1K/vYc0a\nEzVquAAho7WPgkKoE9aO2j33xLBypcZvGl6CEHqh71vP1yVJjnIcOya3vwh0qbnBAC+8YKN0abkK\nq6BtTu6UYMgzKGzatXOzYYORuDgntWu7+eADC/XquUlISKBLl1ujZALJySI//KClalU3L7xgpUYN\nd0avyYIQFUVQKpYXxzGRE+FiiwYNPKxebWbCBNsddV8JFzv4A8UWMsFgh7B21NLTRZ58Us/hw8rO\nCuQI49y5EXTsGENcXAk6dIjhrbf8r+h9K3XqeFi2zESpUh5KlFAikYWFRiM7aytXmtiyJZ0xYxwZ\nMh0tWrho3NjXWTMaBSpVcjFpkp158yJ5/HE7FSq4s1ErV1AIXmrX9jB9upWePbPmFisohCJhnaN2\n//3yWe/SpSb69Cnek/bSJYHHH9eze3dW5b6NG9MLJcH79GmRmBgp6DXoigunTolMmRLF7t0atFqJ\njRvTsVoF5s2LZMsWLSVLenjnHQv9+ztDLpKsoKCgEGrklKNWdHoJhUREhESNGkpC6Z9/qrJ10vR6\niTJlCsdxqlUrfyKUTiccOaLizBmRkiUlGjRwU7Gi4uT5i9q1PSxZYuLcORGdDurW9ZCUJLB/v7ws\n3LghEhUVesf9CgoK/sHlkqvA7XYBlUqiYkUJddh7DcFHWB99Nmrk4rvvjAVuVhvK3Dxfj4qSbkks\nh5Il5bZSdesGp3127FDTvbuBceOiefBBAw8+GM3ff99+yJ4/L5CU5FtIEgx5BsFCZluULg3Nm3uo\nX9+DKILHI2S0eQLZwQ9Xgn1MOBxw/bqslu4J8BQNdlsUFoodZFJTYfbsvTz8sJ64uBhatozhnntK\nMHFiFMePh7XbkIVgGBNh7RuvX2+kdOmivQa7Xa50FEUoXVryS/PcO6FFCzmxfMMGDS6XQLNmblq1\ncgWtkwawcGEEbrc3f+7PP9VMn67jk0/MREVl/zvHjokMHGjAZhP46CMzvXs70WoL6YLDALUaRFHK\nUHk/cCB8HbVgweWCixcFLl0SuXxZ4PJlkaNHVfzxh5qrVwU0Gnj1VWuxT99QKByMRnjrLR2LFkUB\n3sXTZII1ayJITBRZu9bkt7Z0Fy4IuN0QG1t098dgp9ActbFjx7JhwwbKly/PH3/8AcCbb77JF198\nQbly5QB455136NWrFwDvvvsuX375JSqVirlz59K9e3cADhw4wOjRo7HZbDzwwAPMmTMnx79ZlE7a\n1asCP/+sZtGiCI4dUyGK0Lati0cecdC+vZNSpfzzd65fh6NHVZhMAg0beqhRw9fxiouLA7yJ5e3a\nhc4x8M2m7pnZulXD9esCUVHZH4H++KM2Q+j18cf1bNpkpE0bd4YdFMjVFhERErGxUoYkR2qqiMNB\nWDq7RTUm3G755pSUJHLqlIqNGzXs2aPJtiK6Zk0Xb7xh4557AuukKfNDRrGD3E1k0aIIoHO2Px8+\n3JHjRjk/OJ3w009qJk3S43AIPPGEjX/9y0758sGV3hIMY6LQYphjxoxh8+bNPs8JgsAzzzzDwYMH\nOXjwYIaTduzYMVauXMmxY8fYvHkzEydO5GbNw4QJE1i4cCEnT57k5MmTWd4zWFi9Wstjj0Wze7eG\n1FSRa9dENm3SMmJENCtWRPjlKOP0aYGJE/X07x/DiBEG3nxTh91++98LFcaOtVOihK+hmjZ1YTDk\nPJFPn/YOaY9HYO7cyLCySaApU0aifn3fatBAH7sVB8xmOHJEZN06DePHRxEXV4I+fWKYPFlPfLzW\nx0nTaCQeftjO2rVGNm0y0atX4fdoVSi+VKvm4ZNPzJQt6534KpVE8+ZOVq82Mniwwy9ttI4dUzFq\nVDSpqSJms8CHH+rYskUJqWVHoTlqHTt2pFQ2YaTsik7XrVvH8OHD0Wg01KhRgzp16rBv3z4uXryI\n0Wikbdu2AIwcOZK1a9cG/NrvhOTknE37009qnAXcIKekCDz9tJ4tW7yhjt271aSm+s6gYDhfv1Ma\nN/bw449GJkyw0aSJi0cftTF/voUSJXL+nVsLFv77Xw1XrgghbQd/k5stVCp45BGvQHHXrs6wFakt\njDFx9qxIfLya0aP13HtvDGPGRPPttxFZomd6vcSAAQ6+/NLEzz+nM3u2hU6dXIUWXVDmh4xiB9Dr\nYehQJ++/v5Ft29LYvj2NffvSWbfOxH33ufy2aTh/XvBJbQE53SXQ2p75JRjGRJHnqM2bN4+lS5fS\nunVrPvjgA0qWLMmFCxdo3759xmuqVKlCcnIyGo2GKlWqZDxfuXJlkpOTi+Kyb8u4cXZu3BBYuVLr\nMxhbtHDy9tvWAguAHj6sYs8e391HXJyTUqWCK2xcUBo39vD221bMZrn6ULzN1uKee3yjQTabnAOk\nkHdatXIRG+vh0iWBu+9WjHcnnDolsGGDltmzI0lLyzpotVqJVq1cDBjgpGFDF9WqeahUSamoCyXS\n0sh10xjqlCkj0bx54MLp2eW4GQxKnlp2FOmyMGHCBF5//XUAXnvtNZ599lkWLlzot/d/8sknqVat\nGgAxMTE0bdo047z5ppccqMfJyT8zcCBMntyJS5cEfv89gZgYiT597qZ06YK///Lle5ETPTv/82m3\nc889FiIi7i6Uz1fYjw8ezNvrmzeP49FH7SxbtheAu+6Ko2RJifPn5dcEy+cpysdxcXG5/rxaNYlX\nXtlESopAq1Ydivx6A/n4Jv58/yNHRPr1O/BP9ey9VKjgoUyZbdSu7aFXr3uoWtXNhQu7KFPGQ9eu\n3t8/d67o7HHzuaL+PkLl8Vdf7eH993U8+mh7Roxw8Pffu4Lq+nJ7fPq0yOLFe0lPh/HjO9CggadQ\n58fNxyaTQLt2Pdi3TwPsACQmTGiDRhNc9rrdelmQxwC7d+/m3LlzAIwbN47sKFTB2zNnztC3b9+M\nYoKcfvbee+8B8OKLLwLQs2dPpk2bRvXq1enSpQvHjx8H4JtvvmHnzp188sknWd7Pn03Zg5E5cyKY\nNk3O6FSrJebPNzNggFLhCHKi9ubNGhISNDz7rLVYy7MoFD7XrkFamqw9FRkpH2uWLCkpczOMWL9e\nw+jR0QAMHGjn7betxMYG/2nG4cMiw4dHc/GiXM3du7eDL74wF1mLt7NnRXbsUHP0qIrevZ20bu3y\nWzVpKBKUTdkvXryY8f/vv/+epk2bAtCvXz9WrFiBw+EgMTGRkydP0rZtW2JjY4mJiWHfvn1IksSy\nZcsYMGBAUV1+kdKnj5PXXrPw/PNW4uONDBqUvZMWDOfrhU2lShJjxzr48ktzhpNWHO2QE4otZAJl\nhzJloFYtiYYNPdSs6aF8+eB30pQxIZNXO0RGep2y77+P4Kefgv+87uxZkREjvE4awJkzYo6pIYUx\nJqpX9zBqlIOZM63ce29wOmnBMDfUhfWHhg8fzs6dO7l69SpVq1Zl2rRp7Nixg0OHDiEIAjVr1uTT\nTz8FoFGjRgwdOpRGjRqhVqtZsGABwj9lJgsWLGD06NFYrVYeeOABevbsWVgfIaioXdvD1KlKOaOC\ngoJCYVOhggeQAPm+9MorUXTo4KJOnbxF710uCj0f8ddfVSQn++oiDh7sCErnSMGXsO71Gc5HnwoK\nCgoKRYPZDP/6l55Nm7yh0rlzzT4V09mRmgpr1mj57rsIunZ10ru3g4YNPbeVu/jrL5Hjx1WUKCFR\no4aH6tVv/zu3Mn58FKtWec84S5TwsHmzkfr1QzM1RJLgxAkRUYSaNT1hUYQQlEefCgoKCoHir79E\nfvhBU+xa3vgToxG2blWzb58Ks7moryZ40Oth6lQbguCNc6xYocWRu5/GmTMqXnhBz759at59V8f9\n98fw3/+qb6tVuGWLhjFjohk0yEDHjjEsWaLl0qX8eWr163vFzsuW9bBqlSlknTSQ5ai6dImhY8cY\n1qzR3Nb2oYyygoU5wXC+HgwodvAS7rbweOQ+sT16GBg1Kpq5cyPJ7twg3O2QH3KyxblzIkOHGujV\ny8D770dmdKwIV/IzJpo0cTNlii3j8ZkzKtLScrdPRITk49zZbAKPPBLNH3/k3qqtRQsX8lErmM0C\nzzyj57HH9Jw8mfdb+KBBThYsMPGf/5jZsEHu2JIbwTw/0tLgpZd02O0CTqesKXriRGDcmWCwg+Ko\nKSgohBWHDql46KHoDP0ys1nwi5J6cUSl4h/HQmDuXB0zZui4caOoryo4iIyE8ePtPP20FYDatd3o\n9blnEtWo4eFf/7JSq5ab2Fg5muVwCMyfH5Gr3mPz5m6eesrm89yePRr69TPw1195u41Xr+7hoYec\nDBvmCOoez3khPV3gr7+8zq3bLfC//xVy0l8honrzzTffLOqLCASJiYlUrFixqC+jyLmpI1fcUezg\nJZxtkZIiMGqUnpQU7yI+fryN5s2zRg/C0Q6HDqn46ScN588LOBxyBCcvnSVyskVEhMS2beoMex4+\nrKZxYzeNGoX2jT4n8jsm9Hpo3dpF795Oevd2UvH/2Tvz8KbK7I9/7s3SpG0KlJ2yVHbZFFSQRQRZ\nRVFGkcGNRXFBRUfHfUTF0RFXREdAHR0RleWnqOCKooCogIDIToGylrULTZo0672/P95J03ShhTbJ\nTXs/z5MHkt40tyfvfe/3Pee85zQ9vVAzmaBuXdFDt39/P16vRFaWjN8vMXasp9zvymyGjh0DGAwq\n69aFkrGcTonDh2UGDar+DiJavj6cTol58xLweEIrsHPOURg8uPoLdEfTDkePHqV169alXtc9ajo6\nOmfEsWMSv/1m0GQYbN06Izt3hlbWFotKr161p7uC1wv335/IzTfb6N8/hSuusLFwoZn9+89uqrfZ\n4MEHw3eX//3vSZX24tQGkpOhR49ApfK9tm6VueYaG/PmJTB9uoWrrvKSnKxyzz3uCrscNG2q8uCD\nbj78sIB69UKf9e23ZjIzTx86rWk0aqQyZkx4UlqrVjVz8QC6UIsqp07BV1+Z2Lw5eheVFuLrWkC3\nQ4iq2GLHDlEw84orUti5U1s3h0AAFi0KL1g2bZqLjh3LnsBr4pg4//wAH31UgNUqwpXbtxuZPDmJ\nyy6z8c47CeUKttPZondvH5ddFmpO7HBIrF5dM8NMkRwTubnw4IOJFBQEFzgSbdsG+PXXfK6/vnKZ\n8DYbjBjhY9kyB++9V8CoUV7GjvVQp071F2/Q8vVhNMKECR7q1hXXttkcuQWZFuygC7UooSjw+edm\nbr45mZdeshA4fR6njo7m2LxZZuRIG3/+KW7SQgxoQnuw0QAAIABJREFUh1OnpLCk7KFDvYwa5atV\n+WlmMwwd6ufrr+20bRu6cZ06JfPII4kMHWrjk09MHD9eeaOkpsLf/uamQYOQ4F20yKy55tlaZ9cu\nQ1jYEqBBA5Xmzc+8x2ubNgqjRvl4910ns2a5aNOm5nqTyuPccxW+/trBO+8U8NVXDs47LzI31Zwc\niR07ZLZvl2OWn6nXUYsSmzcbGDrUhtcr0bWrn2++cZCYGOuz0tGpHAcOyIwencTeveKO0rixwk8/\n2TXVNsfvh/vvt7JwYQIPPOBm/HhPhTlDNZlDhyS+/dbMM89YcTrDhVm/fj5eftlF+/aVu8E/9JCF\nDh1U5sxJIDPTQJs2AZYts1OvXiTOvGayaJGZO+8MVZdNS1P44Qc7jRvX3jGqVVRVlPdZtszErFkW\njh8XPq3Bg73MmuWiQYPIfGfl1VGrmf5rjaEo8NFHZrxeMVkmJES/KnU84vfD9u0ymzeLOkM9e/rL\nDWPFG3v2yKxfb6RDhwDdu2vTvRoIwJ9/GjhwQOKXX0xFIg1EDSktiTQQ19TUqW7+/ncPaWk1owBm\nVWjRQmXSJA/9+/v47DMzb7xhobBQzEGrV5u44gobH31UQM+eFY+/Sy4JMGlSEnff7cFm85KaqnD0\nqES9etoaA1omLy9cLP/zny5dpGkQj0ekKE2ZklR0vQTZvr3imndnwqFDEtu2GcjKkunYUcFqLfs4\nPfQZBfbvl/noo1BF6Asu8Eet958W4utnQyAAS5eaGDQohXvvTeJvf0vi2mttZGWdXRxLK3Zwu+Gn\nn4wMH27jrruSOHky+nG5ytjC6YTPPjMxcmQyx48beO+90PhNT/czYoQ2q0s2aiQqt1dGpGllTEQS\nSYIOHRQeftjNTz/Zef55Fy1bCmGWkyMzerSNnTvlCm1x/vl+GjRQmTnTwrPPWnjooURuuMFGZmbN\nuoVEcky0bx8SxJMmuRkwwHeao2NPbbg+ymLVKiO33VZcpK0AwGRSmTXLSaNG1SOud+yQufrqZG64\nwcZDDyUxcmRyucfqfp0osH+/jMsVuiFfcom2L1AtsG2bgTvvTCIQCNnt6FGZkycl0tLicxVqt8MH\nHyTw5JNWQKJ+fUWzlcGXLzdx++1JXH658MYEexrKssq//+2ieXNtfAdHjkgUFEiVDuHVVmQZ2rdX\naN/ew7XXejl4UObQIRm7XaqUh6BlS5UPPihg5EgbHo9EIAAHDxr49lsTd92l9xyuDN27+5k/30FC\nApx3np+6dWN9Rjolcbth5kwLqhq+gO7Qwc+rr7ro1at6oh/Z2RL335/I/v3FJVj5i3ZdqEWBP/4I\nmdloVKOa+NmvX7+ofVZ1smWLAZ8vfOCmpirUr392AiHWdigoCIq0UGLiiy+6YrKlvCJbbN0qc9dd\nSYDEBRcEePbZkHvq+ecLK6xoHi02bjQwfnwy55/vZ968M+9vFOsxESsaNFBp0CBAjx7Fv8eKbXHB\nBQEWLCjg+uuTcbvFtTlzpoVrrvFqLgx+tkRyTNStC8OGxU+pmNp4fVgs8PDDbv71L/D5JM49N8A1\n11xA584F1RqmPnBALrWx5HToQi0K/PZbaCfaFVd4SU/XV/8VkZwcflFIksqbbzpp0SL+bgg+Hyxe\nbA4TaX37+ujXT3uTtt0OL75oKfIAi2rpEqDy7LOFjB7t0UTu18aNBq65Jhm7XaZPn/gbE/GIJEH/\n/n6+/NLBM89YWbXKhMdDtebs6OjEmv79/fTsWQCIfPJI7Bo3m1VES7DQLx87tnzPdM1KMNAggQBF\nNz1JUrnrLg8JCRW8qRqJ1zyDCy7wc9ttoiTAgAE+vvjCwYABZy9sYmmHn382cv/9IZGWlhZgxgwX\nDRtGRmCcPCmxZYtMTk7ZPz+dLbZuNfLll6EB2qCBwuWXe/nsswJuucWjiV1+e/eKWm52u5i+Row4\nu1SC09nh0CGJ+fPNmizqGwkqe31Ikiju+v77Bfz4o52vvnLQrFnNEcrxOl9GgtpsC4tFPCQpMnZo\n21ZhzhwnLVsG6NAhwL//7eSppwrLPV73qEUYgwGaNxdLzscec9OtmzbCRlqneXOV554r5P773aSk\nqHFbymTbNpkJE5KLch5sNpUPPnDStm1k3BBbtsjcc08SW7YYmT27gL/+9cxEzM8/h6YEWVbp1s3P\nuHFezexSdjph9uwETp4UIk2W1bAk7erA64XXXrPw3/9aeO45F5Mn6zlYJalblzLbcuno6FSM1Qpj\nxvgYNMiPwaAW5StmZZV9vF5HLQps2mRg2zYDQ4b4qm3HSG0hEBBiNx4pKIAHHkjkk0+EhyoxUeWT\nTxxcfHFkbnBbt8qMGJFSVPl88uRC/vEPd6VFrssFI0bY2LzZiCyrvPNOAVde6ddEqDPIr78auPJK\nG8GQwd13FzJ1qrtad1Hv2iVzySUp+P0SHToE+PZbe4XtfXR0dHSqil5HLYacf35AX32eBRkZMrNm\nJdCvn59rrvEhx1mgfssWA598IhREnToKH39cUCWRpqqirlxWlkznzoGw3a/Hjkncd19SsfY0ULeu\nSmamRJculVscJCSIMgzDhnnp3j3AgQMGHnzQRG6uzPnnB/jLX7y0bh27hKScHIlp08SOWRB9PG+8\n0VvtpW727hVNskGItpMnZerU0ROxtML69Qbmzk1g1CgvPXv6sdlifUY6OpElzm59OmdKvOYZHDwo\nMXFiEh98YGHKlCQOHqzaUI2FHb7+2gRIDBjg45tvHPTuXTWxvmaNgSFDUhg71sbMmRY8xSJyv/5q\nDNtdbLWqGAyi12NJyrPF/v0ynToFmDfPwg032HjssUTmzbPw1VdmnnvOUqpgZ7TZutXA778X34Hq\nqlJ5k/LskJNTfKxJtaLdWzzNExs2GPnoowSuu87Gk09aOXq0+sZlPNkh0ui2EGjBDrpHTUeTfP21\nmR07xPD0eKRSLXDigf79/Qwc6KBbt0CVW44cOiRx++1JRWURPvgggXvucdOypYrdDq++agk7ftIk\nD3PnmrnmGi9w+jw1rxfWrDEyaVIS2dmlBbHJpPLGG046dYqtYvnhh9B01auXj8svj0wfz6NHw20Q\nb57cmk6rVqFxOHeuhYQEePTRQr0umU6NRRdqNZx4rIVz7JjE668XFx4qBkPVhE4s7DBkSPWV39i+\n3UBWVihZz+eDYNmM7GyZnTtDP+vRw4fLBYcOidzIkpS0xfr1otSFopRUPSqDBvl5/PFCzjsvEFPB\ncuKExOLFItevdWs/r7/uqnK+Z3ljwlus6UJioqq55vORIJ7miXbtAlitalHl+LffttCzp0iPqCrx\nZIdIo9tCoAU76GtFHc1x+LDMsWOhodmmjULjxrU7R2j37nDB1aqVQlKSEBBGo0rS/3o9jxjhZexY\nL+++K0SN01lx5fm8PLkoz0uSVM47z8eLLzr58UcHc+cW0L17bEUaiHpuBQUSXbr4+fhjJ+3aRW48\n1KkTEmbp6QFSUmq+UIsnWrdWefFFV9hr99+fxK5d+u1Mp2aij+wajhbi62fKsWPhnp0JE6pevyse\n7VCcks2BJ092F3VpaN5c7CZdssTO6687/5erFqzdV7ogaUlbXH65j99+s7N2bT5//GFnyZICJk3y\ncv75gVI7Rt3uYBHc6NKggcrnnzv4v/8rqLZ2UeWNiY4di/dk9JCSUi0fp2ni6fqQJBg2zBfWb9bh\nkNi0qeoBoniyQ6TRbSHQgh300KeO5ihejsNsVunfX++N2q1bSB21betn+PCQTWSZsLZOw4f7mD9f\neNT69/dXWANNlqlUK6vffzfw1FNWjEYYMMBPt25+zj03EJXeq2YzdO8enRy5Nm0U6tZVCAQkLr5Y\ne90jUNWQ+pblyJRO1zgNGqg895yLAwdktm0TA/zTT02MHu2N23I+OjrloddR09EcGzcaGDLEhqrC\nO+84+ctf4q80R3WTmyvaUDkcEiNH+k5bMDczU2bgwBQcDolFixwMHlw9YmPDBgPDhtnCctkaNlR4\n6KFCLrvMH9PSHdXNn3/KgMR552lwy2cgIMRaEK1UI44Bhw9L/Pe/Cbz+uoWxYz288Ub51d11dLRO\neXXUdKGmozncblEh32qFHj38Z9yVIDtbIiNDJhAQrTqaNq2RQ/y0rFhh5JtvTDz4oLvaWlX5fPDj\nj0YmTgw15Q5St67Cv/7lYtgwnybaTNVIVFU8PJ6QWDOZIteQsIrs2iWzd6+M1QotWyq0bq1E5DS9\nXpHXarGoNaqdlU7tozyhVsv9FDUfLcTXzxSLReyY7NfvzEXazp0y116bzJVXpnD11SncdFMyR45I\ncWmHqjBggJ/nny8sU6SdrS1MJhg61M9XXznCQrEAp07J3HVXMtOmJcZNf8y4GROqKlYvdrtod+Fy\niUdhoXhUA9Vtix07ZIYMSeGmm2xce62NAQNSmDvXzKlT1foxgAiLt26tVItIi5sxEQV0Wwi0YAdd\nqOnUGLKzJe65J5EtW0KhoD/+MJKZWTuHeSTCxZIkcsU++aSA+fMddOkSLtg++CCBV1+14HZX/2fX\nGvx+4SYK7txwucDhgJwcOHYMsrMpMrDXKxqgxmKHx2lwOKSwLhlOp8QDDyTx7rv62NDROVP00KdO\njWHNGgMjRpTeovfNN3Z69dJgrlENIDcXMjIMrF5t4ocfjGRmGmjfPsA77zhrZci5ygQCIsYcCAiB\nJkni/w4H5OcLD1ogILo6JycLd1LdupCUJFyeGslXO3lSYuzY5LBuGQKVFSvsdOtWc/IZdXSqC73X\np06Np6zdXv37+2jfXhdpkSI1FS6+OMDFFwe45x44dUoiJUU945C1TjECAcjLE6FOj0cINq8XTpwQ\ngs3thjp1IC0N6tcHm028R0PbHRs2VHn7bSe33ZZUomyGVKrUjI6OzumpnTGhWsTp4ut2u5j3awpt\n2gQYO9YDqIDKlVd6efVVF/XqaSPPQCtEyhYWCzRpEj8iTTNjIlhuIxjc8HqFq3L/fvj9d/j5Z1i7\nVvx//XrYuxc2b4bdu2HXLjh8WFzMVQiORMIWbdoofPxxAR9+WMCNN3ro39/LnDkFYXXqtIZmxkQM\ncDph1SoDL79sYcMGQ622RXHOxA7798vcc4+VRx+18vvvBpzO6jkH3aNWC8nLg1WrTLz4ohVZVvnn\nPwvx+1UuvDAQ1/3yUlNh+nQXd97pRpLEjSJeRINOLUVVKer6rqoitHnyJGzbJkTY8eMiJ62wkKJM\n/Hr1RJjTbocmTYSHzWIRoVC/X/wes5midhMxpEkTlREjfIwY4UNVNbk5Ved/fPediUmTkgCJN96w\n8MILuh/nTMnKkvj4Y9H+8O23E3jkETe33eYmNbVqv1fPUatlOJ3w2msWXnnFWvTaRRf5qVdPYcgQ\nH7fe6j3Nu3V0dKoVRQkVr/V4RHhz507YulV4zU6cgEOHhGCDkAhLTRWhz/btoVUr6N4d2rUT+WoG\ng1BEVqumwqE62mX3bpnLLkvB6Qwp6U8+cXDZZdrapKJ19uyRufTSlLDw/pQphTzwgJs6dSp+v16e\nQweALVsMvPKKJew1l0ssyGfMsHLypL7k1dGJGkEXk6KIcOexY7B9O2RkQFZWyKsGFLmkfD7x2pYt\n4ud794rjc3JK9wvTiQp+v3BwxiuZmXKYSIPI7Bqv6bRurXDPPeHbmt94w8p335mq9Hv1r6KGUzK+\n/tNPJoJ9IIMMGeLj55+NZGdLeDxRPLkooudbhNBtIdCMHQKBUGjz4EHYsUOItd27w3PPJClU9FZV\nRS7b7t3C63bsmBB2wTCpopyRN00ztogxZ2MHhwPeeSeBG29M5tCh+Fzoulzh5200qhw9uqrC92Vn\nSxw+HJ9/c2U5kzEhyzBunIfevcPbHj7xRGKVxoYu1GoZgRJ5vB06BFBVibw8mbQ0hcTEGhkJ19HR\nJkEPmMslBNemTbBnDxw4QFEmcnGBVhKHQxTBtdshMxOOHhU5a7KsudpqNZV164z84x+J/PKLiT//\njM+073r1wsfWI4+4adr09N7ZHTtkrrkmmX79UvjyS2Ope0ttJS1N5c03nfTtGxJr2dkyBw+evdzS\nhVoNp1+/fmHPr77aR8uWASwWlQkT3Fx9tZc33hANvO+4w1PlpEetUtIOtRndFgJN2CHoGcvMFCJt\n1y6x27N4x4GSAq1kRv7hw+KRny9E2smTQrh5K59vqglbaIAztUNuLkydGsr33bkzPnMCu3QJcOut\nbmw2lSlTCrnhBg8DBpRvC7cbnnvOytatRux2mVtuSWbHjpopJ87m2khPV5k928lrrzlp0kTBZlNJ\nSTl7J0h8yn+ds6Zr1wDff+/A7RYL9mHD6qAoEt26+Rk+XN9IUBG7dsksXmymf38/ffr49V1sOmdP\ncMfnoUPCE5aVJf5vt4fEWNCbVpLirx8/LjYWuFwhL1ogILxqGquvVtM4ckQOE2e5ufE5ITRooPL0\n04X87W9uGjVSMVWQUnXsmMwPP4QO8vsldu0y0KWLniMZpHlzlXHjvAwb5sPvF562s6VmSmCdIsqK\nrzdsqNKihUrHjipffmln0SIHH35YQMuWNTfsWR05OFlZEuPHJ/HSS1bGjElm7974vHz0fCRBzOwQ\nFGhutwh3Hj8O+/aJ/LRgRnrxWhbFVwPlCTeHQ7h3vF7RpD05+YyywfUxIThTOxw/LlM857dt2/iN\n/yUlCTERFGmns4XochYuSk+ejM/5cOdOmQULzGRklH3+Vb02GjdWqyTSQBdqtZ6uXRUGD/bTvHnN\nFWnVxa+/GsnIEE7owkKJrCz98tE5C4LFbX0+kV9WWCiKGwb7eJZ00xYXbcVFmiSFHg5HqP2UzSbq\nrMmyvnUvwuTnh39XLVrUDo9SaqpKmzbhOZDNm8fn3/7JJ2buuiuJq66ysXWrNq8XbZ6VTrWh554I\nqmoHnw8+/TS8gGjxNKJ4Qh8TgpjZoXgHAocjtHMzLy9800DJDQQlw6HFHydPihy1YMVqSRIirZKx\neX1MCM7UDsW/HllW41aslMXpbJGaqvLYY6EyFHXrKpruOHE6gmVJTpyQGTvWxsGD4nkgACdOSPTq\nFftrQ89R09GpBLm5UqkdXVVJDtWpxQRrofn9Qlzl5Ahv2tGjlXt/0MNWXCUEAsJTl5MjnptM4nnQ\n46YTERo2DH0Hd9zhpnXr+BBqigJ//mlg+3YDNptK9+5+WrQ4s/ls8GAfH35YwIYNBkaN8tG2bXz8\n7SXp1CkkMI8ckfn6azMjR3p56y0LixebueEGD5de6qNBA5UOHWLzN+oetRqOnnsiqKodfD6w20M3\nPItFpVmz+BRq+pgQxMQOXq94FBaKh9MpxNqJE+HHlSWwygqBFj/m1CmxGaGgQOS/nUHTGX1MCM7U\nDq1bB2jf3k/79n4mTvSSkBChE6tmVq40Mny4jSlTkpgwIZk77kji2LHw8VaRLVJSYMQIH1Onuuna\nNT69aSB2vIr+0IIFC0y8/34C//63hSNHZF5+eS2//WbiqquS2bUrNpJJF2o6OpWgQQOV884L5WRM\nnuwmLa306srlgt9+M/DTT8aq9MjWqYkEAkKk+f1CTJ08KQSV3R7qPgDhoc2KPGLFjwnu+MzJEe2o\nvF7dmxZhmjdXWbjQyeLFBXHjUcrJkfj73xPx+UJjY80aEzt21M7dwe3bB7jiilDNs0GD/MyZE969\nZ+1aI+npKvv26UJNJwLouSeCqtrBYoGHHnIjSSoXXeRj/HhvqS3s+fnw3nsJXHGFjUceSSzqoa01\nojUmTp2CJUtMLF1qIi8vKh95RkT92ghWBFUUIarM5lC9M4dD/KxkSLN4vlpZFBd1BkPImwZntJFA\nnycEZ2OHVq2UuPKuFxRIHDhQemyU7D4W6TGRny92XG7dKsd0rkxKgr//3Y3BIL5Ds5kS7bQG4PGA\n2axSv35svmddqOnoVJK+ff38/LOdjz920rJl+KzmdsMHHyTw5JOJgETz5gGSkmJznlrht99MTJiQ\nzPjxySxbVrVedzWCYD0zSRL/V1UR8jxxonJes5L/DxL0qCUkhMKqWl0l6MSc1FSlVLP1OnUU0tOj\n4xF0ueDHH41cdZWNPn1S6N+/DnfeWTr0Gk06dw4wZ44TSVI5elSmRYvwUO5FF/lp3z4Qls8WTXSh\nVsPRc08E1WEHsxk6dVLKXFVt3Gjg6adDFcpHj/ZhNpc6TBNEY0y43fDeeyEDPP541XrdVZaMDJnj\nxyv3OVG/NgwGsFqFoEpKEqU4HI7wMCeUrptWUR01VQWjUXjQGjcW7t9gC6lKNmnX5wlBbbCDzQbP\nPuuif38fZrNK165+Fi8uoE2b8LESCVu43bBggZnRo5PZssVIsAbdsmXmSl+3kcBkgpEjfXz6aQEF\nBfDMM4UYjeI6a9lyOe3aBbj/fnfY4jsQgDVrDNx7r5XbbkviP/8xs2WLHJFWWvquTx2dKnLkiMSU\nKYmoqphozObwfLbaSEGBqFQeJC9P5uTJ0ivV6uTIEYmbbkpiyhQPN9+s0S4bBoMQW0ajEGySJO5e\nQQFWXuizLI9b8WPT0qBZM5HhnZIiCt6CEGp6LTWdEnTooPDhhwXk5UnYbGpRVZdIs22bgYceElGH\n4rRr56dJk9iGj81mGDDAT79+Yu5eutTBiRMSublurr7ah9UafnxmpszVV9uKcv0+/dSM0agyc6aL\nq67yVmtERRdqCGWcnS1htaqkpMT6bKoXPfdEEEk7rFhhYt++0KX04INuOnbUbmJxNMaEwaCW2gEX\nTMOKFBkZBvbsMTJzpsSVV3qpV+/0x8fs2lAUsdvT5RKhSo+n7H6eZeWllZer1qyZeLRpI7xqQQ+b\nXkftjKjIDidPSlgsKjZblE4ogiQnQ3Jy+eIoEmPixAmpaEEbpGnTAO++66RxY23k+Rn/N5X36hVc\nVPYp8zizWXjifKF9CPj9EnffnUiTJgoDB1bfYr3WL7WOHZN46SULl16awnXXJbNzZ603iaZwOuHn\nn4189ZWR7dvlojxprZCVJfHkk6GlVuPGCtdc46317RXr1oUOHcK9Z5HegBj04GVmypw4oeHr2O0W\nD5OpbA9aWYYqGRot/r6WLeGcc+D886FFC6hXT4RYjfo6vLooKICPPzYxcGAK11+fzJYtGh5fGqZj\nR4WrrvJgsai0aRNg6lQXS5YUxGWP0JYtFWbNchZtQgghsWpV9V57tXq0+f0iAfzFF62cOCHz++8m\nHn88EZcr1mdWfcR7zsXOnQauvjqZm2+20b9/CjNnWs4q6TRSdjhwQCY3N3gZqcya5dR80ctojAlJ\ngrFjQ+FHi0WNaJsynw+++y44OUqcOFHxGInpteHzCaFlsRDmeqxoU0Hw3+Ih0ebNoWNHSE8XCtls\nFiHWM1gtRNMWLhccPixF1MOamwu7dslnvNu4PDusX2/knnuSOXJE5tdfTYwbl1QqpyojQ+ann4xR\nycWMBpEYE+eco/Dmmy7Wrctn2TI799/vKZUbpzXKs4MkweWX+/jySwd9+/oI1mKrW1fh8st9Zb7n\nbKnVQu3gQZkZM8LrpaxfbyQvr2ZcaFrAbhdey5ycs7Np8XuNoki88IKVRx+1cvSoNr6jAweCJ6jy\n6qsuevWq3blpxenZ08+wYUKs/eMfhaV2ylYnLhccPRoaLG63NsZHmQQ9aS6X+H/xQV5W26iSj+I0\nbSq8aW3big0KJY/RUH5aXp4otDphQhK9etWpdq9DEJ8P3nzTQu/edbjppuRym22fCYsWhe8MOnDA\nyMGD4b934UIz115rY+RIG2vXGiKSVF4TSEoS9ecqSk2IB0wmESKdP7+Adevs/PhjPitW2OnZs3q/\nfO1cxTGgsBA8nvCJr0EDpVTSYDwTi9wTVYUdO2RmzEhg2LAU+vZNYcgQGx9+aD7jVXTbtgGGDQtf\nnSxZksDcuQlnNBFGyg5Wq0q9egrvvefkr3/1kpgYkY+pVqI1Jho1Uvn3v1388IOdceM8EY3Eeb0S\nDkfoWvb7KxZqMcvLMplELM3hEJPQ6TxfJXt6liyCW6cO1K8f2jTg84l/TSYR+tRIjtqBAzKPPZbI\nX/5i44cfzBQWShHbFZ2dLfHf/wov5W+/mbj55qRKFyotzw7Fx1aQkhtq69YVAvvgQQNXXWVj3brq\ny38QKSAGXnzRwqZN0cmr0PMWBZWxQ3IytG2rcP75Ci1bVn/koFYLtXr1VBo1Cr/a/vGPQlJTtZHU\nGI8EAvDNN0YGD07hn/9MZNcuA3l5Mvv3G7j33iT27z+zIZecDE8/XUhaWrgqmznTwt69sR++l1zi\nY+VKO6NGld4VVNPIz4elS01MmpTEE09YWLvWEJZIWxb166v06BGIePJ1IEBY/qKq1bYQqiricn5/\nqD9ncHvYmSTxqaoQY40ahXLRgo3YgztLNUJGhszYsUksWhQK8fbo4adbt8i4nBIS1CLRBLB7t5EF\nC8xV8nBdfXX4LuJmzRRatQq/d1xwQcib7vNJ3HRT9bQcys6WePZZK1dfbWP6dCvvv6/Ruj86ESP2\nd7oY0qyZygcfFNCyZYBGjRRefNHJ4MHVG1uONdHOw9m9W2bChGQKC0vfKM477+y2YHfooPDJJwVc\neGHou/F4JPLzK38zipQd6tcnorlXkeBsbfHVV2bGj09m8WIzs2ZZGTHCxrJl2khYlyTCOkWU7BpR\nFjHJUVNV4fWSJFHQqkEDSEwUA6msXp5Qur5a8GdNmwqhlpgoVjQJCSLnDSpdPy1IpGyRkSEzZkwy\nu3aFxklyssorr0Rul19qKowZEy6sZs2ykJVV8e2uPDv06+fn5pvdgEpamsJ77xWUmss6dAgwYEBo\njsrLk3n+eUulag8risjb27lT5vBhqegrLiyE999P4K23LARLWjRtGp35Jt7zm6sLLdihVgs1gJ49\nA/zwg4OVK+3cequXOnVifUbxjccjlbGYVxk92sM77zhp2PDsJpkOHRTef9/JggUObr/dzQsvOEut\naHUiy9Kl4epHVSWmTEkiKyv23hujUdSvC1Lvh+sOAAAgAElEQVQZoRYTZFkINLNZ1DtLTxe7Nps1\nEz8vq/Bt8U0EwbBnUpIQacEctYYNxe8N/uElc91iQF4ePPWUlYMHQ6G6OnUUPvvMwXnnRfbavfJK\nb9h4cDqlKuW1Nmmi8q9/FbJmjZ3vvy87B6l+fVEoNTEx9LlLliRU2EMzLw9efz2BPn3q0KdPHXr3\nrsNLL1k4eBA2bTLwr3+F51H37KnnwdY2tLEcjjENGpx+Qtu/X2bnTpm9ew0kJKj06eOnU6f4EAlV\nyTPYskVm/vwETp2S6NIlQO/efjp0CJw2D6tr1wDffOPgt9+MuFwSzZopRa03qloAsFkzlWbN/Awd\neuYTlZ5vEeJsbdGnj5/vvgsPu9jtEl4N1JZNSlJp3lzh0CFxU6xTp2KRErMxkZQErVoJD1hyMhw8\nSFFsuPgq53RCq3XrUFmOpk1FrlpwY0J5Gw9OQyRssWmTMWy8dOrkZ84cZ1RKMZx7rsLbbzuZODGp\nqG5XZXIkT2eHpCRo3/70596lS4D33y/gr39NLvrctWuN9O5dftz199+NPPNMaFJ1OiWmT7ditSos\nWWKmeHHYAQN8USumrc+ZAi3YQRdqp8HjgVWrjNx5ZxJ5eSHnY4MGCitX2qPmgo4Fbjf8/e9JrF9f\nfIio3Hijl/vuc9O2bdkTlixDjx4BevTQtzzVNEaN8rJypYkffwy5q+691x3ziuIgIn6DBvn57TcT\ndeooNG6s4YWUogiB1qSJyFWzWET40mYTmwyKU1adta5dhdBr106ItIYNRe20YA9R0MRuz507xbnU\nravwyCNuRozw0qJFdMaKwQBDh/pYvLiAN95IoHNnhbZtozMn9e/vZ/78Am6/PQm7XSzwT0d5G188\nHomNG0Pzb506Cs895yI1tVpPVycOiNrVfMstt9C4cWO6du1a9Fpubi5Dhgyhffv2DB06lFPFgvnP\nP/887dq1o2PHjixbtqzo9Q0bNtC1a1fatWvHfffdF9Fz/vlnI3/9a3KYSAOxEI6XWpJnG1+3WOCq\nq0q6SiQ++iiBW29N4sCB2N8IzgQt5BlohbO1RYsWok7cp586ePvtAhYvdnDvvW7NbKLo2FF4Gi67\nzE+jRhULgpiNCVUVGwlUVdQ9S0wUyUj164uQaFkFcCVJiLJevYRAS08X9dOaNqWozoEshx5nSCRs\nMXy4j2++sbNihZ077vBETaQFsVjg0kv9LFzoZOrUwkqltVRXT+ChQ/0sW+bgP/8p4NZbPac9/rzz\n/GXmRjdvrhR55erXV1iwoIBzz43eAkSfMwVasEPU5MbEiROZMmUK48aNK3pt+vTpDBkyhIcffpgX\nXniB6dOnM336dLZv387ChQvZvn07WVlZDB48mN27dyNJEpMnT+bdd9+lZ8+ejBgxgm+//Zbhw4dX\n+/m6XPD881ZK9iQTvbzOPteqOtmwwUB6etlNwquD667zsmmTgcWLw3sBbdli5NdfjbRqpYGYl05U\nadRIpVGjyoVetm2Tyc6WaN1aicpNOj1dhNn79vVx5IiIDGqSoFBTlJAAa9FCPPf7RbP24v0/rVbx\nx7RrJ3LZkpNF6LNpU5HnFuxlo7F2GOeco3DOObE+i9iZpX17pcJQKUBamlgAbd1qKPKgdenip337\nANOmubBYVAYO9JcbxdCp+UhqFPex79+/n5EjR7JlyxYAOnbsyMqVK2ncuDHHjh1jwIAB7Ny5k+ef\nfx5ZlnnkkUcAGD58OE8//TStWrXisssuY8eOHQAsWLCAFStWMGfOnFKftXz5cnr06HHW51pYCA8+\nmMj8+SGR0qmTn1decXHhhYGYz4knT0oMHJjCwIE+nnnGFbHigdnZEuvWGfnXvyxs3y4mEUlS+e9/\nnVx1Vc3aIatTfezeLTNkiA27XTRij4Y3YP9+iQ8+SGDJEjNPPFHIqFEaHJ+KEhJkXq+oeZKbCytW\nwJYtcOSIeN3hEP8mJYn8s2bNoFMnsUvUZhMbCWw2IfCSk8/ak6ajo6MdNm7cyKBBg0q9HtMA3vHj\nx2ncuDEAjRs35vjx4wAcOXKEiy++uOi45s2bk5WVhclkonnz5kWvp6WlkZWVFZFzs1ph2rRCxozx\n4nJBw4Yq55wTOe/VmeL1ikTujz5KYOhQHyNHRuam1KCByogRPnr39rF/vwGnUyRqt2sX+9VdIAB/\n/GFg7Voj3boFuOgif1F1Ap3YcvCgjN0uhMOhQwZuvjmJzz4riKhnzWKBuXMTyMuTmT7dQr9+/go3\nCkWd4Lo4mDuRkCDCnxddJASczQbHjol/fT4h1BISQmU4GjYU9SdSU0WoNB4qLOvoVJL8fDF3tG1b\nswrPVxXNZFpJkoRUzUUa7777blr+L/6RkpJC165di3ZwBOPOFT2/9NLQ8x07Kj4+Ws+3bv2ZOnWS\nKCi4jAceSMTt/oamTZVSxwffU9XPW79+NYcPywwe3JcWLdSY//2rV69m506Zxx8f8b9k3J945plC\n7rmnd5nHz549+6y+/zN5XlAAffr0IyUl9uPjdM9Ljo1IfN6ePauAJGAAAJmZq/noo0IeffTiiP19\nLhc0ajSCvDzIyFjN5587mTSpT7nHb9myhcmTJ0fc3mHP+/QBVWX1L7+AqtLvvPPE8717obCQfs2b\ngyyz+uhRSEmhX8uWULcuq48dA4dDPK9fn9WbN8Phw+L3SxKrf/21SucXjesjHp4HX9PK+cTyebSv\nD7cbfvllMDNnWnjggW8ZMMCvCXtEcr4E+OWXXzh48CAAt956K2UR89DnihUraNKkCUePHmXgwIHs\n3LmT6dOnA/Doo48CIvQ5bdo0WrVqxcCBA4tCn/Pnz2flypURCX3GAxMnJvHFF2L7+4wZTsaPL50z\ntnr16ipvL3a5YM6cBJ591so113h57TUXyclV+pVVxumECROSWL48tP1/9GgPb7/tKvP46rDD6di2\nTeb++xOx2eCll1yabsweaVsAHDokMWBASthGnNGjPbz1liuiRfMfftjKf/4j3Kqvv+7kppvKz6OM\nhh3KpHgxWkUReRaFhbBrF5w4AVlZIjSanCw8cPXrCxd/aqrYRGC1Ck9b8VIcVSRmttAYuh1CRNsW\nf/xhYNAgGyCRmqqwYoVdE8XEo2mH8kKfMU1quOqqq5g7dy4Ac+fOZdSoUUWvL1iwAK/Xy759+9i9\nezc9e/akSZMmpKSksHbtWlRVZd68eUXvqY0U3yk0Y4aFEydKT9jVMcDWrzfy7LNiY8Vnn5k5fjz2\nBU7z8iRWrw6varpvnyGsjVBxInmhZWdLTJ6cxPr1Jn76ycSHH2q7xUs0Jp0WLVReeCFcNJ84IUW8\nBmufPv6i/y9caMZVtm4HYlgfqfjuTEkKibAOHYQQ69ABOncWNdK6dRN5aK1bi59ZLEKgFX9/NaCL\nE4FuhxDRtoXoYSrGc26uzKFD2si51MKYiFro8/rrr2flypVkZ2fTokULnnnmGR599FHGjBnDu+++\nS3p6OosWLQKgU6dOjBkzhk6dOmE0Gpk1a1ZRWHTWrFlMmDCBwsJCRowYEZEdn/FCp06hukAHDxrI\nyDBUekdeZXG7YdasBIIXkKoGm1/HdqVjNIpWNB5P6EZ18cWxyVHLzJTZutVI585+LrnET3KyyokT\nIq2oNjNsmI9nn3Xx5JNWFEXi5pu9Ec93T0sLeavWrjVy7Jisae8mBkMoby0lRQiyZs2ERy3YWL1k\nL9BgP08dnRpERkb4mC4+t9d2oiZZ58+fz5EjR/B6vRw6dIiJEyeSmprKDz/8QEZGBsuWLaNu3bpF\nxz/++OPs2bOHnTt3MmzYsKLXL7jgArZs2cKePXt4/fXXo3X6miQ9PUD79iFhtmpVad1dPBZ+NmRl\nySxfHvJcybJKSkrs3dENGqhcd10orGU0qlx77enDXJEiJweeespFly4BFi408+qrVu6/P4k9e7Sx\nIixJJG1RHJsNJk3ysGKFnWXL7AwZEvldmGlpCqmpQpj5/RLHjpU/2UfLDhUiSRR1tzebQ707TSbh\nQQsWsg0KtAj0x9KMLWKMbocQ0bZFQUH4tZqfL7F+vSHWndA0MSa0eSfRqRT16sG994aKKc6bl3Da\nG9PZcOKERCAQ+p1du2pjJ53RCHfe6ebuu90MGeLl888ddO0am24IyckwZ46FhQvFjkOXS+Kbb8z8\n5z8J5OeLYvOxnmxihdkMXbooXHhhgJSUyH9e06YqV18dEuyHD8eB5ylYsgNCeWdms3hIkhBoRmPo\nEckkPx2dGBFcYAXJyDBw9dU2tm7VZYpugTjnggv8mExCBRw/LnPkSPhXWtX4eqCE9rnlFm9UbriV\noWVLlWeeKeSjj5z06XP62naRzDPYv9/A8ePhdr/qKi9JSSojRqQwfLiNJ5+08OuvBvLzI3YalUYL\nOReRQpII89z98Uf5g0IzdigZDzYahdcsWMTWZKr2nLSSaMYWMUa3Q4ho26Jv31B06NxzA+zbJ1NY\nKLF7d2wXW1oYE7pQ0xi5ubBunYE1awzk5FR8fOvWCpMnhzLo8/KqdyJPTVUJ5qOdc46f/v2rNweu\nqkiSuK95veKmvGiRiUWLTOzcGb2hXVYD8PPP9zNjhoUdOwxs327kzTetXHllCuPHJ0f13GojHTsq\npKSI1fn+/XFia7M5JMaCwiwo2HQPmk6E8fth/XoDy5cbOXkyNuOtc+cAnTv7MRpVxo/38NlnYlOW\nno6pCzVNceSIxL33JjJ8eAojRqQwdWpihWLNZIKbbvJSt664Mdnt4RdZVePr6ekKU6cW0r+/j7lz\nnbRqpb3E7EAAvvrKxJAhNu68M5k770xmxIhwl3kk8wwuucTHSy856dAhQOvWASZNcjNsmI9x40rn\nzK1aZeLaa5PZtSt2l54Wci4iSXq6wgMPiMXL8eMyhYVlH6cpO8hyKNxZ3IMWpbuUpmwRQ2qrHf74\nw8CIETauu87GK69YcDqjb4u0NJXnnnPxxBOFvP12wv82E6g0bx7be44WxoQu1DTE0qVmvv461LJq\nwYIEduyoeKJu21Zh1iwnoFb7rrrERLjrLg8ffVRAly6hCyYzU2bhQjNTp1pYsMDM3r2xG0p79shM\nnpyEooRE6qlTMps2RWdTc716cOutXr79ViTNv/BCIeeeq/Doo4Xccoubkjtkjx418P331Z8QXtP5\n808Dy5YZOXy44hX/kCE+LBYVr7d0+D4uqOUtoU6elFiyxMQLL1g4dEj3KEaaL74w/69wOLz9dkLM\nwo1+v8TTTyeSmSk+f+xYL+3bx+MFXL1ErTyHzulxuWDRotL1t1yu8EnK54Nt2wz8/LORdeuMJCTA\nmDEeevb08/nnBTRuHL76qI74ekKCeATZv1/mL39J5tCh0MWclhbgs88KihoHe73iPI8fl2jSRKVT\npwDmCJUXy8+X8HpLT+Y2W0ggRSPPoE6d8OdNmogcurFjvXz+uZkPPzRjt8vUr69w/vmxm3ximXPh\ndsOWLQYOHpTp2jVQqabVIHqHXn11Mna7TNeufj744PTe3Q4dFF591cmaNcZyizNrIfdEK2jJFgcP\nSjz+eCJffy0mjJ49/bRoEZ2UCy3ZIVp4vSLsGUJi504DY8dG3xadOgW49FIfK1caufJKL4884sZm\ni/pphKGFMaELtbNgwwYDq1cbufhiP926BaqlJ5ksQ0KCWuI1laZNQzcjp1MU8XzkkcSwnZiLF5v4\n5JMCLrssOpPZli2GMJEGkJVl4I8/DEVC7eefjYwZk4yqSkiSyttvOxk1yheRSE5amkLr1n4yM0PD\n+aKLfHTvHvt8usREuPDCABdcUMhdd7nxeiUSElSaNq1920Bzc2HWLAuvvmoBJCZOdPPyy4WVSsE6\ndCjUO3TLFiPvvmvmiSfc5Yp/WYaRI3306hX7MaBTeRwOeP11S5FIAzCba9+1Ek0MBrBaw218+HBs\nvLlNmqi8846TU6ckGjVSNLNxLdbUXt96Oaxfb+DFFy18/LGZDRtKV7rPyZG4445Epk1L5PLLbSxZ\nYioqgVQVLBZ48EE3khS8YFSef94V5nHYutXAgw+GizRB+RXfIxFfL6+OWrC806lT8MQTiahqqEju\nXXclkZERmeGWlqYyf76TJ590MX68mzfecPKf/zhp2TJ0nrHOM5AkaNZMJT1diblIi4UtAgH47DNR\nYy5YPPnYMbnSefIlo4Bz5ljYt+/04ykpCc45p3xbx3pMaAmt2GLDBiPvvReqWh3tRY1W7BBNDAa4\n/PLwBU2zZkrMbNGggUrbttoRaVoYE7pHrRiFhfDoo4ls3CjMIkkqd97p5vbbvUVhlsJCOHIk6BYS\nAiQ93UGvXlUPZfXt6+frrx0cPizTrJlCt26BsJDjqVMSwZtccUaP9tCtW/RCaZ07B7jlFjfvvRfq\nWNCvn48LLxQXu88X7F4QwueTOHpU5txzI5MY2q6dwt/+5qn4QJ2YsH27gccfTwx7beDAyq9wGjZU\nELl+Ylz5/RJZWTIdOmhvc4vO2ZGdLfHEE+HhiQcfdJ/xBqYTJyTsdokmTZSY9ySOF/r0ETmdbrdI\n4G/TJlAtDgid6kH3qBXDaoWhQ0OjU1UlZs+2MnZsyBuUmqrSo4c/7JgXXrDidFb98xMSoFevANde\n66N370BR55gg3bsHeOopF82aKTRsqNC/v4+PPy5g+nQXDRuWveqMRHy9QQOVp54qZNkyB/PmOfjy\nSzvvvussaqBbr57KFVeU3vGYmBg7T5IW8gy0Qixs8f33Rny+kHhPSlK55JLKhyXT0xWuvDL8zlFe\nX9fKoo+JEFqwxeHDEtu3h3wHTZoo/OUv3kqnS+TmwtKlJoYNS6ZnzxR+++3M/RBasEMs6NxZ4f/+\nr4CLLvIxY4boslJbbVESLdhB96iVYMwYL/PmmcnKCs0Ou3YZ+cc/EnnrrQJSU+GWWzz8+mto196q\nVUYOH4786r5RI5X77vNwww1eFEXU74pFb0sQ7YEuvLBsL57RCHfc4WbdOiN//imG2MSJbjp21Hfv\n1Eb8flixInyX62uvOc/oeklKgsceK2TlSlNRr9nyFic68UlOTshvYDarvPNOQaX7tGZnS7z2WgKz\nZoU8ciW9+jrlI0kiovPZZwVYrXrpPq2he9RKkJ6u8OmnBfTqFb56X77cVNQ0tk8fPxdcEPq5okjk\n50dvZDdsqNK4ceVEWqzi661bq8yfX8DSpXa++srO448XUqyVa9TRQp6BVoi2LWQZWrcWIt1oVHnx\nRSfDhp15XOXccxW+/NLBPfcUMnu2ky5dqib89TERQgu2aNhQwWhUadvWz1dfOejdu3Lfr9MpSkoU\nF2kGg0qHDmc+PrRgh0iQnw/vvmvmsces/Pyzkby8so9LTAyJtJpqizNFC3bQPWpl0L69wn//6+Sn\nn0xMn27h0CGZxESKhFGTJiqzZ7uYMCGJ7duN2Gwq9evrq/uSNGmi0qSJ7kWr7cgyTJniZsgQH82b\nq3TuHMB4ljNP166BmPV01YksnTsrrFmTj83GGXlL16wx8vLL4avWe+91F+1A14EjR2Qeekjk0rz1\nloWbb/bw+OOFNG6s37fiAUlVa2a76OXLl9OjR48q/56cHImTJyUsFmjZUgnbfXb0qKg3U6eOSo8e\n+s1DR0dHJ5qcOgWjRyezcWMotH7ZZT7eeMMZ893VWmL/fpl+/VLC6nLefrubf/yjMOZ1ynRCbNy4\nkUGDBpV6XQ99VkD9+iodOyqkpyulSgQ0baoycKBfF2k6Ojo6MeD4cblolz7AsGFeXnutaiLN7xeL\n8H37JI4ckeKzs0UJWrRQuPHG8F3xb79tOasNFzrRRxdqNRwtxNe1gG6HELotBLodQsSrLVJSVAYO\n9NGzp4958wqYOdNVtPv8TFEUeP/9X3nkESt9+6ZwwQV16N27Ds89Z+Ho0fjOrjcYxAavtLRw1Tln\njiU+euHGEC3YQZfTOjo6OjoRxeUS7fDq11erdUdh06Yq8+aJ2kiJiRUcXAFr1hh4+OFE/P5QvpvD\nAa+9ZqVbtwCjRsV3YbHgBq/Ro22cOCF8NJs3G8jPl0p1JtDRFnqOmo6Ojo5ORFBV0XJv2jQrBw/K\njBnj5ZZbPJrLHwsEYOzYJJYvL92TTJJUvv3WwUUX1YAYKKJv7tKlJv7v/xIYM8bD3Xd7ItaHWefM\nKC9HTfeo6ejo6OhEhM2bDYwcacPjEW60V16xkpamMGFC6YLYscRggHHjvPz0kwlFCbn8WrYM8Mor\nLs47r2aINBBdXB54wMOkSR6s1lDrPx3toueo1XC0EF/XArodQui2EOh2CBEpW/zyi7FIpAX54gtT\nub2JY8mwYT5mzPiajz928MEHDpYutfPttw4GDfLXSI9TSsrpRVp1jQm/H3bskPnxRyObN8txtzlD\nC/OE7lHT0dHR0YkI2dmlE9L69AlosvK92QznnKPQr1/lW5vpnJ6DByXefz+BN9+04PNJmEwqP/1k\np1MnvcbdmaDnqOno6OjoRIQ1awxccYUNVRXKrF490V3i3HP1G3VN58ABmfHjk9i8OdwftHy5ne7d\n48ytFiX0HDUdHR0dnajSo0eApUsdfP+9idRUlWHDfLRvr4u0mo7TCTNmWEqJtP79faSn6yLtTNFz\n1Go4WoivawHdDiF0W4DHAx999Cu5ubE+E20QqTFhNotQ51NPuZkyxaN5kaZfGyGqYovMTJkPPghP\n7KtfX2H6dBf16lX1zKKLFsaE7lHT0dGpdezfLzNlSiJ9+yYzc6aL1q3LFhDZ2RIul4SiiIKokqRi\nMgkBYrWqJCdTpXwrn098RmGhhNstEq+tVvG7rVaoV08t1RFFR0fr+P3hF0WfPj5eeslFx47aFupa\nRc9R09HRqXVs3SrTv38dADp39jN3bgGtW5eeCvfulfnzTwMLFphZudKEzyeEVN26KnXrqjRpEqB1\na4VWrRQaNVJJSlJJTBT/2mzikZKikpJS+hz27JF5440Eli41c+pUuBpLSFBp3FihY8cAF14YoFMn\nP61bK7RsqVS5sKuOTqRxOmHdOiNHj8q0aqXQqZM/7jxpsaC8HDVdqOnoxAnZ2RLLl5vIypK44QYv\nTZrUyEs3Khw7JjFwYArHjwuBdP31Hl54wUVyctnHezxw6JDMwYMymZky335r4vffTTgcp3enWa0q\nLVsKwdW1a4D09AB166rUqaOSkKCya5eBRYvMZGQYOHRIDqvhVRJJUunTx8/f/uamVy9/ueeqE05u\nLjidEg0bqlgsFR+voxMrdKFWDRw9KpGfL5GYqNKiRfW2QokUq1evpl+/frE+jZgT73bw++H11xN4\n9lnhTvn3v53ccMPZFQ2Nd1tUFxMn/s4XXwwter54sYMBAypXmsHngxMnJLKzJU6cEAJuxQoT69cb\ni8Rfxag0aKDSpk2Abt0CpKUp+HziuwaJrCyZPXtk9u41cPKkBIgJR5ZVvvzSwcUXV19Sdk0cE243\nrFlj5NFHrezbZ+CVV1zcdNPpr5maaIezRbeFIJp20Hd9VoGTJyU+/9zE9OlW8vJkkpNV3nqrgOHD\n/XEh1srC7RY5N3oYJT7IyJB54QVr0fNvvzWdtVCLFrm5cPSoTPPmCnXqxPpsSjNggI+lS9UiL9aT\nT1r59NMCGjaseO1qMkFamkpamgqIvJuJE72cPCmRmytx/LhMdrZERoaB3383kJFh/F9j7+IThhB6\n2dkya9eGVx6VJJVmzVQ6dPBz000eWrVSqFtXITVVJTVVoW3bGrm+rjb8flFYd/LkJII2f/NNCyNH\nejU5FnV0TofuUasAhwOmTbPy3nvhPvN69RRWr7ZrrmddReTkwMqVJmbPTkBV4YYbvIwY4dN8GO3A\nAZmjRyWSk1Xat1c0VSlcUUQ/w23bDCQmQuPGCh06BKrVpv/3f2buuCOp6PngwV4WLXJW2++vbjwe\neOUVCy+/bGH0aC/PPFOouTHm8Yhre86c0LX96acOBg6s3oKngQDk5EjY7RJ5eULIZWfLbNliYMMG\nI/v3y+TklBRxZSNJKueco9Cnj4/evQM0barQuLFCgwZqpQRmbWHTJgNDh9rCktqHDPEyb55TU3OH\njk5xdI/aWbJ3r4H33kso9XqjRgoWS/xNjAsWJDB1asiNtnGjifx8F/fd59Hk7jJVhR9/NHLrrUnY\n7TKyrPLPf7qYONF72nyT/Hyw22VSUxWSkso/rjo4flxi7Nhk8vJCBmzWTOGZZ1z07eunceOqj5PN\nm8O/nPPP13YtoqwsmddeswASn3ySQJ8+fs31d0xIgFtu8bBwobnou1uxwljtQs1ggEaNVBo1Kj0O\n3G7Iz5dwOCROnRKpFfn5Evv3G/jzTwMZGQYOHJBxu4XgUFWJzEwDmZkGPvww9HuaNVMYMMDHpZf6\nSU8P0LKlUi3jLl754gtTqZ2Ht9+uNx/XiU80eGvWFmX5G61WlRkz4qMeTPEaMMePS7zxRml18/77\nCeTmajOGu22bzM03J2O3i6GqKBJPPJHIvn3lD12nE6ZOtdK9ewp33JFERoYc0Vo4DRqoXH99uAg5\nckRm0qRkJk9O4tChqts2EAj/HVVpcxONukCFhVLYjXLaNGu12KE6Wb16NW3bKrz3nhOTSVzoy5aZ\nyc+P3jlYLNC4sUrbtgoXXhhg0CA/11zj44EH3Myd6+S77+ysXZvPr7/m88MPdr74ws78+Q7+858C\nXnrJyZQphVx5pZdmzRTWrTPyxBNWxoxJZvToZObMSWD79spN8VqoFVVdFBaKqEFxbrzRQ48eFV8z\nNckOVUW3hUALdtA9ahXQvn2A2bOdPP+8Fb9f4pJLfNx5p4fzztO2R6MszGaVRo0UTpwIn7wvvthP\n3braXH3v2WMo8iYEUVUJ72mcM4cOyXz4YQIg8fXXZv74w8DUqZFbk5hMcPfdbrKyJL74Itz7umKF\niaeftvLaay5strP/jK5dQ+OtZ08fXbpoux+h2awCKsFwXn6+zOHDMi1aaO+6ueQSPwsWFDBuXDIG\ng7bqlqWkQEpK0Jbl4/WCywVut4SqiuJiWmcAACAASURBVNpukhT8HmoXVisMH+5j0yYjsqzy0ENu\nxo3zxMXCWkenLPQctUqSnS0mwHr1VIxxLG83bDDw178mk5sr7kbdu/uZPdup2YrhP/5oZPTocIUz\neLCPOXMKSE0t+z2ZmTK9e6fg84UE3rXXepg50xXRzRMnT0qsXWvk8cetHD5sKHpdklTWrrXTtu3Z\n2/jAAZl7700kKUll2rRC2rXT5vcVJD8frrjCxvbtoYvlk08cXHaZdgXmnj0yhYVSmCjWiU9OnJDI\nzJSx2VTatFH0shw6cYFenkOniAMHZA4fljAYoG1bkYisVbKzJWbPTuC11yzIMowc6eWJJwrLLE4a\nxOuFu+5KZPHikHdLklRWrbLTuXPkBc7x4xK7dom6WDk54sbfq5e/yiLR4QBZJuI5d9XF0qUmxo8P\nFftassROv366CNLR0dEpi/KEmoac/DqRoKz4eqtWCn37Brj44oCmRRqI/K+HHnKzdq2dNWvsvPGG\n67QiDUR7n3vv9YRt9lDVlaVCvpGicWOV/v393Hijl3vv9TBwYNVFGoDNVj0iLVo5Fxdf7GfUKA8A\n6el+0tO15QXUQu6JVtBtIdDtEEK3hUALdtCFmo7msViE569Nm8rv4OzaNcCiRQ5sNiHWJEmlYUNt\nCYWaTsOGKtOnF/LFFw4WLHDSvLm2FwU62qCwsOxNXDo6tRU99KlTo8nIkNm9W6Z+fZUePQL69nyd\nMjl2TNQ3S0lRadpUxWCo+D061UtGhsxPP5lYuNBMr15+HnzQTf36NfL2pKNTJnodNZ1aSfv2imY3\nSuhoA58P/va3RJYtM5OSonD55T5uucVD584BvXNHlNiwwcCNNyYXpSds2mRk/HiPLtR0dNBDnzUe\nLcTXtYBuhxC6LQRBO5hMYicxiCLJCxcmMGyYjcceS2Tv3toxRcZyTGzeLHPNNbawHNK0NIV69aIv\n0vRrI4RuC4EW7FA7ZiEdnWIE9I2HOiW48kofI0YUL84nMW9eAsOH21izRo+DRor8fHj44UQcjvBa\nidOmuWp1ZwUdneLoOWq1iCNHJE6elEhNVWnRokZ+7eVy6hRs3Ghk+XITmzYZaNxY5YorvHTvHqB1\naz00qgMHD0q8/LL1f8WSQyQnqyxZ4tB82654ZONGA4MHp4S99ve/FzJlipuUlHLepKMTJY4elbBY\n1KgVS9bLc9RiFEX0MBw6NIWBA+swYEAK69fXLi/BZ5+ZGT3axuzZFn77zcTnn5u57bZkrrjCxo4d\n+mWgAy1bqjz3nIsFCxykpYXEe0GBxH33JZKXF8OTq9GIRaPFovLKK07uvlsXaTqxZ8cOmf79Uxg+\n3MbXX5vIzY3dueh3qBrO6tWr2bJFdCM4ckR83Xl5Ms88Y8XlivHJRZEvvvi1zNePH5dZtcpU5s9q\nKlrIudACZdnBZoOhQ/18842d994r4IorvKSmKhgMKoWF2upVWp3Eakx07Bhg6VIH8+c7WLXKzrhx\nXurWjcmpAPq1UZzabov8fImcHJndu1dz003JvPSSlZyc2JyLvuuzFrBunSGsnRJAVpaM202t2dV2\n3XVeDh3ys29f+JC32VR69dJuWyOd2NC8uUrz5j6uvNJHdrZEYqKqe3kiQGIi9O2rh5R1tEdamkJq\nqlLkSXvrLQv16qncc4876vdNPUetFvDWWwk89lj4yJo2zcWUKZ4YnVFsOHJEIiPDwN69Mm63RMuW\nCh07BjTfNzNSZGbKbNliIC1N4cILa+fNMj8fcnMlDAYJs1nFZlPjpkWXjo5OZHn7bTOPPlp8QlBZ\nvLiAAQMis7jX66jVYvr29ZGSomC3i9DnsGFeRo3yVvCumkezZirNmvkZMCDWZxJ7Nm40cPPNSRw9\naqBFiwDLlzs0306sujl8WGL8+CT++MOILEO9eipNmyqMGOGje3c/rVoptGhR+W4YOqI37549Mtu2\nGbBYVIYN89e6caVTcxg1ysf33/tYvjyYHiPxr39Z6NGjIKoedl2o1XBWr15Nv379+P57B5mZMjab\nSqdOgZjmgcSCoB10YOHCX5k69XKys4VwLyiQ8NfC6O++fT/z5JMDmDgxiVOnZHJyRE7K1q1iWpQk\nERYfN87L+ef7ad9eQZZFeZecHIn8fAmHQ8LjES2PUlNV6tdXadgw/oRJVa+PggL4/XcjDz9sZe9e\nYb9mzRQGD7ZX1ylGBX2eCKHbAho1UvnrX78jP38Y69cLsbZ+vZFDh2Q6d45eJEYXarWEdu2UWhvi\n0wnh8cBXX5mKRBqIvqipqfEnLqqKJMGll/r5/nsH339v4vnnrWH1vFRVYs0aE2vWmLBYVGbMcNKw\nocp335lYssTM8eMSEJ772aJFgFdecTF4cO1Rvvv3S8yYYWXePDMhe6i8+GLNqoV29KjEwYMyHg+0\naaOQllZz/jad8mnSROWdd1x8+qmZl16yIElEvRWhnqOmo1OL2LxZ5rLLUlCUkMBYtMhRq4RFeezd\nK7N3r8ySJWa++MKM0xmy0ejRHgoLJb76quIZ+vHHXdx/v6dW9AvdvFlmwoQk9u8PX/NPm+bi1ls9\nNWaz0qZNBiZOTOTAAfF3tm3r5+OPnbRte/aL39xcsakrL0+iWTO1Sr9LJ/IEAnDggIyiCKEuRWAT\nuJ6jpqOjw4EDhjCRNmCAjx49dJEGYvJt00Zh0CA/Dz9cyJEjMgcOGPjtNwMdOwb45JPyRZokqQwZ\n4uO22zz06OGvFSJtxw6Za6+1kZMT8s6aTCozZ7q4/HJvjRFpmZky112XHPZ37tljZNs2w1mJK58P\n/vjDwJNPWlm3ToTT6tRRWLnSQcuWuljTKob/b+88A6Mqswb83GmpkxBKAiRAJPSW0FFDEUREBAEF\nAVFkQXetgIiK6IKuIKh8u2BZcQUBURTRFURAlKKAKH1BQEBaQgqQQjKTzGTa/X5cU4YkkD43M+/z\niwxT3jlz7nvPe6oWjzVHF4aalyPyDBSEHBSU3nk7gH40aOBi7txc6tb17Jo8RWk6odUqzW+bNnXS\nq5eT++9XmkYPG2bn4kUll81kktDrlSatdeoouWlRUa5aa5yU9/q4dEniiSeC3IyX2FgHCxfmEhfn\nRFNLO3SWJIfTpzVu3zOfgIDyB6Oys2HNGgMvvBDodmByuSQ0GnUFt8SeqaAGOQhDTaAKzGbQ6cDf\n39Mr8W5atXLRoIGLfv3yePZZq8hbLCMaTX7VsG+2MbmWc+c0HD6s3D7atnUwbZqV3r0dXpWTlk9Q\nUPHvFB9vp2PH8uvCrl16nnuueBnx/Pm5REV5n+wEVYPIURN4HLMZnn02kKQkDS++aKFrV2eNJ2v6\nEleuSISEyPj53fi5vk5amkR6uoRWC35+SkVndR8mcnOVrujOInZAQADUq6eerTo1VWnDERQE0dHO\nGpuF6AmyspQRdG+9FYBeLzNunI3Ro200a1a+Q86lSxIDBoQUTIhRkHnxRSsTJ1qpV69q1y2ofYgc\nNYFqycqS2LjRgNkscffdOt56K5exY23Cu1ZN1Mb2EZ7g7FmJ0aODOXtW2Sb1eplevRzce6+Njh2d\nNG/uJDS04u9vs8HlyxJXrmi4dEkiKUnxUh09qv2zulAx1jQaiIhw8cwzVsaOtaFTwa7dsKFMw4a+\n4V0MDYUJE2wMGWJHo6m4wexyKflp+bRt62DBgly6dnUSEFBFixV4JbU0k0BQVmrDvLZ69WS6d1cS\n2mVZYvr0QH78sWrvRrVBDjWFkIXCjeTQoIHMwIGFhRZ2u8TOnXqmTg1iwAAjw4cb2bJFR1ZW2T/T\nZoOTJzV8842eiRODuOWWUAYMCGHcOCMzZgTxySd+HDmi4+pVDRaLhM0mYbfDrbc66NXLUW1GmtAJ\nhdLkIEmKPlTGq9mokczGjSa++srE1q1ZfP21mfh49RppntIJm00ptsjM9MjHF0MN14Yw1AQex98f\nHn646DgriUcfDebkSaGeAs9hNMKMGRY+/NBMaOi1YS6J//1Px5gxRp5+OpCzZ29cq3/ihIZnnw2k\nd+8QJkwIZtMmxYtcElqtTJ8+dpYuNfPTT9ksXJgr8gm9gJgYF/36Oejc2SU826Xw6686br/dyPvv\n+5PnW1MOS0XkqAlUwZUrEuPHB7Fvn77gsUmTrMyfb/GJVgcCdXPmjGKYLVnix759Oq5tdDt0aB7v\nvptLcHDJr79yBVatMpCXpynWf8lgkAkOlomIcBEWJhMYKBMWBg0b1t4qUoGgItjtMGFCEJs3G9Bo\nZH78MbtGJwB4GlXnqEVHRxMSEoJWq0Wv17N3714yMjK4//77uXDhAtHR0axZs4Y6f849ev3111m2\nbBlarZbFixdzxx13ePgb+AZ2OyQmanA4lPEwpd2UKkKDBjILF+YyZEhIQXf4zz7z44kn8oiO9p0L\nVaBOYmJkYmLsDBxoJzFRQ2KihvPntaSlSUgS9OljL7U449IliR9/1LFpk4H//U+H3V6yF02SlKan\nDz+cx913e08fMoGgrKSkSPz4o3JYd7kkjh3T+pShVhqqiC1JksSOHTs4dOgQe/fuBWD+/PkMHDiQ\nU6dOMWDAAObPnw/A8ePH+fzzzzl+/DibN2/m8ccfx+USP2RpVFV8PTlZ4pVXArjllhB69Qph/Phg\nfv+9atWnQwcXn3xiJjhYcfLm5EhcuVI17Z/VkGegFoQsFCoiB6MR2rVzMWiQg7/+NY9Zs6y8+KKV\n+Hgnen3Jrzl1SstjjwWxf7++VCMNICJCJj7eQXa2xMWLijGYmiq5JaBXF0InFLxNDg4HJCZK/P67\nhvPnNVitSpX9sWMaDhxQDhql4QlZOBwSFkvhmn77zfPhFDXohCo8agDXRmDXr1/Pjz/+CMCECRPo\n168f8+fPZ926dYwdOxa9Xk90dDQtWrRg79699OrVyxPL9hk2b9bz3nuFZZg//aRnxoxAVq0yV6ry\n7Vri4x1s3pzNP//pz7FjOlW1JBAIKkLPnso80UOHtGzZoufwYR05ORJWq5KkHhgIRqPM66/nMnNm\nIMnJGhYsCECrlQkNlenUycFttzlo2dJJkyYuGjVy+WyTYkHZOXlSw7vv+vH1136YzRIGg0x8vJ1R\no2y88EIAWVlaevWy89FHOarpfydJMiCTn1pw+rTnDTU1oApDTZIkbr/9drRaLX/961955JFHuHTp\nEhEREQBERERw6dIlAJKTk92MsqioKJKSkkp83yeeeIKmTZsCEBISQseOHQs6DOdbyeLvsv398cc/\nA3qg35/S3cHu3ZCREUdoqFyln9eunYsHHtiC1QrNm1fN+vMfU4s8Pfl3fHy8qtbjyb/zqc7PMxgg\nN/dHWreGCRPiSU+X2LNnFy6XRPfu8Wg0MocO7UKnk3nxxduYOTMIk+lHnE7IyOjHjh0Gduz4+c+V\n9uWmm1zcfPMPdO3qYNSoWwgOFteH+Nv972++2c3LLweQkJCf77QDmw22bevHwYM67rzzez7/3I9f\nfulHerrE6dM7S3y/fGpq/S1a9CYsTCYzU3HSOBy3eFye1blfAuzevZuEhAQAJk2aREmoopggJSWF\nRo0aceXKFQYOHMjbb7/NsGHDyCxSn1u3bl0yMjJ46qmn6NWrFw888AAAkydP5q677mLkyJFu7ymK\nCaqWFSsMTJvm3lG7d287q1aZMRo9tCiBwAs5e1bDgQM63nrLj9Onr3eWlunXT5lL2rVr6aFXTyLL\nytgkq1UiKEiu0rxWQekkJkr07RvC1avF01P8/WWeecbKvHkBNGvmYPNms2o8ahYL3HdfMHv2KMo8\ndqxSpOMrlFZMoIoctUaNGgHQoEEDRowYwd69e4mIiCA1NRVQDLnw8HAAIiMjSUxMLHjtxYsXiYyM\nrPlF1xKqKr4+aJCdZ56xEBAgI0kyt99u4803c2uNkaaGPAO1IGShoFY5NG/uYtQoGxs3mtm2LYvl\ny8089JCVZs2cKGGhfCR27NAzZIiRn36qXHCkKmVx7pyGrVt1vP++Hw88EMSgQSH07RvCnXcaeeKJ\nQA4cUG84S606UV6aNJFZvdpMs2YOt8cbN3YxZ46FFSv8MBhkPvggt1QjzROyCAiARx4p7MkxcGAN\nJGjeADXoROWu7iogNzcXp9OJ0WgkJyeHLVu2MHv2bIYNG8aKFSt4/vnnWbFiBcOHDwdg2LBhjBs3\njmeeeYakpCROnz5Njx49PPwtaoacHCUx+Y8/NGRnS7Rq5aJLFwdBxUfHVTlWq0RcnIN//jOH3Fyl\n+ee+fVouX5Zo0kQu9zgVgbrJyYFjx7RkZEg0a+aibVvx+9Y09eopDVbj4lwMG2YnPd1KRobE5csS\nubkSdrsyucBolImJ8fyUgIQEiW+/NbBggT/Z2cV9AJcvazh+XIdeLxMba1HFhAVvpmdPJ999ZyY5\nWUNGhsSFCxp+/13L3Ln+tGvnZPlyC507e15vrqVrVwft2ztIS9PQsaPjxi/wATwe+jx37hwjRowA\nwOFw8MADDzBz5kwyMjIYPXo0CQkJxdpzzJs3j2XLlqHT6Vi0aBGDBg0q9r7eFPqUZaVKZ+FCf9at\nM1DYw0lmx45sOnWq/pvo9OkBfPRRyTOd6tRx8corFgYOtNOwoTpc6ILK8emnep58UolTBQbKLFtm\nZuBAR7EeYAIBQEYG/PWvwWzdWnr81d9f5umnrYwbl0fTpmKfqGkyMuDcOS1+fsrBWs3RkIQEibw8\nyeeaPJcW+vS4oVZdeJOhduCAlmHDjG5lywB167rYti27Rja9Y8c0jBsXTGJi6WGLkSPzeOutXP60\npwW1lEuXJG67LYTU1EKviL+/zLZt2bRp41sbp6BsmM3w9dcG/vlP/z97LUr4+8s0beoiPt7Orbc6\naNfOScuWLjSqSLgRqJnERMUDePWqhNMp0bq10yf2HlXnqAlKJylJYsKE4GJGmk4ns2KF+YZGWlXF\n19u3d/HttybefTeH2Fg7Gk3xz716VYPNpk6XixryDKobu105NTtvEM24kSw0GopNg7BaJc6e9a7t\nwhd0oqxUVhbBwTB+vI3vv89m//5sfvkli717s/juu2zeesvCiBF2WrdWv5EmdKKQ0mThdCrj0D77\nzMCkSUE89FAQq1YZKt3zMv99Fy7057bbQhg2LISHHjIycWIwCxf64ymXkhp0QmQJeBiHg+vmaly5\nIpGc7L67de9uZ948C3FxNZtfEBUlM3asjWHDbCQna0hPl8jKktDrITRUJjraSb16NbokwZ+kpUnM\nnBnAgQM62rVzMmiQnW7dHLRs6Sp3LlCDBjKPPmpl9mz31vgip0hwI+rWVTz9Au8kOVli+XI/Fi3y\nd2vevGGDgU2bsmnQoGL3pCtXJFavNjBvXkCxw76/v8xf/5rn02kXIvTpIUwm+PFHPR99ZKBfPwcP\nPJBXYhPL7GzYuVPP/v1aIiJkOnVy0qaNQzS8rCCpqYpLvX17Z0GrgLw8yMqSCA2VSx0DpHZyc+GR\nR4LYtMlQ8JheL/O3v1kZN85G69blu3kmJ0u88UYAK1cqAuna1c6KFTk0buyV24VAILgBly5JPPts\nAN9+W3yTbN7cwbp1ZiIjy78/pKRIzJ4dwNq1xd+3QQNlWk3Xrk6fMNREjprKWL9ez8MPFzYVWrHC\nzNChni9F9naOH9cQHx/CM89YeeIJKxaLxPz5AWzdqqdvXzvTp1uJiamdHoHTpzU8+GAQp065u76C\ng2X+7/9yGDzYXq4KYZNJ6QyelwfR0S4aNfLKrUIgEJSBH37QMXp08QqEmBgHq1bllPswmM9XX+mZ\nPNm9wV5YmIsXX7TQv7+Dm26qnftxRRA5aioiKUli+nT3sNK+fdXTW0gN8XU1kC+HoCClV8///V8A\nX35pYPt2PatW+ZGSouGzz/yYODGIlJTaeXRr2dLFp5/mMGiQze1xs1ni0UeDWLHCj5ycsuuE0Qhd\nuji5+WanVxpp4tooRMhCQcihkGtlobSLyTeaZGJj7SxdambdOnOFjTSAmBgXw4bZGDTIxvTpFtas\nMbFjRzaTJtlUYaSpQSdE1okHSE3VkJ7ubiOHhHhoMT5GZKSLwYNtfPWVHx984Mett7r36fntNx2/\n/aalUaOa7d9z+LCWtWsNjBuXR7t2Fd+cmjd38e9/57B/fx6zZgUU6Wwv8dJLAXTo4FR9QrdAIFAf\nnTs72bYtm6tXlbzkxo1dVXLfio11snx5Tpme63KB1arMx/UlhKGmEnr0qB7DoOgsP18mXw46HYwa\npRhqFy9qCQ8vHm4u2paiJjCb4dlnAzh4UM/XX+vZsMFMdHTFjbU6deD22x3Expo5dkzLd9/p2bFD\nj8kkYbFIDBokdALEtVEUIQsFIYdCSpJFkyYyTZp4xruekQEffujP5s16hg2zMXq0rUZyZuPj4zl9\nWmkaXLeuTMOGFetBZzIp1fP16snlPiwLQ80DREW5aNnSUeDtGD8+j7g40YG5pmjb1kn9+i7S0jT4\n+Sn5EJmZhVdOw4Y1627PzJQ4flzRheRkLV98YWDGDGul37dBA2UWZL9+DrKyLNhsEvXre18IU3B9\nblRZLhDUBvbu1TN/fgAAhw/r+P13La+/nktYWOmvkWWlgEynU/bDinD5ssR99yk9RDUamS5dHMyY\nYaVzZ2eZ9tOzZyW++cbAmjV+ZGVJjBqVx6RJeURFlX09IgjiASIiZFauzOHVV3NZscLMrFmWagt9\nqiG+Xh2kp5evr1dROTRtKvPqqxYAFi3y54UXLPTsaSc01MXjj1vp2rVmjWaXS8JR5COXLvWr8jy5\n0FBlo5KkG+tEdrbSZHn3bh1HjmjIzq7SpagGb702AK5ehe3bdTz2WCDDhwfz2mv+HD1aeh6sN8ui\nPAg5FKI2WZw65b7fr1njx7Fjpev0uXMS//qXH/HxITz3XOAN+0uWxsmTOxkzRsn7dbkk9u/Xc//9\nRh54IIhDh7Rue/e1nDihYcQII6+8EsiJE1qSkzUsWhTA/v3lOzmJc1Y1Y7XCwYM6srOhdWtXQXJk\n69YuWrfOu8GrBSWRmioxbVogu3fr+fJLE927l/8KjI+307ixi+RkDS++GMisWbksWWInIqLmW3SE\nhblo0cLF778rm87lyxqSkzU0auSZOXxLlvjx+uv5SSAynTsrJ8hu3cp2ghR4FqsVlizxZ8GCgILH\nfv5Zz9KlfmzebKpU4reg5rHb4cwZpW9l8+a+W30dFVVcby9e1ALF98mDB7WMGRNMWlqhcVfR9h6S\nBA8/nMexY1o2bixsf7Rvn55Bg3QsWZLDkCF2DAb319lssGBBQInTfPz8yvcbCo9aNXP6tIa77w5m\n3DgjgwYZ2bu3eqo7S8Mbcy727tXx3XcGzGaJf/wjgJwy5KFeK4eoKJmFC5UXOp0Sr74ayKVLGo/0\nUQsJgZEj3Ss109Kqr/L0RjrhPpVA4tAhPePGGXniiSASE2tnRWxJeOO1AZCQoOGtt4rP5c3K0pCU\nVPKW762yKC9qk8OpUxqefz6APn1CGDo0hH37as63ojZZdOjgxGh0N3C02uIGz4EDWkaMMLoZaRMn\n5lW4iCo+Pp5GjWQWLMjl2WctSFLhZzocEo88EsTOncV/l5wc+O234vf7Pn3s5W5WLwy1aiYrSyJ/\niHpamuIGPXKkZsWel6ecyLwBhwOWLSs8uuzapSMxsWLfrVcvB3femW8gSXzzTekDpaubPn3sQOEG\ncO0Ip5pk5Eg7sbHF/fnff69nwYIALJayvY/NpvSt+/57Hd99p+PAAS0mU+XX53TeeEyWLxMYKBMR\nUdz70Lixs9b2CFQLaWkSR49qSE2t/gPLvn1a7r7byPLl/jgcyueFhvqmNw2gVSsXn31mok4dRYcb\nN3bRpYv7PnXihIYxY4IxmQp/n0GDbHTsWPl0lshImenTrWzebKJ//8IiNJdLabd17eE6LAwWLMgl\nJMT1598u/v73XN57L6fcXlHvuHurmEaNZIKCCn8Ui0XipZcCq+SGVRZ27dpFUpKGu+4ylmjd1zay\ns+HChaLfQyIv78abZkn5FqGh8NJLFkJDlQvp44/9POYx6tDBydNP5xcQyNUaYrxR7kl0tItly3KY\nOtWCTue+ji+/NLidVEsjKUlizpwA+vYN4f77jYwda2TgwBDmzQvg6tWKrdtuh82bdQwfHsxjjwVW\n+sCjthycqiIqSuazz8wMHmwjNNRFgwYunnrKwpdfmmnWrGRDzVtlUV5Kk4PFArt3axkxIpi+fUPZ\nvbt6PVu//FLcKxQfb68Sg6OsqFEnbr7ZydatJjZuzGbDBhMxMYX7U1YWvPRSoFvrq1atHMybd/2C\ngxtRVA5+ftC9u5Nly8xs2pTNO+/kMHGilWeftaLXF9+zBwxwsGtXNnv2ZLFrVzZTp+ZVqFJV5KhV\nM82bu5g61crcuYX5Irt26Th1SkvXrjXjFsjMlLhyRcMrrwSwdKm5VvdsczoltxlzULmKtnbtlBEl\nw4cbycrSkJCgoUmTkn+X33/XsHWrnuHDbRUalXI9AgPhr3/NIzJSJjhYpk0bz7qMbrrJxcyZVkaN\nsnHkiI4jR7S4XDB4sL1MVbGff27g/feLh9+WLPFn3Li8glNxefjf/7SMHx+My6X8/t99Z+Cbb0x0\n6iTca9fSoYOLjz7KIT1dQpKUQhJPemlrM7m5sHatgalTA8mPjuir0fl++rTiFcrNLdzn6tVz8frr\nuV45OtDhUIrD8vIk/P1lwsJkN/mazRSM+wNlb7rppuLvc/y4lu3bC1/YurWDlStzuOmmqj/0hoRA\nz55OevZ0Mm7c9Z+rVHdWbg3CUKtmJAnuvz+P777TsX9/vhJJpKfXjOcmPj6ew4cVJdm6Vc/vv2vp\n0aP23tiUC9lVMKjez08ulrdQEtfLt+jZ08mKFWYmTgwmO1tDScmpSUkSY8cGc+GCFn9/mUmTbMXf\nqJI0aiTzyCPVX2BS1twTvR7atnXRtq2N++8v+/s7nZRa1RQX56hwMvS5c5oCIw3AZJL48kt9hQ01\nteXgVDUGA2WWdVFZZGTA1asSCu23lwAAIABJREFU4eGy2w3SF7hWJxwO2LBB72akBQfLtG9fPZ4t\nWYavvzb8uQ8pRES4+PxzE+3b12zYuiauj99+07BgQQAHDui4ckWiQQOZli2dDBlip317B3o9zJrl\nz5IluTRvfn1dPnMm/yQiM3q0jeees9K8eeVlpoZ9QoQ+a4CoKJmlS3N4+GErkqSEQkuqYKkuAgqd\neaxY4UdeLS42NRrhL38p/AKPPmolMrJystRqYdAgB1u3ZtOiRck3/V9/1RWEXP/7X0OFZJiWJvHb\nb4rXzpvRauHlly106VKYx+HvLzN1qoUPPzRXOKwbElL8dfv26a5bHi8oO3a7EnIbNSqYbt1C+eGH\nqnMbpaZKbNyo45dftJjNVfa21c6+fVqeeCKIfCMNYM6cGxsNFeXqVfjii8Ic3P797axfb6JTJ+/M\nLdy+Xc+33xpITdXgdEqkpmrYuVPPCy8EMnRoCHPmBDBqlKPUIpiixMY6WLQoh82bTSxcmFslRppa\n8O47hopo0kRm7lwLP/+czY4d2ZUaE1Qedu3aRWCgXBA/X7PGUOsNhdtuc9C1q4P27R2MH28rU0jn\nRvkWGg20b++iZcviv4vDoYTy8vnjDy1Xr5bPI5qUJDF6dDB9+oTSu3cI//qXHxcveiYfriZyT9q2\ndfHFF2b27Mli+/Ys9uzJ5qWXrJW6wbVr56RpU3dDesAAR4VD32rMwfEUu3bt4qefdNx9t5FDh/SA\nxM8/V13A5dQpDePHG7nrLqWnVXl6INYkRXXi8mWJqVMDcToLr9P7789j+HBbhVs93IjgYHjttVzm\nz89l06Zsli41l7gn1QQ1cX2MGGHjscesaDQl7wu//KLnX//yx794FkUxOnZ08eCDNnr0cBIUVHVr\nVMM+IUKfNUhAAB7pYVSvnkyHDg4OHdLjdEqcO6fx2MVfFURHK3llAOHh1V8FlZYmcfBg4aViNMoY\nDOX73CtXJA4fVt7DZFLagWzapGfp0pxydaiuTYSFKZVOVUWTJjJr1ph57bUAfv1VR9++dkaNqsXu\nYRVx/ryG558PdgstV+VYu6KzGT/7zI+zZzX85z85HhtHVBZ+/11bZFYuDB5s46WXLNWaJ6bXwx13\nOADfcBNHRcn8/e8WRo2ysXevjq+/1nPsmK6gajMszMXdd9sICKi996uqQBhqXk5+fP3uu+1/npQV\nd7OyGdReymugVSbPIDcXt5zCJk2c5Z711qCBTIMGLq5cKfQk7NunZ8UKP154wVrhRO/z5yUaNpTL\ndOLMRw05FxWlVSsXH3yQQ1aWREiI7BbWLy+1WQ5VidkM33wzEIulUMeNRpmOHasul7V5c/exeXv3\n6nnjjQDmzs1VVXFTUZ24dEmRh1artGV48MG8Ki8iUjM1dX34+UFcnJO4OCcPPphHYqKGTZv0WK0S\nWVkS589LHj3MqmGfUKf/WVDltG9fuOmuW2fg8uXSffdnzkjs2KHj/HmhHgA2W2EvPFBCr+UNt0VG\nyvz73zlcW/3z/vv+FR4XdfSolr59Q1m3To/Lhw6c/v7KGLbKGGmCQi5e1FyTjybzzjs5Ver9r1tX\nZsECC0X1/5NP/NizR72+gk6dlDYMP/xgYvp0q08ZaZ4iIABSUzW88kogCxYE8P77/gwZ4qBOHU+v\nzLOIO7GXkx9fb9rUVZAHkJqqKTgtXsuhQ1r69w9l5EgjQ4cGF5uvVt04HEoY5uxZDdbKzyUvoDJ5\nBiEhcpF2EjLdu1fMG3nLLQ4+/dRc0LcNFNf+taNHysrWrUqIYNq0oHI1NC6PLE6d0rB+vZ5PPjGw\nZYuuRhp91hRqyD1RA5mZErL8459/ybzyisWtoWdV0bOngxdfdL+oFy3yr7GekmWhqE60bu1i+HA7\nsbHOam3HoVY8dX1s3VpovPv7V3y/rSrUsE+o9zgjqFKaNnXRrZuDvXuVHSc5WUPHju4n5qwsePnl\ngIL8gKQkLT/9pKNVq6pvRVESly9LfP65gXnzAnA44LnnrDz+uLVKE0MrQni4zJAhdj75xI8hQ2xu\n3sny4O8Pd97pYPt2EydOaMjNlWjXzlmhPLvcXPj2W+W3tFoljhzRVnne4bZtOiZOdO/yPXJkHm++\nWbkGkoKaJT0dduzQs3mzgexspe9gmzZOOnVy0qiRizp1ZDp2dFCnjp3p06106eKolmsuIEAZ5ZOa\nKrFsmRKr/+UXHampGoxGH3IJC0rFZlN0Ip+nnrLSooXQDUmWZa/0527dupUuXbp4ehmq4uOPDUyZ\nouzACxfmMHGiuwF28qSGm28OoWiY77778vjgg9xqX5sswzvv+DF7dmDRR/nhBxNduni+79uZMxp+\n/FHHgAGOUru71yRXrkjcdltIQT+5SZOsvPlmGWc7lYGzZzX06RPi1nQzn59/zqJNG8/LQFA2UlMl\nJk0KYs+ekt1C9es7eeYZK7fc4uCmm1zlzr8sLxkZsGePnpdfDsDphE2bTBXq1i7wPtLTJQYMMJKQ\noKVFCwdffJGjiv22pjh48CADBgwo9rjwqPkQXbo40OlkHA6pxL40isnufmOOjq6Zi+TiRYm33ro2\n6Ugq08D1miAmxkVMTM14FsuCTicTEFB4czt8WIfVSrmKCq6HyUSJRlqrVg7q1RM31dpEw4ZKfuS6\ndQbeeCOAnBz33zUtTcuLLyoHuNtvtzFnjqVa2wfVrQtDhtjp1cuBw6HkGwoEAEFBMq1bO8nLk1i6\n1LeMtOshctS8nKLx9VatXDz0kNLOoKRB5uHhMq1aFc0HkLnjjqrPVSkJs1lyC7GBUnnWtGnVbOJq\nyDOoSoKCoH79wk3s6lWpzMPSyyKL6GgXjz3m/obdutlZtiyHBg2848bqbTpxPZo2lXnyyTy2bcvm\n/fdzGDjQhp9f0d9xBwA//GBg5EgjFy5U/62hXj1ZdUaaL+nEjfCELPz94bXXLGzebCqWmuMp1KAT\nwqPmQ+j1MH68jeXL/f6sZHSnbl2ZJUtymTQpEJNJw+uv59KhQ82EHRs1cnHrrXZ271bCMzqdzJIl\npQ+R9nUMBqWk/ddfFXnl5fFnY86qufGFhsLzz1sZOdLO1asSwcEyMTGuah0WL6heJAlatnTRsqWN\n4cNtJCUpRUWXL2v45RcrMTE5GAwQE+OkXj1x3Qk8Q23u8VldiBw1H8Nmg1WrDMgypc6rvHJFwulU\nQiY1ydmzEjt36snOloiPd9Cpk1MMkr4OGzfqGT9eGcbYr5+Nzz/P8cnqNIHgetjtkJIicfWqhMGg\nVHGHh8sVnmghEFQXIkdNACiemNGjbZjNpbdZ8FRoq3lzmebN1ZMHpnbat3dSp46Lq1c1DBliF0aa\nQHANFy9KLF7szyef+BU09A0NddG3r4O//c1Kp05Ot6kJAoEaETlqXk5J8fXg4Jr3lnkaNeQZVDXN\nmrlYtiyHjh0d9O1b9l5DtUUWeXlK9elvv5Xe968y1BY51AS1URYmE5w7d33dOHlSy4cf+rtNXcjK\n0rB+vYG77jKyerUBR5FLpzbKoboQslBQgxyEoSYQ1GL69nXw9dcmr+s1dPGixJw5AfTqFUKfPqHc\ndVcwx46J7UqgtPf45hs9Q4cG0717CLffHlJqY+727Z0MGVLaPFiJOXMCvaqJs8A7ETlqAoFAVeTk\nwLRpgaxd6+f2+KBBNlauFHl4vkxCgobZs/1Zt85dN77/PpuuXUsufMrMhIMHdaxda2DXLj2XLkno\ndNC1q4OZMy307ClyYQXqQOSoCQSCWkFysoa1a4vP1bJaQSOcaj7LpUsSjzwSyL597pb6rbfauemm\n0qvTw8JgwAAH/fs7SE+X/uwPqBQUVFXfQYGgOhHbnpejhvi6GhByKEQtssjNpcR5rvmVeUWRJJmn\nn86rUs+HWuSgBmqDLHbt0hUz0sLDXcyfb6Fu3Ru/XpKgfn2Zpk1dNG1aspFWG+RQUwhZKJRHDmlp\nEhkZVR9KF4aaQCCoURITJd59148hQ4zcc08wX36pJy2tcHNr1szF6tVmWrRw4ucn06GDg6++MhMf\n79nhzALP8sMP7kZa37521q83VXj2rkDdZGbCnj1ajh6tHXHp1FSJ4cODGTjQyNdf60lPrzqDTeSo\nCQSCGiM3F2bNCmTFCvcco1mzcpk2Lc8ttJmZCTk5EkajTGhoDS9UoDr27dPy3nv+NGrkon9/O126\nOMrkSRPUPs6c0fDKK/5s2ODHlCkWZs8uwfWuMs6c0dC9e+Gs7LFj85g920J4eNlNLJGjJhCoAJtN\nmRAh+WihWXq6xKefFs8/W7w4gDFjbERGFm5qYWEQFuaV50hBBeje3clHH6lk+K+g2jhxQsN99xlJ\nSVFObbXFYxoe7qJbNwf79yue39Wr/YiIcDF9upWgoMq9twh9ejkiz0BBDXLYtUvH3XcbmTUrgIMH\ntW79m2p2HZ6TRb16Mn36FJ8f26SJs8YTu9WgE2pByELhenLIylIOWr6CJ3Ti7FmJCROCCoy0wECZ\nuLjSDbWSclyrmrLKwWiEqVPdW8H861/+7NlTeX+YMNQEghuQmYlbDlVF+fJLPfv363j/fX8GDTKy\nfr2+zIPUvYXAQJg3z8JttxUaa82aOXjvvRzq1RPeM4H6cDiUa/fOO0MYMyaYH37QkZlZM5+dmQmH\nDytNn/NKawfnJaSnS7z8ciB//FFo2Dz3nIWYGBcJCRInTxaaK1lZsHatnuHDg1m3To9LJW0kb7nF\nzqhRRX8oiZdfDqi0vogcNYGgFGw22LFDx8svB2KxwAMP2HjggTyioip2yXzyiYGnnirqA5f55BMz\nd97p8LlQqMkEFy5ocLmUKRnlyeMQCGqSy5cl+vcPITm50FAYOzaPl16y0KhR9eltUpLEc88FsmmT\nAUmS+fe/c7jvPrtXtqiRZVi50sC0aYX7Y7dudlauzEGrhUmTgjhxQsvGjSaaN3fxyScGpk5Vnuvv\nL/Pzz9lER6vDWktI0DB5cmBBCBRg69ZsOne+cQi3tBw1L/zJBYKq4cgRLWPHBnP6tJaLF7UsWBDA\nO+/4k5tbsffr1s2B0Vh0Y5eYNCm41K7q3ozRCB06uOjUySWMNIHqcLkouM6Dg2VatXK/ya5e7cfy\n5X7VGnr7738NbNqk5HPKssS0aUGcP++de8WZMxpmzSoculqnjot//SuXhg1lTp7UsmuXnvR0DQcO\n6Pj9d4lnny18rtUqVXhPrg6aNnXx/vu5/OUvVkDZ2yrr8fPOX72cpKVJ2IunzXgFIvdEoSJySEzU\nIMvurq4PP/RzO1mXh9atXaxcaUarLTRMrFapxsvPq0In0tPhxx91rF5t4Kuv9Bw7psFZO3J+CxDX\nRiFCFooH69139zB/vj/33x/EXXcZefNNP/LyYOZMi9t1C/Dmm/6cPl09t9CMDFi2zL0y2mKRMJur\n5eNKpCZ1Yv9+3Z+NiMFgkPn0UzPt2rn+XEdhKHTtWj0XLmhxOAr35YAAuVjfxaqkInJo3tzFq69a\n+OEHE998k13M0C8vPl/1ef68hkmTApk/30L37rXsTiOoVkrKmdJqQVeJq+bWWx2sWWPmwQeDCzam\ny5dr13nJbIZ//tOf994LKHjMYJBZvDiH4cPtGIoXdQoEquX0aQ07duh5801/0tICgUK9jolxYjBA\nXJyTDz/M4dFHg7Db840EiYwMDVD1ITdZlop5YYKCvLNNjcsFa9YoYcKoKCfLluW4jQM7dKjwIJuY\nqOXsWfeD7ahReTRsqD6vfGAgdOlSNTaFzxtq27bpOHRIz8qVLrp1y/W6XKH4+Phq/4wzZzTs3Knj\n/HkNDz5oIyZGHbkCRamIHOLiHDzyiJX//Ce/HFHm73+3EBlZ8e+n08FttznYti2bAwd0JCVp6N+/\nZt25ldWJlBQN773nXqJps0k88UQQnTpl06aN+n7/kqiJa6O24IuyyMmB7dv1PPZYEDk5+Rt/v4L/\nv+MOGy+9ZClorXD33Xa2bDGxcqWB77/X07Wr87qjqypD3boy48bZmD+/0Gj8xz9yadKk5q6tmtIJ\njQaGDbMzdKidfv0c3HRT4Xe0WiEtrfAgm5cHRdPqAwJkJk2yVerwfCPUcG34tKGWmQkffKC4l3fv\nVip5RAPFsuNwKOGvSZOCyM5WLqa+fR2qNNQqQkiIEvIYOtTGpUsaGjd20amTs0qGgrdq5aJVq9pZ\n61+3rkzLlk5On3bfPpxOqcgNTyBQL7m5yt7/j38EkN+gNJ/QUBezZ1sYMsROgwaFRoFWC7GxTt58\n00JGhpWQELnavMeSBA89lEdwsMy+fTqGD7fRt693FhIAPPxwyXuhJLnP9w0KosDbFhQks2KFmY4d\n1RsJu3xZIjtbws9PpkGDis+W9dKfvWwkJmo4dUq52SQkaMjKqt3iyMyEo0c1nD6tKci5q648A1lW\nvJFjxgQXGGk6nUzDhuo00ioqhzp1ID7eyb332rn5ZmelGxeqgcrqRL16MkuX5hAXV7QRnMyMGZZK\n52LUJCIvqxBfk8XJk9prjDSZ2FgHzzyziW3bTDz8sM3NSCuKRqPMDK3uEH/DhjKPP57HRx/lcM89\ndurUqd7PuxY16IQy97fwnhIR4SQuzsnWrdns2JFN//7V34yyInJITZVYvtxA//4h9OgRSs+eoUyZ\nEsjZsxU7yPq0R03JL1BwuSRqc6OS//1Pw/TpgRw8qEevl3nzzVzGjas+j83Bg1oefjgYp7NQ8R58\nMI8WLdRpqNVmUlMlfvlFx7FjWrRaJSTbsqWT6Gi5SoeUl4cOHVysWWPmzBkNubkSdeu6aNHC5RWG\nrMD7iYx08cUXZrKzlRFl9evLREc7+e0399BbdZKbqxx4a+qacbmUtji1Kc9NkpSQ8/btilV87712\nAgMpU6sLT2G3w3vv+fPOO4XuM6tV4osv/NBq4e23c8u9b/u0oZadXdS69dxNr7ykpEhkZEhERys3\nxjNnJO6911hgeNrtErNmBdKvn71a4uuZmTBjRgBWa6H8mjZ1cPPNDo4d09K+fdWEB6sSNeQZVJSl\nS/1YuDDA7bGAAJnZs3MZNcpGWFj53q+qZFG/vkz9+urdMG9EbdaJqsbXZBEeLjNgQHFvTE3IwW6H\nn3/WMW+eP04nLFxoITa2eq+jpCSJ//zHj+3b9Xz0kZnmzW/slVCLTsTFOZEkGZ2Oa7z4NUN55XDl\nisTKlSW7WzUaKuQQqt2xvkpS1NAIDZUxGNTvUjt8WMuddxrp3TuEffsUO3v/fr2bdxCUzeDa1hJV\nxcmTWg4fLrTEGjZ08fjjNp54IoiBA428844fGRnV8tE+SUknfItF4oUXglixwk81XbkFAsGN2b5d\nx733BrNvn56DB/W88EIAJlP1fV5amsQrrwSweHEAR4/qOH68lngk/qRdOyerVplZs8ZcKwqV6teX\nee65wh5q+bRq5eDJJ60VKnzwaUOtaN+nJk1c1dqLpSo4flzDPfcYSUzUAhL/+59ywZXUW+epp6w0\nbuyqljyDq1cLDcCePe08/bSVOXMCsNslnE6Jf/wjkA8+8CdHRfOT1ZBvUVFuv93OlCklz5p6/31/\nrlwpn0Fem2VRlQg5FCJkoVDdcrh4UeLJJ4NwuQqv2fPntQWteqqDAwe0rF1b2JOt6GdfD7XohJ8f\nDB7soG9fh0eiXuWVg8GgFIJs2mTi/fdzWLQoh6++MrFuXcUNTZ8OfRatJunQQd2J4rm5StzbZCq8\nyMLCFMOye3cnRqP85//JjB5t46GH8qot/NiunZNly8zUry8TGelk48biH/TGG/7cdZeNTp3UfwJS\nO+HhMs88Y2XQIDtbtuhZv97AlSsamjZ18ve/W0pNehYIboTLhaoOVN7OxYsat3YTADff7KB+/eq5\nhrOyYMEC91JDtTskvIHgYOjZ00nPnlUT0vbpWZ8//KBj9GgjAJ98YmLw4JqPf5eVI0c03HZbiFs4\nc8OGbG65RVGEP/7QcOGChrAwpXWC0Vhza3O5lM/ft0/Ht9/qSUjQEBfn5NlnraqZv1Ybsdngt9+0\nhIe73OaLZmZCbq5ESIhco7+zoPZiMkFmpobAQCVxPicHDh/WsWKFgWPHdEycaGXMGBvBwZ5eqXez\ne7eWoUNDCv6WJJmNG01VdkO/lsOHtfTvbyS/utVolNm5M5umTcW+rEZKm/Xp0x61iAgXoPQ2qUi1\nYkqKxJ49OvR66NLFQWRk9dm8Z85o3Yy0zp0dtGlTeHG3aOHyWMWlRlPYF2zcOBs5OeDvX7kO/gIl\nt2TECCOhoS5WrTIXeCfDwgq9qQLB9cjOhl279Lzxhh/HjumIinLx4YdmNmwwsGhRYYHKc88F0r+/\nneBgoVfVScuWLrp1s7N/v57AQJklS3KqtYIxJUWiaJ+4KVOsNdo0V1A1+HSO2k03ufjLX/JYuDC3\n3E1ac3Nh7twAJk8OZsKEYB57LIjLl6svz6BoyFOSZObOzS1Tc96azjOQJMXtqzYjTS35FtfjxAkN\nb7/txxtv+LNnjw6QCQ6WuXhRy4gRRg4frpoEjdogi5rA2+VgscCKFX6MHx/MkSN6nE4Jf3+KGWkA\n9etvV3XqR01R3ToRHi7z0Uc5bN6s9AG7667qHblWtNCobl0XQ4bYyjx9x9uvj7KiBjn4tKEWHAyz\nZlkYPtxW7o7PSUkaVq8uvMJ27dJz4MCNrRO7XUnu3LhRT3p62T8vf2yRn5/Mxx9X/hSWmQnff6/j\n1CmfVgHVcPGi0mJl9uxA5s8PYMiQYL7+2o/HHlOKCDIzNTz8cBAJCeL3qkry8hSvQ3VW3XmKkye1\nzJ7tbpDde6+Nd9+9tj26zOOPW4mIEN60miAyUqZHDyctWriqfWRhZKSMRiNTp46Lzz8307q18KbV\nRnx+1w8Lg4CAGz/vWqzW4u0vfvjh+oaawwHffadn0CDjn6fcsrudunRxsG6diW3bsrnzTjt+fjd+\nDZTeA2bDBgP332/k7ruN/PGH96tBVfYEysyEXbt0fPSRgXff9ePnn7VYrZV7z0uXNKSmaoiIcBEX\n56BePZmXXw6gXbvCjTUhQctHHxkq/Vlq6Y/kaeLj4/nvfw3ccksId99tZMkSP44f19TqxtdFUfpE\nuu9RsizjcBQ+ptHILFqUy6OP3lzDq1Mn3nZttGvnZMsWEz/8YHIbdF4WvE0WFUUNclBZgKr2ULeu\nckq5erXQyLmRV+7oUS0TJxaWZpenrUJYGPTuXTXFDpmZ8Pbbyqk6LU3D2rUGnn/eqpqB9BYLHD+u\nxWyW6NTJUe6GrtVJQoLEa68FuJW7g8wXX5hLbKBZVsLCXDz/vIWsLIlz5zR07+6gcWMXkiTTr5+N\nHTsU7+3ixf4MHWqnS5fa22hWTQQFyWRlaTh6VMPMmTr8/WXmzLEwbJiNhg1rt8XWooWTYcPyWL/e\nD0mS6dnTQf/+dpKTrezapadfPztjx9ro2FF9Dap9jSNHtBw8qCUkRKZrVyfNmlWN58tgQOwVXoD3\nu1KqichImddec+9t1bdv6Tdqmw1WrjS4jVyqic2xpPj61auSmxftk0/8SE9Xh5Umy/DNN3oGDjQy\nYoSRt94KIDe38u9bVXkGK1b4XWOkAUicP3/jSykzk1LzGJs3l7Hblb5o331n4D//8eeVVwJ55ZVA\nZsywUqeOstnKssSbb/pXKlSnhpwLNbBr1y569nQweHDhqDWrVeKFFwJ56KEgTpyo3dtj48Yyixfn\nsnt3Fr/8ks1nn5np2tXFW29Z2LIlmzfesNCli2KkCZ1Q8IQcLlzQMHx4MM88E8TkycEMHmzk6FHP\n657QCQU1yMHz2lBBNm/eTJs2bWjZsiULFizwyBoGD7bx7rtmune3M3duLjffbC/1uQkJGlavdr/B\n10TriqNHjxZ7TKdzT/ZPSpLcmth6kgsXNMyYEUR+yObf//bj7NnKq2lJcigvJhNs2lQ889dgkG8Y\nVkhPl5gwIZj+/UP4/POS8xNLyjs8ckTH2LHBvPNOobX63Xf6MhmGpVEVsvAGjh49Sni4zLx5Fvr1\nc7929+/XM3p0cK1PCwgJgbZtXbRs6SLkz64QWq3ioS/qQVezTiQlSezcqeXAAS1ZWdX7WZ6Qw6VL\nkltkJjVVw6OPBpW7kXVVo2adqEnUIIdauQs5nU6efPJJNm/ezPHjx1m9ejUnTpyo8XWEhcHYsXbW\nrTPz2GN51KtX+nMTEzXYbIUX3s0322nevPpd0tnZ2cUeCw6Wr3GtS27jtDxJQoLkVuEKEleuVF5N\nS5JDeTEaYdo0C5JUGBKLjnawfr2JTp2u/1smJ0vs2qUnOVnDY48F8847xSc39Opl5+mni08gyM7W\ncO6clt69840JidOnK14BWhWy8Aby5dCsmYslS3KYPz/XbYxcUpKWl14KoDaIy2xWDJoLFzT88YeG\n33/XcPy4hhMnlH//8YeG5GSpVO+0WnXi0CEtgwaFcM89IQwcGMLcuQHVaqx5Qg716skEBbmH2U+e\n9Hyhl1p1oqZRgxxqZY7a3r17adGiBdHR0QCMGTOGdevW0bZtW4+sx//aIqoSsLsd2GVeeMFCaGh1\nrej6hIXBoEF23ntPudnr9TIBAerIxykaGs5Hr1fH2gDuucdO69bZpKVpCAqSiY52lalaLjgYtFq5\n4PstWuRPfLzDLa+tXj149lkrffo4eP11/z+riCUCAmQ6dHAyZEgef/tbMHv36jlxQguU7sEVlI8G\nDWQmT87j1lvtLFvmx5o1fuTkSHz/vZ7LlzWEhKirWi49XeLkSQ3nz2vZt0/Lvn06LlzQ/mn8l3zo\nCg110ayZi86dHfTp46BTJwcxMeq5tq7lyhWJRx4JJDm50GD58EN/7r/fVu7EeDXTvLmLv/89l+ef\nd++PUrToQ+Db1EpDLSkpiSZNmhT8HRUVxa+//urBFd0YZUSIsikuXJhLt241s9EkJCSU+PiYMXl8\n+KEfNpvE7bfbC9p/eJqGDV1oNHJBwUXduq4qSawtTQ7lxWDgz8az5VtTeLiLO+6wFwmdSjz3XAAb\nNphp1KjwZhkcDP37O+hv0Gw9AAAL6klEQVTa1czlyxqysiTq1JGJiVFK+T/8MIetW/W0aFFx/akq\nWdR2rpWDRgPt27tYsMDC00/nkZKi9B1TW4PQy5clnn46kC1byteAKytLw5EjGo4c0fHppzIzZ1p4\n9NE8AgPVqROJiRrOni1+i6qKnNXS8IQcJAnuu8+GVgsvvxyIxSLRtau9Utd4VaBGnfAEapBDrRwh\n9eWXX7J582b+85//ALBq1Sp+/fVX3n777YLnbN261VPLEwgEAoFAICg3XjNCKjIyksTExIK/ExMT\niYqKcntOSV9WIBAIBAKBoDZRK4sJunXrxunTpzl//jw2m43PP/+cYcOGeXpZAoFAIBAIBFVKrfSo\n6XQ63nnnHQYNGoTT6WTSpEkeKyQQCAQCgUAgqC5qpUcNYPDgwZw8eZI//viDmTNnFjyuhv5qNUl0\ndDSdOnWic+fO9OjRA4CMjAwGDhxIq1atuOOOO7h69WrB819//XVatmxJmzZt2LJli6eWXSX85S9/\nISIigo4dOxY8VpHvfuDAATp27EjLli2ZMmVKjX6HqqAkOcyZM4eoqCg6d+5M586d2bRpU8H/easc\nEhMTue2222jfvj0dOnRg8eLFgG/qRGmy8DW9sFqt9OzZk7i4ONq1a1dwr/BFnShNFr6mE/k4nU46\nd+7M0KFDAZXrhOxFOBwOOSYmRj537pxss9nk2NhY+fjx455eVrUSHR0tp6enuz02Y8YMecGCBbIs\ny/L8+fPl559/XpZlWT527JgcGxsr22w2+dy5c3JMTIzsdDprfM1VxU8//SQfPHhQ7tChQ8Fj5fnu\nLpdLlmVZ7t69u/zrr7/KsizLgwcPljdt2lTD36RylCSHOXPmyAsXLiz2XG+WQ0pKinzo0CFZlmXZ\nZDLJrVq1ko8fP+6TOlGaLHxRL3JycmRZlmW73S737NlT3rlzp0/qhCyXLAtf1AlZluWFCxfK48aN\nk4cOHSrLsrrvHbXWo1YSRfur6fX6gv5q3o58TeHu+vXrmTBhAgATJkzg66+/BmDdunWMHTsWvV5P\ndHQ0LVq0YO/evTW+3qqid+/ehF0zCLQ83/3XX38lJSUFk8lU4I186KGHCl5TWyhJDlBcL8C75dCw\nYUPi4uIACA4Opm3btiQlJfmkTpQmC/A9vQgMDATAZrPhdDoJCwvzSZ2AkmUBvqcTFy9eZOPGjUye\nPLngu6tZJ7zKUCupv1r+5uStSJLE7bffTrdu3QralVy6dImIiAgAIiIiuHTpEgDJyclu1bHeKJ/y\nfvdrH4+MjPQambz99tvExsYyadKkAje+r8jh/PnzHDp0iJ49e/q8TuTLolevXoDv6YXL5SIuLo6I\niIiCcLCv6kRJsgDf04lp06bx5ptvotEUmkBq1gmvMtQkyfc6Oe/evZtDhw6xadMm3n33XXbu3On2\n/5IkXVcu3iyzG313b+axxx7j3LlzHD58mEaNGjF9+nRPL6nGMJvN3HvvvSxatAij0ej2f76mE2az\nmfvuu49FixYRHBzsk3qh0Wg4fPgwFy9e5KeffmL79u1u/+9LOnGtLHbs2OFzOrFhwwbCw8Pp3Llz\niZ5EUJ9OeJWhVpb+at5Go0aNAGjQoAEjRoxg7969REREkJqaCkBKSgrh4eFAcflcvHiRyMjIml90\nNVKe7x4VFUVkZCQXL150e9wbZBIeHl6w2UyePLkgxO3tcrDb7dx77708+OCDDB8+HPBdnciXxfjx\n4wtk4at6ARAaGsqQIUM4cOCAz+pEPvmy2L9/v8/pxM8//8z69eu56aabGDt2LNu2bePBBx9UtU54\nlaHma/3VcnNzMZlMAOTk5LBlyxY6duzIsGHDWLFiBQArVqwo2KSHDRvGZ599hs1m49y5c5w+fbog\nvu4tlPe7N2zYkJCQEH799VdkWebjjz8ueE1tJiUlpeDf//3vfwsqQr1ZDrIsM2nSJNq1a8fUqVML\nHvdFnShNFr6mF2lpaQWhPIvFwvfff0/nzp19UidKk0W+cQK+oRPz5s0jMTGRc+fO8dlnn9G/f38+\n/vhjdetEtZQoeJCNGzfKrVq1kmNiYuR58+Z5ejnVytmzZ+XY2Fg5NjZWbt++fcH3TU9PlwcMGCC3\nbNlSHjhwoJyZmVnwmrlz58oxMTFy69at5c2bN3tq6VXCmDFj5EaNGsl6vV6OioqSly1bVqHvvn//\nfrlDhw5yTEyM/NRTT3niq1SKa+WwdOlS+cEHH5Q7duwod+rUSb7nnnvk1NTUgud7qxx27twpS5Ik\nx8bGynFxcXJcXJy8adMmn9SJkmSxceNGn9OLI0eOyJ07d5ZjY2Pljh07ym+88YYsyxXbI2uzHGS5\ndFn4mk4UZceOHQVVn2rWiVo561MgEAgEAoHAF/Cq0KdAIBAIBAKBNyEMNYFAIBAIBAKVIgw1gUAg\nEAgEApUiDDWBQCAQCAQClSIMNYFAIKggCQkJGI3GUhtnAhiNRs6fP19zixIIBF6FMNQEAoGggjRt\n2hSTyVTQxbxfv34sXbrU7Tkmk4no6GgPrE4gEHgDwlATCASCKkJNY2cEAoF3IAw1gUBQazlz5gz1\n6tXj0KFDgDJAuUGDBvz000/Fnrt8+XJuvfVWnnrqKerUqUPbtm3Ztm1bwf8nJyczbNgw6tWrR8uW\nLfnwww8L/m/v3r1069aN0NBQGjZsWDAP8fz582g0GpxOJ7NmzWLnzp08+eSTGI1Gnn76aUCZr3j2\n7FkAsrKyeOihhwgPDyc6Opq5c+cWhE2XL19OfHw8M2bMoG7dujRv3pzNmzdXj+AEAkGtQRhqAoGg\n1hITE8OCBQsYP348FouFiRMnMnHiRPr06VPi8/fu3UuLFi1IT0/nlVdeYeTIkQVjdcaMGUPTpk1J\nSUlh7dq1vPjiiwUDvKdMmcK0adPIysri7NmzjB492u19JUli7ty59O7dm3fffReTycTixYuLff5T\nTz2FyWTi3Llz/Pjjj6xcuZKPPvrIbX1t2rQhPT2d5557jkmTJlWVqAQCQS1FGGoCgaBWM3nyZFq0\naEGPHj24dOkSc+fOLfW54eHhTJkyBa1Wy+jRo2ndujUbNmwgMTGRn3/+mQULFmAwGIiNjWXy5Mms\nXLkSAIPBwOnTp0lLSyMwMJCePXuW+hmlFRY4nU4+//xzXn/9dYKCgmjWrBnTp0/n448/LnhOs2bN\nmDRpEpIk8dBDD5GSksLly5crKBmBQOANCENNIBDUeiZPnsyxY8d46qmn0Ov17Ny5E6PRiNFoLBgy\nDRAZGen2umbNmpGSkkJKSgp169YlKCio4P+aNm1KUlISAEuXLuXUqVO0bduWHj168O2335a6ltLy\n1NLS0rDb7TRr1qzEzwBo2LBhwb8DAwMBMJvNZRGBQCDwUoShJhAIajVms5mpU6cyefJkZs+eTWZm\nJr1798ZkMmEymTh69GjBc4saRQAXLlygcePGNG7cmIyMDDejKCEhgaioKABatGjBp59+ypUrV3j+\n+ee57777sFgsxdZyvWKC+vXro9fr3Vp1FP0MgUAgKAlhqAkEglrNlClT6NGjBx988AFDhgzhb3/7\nW6nPvXz5MosXL8Zut/PFF1/w+++/c9dddxEVFcUtt9zCzJkzycvL48iRIyxbtozx48cDsGrVKq5c\nuQJAaGgokiSh0RTfPiMiIjhz5kyJn50fbp01axZms5kLFy7wz3/+s+AzBAKBoCSEoSYQCGot69at\nY8uWLfz73/8G4P/+7/84ePAgq1evLvH5PXv25PTp0zRo0ICXX36ZL7/8krCwMABWr17N+fPnady4\nMSNHjuTVV1+lf//+AHz33Xd06NABo9HItGnT+Oyzz/Dz8wPcvWhTpkxh7dq11K1bl6lTpxb7/Lff\nfpugoCCaN29O7969eeCBB5g4cWLB+1zrkRPtPgQCgSRfr6W2QCAQeAnLly9n6dKl7Ny509NLEQgE\ngjIjPGoCgUAgEAgEKkUYagKBwCcoKbQoEAgEakeEPgUCgUAgEAhUivCoCQQCgUAgEKgUYagJBAKB\nQCAQqBRhqAkEAoFAIBCoFGGoCQQCgUAgEKgUYagJBAKBQCAQqBRhqAkEAoFAIBColP8HVtRHtLs1\n+CsAAAAASUVORK5CYII=\n" - } - ], - "prompt_number": 20 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "The most probable position reveals itself like a lethal wound.\n", - "\n", - "Associated with each sky is another data point, located in `./data/Training_halos.csv` that holds the locations of up to three dark matter halos contained in the sky. For example, the night sky we trained on has halo locations:" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "halo_data = np.genfromtxt(\"data/Training_halos.csv\",\n", - " delimiter=\",\",\n", - " usecols=[1, 2, 3, 4, 5, 6, 7, 8, 9],\n", - " skip_header=1)\n", - "print halo_data[n_sky]" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "[ 3.00000000e+00 2.78145000e+03 1.40691000e+03 3.08163000e+03\n", - " 1.15611000e+03 2.28474000e+03 3.19597000e+03 1.80916000e+03\n", - " 8.45180000e+02]\n" - ] - } - ], - "prompt_number": 13 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "The third and fourth column represent the true $x$ and $y$ position of the halo. It appears that the Bayesian method has located the halo within a tight vicinity. " - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "fig = draw_sky(data)\n", - "plt.title(\"Galaxy positions and ellipcities of sky %d.\" % n_sky)\n", - "plt.xlabel(\"x-position\")\n", - "plt.ylabel(\"y-position\")\n", - "plt.scatter(t[:, 0], t[:, 1], alpha=0.015, c=\"r\")\n", - "plt.scatter(halo_data[n_sky - 1][3], halo_data[n_sky - 1][4],\n", - " label=\"True halo position\",\n", - " c=\"k\", s=70)\n", - "plt.legend(scatterpoints=1, loc=\"lower left\")\n", - "plt.xlim(0, 4200)\n", - "plt.ylim(0, 4200);\n", - "\n", - "print \"True halo location:\", halo_data[n_sky][3], halo_data[n_sky][4]" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "True halo location: 1408.61 1685.86\n" - ] - }, - { - "metadata": {}, - "output_type": "display_data", - "png": 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ixAm2bdvGkCFDspiTMiphwcHBGI1GPvnkE06dOsWaNWt49tln3VZr0pSu/v3789BDDzFn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\nixKIWnlWGwAAAABJRU5ErkJggg==\n" - } - ], - "prompt_number": 24 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Perfect. Our next step is to use the loss function to optimize our location. A naive strategy would be to simply choose the mean:" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "mean_posterior = t.mean(axis=0).reshape(1, 2)\n", - "print mean_posterior" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "[[ 2324.07677813 1122.47097816]]\n" - ] - } - ], - "prompt_number": 25 - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "from DarkWorldsMetric import main_score\n", - "\n", - "_halo_data = halo_data[n_sky - 1]\n", - "\n", - "nhalo_all = _halo_data[0].reshape(1, 1)\n", - "x_true_all = _halo_data[3].reshape(1, 1)\n", - "y_true_all = _halo_data[4].reshape(1, 1)\n", - "x_ref_all = _halo_data[1].reshape(1, 1)\n", - "y_ref_all = _halo_data[2].reshape(1, 1)\n", - "sky_prediction = mean_posterior\n", - "\n", - "print \"Using the mean:\"\n", - "main_score(nhalo_all, x_true_all, y_true_all,\n", - " x_ref_all, y_ref_all, sky_prediction)\n", - "\n", - "# what's a bad score?\n", - "print\n", - "random_guess = np.random.randint(0, 4200, size=(1, 2))\n", - "print \"Using a random location:\", random_guess\n", - "main_score(nhalo_all, x_true_all, y_true_all,\n", - " x_ref_all, y_ref_all, random_guess)\n", - "print" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "Using the mean:\n", - "Your average distance in pixels you are away from the true halo is" - ] - }, - { - "output_type": "stream", - "stream": "stdout", - "text": [ - " 31.1499201664\n", - "Your average angular vector is 1.0\n", - "Your score for the training data is 1.03114992017\n", - "\n" - ] - }, - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "Using a random location: [[2755 53]]\n", - "Your average distance in pixels you are away from the true halo is" - ] - }, - { - "output_type": "stream", - "stream": "stdout", - "text": [ - " 1773.42717812\n", - "Your average angular vector is 1.0\n", - "Your score for the training data is 2.77342717812\n", - "\n" - ] - } - ], - "prompt_number": 25 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "This is a good guess, it is not very far from the true location, but it ignores the loss function that was provided to us. We also need to extend our code to allow for up to two additional, *smaller* halos: Let's create a function for automatizing our PyMC. " - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "from pymc.Matplot import plot as mcplot\n", - "\n", - "\n", - "def halo_posteriors(n_halos_in_sky, galaxy_data,\n", - " samples=5e5, burn_in=34e4, thin=4):\n", - " # set the size of the halo's mass\n", - " \"\"\"\n", - " exp_mass_large = pm.Uniform(\"exp_mass_large\", 40, 180)\n", - " @pm.deterministic\n", - " def mass_large(exp_mass_large = exp_mass_large):\n", - " return np.log(exp_mass_large)\n", - " \"\"\"\n", - "\n", - " mass_large = pm.Uniform(\"mass_large\", 40, 180)\n", - "\n", - " mass_small_1 = 20\n", - " mass_small_2 = 20\n", - "\n", - " masses = np.array([mass_large, mass_small_1, mass_small_2], dtype=object)\n", - "\n", - " # set the initial prior positions of the halos, it's a 2-d Uniform dist.\n", - " halo_positions = pm.Uniform(\"halo_positions\", 0, 4200,\n", - " size=(n_halos_in_sky, 2)) # notice this size\n", - "\n", - " fdist_constants = np.array([240, 70, 70])\n", - "\n", - " @pm.deterministic\n", - " def mean(mass=masses, h_pos=halo_positions, glx_pos=data[:, :2],\n", - " n_halos_in_sky=n_halos_in_sky):\n", - "\n", - " _sum = 0\n", - " for i in range(n_halos_in_sky):\n", - " _sum += mass[i] / f_distance(glx_pos, h_pos[i, :], fdist_constants[i]) *\\\n", - " tangential_distance(glx_pos, h_pos[i, :])\n", - "\n", - " return _sum\n", - "\n", - " ellpty = pm.Normal(\"ellipcity\", mean, 1. / 0.05, observed=True,\n", - " value=data[:, 2:])\n", - "\n", - " map_ = pm.MAP([ellpty, mean, halo_positions, mass_large])\n", - " map_.fit(method=\"fmin_powell)\n", - "\n", - " mcmc = pm.MCMC([ellpty, mean, halo_positions, mass_large])\n", - " mcmc.sample(samples, burn_in, thin)\n", - " return mcmc.trace(\"halo_positions\")[:]" - ], - "language": "python", - "metadata": {}, - "outputs": [], - "prompt_number": 9 - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "n_sky = 215\n", - "data = np.genfromtxt(\"data/Train_Skies/Train_Skies/\\\n", - "Training_Sky%d.csv\" % (n_sky),\n", - " dtype=None,\n", - " skip_header=1,\n", - " delimiter=\",\",\n", - " usecols=[1, 2, 3, 4])" - ], - "language": "python", - "metadata": {}, - "outputs": [], - "prompt_number": 10 - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "# there are 3 halos in this file.\n", - "samples = 10.5e5\n", - "traces = halo_posteriors(3, data, samples=samples,\n", - " burn_in=9.5e5,\n", - " thin=10)" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "output_type": "stream", - "stream": "stdout", - "text": [ - " \r", - "[****************100%******************] 1050000 of 1050000 complete" - ] - }, - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "\n" - ] - } - ], - "prompt_number": 11 - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "\n", - "fig = draw_sky(data)\n", - "plt.title(\"Galaxy positions and ellipcities of sky %d.\" % n_sky)\n", - "plt.xlabel(\"x-position\")\n", - "plt.ylabel(\"y-position\")\n", - "\n", - "colors = [\"#467821\", \"#A60628\", \"#7A68A6\"]\n", - "\n", - "for i in range(traces.shape[1]):\n", - " plt.scatter(traces[:, i, 0], traces[:, i, 1], c=colors[i], alpha=0.02)\n", - "\n", - "\n", - "for i in range(traces.shape[1]):\n", - " plt.scatter(halo_data[n_sky - 1][3 + 2 * i], halo_data[n_sky - 1][4 + 2 * i],\n", - " label=\"True halo position\",\n", - " c=\"k\", s=90)\n", - "\n", - "# plt.legend(scatterpoints = 1)\n", - "plt.xlim(0, 4200)\n", - "plt.ylim(0, 4200);" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "metadata": {}, - "output_type": "pyout", - "prompt_number": 14, - "text": [ - "(0, 4200)" - ] - }, - { - "metadata": {}, - "output_type": "display_data", - "png": 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P8/rrHo2NcPzxpV6Vu+5KMW/e7p2Qur04/vjjd8q4nTuXErX163fPDP1UCvr2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ZzorqSriOIqpMzYKVkpPSvqd5x4Mlcj5ebLHFICnVyOByASku14HvgRkdagJCKU+K5PlM9Rdhzb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\nqFAmKHSigwC0wRQVyoCT9XAcD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/vtXmr2uDWxerXgC19o4KSTmrnooibOO6+J445r5rTT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oLKK10+rillVFqMwYWq4+D1HD70fqEQ011WG3gpYoPlnMWLCyTiHx2JA7QTVyfjRnLeStWR9H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D4JlnEby46V/bfvDyilwG88Gepob4cPPrBYuFDS3CwYPVozaZLHlluqYso0PcI6WaNWRRU9\nxWabKX7963YuvrgOpQRPPx3nmWdinH12mrPPTrHZZsPumabPeOcdi29+s55lyyQNDZpf/KKdo4/O\nlJxaqKIXyCME5SY8pd5QpW0XeFVGa9xE4BmpCQVdhzrya6WUUhjNJ9FlWk5rjXYc00kK4DcFaHRW\noDYSOdIREqcc09igXM8IG1uWibZBNgUa8Wnt1whrD2Hsntzwb3sIP/Gm03DnnQn+3/+rIZq/jsc1\nf/xjG4cd5vTbQ+qwr1Fbl1Ep+fXBRqnzEIvB8cdnuOCCrECv1oL/+Z8khx7awLx51pC3pyr3MfH4\n4zGWLTOXkZYWwQUX1PHkkxWgUdMNhvK5YfSnpF9U3f1NWWv45z8tbropwSuvFC7bl7kwxeu55t9Z\nguFGrI2kKY7vQy1df6OUeYjWSgkp0Y7r2xkF3pWRbkX/Nwp+J41A+fVtKvBmzYmoBSK6KusfqhVC\nWFl7LhUI8BamZENR4R5aeRWrHeztMaG1xnMc34tTRbTPAEXu6yGA6DwsWSL42c9ySRoYUflzzqlj\n4cL+o1NVolZFFRGMGAHnnJPippvaSCSyF6+lSy2OPLKBf/zDLtWWbp1AsXD/z35WU1RBvYryQUgZ\naqZ1hkDT7PXXLQ4+uIGf/7yW445r4OOP+/Gyn9fhGI7X98Ms6i9ark13YZxe0vcDw+9u1iECJf1u\n/CoDzbSgzkr7aVPjG6rCuj7hm7gHxFY5LiqdQXsKpyOF05FCOWY8msDX0p/DHnZA5iMU9fWFfXuD\n6LyFJvGukTiJ2osNdWywgebEEzNFP9tuO7egu7ScqNaoVVFFESgF775r8Ytf1PDii1mV5ERC8+ij\nLey00xAPrZUJ//d/Fvvt15DT5Vxbq3nllSY23njYXVqGDIJaqqXLbQ45tJHPP88Sur//vZnp0/vn\n+M2pn4t6YvZzLVV+XVdvtldQf9ZNHZ0hhl4YzZIxCxlRVM+fCy+VyVo8SWnSm/6YhWW8WlEK1ydp\noFGuL/yqNVYyjl1bE3akRuvi8rfV1b6H0TYh+jxnAG4qhdHrVX6XquWL1QrsRBzPtwOSUhZ00A41\nLF8ueOUVm7vvjvPJJxbrr6845hiHAw902HzzvgnLV2vUqqiih5ASttvO4/bbW3ntNZvf/S7J66/b\npNOCm29OcMst7QyD2tg+Y5ttPGbObOXss+t8b13NT37SEQpwVjHwiKbUPlhg5ZA0gJqafnzylzJM\nywU1a8Hf/Yr+iDfkaY9pnzAFZMvIaQCW2eestZQhLMpxI0RKhylNIQTKcxG2jQ7YrBAox0EIaYif\np1A+8RLxGEIrZCyWjeaRO6fBvGutEcEYi0TaomRUkzWO7w4ffihxHGNmHi0zMzIlwS5IlBd5rQUa\nhnRdWj7GjNEccYTDwQc7tLQIamr0gHSSVlOfwxhDuQ6nnOjLPIwcCQce6PLQQ628+GIz993Xwne/\nmx6yJK3cx4Rtw777ujz/fDOzZzfz9NNmfir9wXk4nxtRPbPFi3Mv8WPGKMaOLU89UlfbFxGyZlJ7\nKptW7AdSZYhK7hh6irkvvxxZAWE3Z+C/qRwHL51BZVyUZ/Ynmt4MEIrcao3T1oHTnkJ7HjIeC2v0\nrHjMRJiCejdfpkJIYQhZzA5JmZTSvJbZceVD+52V2jVjC7TtcpbJq4kTiNw6ukgaPXpMvP++5OCD\nG9h770YeeCBOOh1ZR968y5ivPRezkPFYv1mZDRQ6OzficVh//YEhaVCNqFVRRUloaICpUxVTp1Z9\nU4thk000m2xSTQdXCoRlgVKk07m3yssvb2ejjQY22mk6QbPnTVQvrNiy0DuiJSwrjKz1VtNL2Fao\nhB+MFU22jktrQ8x8T85sjZlPjITxX5W2jXJV2JGpPIWdkDmdoUHjAEoBlrGZ0gppW2BbyEQcoRVa\nGB9R6euteakUyu8UtRIJE+XzFEopVDoTis/KmJ1DlPK7SQPS191cvfaa7UfL4T/+ozbUEg3mWdiW\nscwSYNmJ3Lq0CmwaGYqoErVhjD322GOwh1ARqM5DFtW5MBju8yCEAMtihx08hNBoLTj55DT77+8U\nLFspc5FTI9YLiYneCqIGCOchz8oJMN2aGccU9QtNrLYGKQVSGIkS5fn+nT75MfuisZOJbCRL4Etr\nBL6str+slyWm0gJpHB+EACuezKk/U56H15FGSMsMTSlD1ghcJIRf01bcuSAg8OHf3c0FsHx5xMtV\nCWbPjoVEDcCKxSBbmmcM57U2+xpJBwep5P5qJukPVMq5USVqVVRRRRUVDMcxlpK9ub9tv73Ho4+2\n4HmmnnDkyPKPrzvkR3KKpu4KPB81ogKkwIQ00TChASGQMRuU56cMs/VnYY1cdDkpwPM/Ez6hKdhA\nrmuA9ny9OemnizMZZDyek07VGgiicdpCxGImjSkEWL45vN9lW7g5ketPWgJGjswlfE8+Gee881I0\nNBQua+Q3RLY+USmU4/i/Z4SkDiGyVgmoztYwxnCuw+kJqvOQRXUuDAZrHjIZ+OILwdKlAqcwuJWD\nL7+Ev/41xjHH1HPkkfVce22Sf/7ToidSVPE4TJvmMWNG5yStv+YilG1w3Kz+mG0VvUkLIYz4q+d3\nUQ5CxqzYPAjLMinEmIWViCODlGTUhSGoGwtqvfyokRWPI6xATsPCTaVw29tx2tpNpyRZTTwR1Kf5\n5MpIhCgj1+G6vhSL9OvcBMo1EhjGecnUJMqYXxsW8Qotx1xsvXUuUUun6fwYzCPbyvUtt6K+sUNI\naKJSrpfViFoVVawjSKXgo48kCxfGWbFCsskmHrvt5jJhwtC5cA5lLFgguemmJA8/HCcW03z72xm+\n//0U48YVn//5823OOqs+fD1nToxrrklyzTXtHH98hrq6gRp5z6G1xkunwwiT8DyEX0DfxZeyjQYV\ndDMXQpioluOg0caFwZJh6lBYlmkWiNlhai+MHFkWQpLVGPNU6O0ZRMtyGhG0Bu2FqdLQgD2om9Oa\nWG0SN5VCK4xJOwHhs8KOU6DTzs+eYtttXXbZxeH1101EcNIkr/NjL78GDl+KxFORtHY1PtRTVHXU\nqqhiHcCqVYI//SnBtdcm0Tobrvj61x1uu62VESMGcXDrAD7/XHDYYQ0sWpSbdrriinZ+8IN00e/M\nm2dx6KGNRT7R/P3vLf2mhVYOBNZB2lfgl7aJSknbLtooUKCDhokQVQICWY7emJsHdXfK9UVs/bSg\n6fy0O9UV8xwnK52Rp28WRtv8Av4g2patjaPo9/qCDz6QnHVWHZ99ZjFrVgtf/WrxYy+0ECNLYIN6\nOSEwadpqg0FRVHXUqqhiHccLL9hcc01Nwfv/+pdFKiUYMWLYPa9VFD77zCogaWBElTvDlCkeF1/c\nwdVXJ8nNBQpWrJBAZRK1oN5MSIHnmDolbWtkUOhe7EatNVr5XpWBfVLO+vSg1DVFvUsBvwas9HGY\n7k/XEKlE3Ajcag2WoCuNHysWy/FRjSJIu+rAHzRaoB89jTX8+9+CTz6xWLFC8JWveGy/fe+61rfe\nWjF7dgstLZJNNul8HaZzNrtfIhDmpWvx4Cq6RjUGOYxRKfn1wUZ1HuDFF4OL5ws571966bopTjvQ\nx8SIERrLyp9nzTe/WdySBqCxEX70oxR/+1sLhx+eYaONFKNHK845J8XOO5fPM7E/dNRMvZYwURRL\nIhChVEU+gq7GrGm7zkpYKOXbG+X5RvYDis6DUnnkp+tzJZDpiHZcStvGisex4jHsmgQybpt9VapL\nTbl8H9Xw/UBsNxYr0HAT0iy7ao3kvgdr2GuvERx7bAPf/349f/976eKGL730UsF7o0bBppuqHjfW\nil5EIisFlXLvqEbUqqhiHcDpp2d46qk4K1ea1xMmeFx9dQd77OFUpY4GAFOmeNx7bysXX1zLF19I\ntthC8etft7PbboXkY80a+PxzSSol2HRTxYwZHrvu2saXXwqUgtGjdcULLkvbRmkHKxHPapuVYMZe\nEE2LSkwEKbSBjKyJaNFV18ixcSJXzy1ISQbdm9KSYYG9iJJS/3PRw8hdOFzL4pPPBBddVMcLL2S7\nTIXQ7LdfN90rRCKIgaBvEaJYxcCjWqNWRRXrCL74QrBypcC2YexYzQYbDLtTv+KxerWgvR3q63VB\nF2ZrK7zyis3PflbDggXm5r3LLg4zZ7YyatQgDLZENDebxoeWFsFWW3lstVW2mD0qdNsZ+civT4su\nV+C/2UsCE0VbG7S2CjbcUJf0kBLU2QWRrC6Xi4i9iogWnHIMIVeeZzTSfB/RYssE6E2N3vvvS447\nrp4lSwprIc86q3vHkK72YSigvZ0BcwsoN7qqUaumPquoYh3BxhtrdtzRuCtUSdrgYP31NRMmFJK0\npib4wx+SHH98Q0jSABYvtvC8yo5ovPmmzTHHNHDqqfUccEAjzz1n43mB6r0IbZM6I1iBI4AhBbnL\nSdvOyl5I0WeS5jhw660J9t67kT//OU5zc/ffMZ6edtckLdqxGn4xoo+G9n0xNUr5pDTo6uxinT15\nf8kSwQ9/WJdD0oTQXHllOyeemCZmeQUiuMVStZ3tw0AgtBnzelZ/uWSJ4D//M8Ghhzbw8suDTyyX\nLxc88YTNCy/YrF7d9zmsErVhjErJrw82qvOQRXUuDCptHp57LsZVVxU2e1xySUe/k+q+zsXKldkb\nUUuL4IQT6vnnP7PSFdJX4O8KQbSq2HLStrslSqVi+XLBNdfUsGKF5Lzz6rj33nioCdbTeQhSlUEd\nnZHRUEUJpxDCt3ryEEKCNsbuoW4c2fqy4O/8lGOgS6ddr6hn6vz5Nv/8Z5bkjxvn8fDDrZx6aor1\nGlxjDO/lyncEWm3B+0Hqee7cuZ36ivYXwqYNTWhiXwoWLxacdlodv/pVLW+9ZXPDDcmyqbv05tzQ\nGu6+O8G3vtXA0Uc3cNllNX0ma1WiVkUVVVQxiGhthd//Plnw/oUXdnDooZ03G1QKJkzIvaG6ruDa\na5O0t+cuVwlVNr5Yfohf/KKW998TvsaZV/IYoxIZKqJcLEReF2b2AyONFnRsuh4qIHc+KRGWlRUF\nLkZKo40NmnBHMhl4/XWL2lpFY6Piq191uPnmNh59tJW99nJJxA1BVJlMGLEKJyN/ciAUzC2XtEep\n6M3x4XnwwAPxUOMNoKZmcC1GV64U3H57Inz9wAMJnn++b3NZJWrDGJXiUzbYqM5DFtW5MKikebAs\n2G67oD5Js8MODg8+2MKPfpRivfX6f/t9nYutt/bYZ5/cQvWnn46xeHHEI7KLSFB/IioAC6b7durU\nbC2Y4wieedYUbs2YPiOXxXWxzi77C/JYQpDyJBhLFynPHnVI+svNn29x0EENvPuuzSuvNPHww62c\ncEKGTTdV4fa9jGucDBwzFl1MJiXyuq/HRJhSLeG31p5niHK0C1ZQEtv66CNZIDv0ta913zRRKnoz\nD1KCbefu93/+Z7KkNHun6+z9V6voDFrDu+9K7rgjzm9+k+T+++MsWlTZdSZVVFHF4KCmBq64ooPn\nn2/ipZeamTWrlX33damv7/67lYD11oPf/radrbfOEqBkMmspmaNDFokE9TdMWlHlSHs0NlIgMHzH\nHQlWrenBrTBfLsOycmvx/M+V5+FlMmFxvozHEbb0U7mRNG8XpERrHRKYnI7YwPxdwV/+kkBrwXXX\n1ZBKyQLXACFk1qZKCN/twOjShe+XoUkjHHM0pep2TdYMkdbhOIM57EwYOR8LFlik09nlGho0M2b0\nr4xLdxg5UrP//rlkceFCi5aW3nOAKlHrBzz9tM0BBzRy/vl1XH99DeecU8d559WxZs3AjqPS6nAG\nC9V5yKI6FwaVNg8jR8L22yu23VbRWMyMoB/R49osrXNqqwAmT1bcf38r113XxhFHZPjjH1u7FEYd\nCES7FwMbJoBdd3XZdNPszbypSeJkJHPnzS3J3ihwFggaHIL6uWgtnnIcVNpBOR5uR8pEEn1pEePJ\nGfNTnLKoBIZWKoxCak+FhEfatvm+n5Zctkzw2GMm7dfWJvjss1w7KhPVUshgO0HThj9OQ9YKawP7\ndH7kE7MeEHNRLG3cBZqacufthhvamDSpfMddb+bBsuCUUzLU1GTnYcMNFTWFJaglo0rUyoyFCyVn\nnFFPKpV7AD33nM3atUM7qtbRYVrbq6iiinUXgYRDYBgeYMIEzemnZ7jjjjYOPdQNtd4KIkEDJfcg\niv89bpzmzjvbGD3a3NC32sqlroGihKnTVfsEByGKRoyULzeilUJnHEPWMk5OdC8gJfnbDOvf/FRx\n9oNCAtLRIVi7Nnsb//LLSKep/zsJYaJm0jeW78n8Bw0MQQ1fSSiSUs1PQYcfBWb20dc9QPAwEItp\n/uu/2gpS8IOF7bbzuO++Vjbe2KO2VnPtte2MGtX7lH9VR63MePddyV57NZJ7lYB99nG4/fah56nY\n3g6ffiqZP99m5sw4dXWa//mfdkaPHnaHTRVVVNENKtmTMx/a7xwI0ob5hOjDDyXvvmux1VYe227b\nsyhMvrVUfurQS6fxHA+VcfxltIlk2RZ2MhnqqBVdb0DyfKIVzG+x9OSCBZLdd8/eVG64oY2TTsqE\n6Uel4IslNs0tgvp6wSabqB6JJRfo2HUy7oL9UCq0C8up6evEfzSgIT0V121pMenP+nrN5MmKSpN8\nW7lSkEoZaaTudq3q9TmA2GQTxfnnp7j++qw/3yGHpLn88tSQImlaGyPeP/whyV/+Eg+NvC+/vJ31\n16+StCoGDqmUiVS3tAjq6jQTJigaGgZ7VOsmhBDoqFh/BScJhBBgWZ0OccstFVtu2cs0me9nGr7M\nc0wQlgXpjCGJUoAShnQJ6bsRFGcUQgijs6YBKRHCNB90lhLML1oPwy5CkErD/86q4ZJL6mhvF8Ri\nmnPPTXHKKWnGj+/lNbwzr9b8/fDHqvPmqbMmjN66HzQ00KlB/GCio8NMVbmkdaqpzzKjsRHOPTfF\ns8+28PDDLTz7bDM33dTOFlsMfL1Gb+sMVq4U3HVXnP32a+SeexIhSTv66DTHH58ZcpZDlVaPNJgY\nanPR3g633ZZgxssRjnwAACAASURBVIxGDjywkT32aOTb367nrbdkn7SShto89Cd6OhdB8XxQnzVc\n0JdjIko0AnJiJZPEapLIWAwZs5Ax29S2FdFIC6BcF4T016EQsViXGnKJBCSTOvI6G5n61/sJfvxj\nQ9LAdLhed10Nt96a6LZsLDoXYcqyF7pqoe9r+EaPvj7o6Okx0dwMjz4a46ij6jniiHoefDDG6tV9\nH0eVqPUD6uthxx099t7bZccdvSEVSXv/fcnZZ9fxH/9RR0dH9qw69tg0V1zRwdix1WhaFQOH5csF\nv/hFTfiwAII5c2J84xuNvPVWheU51hGE4rSVlmcaQAQdk6FjQpG5CBwXrJiFlYxj1yRD8d58RGvB\nwNcyk92nGUeN0uy4Y7aOLVqSYsrbCr//0EOJkgRYw7SnEGh0r0l5lNjnz1OvauAqGC++GOOkk+p5\n7bUY8+fH+O5363nssW58u0pAlagNY/RUA+bNNy2+8Y0GXnwxKx4Yj2tuuKGNq67qYKONhiZJqyTN\nrMHGUJuL9dfX7LlnYbt9KiV48slYkW+UhqE2D/2J6lwY7LHHHqEcRlcIOl6FlEWjXYGHJ/hdofE4\nVjxuasxs04CgXBcvnTb/Ow5eOo12vdCtwHy5+5Rgba3pMASTBo122k6erDjssHTBd775zTTrrdeF\nZIbnsftuu4U+rUIIRB9CYVFiX9DdGqnz64kbwUChJ+dGKgV/+EOi4P2bb07S1NS3cQyfuHUVfcLb\nb0uOOaaepqYsd99jD4crrmhn6lRVStd6FVWUHY2NcO217fz0p7U8+2yUmGm+8pWh/wReReUgakiu\nlSoaQYoW12vt5ixjxGxFhJiQ81lAfLTyt6NBOWlD9LTxAw112KRAlhix3HVXl622cjn2WIeJE7NE\nZ/RozbXXdnDccQ6zZ8cRwuh77bWXS6yTZ5ywUxQRepLmd2b2JwKiNpDWVeVCLEbR2r/Jkz2ShcYj\nPcLQm40qSkap+fXlywWnn14XkrSJEz3+/OdW7ryzle23H/okbTjUI61YIXj7bckHH0jWru39eobi\nXEyapLjlllYeeaSZm25q47rr2njkkdYCUcmeYCjOQ3+hOhcGOfOgKYjudFUYH5XUKJbCC0ma1mhP\nRwih+VtHViYsWTJJA5g4UfHQQ62ccUaqgIBtuKHm0EMdbr21jT/+sZ3jjnMYM6aLaJpf+Dl37twu\nU5blQlS6RXmGBEclTAYbPTk3LAt+9KMORo6MOmEo/uM/UiQKA209QjWiVgVNTYLddvM44QSHGTMc\nJk9W/W4EPVygNbzzjqS5WTBxomLjjbuet1QKbJsetch/9JHk9NPr+Ne/bIzFkMtvftPBLrt4PVpP\nT7BokWDWrDgvvWTzwx+mmT7d7bdtlYL114c99vCAahStigFCvgNBJx2vgfyE1saaSSCwihAbQ/QM\nKRNShLId2vNMZE4a+YuekLQAve7ijI4vMJj3lBmjX2PX247MUmC2YaOUQkbpyBC9/Wy3neKpp1r4\n6CPjGrH11orNN+97Oreqo1ZFFX3AokWCadNG0NEh2GADxVVXtXPAAU6B/Y9S8NRTNtdfX8OkSR4/\n/GGabbctjXQ8+qjNSSfl6lFYlubee1vZf//yP3mmUnDxxTXcfXcy3NaTT7aw005VklTF8EbgTylk\ncUslrYwJuxCm9gwMAfNSaRMZ8zyEZWElYjlpUeV5qLSJAAtpUptaqdDEPbB0KqZJp7XuF7K0fLlg\nwQKLjg4jGDt2jGLCxi61SQ/QxvJqAFv8czTbOtFbG87oSkdtiCe1KhOeB2+8YfGTn9Twpz/Fq2r+\nwxhSmoYLgJUrJWeeWV+0ePSjjySnnVbP/Pk299+f4NBD63nnndKenMeN00iZ+zzleYIf/KCOZcvK\nfyH95BPJPfdkY/WeJ3j77XW3w6+KdQf5VlABtNZ+0X8Gv9UzJz0npPRTpb4cRV7qVIBvHeWTD6UR\n0vLJmihaB2ZIoVvoUFAm3H9/nCOPbODEExs49thG9txrBEcfO4JHHqtl0eJEr0haaH3Vi6aAgUi1\nDlVUiVo/YP58i0MOaeDPf05y0UW1/Otfg3PQVWtPDPpzHsaP15x3Xirnvd/+toaZMxNkMtn31q4V\nOebBTU2S669P5izTGaZM8bjllrYCstbamrvOruD45VylzMXatSIih2GwatXwulRUz40sqnNh0NU8\naM8DvwFAe6rANkpIiRXzzdaLEZyozprS2aaDwIKqiLVWDtmJeJWWC3vt5VBbm12n1oL582OccUYD\ne+/zT154wSaV6mIFeQgbJoI56iFZ66o7dLBQKefG8Lr6VgCWLhV897u1OE5W9ynqv1bF8MPhhztM\nmZL7xPuzn9Xw4YfZ02uDDXQYeQvw1FMxli3r/hSMxeCIIxyefLKF7343xdZbe+y0k8PMma1MmND5\nxXDRIsFDD8U4+eQ6DjusgauuSpYUgTOedLljnTq1Mop7q6hiUKCL+FL6ZCKQ4xCWZerMrFzjc/B1\n16TwCVnEFN22QpP1gSYnO+ygeOyx5oJrF0BLi+Too+t5/vkepB/ziWQviGWoq+a6ZSemQxnVGrUy\n44UXbI4+Oree6PHHm9ltt2p9z3BAe7vRLsqHSW3W8d572Qvbtde2ccYZJmTmunDjjQmuuCL75dpa\nzcsvNzFhQs9OweZm04xQbBwB3ntPcsopdXzySe6F9vjj09x8c3uXnbxtbXD55TXcdpupUdtpJ5c/\n/7mVceOG3aWiiipKQo50h1ZF06MlryvwCYVOa+EAlFJo1w1N1fsrHbhsmeC99yzuuCPB00/HyGSy\nhHH33R0efLC1y2tNgKgECRT3Ju0O63KdWtXrcwDxxRe5B+bYsarLqEcVQwMffSR56KE4Tz8d44AD\nHE48McOmm+aKS/7lL23cckuC229P4DgixyDYtuHb386QTguuvz6J58GVV7Z32yVaDI2NXX/e0gLn\nn19bQNIARozQ3cqt1NXBRRel2HdfF8eB7bd3qyStinUaJlpmujalLH7bLFUDLOh0LLoOn8QFqUNp\n20XTouXEmA1cNtzLYcbuab5YEuOLLwSplMS2NZMmqZJIGgQRRxH6gfYqQpgnf9JfjRRDDVWiVmbk\npuU1113XPmg3uTlz5lRVx+n7PCxcKDnuuHo+/9xcLN96y2bNGsFVV3XkkLFNN1X86lcdnHZamjVr\nRA6RA6NpdN55KY4+OoNSZvn+uAY1N4ucyF6A8eM9tt/+WWB6t+vYYAPNQQf1Xqes0lGuc6OtzTh6\nzJ0bY9QoI8K77bYuo0aVYZADhMG8TkSjMINdRN7dPBjfyi48OoPLvNYl7UeQzMrxCfWV+kPJD9/s\nPd/0va9YuVIwcqTGEiZSqLX5e7NNFJttAnPnzmPGHjP8bZa+3a7mqKTvSxFGLktxZuhvVMo9tErU\nyoztt/eIxzWuC1dc0cFeew3fm926gtdft0KSFuDvf49zwQUpNtwwl4THYrDllp1HUBOJ3M/b201a\ntKGhT9e3HIwbp7nzzlYuvLCWJUskY8Z4XHxxip139li+vBrdLSdef93m6KPriRYvHXFEml/+soNN\nNqlGIbtDNFWmlQZZ+RGUQA8tIE4BqYp+3t0eRFOplEJQyzgnCxZIvvOdei6/vJ1vHGQEepXjGsJm\nCdONis4SxiBKRvFoYTmjXkYAd+i6E/QXqkStzJg61eP555sRAjbfXBHvux9rr1EJTwKVgL7OQ346\nG2DHHV0aGvp2I37rLYtLL63hyy8lU6Z4nHRSmqlTXUaO7NNqEQL22cflqaeaaW+H5mbJ73+f5Kqr\navjTn/amKhpbvnOjpUWQr6swe3aChga4+up2amrKspl+RaVcJ7TW4HmGEwxCfVIp81DUZqqHJMX4\niUa6LZUO7aaEZYVabFp5YZ1XOcnrgw/G+eQTi3POqeeF510mjEmHc64xpGzG7tPDsYGXQ0RDghrU\n2mnQZfq9Ks1CqlLOjcqYjWEEKeErX1FsvfXgkrQqyodp01yiV6raWs0FF6T6fBOeN8/mlVdiLFhg\n8de/Gk2j73+/jg8+KM9pOWoUWJbg3HNr+etfEyxaZHHddUkqxJ1lWGDKFI+NNiqMUj70UJzVqys7\nMlQJEFakM5KIRVMRC6dKQJRgRWuohCV9eTUREpbAqaBb5HWSBt2lVizWp6aFcJie51tceaxcKbjv\nPqOR2NpqBG+RArQXbl9aMiSfWQeFYP8jv0k0kqgpap3VE4Q2XJ7q87qGG6pEbRijUjRgBht9nYcd\nd/SYPbuF005LcdllHTzxRDM77tj3C8m0aS6xWO6F/Mkn45xwQj2fflqem/yLL8aYPz9rAPjJJy+V\npN023FGuc2OzzRQPP9xSUOJw5JEZ1ltvcFKfShnV+VI9YQfzOhGo8cuYPegipyXNQ+S01MrzI2ym\nfkza2X3Qnmd8P4t4f4bEzl9flIgFNXsCETod9AXGFipIY2pammHJkuz2FiyQuG0dIPzInQSZiDPv\n1VfQysNznFxh3zKnpQOBXC/joF0v8n5llA1Uyj10QIja6aefzpgxY5g6dWr43po1a9h///3Zcsst\nOeCAA1gbuapcddVVTJ48ma233pqnnnoqfH/+/PlMnTqVyZMnc+655w7E0KtYB7BwoeS11yzeesti\nzZrCz5NJ2HNPj+uv7+D881NMmVKeJ/3tt/e49da2ArL2+ecWDzzQRxdfTPfnLbfkhnU326z0Lq4q\nSsOWWyruuquVZ55p5v77W5g9u5lf/7q9wEZsoPDYYzZf+1ojhxzSwGOPxQpcMioWUZ0yUTnprygC\nE3GtPPxcYVFx16yUh0Z1IpAb6KcR0Q7rjfZYl8hbX/44Pv3UwnNcY4tlSaTtP9R5HtrTCC2MSbpW\nBc0eUUP13namBvV9gfBvOL5qMDoHA3ImnHbaaTzxxBM57/32t79l//3358MPP2Tfffflt7/9LQDv\nvfce999/P++99x5PPPEE3//+98Mf75xzzuG2227jo48+4qOPPipYZxW5qJT8+mCjq3l46SWbvfdu\n5KCDGvn61xs55ZT6sqUeu4NlwSGHODz1VAuHHJIhmmNYtEj0+Zrd1CT48MPcupGzzprWt5UOE5T7\n3BgxAnbayWP//V323NMbtK7Ptja47roali+XvP++zXe+U8+NNxZamkVRKdcJIUzaUNjWoOhnlTIP\nwRgLUpJFTtZoVI1O0rjRiFdR94E+RrCUH7FSrgsC7JjAtrPbSKcFEonKeLipDMrJIIRg92nTsilT\npRC+5EY+pG1nCWcfEQoK97McSU9QKefGgNyR9txzT0bmVUg/8sgjnHLKKQCccsopzJo1C4DZs2dz\n4oknEovFmDhxIpMmTeLVV19l6dKltLS0sOuuuwJw8sknh9+pooru8OWXsGZN7vV0xQrB975X5xeE\nG8ydG+O7360bsPoiyzKRtVtuaeP551t44IEWHnywhUsvTfW50UsI04UaYO+9nbKkbKuoXCQSMG5c\nLin43e9qePXVodM3Vuldn0ABadGQVdRXCmHJMKoW/F2qtrywLdNEYFvZwn3PpFCDVGQpKVHteQhE\nllQKQW0tOZ3qNbUakbDNHngenh/9E37Dg1Ya5SqU0qgiady+Iur2IG0rW5dX5mNgwQLJs8/aLFxY\neVHaUjBoZ+/y5csZM2YMAGPGjGH58uUALFmyhGnTsk/9G2+8MYsXLyYWi7HxxhuH748fP57Fixd3\nuv4f/OAHbLLJJgA0NjYyderUkB0Heefh/jp4r1LGM1ivL7zwf3j88V1JJPZm111ddtzxGSZOVOy0\n055YlgZe8GfrawC8884cnnqqjRNPnD5o4//sMxg/vm/rmzZtDy68sIOf//w1ttnG5ZprdmHBgpdY\nsIAB359Ke/3OO+9wzjnnVMx4yvXatmGPPZ7hiSdqCY5neIFLL/WYNm0nGhsLv/+HP/xhnbw+9vV6\nOWP6dNCaOfPmgVLMmD7DfP6PlxC2xfRp00DD3Llzzff33qtwfUIwd95c0DBjhtEtC5f3t/fSiy+C\nhunTpqG1Zt6rr5rP99oTIWXn49t9d8BsX6PZY889GT1as9tuT/Pwwwnga8yY7vHKa6+htWKPGXsg\npWTOSy/xzjvvcPbpZ6CVYu68l0HAHtNn4CmPl+fNQwjR6fy89NJLXX4efS2kZO68ef36+/7hDy9z\nxRU1pFL7cMwxaU444SkSidK+n39slHN8wW/z+eefA3DGGWfQGQbMQmrhwoUcdthhvPPOOwCMHDmS\nL7/8Mvx81KhRrFmzhh/96EdMmzaNb3/72wCceeaZHHzwwUycOJFLLrmEp59+GjAHwzXXXMPf/va3\ngm0NpoVUJaFSxPoGGz/+8Wvcc8+BOe9961tpLrigg3fesTn11LocE/LddnO4++42Ro+ujILWvqC5\nGZYtk4werRg1qnpMBBjO89DaCjfemOTaa7NtyQ0Nmnnzmhg/vvCYHs5z0RP0ZR6U46KUMqKIUmIl\nE6B1mNqUkehYMQR6ZcUiScoxxfyBqK7wjd+DhgSzDfN9KWW2oaGIy4GQgjfejHPggQ1ICc8918w2\nW7ajHA8pBTIeR0jBnHnzmDFtd1Nj5ziAyHqadpKa1lqjMhlfbkQiY7GyRsZKle74978FS5ZYbL+9\ny8KFkoMPbgyzJrW1mldfLX4eFMNAnhsVaSE1ZswYli1bxtixY1m6dCkbbrghYCJlixYtCpf74osv\n2HjjjRk/fjxffPFFzvvjx48f8HEPJVQvvgZnnLE7Dz2kSaWyF417700wf77FzJkt/OUvrcyaFWfV\nKslWW3k0Nmra24c+SQNjN9XYmE2FDYVjQmuTlnYcc2Htj3qvoTAPvUV9PXzveym23trjpz+tZeVK\nwRlnFIozBxjOc9ETROehO1IQpgB9OQ2NRmUcUBohNdpxQMosyRJgdUEwigrJBnVtgtAUXivlq/+b\nbQe6btpVprfBFoDRYQusqjzlZCVDlGbKFJeZM1uxLCMlZceSKNuQQAQgJXvuuWeYAkUKcL1wXzuD\ndhy05zdRuAotvRyrrJBQ6p67UESdH0L9umJj0HDXXQn+8z+T3HJLG//+t8wpbRk9WpFMlrzZijk3\nBi1he/jhh3PXXXcBcNddd3HkkUeG7993331kMhk+++wzPvroI3bddVfGjh1LY2Mjr776Klpr7r77\n7vA7vUFTE7zyisXs2TEeeSTG229bdHSUZdeqGES8847FRRfVcM89cd57T+I4sN12Hnfe2UoymXuj\nWrDA5s47k0ipefNNm5YWwUMPxbn66hpWrKiMYtZ1DZ99Jrjsshr23ruR3XYbwQEHNHLJJTW88YZF\nOj3Yoxs6GDkSjjrK4YUXmnn99SbOOy+VU69YRecIo1CeypGmyPncr9/SQU2XT2JMfZmF56v9h00C\nrtcjXbioplgQyZK2hUzEcyNaGhO501kNumwkzTNjk7lRrWQSDjzQZb/93PCYiDZxBFGwYJ8s2zZk\nDbos9C94DMjvOI3ornVVs6dc10QoXTfbCZrnAdoZVq8W/PWvcUBw8cW1Bcf84YdnWH/9ofcQPiBE\n7cQTT2T69OksWLCACRMmcMcdd4RpzC233JLnnnuOSy65BIBtttmG448/nm222YaDDz6Ym2++OTxw\nbr75Zs4880wmT57MpEmTOOigg3o1nuZmuPrqGr7xjUZOO62eU0+t5+tfb+BnP6th6dIhUMhaIipF\nA2YgUVOjuffeBD/+cR1f+1ojF11Uw333zWWDDRRXXtnOvvs6RM/0uXNtJk3SNDUJXn/dZuVKc0oM\nV73FSj8mfv/7JLfckmTFCklHh+DTTy3++MckBx3UwIMPxjtrnusxKn0eyoWxYzWbb65paOh8maE4\nF/1RsRPMQzFR2y63rTX47gHBvUr21pQ8WH+OyKzxDhWWZVKbESKldUQgVit/eRUhkiYSFhTsC9n5\nuIQfofMyGf7x/PNh1NBNp/HSjtE6CyJ6RRCkVs0LkLGYrwvnlfx75dhxaSAaQQwH2vn3W1sFixeb\na3hTk8R1BVKaFcbjmmOP7ZmlY6WcGwOS+pw5c2bR95955pmi71966aVceumlBe/vvPPOYY1bX/DF\nF5JbbsmNf2otuP32JLvs4vHNb1YVQYcqJk1S3HprK9/5Tj2uK7jrriS2bXP++Y2kUsZa6ec/7yCT\nEUgJO+/ssvnmij/+sY3jjjPfGTNGFXTOVTEw2Gcfl3vuKXxfKcGFF9ay555ugdl9FesWgjSY9qM7\nZe8S9VONwd/56w80v8JlhUAKAXE7lOGQ8Tie4xjFf01oBVXS5oVA542h02WlBAssy9dLtCQi+pAZ\nbNvfh0Bg1tS45UbGzGdBTZtGOS5CKVTGBZ+8emmn09ozISUyESfwQQ3EewFQnu+AEHiGFhLGrshc\naK0lhNHb6wSWpbFtQlHvDz6QbLWVYsECya23tjFlytB8Ah+wZoKBRHfNBKtWCY49tp7/+79Cnnr1\n1W2cdVaVqA1lpNPGz+7HPzbKrpdemuLKKwv9nqZMcbn77jY23VThuvD22xbvv2+x/fYeU6cOzRN6\nqKO1FebMiXHBBbU5CupSai67rIOzzkoPmpBsFeVH1C+ylLqlHDNzel7r1KMx0TkRNJGfbCStq3UB\nOUSps6aB/PWHdXJdkNFo7RaYRgMCbTbI8UzVWueo/+f7qRrdNC9M50pLoqVAdWRyvhNrqCuJHKtM\nBuXXzgXRNmFZBSbuUUInpMhGFHtBxNesgf33b+Szz8wxscUWHldc0c7662t22MGr6PR/RTYTDCZG\nj9bcdlsbt9yS4K67EriueXw55pgMBx3Us9BoFZWHRAKOOipDY6PmnHPqsG3NNtu4vPeeOdxHj1ac\ne26Kww/PMGGCuaDZNuy8s8fOO1cJ2mCivh4OOshhxx2bWb5c8OWXAqUEG22kmDixZ4XAVVQ+ApIG\nfspR6vJHyHqIoAi/y2V6EB0LkEOquomwGTun7rcRRK5CoiuEEWcUWSLZKfJDNFKihYfyPOOWIMCO\nJyDu4aUdhBBYiXhJv49WKlui5vuACsuwpIJIWqSeQSttyGaR5UrBqFEwfbobErXFiyXbbuuF1/mh\niqGp/lYGbLGF4sorO3jllWaef76J115r5oYb2of8DxpFpeTXBwN1dXDYYQ6PPdbMXXfNY6edPC65\npIOLL+7g5JPTHHBAZlj91qViqBwTY8ZotttOsffeHvvs47L11uUlaUNlHgYCgzoXPTwFy2Fb1BnK\nNQ/al+XIeS9aewU9aizoCoHHaL5XqvBlOqJkJ7/WK7/JQPjyHjJm8/Ibr4f2VjIWw6pJIpOJHjkQ\nGLIp/N+p9NRvONZe4utfzwZbHMeUTfQWlXKdWCcjagFiMdh882q9y3CFELD99orLL0+xaJHHr35V\n40dP4ZFHYjz0UCubbLLukbUqqqgUCEtm65iK1IMVQylkYc0a87CW6Ltlbo8QTeUahwKfLBWpcxsM\nSNvuUnpECIH0mxbQ2q+zy0b4tNYl2XCGUiKWZXoZuiDURaOCfcB223k0NiqamyXjxyvq68tzjf+/\n/7N49NEYngfHHZdhq60GjjuskzVqVax7cF147z2LJ56IcdNNSVpbBbfd1spRR1VT3VVUMZjIr+Pq\nC5qa4JFH4tx4Y5Ldd3c499x0vz2MB9Id0cL8rmroArmJqChtJSJI0SrP/z/jggArmfBlQkqP7+TX\now0UHnggxve+V8f556e47LJUn9f33nuSAw9spK3N7MvYsYrHH28pa2NTtUZtHcfChZJFiwSNjZpt\nt1UMgt/xoMO2zZPW1Kkexx+fYdkyMST1dKqoYrihnDfyefNinHtuHQAff2zR0SG48cb2skfWcgRY\ndRe1df57oatASfGowUMov2FJ8LXcwPh9StfBqjUNWqbgX3ebzhysyOEhhzg8+mgL48eXh0g99lg8\nJGlg3F4+/lgOWAf6OlujNhyhlMLxMmTcDEp5zJkzh/nzLfbfv4EjjmjkgAMaeeqpdY+lResMhICJ\nExXTpnlMnrzupb0rpeZisFGdhyyGy1yk03DLLbmMbPbseKir1R36NA9BVNCysnVZUuSk9bKLFn9A\nHOzkViCyqzzFP5573rznmPesmA1C+hFDZQRpMw5epjIVEurqYPfdvT6XtgTHxPvvF0ZAnQFMxlSJ\n2jCB1hrHSxtFbOXhKo9VqwSnnVbH6tXmZ3YcwbXXJlm8uPxPOUorlPJQemDJj1IennJRqtqtWUUV\n6zIyGVi1KveW5jj9I16dE0kSua+F5Sv8B+nNUqQsXBftemF6FCibuHPJCLs0I6TTtkyHqpX1KlWe\n5zstGOsqNZCMpcxYvFjw+usWr79usWhR57/T9Om5+1hbq5k4ceB+oCpRGybQ+QRJaxoa9uKLL3Kf\nBL78Uvb5wqW0ynn6i5I0pUpXoe4rlFbhWIJtF0Ol+LVVAqpzYVCdhyyGy1w0NMBBB+VGeHbf3WXs\n2NJuqD2Zh6xdlCxuUO4Ly5qUpzEpN+K4hYX1+Wr82vN4+23JmWfWcfHFNXz8cc9v00YTzc16khYZ\nX8F1OuymFcyYPj2U47ASMdNVKqWR+8h3aujx6AYfHR3w2GM2X/96IwceaP7ts08jr76a+9sEx8S+\n+7ohWUsmNX/8Y+uANhOse3mw4QohEEKGhE1IwZo1hSf4Lru4jBvX+1PLU9knPikkUloFJFGju63F\nWLvWhJOVgsmTVaeG0Z1tXwhR8fUeVVSxLuDjjyXt7bDddv1/4/r4Y8lbb1msXCnZZhuPr37Vpa4u\n+/k3v5lh9uwYn35qM3Kk4te/7ujSPqsvKNbNGSDsZCVrIl6qPMUnn9oceWQDTU1m+XfesbjnnlZG\njSptXIFwLVqjpUSSSw5z9NwizQ7Sto3eGQJtW8aQXWnwr/HC9wGVsRielw7nQAbdoIOsf9cTvPmm\nxXe+U09Ur2TNGsn559fy+OMtBcfMxImKO+5o4/PPJSNHajbbTJUSKC0bqhG1YQIpJLYVw7ZsbGlj\nyxhvvz2HTLKGjAAAIABJREFUKVOypsLrr6/4/vfTvWomUFrh5UXLgjSnELmHUSkE6sknYxxySCOH\nHdbId75Tx4IF3R+K0UheYNabc3Ho5MwZLjU45UB/zMVHH0lmzozz1FM2y5cPjYv1cDgmPvtMMmeO\nxZNP2rz3Xu8v5X2diyeeiHH44Q0lncN9wfvvSw47rIGzz67nsstqOeqoembNiucss+WWitmzW3n0\n0Waee66FHXcsPX3Ql3kIZDmU66KiAq5a53qHFoGQMkcb7v0PYiFJA3jllRiff1763AZK/yY1mXvN\nLuYjmjMW31N03rx5/vVU+B6mMszFCiGwkgkTZbMtlFJh2jZAEE3sjV7c6tWCd96RfPSRpK2tx18v\nCcaVqPBaNXlyrl5j9JjYYAPNzjt7bL75wJI0qEbUhhWkkCA0CoWnXMaP9zj0UIeDDnJYbz3N9Oku\nO+zQ/YUrnwAFUazgn/SfDLMGxBIllDHQlaVZfjz0UPYC+8YbMU46qa57XbO8kLunsheGmJ3I2rRo\njdKeP7bKbYMfLnj22RiXXmq6wSZNcrnrrja+8pW+RVeeecbm3nsTHHVUhl13dRkzZigmWPoHixYJ\nHnsszlVXJWluNudiQ4Nm7twmNt544OfpxRdtmpsljz0WY6ut0v2yDc+DG29Msnx5lLAI/uu/knzj\nGxlGjsy+O368Zvz4ga1ZjTosmOugMHZMfhelct0uZS2inxV72Glt7QEzCIRtfRumrpctfbU58Amo\ndl00vkUUImvAHnTEeqVZZgX45BPJD39Yy6uvxgDNUUdluOyyDjbfvLzH9bRpLjU1mo6O7LgmT3a5\n+OKOirSZqhK1CkMQpZKiF3UJfq1WgDPO3IWlSzIorRi3kSaR6P5kiaYWA5IT1TnSaLRWaDQo/4kR\nc2Ias2KF1t373+24k8uzz2bJ2scf27z2ms0mmzg5y0XXI6VlLg5am4YJzwtJo6dcbN+iRGkPz/PQ\naKRUw6YGpxzoj7moqcleRD/+2ObYY+uZNau1T121zz8fY9asOLNmxZkyxeXWW9vKWhPSH/OwfLkg\nk4G6Ol1ymqqnePtti9NOq2XhwtxL9+abe9TV9e5m1pe5yGQIoz833pjkmGMy/SIi7TiwYEHhQ9fo\n0aps0ht9OiZ03t+WBKkQwn9wDQRwi6Q/wzoy3zc0X1LCtjUbbFD6nAauBGhtSFK00cGX3oj6iBZD\nMBdh/VxebZ2J2mUN3DUgOmM4/jhKwZw5tk/SAAQPP5xg0SLJ3Xe3lfVhbYcdPJ58spkFCyxaWgTj\nxim2285j7NjcbVTKvaOa+qwgKOWF/6LRot7CsgQbT8gwYYKDZbvddmTmpxaDqFSODQlBqlOgtDb/\nlMqpU9PdlJcq7XHQgQ6WlbvcI4/E6EiZ9QRz4KnccVvSRgoLjfbTsa4/XhWO2/O8cF88z8NbRztC\n58+3uOiiGmbNirFqVf/F6o2Bffa3XLrU4qc/rWX16t6vc6+9soT93XcN+fvgg8q8XDkO/O1vMfbZ\np5Gddx7B/vs3ctttcZYuLe+cf/ih5JvfrC8gafX1mhtuaMuJKg0UXNeQNYC1ayUff9w/EexkEk45\nJZ33nuYXv+jAl/YaVOTYMfkOC8G/kNQUSQOa9KAfnfIJ27bbKjbZJHvN+vGPU2y2WekPKcZWygr/\nBRIhynFRjrleSts2UTB/fF4mg8pkCpoPpG3Sm8GyAMpxcNs7cDvSprlA+EbqRUzUu7sXFIy9yCnz\nxhsxPvmkvOe+EDBliuKYYxxOPTXDAQe4BSStklCZV751FNGD2shtZHA9p2TSZqJgMiQ2c+fOy6tP\n6FlEQvj1CdJ/KgyaBwIyGUbaEDljL6VGbZtt09x4YxtSZr+3774O5/2knntnxljbFIxZ55Aw/13M\noavxVNDtKUg57aQyHbgqE2ZJhYB5c+f1aL+HAxYvFpx4Yj1/+lOS00+v57//O0Fra//UZm2zjcdP\nf5qr/v3cczE++aT3N+3ttvPYdNPscb94scVZZ9X1qFanK5RzHpYsMR16y5ZJXFfw2WcWF15Yxymn\n1PH55+Uja889F2PFitz93357l9mzW/pUyN+XuaipgY03zm673DfUKI48MsNf/tLKqaemuOyyDh5/\nvIVddinfQ1hf5sHUdsmcLlBhmQfKsLFAU9iFmReJ01qz6aaKhx5q5aab2rj33ha+9700MVtl04ql\njCeIqgmBCpoLgs14Zl3KcfEyGTzHNTIbrjLpWs/L0570S0o8DzedxktlTIkLoJwMVtzGjviAhrIe\nwr83eCqnfq0r7Laby+jRhcfyYIm0V0ota5WoVSiU8kBHaq5KjAppdJdp0yAK5XmFJ44U2ZRlfsTK\nkrYhaVqhtImFu8oQSY0J8Rty6dCebqE91YLrRcxxvQwZN41SHkJIbBuOOLKdRx9t5tvfTnH66Sm2\n287lgQfi/PAH9fz1oRrSGfAiEUbHTdOebiPtdIAOomsmuueoDK7rkXZSZFwHTzlIKcN06LqGNWtE\njqbUDTfU8NZb/XO1Sybh5JPTnHhibsTj3//u/eVlo400t9/enpNW/de/bGbOjA+8vlQ3aGjQbLZZ\n4fn5xhsxXn65fHM+bpyitlaTTGp23NHh7rtbmTmztUcF8+WGELDTTtntP/FErN+EQBsb4eCDHX73\nuw7OPz/F9tt7A17U3RUCP8zwdeCbGTFMzydaxSJxAJMmKb71rQwHHeSy/iiv0+aArqC1xkunUWkH\nL5VG+SRRKxU2EWjHxUulswTSr0MO16FU5J/pAtVK+2btdvgvP4VaUPqiSzOi32orxf/+bwv77ZfB\ntjWJhOaKK9rZeut1MysSoOr1WWFQyvPrwHJ/liCa1eV387TEgm4dHenONGlBc7JbUhKzcws8gjo3\nT5mOHS3AEhYx29STOW4GV3m4XgbXVQg00hKGqCkPx0mDH4FLxBLE4wmEBjeIwAlNzE5gCSuyr6C1\nx9KlCXafNpJUSiCE5pFHmvnqrm1oBFp7aG3cF5TyQGiksInZNkJYZJw0jptGKVMPkYwlSCRqsERp\nzQ3DDZ99Jtl110Y8L7vvp52W4vrrO/ptm8uWCR57LMavf11Dc7Ng9uwWZszo2wX2xRdtTjihnnTa\n7EdNjebFF5uZNKmy2Npbb1mceGJ9XrE7/Pa37Zx9dnkK7JUykVIhYORInSNLMZiYPTvGaafVA7DB\nBooXX2yu6DTSQEJrQ64CRL0/w2W6MEmHPDkNjJF9KVIfynWNTyd+JE+AlUgQFJ0ZrTfTrSkQxscz\nHjPpUsvK8S3VykP49x83lTLL24aEFtWR8zx/m1Eh4NLGDdDeDitWSKSEjTZSFVngX25UvT6HEKJk\nLEczrITmgvyUo0D4naBBwb2H4xkyY6Jn2eYF7YvHCoSJinW0+QUDCkvGSMQdbBlDaQ/XzZDOpHG8\nDlDgobGkjacyeMojZiXMeMP2bkwI3k9RSlyknU2XmlpbyYgRis0393jvPRutBb/6VS33/CVD4wgP\nHRmjJhv9E35Q2JYWgdSlLSVS2mHqdl3E2LGKQw/NMHt2loj/85827e30W03P2LGa00/PsP/+Do4D\nEyb0/Wa9114uDz/cwve+V8fnnxvvxhUrBJMmlWHAZcQOO3j8/e/NYRNEc7PgsMMcvvGN8lnsSFme\nOS03ooKyK1cKv0Ox8sY5GBBCgG0Zlp1X2B8uU4JfZs6De5D18CNdwTq6W49GgxRIy84ayksjtWFq\nRXRW2JY86Q4hQ31MuyZpqJ6UYTNXFCGxFBLluWF9W6kkDcw1aiCV/ysd1dRnBcOSdvivFMJhxAez\n9WTz5r2cu0AkrG0Ij8DzTErx008s/ja7lvnz42QyHaQyrbS0riaV7sD1MjiuQ3Prl6xau4KlX37B\nyqYlNLV9SVPqS1Y1r2LZ6k9Z9uUXrGlZxYovl9DUspqmtlWsbV9Na0cL7almOlLtZNwOHNehI91u\nujOVIV+WlKw3wuKkk7I3ttdfj/H+e3FAE5MxpF+ca0kLW8awpQVCY0uLeCxBIp4gZseI2QmkBMsn\nvZVSZzCQqKmB889P09CQvdhuuqnijTf6fy4mTNBsvrkuy1OwEDBtmsejj7bw5z+3cv31bTk1Ub1F\nfxwTW2yhOfPMDLNmtfL44y1ceGFqUOQyeoq+zsWYMSZFZSBobh6aD0f9dZ0QQuRYMPX4+0H9mxTm\n/whRM0+wxdOKxsbKRM4QYMUTfurSF+ANUpdSIi0LKx4Pxzhnzpwc6Q4hhb8+U/tm2XZRkpav0yYt\nO9dOa4ihUu4d1YhahUFrjasc0AJLdp3uLKYGHY2gFUBAzIrjKYeM56BcD9d1WPz5SE44fgRLl1o0\nNGgefaIdUfdv2tPt4DqMaBxDvVVLi9eBcjtoal1FW3sbWkhcnUY4inbXRXkpXBdqampoqFuPkfWj\nqKtbjxpL4eKScTJIaWNbTSRkEsu2SCRqSMZqQgI5fbqDEBrt1+c98ECSr+6aIpGMY9txPM81qVuy\n6WApJEp52DIOVgZPu8RkzZBTyy43pkzx+N//beHnP69h9WrJeed10Nw82KPqHYw21tDwFLTtwSt+\nHgyMG6c44ogMDzxgore95CNVdIGiJC9fEqQIrEQCYblFP5e+JZQOon1518og/Rn83ZUTQ/gdIUxp\ndZa3V1EGVGvUKgwZN2XqrDBEJGbHC06gQDojICKWtHM+yxd+1TpIdUqTuvRcXM/FczOsWm3x/e+O\n47XXsppmD/7v5+jG53CdNEor1qtdD4RFyjFp09a2taxpWQIiRsZL057qQNqQcTNoNOslR9CQHMF6\njRswomEUNbEkWGARQ2iJkGBZNsl4LXWJBuprGojFEsSsGKmU4IILapk501z0YzHNvHlNbLFF7mEa\npGmDfXU9x9Sv+alcS1pY0uq2rm9dQHs7pNMMinxDFesGXnrJ5ogjjO/OP/7RxJQp1bRVfyIwcdda\nGxN4P9JVDKFTgdZhjVx/P8BGCV4VpaFaozZEoPM6bjrTPdP5emd+J2U+eQtegynml0KF6VFLa9Ja\n8fFHI3JIGmisWDNLVi4iLRQxNC3Na0nWNvBl0ypWNq+grb0DrdJoB9CCTFsKHUthuUmsBhu3UdOR\naSftOKQy7dQlG7BiNnFpk4g3kLAtLAs87eGqDGk3jW3beEqQSFqceWaa+++Po5TAcQSrV0u22CJP\n3yfftkoIPF/oVkqQuvpY39EBzc2CZFJXSVoV/YpttvHYaSeHBQtsGhsr/9m/pQXWrhWkUoJRozTr\nr1/5Yw4QpDyzorZ+9KuTpgQhpen41DpYvN9RJWjlRZWoDQCi3ZjddW+apgGF1mDJrhX+I1/KIWVB\n5+acOXOYMWMGSmlcz8GybJNORaClwLJs5r+ezFnV1lu7uLGFLG5eTltzE7FEAq0ctGeR6Whldesa\nQJLEwkXjkAJsUk4Km2bqmutpbV5LS90IOuo92tJNNMRGYCcTxO0kI2vTePUjTE2ZFUcisYTMWj1p\nzZQpHtdf385555m2tpaWUurzzHqQgYy2Dud5zpw5FaMwPVD4978lv/xlknnzYqy3nubYYzMccIDD\nmjUv8rWvDcxcLFsm+OADi5UrBa4rWH99xaRJiokT1aCnx9bFY6IzlGMu1l9f89//3c6HH1oV2fAQ\n4NNPJW++aXHLLQnefdcmkxFMnuxy331tLF78jyF3TAjfLiraGRrUoAXQymQfkFk9NNFNbn7OnDnM\nmD7dEMFS70PDEJVynagStQFAVDJDaWXSf0UOfCEEthULI2bRlGYUUSuloHHAKxJ9k8JCa3CVg+Ol\n8ZSp8YnHkgghiFtx3nor19T4Jxes4N+rX6VtzRqamtYSw8IDHBQp2mhhhd/9A5paLDw8BIIMGo8W\nVhNnBHVtLm5bK61N9XzZ2ExtXQ0NNQ3YtmCEPRohEmRcl3isBtuOjEEIYjEjbrlmjeCqq2oYNaq0\nC7+MpDrX1QtLgJUrBbNmmfTxihVw5ZU1XH11kuOOi7PVVoKNNurfm+nixYLvfreOefNyOwpqajRX\nX93OUUdlKkZeooryYKutVFltvsqJFSuMdMwvf1mTY3gOxlmhtrZv50NrK7z9ts0XXwhs20hKbLGF\n6heP2sBpIGrtFJUACYRzcxwClAqtnKTdfbQrSJeaF90Tu4GA48C771qsXSvYdVd3nbp+VGvUBgBR\n4Veg5C7OUqG0wvNcIzyLldOE4CmPjJMi42ZwPQ+tPGqSdX4ES/H7343kumvNEX/mWS3sc9ST/GvR\nM6xauJw1eg0eGSxsJIImVqIxmlBZNwIbcENpkKhDQR0bsh4bYkmoGzmSmhGNbFg7gk0mTGZ0zQbU\n1oygPtlAMllPbdwQtmhK03FMZGj8eEVNTffzkO9Tui6TtTVr4Cc/qeXvfy80QvzOd9L88pft/ZoO\nffNNi/32a6B4okXz+OMt7Lbbui1iWcXAYMkSweWX1/DQQ4XnwkYbedx3XytTp/aNYM6fb7H//o05\n740bp/jZzzrYc0+HcePKf5uNkrEcrTVBQURNZRwjtyHASsQ77UANszJu7rkp7PJfT5cvFyxebMax\n+eYe663X9fJPPWXzrW/VoxQ8/HAre+/dd5vFSkJXNWrVQp4BQDTVGVX/j6K3fDlbo2bIiZSiYHsB\nefK0OZldzyXttNORaeeII5q56KJWbr9jDSec9C8yzhKEZ9OmO3BxafOjaE2sAYppQuWStOBvgaCD\nVSzmc1pVO22rm2hdu4Zl7atoXruGL9ub8JSD0ho3kw67OKOIxYxCd0DS8k3n89FTOZOeYulSQWtr\n2VfbLxg1Cn7zm46iOl733GPSPv2JLbf0uOCCFMXazRIJymakXUUV3eHhh+MFJE0Izamnpnj44b6T\nNDARtEmTconDkiWSc86p4+yz6/jss/Jfj3I8mC3LuBxE6tXCe0rQcBCI03Zyr9FKmQaF/8/emYdJ\nVtb3/vMu59TaPRvDMAwDgyAgssgioMwIV1kuoKOo4IomIqghilHi1STk0Xv1yk0i99GoubnXaIiJ\nQUUFxQVF2YYdF9ZMdBCQZcRZe6mqs7zL/eM9VV3dPft0T9fM1GeeeZ6u6lpOvX3Oqd/5Ld+vsbhu\n5xoxtRWKdevguusiXvWqQc44I/z/9KcrpFvQhf7P/5S86111nAvanCtWzHyGb1fSD9R2AVIEKyOt\nokn9ac45chNU9bszb867LQYlm6M74FuxYkUYLCj6v7SMkVoVDgECHMze9w+885LHefGJ/0HCU2hV\nohRFlFF4bFHSzIHJivab8/RsZ9scDhgmwdBgFN/IoOXIk4QkGaXVagbDdCm2aHvVXg/rzFYN6zd1\nQpkKLZx771WcdtogH/94hT/8YffI1C1e7PnCFxp8+9sjvPKVOSFoupV6vVv3anqo1+HyyxN+9KMR\n/vqvm7zqVRlnnpnxsY+1+MEPRjj22JnNpvWKPlIvsCevhbUwOiqQ0iOlZ9Eix5VXNvnpT0f49Kdb\nHHbY2Dl2Z9Zh//09//qvDY48cvK56a67Iv7yL6s0Gjv88lulo9XWdhSwRdBVSG9MePAmX6Nbi+3u\ne+4F/CadFHaGdevgM58pc+mldZ57buycf/vt0RYDtSDWPbbdq1fvmtClV46NvSss7UGsy7HFAeKd\nCf1n3VOduKAAvZlAZqIR+6YGFbSOKBXv5QuRG4HHRpLYW5xzVOMKA9U5PD/8PE07jEViEXjGn3i6\ng7N2pq47k7YpWjyDY1/KaRmV1Wm4lEHvkToMN0RRqaO+vbkrt25D+XZmbWvB3VTx+98L3v3uOmvX\nSr785RLLl2c895xnyRK31XT9TDNrFpx+uuGlLx3l2Wcld93V4BWvGObgg6e/l6hWg5NOspx0kuXy\ny9N2X3KfPrsMpeADH0i44IIUKQW1mmf+/GkoQzrHoQcbrv13x733RXz60xV++9uxc/E992g2bAjv\nP61MEJwdN1hQXKBvq/Cu0FNfmVixIuL//J/JfSyXXpowOLiJJwDGBJuybk4+ec8qe26NfqA2DUzU\nL5NSdQYK2lZQ7cCk7V/ZNlPvluhwzuK8R6Pxwm1xuED4sddt055WEUKiVTAwt86EIQM8Lk9QUuKd\nDwrSIiaSEWVZJY4lKrOA6+pHK94POe52NxMDNl9IZ6e0GKGBXi9ozK4h9jmouFIbM5x33qLEtu2S\nWwoMJ7KzUzvPPCM7vRTLl+d89rNlbrkl5oILUj7+8dZ2N+avXRtskIwJqu7T0XA8kVoNDjvMcdhh\nLwd2fcP3Nmhl7lJ6YZKrV9jT16JSgRe8oJDw3wI7ug7e+07j/f77GV57XsIrlqU8+aRm/QaB94KD\nD3Yz4lLR/j7YpuBMCLwPEk5Lly2dlvaR66+PJ933rnclvOY1mxez3rhR8Oij4xMQu8qkvVeOjX6g\nNsW0nQXagURo9LdjfVzOdII1KRUIyG2G9xBpiRQVXGHK7iaI124p4zTJD64LKQr7EeGQUuJ90DDT\nKioOzgxvQQlPXQdXAc+zVBikRQNIxn/GtkfnJrxFffGv8960PeJGsJSxvsZIYsiSZhhREBECgXEG\nLfVmP6OSumPiLjbT5wdjpvbt50wFQ0Nj73XkkZarrgpXhN/8ZokTTrC8+93pNmWKRkZCiv/KKys8\n+WQ48bzwhYZrrmlwxBG9OS3Xp0+f7cTBvDmOeXNCf+h0NOJvDiFlxyqwXQ7dFMHqyXee0x5GCObs\n226evr289rUZP/pRKHO++MWWj3wk4dRTc+bO3fxz6nXPfvs5nnkmfJalS3MOPbQ3B5FGR0Pbx1TT\nL0RMIe1MmnOuM4EY7g//jbWkeYaxprjP4ZwJjfRSIEWEc7Yzsahkl77YFnDeYWze6eGCELDcfsdt\nnZJou0Tq8eQ2I8uDf6dxntwZjMlwwlGp1IlUibhaxyPZUizfDsq6hwkmZtq6y6NNMiwO7w3W5EEr\nToUA09nJvWcTxX89frPBaHsNcpvjCumS9uvtbJ9B97lu4tt//OMVnnhi64dRksCXvlTioovqnSAN\n4De/0fzqV7tOHLJXei5mmv46jNFfi8COrkMwHO9u7O82ydz1UkFCqc36a3rvccbg0gybZjhjsVk2\nqVw6XfvEa16Tc+edw9x99zDf+94Ir3nNloM0gHIZLrkkNLAddFDQ2NxVAt7bug6rVkmuvLLCOecM\n8MlPlnnyyakNrfoZtSmk3VsmCu9J6y1KKaQQWGcxNgsBhw+uAXiJcRY8YfpR5MTExQCARgpFboNt\n05Y9P8eyMc47vBvbFucsyC45Dd/OhHkcnjRtkGSt8BpCEsdV5s9ayNDc9SQb1zNMGU9jXADWDs66\nhwbGMmdiUrDWfo7Co1HIWCOVJo4jpIhQKuyGzoUgUomQaex2Weju23POItXYgdD+nK79mbGdAYqp\nYOFC1/EfdQ7i2JNl4eSbJIInnpAccsiWM2JPPin55Ccn92YI4XdJv1ifPn2mD6FUIbYNUuiOhVLP\nNWUW+mu+sCnEueD3uYt8kZWCF7xg+893Z52Vc9NNw+y/v2PRot5SFFuzRnDZZVXuvz/00T36qObR\nRxX/+I+NzfbdbS89thftGch2X4AoghnvEBTTn52gw5GZDGfBe4uUIYPWDlqAom9NhayaHx+QbZEi\noDn11FPDTeeKTJ8tslKu6FdzWO9BQu4yBD5MhSJQOqIyezY1KoWuoiB4GohNaqa5rl420fWv+zGW\nFlAiEoJabRbOCSSeWJfwgLEZuc0wNp/ksjAxk7apzFqQPhn7XbvEvLN9BosXOy64IJQxVqzQnH32\n+H6K7tLologntGeUy54vfanBS16y69L4vdJzMdP012GM/loEdnYdRJexeXsCs+e0HNvb0530kyJc\n+AblC6TWPbdPzJoFL32p3eVB2rasw29/KztBWpubborGTbXuLP2M2hTS7RggxZiemfchI6YIwwMI\ngXe2kOZoIYpSZ6zLk14z2E+1A7RNZ9akUDjGhhcQoigtFtkuEQIsWUyPaqXJnSEMCng8kiRNkUoh\nvSKKY2qlCKk1VarkzKXF2nHvuaVhgokB2tjPEYYEYx04izUthNRIKcjb5WAHVuQIMZahk1KNn2yd\n0KPWPkG2s5miKJF673B+y9nIbaFahY9+NOGggxxHHGFYvNjzgx9EWBu2YVtEuw8/3PGDH4xw440R\njYbgqKMsxx9veNGLXE812ffp02fPpe1qILXGF20y3oWL9Z4MLHcDomjyfVM9PNXPqE0xSmq0isZl\nxlQxcRm01MLPUiicc0WgIjslvm6C/EQ7OyQAuUlttfZzOzptRRp7xV0rwkSp8xhncH6syT5WMdVS\njVKpSqQ0A9UBylEVZzK8y6lEsxgcqBPrGE0FCHtjuw+tnV3rbEPXIIErpgq7g7UQvjVokdNq5qwd\nXoPzHuuz4PcpY5TSRcAlQmHWh1eDEAS3xWwnadF5hyjWVCCBUGq21mCc4bY7btuhv2U3S5Y4Pvax\nhPPPNxxzjOUf/qGB1p5Zs9w2TSAJAccdZ7nyyoSrrmrx9rdnHHnkrg/S+v1Igf46jNFfi8BUrEOw\nXrJjpc8eRGodxG+jCCGL4Mwzbpv7+0RgW9ZhyRLLaaeNr7Jcdlm4sJ8q+hm1bWR7a/hBAqPdyD8+\nA2SdwRaas+0Ml97MhKKSGoHvylhvfRvCZOTYtKgTvvObsF1grcUjKEVljDFEMsZaQyPbSG49Qkkq\ncYnyQJ1ZGywWT5NnOtswcZBgWzGMkg4PMzS6lnUja1kw9wCcd2glC9VpEEzwOfV+s02544Y2is/d\nrooalxf9Ii70te1kZq1NHMPrXpdzzDHDAONEM/v06bN9bNwYVPylhIMPdruta8U4f0wA7JSKxfbp\nTebOhc99rsFNN0U88IDmzDNzli41lCcXyHaYvtfnVujWRNtU1mtHcEWPWm4ynHNIqdBSoXXcKdnR\nntLchCbbpNebIEnRbqy31mC9RRCspaIi4xYmRG3RCwbWBtFdYwzrRv/A8Ogannju16wdXcPGoZzW\nhtWIFyulAAAgAElEQVSsz0bYwCqASaXNTd3X7mnrzq6Fx2j24SD2O2ARx7/gJF4w5zXce+9sXnio\n46STk85naAdg3juUilBSdfWejQWh3ZOibcMF61zH5SFkMBVCgFbRuPJpnz59Zpb/+A/Jn/1Zlfvu\n00gJV1yR8L73JcyaNdNbtv14a8ea9GHKVf2ng45HqOiXPmeaLXl99jNqW6EdJMHUKeKHPjKJivW4\n4MM6i/OF5poHRNHbtgUR2In+l9aZEEz6cMBJr4vXZ1zRPAwpeKy3lOIKjWQY5w3OGHIvKZXKlEyZ\nWQiyRoU4G0UxC8fwuOnOieXPbix2E7/LGWEDs9fPpv6C47n8A/ty//0xBx9suenHlrlzgrSJsRbj\nUpSI8ORFMGkRQhLpqOPnGQYzQtZSSlG8U9CICxZYsugXEOOyb+217dNne3juOUGzKTjkkH5v4c6y\nerXg4otrrFzZnvqGv/mbCqefnnPKKb1bOtwsUoLr2u7dYAeRevPalX16h35aYStsb2lvu1+/aIQP\nHpYW26UntrmG/W429xgpJPfcfS9KqaDHVjTkt38XnhucB1ITGvwFAh3HSGEYqM9jdjybSACliJgK\nNWpAddz7dk95tm9vTp6j3deW0WLBwMFcd+3h3H9/GIUcHRU0mwnNbJQ0T0nzJsY4cpuTZimj6Si5\nNRhryE1eDFlYKKRGwmCEDNO1Mnxm4RW5bXHb7bfi7PjJ0R3xUd0T6PeeBLZ3HYyB22/XnH76IMuW\nDfLoo3vOqXOm9onf/lZ2grRuGo2ZCRp2dh2EEEHcVgqEmj7R2KlmuvyRIVQ5HnlEcuedmpGRKXnJ\nXUqvnC/7GbWtMH6SM0xNWgsPPaR44gnJ4KDnkEMcS5Y4KKQv2s/bHpwv5C28D7ppwm9T5k4KiReO\niZIU3b+fGGsGRwSBJ8ZLh82amDzFA/XSAM14mNzkVEo1dCti7mCNYSWQazzKV9jI83hGw/ttQTdt\n0mcMnguUqLL/vDfw8a+O1Tf23deRiw00E0FJl7HOFbZ1RdbOebwIvWrtIKvdkybammntmK3A+hwh\ndNC1K7Te2gFl/wqyz/Zw332KN7yh3pn0/d3vJEcdtXcG+1PFpnrRFixwO6Sz1SsIIcYrZO/l/OpX\nile/eoBWS/CpTzW59NK0vzw7QD9Q2wYm9qWtWiU5++wBjAkn7VrN8z/+R5Nzzk2YN684ybjtC9aE\nEGSmRRi8cWgmTzduafvagV43W9KAEYig9yYUcVSmUnakeYr1joHKHCIVo5CY3FArNaiXR3kOi1qv\nsMYwgkWQTtJPm/gebSQSS40Kc1gyeAAPPrCkMIgPvOWtI2T2ebJ8NloqQGLJcTlEqt2/55ASdEeu\nYyx719asE1KCawe+IXA95WWnYF1hmdUl+bE30mv6SDPF9qzD6tWCD36w2gnSIPhH7inM1D5x2GGW\nD3+4xdVXl/FecOCBli9/uTFjAtB72rGxZo3gySclw8MCpYJQ99y5nn32Cf+3xFSshfdwzTUxrVY4\nbj7xiQpnn53vVoF4r+wT/UBtB9A6XDSZoo+90RB86EM1HntMccWfN5g7124yo7QlPICXKAlCaNjO\n57cN19v9Bm0bqknv09UT19YmU1JSKdWItCbJEpSo451jdm0Omc2RLUW1MgBasb60Fp4DaRU5CRkG\nwwZEmCXdjGF7iYjZzGcOs2tzOeaFr+ej/3ufzm+19hx3wgipy5ijggQH0iNdyPg5D87lSATOOGQ5\nBFlSqo6/eHuytq2lpotALDfB2UHJIHUyVf6fffYeHnxQsWrV2H5TqXgOOGD3+bLpVQYH4cMfTli+\nPCPPBYsWORYs2ONm22aMRx9VvP71AxPu9Sxe7HjlK3POOCPn4IMdixc7BiY+bApYu1Zw881jKt9Z\nJnj6ablbBWpTjXPw2GOS3/xGkSSCgw+2HHmk3aqDwe5RRO8xlixxfPKTzUn3f+lLZe5cEXbM7e1t\nk8ggSCvlDvWgdqv3tydFJ9bXQx+c6XiCSqnQKgrenlFEpMuU4wrlqIpUAuMskdLUy7MoR1XmVGcz\nd85c9lk0h30H5rGABcxjLoPsT4V9CpOoMp4qnkEUc4iZzTyWcFDlYBYesIijjziG/eYcwZo1Yx/y\n0ksb7LdoDfMH9qVemkUpLqNF4eBQ2GFZ63DOYwpHB2MKb9MuL9OJn0+rCK1j7r/3AaJionZv7U1r\n0ys9FzPN9qzDN74xvkZ32WXJVi3Ddidmcp8ol+Hoox3HH29nPEjb046NE080/L//N8rs2d37quDp\npxXXXFPmoosGWLp0kLe/vc6tt2rWrRs7J0/FWuQ5NBrj70uSnX7ZXcpU7xMrVmjOOGOQiy+uc9ll\nNc49d5DPf75Mc3I4MY5+emEHUAouuCAjywRXXlnp6H8B3HRTzGtfl233ZKiUIQtkXLCT0jLe4uO3\nV2ZiYpDivEMSsk5tb1EjchCQmAQtYoSQlEtVBC3Qmpq3aBkhrALWk9cUcdZkYOMITTdKmTItEiIi\nqpQpUw16bPsMctD8A9l37v7sM2chZTOAUmAtvOQlhj9+V8K82fPC9hUfRymNdhaDD6K9NsepKGTs\nvMN6gyomWp134MUmP5/sTIMGpns4pM/0sHKl5KGHFI89pqjX4dhjDS96keWAA6b3y73VYpzB8ty5\njje/Oe05C8c+vYl3QWppJnpi63V4wxtyTjhhhLvv1vzt35Z58smJLR+CO+6IuOOOiBNOyLn66iZH\nHz01FyGDg54XvMDyy1+OHSwDA3tvxnRoCP7iLyodn+g2f/d3ZV7zmmyLz+3rqO0EWQYPP6y48caI\n66+PKZc9n/lMi5e/3Gz9yTtBWycNxlwJuu/fVOnTe09mko7WmFbRuDKgdYbcZGQmI0lGaWYJo8kQ\nxqbgBcYbWklCkjZoJSOAI01zGslG/rBhIxs3bASRYtIMryDyFWrzB5lVm8Ws6gDzZx3AvNkLmD0w\nm1nl/fjavy5k4wbJRRclHLQkJ8mS4jN5YhUTRyWcd+QmJzUZzuaF6K2iHMdEanyWQ0pVTIGOEXrS\nxnTmRDEM0mf34rHHJOedN8DQ0Pi/3eLFlq99bZQXv3j6slvWwkc+UuErXymzcKHlX/+1wXHH7YbS\nEX12OR2NMuiJKdB16wRPPy14/HHFzTeH4GyiH+Uhh1i+970R9ttvasKCf/7nmA99qAaEi5xbbhlm\n8eI9LuTYJkZG4E1vqnPPPeM9p6T03HrrMFn2wGZ11PqB2hSxbp1ASs+cOdP/Xm0x1zZtTbEt4ZzF\nONuZStWFiGybdqBmrA3BUdqgmY6SmCbWQmYzKroChUnUUGMD60afJxsZZcg2aSWjpJkhcy3KUYlK\nVKOsy9TKNebMWchgZZA59fnUSlVKlToVXUPrIMQrkCRZMwRaQoDwlHQFj0MKFfTTCKVYvKMUVRAy\nlDp94VqgZRS2rAjWuuVI+uze/OQnmje9adNNNOefn/GP/9jYJr/VHeXxxyVPPCE55BA3Y43uextD\nQ/DAA5qREcELX2hnxG5te7EWnnpKMjQUMkcL9zNUSu1ILWiW9RJr1gjWrhW0WoIsCzJw++3nWLzY\nT9laP/204KMfrXLHHRFf/eoop502vUmMXucXv1C88Y11Nm5sfzd5PvWpJhdfnPHII33B22ln3rxd\nF++2m+bbP28uSFuxYsW4qZX2lCdMUuwYm4S0BikFlXKdKC5RSiu0TIsBMYiUGokgtynWe0pRmUZl\nmFqWkGYZw6015EmTWm2ASjwb76BSKqOkIIojokgidUysIlRQCCkM6wVCCvAS7y3t+qcUCll40Xnv\niTueqGNyHK4Q1TXWgCgmOidkziauw97M7rgWRx1lOf30nFtvnex+/KIX2R0a99+edTjkELdH9aRN\npBf3iUceUVxwQQjOy2XP3/1dk1e/Ottq0/XOsDPr8Oyzgq98pcQXv1gmScJF+1venPGRjzRZtHDL\nwclMlUfnz/fMn7/p762p2icWL/Z88YsNRkbEtLcpTAdTfWwcf7zlpz8dYdUqSZrC4sWOww93xFvu\ndOoHar1EtxXU5qY2279rByhSbNu3lBAyiGi0p0InyFNIqYhEMDSnGEYoiwqRKqOzJtIHswOtIyQ1\nKqU6SdZgzsAcmlmLPGvRyvYFb1BK0zStcIkpNMJLFJpIVanGtcI1oP05Q/ClVYQUDutCwGZcjkCi\n8EQqxpisKF927bJdumnGZngcWkYhzvOin1HbQ1i40PMP/9Dg4YcV3/1uxH/+p+aggyznnptz6qmm\n5zMtfbaf7j6eJBH86Z/WSBJ4xzuyac2e7gjew9e+VuLqq8c0W5wT/NvXShx3vOGP3mE2ayXVXR6l\nB8qj08GsWTBr1u4XpE0XBx+8/Zn5fumzR5joWznRV9QUv2tPh+7M+2wuAOzeBu/btzOSLMW5UHqo\nlWsoHZNmrcJFwWGFxeYZrTQBPN4ahtMRsjwF4UFIBkpVBipzqFUGKZeqSEK/Wds1od1f5z0YlyJQ\nneyZLzaovd1SKgSi45nqvCc3WceVQEpZBH573kmvT5gmiyYn1/rsQTz1lOSsswZYs2bsGI4iz803\nj3D00b3VI9hswnnnDfDgg5MjyE99qsn73pdu8nmTTNx7sDy6erXg4YcVeQ5HHLFnZ5Znmr7X527A\nlnTXjDNkWYrHo5QkprzDwdqW0uvtMqp1wZ5JFsFiHENuM7SMiHQJKRVWRyihQAa9fx87ynFCkrXA\nQ6U6QJY0adkUvCdSiixPkCpmaP0gIyOaShkOWJwTRUWGz7ddA0qdoQfnx/rOhCjEfa3p+OgF8/kc\n8B2HAsHkadhxAxiFMG4/kNs96Qdpez4HHeT47GcbvPWtddqNGnkuWLFC91ygVq3CRz7S4qKL6uMU\nAI44wnDmmfnmn9jjqeDf/lZw6aV1fvGLECYsXOi48caRfp/mDND/puoR2iXANt1WUMakHZ00YyzG\nb1tD5vZowAQj9LyQrwhBo/Me5z1SCMq6QqR0J6As6TJRFBMpHQIopamWasyqzWXO4DwGq7OZO2cB\n8wb2LXTY6gyvW8I//+NBnH7aPF6xbA7Lls3mwQdLIX1XrEFYBwnCF1k92ynTtrN87ZDWOUduMrwP\nJdt2FlKreJyv5x133IF1Fu/BOotxeQjcXG+d8HcFe5pW1I7SX4cxenUtli0z/P3fN4misWN5aGj6\ngpudWYczzjD8+McjfP7zDf7n/2zy9a+PcN11oxx66OaDGiGK3lxBmGjvIW+lFStW8O//XuoEaQCr\nV0seeaR3tnFX0CvHRj+j1kMoqccNCbSZqP0lpzi+7kxPQqec2Pmd96hignJiNq5dmhVC4pxFCEGk\ndTBHFwJBTEmX2ZDl3H57nQ/92SxGR7t7T+jYPI3fFod3oaQpZXtwQuC8xVuPcVmhARfKquExEgq3\nhTRvAQJduBw4HwzvfdGjp2TblL73qv4bN4ZG6sWLPQcd1FtXro1GUOn/3e8kL3yh4yUv2bFG/r2B\nRgOefloiZWgY3pMsp3YVtRq8+c0ZRx1l+f73I9avFyxfvmW9qZkiikKj+PHHb9/Fn1Bqlyk7buq7\nZXOMjMB3vjO5w13KzZ8zH39cct11MQMDnlNPDTqHW2uS77Nt9HvUdgOcd2RZC4dDqYhYlaZ0Qqi7\nLAihd8IxvkzYDhaDgOzkb+cgOus7Vk7t+4yB675Z5k//tDbpOe9/f4s///OEen3sPmNznHNBkkMI\nnHNktoVzIVALE6ACJUFJhZJjMiNKKpJslCy3CAmlqEIpKhWf0QWjd2ynf21zn2Um+fWvJaecMov5\n8x1f/vIoJ59se6Z5+hvfiHjve2uAQGvPDTeM8LKX7X1Zya2RJPCZz5S5+uoyQsC55+ZccUWLY47p\nrcC7z97DOE03KbaavWs24Q1vqHPvvWN9BtWq5+abhzniiE3vx9/5TsTFF4eTuZSez362yetel1Gb\nfOrvswm21KPWL33uBkghKcVVynGNuBB6bVslTUWc3R1cCSHQOu4I4iqliVRcNOmrzQY27aCnO4CU\nQrLyPzQf/GB1wqM97/uTFpe8p0m5ashNSpYnZCYlsymZycnyjGah5Waswxd9emmS4l0oi+JDNi0M\nD4RoJrdhPax1pFkT5woHh+IxsS6hpe7JIA2C/tL8+Y41aySve90AN94YkW+hzWVX8fjjkg9/OARp\nAMYIrrmmtOUn7aUMDQm++tUS3gucE9x4Y8w55wxy//29t7/12fNxzo2zjvZu698Z1Sp84hMt6vXw\n2DlzHNdeO7rZIA3GT3Y6J3j/+2tcf33cE+ev3Z1+oLab0DZRF6IoAfpQxjM2w9h8k0HbttbX271d\n7f8Tb0PRQ4fY7sBw7VqJMWPB2wkn5Fx/wxAfumI9s+eMkmRNrHNkJqeVjGLyvPhMKSCw3mLynCxP\nSE1CZls0Wxux1qCUJFIxWmq0ijA2x1uDsRnW5GHQQUpWrLizo9cWPl9vBmkQpCg+8IFgiGet4JJL\natx999Sl1Ha052LNGkGjMT6L++STarc9CU9n78ns2Z5XvGL8wrRagj/6ozpPP917DeS90ocz0+xp\n6+Cdw+UGbyzedmW+t2EXXLFiBSedZLnllmFuummYn/1shKVLt9wbffjhloULxwdyl19e5cEHe/Nc\nuy30yj7RI0WVPttKO0Br/2ydQysZvDyxKLHjf9KJ5dTu2867runL8dIhW+LYYw033DBCswnz5jkW\nL06Ia6NIIbGF4brUmtzmQfgRi7UWhw/TpM7RSBsIPFIqPKGEGa4QRXtDQ6CKgMKxQOmIWJWDrEmX\ntEc7yN2UzVav8F/+S06l4mm1BNYK3vGOGj/60cgWr2anm1rNExZ9bL3OOSfrT2BuglIJPvzhhJ/9\nLGL9+rFr4dWrJb/7nWTx4n65uM/005b+EELghSh0KLde9uwmiD1v22MXLfJ85SujvPa1A6Rpcb51\ngu99L+LEE2d+nx8dDRecUgr239/tVueufo/abkg7exb6wuhIdWxPALWj79lmRyyarAv2VJlJMMaE\nQQIp0LqEMTnW5TgbAs48S8mdwQGCHC1jcpujZYTWMbEuEemIclxCCIkxOZnJAYF14XGluIzzFq3i\nIhPpkGJMCHc612tn8B6uvTbmssvGmjvOPjvjC19oMHfuzGzTyAh85CNVvv71UO7cf3/LDTeM7rW6\nSsPD8NxzktFRQbXqOfBAN67XEuCRRyRXXFHlvvvCN0Kp5PnJT4Y56qi9c8367FpcPj4DJvT0X5h6\nD3feqXjrWwc6g2Mnn5xzww2jMzpY8OCDkr/8yyp3363RGi67LOG9703Zd9/eCX+21KM244HakiVL\nGBwcRClFFEXcd999rF+/nje96U089dRTLFmyhG984xvMnj0bgE9/+tN8+ctfRinF5z73Oc4666xJ\nr7mpQK1toL56tWD2bM8LX+hYsKB3/kjbS7v53xeyHTC9/pY7E6j5wunAWoMHrLXkNkcKUXh0WnJn\nyfOU3OTgHcY58jwNPWhK4a3DCU9JlYL8Bp6SDkFbZi153iJ3BiU1EqiVB4mjmNzlCC+KrJtFS0Wk\nwxfn9gRq7fXeVdpr69bBn/1ZlRtvHOsD+7d/G+Wcc2au1viHPwgeeECT53D00ZYXvGDvCzi8h1/+\nUvGpT1W45RZN2x7jDW/I+MQnWuy///hzyoYNsGqVYu1aweLFjhe/uPc9K/vsGXjncEXZU0iBjONd\nVkFYuVJy660Rt96queSSlFe9auY8Ph99VPJf/+vgpNaNf/mXUV796t7p3ejpYQIhBLfeeiu//OUv\nue+++wC46qqrOPPMM/n1r3/Nq171Kq666ioAHnvsMb7+9a/z2GOP8aMf/Yg/+ZM/6TSLb40f/jDi\nrLMGeMc7Bli+fJDzz6+zcuWMf/wdpj212N1LNjGImMr6eneZcKKX5tZoy2IEGQ4ftlsF1wHrDUmW\n0GqNkiSjjDSHaKQjZDZFajAux1pLKa4wUBmkUqmhVESkIqSKSPMEa7JiwrRFmjUxLiO1STB194Lb\n77idZnMjadYkzRNyazqlz23BOtPRXet2j5hO5s2D//7fWxx66Nj7XX11iY0bd+51d2af2Hdfz7nn\n5rz2tfluH6Tt6Do89JDi1a8e4JZbIsbKwIJvfavEww9P3p/mzIGXvtRyzjmGo47qzSCtV/pwZpo9\nbR2ElCFA0xoh1fg+ta2ws2txxBGO97435dprGzMapAE89piaFKRBSN5sjV7ZJ3oiUpmY1Pvud7/L\nO9/5TgDe+c53cv311wNwww038Ja3vIUoiliyZAmHHnpoJ7jbGl/5Soz3Y3+slSs1b397jdWre/DM\nuZ1syZh9Kt9DFU37O9qI334NIUERkVvDSGuUVtogyRMymyLw5NZiTUqaG3CCqD2FKiKEh0iHCc7c\n5qF3zodhhMRkZDbFWE+atEjz4Obg8WQmJ80SsjyfJCMC7X4/O05Trn3/xNu7iiVLPNdc0+Cww8KJ\n7uc/j3jiid23MXdPYOVKSZJMPtbi2LNo0e4dvPbZA/Hjf94DO522SntytZu5cx0vfvHM981tKzPe\noCOE4IwzzkApxXve8x4uueQSnn/+eRYsWADAggULeP755wF47rnnOOWUUzrPPeCAA3j22Wc3+bqX\nXXYZBx54IACDg4MccMAJwNnFb28F4Le/PZ2nnpI8/vhtACxduhQYi6J3x9vee1asuKO4vWzGtwfg\nrjvvwnvHy099OQB333UPuc156UkvRQnBvff+nNzmHHPcEQiheODen+MwHHfiS6iV6txz19147zju\nxOMoxyV++cDDSKU5+ZQTEUJz/71347AcefQROO+4884VREqxdOkyyqUaWdbi1jtu46STT8R5wy9v\n+znlcpWlS5eipOaOO27HOsspLzsFIQT33H0PUiiWLVuGEIK77roL7z2nnnoqzltuv+MuBIJly14x\nLet1660rUAqWLVvKi17kuOKKm/jmN2NuvvkMms2de/2lS5fO+P7QK7fbbM/zjz7aMmvWzxgaksDp\nACxc+FPe//6EI498eU99vm293b6vV7anf3sKbwu4c8WdAJy69FSEEFN6fDQacOedK6hWe+TzbuI2\n3Mq73hVx/fVnkeeCY4+9mTe9KePww7d+vE7n+RLgzjvv5He/+x0AF198MZtjxnvUVq9ezcKFC1mz\nZg1nnnkmf//3f8/y5cvZsGFD5zFz585l/fr1vP/97+eUU07hbW97GwDvfve7Offcc3n9618/7jU3\n1aP25JOSSy6p8fOfj8WmUeS55ZZhjjxyz7kS7u4l65Vm+WD7VDgfuGDknmQtrHV4nxXSHE2sS0ly\nj/VNjHfowlvFA7nJyV1KSZUYqMxh9sA+RflT4YwhMQlJ0mQ0HcGYlHK5SqxjylEd73Kst4BASs2s\n2mxq5QEguCtkeUJuU/BBQy7ox4314LV77MLU61j2cjp6Ah95RPLXf13h7LMNF16YMmdOuL/RgGef\nlcyf7zr39ZkZnnxS8sQTkiSBwUHPIYc49ttv78tU7Cls2ABPPaWYP9+xaNHM/h29HZtKnypLKV+0\nB4kd9IfeFM7BnXdqPvnJMs2m4NJLU844I2fhwt48DryH558XWAv77OMp7YQE5DPPCH7/e8nGjQJj\nYP784CKzzz4799l72pR94cKFAMyfP5/zzz+f++67jwULFvD73/+e/fbbj9WrV7PvvvsCsGjRIp5+\n+unOc5955hkWLVq0Te+zZElQer/rrogf/zhCKc/FF6ccfvieE6TB+NT2ihUreMWy02ZUgqLteuCc\nw+MQCHKTBUN3Bd7HRIAvVbAmQqmMZprj8wyEDZOfXtBoJTgSXOyJsiaN1hCVUo3IR+AFxiQoJQv3\nAgd4rHVYlfHQzx/mhFNOQjLWl2asCYMKKIwzOFfYZ9kslGe7ZCiEECgR7ut2cAjO8VO3Vn/4g+Di\ni2v85jeaW2+NOfBA1xkeqNXgsMN2fl/tzpzszezMOixZ4liyZM85b+zt+8SGDZKzzx6gVruF//W/\nTuK008yMTAN6aztitOE8bqckWNuRAG1r+8SqVZILLqiTZeEEePnlmre+NeXTn24yMDD+s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nnxy46qrtN7OVh8+y7IgbGcbIzMxK8uUpInRkB0Kbtnq1MDkpzM4q3va2DrffbviTPxmw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\n9NBDPProo+R5zpe//GXOOOOMF/q0atSoUaNGjRo1nnfsd6VPay2f+tS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- } - ], - "prompt_number": 14 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "This looks pretty good, though it took a long time for the system to (sort of) converge. Our optimization step would look something like this:" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "_halo_data = halo_data[n_sky - 1]\n", - "print traces.shape\n", - "\n", - "mean_posterior = traces.mean(axis=0).reshape(1, 4)\n", - "print mean_posterior\n", - "\n", - "\n", - "nhalo_all = _halo_data[0].reshape(1, 1)\n", - "x_true_all = _halo_data[3].reshape(1, 1)\n", - "y_true_all = _halo_data[4].reshape(1, 1)\n", - "x_ref_all = _halo_data[1].reshape(1, 1)\n", - "y_ref_all = _halo_data[2].reshape(1, 1)\n", - "sky_prediction = mean_posterior\n", - "\n", - "\n", - "print \"Using the mean:\"\n", - "main_score([1], x_true_all, y_true_all,\n", - " x_ref_all, y_ref_all, sky_prediction)\n", - "\n", - "# what's a bad score?\n", - "print\n", - "random_guess = np.random.randint(0, 4200, size=(1, 2))\n", - "print \"Using a random location:\", random_guess\n", - "main_score([1], x_true_all, y_true_all,\n", - " x_ref_all, y_ref_all, random_guess)\n", - "print" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "(10000L, 2L, 2L)\n", - "[[ 48.55499317 1675.79569424 1876.46951857 3265.85341193]]" - ] - }, - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "\n", - "Using the mean:" - ] - }, - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "\n", - "Your average distance in pixels you are away from the true halo is" - ] - }, - { - "output_type": "stream", - "stream": "stdout", - "text": [ - " 37.3993004245\n", - "Your average angular vector is 1.0\n", - "Your score for the training data is 1.03739930042\n", - "\n" - ] - }, - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "Using a random location: [[2930 4138]]\n", - "Your average distance in pixels you are away from the true halo is" - ] - }, - { - "output_type": "stream", - "stream": "stdout", - "text": [ - " 3756.54446887\n", - "Your average angular vector is 1.0\n", - "Your score for the training data is 4.75654446887\n", - "\n" - ] - } - ], - "prompt_number": 35 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## References\n", - "1. Antifragile: Things That Gain from Disorder. New York: Random House. 2012. ISBN 978-1-4000-6782-4.\n", - "1. [Tim Saliman's solution to the Dark World's Contest](http://www.timsalimans.com/observing-dark-worlds)\n", - "2. Silver, Nate. The Signal and the Noise: Why So Many Predictions Fail \u2014 but Some Don't. 1. Penguin Press HC, The, 2012. Print." - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "from IPython.core.display import HTML\n", - "\n", - "\n", - "def css_styling():\n", - " styles = open(\"../styles/custom.css\", \"r\").read()\n", - " return HTML(styles)\n", - "css_styling()" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "html": [ - "\n", - "\n" - ], - "metadata": {}, - "output_type": "pyout", - "prompt_number": 1, - "text": [ - "" - ] - } - ], - "prompt_number": 1 - }, - { - "cell_type": "code", - "collapsed": false, - "input": [], - "language": "python", - "metadata": {}, - "outputs": [] - } - ], - "metadata": {} - } - ] +{ + "metadata": { + "name": "" + }, + "nbformat": 3, + "nbformat_minor": 0, + "worksheets": [ + { + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Chapter 5\n", + "____\n", + "### Would you rather lose an arm or a leg?" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Statisticians can be a sour bunch. Instead of considering their winnings, they only measure how much they have lost. In fact, they consider their wins as *negative losses*. But what's interesting is *how they measure their losses.*\n", + "\n", + "For example, consider the following example:\n", + "\n", + "> A meteorologist is predicting the probability of a possible hurricane striking his city. He estimates, with 95% confidence, that the probability of it *not* striking is between 99% - 100%. He is very happy with his precision and advises the city that a major evacuation is unnecessary. Unfortunately, the hurricane does strike and the city is flooded. \n", + "\n", + "This stylized example shows the flaw in using a pure accuracy metric to measure outcomes. Using a measure that emphasizes estimation accuracy, while an appealing and *objective* thing to do, misses the point of why you are even performing the statistical inference in the first place: results of inference. The author Nassim Taleb of *The Black Swan* and *Antifragility* stresses the importance of the *payoffs* of decisions, *not the accuracy*. Taleb distills this quite succinctly: \"I would rather be vaguely right than very wrong.\" " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Loss Functions\n", + "\n", + "We introduce what statisticians and decision theorists call *loss functions*. A loss function is a function of the true parameter, and an estimate of that parameter\n", + "\n", + "$$ L( \\theta, \\hat{\\theta} ) = f( \\theta, \\hat{\\theta} )$$\n", + "\n", + "The important point of loss functions is that it measures how *bad* our current estimate is: the larger the loss, the worse the estimate is according to the loss function. A simple, and very common, example of a loss function is the *squared-error loss*:\n", + "\n", + "$$ L( \\theta, \\hat{\\theta} ) = ( \\theta - \\hat{\\theta} )^2$$\n", + "\n", + "The squared-error loss function is used in estimators like linear regression, UMVUEs and many areas of machine learning. We can also consider an asymmetric squared-error loss function, something like:\n", + "\n", + "$$ L( \\theta, \\hat{\\theta} ) = \\begin{cases} ( \\theta - \\hat{\\theta} )^2 & \\hat{\\theta} \\lt \\theta \\\\\\\\ c( \\theta - \\hat{\\theta} )^2 & \\hat{\\theta} \\ge \\theta, \\;\\; 0\\lt c \\lt 1 \\end{cases}$$\n", + "\n", + "\n", + "which represents that estimating a value larger than the true estimate is preferable to estimating a value below. A situation where this might be useful is in estimating web traffic for the next month, where an over-estimated outlook is preferred so as to avoid an underallocation of server resources. \n", + "\n", + "A negative property about the squared-error loss is that it puts a disproportionate emphasis on large outliers. This is because the loss increases quadratically, and not linearly, as the estimate moves away. That is, the penalty of being three units away is much less than being five units away, but the penalty is not much greater than being one unit away, though in both cases the magnitude of difference is the same:\n", + "\n", + "$$ \\frac{1^2}{3^2} \\lt \\frac{3^2}{5^2}, \\;\\; \\text{although} \\;\\; 3-1 = 5-3 $$\n", + "\n", + "This loss function imposes that large errors are *very* bad. A more *robust* loss function that increases linearly with the difference is the *absolute-loss*\n", + "\n", + "$$ L( \\theta, \\hat{\\theta} ) = | \\theta - \\hat{\\theta} | $$\n", + "\n", + "Other popular loss functions include:\n", + "\n", + "- $ L( \\theta, \\hat{\\theta} ) = \\mathbb{1}_{ \\hat{\\theta} \\neq \\theta } $ is the zero-one loss often used in machine learning classification algorithms.\n", + "- $ L( \\theta, \\hat{\\theta} ) = -\\hat{\\theta}\\log( \\theta ) - (1-\\hat{ \\theta})\\log( 1 - \\theta ), \\; \\; \\hat{\\theta} \\in {0,1}, \\; \\theta \\in [0,1]$, called the *log-loss*, also used in machine learning. \n", + "\n", + "Historically, loss functions have been motivated from 1) mathematical convenience, and 2) they are robust to application, i.e., they are objective measures of loss. The first reason has really held back the full breadth of loss functions. With computers being agnostic to mathematical convenience, we are free to design our own loss functions, which we take full advantage of later in this Chapter.\n", + "\n", + "With respect to the second point, the above loss functions are indeed objective, in that they are most often a function of the difference between estimate and true parameter, independent of signage or payoff of choosing that estimate. This last point, its independence of payoff, causes quite pathological results though. Consider our hurricane example above: the statistician equivalently predicted that the probability of the hurricane striking was between 0% to 1%. But if he had ignored being precise and instead focused on outcomes (99% chance of no flood, 1% chance of flood), he might have advised differently. \n", + "\n", + "By shifting our focus from trying to be incredibly precise about parameter estimation to focusing on the outcomes of our parameter estimation, we can customize our estimates to be optimized for our application. This requires us to design new loss functions that reflect our goals and outcomes. Some examples of more interesting loss functions:\n", + "\n", + "\n", + "- $ L( \\theta, \\hat{\\theta} ) = \\frac{ | \\theta - \\hat{\\theta} | }{ \\theta(1-\\theta) }, \\; \\; \\hat{\\theta}, \\theta \\in [0,1] $ emphasizes an estimate closer to 0 or 1 since if the true value $\\theta$ is near 0 or 1, the loss will be *very* large unless $\\hat{\\theta}$ is similarly close to 0 or 1. \n", + "This loss function might be used by a political pundit who's job requires him or her to give confident \"Yes/No\" answers. This loss reflects that if the true parameter is close to 1 (for example, if a political outcome is very likely to occur), he or she would want to strongly agree as to not look like a skeptic. \n", + "\n", + "- $L( \\theta, \\hat{\\theta} ) = 1 - \\exp \\left( -(\\theta - \\hat{\\theta} )^2 \\right) $ is bounded between 0 and 1 and reflects that the user is indifferent to sufficiently-far-away estimates. It is similar to the zero-one loss above, but not quite as penalizing to estimates that are close to the true parameter. \n", + "- Complicated non-linear loss functions can programmed: \n", + "\n", + " def loss(true_value, estimate):\n", + " if estimate*true_value > 0:\n", + " return abs(estimate - true_value)\n", + " else:\n", + " return abs(estimate)*(estimate - true_value)**2\n", + " \n", + "\n", + "\n", + "- Another example is from the book *The Signal and The Noise*. Weather forecasters have a interesting loss function for their predictions. [2]\n", + "\n", + "\n", + "> People notice one type of mistake — the failure to predict rain — more than other, false alarms. If it rains when it isn't supposed to, they curse the weatherman for ruining their picnic, whereas an unexpectedly sunny day is taken as a serendipitous bonus.\n", + "\n", + "> [The Weather Channel's bias] is limited to slightly exaggerating the probability of rain when it is unlikely to occur — saying there is a 20 percent change when they know it is really a 5 or 10 percent chance — covering their butts in the case of an unexpected sprinkle.\n", + "\n", + "\n", + "As you can see, loss functions can be used for good and evil: with great power, comes great — well you know.\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Loss functions in the real world\n", + "\n", + "So far we have been under the unrealistic assumption that we know the true parameter. Of course if we knew the true parameter, bothering to guess an estimate is pointless. Hence a loss function is really only practical when the true parameter is unknown. \n", + "\n", + "In Bayesian inference, we have a mindset that the unknown parameters are really random variables with prior and posterior distributions. Concerning the posterior distribution, a value drawn from it is a *possible* realization of what the true parameter could be. Given that realization, we can compute a loss associated with an estimate. As we have a whole distribution of what the unknown parameter could be (the posterior), we should be more interested in computing the *expected loss* given an estimate. This expected loss is a better estimate of the true loss than comparing the given loss from only a single sample from the posterior.\n", + "\n", + "First it will be useful to explain a *Bayesian point estimate*. The systems and machinery present in the modern world are not built to accept posterior distributions as input. It is also rude to hand someone over a distribution when all the asked for was an estimate. In the course of an individual's day, when faced with uncertainty we still act by distilling our uncertainty down to a single action. Similarly, we need to distill our posterior distribution down to a single value (or vector in the multivariate case). If the value is chosen intelligently, we can avoid the flaw of frequentist methodologies that mask the uncertainty and provide a more informative result.The value chosen, if from a Bayesian posterior, is a Bayesian point estimate. \n", + "\n", + "Suppose $P(\\theta | X)$ is the posterior distribution of $\\theta$ after observing data $X$, then the following function is understandable as the *expected loss of choosing estimate $\\hat{\\theta}$ to estimate $\\theta$*:\n", + "\n", + "$$ l(\\hat{\\theta} ) = E_{\\theta}\\left[ \\; L(\\theta, \\hat{\\theta}) \\; \\right] $$\n", + "\n", + "This is also known as the *risk* of estimate $\\hat{\\theta}$. The subscript $\\theta$ under the expectation symbol is used to denote that $\\theta$ is the unknown (random) variable in the expectation, something that at first can be difficult to consider.\n", + "\n", + "We spent all of last chapter discussing how to approximate expected values. Given $N$ samples $\\theta_i,\\; i=1,...,N$ from the posterior distribution, and a loss function $L$, we can approximate the expected loss of using estimate $\\hat{\\theta}$ by the Law of Large Numbers:\n", + "\n", + "$$\\frac{1}{N} \\sum_{i=1}^N \\;L(\\theta_i, \\hat{\\theta} ) \\approx E_{\\theta}\\left[ \\; L(\\theta, \\hat{\\theta}) \\; \\right] = l(\\hat{\\theta} ) $$\n", + "\n", + "Notice that measuring your loss via an *expected value* uses more information from the distribution than the MAP estimate which, if you recall, will only find the maximum value of the distribution and ignore the shape of the distribution. Ignoring information can over-expose yourself to tail risks, like the unlikely hurricane, and leaves your estimate ignorant of how ignorant you really are about the parameter.\n", + "\n", + "Similarly, compare this with frequentist methods, that traditionally only aim to minimize the error, and do not consider the *loss associated with the result of that error*. Compound this with the fact that frequentist methods are almost guaranteed to never be absolutely accurate. Bayesian point estimates fix this by planning ahead: your estimate is going to be wrong, you might as well err on the right side of wrong." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "##### Example: Optimizing for the *Showcase* on *The Price is Right*\n", + "\n", + "Bless you if you are ever chosen as a contestant on the Price is Right, for here we will show you how to optimize your final price on the *Showcase*. For those who forget the rules:\n", + "\n", + "\n", + "1. Two contestants compete in *The Showcase*. \n", + "2. Each contestant is shown a unique suite of prizes.\n", + "3. After the viewing, the contestants are asked to bid on the price for their unique suite of prizes.\n", + "4. If a bid price is over the actual price, the bid's owner is disqualified from winning.\n", + "5. If a bid price is under the true price by less than $250, the winner is awarded both prizes.\n", + "\n", + "The difficulty in the game is balancing your uncertainty in the prices, keeping your bid low enough so as to not bid over, and trying to bid close to the price.\n", + "\n", + "Suppose we have recorded the *Showcases* from previous *The Price is Right* episodes and have *prior* beliefs about what distribution the true price follows. For simplicity, suppose it follows a Normal:\n", + "\n", + "\n", + "$$\\text{True Price} \\sim \\text{Normal}(\\mu_p, \\sigma_p )$$\n", + "\n", + "\n", + "In a later chapter, we will actually use *real Price is Right Showcase data* to form the historical prior, but this requires some advanced PyMC use so we will not use it here. For now, we will assume $\\mu_p = 35 000$ and $\\sigma_p = 7500$.\n", + "\n", + "We need a model of how we should be playing the *Showcase*. For each prize in the prize suite, we have an idea of what it might cost, but this guess could differ significantly from the true price. (Couple this with increased pressure being onstage and you can see why some bids are so wildly off). Let's suppose your beliefs about the prices of prizes also follow Normal distributions:\n", + "\n", + "$$ \\text{Prize}_i \\sim \\text{Normal}(\\mu_i, \\sigma_i ),\\;\\; i=1,2$$\n", + "\n", + "This is really why Bayesian analysis is great: we can specify what we think a fair price is through the $\\mu_i$ parameter, and express uncertainty of our guess in the $\\sigma_i$ parameter. \n", + "\n", + "We'll assume two prizes per suite for brevity, but this can be extended to any number. \n", + "The true price of the prize suite is then given by $\\text{Prize}_1 + \\text{Prize}_2 + \\epsilon$, \n", + "where $\\epsilon$ is some error term.\n", + "\n", + "We are interested in the updated $\\text{True Price}$ given we have observed both prizes and have belief distributions about them. We can perform this using PyMC. \n", + "\n", + "Lets make some values concrete. Suppose there are two prizes in the observed prize suite: \n", + "\n", + "1. A trip to wonderful Toronto, Canada! \n", + "2. A lovely new snowblower!\n", + "\n", + "We have some guesses about the true prices of these objects, but we are also pretty uncertain about them. I can express this uncertainty through the parameters of the Normals:\n", + "\n", + "\n", + "\\begin{align}\n", + "& \\text{snowblower} \\sim \\text{Normal}(3 000, 500 )\\\\\\\\\n", + "& \\text{Toronto} \\sim \\text{Normal}(12 000, 3000 )\\\\\\\\\n", + "\\end{align}\n", + "\n", + "For example, I believe that the true price of the trip to Toronto is 12 000 dollars, and that there is a 68.2% chance the price falls 1 standard deviation away from this, i.e. my confidence is that there is a 68.2% chance the trip is in [9 000, 15 000].\n", + "\n", + "We can create some PyMC code to perform inference on the true price of the suite." + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "%matplotlib inline\n", + "import scipy.stats as stats\n", + "from IPython.core.pylabtools import figsize\n", + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "\n", + "figsize(12.5, 9)\n", + "\n", + "norm_pdf = stats.norm.pdf\n", + "\n", + "plt.subplot(311)\n", + "x = np.linspace(0, 60000, 200)\n", + "sp1 = plt.fill_between(x, 0, norm_pdf(x, 35000, 7500),\n", + " color=\"#348ABD\", lw=3, alpha=0.6,\n", + " label=\"historical total prices\")\n", + "p1 = plt.Rectangle((0, 0), 1, 1, fc=sp1.get_facecolor()[0])\n", + "plt.legend([p1], [sp1.get_label()])\n", + "\n", + "plt.subplot(312)\n", + "x = np.linspace(0, 10000, 200)\n", + "sp2 = plt.fill_between(x, 0, norm_pdf(x, 3000, 500),\n", + " color=\"#A60628\", lw=3, alpha=0.6,\n", + " label=\"snowblower price guess\")\n", + "\n", + "p2 = plt.Rectangle((0, 0), 1, 1, fc=sp2.get_facecolor()[0])\n", + "plt.legend([p2], [sp2.get_label()])\n", + "\n", + "plt.subplot(313)\n", + "x = np.linspace(0, 25000, 200)\n", + "sp3 = plt.fill_between(x, 0, norm_pdf(x, 12000, 3000),\n", + " color=\"#7A68A6\", lw=3, alpha=0.6,\n", + " label=\"Trip price guess\")\n", + "plt.autoscale(tight=True)\n", + "p3 = plt.Rectangle((0, 0), 1, 1, fc=sp3.get_facecolor()[0])\n", + "plt.legend([p3], [sp3.get_label()]);" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "display_data", + "png": 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I5557jqqqqmE917e+9S3efPNNNm7cSDQaxe12s2/fPgD8fj9ZWVlYLBY++OAD/vSnPw17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\nM8j4fFsvx/7fOS59MUgikVtBgRDZdMNqx6k+kExlu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+ "text": [ + "" + ] + } + ], + "prompt_number": 7 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import pymc as pm\n", + "\n", + "data_mu = [3e3, 12e3]\n", + "\n", + "data_std = [5e2, 3e3]\n", + "\n", + "mu_prior = 35e3\n", + "std_prior = 75e2\n", + "\n", + "true_price = pm.Normal(\"true_price\", mu_prior, 1.0 / std_prior ** 2)\n", + "\n", + "\n", + "prize_1 = pm.Normal(\"first_prize\", data_mu[0], 1.0 / data_std[0] ** 2)\n", + "prize_2 = pm.Normal(\"second_prize\", data_mu[1], 1.0 / data_std[1] ** 2)\n", + "price_estimate = prize_1 + prize_2\n", + "\n", + "\n", + "@pm.potential\n", + "def error(true_price=true_price, price_estimate=price_estimate):\n", + " return pm.normal_like(true_price, price_estimate, 1 / (3e3) ** 2)\n", + "\n", + "\n", + "mcmc = pm.MCMC([true_price, prize_1, prize_2, price_estimate, error])\n", + "mcmc.sample(50000, 10000)\n", + "\n", + "price_trace = mcmc.trace(\"true_price\")[:]" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + " \r", + "[****************100%******************] 50000 of 50000 complete" + ] + }, + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "\n" + ] + } + ], + "prompt_number": 8 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "figsize(12.5, 4)\n", + "\n", + "import scipy.stats as stats\n", + "\n", + "x = np.linspace(5000, 40000)\n", + "plt.plot(x, stats.norm.pdf(x, 35000, 7500), c=\"k\", lw=2,\n", + " label=\"prior dist. of suite price\")\n", + "\n", + "_hist = plt.hist(price_trace, bins=35, normed=True, histtype=\"stepfilled\")\n", + "plt.title(\"Posterior of the true price estimate\")\n", + "plt.vlines(mu_prior, 0, 1.1 * np.max(_hist[0]), label=\"prior's mean\",\n", + " linestyles=\"--\")\n", + "plt.vlines(price_trace.mean(), 0, 1.1 * np.max(_hist[0]),\n", + " label=\"posterior's mean\", linestyles=\"-.\")\n", + "plt.legend(loc=\"upper left\")" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "pyout", + "prompt_number": 9, + "text": [ + "" + ] + }, + { + "metadata": {}, + "output_type": "display_data", + "png": 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qR8vK6NixY/D19a12PjMzs86529rm4+OD9evXY8CAAdoOhRpAGw8tq0lTv7+J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\nysql9u9bXyuxoZz4vEC8uF4zcT0mhmvGlveaieGYuF4zEtCLBn9P9Kf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+ "text": [ + "" + ] + } + ], + "prompt_number": 9 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Notice that because of our two observed prizes and subsequent guesses (including uncertainty about those guesses), we shifted our mean price estimate down about $15 000 dollars from the previous mean price.\n", + "\n", + "A frequentist, seeing the two prizes and having the same beliefs about their prices, would bid $\\mu_1 + \\mu_2 = 35000$, regardless of any uncertainty. Meanwhile, the *naive Bayesian* would simply pick the mean of the posterior distribution. But we have more information about our eventual outcomes; we should incorporate this into our bid. We will use the loss function above to find the *best* bid (*best* according to our loss).\n", + "\n", + "What might a contestant's loss function look like? I would think it would look something like:\n", + "\n", + " def showcase_loss(guess, true_price, risk=80000):\n", + " if true_price < guess:\n", + " return risk\n", + " elif abs(true_price - guess) <= 250:\n", + " return -2*np.abs(true_price)\n", + " else:\n", + " return np.abs(true_price - guess - 250)\n", + "\n", + "where `risk` is a parameter that defines of how bad it is if your guess is over the true price. A lower `risk` means that you are more comfortable with the idea of going over. If we do bid under and the difference is less than $250, we receive both prizes (modeled here as receiving twice the original prize). Otherwise, when we bid under the `true_price` we want to be as close as possible, hence the `else` loss is a increasing function of the distance between the guess and true price." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "For every possible bid, we calculate the *expected loss* associated with that bid. We vary the `risk` parameter to see how it affects our loss:" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "figsize(12.5, 7)\n", + "# numpy friendly showdown_loss\n", + "\n", + "\n", + "def showdown_loss(guess, true_price, risk=80000):\n", + " loss = np.zeros_like(true_price)\n", + " ix = true_price < guess\n", + " loss[~ix] = np.abs(guess - true_price[~ix])\n", + " close_mask = [abs(true_price - guess) <= 250]\n", + " loss[close_mask] = -2 * true_price[close_mask]\n", + " loss[ix] = risk\n", + " return loss\n", + "\n", + "\n", + "guesses = np.linspace(5000, 50000, 70)\n", + "risks = np.linspace(30000, 150000, 6)\n", + "expected_loss = lambda guess, risk: \\\n", + " showdown_loss(guess, price_trace, risk).mean()\n", + "\n", + "for _p in risks:\n", + " results = [expected_loss(_g, _p) for _g in guesses]\n", + " plt.plot(guesses, results, label=\"%d\" % _p)\n", + "\n", + "plt.title(\"Expected loss of different guesses, \\nvarious risk-levels of \\\n", + "overestimating\")\n", + "plt.legend(loc=\"upper left\", title=\"Risk parameter\")\n", + "plt.xlabel(\"price bid\")\n", + "plt.ylabel(\"expected loss\")\n", + "plt.xlim(5000, 30000);" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "display_data", + "png": 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EBQUhIiJC4VfFdu/eHf7+/ujfvz+WL18ODw8PPHz4EKdPn4aOjg5Gjx4NAFBX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\nGNFTBlwVBUTj2SwavngDY8YmFEs9AOqQKAIG/5KAIXfz1dF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ibKOnUql4+OGH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\nxe23387jjz8OQDqd5qGHHmLnzp0Eg0GeffZZ6usnt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Xk5nwuNaQmaBpI0dsc50BPn/feb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\noDlSqGo/arYdEkchsh8l24YihhurjvoLqhpayTSU4lrMwkpSvmLi7gLCT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+ "text": [ + "" + ] + } + ], + "prompt_number": 11 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Minimizing our losses\n", + "\n", + "It would be wise to choose the estimate that minimizes our expected loss. This corresponds to the minimum point on each of the curves above. More formally, we would like to minimize our expected loss by finding the solution to\n", + "\n", + "$$ \\text{arg} \\min_{\\hat{\\theta}} \\;\\;E_{\\theta}\\left[ \\; L(\\theta, \\hat{\\theta}) \\; \\right] $$\n", + "\n", + "The minimum of the expected loss is called the *Bayes action*. We can solve for the Bayes action using Scipy's optimization routines. The function in `fmin` in `scipy.optimize` module uses an intelligent search to find a minimum (not necessarily a *global* minimum) of any uni- or multivariate function. For most purposes, `fmin` will provide you with a good answer. \n", + "\n", + "We'll compute the minimum loss for the *Showcase* example above:\n" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import scipy.optimize as sop\n", + "\n", + "ax = plt.subplot(111)\n", + "\n", + "\n", + "for _p in risks:\n", + " _color = ax._get_lines.color_cycle.next()\n", + " _min_results = sop.fmin(expected_loss, 15000, args=(_p,), disp=False)\n", + " _results = [expected_loss(_g, _p) for _g in guesses]\n", + " plt.plot(guesses, _results, color=_color)\n", + " plt.scatter(_min_results, 0, s=60,\n", + " color=_color, label=\"%d\" % _p)\n", + " plt.vlines(_min_results, 0, 120000, color=_color, linestyles=\"--\")\n", + " print \"minimum at risk %d: %.2f\" % (_p, _min_results)\n", + "\n", + "plt.title(\"Expected loss & Bayes actions of different guesses, \\n \\\n", + "various risk-levels of overestimating\")\n", + "plt.legend(loc=\"upper left\", scatterpoints=1, title=\"Bayes action at risk:\")\n", + "plt.xlabel(\"price guess\")\n", + "plt.ylabel(\"expected loss\")\n", + "plt.xlim(7000, 30000)\n", + "plt.ylim(-1000, 80000)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "minimum at risk 30000: 13945.51\n", + "minimum at risk 54000: 12716.02" + ] + }, + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "\n", + "minimum at risk 78000: 12063.18" + ] + }, + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "\n", + "minimum at risk 102000: 11369.82" + ] + }, + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "\n", + "minimum at risk 126000: 11273.77" + ] + }, + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "\n", + "minimum at risk 150000: 11273.77" + ] + }, + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "\n" + ] + }, + { + "metadata": {}, + "output_type": "pyout", + "prompt_number": 13, + "text": [ + "(-1000, 80000)" + ] + }, + { + "metadata": {}, + "output_type": "display_data", + "png": 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h5+eH/Pz8Wvf5RdTVtkDF+x/PnleVv1fuf7du3ZCamoqzZ88iMDAQCxYswOLFi3Ht2rUq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3HwRz9Id5zenFVroGa9ma+Lb0AnRXBqYyaX3yNprTh+hrew3ftj/T2ttAS08d3b6xAQaApukU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\nD/8nA4ER+2N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+ "text": [ + "" + ] + } + ], + "prompt_number": 13 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "As intuition suggests, as we decrease the risk threshold (care about overbidding less), we increase our bid, willing to edge closer to the true price. It is interesting how far away our optimized loss is from the posterior mean, which was about 20 000. \n", + "\n", + "Suffice to say, in higher dimensions being able to eyeball the minimum expected loss is impossible. Hence why we require use of Scipy's `fmin` function.\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "______\n", + "\n", + "### Shortcuts\n", + "\n", + "For some loss functions, the Bayes action is known in closed form. We list some of them below:\n", + "\n", + "- If using the mean-squared loss, the Bayes action is the mean of the posterior distribution, i.e. the value \n", + "$$ E_{\\theta}\\left[ \\theta \\right] $$\n", + "\n", + "> minimizes $E_{\\theta}\\left[ \\; (\\theta - \\hat{\\theta})^2 \\; \\right]$. Computationally this requires us to calculate the average of the posterior samples [See chapter 4 on The Law of Large Numbers]\n", + "\n", + "- Whereas the *median* of the posterior distribution minimizes the expected absolute-loss. The sample median of the posterior samples is an appropriate and very accurate approximation to the true median.\n", + "\n", + "- In fact, it is possible to show that the MAP estimate is the solution to using a loss function that shrinks to the zero-one loss.\n", + "\n", + "\n", + "Maybe it is clear now why the first-introduced loss functions are used most often in the mathematics of Bayesian inference: no complicated optimizations are necessary. Luckily, we have machines to do the complications for us. \n", + "\n", + "## Machine Learning via Bayesian Methods\n", + "\n", + "Whereas frequentist methods strive to achieve the best precision about all possible parameters, machine learning cares to achieve the best *prediction* among all possible parameters. Of course, one way to achieve accurate predictions is to aim for accurate predictions, but often your prediction measure and what frequentist methods are optimizing for are very different. \n", + "\n", + "For example, least-squares linear regression is the most simple active machine learning algorithm. I say active as it engages in some learning, whereas predicting the sample mean is technically *simpler*, but is learning very little if anything. The loss that determines the coefficients of the regressors is a squared-error loss. On the other hand, if your prediction loss function (or score function, which is the negative loss) is not a squared-error, like AUC, ROC, precision, etc., your least-squares line will not be optimal for the prediction loss function. This can lead to prediction results that are suboptimal. \n", + "\n", + "Finding Bayes actions is equivalent to finding parameters that optimize *not parameter accuracy* but an arbitrary performance measure, however we wish to define performance (loss functions, AUC, ROC, precision/recall etc.).\n", + "\n", + "The next two examples demonstrate these ideas. The first example is a linear model where we can choose to predict using the least-squares loss or a novel, outcome-sensitive loss. \n", + "\n", + "The second example is adapted from a Kaggle data science project. The loss function associated with our predictions is incredibly complicated. \n", + "\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "##### Example: Financial prediction\n", + "\n", + "\n", + "Suppose the future return of a stock price is very small, say 0.01 (or 1%). We have a model that predicts the stock's future price, and our profit and loss is directly tied to us acting on the prediction. How should we measure the loss associated with the model's predictions, and subsequent future predictions? A squared-error loss is agnostic to the signage and would penalize a prediction of -0.01 equally as bad a prediction of 0.03:\n", + "\n", + "$$ (0.01 - (-0.01))^2 = (0.01 - 0.03)^2 = 0.004$$\n", + "\n", + "If you had made a bet based on your model's prediction, you would have earned money with a prediction of 0.03, and lost money with a prediction of -0.01, yet our loss did not capture this. We need a better loss that takes into account the *sign* of the prediction and true value. We design a new loss that is better for financial applications below:" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "figsize(12.5, 4)\n", + "\n", + "\n", + "def stock_loss(true_return, yhat, alpha=100.):\n", + " if true_return * yhat < 0:\n", + " # opposite signs, not good\n", + " return alpha * yhat ** 2 - np.sign(true_return) * yhat \\\n", + " + abs(true_return)\n", + " else:\n", + " return abs(true_return - yhat)\n", + "\n", + "\n", + "true_value = .05\n", + "pred = np.linspace(-.04, .12, 75)\n", + "\n", + "plt.plot(pred, [stock_loss(true_value, _p) for _p in pred],\n", + " label=\"Loss associated with\\n prediction if true value = 0.05\", lw=3)\n", + "plt.vlines(0, 0, .25, linestyles=\"--\")\n", + "\n", + "plt.xlabel(\"prediction\")\n", + "plt.ylabel(\"loss\")\n", + "plt.xlim(-0.04, .12)\n", + "plt.ylim(0, 0.25)\n", + "\n", + "true_value = -.02\n", + "plt.plot(pred, [stock_loss(true_value, _p) for _p in pred], alpha=0.6,\n", + " label=\"Loss associated with\\n prediction if true value = -0.02\", lw=3)\n", + "plt.legend()\n", + "plt.title(\"Stock returns loss if true value = 0.05, -0.02\");" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "display_data", + "png": 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0dOLj41GpVDRr1gxr68IX1NVqNadPn+bu3bvUq1cPT09PANauXcuoUaNwdHTE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\nmhf1KAeSPyPF1tnZg4aXt8FjswMAJPFK5K6/DdIk1bDnktHRecsfii1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vrKyETqeDyWTC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\nT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+ "text": [ + "" + ] + } + ], + "prompt_number": 15 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Note the change in the shape of the loss as the prediction crosses zero. This loss reflects that the user really does not want to guess the wrong sign, especially be wrong *and* a large magnitude. \n", + "\n", + "Why would the user care about the magnitude? Why is the loss not 0 for predicting the correct sign? Surely, if the return is 0.01 and we bet millions we will still be (very) happy.\n", + "\n", + "Financial institutions treat downside risk, as in predicting a lot on the wrong side, and upside risk, as in predicting a lot on the right side, similarly. Both are seen as risky behaviour and discouraged. Hence why we have an increasing loss as we move further away from the true price. (With less extreme loss in the direction of the correct sign.)\n", + "\n", + "We will perform a regression on a trading signal that we believe predicts future returns well. Our dataset is artificial, as most financial data is not even close to linear. Below, we plot the data along with the least-squares line." + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# Code to create artificial data\n", + "N = 100\n", + "X = 0.025 * np.random.randn(N)\n", + "Y = 0.5 * X + 0.01 * np.random.randn(N)\n", + "\n", + "ls_coef_ = np.cov(X, Y)[0, 1] / np.var(X)\n", + "ls_intercept = Y.mean() - ls_coef_ * X.mean()\n", + "\n", + "plt.scatter(X, Y, c=\"k\")\n", + "plt.xlabel(\"trading signal\")\n", + "plt.ylabel(\"returns\")\n", + "plt.title(\"Empirical returns vs trading signal\")\n", + "plt.plot(X, ls_coef_ * X + ls_intercept, label=\"Least-squares line\")\n", + "plt.xlim(X.min(), X.max())\n", + "plt.ylim(Y.min(), Y.max())\n", + "plt.legend(loc=\"upper left\");" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "display_data", + "png": 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OVreTk5Px8vIqs09KSgqenp4afZycnHj++ec5evQoHTt2fOg4I0aMwMfHR923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+ "text": [ + "" + ] + } + ], + "prompt_number": 17 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We perform a simple Bayesian linear regression on this dataset. We look for a model like:\n", + "\n", + "$$ R = \\alpha + \\beta x + \\epsilon$$\n", + "\n", + "where $\\alpha, \\beta$ are our unknown parameters and $\\epsilon \\sim \\text{Normal}(0, 1/\\tau)$. The most common priors on $\\beta$ and $\\alpha$ are Normal priors. We will also assign a prior on $\\tau$, so that $\\sigma = 1/\\sqrt{\\tau}$ is uniform over 0 to 100 (equivalently then $\\tau = 1/\\text{Uniform}(0, 100)^2$)." + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import pymc as pm\n", + "from pymc.Matplot import plot as mcplot\n", + "\n", + "std = pm.Uniform(\"std\", 0, 100, trace=False) # this needs to be explained.\n", + "\n", + "\n", + "@pm.deterministic\n", + "def prec(U=std):\n", + " return 1.0 / (U) ** 2\n", + "\n", + "beta = pm.Normal(\"beta\", 0, 0.0001)\n", + "alpha = pm.Normal(\"alpha\", 0, 0.0001)\n", + "\n", + "\n", + "@pm.deterministic\n", + "def mean(X=X, alpha=alpha, beta=beta):\n", + " return alpha + beta * X\n", + "\n", + "obs = pm.Normal(\"obs\", mean, prec, value=Y, observed=True)\n", + "mcmc = pm.MCMC([obs, beta, alpha, std, prec])\n", + "\n", + "mcmc.sample(100000, 80000)\n", + "mcplot(mcmc)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + " \r", + "[****************100%******************] 100000 of 100000 complete" + ] + }, + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Plotting prec\n", + "Plotting" + ] + }, + { + "output_type": "stream", + "stream": "stdout", + "text": [ + " beta\n", + "Plotting" + ] + }, + { + "output_type": "stream", + "stream": "stdout", + "text": [ + " alpha\n", + "\n" + ] + }, + { + "metadata": {}, + "output_type": "display_data", + "png": 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tqKiIwMBAGhoaqKysxNdXd/LvC1vewLNXc5LrTl270y0wTPVBUzps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sDAzDoEuXLsjIyEBYWBi++eYbo9qY7du3G7VHt4fX1tuaL3I+rq96iQvFHnPr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wNPoze+NXuC3thuso+ba4uABPZjejzTdMa//Xf7IXTdduadXv/bwqNJUX4+2p\nItS4ifBbVZPW811TKgE8gtXqX/O8V6O9Q+IGredP0ugMTLl7fyiu37bjEpXzAzSXn8LtG3XyjfGr\nQVgO2+tH0tqptHYqW7Atn2ksMuImTJgAsViMiooK+Pv7Y9euXcjMzFQrM2PGDGRkZCAlJQX5+fnw\n8PCAr68vvL29ddYVi8UQieQP96ysLERFaZ+NN2qu+uLOzir/Ky5S0TG5odjTe+MWGIm4uCiN8oDc\nQ9CzvHDMBMTFBQBnizTakwEQhEXDrcJdrf2e8vTJj7nvfkzbfgr4Xoys1HEQhEWjprpJZ30AkPqP\nxcnqJkQL3Qz2/9LAIKSLAUDdm3WzvQvfllzBda8QOHgBtU0dGO45AHFxcSi70opFX5fJV1gYEIhR\n/s5oueOh2VzpgYOLovDr5Uad+g31c8WtDin6OzkgLi4ObmddjD4/PX9kboGRGHfPKOw+cFEjJk5X\neX3bMsFYuAV64Ey93BPoJYoCTyVO0djrpxgOVRzv6pZh2uen4DXQA3HjAnC69Jry+H33hwPlJWrl\nFd7Knufn5uAQuAXKDb7M4no1+dfOF2r0hz9iHFSzvQVFxuBX6d2h0Z7lr3gEw+3u7apVv3vvj8SU\nz4q1Ho+Li8P3zRdQfycNiOJ49x1voDHnz1/Fw6fv+qnXpbFZrkAxVfYNXT/bYJER5+TkhIyMDCQl\nJUEqlWLhwoUIDQ3F1q1bAQCLFy/GlClTkJ2djaCgILi4uGD79u166wLAunXrcO7cOTg6OiIwMBAf\nffSRhWpqRyaTob2rG858R4Nl9Q27yWTATyqLgWspobft07UtailP2ju7jRoe/uCOgdoz8N2UseVX\nD5aj7MrdIT2pTIYPf61GZWM7imrUY8guqgyxAcCLWedwtbVDZ9s327sw84vTCPJ2xpZZIUb3yRxa\nbnehvasbg12MW2S+5xC/uaPxqvGRwN3JHw23ujSGk7WFH2T8rxrbZodoHPukoMbMHhmHMaaQoZxu\n2g6bkjqHB6DyRjv8BvVDPyd5ZMd1K88MJ+Sw7Ykg+RQTx1X5TGPxig3JyclITk5W27d48WK17YyM\nDKPrAsDXX39tabeMYsNheT64HXPDMHRQ/7sHtLzRDb2bzPEPbDsuwaIYf7x+SH226/dnr6GgSv9M\nzp6ejYPnr8PD2Qkxw9x11NCOqgEHyJMYZxmZDFgRo6YLRfzghettessZy8Yj8nVLtXklZ++Ue7j2\nLBgHvqOizDyoAAAgAElEQVRhk0zDSDLDimu41YnfqnRPluh5T2j7ELh8ox1nr95CqI+LxjFdeImi\nrJ4GBwA2H9Odn7GpvQsXtCTfrW3WbdT3pKimBYu+KUOYjwv+OUM+LPtCj0kqBEEQhG76zIoN5qBI\ncnq0hxdNW442bek1FJSZmXvt65Ir+L7smtqsRQDYWVhnUjsNtzrx9s+V+PMBuTFoyRwPU3K02Rpj\nVnIwdpmzTiM9RvoWK0j56ncNg1fNodZDhK6ZuFbJYWeGF60nB8436Dz2xJclZieN7onq5BZT1qYl\nzIftXFmUJ47yxLEF2/KZpk8acYr0DFWN7eg0YlV21Rda8+0uXNdisJVeadW5QkKHVIaLerxN+t7R\nu+7kcTMV1cDvnv2yxIjrRXlhAUBrCg5V3ZnCmOTKptJz1YHTddoT3Zo6ebv89G8Gy/Qc+taQqfK/\nlHKAAADa29sRGxuLyMhIhIWFYd26dQCAhoYGJCYmIjg4GJMmTUJj490UKxs3boRIJEJISAgOHjyo\n3H/y5EmEh4dDJBLhpZdesrkufYG0tDSKq7Jj6PrZhj5pxLV1SFFU04yFX5ch5/x1o+oUVN3E2Sut\navmtepKhZ3jprJ6hxf9V6l7WiIlhMUc9yVntldtd3ThT34InvixhtR+WZCDpWVXbGrzA3QS9xvDz\nJX2xl3fJqzB+2bjMYvM+JPoaAwYMwJEjR1BcXIzTp0/jyJEjyMvLQ3p6OhITE3H+/HkkJCQgPT0d\nAFBaWopdu3ahtLQUOTk5WLp0qTLWcsmSJfj0008hFoshFouRk5PDpmoasB0XRPIpJo6r8pnG4pi4\n3ogMMGltyu1aEpxqo+ewq7FYsk6mLlTjwnRl/e9N/M/EtWinf35K5zGDOfJYdCyt/uHC3W4Y2Y8m\nE4YlvyqqN6x/L+OkDuO1NzJw4EAAQEdHB6RSKTw9PbFv3z4cPXoUAJCamoqJEyciPT0dWVlZmDdv\nHvh8PgICAhAUFITjx49jxIgRaG5uRkxMDABgwYIF2Lt3LyZPnsyaXgRB9E36pCfOWu/w3jro9OH/\nNJO5mou1vHivHbJ8qTJjMTQpRBvahtDNQdJkXEyeufTVoc/vjJxMY226u7sRGRkJX19fxMfHY8yY\nMaivr4evrzy/oq+vL+rr5Z7LmpoatdyWqqvRqO4XCAQaK9mwDdtxQRQTRzFxbMG2fKbpk544ADh3\n1fyF3nXRYUR8na1QzZWWp7IMEtOrLvRGtOWJUyCTAYU1pnl+dpw0zhNrKoZSdJiLPv3tlc2/VmNi\noCfb3YCDgwOKi4tx8+ZNJCUl4ciRI2rHeTyeRUvNEcZD8VT2DV0/29A3jTgZIL7GTFoLeyP5M+aD\n/vs6/y4ybTawseib3dmTnmuZcpHHd7Ib/6iKu7s7pk6dipMnT8LX1xd1dXXw8/NDbW0tfHzkq4bo\nWo1GIBCgurpabb9AINAqZ+nSpRg+fLhSZnh4uNZVZJjejouLs2r7JN94+QqMWSUGABCVZPP+0rZ5\n2yUlJbh5Ux5KVFlZiUWLFoFpeDJbr+DOELm5uVhbqP2LeLjHAI01TgnjmBzsbfRkkN7IhzNHY/+5\n6zrTefRWovwHaSRX1obQvT+qtSx4zxXSx8uQkJBglbavXbsGJycneHh4oK2tDUlJSXjttddw4MAB\neHt7Y82aNUhPT0djYyPS09NRWlqK+fPno6CgABKJBI8++iguXLgAHo+H2NhYfPDBB4iJicHUqVOR\nlpamEROXm5uL8ePHW0UXgn2u3zKcM1EklC8befBUBdYfKDeq3aeifJEa7W9R3wh2KCwsZPz51Sc9\ncWTAmU9nN3mE2MAYAw4AOqyRU44AANTW1iI1NRXd3d3o7u7GM888g4SEBERFRWHOnDn49NNPERAQ\ngN27dwMAwsLCMGfOHISFhcHJyQlbtmxRDrVu2bIFzz77LNra2jBlypReN6mB7fUjubB26tZ8CYpr\ntKcVahAXwUt0d6Wdv5owQ91SaO1UWjuV6AVYKy4q94J5M3BtiSHd+3LE0pWWzj4ZE9cbCA8PR2Fh\nocZ+Ly8vHD58WGud9evXY/369Rr7o6OjUVLSe4aH7RF7j6lquS3VmTy9pUMKB5VjunKQ2jP2fv3s\nBYtnp+bk5CAkJAQikQibNm3SWiYtLQ0ikQgREREoKioyWPdPf/oTQkNDERERgdmzZyvHlAnCEB/+\nWo1bWhIEEwRxF7Y9EVyXz+ZHGNu6c10+01hkxEmlUixfvhw5OTkoLS1FZmYmysrK1MpkZ2fjwoUL\nEIvF2LZtG5YsWWKw7qRJk3DmzBmcOnUKwcHB2LhxoyXd7JNw2ROjT/fSK6124U20BC5fe4IgCOIu\nFhlxBQUFCAoKQkBAAPh8PlJSUpCVlaVWZt++fUhNTQUAxMbGorGxEXV1dXrrJiYmwsHBQVlHdaYX\nQRAEYRls58riep44aywdaCyUJ47yxCmRSCQYNmyYclsoFOL48eMGyygSYhqqCwCfffYZ5s2bZ0k3\n+yRcjovisu4A6U9wA4qpsm/o+tkGizxxxia9NDeLyRtvvIF+/fph/vz5ZtUnCIIgNGE7Lojr8ikm\njrvymcYiT1zPZJdVVVVqy81oK6NIiNnZ2am37ueff47s7Gzk5ubqlH9x1yb095Tn2XF0dsFA/yCD\niRL7yrZiX2/pjy233QIje1V/SH/rbQNAc/kp3L5xJyHz+NUgCIIg5FiU7LerqwujR49Gbm4u/P39\nERMTg8zMTISGhirLZGdnIyMjA9nZ2cjPz8eKFSuQn5+vt25OTg5WrVqFo0ePYvDgwVpl60v2SxBE\n38SayX5tDZvJftnOlcWFPHHr91/ACYn2/I+KD/ATq+X38oS3dDsremJpsl/KE8ee/F6X7NfJyQkZ\nGRlISkqCVCrFwoULERoaiq1btwIAFi9ejClTpiA7OxtBQUFwcXHB9u3b9dYFgBdffBEdHR1ITEwE\nANx3333YsmWLJV3tc3A5LorLugOkP8ENKKbKvqHrZxssTvabnJyM5ORktX2LFy9W287IyDC6LgCI\nxWJLu0UQBEHogO24IK7Lp5g47spnGouT/RLswGVPDJd1B0h/giAIQg4ZcQRBEByD7VxZ9pgnrqm9\nC3XNt436a7jVidt61jmmPHHswbZ8pqG1U+0ULsdFcVl3gPQnuEFvi6mqb+nAsr3n2O6G3dDbrl9f\nhTxxBEEQHIPtuCCuy6eYOO7KZxoy4uwULntiuKw7QPoTBEEQcsiIIwiC4BhsxwXZY0wck1BMHHuw\nLZ9pKCbOTuFyXBSXdQdIf4IbUEyVfUPXzzaQJ44gCIJjsB0XxHX5FBPHXflMQ0acncJlTwyXdQdI\nf4IgCEIOGXEEQRAcg+24IIqJo5g4tmBbPtNYbMTl5OQgJCQEIpEImzZt0lomLS0NIpEIERERKCoq\nMlj3v//9L8aMGQNHR0cUFhZa2sU+CZsPAbbhsu4A6U9wg7S0NIqrsmPo+tkGi4w4qVSK5cuXIycn\nB6WlpcjMzERZWZlamezsbFy4cAFisRjbtm3DkiVLDNYNDw/Hnj178NBDD1nSPYIgCEILbMcFcV0+\nxcRxVz7TWGTEFRQUICgoCAEBAeDz+UhJSUFWVpZamX379iE1NRUAEBsbi8bGRtTV1emtGxISguDg\nYEu61ufhclwUl3UHSH+CIAhCjkVGnEQiwbBhw5TbQqEQEonEqDI1NTUG6xIEQRDMw3ZcEMXEUUwc\nW7Atn2ksyhPH4/GMKieTySwRQ2iBy7nCuKw7QPoT3IDiqewbun62wSIjTiAQoKqqSrldVVUFoVCo\nt0x1dTWEQiE6OzsN1jXExV2b0N/TDwDg6OyCgf5Bypeb4kunr27fqrnQq/pD27RtjW0AaC4/hds3\n6uQb41eDsBy244K4Lp9i4rgrn2l4MgvcZF1dXRg9ejRyc3Ph7++PmJgYZGZmIjQ0VFkmOzsbGRkZ\nyM7ORn5+PlasWIH8/Hyj6sbHx+Ptt99GdHS0huzc3FysLTTOE0gQRN8gfbwMCQkJbHeDEXJzczF+\n/Hi2u0EYifjaLSzbe47RNk+slt/LE97KNbrOU1G+SI32Z7QfhG0oLCxk/PllUUyck5MTMjIykJSU\nhLCwMMydOxehoaHYunUrtm7dCgCYMmUKRo0ahaCgICxevBhbtmzRWxcA9uzZg2HDhiE/Px9Tp05F\ncnKyhWoSBEEQCtiOC6KYOIqJYwu25TONxWunJicnaxhZixcvVtvOyMgwui4AzJo1C7NmzbK0a30a\nLsdFcVl3gPQnuAHFVNk3dP1sA63YQBAEwTHYjgviunyKieOufKYhI85O4bInhsu6A6Q/QRAEIYeM\nOIIgCI7BdlwQxcRRTBxbsC2faSyOiSPYgctxUVzWHSD9CW5AMVXa+b7sOsqvtxldful9QvgN6m/F\nHmmHrp9tICOOIAiCY7AdF8R1+ZZ8hN1s70J+ZZPR5Zfcq77Ntu5cl880NJxqp3DZE8Nl3QHSnyAI\ngpBDRhxBEATHYDsuiGLiKCaOLdiWzzQ0nGqncDkuisu6A6Q/wQ0opsq+oetnG8gTRxAEwTHYjgvi\nunzKE8dd+UxDRpydwmVPDJd1B0h/giAIQo7FRlxOTg5CQkIgEomwadMmrWXS0tIgEokQERGBoqIi\ng3UbGhqQmJiI4OBgTJo0CY2NjZZ2kyAIgrgD23FBFBNHMXFswbZ8prHIiJNKpVi+fDlycnJQWlqK\nzMxMlJWVqZXJzs7GhQsXIBaLsW3bNixZssRg3fT0dCQmJuL8+fNISEhAenq6Jd3sk7D5EGAbLusO\nkP7WoqqqCvHx8RgzZgzGjh2rfAG9/vrrEAqFiIqKQlRUFPbv36+ss3HjRohEIoSEhODgwYPK/SdP\nnkR4eDhEIhFeeuklm+vSF0hLS6O4KjuGrp9tsMiIKygoQFBQEAICAsDn85GSkoKsrCy1Mvv27UNq\naioAIDY2Fo2Njairq9NbV7VOamoq9u7da0k3CYIgDMLn8/Hee+/hzJkzyM/Px4cffoiysjLweDys\nXLkSRUVFKCoqQnJyMgCgtLQUu3btQmlpKXJycrB06VLIZDIAwJIlS/Dpp59CLBZDLBYjJyeHTdU0\nYDsuiOvyKSaOu/KZxiIjTiKRYNiwYcptoVAIiURiVJmamhqddevr6+Hr6wsA8PX1RX19vSXd7JNw\nOS6Ky7oDpL+18PPzQ2Sk/Ny6uroiNDRU+UxSGGeqZGVlYd68eeDz+QgICEBQUBCOHz+O2tpaNDc3\nIyYmBgCwYMEC+hAlCMIqWGTE8Xg8o8ppewBqK6OtPR6PZ7QcgiAIJqioqEBRURHuvVee7n7z5s2I\niIjAwoULlTG6NTU1EAqFyjqqH6iq+wUCgcbHLduwHRdEMXEUE8cWbMtnGovyxAkEAlRVVSm3q6qq\n1B5e2spUV1dDKBSis7NTY79AIAAg977V1dXBz88PtbW18PHx0Sr/4q5N6O/pBwBwdHbBQP8gpZdC\n8SPpq9t1v3zNKX1Vt1UfgL2hP6S/9bYBoLn8FG7fqJNvjF8Na9PS0oInnngC77//PlxdXbFkyRK8\n+uqrAIC//OUvWLVqFT799FOr94PrUDyVfUPXzzbwZMa4yXTQ1dWF0aNHIzc3F/7+/oiJiUFmZiZC\nQ0OVZbKzs5GRkYHs7Gzk5+djxYoVyM/P11t39erV8Pb2xpo1a5Ceno7GxkaNyQ25ublYW6juoYv0\nd8UIjwHIKr1mrkp2A5cTvvZl3eMDPXGk/IbeMn1Zf1XcBzjhZnuX2r708TIkJCRYTWZnZyemTZuG\n5ORkrFixQuN4RUUFpk+fjpKSEuUzae3atQCAyZMnY8OGDRgxYgTi4+OVE7UyMzNx9OhRfPzxx2pt\n5ebm4pNPPsHw4cMBAO7u7ggPD1fG7Cg8BrTdO7b/88Nh/DOvitEPlfNbVwEAJryVa7UPoT3r5mOo\nW3/Wzx8Xt0tKSnDz5k0AQGVlJRYtWsT488siIw4A9u/fjxUrVkAqlWLhwoVYt24dtm7dCgBYvHgx\nAChnobq4uGD79u0YP368zrqAPMXInDlzUFlZiYCAAOzevRseHh5qcnsacX96eDjuG+6OnYV12HPm\nqiUqEQRrfPtMOGbvLGG7G72CVQ8Nxzs/V6rts6YRJ5PJkJqaCm9vb7z33nvK/bW1tRg6dCgA4L33\n3sNvv/2Gr776CqWlpZg/fz4KCgogkUjw6KOP4sKFC+DxeIiNjcUHH3yAmJgYTJ06FWlpaZg8ebKa\nvNzcXOWzkOj9iK/dwrK95xht88Rq+b084a1cRttVZcecMAx162+19gnjKSwsZPz5ZfGyW8nJycrZ\nWgoUxpuCjIwMo+sCgJeXFw4fPmxSP+IDveDkwAMofK5PMXecD3advsJ2N2wG35Hyb7PFsWPH8OWX\nX2LcuHGIiooCALz55pvIzMxEcXExeDweRo4cqfxIDQsLw5w5cxAWFgYnJyds2bJFGb+7ZcsWPPvs\ns2hra8OUKVM0DDi2ycvLY3WWnjHyFfFU1hiWY1t/Nr3pttJd1/Vj+9yzLZ9p+szaqQrbzXsgn9V+\n2ApDD4EhLnxcbe20YY+sw7xIPw0jzpDuY3xdcKa+1dpdYw2uDKdaNkZgOnFxceju7tbYr+1DU8H6\n9euxfv16jf3R0dEoKSGPqiVQTJV9Q9fPNvS5z/6ZYUPY7kKv4JEgL8baWhc/AunJgYy1ZwpOjtpd\nq39+JMC2HSGIPgTbngiuy6c8cdyVzzR9zojr59TnVNKKLR8CD470RJivq1l1X7xfiL8njVLb5zXQ\nMgewW2AkHhrlqfN4Xx9R54IXDgBs7IgjCIKwO7hh8XAQJg0ZHoABZhrH08OGIGaYu0WyrUHIkIFW\naplggkcCPW0/nsoh2M6VRXniig0XshKUJ65v5YnrM0Zcb8gH/J/5Y5EUrD6MGeU/yCqymHgIjPAc\nwEBPzMCEd7O2RM+GdPdx7cdkFxhjrK8LI+0w/QIY1N+RsbZWPjjc4jZevF+INRNHwMGhF/yoCdag\ntTftG7p+tqHPGHG9AUcHHlo7NAOjTeWTJ0INFzKAMa8/Y71rphrIoxn0cqmKvkfoZlQdRwce+AYM\nADacPO9OD2akneX3CQ0XshJOBs5r7HDjrpE++jk5gMfjWe0DiGA/Lojr8ikmjrvymabPGHG6Xi1e\nzrabgOvIA5z5lp/S4R6GPWRMPARSo4caNZvXVH+Iof73nKywYLyfUe0q6il0z5w/Fu/P0G4YxQzT\nb0x02/FQ3dMzElmTbSitJJO+MyZ+SwRBEH2ZPvOU1PVq2fa45V4tY3Fkcfinn45ZnIDuYbxwP1d8\naoTXz9S1a7Vdi91PjVX+P9xjgPqws4H2PQbIDXEfF3WD03sgH36DNIdOjentMCMMZTYw1rTc/mQY\nXtYxdDkv0pe5DkH9Q8hQ/5hc53hQfyc8f89Qm36IcQW244IoJo5i4tiCbflMY9dGXJC3s/J/B5WX\nh6ot5TbAlp44nsWxVgui5ZnhR3npNjL6OfKQ7FKrti8rNUK9kMo5cOmnGfP0l4SR6G/DmbwezncN\nMB54WPXQCOW2tmHdoYP6wceVDwce8N70YPxzejC87ngN1R6AZp7wZSwOSVpKXl4eBO79kTzaW+vx\n5yb4MypPNTbN0D3D9GdMSoQfpoYOZrhVwh6gmCr7hq6fbbBrI040WHvsVbCO/dZGWyB2SoRur0is\nliG/p6PkQ4tbZoXorPfF3DEazit9XkCBu+aSKwrDyVCMkzkYalHR92+fCcd/nw7X2oftc8KwY84Y\n8Hg8CNz7I8zXBRPuxMQNNjAEfN8Id4O2ndsAJ3z/XASW3CvQODYjTN1oMBSbtXEyczn0DA1X+rsZ\nnrTBNKpXZ+PkIP1lreCMpukNzMN2XBDX5VNMHHflM43ZRlxDQwMSExMRHByMSZMmobGxUWu5nJwc\nhISEQCQSYdOmTQbrNzQ0ID4+HoMGDcKLL75obvcM8o8p6i+jPycEWNxmT1tk5YPDESXQbQAMcHLQ\nmerCQc/b0GsgH2OiY43u1/xIzZgz2R0zp5+TA/6cEIANiaM0ygDABKHpweXGOsdc+zvBXYen1IHH\n0zBMRYMHYvuTYfh63XydsiaJvHD/CONSmvRzdNBq4A7q74S5Ksb3eD3XUN9xhVfVEFH+8hx8cQHG\n9JvH6kMozMAMWx6At6eKbNMZgiAIjmO2EZeeno7ExEScP38eCQkJSE9P1ygjlUqxfPly5OTkoLS0\nFJmZmSgrK9Nbf8CAAfj73/+Ot99+29yuGUVED+/KQyN1J481FgceT23a42Qdw12qvD8jGFNC9JeL\nC/AwSv7OuWO07nft74h79cwafGikJ+4b4Y4dc8MwLUTdCzV0EHMLJys8boFezgZK6kbg3l/vrFrR\n4IHg8XhIjR4KJwceHh6l/9zp8rItGO+H1Oih+GjWaL31w/1cwePxEOTtjBEqcXb/nB6s9KoaYrBL\nP3z3bAT+kjDSqPK9GR6Ph/5O5Dvr7bAdF0QxcRQTxxZsy2cas424ffv2ITU1FQCQmpqKvXv3apQp\nKChAUFAQAgICwOfzkZKSgqysLL31Bw4ciAceeAD9+zNnPDDBnxMCMNhF+zDeygeH408P686Ptf1J\nHZMHePKXnoOBAaNZY+8uJaaYTXrm5HGNcr49gvzfSArE3yaN0urVG+GhaUgNHdQfwT08g6lGepOM\n4V+Ph2LRPf6Yb6RxowtjfoQjvZzx/XMReHKc/iB/bQvO8+7sfyrKD4Hexg3NfzhzNLY+fncI3PNO\nML4hAx2QexP730mrYQgeTH8IzR47BL6u/fDao9qNxF4/Ubc3JIEkbA7FVNk3dP1sg9lGXH19PXx9\n5S9IX19f1NfXa5SRSCQYNmyYclsoFEIikRhVn8lZbsbieydJrLYUGQ+N9NSZjmPyaG8kinS/rAXu\nls2EdOTxMPGOR+kPMcYFrfMA3DPMDbHD5UN0qi/qrbNDNAw+BT3f50xODBG498ecCF9GJ1T07K/q\nbaNvSFofY/3UhwyNyX3G4/HU5HXf6ZipBpI1DKog74HYmTIGD+jx6Hrouc6mnEZLf7VODjzcN1x9\nWNmuA3d7KWzHBXFdPsXEcVc+0+h9PiYmJiI8PFzjb9++fWrleDyeVqOr5z6ZTKaznDlGm64Xnrnv\nwbemBOGxsMEWLfZujmyZjlpzx/kgyt8Vo4cMxJqJAfh8TphyYXtDMXG6Ys0AuZdKF4Hepg91jhcM\nwsJ7/OE+wMms9BamXnlTfoROJt5Xs8YMwXiButEW4OmMzPlj1WZDG8b4O0HXLFMFqjOVebze9xCa\npjJ7VNfp3pSsf0IEADx/z1B892yExofD9LDBGO4xwOgPGIIgCK6g181y6NAhncd8fX1RV1cHPz8/\n1NbWwsfHR6OMQCBAVVWVcru6uhoCgcDo+obIev8vuOYoj2X7qDMf4eHhyhfc3ZiDKMyL9MXWbw4A\nuPsFlJeXh1keLdjT6Ivk0d7KIaplPeqrlq8/WwV4h+g8LkeoPJ6X16rRH0X5pvJiVN1yBR4ZqdFf\nRXujASycEqfWvv+d9n4/cRxN5fUa8t9IGoe8ikZ4NJxFXt55pXxJ6Uk0XWnVKK84rtiOirlPZ3+a\nysVq/Vfok54chLy8PKSNkOHBCeF46+hlrfW1ydN1fgyVV2yHjo9V7+/9QrXjDzzwgFHtK46HJ8zS\nerys8Diunde8/jw/9f4Aci9eQf6vGOLSD8BwZfm8vFb4DfJEXXMH3K+dRdXNdrgFRiLcz1Xn+XcL\njIS/W38U/5YPAHCIvlerPG33lzZ9tZWXAWgQF6GlQ6q1vkymeT+oHvcayFc5Pk6r/NMn/oemconO\n/jWVF+M8vwqOETN69Ff+f7/KShz5EQhctAiE5eTl5bH6MWCMfEU8lTWG5NjWv6m8mDVvnK1013X9\n2D73bMtnGrPHymbMmIEdO3ZgzZo12LFjB2bOnKlRZsKECRCLxaioqIC/vz927dqFzMxMo+obSrUA\nADNX/A37z10HACxZFKXc7+faT+0HEuDprPGDiYuLQxyA1A4pnPkO4PHUY9q0ld91/Rwar97SeRwA\n8o5UKI/Hxd3tU8/yboGRGKYSdK+rPV3bPeuoHr9nmBsUxoMCQVg0qgc1GWy/rVOqsz9uZ+8OMxrq\nr6n6mFJe9UfYKe02WP+JcB98Dcv7e9mlDjtO1mL0kIE4p6u9s0UAgOjY+zHcYwBO/VqlbD8uLgox\nXd1obO/C5yc8cfPCDY36rR3az/8/l8zGx/kSrIsfof4QuiPPLTASEUNdlTGMwZExqGvuAACIBjtj\nhEizvCpeoig4tHdpPR8yLeVVt/s58JTbDjwe/N36a5SPirkfblfFWusrtoMj78Zfqp5/1f8LCwtB\ncAOKp7Jv6PrZBrPDTdauXYtDhw4hODgYP/74I9auXQsAqKmpwdSpUwEATk5OyMjIQFJSEsLCwjB3\n7lyEhobqrQ8AAQEBWLVqFT7//HMMHz4cZ8+eNalvS+8XIinYCx/OlM8s1DegNrCfo8GhXCYW9daH\nLeLKjZVhbhyZJViiP9/RAXsWjNPfPkOBZnMjfPF64kjj8sLdETk/yg+jhwzE6oflyY37OTnAx7Wf\nyTrfO9wdn88J0znRwte1H/4xVYSxfvJ0JenJQXh4lAc2JI7CCE/9w8CtHVKk3BkGn6plIoauO2L7\nk6E4uChKrUB/JwcM6u+Ef88bo3ZdeDzA300+Wemvk7Sns+n1Eyz6EGx7Irgun2LiuCufacz2xHl5\neeHw4cMa+/39/fHDDz8ot5OTk5GcnGx0fQCoqKgwt1sAAE9nvtqKAOF3XmzmEOnvalSqEHOwxFwa\nEx2L/T9XMtYXBSyuHGY0PX+EqitSWLP7Tg483D9CfXKALpu3+46Z5unMx+bH9KcpUUXb+e9p3Bjz\nEPJ3649XHjEuZckz4/0wa8wQ3DvcHZ7OTvjh7HW147p0VBj82g7Lh5LV+dfjIWjtkMLDmY+Jozzw\n0xyPsmIAACAASURBVEXtuSUJgiAI4+DExC9vFz74KmuLmhKgrm+CgDZMcSYoyvIdLLsMrlqW1dKQ\nZWTH9HnidCUm7g0kirzgwAMeHKk5A1M1UP5RkRdeT9Rj3DBkBWpb6swYnPmOmBfha/IEEXPW7X31\n0ZH426RReHKcL3h3hkG1oeveae/qNlqWIm2L6vJrBHuwnSuL8sRRnji2YFs+03BmZel3poqQtu88\nAGCMgazzAJCeHIhvSq7ihXvvrrFpzGtSVxoSfTwV5YuzV1s1lnvShzxPnDyG6MlxhieF6JoB2xN9\ntsCGxFGY+9XvRrVjCqYOd2oLTP3TwyOw8sHhWo2ZWWN9UNnYjvhAT8QMM241B3P5e9IoNNzq0uqJ\nMpbn7vGHTCZDZrFm2h5Au/6mLp/29lQRxg0130Otijl2L42cEoagmCr7hq6fbeCMERfiY9hwU2W8\nwE0j1YQxPBXlh+bbXXrzxilQvPw8TBxy68kcAwltTUFffKDnQD7G+rng97pWxuQxiS5v1AAnB6yZ\nGMCoLL4DD53dMo10LdYwEkP1fHTMjfDFrlP1Rq8OocB7oPafvjkevXFD5ateDOqv2/uozzP5aJAn\nDl+4gYQ76XMI68N2XBDX5VNMHHflMw1njDhb4dLPUS0eTxvj/Fxxuq4FD48yf6mvKY8+jP1Zcs+i\nOS9efUwO9kbO+euGC1oBZ74DUiL0G6XW/BGOMzJ+cuvjIfip/AYeDzc9NY6pPNBjLVhV/Z+fMBRP\nhPswNuzfz9EBrzwSACcHHjYcvgTAcLLf4CED8dGs0cpk2aqsjw9A9c12DWNXtcnVEwPw8oPDta6e\nQRAEQeiGk09Nc4dyLJm4qbp01pvJgfjX4yF6M+gbYvQQF/x10ijdS3pZQM+lt1Th9Rg807bc2ORg\nuRfS2IXoVY3QvQvGYV6kZctymcu0kMFGr1AhdB+Ap8cPhTPfvNg309B94/F4PJMNOEM8PMpT7d7U\ntoIJoB4rF+g9EK79NfsxMdATT4/XXLptglDu5RbcicMjA862sB0XRDFxFBPHFmzLZxryxNmIiaM8\nsef3qwDk3g5DaR8MYWrCQqbSN6iaE7ufGqs1UH3cUFfsmj8W7s7G3V6JIi/kXmjAQyM9jVq5w1rJ\nGgfwbWdI+GjxWhmLrZJVfpkyBldaOvBLRSNOVDcz2vajIi8McemHoMGW/Q6IvgvFVNk3dP1sg10b\nccN0eAgMwUYWDVMDz+0BfTMNPU2Y4OHMd8T7M8yPCWQKc+8nc0iJ8EVbZzfiA7UPqasaszfbuyBw\n1z5z1Jr4uPaDj2s//FKhPRWIsZNltOHA4yFKMMjs+oRlsB0XxHX5FBPHXflMY9dG3GNhg9HV3Y1Y\nK884VPDM+KFYn1OO+ZG++ErHzEFdBHk746GRHnrXLTUFU29Ek1Kf6HHbsZALWAOmf4RbZ4egqKYZ\nk0S2C6x35jti6X1CwwUBXL/VqbbNhP6meGZ7wSUnCIIgtGDXgSh8RwekRPgxZhgZYoLQDVmp4/Ds\nBNMX4ubxePhzwkg8ZeIsQqYw5aXt0Ae9hvoY6eWM2WN9GJ8gwhSWeLwIQhtsxwVRTBzFxLEF2/KZ\nxq49cWzQM5BdxFJMjzXjoh4J9MQPZde0Js7tDfS1BYwNMarHRwrX9Ce4CcVU2Td0/WyD2Z64hoYG\nJCYmIjg4GJMmTUJjo/a4mZycHISEhEAkEmHTpk0G6x86dAgTJkzAuHHjMGHCBBw5csTcLmoQM0w+\nI+4RBvNRufazDzs4wMv4eC9nviO2zArROku0Nwyncg1zEkgThD7Y/gjgunyKieOufKYx24hLT09H\nYmIizp8/j4SEBKSnp2uUkUqlWL58OXJyclBaWorMzEyUlZXprT9kyBB8//33OH36NHbs2IFnnnnG\n3C5q8NdJo7DrqbEINTHxrz7YMmpMvRGfjR6Kp6P88MnjlqUkWRQjgAMPeOFegUXtWEJf+xEawrHH\nTWZr/cluJwiC6J2YbcTt27cPqampAIDU1FTs3btXo0xBQQGCgoIQEBAAPp+PlJQUZGVl6a0fGRkJ\nPz+5BygsLAxtbW3o7OzUaNscHHg8eHJ07UZnviMWRA/FcE/LZmAGDx6I7OcjMXus9ZPcEnKY/FCY\nGuKNSH9XRma7MpW2hrA9bMcFUUwcxcSxBdvymcbsscD6+nr4+soz6/v6+qK+XnO2pkQiwbBhw5Tb\nQqEQx48fN7r+N998g+joaPD53DS89MFmXJQDy2OqXIsJ63m+LdH/pTjN5Mzm0lsnghB9A4qpsm/o\n+tkGvUZcYmIi6urqNPa/8cYbats8Hk9rktae+2Qymc5yPfefOXMGa9euxaFDh/R1kXXoNUZYG7bj\nEAf0mMzz/D1DUdl4GwEWenUJ9mD7I4jr8ikmjrvymUavEafPgPL19UVdXR38/PxQW1sLHx/N4TWB\nQICqqirldnV1NQQCgcH61dXVmD17Nnbu3ImRI0fq7MPSpUsxfLjcs+Du7o7w8HDlBVK4TK21rXSH\nCx60ibye24p9tpLXm7bj4uJ6VX+stR0lu4bAcffAgcdjVf8nwn1w+MjPiBk+CEAUUiL8kJeXh2PH\nqqwuX/F/ZWUlAGDRokUgCIIg5PBk+jK76mH16tXw9vbGmjVrkJ6ejsbGRo3JDV1dXRg9ejRyc3Ph\n7++PmJgYZGZmIjQ0VGf9xsZGPPzww9iwYQNmzpypU35ubi7Gjx9vTtcZYdInRQCAhCBPrJkYwFo/\nCIJLFBYWIiEhge1uMAKbzzC2QxKMka+Ip7LGsJw5+ouv3cKyvecYkd9UXgy3wEicWC2/lye8lctI\nu9rYMScMQ93uxsDa6trrun72cO9ZC2s8v8ye2KAY6gwODsaPP/6ItWvXAgBqamowdepUAICTkxMy\nMjKQlJSEsLAwzJ07F6GhoXrrZ2RkoLy8HBs2bEBUVBSioqJw7do1S/VknLenivDgSA/8MZadWZp9\nLTjTFLisO0D6E9wgLS2tV8VV9XOk4BlT6G3Xr69itieObdj2xLEN218zbMJl3QFu60+eOIJJ8i41\nYv+560aVbbrdiXNX2xiVz4YnjmAPazy/7CNTLaEBV1/iALd1B0h/gmCK2ubb+K26ie1uEITZ2PXa\nqQRBEITpsD0kT3niKE8cW7Atn2nIiLNT+tqNaApc1h0g/a1FVVUV4uPjMWbMGIwdO1b5AtK3xODG\njRshEokQEhKCgwcPKvefPHkS4eHhEIlEeOmll2yuS1+AYqrsG7p+toGMOIIgCAB8Ph/vvfcezpw5\ng/z8fHz44YcoKyvTuURgaWkpdu3ahdLSUuTk5GDp0qVQhBgvWbIEn376KcRiMcRiMXJycthUTQO2\nh+S5Lp/yxHFXPtOQEWen9LUb0RS4rDtA+lsLPz8/REbKX66urq4IDQ2FRCLRuURgVlYW5s2bBz6f\nj4CAAAQFBeH48eOora1Fc3MzYmJiAAALFizQuiwhQRCEpZARRxAE0YOKigoUFRUhNjZW5xKBNTU1\nEAqFyjpCoRASiURjv0AggEQisa0CBmB7SJ5i4igmji3Yls80NDvVTuFymgku6w6Q/tampaUFjz/+\nON5//30MGjRI7ZiuJQbNhc1VZ3r7ds/0K9aQd678BgC5wa0wrBRDnbbaVmC99sPU9FfA1vWzlXx9\nq8DYSl5JSQlu3rwJAKisrLTKijOUJ85O4fKLnMu6A9zW39p54jo7OzFt2jQkJydjxYoVAICQkBD8\n9NNPyiUC4+PjcfbsWWVsnCJR+eTJk7FhwwaMGDEC8fHxKCsrAwBkZmbi6NGj+Pjjj9Vkcf0Z1hv4\n7+l6/KughjX5lCeOW/SqFRsIduHqSxzgtu4A6W8tZDIZFi5ciLCwMKUBBwAzZszAjh07AAA7duxQ\nLgc4Y8YM/Oc//0FHRwcuXboEsViMmJgY+Pn5wc3NDcePH4dMJsPOnTv1LiFIEARhLmTEEQRBADh2\n7Bi+/PJLHDlyRLnkX05Ojs4lAsPCwjBnzhyEhYUhOTkZW7ZsUQ61btmyBYsWLYJIJEJQUBAmT57M\npmoasB0XRDFxFBPHFmzLZxqzY+IaGhowd+5cXL58GQEBAdi9ezc8PDw0yuXk5GDFihWQSqVYtGgR\n1qxZo7d+QUEBFi9eDACQSqV45ZVXMHfuXHO72Wfh8pAal3UHSH9rERcXh+7ubq3HDh8+rHX/+vXr\nsX79eo390dHRKCkpYbR/XINyjNk3dP1sg9meOF25k1SRSqVYvnw5cnJyUFpaiszMTGWciK764eHh\nOHnyJIqKinDw4EEsW7YMUqnU3G72Wbj8guCy7gDpT1gO2x8BXJdPeeK4K59pzDbidOVOUqWgoABB\nQUEICAgAn89HSkoKsrKy9NZ3dnaGg4O8W21tbXB3d4ejo6O53eyzKGa8cBEu6w6Q/gRBEIQcs404\nXbmTVJFIJBg2bJhyW5FHyVD9goICjBkzBmPGjMG7775rbhcJgiAILbAdF0QxcRQTxxZsy2cavTFx\niYmJqKur09j/xhtvqG3ryp3Uc59MJtNZTnV/TEwMzpw5g7Nnz2Ly5MmYOHEi3N3d9WvCMSorK9nu\nAmtwWXeA9DeFBQsWYN68eUhOTma7K4SJUEyVfUPXzzboNeIOHTqk85ivry/q6uqUuZN8fHw0yggE\nAlRVVSm3q6urIRAIjK4fEhKCwMBAXLhwAdHR0WrHWlpaUFhYqF+7PsyiRYs4qz+XdQe4rX9LS4tJ\n5f/1r39h165dmDt3Lu6//34sWrQILi4uVuqd/cB2XBDX5VNMHHflM43Zs1MVuZPWrFmjljtJlQkT\nJkAsFqOiogL+/v7YtWsXMjMz9davqKiAUCiEk5MTLl++DLFYDJFIpNH2Y489Zm7XCYLgCNevX8fF\nixfh7u4OX19fPP/889i1axfb3SIIgmAEs2PidOVOqqmpwdSpUwEATk5OyMjIQFJSEsLCwjB37lyE\nhobqrZ+Xl4fIyEhERUXhySefxLZt2+Dm5mapngRBcJB33nkHzzzzDLZt24aUlBQa4rkD23FBFBNH\nMXFswbZ8pjHbE+fl5aU1d5K/vz9++OGH/2/v3uOiqvb+gX+Gi2Zq3kVlMFIGAQVECVIfOxresLJj\npkmWpmimmVmWmj2Wdo6J/U6Xk+bR00G7nBNhnRR91IkkNdEEFTheBhVT4iqJiuDlCAz79wcxgczA\nIHv2mj3zeb9evGTv2TPftWYtZxZrf/fapu3IyEiz+SiWnv/000/j6aefvtNiERGZDBs2DL179wYA\n7Nixw/QHJtk/DrjVje2nDFXesUGv18PPzw86nQ6rV68WXRzZeHt7IygoCCEhIQgLCwNQvSjyyJEj\n4evri1GjRqGkpMR0/KpVq6DT6eDn54fExETT/qNHjyIwMBA6nQ4vvfSS4vWwxowZM+Dh4YHAwEDT\nPjnreuvWLTz55JPQ6XR44IEH8MsvvyhTMSuZq//y5cuh1WpNdwvYtWuX6TFHqn9ubi6GDx+Ovn37\nol+/fqa/1m3R/lOnTjXVf//+/cpV0s6Jzgty9vjMiXPe+HJT3SCuoQWE1U6j0WDv3r1IT09Hamoq\nAMuLIhsMBsTHx8NgMECv12Pu3LmQJAkAMGfOHMTGxiIrKwtZWVnQ6/XC6mTJ9OnT65VLzrrGxsai\nU6dOyMrKwssvv2y6U4i9MFd/jUaDV155Benp6UhPTzfNYDta/d3d3fHBBx/g5MmTOHToED7++GNk\nZmbapP3HjRuHESNG4NlnnzW7DBIRkZqpbhDX0ALCjqDmy6mGpUWRExISEBUVBXd3d3h7e8PHxwcp\nKSkoLCxEWVmZaSZv6tSpZhdiFm3o0KHo0KFDnX1y1rX2a02YMAFJSUlKVc0q5uoP1G9/wPHq361b\nN/TvXz0T0aZNG/j7+yM/P98m7f/RRx+hW7duOHz4MD788EMBtbVPovOCmBPHnDhRRMeXm+oGcQ0t\nIKx2Go0GI0aMQGhoKD755BMAlhdFLigogFarNT235n24fb+np6dq3h8561q7n7i5uaFdu3a4fPmy\nUlW5Y2vWrEFwcDCio6NNpxMduf7Z2dlIT09HeHi4Tdo/JycH165dQ4sWLczeGpDs1/z585lXpWJs\nP2WobhBnbrFgR3HgwAGkp6dj165d+Pjjj+vl8FhaVNkROVNda8yZMwfnz59HRkYGunfvjoULF4ou\nkk1du3YNEyZMwF//+le0bdu2zmNytf/777+PRx55BG3atDG7DJKzEp0X5OzxmRPnvPHlprpB3O0L\nCOfm5tb5a1zNunfvDgDo0qULxo8fj9TUVNOiyADqLIpsbiFlrVYLT09P5OXl1dlfs8CyvZOjrjV9\nwdPT03Rng8rKSly9ehUdO3ZUqip3pGvXrqbBy8yZM015kY5Y/4qKCkyYMAHPPPOMaXBli/bv168f\n/Pz8cPPmTYSHhytVPSIiRahuEFd7AeHy8nLEx8dj3LhxoovVbDdu3EBZWRkA4Pr160hMTERgYKBp\nUWQAdRZFHjduHL766iuUl5fj/PnzyMrKQlhYGLp164Z77rkHKSkpkCQJX3zxhWpmIOSoa80i0LVf\n65tvvkFERISYSjVBYWGh6fctW7aYrlx1tPpLkoTo6GgEBARgwYIFpv22aP89e/YgPDwcd911FyZO\nnKh8Ze2U6Lwg5sQxJ04U0fHldsfrxIlSewFho9GI6Oho0wLCalZUVITx48cDqJ45mTJlCkaNGoXQ\n0FBMmjQJsbGx8Pb2xubNmwEAAQEBmDRpEgICAuDm5oZ169aZTj+tW7cOzz77LG7evImxY8dizJgx\nwuplSVRUFPbt24fi4mJ4eXnh7bffxpIlS2Sra3R0NJ555hnodDp06tQJX331lbC6mnN7/VesWIG9\ne/ciIyMDGo0G9913HzZs2ADA8ep/4MAB/POf/zQtpwNULyFii/bPzMxEq1atsH//fri5qe7jzqkx\nn0rd2H7K0EjmLocjInIAs2bNQosWLfDxxx9j7ty5WLdunegimSQlJWHAgAGii+HUvj5WhE9SC4TF\nP7KoeoY89F3bXT3+2aQAdL+npc1en6yXlpYm+1kR/mlKRA6rTZs2pqVcWrVqJbg0RETyUl1OHBGR\ntTp37oyDBw9i4cKFcHHhx10N0XlBzIljTpwoouPLjTNxROSw3njjDZw6dQpVVVUICAgQXRxqAuZU\nqRvbTxkcxBGRw4qKigIA3Lx5EwDs8u4lIoheK8vZ43OdOOeNLzcO4ojIYcXFxQGoXtbkgw8+EFwa\nIiJ5MUmEiBzWyZMnYTAYcOzYMZw8eVJ0ceyG6Lwg5sQxJ04U0fHlxpk4InJY33zzDQCgZcuWzNFR\nGbaXurH9lMFBHBE5rNDQUNPveXl5yMvLw8MPPyywRPZBdF6Qs8dnTpzzxpcbB3FE5LD+8Y9/YMiQ\nIdBoNEhOTlbNLeiIiKzBnDgiclh+fn549dVXsXDhQvTp0wfTpk0TXSS7IDoviDlxzIkTRXR8uXEm\njogcWnR0NDQaDTw8PEQXhZqAOVXqxvZTBgdxROSwVq5ciby8PLRv3x4tW/L+kTVE5wU5e3zmxDlv\nfLnxdCoROawFCxZgxYoVuOeee/Diiy+KLg4Rkaw4iCMih+Xi4oJ7770XANC+fXvBpbEfovOCmBPH\nnDhRRMeXG0+nEpHDatmyJQwGA9asWYMrV66ILg41AXOq5KERFJftpwwO4ojIIUmShCeeeALFxcWQ\nJAlz584VXSS7ITovyNnjK5kTt+fnK2jd0vX3HR37YJvhotljA7u1wX0dW9m0PKLfe9Hx5cZBHBE5\nJI1Ggz179mDRokWii0IkzKajhVYf+8ZD3jYfxJG8mBNHRA4pISEBCQkJiIiIwMSJEzFx4kTRRbIb\novOCmBMnLidOqdjMiVOGamfiEhMT4erq2viBRORQIiIirDpOr9fjwIEDmDNnDv72t7/ZuFQkN+ZU\nqRvbTxmqHcS5urpiwIABooshTExMDJYsWSK6GEI4c90B565/Wlqa1cfm5ORgx44dyMnJwc6dOwEA\nY8eOtVXRVEV0XpCzxxe5TpzI2ID49150fLmpdhBHRNSQiRMnori4GJMmTcLFi+YTuYmI1IyDOJXK\nyckRXQRhnLnuAOtvrWeffVZ0EexWcnKy0BkJa+LX5FPZ4rSc6PqX/pwhbEZMqdiW2k/0ey86vtx4\nYYNKBQYGii6CMM5cd4D1t5UZM2bAw8Ojzvu7fPlyaLVahISEICQkBLt27TI9tmrVKuh0Ovj5+SEx\nMdG0/+jRowgMDIROp8NLL72kaB0cyfz585lXpWJsP2VwEKdSc+bMEV0EYZy57gDrbyvTp0+HXq+v\ns0+j0eCVV15Beno60tPTERkZCQAwGAyIj4+HwWCAXq/H3LlzIUkSgOr2iY2NRVZWFrKysuq9pj0Q\nPRPh7PGZE+e88eXGQRwREYChQ4eiQ4cO9fbXDM5qS0hIQFRUFNzd3eHt7Q0fHx+kpKSgsLAQZWVl\nCAsLAwBMnToVW7dutXnZicg5KT6IM3fK4nbz58+HTqdDcHAw0tPTFSydejjaWjdN4cx1B1h/pa1Z\nswbBwcGIjo5GSUkJAKCgoABardZ0jFarRX5+fr39np6eyM/PV7zMjRHdh7hOHNeJE0V0fLkpfmHD\n9OnT8eKLL2Lq1KlmH9+5cyfOnj2LrKwspKSkYM6cOTh06JDCpSQiqj41+uabbwIAli1bhoULFyI2\nNla21587dy569uwJAGjXrh0CAwNNp3tqvmycdfv2JaRsEe/0z1cAVA+6awY3NacbldquYQ/xTtxz\nAX/oFWn1+9fQtqX2u31b6f6lZPzjx4/j6tWrAKovSJs5cybkppHMnSuwsezsbDz66KM4fvx4vcee\nf/55DB8+HE8++SQAwM/PD/v27YOHh0ed45KSkpx6nTgiZ5SWlmb1Yr93oqHPptqPxcTEAIBpvb4x\nY8ZgxYoVuPfeezF8+HBkZmYCAOLi4rBv3z6sX7++3uvxM0y8r48V4ZPUAmHxjyyq7suh7yYJK0Nt\nbzzkjT/0qp9SQPKwxeeX3eXE5efnw8vLy7St1WqRl5cnsERE5KwKC3+/7+SWLVtMaSDjxo3DV199\nhfLycpw/fx5ZWVkICwtDt27dcM899yAlJQWSJOGLL77AH//4R1HFJyIHZ3eDOKB+IrFGoxFUEvvl\naOf1m8KZ6w6w/rYSFRWFwYMH4/Tp0/Dy8sLGjRuxePFiBAUFITg4GPv27cMHH3wAAAgICMCkSZMQ\nEBCAyMhIrFu3zvQ5tW7dOsycORM6nQ4+Pj4YM2aMyGqZJboPMSeOOXGiiI4vN7tb7NfT0xO5ubmm\n7by8PHh6epo91pnzSWpO99hLeZTa3rJlC06cOIHnn38eXbp0EV4ebts+fyU5Odm0wLEtckpqxMXF\n1ds3Y8YMi8cvXboUS5curbd/4MCBZk/HUtNwjTF1Y/spw+5y4nbu3Im1a9di586dOHToEBYsWGD2\nwgbmkzin8PBwZGVl4aeffkKfPn1EF4cUZuucOCXxM0w85sTVxZw427LF55fiM3FRUVHYt28fiouL\n4eXlhRUrVqCiogIAMHv2bIwdOxY7d+6Ej48PWrdujU2bNildRCIiIiK7p/ggztwpi9utXbtWgZKo\nm6Pd/42sx7an5hLdh3jvVN47VRTR8eVmdzlxtpScnIzExES8/fbbZh+PiYnBgAEDMGrUKIVLRkRE\ntTGnSt3Yfsqwy6tTbaWxq1xFXgVbOzXRmjRFR/pLgpqGbU/NJboPOXt83jvVeePLzWFn4gwGAxYv\nXozy8nL0798fq1evrjM4GjZsGEJCQmAwGPDII4/gxRdfBFB99WNsbCxu3LiBr7/+Gi1atMCECRNQ\nWVkJd3d3fPbZZ2jbtm2jcRYtWgSDwQA3Nzds3LgRRUVFePXVVyFJEkaPHo0FCxYgJiYGubm5KC4u\nxrJly7B48WJ069YNgYGBWLBggeLvGREREamHw87E9erVC9u3b8d3332H/Px8nDt3rs5M29WrVzFv\n3jzo9Xp89913KC4uBgD07t0b8fHxCA0Nxd69e+Hi4oIvv/wS27dvx8iRI7Fly5ZG4+j1eri6umLH\njh1ISEhAx44d8ec//xl//etfsWvXLuzfvx+5ubnQaDTQarWIj4/HPffcgwsXLmDDhg1WDeAcba0b\nsh7bnppLdB/iOnFcJ04U0fHl5rAzcdnZ2XjzzTdx8+ZNZGdn48KFC3Ueb926NXr37g0A6NevH375\n5RcAQFBQEIDq9epKSkpw/fp1vPzyyygsLMSVK1fw2GOPNRonKysLgwcPNh2j0Wjw66+/QqfTAQCC\ng4Nx/vx5AEBISIjpuL59+8LNzWGbhIjIasypUje2nzIcdibu008/xQsvvIDt27cjKCioXp7Z9evX\nce7cOUiShJMnT5oWDa5NkiT88MMPuPfee7F9+3ZERUWhqqqq0Ti+vr44ePCg6Ziqqip06dIFZ86c\ngSRJ+M9//oP77rsPAODi8nsT1P69MY52Xp+sx7an5hLdh2wV//KNCvx47gr2NfJj7NEXP567giN5\npTYpR2OYE+e88eXmsNM+o0ePxuuvvw6dTgdJkqDRaEz/AkD79u2xfv16ZGRk4JFHHkGXLl0A1L24\nQaPRIDQ0FB988AGOHz+OLl261Lmvq6U4Y8aMQVJSEsaOHQt3d3ds3LgR//u//4uXXnrJlBNX8zo1\n8TQaDW8vRkTUDBVGCav3/oKKKsXXsCcSQsgdG+TQ3NXOIyIikJRkH6tk3wlHW+vGWrxjg/O2PcA7\nNshFdB+y1TpxRWXlmPG1odFBnMh12mrHF3HHhobqLucdG7hOXH0OcccGe8FZLyIi+8WcKnVj+ynD\nYXPiGrN7927RRWgWZ52JIbY9NZ/oPiQ6vui8MObEOW98uTntII6IiIhIzTiIUylHW+uGrMe2p+YS\n3YdErxMncp020fG5TpxjfX46bU4cERHZL+ZUqRvbTxmciVMpRzuvT9Zj21Nzie5DouOLzgtjToEP\njgAAIABJREFUTpzzxpcbB3FEREREKsRBnEo52nl9sh7bnppLdB9iThxz4kQRHV9uzIkjIiK7w5wq\ndWP7KUPITJxer4efnx90Oh1Wr15d7/Hi4mKMGTMG/fv3R79+/fDpp58qX0g752jn9cl6bHtqLtF9\nSHR80XlhzIlz3vhyU3wQZzQaMW/ePOj1ehgMBsTFxSEzM7POMWvXrkVISAgyMjKwd+9eLFy4EJWV\nlUoXlYiIiMhuKT6IS01NhY+PD7y9veHu7o7JkycjISGhzjHdu3dHaWkpAKC0tBSdOnWCmxvP/Nbm\naOf1yXpse2ou0X2IOXHMiRNFdHy5KT4yys/Ph5eXl2lbq9UiJSWlzjGzZs3CQw89hB49eqCsrAyb\nN29WuphERCQQc6rUje2nDMVn4qy58fw777yD/v37o6CgABkZGXjhhRdQVlamQOnUw9HO65P12PbU\nXKL7kOj4ovPCmBPnvPHlpvhMnKenJ3Jzc03bubm50Gq1dY45ePAg3njjDQBA7969cd999+H06dMI\nDQ2tc9zcuXPRs2dPAEC7du0QGBhoaqCaKVNuO9Z2jbS0NFy8eFF4ebht+/ZOTk5GTk4OAGDmzJkg\nIqJqGkmSJCUDVlZWok+fPkhKSkKPHj0QFhaGuLg4+Pv7m4555ZVX0K5dO7z11lsoKirCwIEDcezY\nMXTs2NF0TFJSEgYMGKBk0e1KcnKyw/1FYY3w8HBkZWXhp59+Qp8+fUQXRwhnbXugevAeEREhuhiy\nEPkZJroPWRO/Jp+qKaflisrKMeNrAyqqGv5aK/05Q+iMVE38I4uq+3Lou0mKxzbnjYe88YdeHWSJ\nY6n91ND3bMUWn1+Kz8S5ublh7dq1GD16NIxGI6Kjo+Hv748NGzYAAGbPno2lS5di+vTpCA4ORlVV\nFd599906AzgiInJszKlSN7afMoRc8hkZGYnIyMg6+2bPnm36vXPnzti+fbvSxVIVZ52JIbY9NZ/o\nPiQ6vui8MObEOW98ufG2W0REREQqxEGcSjnaWjdkPbY9NZfoPsR14rhOnCii48uNK+gSEZHdYU6V\nurH9lMGZOJVytPP6ZD22PTWX6D4kOr7ovDDmxDlvfLlxEEeqUFJSgkWLFuHSpUsAgL/85S8ONy1O\nRETUFBzEqZSzDWCuX7+Of/zjH7h69SoA4N///jcMBoPgUonhbG1P8hPdh5gTx5w4UUTHlxtz4oiI\nyO4wp0rd2H7K4EycSjnaeX2yHtuemkt0HxIdX3ReGHPinDe+3DgTR0RERPjplxI0cscyk7vdXRDU\nvQ1aubvatlDUIM7EqZSjndcn67HtbWPGjBnw8PBAYGCgad/ly5cxcuRI+Pr6YtSoUSgpKTE9tmrV\nKuh0Ovj5+SExMdG0/+jRowgMDIROp8NLL72kaB2sJboPMSfOPnPifvi5BKv2ZFv18/fUfBgbGPEx\nJ04ZHMQREQGYPn069Hp9nX0xMTEYOXIkzpw5g4iICMTExAAADAYD4uPjYTAYoNfrMXfuXEhS9Rfa\nnDlzEBsbi6ysLGRlZdV7TbLO/PnzmVelYmw/ZXAQp1KOdl6frMe2t42hQ4eiQ4cOdfZt27YN06ZN\nAwBMmzYNW7duBQAkJCQgKioK7u7u8Pb2ho+PD1JSUlBYWIiysjKEhYUBAKZOnWp6jj0R3YdExxed\nF8acOOeNLzcO4oiILCgqKoKHhwcAwMPDA0VFRQCAgoICaLVa03FarRb5+fn19nt6eiI/P1/ZQhOR\n0+AgTqUc7bw+WY9tL4ZGo4FGoxFdDFmI7kPMibPPnDg5MSdOGbw6lYjIAg8PD1y4cAHdunVDYWEh\nunbtCqB6hi03N9d0XF5eHrRaLTw9PZGXl1dnv6enp8XXnzt3Lnr27AkAaNeuHQIDA02ne2q+bJx1\ne8CAAXXeK2uef+VGBYDqU+I1g5Wa04f2ul1DbfEunk7DT50uYuTwPwCwvv1u31a6fykZ//jx46YF\n6nNycjBz5kzITSPVZOOqTFJSUr1OQo4rPz8fgYGBcHV1hdFoBFCddP7cc88JLhkpKS0tDRERETZ7\n/ezsbDz66KM4fvw4AGDRokXo1KkTFi9ejJiYGJSUlCAmJgYGgwFPPfUUUlNTkZ+fjxEjRuDs2bPQ\naDQIDw/HRx99hLCwMDz88MOYP38+xowZUy8WP8PkV1RWjhlfG1Bh7ToZgh1ZVN2XQ99NElySpvNq\n3xJ/fdQXbVpyLshatvj8EnI6Va/Xw8/PDzqdDqtXrzZ7zN69exESEoJ+/fph2LBhyhaQiJxOVFQU\nBg8ejNOnT8PLywubNm3CkiVL8P3338PX1xc//PADlixZAgAICAjApEmTEBAQgMjISKxbt850qnXd\nunWYOXMmdDodfHx8zA7giIjkoPgQ2mg0Yt68edi9ezc8PT1x//33Y9y4cfD39zcdU1JSghdeeAHf\nffcdtFotiouLlS6m3UtOTna4q2zIOmx724iLizO7f/fu3Wb3L126FEuXLq23f+DAgaaZPHslug9Z\nE78mn8oWy1SU/pwh9CpNkfGVim2p/dTQ99RE8UFcamoqfHx84O3tDQCYPHkyEhIS6gzivvzyS0yY\nMMF0lVfnzp2VLiYREQnENcbUje2nDMVPp+bn58PLy8u0XXNpfm1ZWVm4fPkyhg8fjtDQUHzxxRdK\nF9PuOdJfEtQ0bHtqLtF9SHR80WulcZ04540vN8Vn4qy5RL+iogJpaWlISkrCjRs3MGjQIDzwwAPQ\n6XQKlJCIiIjI/ik+iLv90vzc3Nw6i2MCgJeXFzp37oxWrVqhVatWePDBB/Gf//yn3iDOmS/P/9vf\n/uZU9T18+DBu9/PPP5t+F10+JbdrXypvD+Wx5XbN7zk5OQBgk0v0nZHovCDmxDEnThTR8eWm+BIj\nlZWV6NOnD5KSktCjRw+EhYUhLi6uTk7cqVOnMG/ePHz33Xe4desWwsPDER8fj4CAANMxzn55vqN1\nxMZwiZHfOVvb12brJUaUJPIzTHQfslV8a5cYsZdBnIglRuSq+50uMeKofc8atvj8Unwmzs3NDWvX\nrsXo0aNhNBoRHR0Nf39/bNiwAQAwe/Zs+Pn5YcyYMQgKCoKLiwtmzZpVZwBHjnden6zHtqfmEt2H\nRMcXnRfGnDjnjS83Iav0RUZGIjIyss6+2bNn19l+9dVX8eqrrypZLCIiIiLV4L1TVcrR7v9G1mPb\nU3OJ7kO8dyrvnSqK6Phy4/0yiIjI7nCdMXVj+ymDM3Eq5Wjn9cl6bHtqLtF9SHR80XlhzIlz3vhy\n4yCO7F5eXh727dtXb39mZibS0tIElIiIiEg8DuJUytHO6zdk3759mDdvXr39n332Gf7yl78IKJFY\nztT2ZBui+xBz4pgTJ4ro+HJjThwREdkd5lSpG9tPGZyJUylHO69P1mPbU3OJ7kOi44vOC2NOnPPG\nlxsHcUREREQqxEGcSjnaeX2yHtuemkt0H2JOHHPiRBEdX27MiSMiIrvDnCp1Y/spgzNxKuVo5/XJ\nemx7ai7RfUh0fNF5YcyJc974cuMgjoiIiEiFOIhTKUc7r0/WY9tTc4nuQ8yJY06cKKLjy405cURE\nZHeYU6VubD9lcCZOpRztvD5Zj21PzSW6D4mOLzovjDlxzhtfbhzEEREREakQB3Eq5Wjn9cl6bHtq\nLtF9iDlxzIkTRXR8uQkZxOn1evj5+UGn02H16tUWjzt8+DDc3Nzw7bffKlg6IiISbf78+cyrUjG2\nnzIUH8QZjUbMmzcPer0eBoMBcXFxyMzMNHvc4sWLMWbMGEiSpHQx7Z6jndcn67HtqblE9yHR8UXn\nhTEnznnjy03xQVxqaip8fHzg7e0Nd3d3TJ48GQkJCfWOW7NmDZ544gl06dJF6SISERER2T3FB3H5\n+fnw8vIybWu1WuTn59c7JiEhAXPmzAEAaDQaRcuoBo52Xt+SsrIyXLt2zeLj5eXluHTpkoIlEs9Z\n2p5sR3QfYk4cc+JEER1fboqvE2fNgGzBggWIiYmBRqOBJEkWT6fOnTsXPXv2BAC0a9cOgYGBpqnS\nmoZy1O3jx4/bVXlstf3555/jm2++gSU//PADAgMDsXnzZrsoL7fl3a75PScnBwAwc+ZMkHNgPpW6\nsf2UoZEUTjg7dOgQli9fDr1eDwBYtWoVXFxcsHjxYtMxvXr1Mg3ciouLcffdd+OTTz7BuHHjTMck\nJSVhwIABShadBHjuuefqDOJcXV1hNBrrHHPXXXehoKBA6aKRAGlpaYiIiBBdDFnwM0x+RWXlmPG1\nARVV6sijPrKoui+HvpskuCRN59W+Jf76qC/atOQ9A6xli88vxd/90NBQZGVlITs7Gz169EB8fDzi\n4uLqHHPu3DnT79OnT8ejjz5aZwBHRETOocJYBWuHZO6uTL0h56L4IM7NzQ1r167F6NGjYTQaER0d\nDX9/f2zYsAEAMHv2bKWLpErJyckOd5UNWYdtT80lug9ZE78mn+p/JjyLTUcKrXrdCqNk1Sxc6c8Z\nQq/SFBlfqdg17Xf7aVU19D01ETIPGhkZicjIyDr7LA3eNm3apESRiIjIjtR8+Sdnl+D0xRuCS0NN\nxZw4ZfCODSrlSH9JUNOw7am5RPch0fFFr5XGdeKcN77cOIgjIiIiUiEO4lTK0da6Ieux7am5RPch\nrhPHdeJEER1fbrw2mIiI7E7tnDhSH+bEKYMzcSrlaOf1yXpse2ou0X1IdHzReWHMiXPe+HLjII6I\niIhIhTiIUylHO69P1mPbK8/b2xtBQUEICQlBWFgYAODy5csYOXIkfH19MWrUKJSU/H7ab9WqVdDp\ndPDz80NiYqKoYlskug8xJ445caKIji835sSR3Ro4cCByc3MbPa68vBze3t74+uuvcf/99ytQMnI2\nGo0Ge/fuRceOHU37YmJiMHLkSCxatAirV69GTEwMYmJiYDAYEB8fD4PBgPz8fIwYMQJnzpyBiwv/\nZm4K5sSpG3PilMFBnEo52nl9c8rKylBZWdnocZIkobS0tN49VR2VM7S9Pbr9NtPbtm3Dvn37AADT\npk3DsGHDEBMTg4SEBERFRcHd3R3e3t7w8fFBamoqHnjgARHFNkt0HxIdX3RemCPkxN0or0LRtXLk\nXb1l1fHtW7mhW9uWwttedHy5cRBHRNQIjUaDESNGwNXVFbNnz8asWbNQVFQEDw8PAICHhweKiooA\nAAUFBXUGbFqtFvn5+ULKTWQrl25UYM6W01Yf///G+qBb25Y2LJFz4vy+SjnaeX2yHtteeQcOHEB6\nejp27dqFjz/+GPv376/zuEajgUZj+ebrDT0mgug+xJw4x8+Je+TGfjxyY3+9/Wroe2rCmTgiokZ0\n794dANClSxeMHz8eqamp8PDwwIULF9CtWzcUFhaia9euAABPT886uZx5eXnw9PQ0+7pz585Fz549\nAQDt2rVDYGCg6XRPzZeNs24PGDCgzntVM/ioOR3oKNtK10+peF8Wtv1tuzpeRupPKOt8tym+qP6l\nZPzjx4/j6tWrAICcnBzMnDkTctNItyd6qERSUlK9/+TkWHx9fVFcXFxnn6ura73cN41GA0mSsHPn\nTrvKOyL5paWlISIiQtGYN27cgNFoRNu2bXH9+nWMGjUKb731Fnbv3o1OnTph8eLFiImJQUlJienC\nhqeeegqpqammCxvOnj1bbzaOn2HWSc4uwdu7z4suhk0cWVTdl0PfTRJcEtv7f2N9ENyjrehiCGWL\nzy/OxBERNaCoqAjjx48HAFRWVmLKlCkYNWoUQkNDMWnSJMTGxsLb2xubN28GAAQEBGDSpEkICAiA\nm5sb1q1bZ3enU4nIMTAnTqUc7bw+WY9tr6z77rsPGRkZyMjIwIkTJ/D6668DADp27Ijdu3fjzJkz\nSExMRPv27U3PWbp0Kc6ePYtTp05h9OjRoopukeg+xJw45sSJIjq+3DgTR0REdofrxKnb/909VHQR\nnIKQmTi9Xg8/Pz/odDqsXr263uP/+te/EBwcjKCgIAwZMgTHjh0TUEr75mhr3dT266+/4r333sN/\n//vfJj3vq6++wsGDB21UKvvhyG1PyhDdh0TH5zpx4ohue9Hx5ab4IM5oNGLevHnQ6/UwGAyIi4tD\nZmZmnWN69eqFH3/8EceOHcOyZcvw3HPPKV1MEujXX3/FypUrcfPmzSY97/PPP8ePP/5oo1IRERHZ\nF8UHcampqfDx8YG3tzfc3d0xefJkJCQk1Dlm0KBBaNeuHQAgPDwceXl5ShfT7jnaeX2yHtuemkt0\nH2JOHHPiRBEdX26K58Tl5+fDy8vLtK3VapGSkmLx+NjYWIwdO1aJohERkZ1gTpy6MSdOGYoP4ppy\nqf2ePXuwceNGHDhwwIYlUidHO69P1mPbU3OJ7kOi44vOC2NOnPPGl5vig7jbVzPPzc2FVqutd9yx\nY8cwa9Ys6PV6dOjQwexrcbVzx90G6t9wvClEl5/b8q2unpycjJycHACwyYrnRERqpfgdGyorK9Gn\nTx8kJSWhR48eCAsLQ1xcHPz9/U3H5OTk4KGHHsI///lPiyvwO/tq58nJyQ73F0WNEydO4MEHHzR7\nd4aG7tgAAIsWLcKSJUsUK6sIjtz2jRFxxwZbEfkZJroPWRO/Jh9uwLipst+xofTnDKEzUjXxRdyx\nQam61+TD1ZxWrbljgxr6nq04xB0b3NzcsHbtWowePRpGoxHR0dHw9/fHhg0bAACzZ8/G22+/jStX\nrmDOnDkAAHd3d6SmpipdVBIgJSUF8fHxd/z85ORkfPHFF3jmmWdkLBURKY05cerGnDhl8N6pZFfW\nrl2LN998E4D5WbfGZuIAICwsDHq93vaFJcVxJk79KiqrcOriDZQbq6w6/tiFa4jLKLJxqcTgvVOd\ni0PMxBERkfOqkiSsP5SHrEtNWweSiOrjvVNVytHWuiHrse2puUT3oaJTaY0eY2mdMTlwnTjb4zpx\nyuBMHBER2R3mVKkb208ZnIlTKWe9OpHY9tR8ovuQh5/YXEDRa6VxnTjnjS83zsSR3YiKisLu3bub\n/TpHjx5F9+7dce7cObRq1UqGkhEREdkfzsSplKOd1weAioqKelee3omqqircunVLhhLZJ0dse1KW\n6D7EnDjmxIkiOr7cOBNHRER2hzlV6sb2UwZn4lTK0c7rT5o0CRkZ8v6FOGXKFIdcJNrR2p6UJ7oP\nMSeOOXHOGl9uHMSRXfjhhx9w+fJlWV9z7969uHTpkqyvSUREZC84iFMpRzmvX1xcjO3bt9vs9Q8f\nPozjx4/b7PVFcJS2J3FE9yHmxDEnThTR8eXGnDgSKjMzE9OmTbPZ63/44Ye4fv06Vq9ebbMYRCQ/\n5lSp2+3td/7Kf1FZJeHMxetolVfa4HPbtnSFb5fWtiyew+AgTqUc4bz+5s2bsWnTJpvHSUxMBACH\nGcg5QtuTWKL7kIffAJQKvO2W6LwwZ8yJW/dT3m+/dcVX+p8bPHa0b0cstNEgTnTflxtPp5IQmzdv\nxr/+9S+kpKTYPNYvv/yCrVu3Ys2aNSgrK7N5PCIiIiVwEKdSaj2vbzQaceLECXz44YfYv982+S7m\nXLlyBW+99RYOHz6MK1euKBbXFtTa9mQ/RPch5sQ5b06c6PdedN+XG0+nkqKuX7+OBx98EC4uYv5+\neOKJJ7BmzRpMmTJFSHwisg5z4tSN7acMzsSplBrP6yclJeGhhx4SXQz8+c9/xptvvim6GHdMjW1P\n9kV0H+I6cc6XE2cv8UX3fbkJGcTp9Xr4+flBp9NZTDafP38+dDodgoODkZ6ernAJSW4bN27EqlWr\ncO7cOdFFQVFREb799lu88MILootCRER0xxQfxBmNRsybNw96vR4GgwFxcXHIzMysc8zOnTtx9uxZ\nZGVl4e9//zvmzJmjdDHrKS4uxrZt2xAaGopevXohODgYmzdvRkFBgZDyqOm8/rPPPovVq1cjLa3x\nPBilFBQU4Ntvv8WYMWPsYmDZFCLafuvWrfjjH/8If39/BAYGYtmyZcjOzla8HCQP0Z8fzIljTpwo\novu+3BTPiUtNTYWPjw+8vb0BAJMnT0ZCQgL8/f1Nx2zbts20dlh4eDhKSkpQVFQEDw8Pxcp59uxZ\nxMfHY+vWrbhx4wbc3d2Rk5MDAHBxcUFJSQmef/55PP/887jrrrug0WgwaNAgDBkyBK1atbL4uqWl\npaioqEDbtm3RokULpaojRF5eHh5++GH8+uuvdnlD+srKSqSmpuKRRx7B4sWLbbpenb24fPkyJElC\nhw4dGsxLTElJwdGjR1FaWorWrVvjrbfeqvP4xx9/jM8//xzt27dHmzZtEBgYiHHjxmHs2LG2rgLZ\nocLSW/j1WrlVx7q5anC9wtjoccypUje2nzIUH8Tl5+fDy8vLtK3VaustM2HumLy8PMUGcStXrsQn\nn3yC0tLqBQk1Gg0kSTJ77Pr16wEAbm5u+OCDD7Bx40YMGjTIVNZr164hJycHGRkZ2LBhA3JycnD1\n6lUEBgaiT58+GD16NCZMmIDz589j//79SElJQXZ2NrRaLd5++22Ldbbn8/q5ubk4fPgwfvrpJ+Tm\n5sLNzb6vn7lw4QK2b9+OkpISjBgxAn379hVdpAZZavsVK1bg6NGj8PLyQs+ePfE///M/GDJkCNLS\n0rBz507s378fGRkZqKioQP/+/REREYHBgwcjODgYHTt2BABUVFTg8OHDWLBgAc6ePdtgOW7cuGFa\nsiUzMxMJCQnw9fXFvn375K0wyU7uz49LNyrw2s6G+0sdPfrJGr+pROdlMSdOHHv+7rwTin+7ajQa\nq467fdBk7nkdO3aQpUz1/eW3n5qy1H20qqr+Myorq/+dMeP2RzoA8AIwBMDvOVjHj1f/fPMNMGtW\nzXF1k32//vpOym4POgAIAhAN4B+m96Y2c+/h7Yxm/lg3t+/29jE33jZXhtqv9cMP1T8rVjReLvv1\nYZ2t39NNI377+V1GRvXPe++Ze52Hf/tp2O1tcetWdZ/+bTxoE7t32+61iYjURvGcOE9PT+Tm5pq2\nc3NzodVqGzwmLy8Pnp6eZl7tWQDLf/v5EMDeWo/tdfBtZ6tv7e29jTzu6Nt7G3nckbb3ovr/97O/\n/ZAcROcFWZMXxZw4dcdmTpwyFJ+JCw0NRVZWFrKzs9GjRw/Ex8cjLi6uzjHjxo3D2rVrMXnyZBw6\ndAjt27c3e1rx8uUPTL8bDAbs27cP+/atwqlTp9CiRQt0794dZ86cQVFRUZ1TogMGDEB4eDiGDh2K\n/v0z0aVLF7i6Bv/2SjULwdrf9pUrV3Dq1E58//332LBhAyorK1FRUQGdTocnn3wSHTt2xM6dK2Ew\nGEwXXLi5uaHytmmo208Pu7i4oOq2qTFzz3N1dYXxt+mXBx98EBMnTsSTT/b97XSpcu9HcnJZrSlx\n28czGo1ISyvH5s2bERs73Ox7Y+49vF3t98/SvrZt26Jr166YNWsWevTogY8+uh/p6ekwGo1o27Yt\nRo0aBU9PT8yaNeu3P2zsp39a2r506RLOnv0vTpw4gR07VmD//v116tyuXTt07twZXbp0wZUrV9Cp\nUyf4+fnhkUcewbBhw2q9Fuzq4hiyLeZUqRvbTxkayVKylw3t2rULCxYsgNFoRHR0NF5//XVs2LAB\nADB79mwAMF3B2rp1a2zatAkDBtQ91ZiUlFRvnzkXLlxAYmIi1q9fDzc3N/zpT39CYGCgKQdIzU6f\nPo3S0lL4+vqiXbt2dfZv374d77zzjqyDuFatWmHIkCEICQlBZGQk+vcXm9ugtKtXr+LLL7/Enj17\nkJ2dXSdnTI5B3GOPPYaoqCiMGjWqzjFHjhyBJEkYOHCgsEWS5XTw4EHExsYiKysLDz30EMaOHYuw\nsDCrnpuWloaIiIjGD1QBaz/D1ODEhWt45f+yRBdDdY4squ7Loe8mCS6JfRnt2xELH7xXdDFkZ4vP\nLyGDODk40gegLVy/fh1bt27Fhx9+iPz8fPz3v/9F586d4efnh0GDBqFjx44oLCzEqVOnAAA3b97E\npUuX4O3tjfLycqSkpNS5z6iHhwcGDRqEjRs3iqqSXVm/fj2+/PJLnDhxAsDvg7iIiAi0bt0aJ06c\ngKurK8LDw3Hx4kV07twZ3bp1Q9u2bZGdnY3du3cjLy8P7u7uaNWqFRYsWIDIyEj06dNHcM3sGwdx\n9omDuDvDQZx5HMRZz74vGySLkpOTG7zKpnXr1pgyZQqmTJmCtWvXIiEhAXPnzsX48eOtev3hw4fj\nl19+wTPPPIOAgAAMGDAAOp1OruI3S2N1V8Lzzz+PiRMnwmAwYO/evdixYweuXr2Kt956C/36NX7l\n3a+//oopU6agS5cu+PLLL5sU2x7qT+omug+V/pzR6FWKNflUtjgtZ018WxIZX6nYltpP9Hsvuu/L\njYM4JzBv3jzMmzevSc/Zs2ePjUrjODp16oShQ4di6NChWLZsWZOe27VrV3z//fc2KhmR+jGnSt2a\n034nLlyD/nSx1cf379EW3dq2vON4asZBnEo50l8STeXMdQdYf2o+a/rQxevlqKqyLtvGuoWjfid6\nrTBnjq+GuueXluP9/bmNHlfjkwl+Vh/raJ+fHMQREVE9W09exJYTF606tkqdqdVEqqf+S92clKOt\nddMUzlx3gPVXC71eDz8/P+h0Oqz+feVlu2BNH6qqklBp5Y+VE3YmXCeO68SJ4mifnxzEqdTx48dF\nF0EYZ647wPqrgdFoNC2TZDAYEBcXh8zMTNHFMhHdh24UNH6Lrv+7e6jN8uKsiW9LIuMrFdtS+9ki\n/o2KKpy7fNOqnwOH02WPLxJPp6rU1atXRRdBGGeuO8D6q0Fqaip8fHzg7e0NAJg8eTISEhLg7+8v\nrEw3yitxrbx6LcOCi5cbvGG9qwtwy2jFvfHukPHmdZu9NuPbb2xbxX9p2xmrj723wPoLJtSAgzgi\nIpnl5+fDy8vLtK3VapGSkiKwRMDlm5WYu+U0AOAXQzH+803DM4O3Km03iCMSRQJws8L4I0L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+ "text": [ + "" + ] + } + ], + "prompt_number": 18 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "It appears the MCMC has converged so we may continue.\n", + "\n", + "For a specific trading signal, call it $x$, the distribution of possible returns has the form:\n", + "\n", + "$$R_i(x) = \\alpha_i + \\beta_ix + \\epsilon $$\n", + "\n", + "where $\\epsilon \\sim \\text{Normal}(0, 1/\\tau_i) $ and $i$ indexes our posterior samples. We wish to find the solution to \n", + "\n", + "$$ \\arg \\min_{r} \\;\\;E_{R(x)}\\left[ \\; L(R(x), r) \\; \\right] $$\n", + "\n", + "according to the loss given above. This $r$ is our Bayes action for trading signal $x$. Below we plot the Bayes action over different trading signals. What do you notice?\n" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "figsize(12.5, 6)\n", + "from scipy.optimize import fmin\n", + "\n", + "\n", + "def stock_loss(price, pred, coef=500):\n", + " \"\"\"vectorized for numpy\"\"\"\n", + " sol = np.zeros_like(price)\n", + " ix = price * pred < 0\n", + " sol[ix] = coef * pred ** 2 - np.sign(price[ix]) * pred + abs(price[ix])\n", + " sol[~ix] = abs(price[~ix] - pred)\n", + " return sol\n", + "\n", + "tau_samples = mcmc.trace(\"prec\")[:]\n", + "alpha_samples = mcmc.trace(\"alpha\")[:]\n", + "beta_samples = mcmc.trace(\"beta\")[:]\n", + "\n", + "N = tau_samples.shape[0]\n", + "\n", + "noise = 1. / np.sqrt(tau_samples) * np.random.randn(N)\n", + "\n", + "possible_outcomes = lambda signal: alpha_samples + beta_samples * signal \\\n", + " + noise\n", + "\n", + "\n", + "opt_predictions = np.zeros(50)\n", + "trading_signals = np.linspace(X.min(), X.max(), 50)\n", + "for i, _signal in enumerate(trading_signals):\n", + " _possible_outcomes = possible_outcomes(_signal)\n", + " tomin = lambda pred: stock_loss(_possible_outcomes, pred).mean()\n", + " opt_predictions[i] = fmin(tomin, 0, disp=False)\n", + "\n", + "\n", + "plt.xlabel(\"trading signal\")\n", + "plt.ylabel(\"prediction\")\n", + "plt.title(\"Least-squares prediction vs. Bayes action prediction\")\n", + "plt.plot(X, ls_coef_ * X + ls_intercept, label=\"Least-squares prediction\")\n", + "plt.xlim(X.min(), X.max())\n", + "plt.plot(trading_signals, opt_predictions, label=\"Bayes action prediction\")\n", + "plt.legend(loc=\"upper left\");" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "display_data", + "png": 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HmzZtknrM6Oho5OTkYOnSpeDzS79vlz2oW1kcDhw4gOHDh6Np06YAgIULF8LW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+ "text": [ + "" + ] + } + ], + "prompt_number": 19 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "What is interesting about the above graph is that when the signal is near 0, and many of the possible returns outcomes are possibly both positive and negative, our best (with respect to our loss) prediction is to predict close to 0, hence *take on no position*. Only when we are very confident do we enter into a position. I call this style of model a *sparse prediction*, where we feel uncomfortable with our uncertainty so choose not to act. (Compare with the least-squares prediction which will rarely, if ever, predict zero). \n", + "\n", + "A good sanity check that our model is still reasonable: as the signal becomes more and more extreme, and we feel more and more confident about the positive/negativeness of returns, our position converges with that of the least-squares line. \n", + "\n", + "The sparse-prediction model is not trying to *fit* the data the best (according to a *squared-error loss* definition of *fit*). That honor would go to the least-squares model. The sparse-prediction model is trying to find the best prediction *with respect to our `stock_loss`-defined loss*. We can turn this reasoning around: the least-squares model is not trying to *predict* the best (according to a *`stock-loss`* definition of *predict*). That honor would go the *sparse prediction* model. The least-squares model is trying to find the best fit of the data *with respect to the squared-error loss*.\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "##### Example: Kaggle contest on *Observing Dark World*\n", + "\n", + "\n", + "A personal motivation for learning Bayesian methods was trying to piece together the winning solution to Kaggle's [*Observing Dark Worlds*](http://www.kaggle.com/c/DarkWorlds) contest. From the contest's website:\n", + "\n", + "\n", + "\n", + ">There is more to the Universe than meets the eye. Out in the cosmos exists a form of matter that outnumbers the stuff we can see by almost 7 to 1, and we don\u2019t know what it is. What we do know is that it does not emit or absorb light, so we call it Dark Matter. Such a vast amount of aggregated matter does not go unnoticed. In fact we observe that this stuff aggregates and forms massive structures called Dark Matter Halos. Although dark, it warps and bends spacetime such that any light from a background galaxy which passes close to the Dark Matter will have its path altered and changed. This bending causes the galaxy to appear as an ellipse in the sky.\n", + "\n", + "\n", + "\n", + "\n", + "The contest required predictions about where dark matter was likely to be. The winner, [Tim Salimans](http://timsalimans.com/), used Bayesian inference to find the best locations for the halos (interestingly, the second-place winner also used Bayesian inference). With Tim's permission, we provided his solution [1] here:\n", + "\n", + "1. Construct a prior distribution for the halo positions $p(x)$, i.e. formulate our expectations about the halo positions before looking at the data.\n", + "2. Construct a probabilistic model for the data (observed ellipticities of the galaxies) given the positions of the dark matter halos: $p(e | x)$.\n", + "3. Use Bayes\u2019 rule to get the posterior distribution of the halo positions, i.e. use to the data to guess where the dark matter halos might be.\n", + "4. Minimize the expected loss with respect to the posterior distribution over the predictions for the halo positions: $ \\hat{x} = \\arg \\min_{\\text{prediction} } E_{p(x|e)}[ L( \\text{prediction}, x) ]$ , i.e. tune our predictions to be as good as possible for the given error metric.\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The loss function in this problem is very complicated. For the very determined, the loss function is contained in the file DarkWorldsMetric.py in the parent folder. Though I suggest not reading it all, suffice to say the loss function is about 160 lines of code — not something that can be written down in a single mathematical line. The loss function attempts to measure the accuracy of prediction, in a Euclidean distance sense, such that no shift-bias is present. More details can be found on the metric's [main page](http://www.kaggle.com/c/DarkWorlds/details/evaluation). \n", + "\n", + "We will attempt to implement Tim's winning solution using PyMC and our knowledge of loss functions." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### The Data\n", + "\n", + "The dataset is actually 300 separate files, each representing a sky. In each file, or sky, are between 300 and 720 galaxies. Each galaxy has an $x$ and $y$ position associated with it, ranging from 0 to 4200, and measures of ellipticity: $e_1$ and $e_2$. Information about what these measures mean can be found [here](https://www.kaggle.com/c/DarkWorlds/details/an-introduction-to-ellipticity), but for our purposes it does not matter besides for visualization purposes. Thus a typical sky might look like the following:" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from draw_sky2 import draw_sky\n", + "\n", + "n_sky = 3 # choose a file/sky to examine.\n", + "data = np.genfromtxt(\"data/Train_Skies/Train_Skies/\\\n", + "Training_Sky%d.csv\" % (n_sky),\n", + " dtype=None,\n", + " skip_header=1,\n", + " delimiter=\",\",\n", + " usecols=[1, 2, 3, 4])\n", + "print \"Data on galaxies in sky %d.\" % n_sky\n", + "print \"position_x, position_y, e_1, e_2 \"\n", + "print data[:3]\n", + "\n", + "fig = draw_sky(data)\n", + "plt.title(\"Galaxy positions and ellipcities of sky %d.\" % n_sky)\n", + "plt.xlabel(\"x-position\")\n", + "plt.ylabel(\"y-position\");" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Data on galaxies in sky 3.\n", + "position_x, position_y, e_1, e_2 \n", + "[[ 1.62690000e+02 1.60006000e+03 1.14664000e-01 -1.90326000e-01]\n", + " [ 2.27228000e+03 5.40040000e+02 6.23555000e-01 2.14979000e-01]\n", + " [ 3.55364000e+03 2.69771000e+03 2.83527000e-01 -3.01870000e-01]]\n" + ] + }, + { + "metadata": {}, + "output_type": "display_data", + "png": 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6CAgQqiVWxePQ6SiwvqpKyQkIgIAA9Z6WhPR0iIvTEhTkIDq6/EsYQhUo9bRx\n48Zi75OcLDF2rDevv+7tVM5AqTe2a1fRa8sZDORzLvz4YwNnz7qHA2xyssTq1VoGDfKhXTt/YmP9\nefhhE8nJ7tG+0qYksuAOBAcLwsIcREYK6tRRlbNczGY4dkxmyxYNy5dr+eMPLdu2aZzZ729GZZUH\nldJHlQWVXHJl4fRpmfvv9+Wee/z47TcdGRnl3xbVglYACQkyK1fmd842GAStWxfdwTIkxEG/fjku\n0UmXLilFZUNCKs5KZbcr5XNee83Inj2uYYBBQcKlCK6Kirtx+TLs3Kll8mQD27ZpsdlcFbKuXXOY\nNi3T46dzhICjR2USEmRSUpTcYZmZUKuWICjIgb+/IDBQ+atd24G3d0W3WEWl8qDTgSQpgStPPeXD\nf/+bydChOeUaOe/xClpJInOqVRMEBjq4dCnPehYTY+Pzz7No1qzoCprRCP/6l5kDBzQcPqzc6gYN\nbBU6hSgErF+v5dFHffINbCEhdj74INtjO3JPi9KqiiQlSbz6qpGlSwvPyVW/vgODodCfnVR2eUhK\nkhg40Ifjx29s1ZdlQWysjSFDLNx+u71CnZ7dlcouCyqlR64shIY6aN/e5qyI8eqr3jRsaCc2tvyi\nYNUggUJISFC+TIVQrEr16ztKrFidPi2xbZuWjAyJdu1sNGpU8g7y2DEJk4mb1iIsjIMHZe6918+l\nqDpAr14W3nzTTHS02nmruC9//aXlwQd9C/wtMNDBv/+dxd1326hRwyO7tXwkJMj8/rsX06fr/5ff\n6sb4+CjpWWJj1fQsKio3Y9UqLY88ktffhIbaWbYsvVTLkFXpIIGS5reJinIQFVU6yooSan7rxX+P\nH5fp0cMXHx8HP/2UWSKH2osX5WuUM0HXrlZGj7bQrJnN44tAe2Kuo6pGs2Y25s5NZ/NmLQkJGkJD\nHTRrZic83E5YmKNYHacnyIPBIGjTxkbHjlZ0OsGxYzLx8Vp27NCSlCSTmqoE/wQGCqpXd9C5s1V1\nGi+A5cs3EhHREW9vqFtXvT9VmWv7hTZtbPTubXFa7BMTNaxZo+Pxx3PKpS0er6B5EqdPy6SmKn/D\nh5uYPz+DsLDiafKtWtlYuzYNi0WZyg0JcahO5yqVhsBAJU/RzTLTVxZycpQPL6XckaNYOcYAFi70\nYuJEb0DQsaONDz/M4uGHzdhskJEB2dkSNptSwNxkEphMZXIZlZoTJyTee89IfLw/vr6CqVMz6drV\nWiG1F1Wgap3IAAAgAElEQVTcC39/mDDBzPbtOi5eVF7OadP09O2bQ0BA2Z/f46M4K/sX8rXYrhmT\nEhK0bN9efP3a1xfuuMNO27Z2oqOrlnLmSbKgcuu4gzzs3q0hNtaPu+7yY8oUfbEjvPMcliX+/ltH\nr16+7N2rQauFatWUgIE6dQTBwapyVhg//6wnPr4roGTfHzrUxMGDRY/WV/Esru8XoqIczJmTQfXq\nimX1yBGtU1kra8pVQbPb7TRv3pz7778fgEuXLnHvvffSoEEDunXrxpUrV5zb/uc//yEqKoqGDRvy\n559/Otfv2rWLpk2bEhUVxYsvvlieza9wAgJcrWWTJxu4erWCGqOiUkxsNqWA84EDMmfOeGYql+Jy\n6ZKEEBLZ2RITJ3rzxhtGkpKKfm86drSi0eT1C5cvyzz8sA/x8R7/7V0qOBywfbvmunVK9RcVlVxa\ntLCzdGk6jzxiITrafsNMBxkZiq/sRx8Z+OorPZs3a0ucoqNcpfCLL76gcePGSP/L+Pbhhx9y7733\ncuTIEbp06cKHH34IwKFDh5g3bx6HDh1i5cqVjBo1itxYhpEjRzJjxgwSEhJISEhg5cqVNzxncfPb\nXL6svLBxcTLp6SW4yDIkNNRBrVp5/hEHDmg4e1btSArDaoXERIn4eJmkJIm//1ZzHVUUCQkyH3xg\noE0bPzp29KdLFz/i4irWSuEOua/q1MktzqyweLGeWbP0ZGcXbf/oaAeff57lcozUVJmlS9X5uaIg\ny9Cxow1Y57K+PFMpqJQfx4/LbNumITW18I+gwvqFBg0cTJmSxbJlaYSGFq6grVql48EHffnwQyNv\nvulN796+fPSRgdTU4re33Eb3xMREli9fzlNPPeVUthYvXsywYcMAGDZsGL///jsAixYtYuDAgeh0\nOsLDw6lfvz7btm0jKSmJ9PR02rRpA8DQoUOd+5QW27bp6NHDj86d/Xj0UR/273cfBahmTcFLL13b\nc0tcuaJaIgoiNRU+/dRA+/b+tG/vT4cOfkydqmfHDg3WW4/XUCkGO3ZouO8+X774wojVqshrSopc\n5ISynkxkpIMnn3StLPLRRwYOHy6a8qrTQb9+OUydmumSFHv+fC/Vul5E+vbNITIyL3VCdLSNO+5Q\nC4p7Ihs2aLnvPj+GDzdx+HDxx3atlpvmV9yxI7/r0ZdfGtm9u/guSeWmfbz88sv897//Rb7GC/bC\nhQvUrFkTgJo1a3LhwgUAzp07R2hoqHO70NBQzp49m299SEgIZ8+eveF5i+tnkuMMzpDYskVHr15+\nbN3qPv4IXbrYqFMnr/NQv/QK5swZDZMmGcnMVJSAy5dl/vijGz17+rJokc7Fn0+l7Dh+XGbwYB+X\nnIIA9erZaNCgYgdBd/BBM5lg9GgLTZteK5BSkRU0AG9vePBBKytWpDNihJmICDuDBlk8Np9haRMZ\nKfj995b8/HM6c+ak8/PPmWokp4fi46N8xGzcqKNnT1/i4vKrQLfaL/ToYeVai3Yu584VX90qFwVt\n6dKlBAcH07x5cwpLuyZJknPqsyJp1MiOt3deGzMyJB55xJcDB9xDSYuMdPDDDxnUrWsnJsZGWJja\nkRREaKiDDh3ym8rsdonRo02cOuU+llFPJj5ezpefKzTUzowZmTecJqhKhIU5+O67TO68M09ec4oZ\nxa/VQsuWdv7zn2xWrUpj1CiL+vFWDEJDBd262ejRw6YqZx5Mo0Z2ZFnpd65elXniCRPHj5eu3tG6\ntY25czMICsqTo3r1bLRrV3yrQLmk2di8eTOLFy9m+fLlmM1m0tLSGDJkCDVr1uT8+fPcdtttJCUl\nERwcDCiWsTNnzjj3T0xMJDQ0lJCQEBITE13Wh4SEFHreUaNGARAWFoa/vz9NmzZ1ase588zXL8fG\ndmDKlEyefHIHIAGdSU+XmDRpK089ZaFTpxvvXx7Lt9/u4N13V2C3Q82asRXeHndc/uefDTz+uERM\nTFe+/15PTs56YC/wEvXq2YmL20BSknCb9nra8sKFmzh4UEN09F3UqOEgOflvDAbBa6+1pU8fK4mJ\nf7NxY8W2d//+/YwcOdIt7ldS0t+MGgXjxnUmJUXCZlvHxo0lk8/AwIq/nsq2PHXq1CKND+60bLcr\nyxqNe7SnMiy3bNmB4cMtzJixFYDjxzszZYqRnj3/xGhUtr/WB60k5zMawWRax0cfSYSGdkQIOHfu\nb5KTBdHRyvHnzJkDKLpJt27dKIxyrySwfv16Pv74Y5YsWcK4ceMICgri1Vdf5cMPP+TKlSt8+OGH\nHDp0iEGDBrF9+3bOnj1L165dOXr0KJIk0bZtWyZPnkybNm3o1asXL7zwAj169Mh3ntxKAiVJRmk2\nw/LlOkaONDl9ZqpXd/D332klzuCvUjFYrXDypMzp0zLbtm2kXbsOREXZSzUTtIorp07JDBpk4vBh\nLQEBDgYNyqFePRt3320jLEzgBoZywDMS1aqUDpVFFs6elThyRMPOnVo2bdLg5aW4vXTvbiU8XLX8\nFYXjxyXuu8/PxbK/aFEad92luFyUtyy4XSWB3KnM1157jQEDBjBjxgzCw8P55ZdfAGjcuDEDBgyg\ncePGaLVavvrqK+c+X331FY8//jjZ2dn07NmzQOXsWkpyow0G6NvXSt266fz4oxd//OFF//45+Pqq\ng3plQ6fLqwrRpUs7oPhm5lvhzBmJpCQZf39BVFTxE5FWRubM8XLWnr18Web//s9ASIiDXr3S3EY5\nA/fwQVNxDyqDLOzbJ/Pssybi412H7dWrvdi/38yXXxYx9LeKExkpmDUrg759fZ0GmFmz9LRpk4Ve\n716yoNbivAk2m5KryN9foC+8PjMOB1Vi8FUpOvv2yTzyiC8XL8oYDIJffkmnQwfPjg7LyoJevXzZ\nt891EHnppWzefNOsviMqKiXg9GmJrl39SEkp+AWaPTuD3r3V8PSiYrfDn39qGT7ch5wcCS8vwdat\naRVihbyRBc3ju8tbzXWk1UJwcOHKmcMBa9ZoeewxE7t2uUcggUrBlGfeqwsXJB5/3OTMOG02S4wb\n5801uZidpKRI/PKLjsGDTXz5pZ6EhMr7Wnp750Yx5REba+Xxxy1up5yVpzyouDfuLgs5ORIFmVIC\nApSgsc6dVeWsOGg0Ssm4FSvSadvWio+PcKapcSdZqJApTk/i2DGZIUN8MJsltm7VsmpVOvXrq74A\nVZ2zZ2VOnXJ9vZKTcwvVu/a0f/2l5dlnlZpby5d7MXWqg99/TycqqnLK0eOPW2ja1M7JkzINGthp\n2tROzZoeaahXUSkX6td3sGxZOocPazhzRiY42EHt2g7Cwx1qNHQJkWVo3tzOvHkZpKdLhIS43330\neAWtrOeTT5zIHXSVsN3Nm7XUr18+le5Vikd5+hZcW34nl/btbVSrln/98uWuWd+TkmQWL/Zi7Fhz\nmbWvLKlZU9Czp/t/0buTr4lKxVIZZKFBAwcNGlTOjzZ3xs8P/Pzy+mV3kgU3m3SofFgsrl7P69ap\nyYdUIDzcwWOP5WWIDw528Npr2RgM+bdt3z5/4MKmTep0uYqKikpVxuMVtLKeT/bxcXDffTn06aNY\nzRIT5WInmVQpH8rTt8DfH954I5t589L54Yd0li1Lo3Hjgr9+u3a1EhHhqqQ99JAqRGWNO/maqFQs\nqixULsxlOLngTrLg8VOcZUlmpmJBu3hR4s477YSG2gkMdLhVKgGVsiEzU5neTkuT8PMTREQ4MJlc\nt7ntNsFtt908rUdkpIP58zNZu1bLli06evTIoXPn8k0HoqKiUnWx2xXH+crA8eNKwNUHH2QTHe3Z\nU74eb0Erq/nkc+ck3n/fwKBBPuzapUMIpSzUo4/mqCVW3JTSkoXUVHj/fSMdO/rRu7cfHTv68fLL\n3rdUMiQy0sFTT+UwY0YmDz9spUaNinNYPX1aYsECHRs3asjMrLBmlDnu5GuiUrFUZVnYu1fDkCEm\ntm7VFBgp6m78/beOtWu9mDpVXyY1ld1JFjxeQSsLzp+XeOstI19/bQQkNBpBixZKKoGS1NtSqVwc\nOqTh668NKKXAACR+/VXPe+95l6npvTy4dAnGjjUxYoQPffr4smmTamRXUfFkpk/Xs3KlF/36+bJ7\nt3ub0Ww2WLZMsYDMn6/nzBnPVmE8++oo/fnkK1fgk08MLFyYlxhtxAgL991nY8IEs1oKyo0pLVlQ\npjLzP+e1a3VculS557ePH9ewZk2uCVjik08MHmtFcydfE5WKpSrLwtmzSp9lsUg8/7w3qanu24el\npEjs3at8NGZnS5w+XfoqjDvJgscraKWJ1QpLlngxY0ZeKF79+jaeecaMXo/qe1ZFaNjQzscfZzkT\nG+Yyblx2hU5NlgYXL7oK8c6dWlJSVMFWUfFUgoPz+qz4eC3x8e6rFjgcStLeXK5e9ey+yePnL0pz\nPvnQIQ1jxng7l319BdOnZ1K3buUelKsKpSUL3t4wZEgOrVvbOHZMg80GISEOmjSxl5v/4alTMrt3\na8jKkujQwUbduqXjLHu9o7CynD+5rifgTr4mKhVLVZaFnj2tzJ+fNyO0ZYuOO+90z5J0kgSyLMh1\nL8nIKH0FzZ1kweMVtNIiJwd++MELu10RCG9vwfz56dx+u2dHkagUjE4HTZs6aNq0/J9/YqLEsGEm\n4uKU17d79xymTcvE3//Wj12njgNJEgihyHm7djZq1lRlXEXFU4mOtuPlJZyWqSVLdIwcacbb+yY7\n3oCzZyUSE2Vq1XIQFlZ6H3d6vaBaNcHVq8qyxXLj7Ss77mvLLCVKaz75zBmJ2bOVr4zwcBuLFqXT\npk3Ff2VkZUF2dkW3onLgTr4Ft8Iff+icylnu8vnzpfMqR0Y6GDdOiXTw8hKFJtf1BNxRHjIylCTF\n27ZpSEur6NZUHdxRFkoTxw2+serVczBiRJ6mY7dzS9Gc8fEy99/vw333+fHIIz6cOFF6aoavL9Sq\nlXcxZRHF6U6yoFrQiojDIdGokZ1+/XLo399KWFjFWxUOHZJ5800jJpOSFLVhw4pvkzthtSqWz+vz\nk1VmbDZYuNAr3/qS+D/a7UpRd5tNIihIyeNmMMCzz5q56y4rvr6CmBhVpsoLux1+/NGL119XBHb8\n+Gyef96M0VjBDauEmM2KQ3lGhoQkgVYrqFFD4OdX0S0rX06ckJk3z4vNmzU0aeKgRw8rd9xhc7kP\nOh08/bSZjRu17Nun5Y47bCW2nmVmwkcfGTh5UlEt4uO17N+vISKidPoRnQ66dLGxdaviS3Kt/5wn\nIglRGTKfFJ81a9bQokULQEkdoNMp2vetkJEBPj6l0LhSIDVVol8/Hw4cUF6EZs1s/PprBkFBHvk4\ni4zVCgcOaFi9WseaNTqys6FPnxweeSTHI4oK5+RAv34+bNmS5+zWqpWV+fMzijzFabdDXJyG777T\ns3y5jqtXJQYMyGHChGxq1ar896iycuqUTLt2fs7ycZIkWL06nebNK95S7+7Y7Yoycvq0zJ49Wlat\n0nLokPYaHyVBu3Y2pk7NKjV/zcrAiy8a+eEHVxP4yJHZvPSSJV9A06lTMnv3amjUyF7imp/x8TJ3\n3unndJEA+OSTTIYPL73KKJs2abj/fkXDXLEijbZtK/f7sXv3brp06VLgbx5vQTtyRGb0aG/atbPx\nyivmW1Kw3EU5A8UPKVc5A9i3T8vJkzJBQZVbWG+FtDSYM8eLCRO8nb6CAPv3a4mIcBAa6v4FvG+G\nl5eS1iVXQTOZBB99lF1k5cxqheXLdYwYYcJmy7tHP/+s56mnLNSqVXXlp6K5etW1tq8QEgkJsqqg\n3QC7Hf75R2bBAi+++srgEuF3LZIEPXpYCQqqOsoZUKB7wtSpRlq2tNO/v2t/WLeu45aV16wsXJQz\noNSNBtHRDtq3t3L5skR4uGc/T4/2QcvIgLFjt7Fjh44pUwylOhde0WRl5e+Irlzx7JDjm7Fjh5bX\nXze5KGcKgtq1HW7lW3ArdOli5Zdf0pk2LYOVK9O4446iD+BxcRqefNJVOQOIiLC5+HZUBdxNHkwm\ngUbjOphd/5xU8rDbYcUKHV26+PH558YClTNJEgwaZOHPP9N5+mlLoR/Z7iYLpcWQITkEBOR/r7dv\nLxvbjJ+f4sifS7VqDmJiStdRrHp1wZdfZvH995nUrFn6Fn93kgXP0VgK4J9/NGzalJd088IFz7nc\nwMD8nbm/f9WenipIATcYBF9/nVksJaY8OHNGYt8+DfYSNMvXF7p2tTFggLXYPmLHj8s4HK4DWUiI\nndmzM9XpzQomNFQwdKjlunVVS2kuDpmZsHmz1sWh3WhUqrqMHZvNzz+ns2lTGh9/nEXLlnaPDXa5\nEU2a2Fm6NJ3+/S3/S08BNWo4GDCg9KYcryU83MF//5sFCPz9HcycmUm9eqXfr0REODy+Did4uA/a\niRNtGTEi75Pp55/T6dbNM0oxmc3w2mtGZs9Wep2mTRUftMqeKPVWOH1aYt48PX/8ocPf30H37jZi\nY600buxeBeyPHpV5+GETZ89qWLYsndaty095PHRIZtQoE3FxGiIjHQwdaqF37xwiI6uu3LgTx47J\nvPSSN5s2aXnuOTMvv2wmMLCiW+W+5OTA+fMyOTlK5KHBIAgKEreUIsITMZshKUkJmggMFISElN37\nnp2t+LN5e4tSTbHhqVRZH7RDh1yzbvr4eI6wGAwwZoyZiAgH58/LDB+e3+mzqhEWJnjlFTOjR5de\nZQe7Xcmub7XmRTreCmYzfPutnlOnlFfvzz915aqgNW7sYOHCdNLTJXx9hTr4lyNHjsicPCkTGuqg\nQQMH2gJ633r1HPz0UwbJyTK33Xbr8ubpeHlRooj6Y8ck0tMlatcWHh8JCMp4EREhKI+E00YjakaB\nUsJz5vwKICFBA6wDQKMRHpdwMyxM8OKLFv7zn+wSR914IgZDwcpZcX0Ljh6VmTDBSIcOfrRs6ceL\nL3pz8uStvTLnzsnMnJmXtXvjRh05ZTPbUCiBgVC3rqqcFVUerFY4d07i3DmpxPmhLBYYP97Io4/6\ncvfdfkydqufy5YK39fNTFDVVOSsb1qzR0qmTP/fc40///j4cOSK7ld+RSsXiTrLg0QpaRESeZeLu\nu61qIXOVIpOQINO/vw/Tphm4fFnGbpdYuFDPhg1a/vlH4vhxmUuXin/c8+cVa1wu1as78Mqf1kzF\nTUhMlHj7bSPt2/sTG+vHrFleJUoga7NBaqrS3VqtEm+/7c2sWXo1yXQ5c/q0xJNPmpxBVocOafno\nI4PHZ6RXqZx4tIKm5EfpjCwLxo0zq1+kVZzi1FhbvVpHYqIm3/rkZIk776xGmzZ+3HuvHzNnepGY\nWPS51OuL+7ZuXfE+kTYb/PWXlmee8eabb7w4c8aNHPbKkJvJQ3Y2fPSRkWnTDKSnS1y9KjNmjIk9\ne4rvGWIykc8x+913jezcmV/GVMqOy5cl0tJch71ly7xo0OCuCmqRirvhTrU4PVpBa9XKxquvZjNv\nXgbNmrlXFJ/KrXPqlExqatkcu6AivK1b20hOVl4Zh0PixAkNY8aYGDXKREpK0ZQa+bo3rkmTipfL\nAwc0PPKID/Pn63ntNRP/+pc3Fy5UDSXtRly4IDFnTn7z5vnzJbs33btbCQ6+1hVB4ssvVetNeeLv\nr6QzuZbq1UWVjPBUcX88WkELDhbExq6mSxcbOt3Nt1epPBw6JNOtmy/TpxuwFjH/bHF8C/r3t9C/\nv4WAAAfR0XYmTMiiRQsbX3+tz7ftvn3aIk97KbnGlAGiZUsrTZtWvIKWmKiUw8lN27JqlRd793q+\nZedm8uDlBX5+17tFCOrUKZmrRL16Dn74IQNv77z9N2zQkZysKsPlRXi4g88+yyTPWV7wzjtZxMdv\nqMhmqbgR7uSD5tFRnCoVx7ZtGpKTZTp2tJZ6/TulZqGe5GSZTz818PDDllJPE1GvnuD//i+LS5ck\nvL0FWi3s26fh8mWJXbu0XLokodVC7945DB1a9PPXq+fgjTeyWbNGxyefZLlF5G1QkIO3385Gq4Uf\nfvDi4EEte/dq6d694qdfK5LatQXffpvJkCE+mM0SGo3gww+zaNas5PeldWs7ixalM2GCka1bdbRs\naStACVQpS3r1srJiRTpnzigRtXfcYWfnzopulYo7k5WlJPneskWLVqskC2/cuOwD8zw6D1puLU6V\n8iUrC/r29WHXLh2TJ2cyaFBOvqm9W+HECZkOHfzIzlYsD4sXp9GhQ/lZoi5fzivJU7OmKHY6D7NZ\nyd/kLoWb//hDy8CBvoDg3//O5vXXjbz9djYvvqjOvQmhBIykpkpUqyaoX99RKtb4K1cgKUnG319Q\nu7ZHdsFuQ3Y26PX53QtUCkYIRT7NZgmbTbEiF7WUnCdiscCsWV689po3kNvvO1i1Kq1U6jtX2Txo\nKhWDxQJXrii94b/+5U3TpvZS9QFMSZGcyhlAZmb5ThEFBMCt5BMyGAqukVcRWCwwZ07utK3Epk1a\nOne20rVr5a9bWhpIEmWSwqZaNaUMjkrZceiQzPz5XmzYoKN2bQfDhllo3drmNh9G7kRaGpw8KXPi\nhIY//9SxfbvW2c9GR9v55pvMQjP3JyYqitxtt3mmL9/+/RrGj89TzgAuXJBJSZFKRUG7ER7/TeFO\n88lVBb0efH0Vwc3JkfjpJ68SlTQqjLQ0V4WsqF/Gqizk4XAozu4JCTI7duR9p+3YoeW997KLXUKq\nMrJx40aSkyUOHpRL7Piv4p4cPy7Tr58vX3xhZPduLUuXevHww7789lvBOW2qat9w7JgSCNO3rw+d\nO/sxfLgPc+fqOXZMw9WrSoWGu++2FlinNzsbfv9dR8eOfrRq5c9//mMsNLdfZeJ6WThxQs5XAL5m\nTUe5uKd4vIKmUvpYLEoS18LSS2g00LlzngXmhx/0pVqo3nadC9C1Tte3wrlzEjt3arhypVQO53bY\n7Uo2+5Urtbz0kpFOnfz44Qe9S5BFSoqE2Vw1lJXTpyX69/fhrrv8eeghH06frhrXXRU4e1ZyRlxf\ny0cfGbl4UX3OFy9KzJ3rxb33+vH88yb27dNxrYUIoHFjG++/n83RozJJSfnv5e7dGp54wsSVK0p9\n3ylTDOze7XmTctdXmvDyUnxTy7JcVi6edzevw51ymngCqanw1VcGJk82EBQkmD07gzZt7GRmwuHD\nGvbs0bBggRd9+uSN+haLxLFjMvXrl45VxtXnS1CtWtFelBvJQnKyxPPPm1i3TsfQoWbefjv7f1OZ\nnkF8vMxvv3nx+ecGcnLybuClSzIBAcKZrkSjgcBAz7eeJSZKfPppD44fV7rAQ4e0xMVpCAur2oER\nnkJ4uIPate2cO+cajdymjTVfmg2oWuPEuXMSEyYY+e23/BHpPj6CRx+10LOnFS8vBw884IfNJhES\nIpg4MdtlCvOPP/IrdZ4QkXy9LLRoYWP27Azmz/eicWM73btbuf328vF59ngFTaV02bVLy2efGQHl\nK+zJJ3346ad0Jk82sHChF7kvbNeuVvz8HM6kkGvX6kotKvDakl0tW9oIDb11hSI+XmbdOsX7e/Zs\nA/36WenUyTMG682bNQwc6Et6ev7O8+hRmZgYG0ePKgNZRIS9yApvZebgQY1TOcvFZqv8g4uncOkS\nJCbKTl/ToCBBUJCjyB9NdeoIfv01g++/17NwoRdaLTzwQA4jRliqfMLy48dlfH0FrVrZMJkchIYq\n/9evb6dOHWVZlpXpy9x34rvv9Dz5pMXFH/N6VxPIb23yBHx9oXdvK717l79frscraBs3bqxSX0dl\nzfLlriFsZ8/K/PmnjoUL877GfHwE3btbsdslJk1SlLl9+7RYrZRKBFxoqCA62kZ8vJYxYyxFjjC6\nkSxcPx2ybJnOIxQ0mw22btX9zwdQSRdSo4YgNtbKPffYqFfPhtkssWiRolyPGmXxKMthYZw6JaPU\n6e3sXFe7tudbDisD585JPPGEie3b8zoLSRLUq+dgwIAcOnSw0qSJHR+fGx+nYUMHH3yQzcsvm5Fl\nRe4Li7iuSuPE3Ll6tmzRUr++g9BQJe1PUFD+7WrUcDB+vFKLzMtLcOGCRIMGeb8PGJDDDz/onf5Z\nDzxgKTfLUlniTrLg8QqaSumSv4MTXGvmrllTScbZtKkDozGH6dP1pKbKZGUpqSVKQ0ELChJMn57J\nyZMysbFlo0Tt2KElKwu8vcvk8OWGVgsvvGBmwAALdrvy/AwG18EqMxOmTcvkn380VSZ683oH34ED\nLTRsWPkHF0/Ax0fQqJHdRUETQuLoUQ3//rcRMNCvXw6vvmq+aYStVotag/k6rlyROHlSw8mTGkBH\n797Kx9q1HDigYcgQH2c0vlYrmDAhm9at7c5pzpYt7SxenE5cnJaQEAdt2tioXl2916WJxwcJuIsm\n7Cn06OE6gHfsaGP7di2SJBg5Mpvly9No1UoZ6OrXdzBjRiZaraBJE3uphmDHxDjo1at4IfM3kgXX\nEjxK4EFFVZ/IyoKkJKnUIl+1WsXqWLeuICxMEBzsaklQ6kRaeestc5XJydWmjY377ruTwEAHo0dn\n8/rr2Wr6BTfBzw/eeMPM9OkZVK9ekAIm8dtveh5/3FRqJcmq0jjRqZNrH/7rr/mj7OfP1zmVM1Cm\n/99+20h8fN46vR5iY+2MHGmhTx+rxyjC7iQLqgVNpVi0bm3jtdeymDbNQIsWdjp1srJjh8yff2bT\nuLEdo9F1+9hYG6tXp6PXCzRuXD2ofn0H4eE2Tp5UXolOnZTyYFYrZGQoeauKm5C2JCQkyLz7rpGt\nW7V89lkmvXtX/mlWdyQkRPD115mkp0tUr15xyrhKwVSvLujf30rr1mmcPKkhLk7D2rVaDh7UIkkQ\nGCh48kkLXl6eoRSUJy1b2rl25mPVKqXc2LUKVkhIwYpxrt+Zkp5Gw/79Gu64w0779jZOnZLZvl2L\nViuIjHQUOB6oFA+PryTgTvPJnsLBg0rYtV7vIChIscxUBsfbm8nCjh0aBg3ywWAQzJ+fgbc3fPyx\nnt04oMUAACAASURBVG3bdPTvn8PgwZYyDa0+c0Zi8GAf9u9XlMTgYAfr1qV5zJepu6H2DZULmw1S\nUxUFwdtb4Oub91tWljJ1FxhYsmSpVUkWMjLg6adNrFyp5ISrUcPB+vWu/czx40oA2L59eTac9u2t\nzJiRgcUiM3asN2vXKl81Pj6CLVuu8vvvXkyYkOsTIhg1yswzz1hKXLu2oihvWVArCaiUKjExDo9M\nZNq6tZ01a9KQJMXC8uabRn78UentJ00ykpkJr79uLrNs2evW6ZzKGUBGhpQv55uKSlVFq1VKq12P\nxQKTJxuYOtVAt26Kb1pppfTxRHx84P33szlxQiY+Xsvdd1sJCHC9r5GRgp9/zmD/fg1nzsikpUl0\n6GAFJF56yZv16/NMzt7eyuyIazJbia++MrJ9u5Zp07KIjFSfR0nweAuaikpJuHQJunXz4/jxvHlZ\nWRZs3pxWJqV/srKgTx8fdu/O6/jatLGycGFGvkAFi0VJE3H6tEzNmg6aNy9d/z4VlcrE8eMSbdv6\nY7cr1rWwMDvz52cQFaUqBTfi1Ckl8CIiwnFTBersWYkaNQRz5ngxZozrdMmECVm8/LKFs2clevf2\n4dQpV7uP4uNpZuNGLTVqCI+I9CxNbmRB8/ggARWVkqDXQ0CAa6flcEhkZ5fN+dLSJE6fdnXSGz3a\nkk85S02FL74wcO+9vjzxhA+9evmyZ49qCFepumg0kosP4enTGqZMMWCxVFybKgN16wq6dLEVyboV\nEiLIyIAvv3T9Erz9dhsPPZTj3Gbu3Eyio13N/lOnGjh2TGbECBM9e/qye7cbOyO7GR6voFXVGmsq\n+SmOLJhMMGaMaw8fHOwoszByf39BixZ5HduQIRbat8+f8mLlSi8+/NB4TW04qdCSWyo3piz7howM\nJZ+X2Vxmp1D5HyEhDqeSkMvPP3tx8mTRhzd1nLg5OTkSV67k9TXNm9uYMSPTxcesYUMH8+ZlMH58\nNn5+iuIXEmJHqwW7XSIrS+Kpp7yL9WzKG3eSBfXTW0WlEO66y8qXX2bw8cdGDAbB5MlZZRYkYDTC\nxInZtGhhJzpaiYoKDHTdJjFR4q238odFFRxxpVIRXLkCW7dqmTzZwMGDWqZNy+C++1RHwrJEq4Wn\nn7awYIGXs/KAzSaRkiIRHV3BjfMggoMFM2ZksmGDllatbDRrZqdWrfz9YViYYMwYMwMHWrh8WYmS\n9vMT1K1r58ABLSdPalm+XMeoUaqJ82aoPmgqKjfh0iUlxUZFZ9j/5x+ZO+90LZvQr5+Fzz7LUnN4\nuQHnzkl8/LGBmTPzpoEmTcpkxIicG+ylUhoIAVu2KFHYaWkyXl6C9evTiI5WP17chXffNfD558oH\npp+fg7/+Siciouyfz6lTMidOyGRnK4nHg4MdREQ43MZvV43iVEEIZYC3WqFRI4ea96kYXG/Jqihq\n1nTQubP1fzVDBSNGWHj+ebOqnLkBFy4o1s1rS55JkvhfzimVskaS4M477axalc6xYzI1agg1ktPN\n6NrV6lTQ0tJk9u/XlLmCtnWrhoEDfbh69dopVcHTT1t45hlLuSiIt4L7TgSXEu40n1yRbNmioUsX\nP+65x4/Fi6umdlbZZSEgAP7v/zJZvjyNdevSeOed7EqXY8idKE15WLLEtR4twOjRZho1UhW08iQq\nykGPHjZatrS7JMZOTZWIj5fZtUvDzp0a/vlHKT+XS2XvGyoD9es7iIjIm+7/7ju9yzMoC+bO9bpO\nOQOQ+OYbA//9r6HAoC93kgWPV9BUFIflt94yYjZLOBwSY8aYOH1adSyvjNSqJWjXzs7ttzvULN1u\nwqlTMu+/7/owhg618NxzFvUZVTApKbBokY6ePX1o396fe+/1o1s3P2Jj/Rg40Ie4uMozBFZ2Z6Tg\nYMHrr+dFzWzYoCUpqWzHoSeesBAYWLCVLC1Ncvt76vFTnFUlO/SNuHBBYu/evEedni6RmCgTFla1\nvu5VWVC5ltKSh7Q0ZcoGwMtL8Pbb2QwYYCEoqFQOr3ILLFnixdix+cucCCGxYYOO554zsWxZulv3\nDUePyqxdq2X1ah3332+lX78cfHwqulUlo00bGxERNk6c0CKE9L96n2U3DjVr5uCPP9LYuFHHn3/q\nyMmB2FgrTZo4CAlxFKiguZMseLyCpqJENDkcrl8qFotqQVNRKQ3Cwhz8/HM6ZrNEdLSdevUcaNWe\n1S1QMuTn1Z28Fl9fwXvvZTt9OLOylOodWq1S67OiEQI2b9YweHCeD9Xq1Trat7dVWv+6OnUE33yT\nRa9evuTklF1eyWupV09Qr14Ojz2Ww/z5Xrz9tpErVyQ0GoiOtnH//TZat7YREWF3O5cRj+9GqlKN\ntcIICBCEhDg4ezbPnB8UVDlf8FtBlQWVayktefD3h27d1FQa7kj37lb+/DOdXbu07N2rQQiIiHDQ\nqJGdJv/P3pmHN1Wmffg+J3vTBcpOoUDZKWtlEWSTTcAFEBdQYMQdFPUbVNTRwVERxIFRVEZRFFBA\nAREcNhcEtIoiICCUfWtL2dvSNHtyzvfHsU1DC6Vt0qbpua/L6zJtkxyS57zv8z7L72nrISFB2ZCX\nLPmZr74axN69WkwmmdGjXQwc6KZVq4qb0rF7t8gdd0T5HaZjY2VMptByIkpKp07KpIcXXzSW65xh\njUaZwnLhgrIPejywZ4+OPXuUmuzYWInXXrNjNm/i1ltvuOLr/PGHhrffNvL003batg3uPhr2DpqK\nkvt/8kk7zz6rhPr79HETH1/1HDQVFZWqhckEnTt76dz56mm0Q4c0bNyoz388fbqJGTOMTJni4KGH\nHOUusZOTAy++GFEo0zFtWvC0GMsLUYRevTx8/XUuMTHF/32gEAQYMcJFTIzM5MkRf6VXfWRmikyc\naKZtWyMdOwpFRtMuXhR49NEIDh/Wsnu3yLp1uUVqwQWKsHfQ1IiJwrBhbvR6K6mpIqNHO6lWraKv\nqPxRbUGlIKo9qOQxcmQPPv5YJjfX5xDJssCMGSZq1JB44IHy1bI7d07kl1/8t+eHH3YwYEDh6SKV\nlfJ0zgq+54gRbtq1s7B7t4aFCw1s3arNn+MKsHfvAA4etNCwYeGoeFqayOHDyvdy8qSWP//UUK9e\n8KLnYe+gqSjUqiUzbpwqmKmioqJyOe3aSaxcaeH++82kp/vPily40MBdd7mIiiq/64mKkmnRwsuh\nQ1rq1JF4/XUbffu6K1wsO1xo1kyiWTOJIUPcnD4tcvq0QE6OgChCjRrKZ18UFov/4337NEEtbwh7\nB620dSaZmWC1CphMBG3+osqVkSQ4d07AalVOsnFxZZeVUGvQVAqi2oNKHnm28M03Fv78U8OXX+o5\neFBDzZoSzzzjKFfnDKBOHZlVq3K5cEEZlVSetVpViYgIaNpUomlT38+Sk5OJiSl6Xbhc4H3fPi0Q\nvJFVYe+glZS0NIGvv9bz8ccG0tNF6taVGDPGxZ13umjcWK3bCjaXLkFKioa1a/V88YWeixeVU83M\nmTbuv1+NAKqoqASPevVk6tXz0K+fB5cLDAb8BG/Lk7p1Vccs1IiJ8f8+gt2FGvYOWklOyDYbzJxp\nYvFinyJ4WpqG6dNN7N0r8u67tnI/SVUV3G7YuVPDq6+a+OUX/2OKJMk0alR251iNlqgURLUHlTwu\ntwWtlgqTSvF6lQ5Dg6H4v1UJPEWtC1lZcOKEBocDXn/dyv/+p+fXX7V07Rrc7u2wd9BKgs0m8NNP\nRX8kO3fqcDgEoqLUE02gsdmUUTmPP272K9YEEEWZt9+2cf31gb8RJAmysgQcDqX92uMRMJlkTCal\nnV2sPCLjKhWMLCtdYioqpUWWYe9eDQsW6PnzTy1vvGGjU6fQFBNPSxM4elSDVivTooVE7drhuy9a\nrfD002a++krp8tXpZPr29fDqq3a6dVOaNrKyYMcOLb/8oqVRI4k+fTwBybiFvYNWkjqTmjVl3nnH\nxpgxkVgsvtU2Olriv/+1UqtW+BphRbJjh4YJE8xcLibZt6+bKVPsJCV5AzLcfdOmZBo06M3RoyJ/\n/qll+3YNBw9quHAhby6fgE4nU6eORP/+bh55xEmrVmpaOxBkZsL58yKSpAi7mguLu5c7gahBs9ng\n55+1zJtnoF49iSeecJZZRFSWITVVxOFQNAzDefMLFUKhHnHbNg3Dh/t0z778UheSDlpKishdd0WS\nkaHkfjt29DB/vjXkB49fK5fbgk6nHObzcLsFvvtOx3ff6bjnHif16tlYvNjI9Om+Iun27T18/nlu\nmVPUYe+glZRevTxs2pTDiRMiOTkC0dEyTZpIYWN8oYjNJmA2g8slU7++xB13uBgwwE3r1t58le+y\n8uefGt56y8DWrdF4PFcOdbjdAunpGjZvlnnwweAVf1YVHA7FAf/HPyLYs0eDIMCsWTbuuy886gnX\nrdPx8MO+w4XFIjJ3rrVMDS179mi47bYoLBaoX19m4kQHrVp5uXhRoHNnr7oWhSFHjojce2+kn+5Z\nMPW1SovXCx9+aMh3zgB27dLyww/acpciKS/0enj+eTv79okcOeLvMi1ZYqBXLzczZvirGe/ZoyU1\nVaRu3bI52GHvoJXmVJSQIJGQoC6C5cXAgR62br2EJAlERsoBH7Ny5ozApEkm9uwZdNW/i4qSGTnS\nyc03KwrilV0QsqLJzoZFiwy8/LKJPAdGlhVnORQoa8Tk5EnxrzmPvk31xx+1XLoklEntXZbz2vkF\nMjIEXnwxgvr1JZ580sHkyXreftsWciNpKjsVHT1bvlxPZmbBmgqZ664LvekULhfs3l3Ybdi3LzTu\n6UBQlC20aCHx+ee5fP65gTlzjLhcvns+LU1Eli8/9MsByfqEvYOmEvqIIjRokDczL/DUrSuzdKmV\nY8dEsrIErFYBl0vAbFbGpkRFKU5htWpK15RaexYYfv5Zx8svR1z2U5mRI8PjpH3+vOBXCgHQtKmX\n6Oiy2XHz5l4ef9zBu+/6wnAZGSIvvGDi9dft/PijlnvvDR/B0qpOVhasXKn3+9mjjzpp3z700psm\nE4wb52TXLn/XYfDg8LfHhASZKVMc3HGHiwMHlPIYr1eZzLNmjYc9e3yfyfjxTpo3L/v3F/YOWijU\nFqhUPPXqyRw9uoVbblFtoTy4dAlee+3yPJ/Mv/5lp0OH0Nh4yro2REbKaDRygcYWmaefdhBxuU9a\nQsxmeOQRJ9nZIp995mvl83oF3nnHwMSJjrK9gUohKnKfkCQBT4FgWf/+bh5/vOx2FCyGDnVjsdh4\n5x0jBgNMmWKnW7fQi/aVlqvZgkajRNNatJAAn1P68ce5rF2rJyVFw6BBbrp39xAZWfZrCXsHTUVF\npWKIiJAAJfURF+fN78YN1Y2npDRrJjFnjo3/+78IIiJk3nzTRs+egdmo4uJkXn3Vxk03uXnuOROn\nTimfY3q6GLC6zHDB41HSzVar0oBS2cbY1aihdKqvX6+jd28PnTt7yq0hze2Gs2cFHA6lvKR27eIz\nCLVry0ya5OTOO11oNKjNcyjRtUmTAl+zLMiyHJaf7saNG0lKSqroy1BRqbKcOCFy9KiI2SzToIH0\nVxq7fHG7C6t/BxKPB06fFtBolIL+0uJ2w+HDImfPin+l/CWaNlXqYLdvF9m8WYcsCxgMMh07eujd\nOzSikMFk/36RHTu0aDTQs6e7yLq7fftEPv7YwOLFBlwugRUrLPTrFz7RnGCSmirw9ttGli83kJur\nOFpDh7oYNcpFx45eVYetnNi5cyf9+/cv8ndqBE1FRSUoNG4sVdj0jX37lPTg7t0a+vf3MHy4k6ZN\nr+5ApaUJXLggUKOGTMOG8jXpmmm1lLlg3+VSisSfeioiP10aFSUzY4aV225zk5QkodF42LVLQ6NG\nEp07h79ztm+fyK23RpGdrYRzRo92cu+9TurVU7rqHQ7YvFnLww9HFhhwLhMZGZbxhqCwb5+GTz7x\ndR+ePy+wcKGRRYsMzJxpY8wYF1arItB68qRIbq4iQ9Sxo1eVHyonwt5BU2vQrozdrrR3V6smV4mu\nMNUWqgYpKSJDh0bnF/D/+quOH37QsnCh1W+u7uX28P33OiZPNhMVJTN2rJORI120bRsYDb6rkZEh\n8n//F+En0myxCDz2mJlGjXLp0cNDp07ekNTECgZ2O8yYYcp3zgCWLdPToIHEvHkG3n3Xhtcrc999\nkRTsoB071kWbNqX7jKri2tCihZf69b1+khmgzD6eMiWCJk0k/vEPEwcP+rsJY8Y4mDMnyDOOKpBQ\nsgW1X62K4nDA4sV6+vaNZvZsI05V8kslTPjzT02h7sqtW3Wkp189JJaU5EWvl7FYBObONTJoUBRz\n5hiLfV5ZqVZNol27otJyAufOVb3xBBcvCmze7O8VGwzgcglcuiQydqyZtDSNn9hxhw4ennzSHpDC\n7KpC06bKQPYxYxwYjf4H9B49PKxdqy/knMXESDzwgLpZlBdh76CFiiccamzbpuXZZyOQZYH//U9P\nVlb4bwSqLVQNihKJjYiQiYnx/9nl9tCunZf5863kyb14vQLTppkYNSqSPXtKvlS63YoGnzKl4spU\nqwZz59ro29dfqqBXLzdJSVWvnkoUQav1dxiGDHGzeXOes6AouXfsqHw2Awe6WLAgl4SE0mcBqura\n0KyZxOzZdpKTc1i7NoeFCy3885826tWT+OQTf+mPrl3drFtnoUOH8E5vhpIthL2DplKYS5dg2jQj\neekBu92/zVtFpTLTubOHPn18zo7ZLPPRR7nF1sOJoiJx8NFHVgwG32afkqJl6NBofv/92sU4z54V\nePZZEz17RnPPPZF8952W7Owr/33LlhILFuTyww85rFxp4bvvcvjkk1zi48O/9OBy6tWTefFFXwqt\nbVsPXbq48wVSBUGmTx8PFy8KvPmmlffes9GoUdX7nC7n3DmlhrKkaLWKOHv37srkltdeM7F8uQFQ\nZk//7W8O1q61sGRJLq1bh7dzVhoOHBDZuTM4Qr1h38UZSvnkUGHXLg39+kWR56C1b+9mzZrcsE8P\nqLZQdbhwQeDIERGrVaBhwzzdIn+uZA+SBLt3a5gwIYJDh3wpnthYiTVrLNdUIL1jh4aBA/31MB54\nwMFzzzmoUSO4S67NpshxpKWJpKRoOHpUJCNDpFYtmYcectKxY+jXsuXkKIPD3W6B5s29GI0y6emK\n0LQsK+N3GjSQiY8PjMNQ2deGQ4dE7r/fTIcOXmbMsBEVVbrXcTjg6FFlzKFeD7VqKd3XVUm8uyS2\ncOaMwLBhkaSna/j22xwSE0tuj2oXp4ofJ06IFCyuvesud9g7ZypVi5o1ZWrWLJ0jIorQqZOXr77K\nZe1aHf/6VwRWq0BmpiLp8MYb9mI7PKtXlzGbZaxW3x/On2+kdWsv998fnEkKR46I7Nun4dNP9Wze\nrEOS/C9Sr5e5777KUT8UHQ09evh/f7GxavSmKKxWmDXLSEqKlpQUDY895qBNm9J9VkYjpXIyqipH\nj4ocPqy4Ub/9piUxMbD3dtg7aJX5VBQszp71n/nWo0f55TcdDjhzRiQzU5lXWKeORGxs+by3agsq\nBSnOHurVk3ngARf9+3s4dEjk99+1tGzpxe1WIjhXo0kTibfftvLgg/4nn9deMzF4sLtMmmmXk5Eh\n8O23OqZOjSjUHJFH795uXn7ZRvv26uZbFJV5bThwQMPy5XkGKZCZGbx6Yq8XTp0SOHdOxGZTRHbj\n46VSR+xCkZLYwrFjvtTmZ5/puftul1/zSlkJewdNpTBRUb7NYcIER0BmhhWHxaKcMObNM7B5sw6P\nR1lEOnd28957Npo3VzcOldBDEBRnq0kTiZtuuvaDjCDAoEFu5s7N5amnzPnDla9FW60kHD0qct99\nZvbtK7yU63QyN9/sYuxYFx07eqhevfDzZVnZcE+fFhEEqF1bqpJ1b2UlPV3g+HElpa7VKhHc5s29\nAd2sr8SRIxoKZkSCxbFjAvPmGVm61FDgICBzzz0uXnrJTp06Vc9uLlzwBTvS05XucbM5cJ9D2Dto\nlb22IBi0bu1Fq1VUoydOdAZ9EcnOhtmzjX7Dn/PYvl3HiRNiQBy08+cFduxQTjRt23oLKdertqBS\nkGDbQ2SkUj7QsWMO+/ZpuHhRoEsXb0CjZwcOaPJP8UajTN26Ejff7KJnTw9NmihCwVeK9h0+LLJ6\ntZ733jNw6ZKy0dSsKbFiRW5IDuoOJqW1BVmGTZu0TJhg5vx5/8zELbe4eeUVe9DFmrdu9S9Qr1Yt\n8I7S8eMiI0ZEkpZ2eTG8wJIleiZMcISNg1YSW3AUGIubnS3gDvDM+LB30FQK066dl61bc6hdu3xC\n0wcPaop0zgD69XOTmBiYzWDVKh1TpijeZocOHhYurJpdcCqhgyhCq1ZS0JTXb7rJzdatl/B4lLRr\nRIR8TSUDBw+K3H13JKmp/hvuhQsi6ekC7dsH5XLDjtRUkbFjI7HbL49gCaxZo6dvX3fQag5BcRD2\n7vVt47VrS35izIHiyBGxCOdM4ZlnHBU2MaSiqV7d91lrtYGPkId9b4YaMSmMVgtNm5Zf3UDNmjJJ\nSf5Hi+bNPbzzjpW5c60BiSjk5MCCBb6xJbt3a/nsMwMFe5RVW1ApSDjYg1YL8fEyCQkyDRpcm3Mm\nSfDf/xoKOWegHGwCdWCqTJTWFqpVkxg5smgHzGiUgx6JFEWl+SOP4cNd1K0beAdNaW5xYDIpr20y\nyQwZ4mL5cguTJjnKJZVbXpTEFmrW9DmmkZEy2gCHvKpkBM3jIeAfpMqVadpUYulSKxkZAlarQLVq\nSiomkM0BOh1+2lUAH35o4L77nAFNKamoVHZkGSIi/H+m08mMH+/k0UcdqqZYCYiJgX/+086wYS7W\nrNGRmioSEwNduihafMHWDdProXt3D7/+qkOnkxkzJjhdug0ayLz+up0nn3SQm6voo9WuLRfbLBPu\nFIwc9uvnplatwN47Ye+mXJ5PPn9e4KOPDIwf7wzKSUOlaGrVkgNuvAUxmWDkSBe7dvlM+tIlEXuB\nkXFqDZpKQaqqPWg0MHmyg4ED3WRnC0REyDRuLJGQIAV97mioUhZbqFlTpn9/D/37V4za9223uVm2\nzMDMmdagOoR6PX/NbA7vfbMktpCQ4KVtWw9792oZMcKFJsB6tWHvoBXE44HPP9fz5ptG7rqrcugB\nqVw7Q4a4mT/fw4kTilk3b+6hWrUKvqhr5OBBkYMHNRiNMvXqScTFlZ/8iErVo0YNmRtvVMeHhAPt\n23vZuDGH2rXD23EKRWJj4YMPrPz+u5auXQN/P4X9JIGC7N0r0r9/NIIA27ZdUgvIw5BDh0QWLTJw\n/LjIlCn2SqP79MUXOiZM8GlmJSZ6mDLFQadOHuLiVDtVUVFRCUfUSQKAywWLFxtwuwXatPH4dV+o\nhA8tWki89podSaJSjSe54QYPPXu6SU5Wckz79mkZNy6Shg29vPmmjc6dPWpETUVFpdzxeJQ5n1ot\napSunKlEW1jpSE5OBhS9oA8/NADKZhhOyscqhSnKOcuzhVCkQQOZuXOt3H23f+o9LU3DqFFRPP98\nBOnpwRejrEqEsj2olC+qLRTN/v0iL79spHv3GPr1i2b79uAMBQ8lQskWwt5By2PTJm3+bLouXYJX\ne5GVBZmZ/j/LU+s+eVLEqZa+qVwBpVPKxhdfWIiP97fR5csNTJhgJi3N56TJsqJgXlAsUUVFRSUQ\n7NypYejQKObONWGxCGRkiPz0U5VJuoUEYe+g9ezZk9OnBf77X59GVtOmwalLOnFCZPz4SP7+9wjO\nnVM20uPHRf7zHyM33BBNt27RLFhgQKocZVFhR2Xo2KteHQYO9LBuXS6ffppL27Y+R+3nn3X5KVCA\n3btFbrghhpdeMnH2rBpdKymVwR5UyoeKtoWTJ0XWrdPy7bdaMjIq/l4+eVJk/Hhz/oSJPJo1C//N\nq6JtoSBVwh0+fFjDuXOKoTVr5qVRo8CLB8oyfPmlnh9/VDbQ8eOdZGfLjB5t5vhx38e8aJGB0aOd\nREcH/BJUAkhFa+XVry9Tv76b7t3dZGSInD4tYrMJtGzps92vv9ZjsQjMn2+kcWOJRx5xqvp+xZCR\nIbBrl5Y9ezRoNHDrra6gqfwHGklSlOuzsxX7UOuBwoNz5wQeeSSCbduUvaNbNzdz59po0qR0dulw\nKDNaMzMFdDpo2FAqcaPR3r2aQpMDunRxBzX7pFKYsI+g/fRTMhs2+KIO993nDEqxdWqqEinLIydH\n5NlnI/ycM4ABA1xq/VsFca21Bfv3izz4oJmTJyv+9oiNhbZtJQYO9DBsmDvfmfB6yZ87CjBtmonU\n1Iq/3lDF7YZfftFw882RjBkTycyZJqZP/43vvqs8wl8bNmjp2TOafv1iuPXWSHbtCv96oPKiIuuO\njh8X850zgN9+07FkSekUYG02+PhjA717RzNsWDRDh0YzYEA069dr/TQhi8NzmR/WrZub996zVQnt\nULUGrRy5cEHg8899xh4MrRJQBHBtNl9o2uEgP5qWR506EuPGuQI+r0slcJw5I/DQQ2a+/lrPoUOh\ne3toNPgNJ3Y4BI4fD93rrWg2bNBx221RnDzpf2Bq06ZyjDU6cUJkwoTI/DXm8GEtY8dGcvq0uphU\ndoqKei9frufixZJ/t2fOCLz0kglZ9j337FmRe++N9DvQFUdSkocZM6w8+qiDL76wsHChtVTpTasV\nkpM1LFqkJzlZw4YNWnbs0JCbW+KXqpKE/Ypeu3ZvsrOVf2ZiooemTYOzIFss/jfT5YrCrVt7WLHC\nErT6t3AhO1spfM/KCvxrX0ttwS+/aElJUVbMggOQz58XCjV/VDS9e/sfNtQIWtHs3y8ycaI5v0ko\nj9Gju9O5c+VI2eTkFF5jTp0SSUtTv3NJUiKkZaEi644aNpRo1crfDgWhdIO3a9aU6dmzKJsW/Kas\nFH9NMg8/7OL11+0MHOgpVTrd6YQvvtBz221RXLokcNddUdxzTxQDB0YxeXIEqamhebgIpRq0DwwY\n/AAAIABJREFUsL+7//zTZ5QTJzqpXj0473P5AhEbK/HZZ7lMnWpj2TILK1fmkpioOmdX4uhRgblz\nDQweHE3XrjEMHRpVohNfILh4UWDaNFP+Y0FQFqXUVIFx48w8/bSv+SMUaN3a/7Bx8WLY386l4sQJ\nEavV971ptTL/+peNqVPtxMRU4IWVgPr1ZRIS/DdeUZQxm0ufcvrpJy3DhkXyzjuGkN0siyM1VeCV\nV4w88IC50kaQa9eW+fBDK3FxefezzNSpdmJjS/7dRkfD7Nk2Ro92UnAkU506EjfeWEYvtoTs26fh\nmWciAAGnU8DhyLMxgeXLDcyebcJqLddLqnSEdUmxxwMrVvwMDMRkkklKCt5puaDwrSjKxMbK9O1b\nvjdEsLl0CQ4d0nD2rIDXK9CmjZfmzcvudO7Zo4TgT53yOWQHD2qZOdPI0qXWgAnOFjdjLTVV5Phx\n3zVUq6Z8p9u3a/ntNyVdfe+9rgqbuXc5zZt7ueceJ0uWKPp+wYoOV3aaN5cYN87B8eMivXt7GTTI\nTa1aXnbtSmbQoNA5LV+NmjVl5s2z/ZXWFAGZf/zDXuqIfGYmTJ4cwZEjGn76ScfatTref9/mN/w5\n1LFa4fXXTSxbpth/584enniidDpGgZ7LKknKVJNLlwSaNJGKjUAlJkqsXWvh5EkRs7lsqfemTSXe\nfNPGhAkOzp8X0etl4uOlv+Zolh/79mnyU616feH3XrRIz/jxDjp0CC2bC6UZvWHtoJ0/L3DkiLLh\nPvusnRYtgmcIDRtK1K8vkZEhMn68k5YtS/5eTqciqFujhkSDBqFTjGmzwa5dGqZNM7F1q6+ubswY\nB3PmlKDytAguXFBqvgo6Z3ncequ7XKcBHD3qezNBkKlTR8bhgE8/NeT/fMUKPf36eUKijjA6Gp5+\n2kFWlkBKikj79qHhOIYazZpJzJ5tR5aV0oOMDIHHH49kwIDKFXFJSvKyYUMOJ0+KREfLNG0qYTQW\n/7yikGXBT5Nx2zYdc+caeOUVe6lfs7xJSdGwbJmvvnjjRl2pHbRA4nbD2rU6Hn3UjMslMHask2nT\nbERGXv158fEy8fGBOWRFRCjNRVBxzk+ecgJAcrKO225z8vXXhgJ/UTCqplIUlWuFKiE5OQI5Of2I\nipIZOtQd1E21bl2ZTz/N5ZVXbEya5MBgKP45l5OeLtC/fxSDBkWzbZuGUJiSeuGCwIwZRm65JcrP\nOQMYMqTsDkFODhw7drlzJvP3v9u56abARiCLOxUlJ/vOK+3aeahbV8Jmwy91sn+/pkTdUMGmcWOJ\nDz6wsmFDLk2bhoDBhCii6KsL3bJFxw8/6IiJ6VOxF1UKGjaU6dnTS/v2EmZz6V+nRg2ZO+90+f3s\n448NlSpNuHevBvAt6hqNXOo1M5ARk507NTz4oOKcAXz6qZ6MjMrzuQaK7t3d5KVZf/pJy4QJTl56\nyfZXWl7mlltcIRmxDZXoGYR5BC1PYX36dFtAUnHF0amTl06dynICEhAEOHNGZNiwKJYty6VXr4qL\niths8NFHBt5911Tod889Z6dnz7I7UA0byixdmstbbxmx2wV69PAwdKiLDh28RESU+eWvmUuX4Ndf\nfQ7o2LEuoqMVjSKn07cJWCyKcn9pr015PdDplBRqIKIVkZEQGak6Z9fCmTMCr7+u2HPB77UqMmyY\nm/feM+Z/DpIkkJoq0rp16G2aRXHihL/T06dPxUe2JQk+/NDo15AiCJVrLnCg6NjRy+rVFs6fF2ne\n3EvbthJdu3oZMcKN3Q4NGkiq5FQxhLXZREfL3HvvBoYMcRX/xyFAXJyU75A5nQL33WeuUKmH48dF\nZs709yBq1pRYvDiXRx5xBOTm0ulgwAAPK1fmsmaNhVdftdO9e3Ccs6vp23g8vpFJGo1M586Ko20w\nyERH+5wfo1G55pKSmirw7rsGbrwxmi5dYujZM5p77jHz008atVC2HElJ0XDqlHJPnTz5YwVfTcXS\ntq2XTz7JRav1t+/KQkGxb0GQC3U1l4RAaV9lZgps2+afEUhK8lCrVuVwegNJRAT06uXl9tvdtGsn\n5XemNm4s0br1lZ2zzExlLGJFTdxRddDKiSZNZEaOdAetczPQGI3wwAO+GoqsLJEZM4xYLBVzPWaz\nUgeWkODlpptcfPhhLt9/n8OQIe6Ad7/p9WAqHKgrN0RRRv9XOcvEiY78Il2zGRITfVHRVq28Jb5O\nrxfeftvIP/8ZwenTIi6XQGamyObNeoYNi+L77yuPWGpl55tvfJ91aRztcEIQ8saKWXjsMTtTp9oK\ndQaHMt27u/M7rZ991hES1240ytSs6fMstFqZV1+tPN3CFc2+fSK33hpJ9+7RbN4c1gm+ayLsP4G+\nfUMnn3wtdO3qoVMnN3/8oeweq1YZGD/eSa9e5b/4NG4sMW+eFZsNYmIqf5j+arUFMTEwcKAbjUbm\nb39z5m/eWi2MHu1k1SrFe7vrrpKPUxIE/KJwl/2W5GQtw4ZVzo5ft1vpVjtzRqRePYk2bUI3UnDu\nnMDatb6i8p49bwAqflOvSDQa6NzZmx8xrkxcd52XVasseDwCHTp4yhT9C1TdUWQkTJ9u5/77NZjN\nMv/+t40uXSrfZ1sRXLwoMGlSBPv3KwvsxIlmNm3KoV698i3fUGvQVK5IrVoyM2faGTpUi9ut1DHM\nnWukWzdrfoSnPDEYKFXDQ6Cx25XaPK9X0ZgL9LguUYSHH3bw6KMUakfv0MHL6NFOHA7l/0vz2g88\n4KRaNZmZM035AriiKHPLLW4efbTiO89KQ3q6wMcfG3jnHSNer0BkpMzmzTkkJISmk3b6tOBXrF2r\nllq3V5kxGKiQg2txdOvm5YcfctDp5KCMFQxXDh4U2bXLF9Y+d04kK0sodwctlAh7By2UNE2ulY4d\nvbz5po2nnlLatH74QUdamlglpxBIEvz+u4bp0038/LMWr1eJ7E2e7GDIEFeJFsDibKFRo6IXgtq1\nZaZPtyHLlDpV0aCBzKRJTkaMcJOVpdS8mc0yjRpJFZraLS1nzgg8+aSZTZt8C2purhBSHa6Xc/as\nzzmrX1/i6NGfaN36hqs+JytL0cez2QRiYhQ9qeLkElQqH8WtDQcPivz0kxarVaBxY4nERC9Nm0pX\nbEooOIYtVJFlSEsTsFgEateWK/zAcuHC5SkauUKyNqHkM4S9g1YZ0WhgxAhlZudTT0XgdgtVdnbZ\n/v0iI0ZE+enlnDihYdIkM4sWKRGo8qBgQXJpEUWIj5eIjy/7a1U069fr/JwzgF693MTFhe4houBY\npFtuceULEV/57wWefjqC777LC13L3Hqri+eec1xTp6PDAVar4tiVNC2uEnwcDjh4UENGhsCxYxqa\nNi06WuP1wj//aSpgB2AyyUydauPWW92VMsJjs8FXX+l44QUzFotAQoKH//63YtOxBoP/59iunZfa\ntUN3PSkPKnlVUfGEiidcUqKiYNQoF998Y2Hu3Fzq1q18i0AgyM29sphhSYcJV1ZbCDUuXBB46y3/\ngp/ISJnXXrNTrVoFXdQ1sGOHz0vq3dtdrD2kpGj8NmUQ+N//DNx5Z2Sxo5GOHRN5+GEz/ftHcfvt\nkXz1lY5Tp6q2rEcokZUFs2YZ6dcvinvvjeKll4YycmQkx48X/o40GujRw79D1G4XeO45MzNnmoIy\nNzjYpKQoh9y8+a7HjmkZMyayQm20cWMJkylvn5N5+WV7haSIQ2mfCHsHrTKj0ykFvKNGuStFyDwY\nJCZ6mTrVhkZT8N8vM3y4s9xny6koiKLsl5Zt3tzDqlUW2rULvXqggly6pGw+BoNMs2bFn8zr15eK\nHFGTkaEhPf3qS+eZMwJr1uhJTdWQnKzjgQciue22SH79VVNh8gEqPv74Q8usWab8UUQABw5o/bQQ\nC3LHHS569y683ixcaGDPnsoXHlXs198ZO39e9CsDKG9atJBYudLC/fc7WLkyl+uvVyejhL2DFkqa\nJiolJzJSGXKfnJzDihUWvvjCwpYtObz9to34+JI5raotBIbYWJg/P5d583JZtszC6tW5JCWFtnMG\nSloHlIaNpk2lYu0hMVHiyy8tNGrkv1H07esuVgE9IUHiuuv8N/Tjx7UMGxbF9u2Fx5qplC8XLlwe\nKdoMXLnbOi5OZu5cK2+9ZaVGjYLffemnF1QkjRpJ+RIledSvL1GnTsWdHgRBabD497/t9O3rqbDa\n3FDaJyqf669S5dDpoGVLqVTzTVWCQ2KiRGJi5fo+YmOV6N8dd7jyxz5dDVGEG27wsm5dLsePi+Tm\nKp2qzZoVP/y6bl2Zd9+1MW6cmcOHfcus2y3wxBMRrFuXS2xsJdzZw4ROnZT6poLzIgcPdtGp05Wj\nNvXry4wb56JfPzfHjikj32rWlENCf62kJCZ6WbQol2eeMXPmjEjbth7eestGXJxqk6GEIMuV0f8v\nno0bN5KUlITXq9SD2O1KZ01VTRWqqFR11qzRkZ0tcNddrnKTrDl1SmDdOh3TppnIyVGcgerVJX76\nKYf69dW1qCI5elQgJUVLTo5Aw4YS7dp5Ko2oeVmx2ZTmB6tV6eKsVUsK6frRcGbnzp3079+/yN+F\ndQTN64Xly/U8+aTSCRkXJ/Gf/1jp08dT5VXEg8nx4yKZmQKNGknUrKluQirXRnY2nDolYrUqthPo\nw9SNN7rRaChXPcG4OJmHHnIxYICHU6cE7Hbl36Y6Z8HnzBlljm69elKR33nTpjJNm1a9OtYDB0Se\neCICq1XkiSfs3HijR3XOQpSwrkE7c0bg73/fli/4euqUyKhRkYVmpakEBq8XNm7U0rdvNAMHRvPJ\nJwa8IRT9D6XaAhUfViv8+KOGW2+NolevaAYPjmbNmsCfoMxm/1mT5WkPTZpI9OzpZeBADy1aVK7U\ncGVk/36RPn2i6dYtmvvvN7Ntmwb3VXyxqrQ2HDqkYft2Hfv3a5gwIZLHHjOTnq52GOcRSrYQ1g6a\nVkuBtl0FSRKYPduIq3LMT69UbN+uYfToyPzW7U8/1ZOdrd74KlfmzBmBN980Mnx4FPv2acnrLFMj\nryplwWoVOH9emXu7bp2eoUOjWLBAz6VLFXtdoVBQFBPjfxEbN+p45x1jSItMV1XC2kGrU0dmzpyu\ngL9BejxcUQFapXRkZ8M//mHC4/F9sHXqSBiNIbAi/UUo6duoQGYmvPCCiTlzTBRs+e/QwUPXrsFv\nsVftIXxJSPDSrZsvZCZJAlOmmPn4Y0ORh/Ng28KZMwJTp5oYNcrMggV6du++ekQvmCQmeunc2f/N\nP/zQQEqKmlmC0FoXwtpBA6XuZOnSXFq29AIyCQkeXn7ZodagBZj0dJGdO/1LGu+914XZXEEXVMU5\nfVpgyxYtW7ZoOXBAxBOCkkLJyTpWrfIf9NqmjYf337dWSnV2ldAhNhZmzLBRrZp/OnnaNBP79l2b\nI+J2w9GjgdkinU6BefMMfPednr//3cyAAVHMnm0kLa38IwU1a8rMnm2jevWCn43AiRNh7w5UOsL+\nG9m5M5mbbvKwfn0O27dfYv36XDp1CqHCqDBBSWv6Fpu4OC99+4aWVxBKtQXBZtEiAyNGRDFiRBR9\n+kTz738bOXkydG53SYIFC3yV24IgM2mSnSVLrOUmp1KV7KEq0qGDxOrVFlq29K1DkiTwxx+FHbSi\nbEGrhc8/13PgQNnvm7g4iRdf9OUQvV6BN94wcffdkezbV/73Zdu2Ev/7n4X+/ZVImiDI1K2r1kZC\naK0LYd3FWZBq1Sh29p5K6alfX6ZmTYkLF0QaNfKweLG1WDFPleARFeWzdbdbYOZME8uX6/j0Uytt\n2vi+l6NHBTZv1tGnj+ea1PUDhSjCU085adRIol07Lx06eElM9PoV8auolJV27SSWL89l0yYdn3yi\nJzNTvGY7FwTo2NHDPfeYWbEil4SEku8fLhf89puW8+cFbrjBw4QJdv77X58C64EDWkaPjmTVKkup\nXr8stGkj8eGHuZw8KSKK0Ly5ul6HGmGvg6Zybchy2evyDhwQuXBBoEkTSRU8rGCOHhW5+eYoPyFO\ngOuuc/PZZ1bq1JHJyBAYNSqSvXu1PP+8nWeecVTQ1QYer5drEqNVqTpYLOByCdSooaxNJ06IHDwo\ncuiQhqNHRZxOAbNZ5oYbPLRq5aVVK4nDh5Vu0OHDXUyfbiuxHMWxYyLXXx+NxyOg08lMm2YjJkbm\nscfMfvW6EyY4mDZNrdKvilRZHTSV4nE64ZtvdEgSDB9etqrVVq2CewLzeCAtTeTYMZGjR0XS0kQM\nBrj1VhcdOqinv4I0bSqxbJmFRx4xc/Cg7zbfsUPH0aMidep4Wb1az969yu/CQXrG5VKGQC9bpicl\nReSJJ5z06xdaaXaViiMqCvJGM23cqOXBB8354sEF+fhjZV7r119b6NTJy9/+5mTePCODBrkZMeLK\na+Tp0wL792to2FDKj0ZpNMokFI9HiWQ/+6yZt96ysmlTDrNnm1i3TofTKbBtmwarFbVmV8WPsHfQ\nkpOTQ6orI9TYs0fD+PFmmjWT6NvXHZKChVYr7N+vYcUKPZ9+asBu9w/11asn0aFD8bopVc0W2reX\nWLEilx9+0DF7tpHUVJH4eInq1ZXo2Vtv+fKJdrtQqaNONht8+aWev/89Aq9XsY/sbJHrr7cQEVH0\nc6qaPagoWCzwxhvGy5yzzUDf/Ed5A+21WrjzThfz5hl48kkzrVvnFHkQzcqCp5+OYP16PVFRMl9/\nnUOHDhJxcRIjRzr57DPfvTZ5cgTr1lmYO9dKRoaSdahdW1adsxAhlNaF0KkaVil3cnJg5kwTsiyQ\nlSXgcISe9khqqsC0aUYGDYpi3jxjIeds3DgnQ4dWPTXwayUuTmbsWBcbN1rYvv0S335roXVriRMn\nRM6f993+vXt7Kq1zBrBli44nn/Q5ZwAtWngxFGgSlWVISxM4fFgkN7cCLlIlJIiOhrlzbbzwgp3G\njX0NYxERMs2be5k61cb33+dw3XXK71q18jJkiJvcXIFXXjGRlVX4NY8c0bB+vdL0YrEIzJplwm5X\nHLzHHnP6dZN6vQKffaZHq1UEjLt08RIfL3H8uMju3aIqGquST9hH0ELFEw5FDhzQsHGjojciCKGn\nDZeWJjBuXCR79hQ207g4iWnTbPTt6yY6+tpeL5xtISVFkTmpW1eid29PodE2sbEysbG+x+np/mez\nqw2JDnVSUwUmTYqgYBexRiPz6KPOfKfzxAmR5cv1vPuuEYsFRo92MW1a+NqDytVp3lzi6acd3H+/\nE4sFZLkjOt0lzGa5UBbBbIaJE52sX69nwwY9Gze6uOMO/0PhxYv+i+fatToyMgSaNpVp2VJi6dJc\n7rgjCqtV+bvvv9eTmemgVi2lHm7nTg233x6FxSIQGysxaZKDkSNdNGig1vKWN6G0T6gRtCrM7t2+\nkEnt2hIREaG1GBw7pmHPHt81ms0yo0c7Wb7cwnff5XDbbdfunIUzO3ZoGDw4mieeMDNqVCQHDxZ/\nW6en+z5Xk0mmadPKW8N36pRIZmbBf7PMnDlW2rVTIiBHj4rcdZeZ6dNN+XIwS5fqycoKsROJSrkT\nGyvTqJFM48YycXGFnbM82rTx5Iu7/t//mQvdYwZ/OT9kWcBm89lXt25e1qyxMHy4E41GZsAAF9HR\nvvX21CkxfwJLZqbIv/4VwX33mUNKGkel/An7bz+UNE1CicxMWLrUF2bp18/9VxFt6HDddR42b85h\n7docfvjhEsnJOcyZY6N/fw9165bcmQxHW0hNFRg7NpLcXGVxlySBixeLv61jY30O2dNP24mPr7wO\nWmysnC8r0qKFh1Wrchkxwo1OB7m58OqrRo4c8Y/Cduni4dChnyriclVCkOLWhurV4dlnlS5nq1Vg\n/nyD32ikRo0kP2kbg0EmOlrpJk5LU7TXcnPhwQedrFuXw+jRTk6cEJEkpVGrSRMvY8Y4qVPHdx/u\n3KnjP/8x4HQG9t+qcnVCaZ8I+xRnqHLihEhWlkDbtt5ynWpw/LjIN9/oEAT480/f19+lS+iJ90ZG\nKoXuKldm1y4tZ874O2Q1ahT/mTVrpnzf3bq5uftuF9pKvBK0bCmxZUsOOTl5eny+jTItTeTrr/3z\nvSaTzMyZNiyW8r5SlcpMUpKHbt3c/Pabjo8+MnDnna78dTMhQSm5eOIJpdL/yScdGI0yb71lYM4c\nU350TBBkEhIkhg93odHIdOjgYckSIz//rCU2Vubuu52cPy+ydKkSklu82MDkyU4aNlTXwapIJV6W\nr41QyifnceCAyLBhUVy8KLB6tYUbbigf5+jQIZG77ookNVXDCy/YCxRUy37FsuFKKNpCWfnmG3/v\nvmtX9zUt5h06eFm7NofGjaWwGKt0JVFkg0Fx9POaApo39zB3ro327SUEIfzsQaV0FLU2XLwIv/yi\n4/RpgV69PLRuLfHPf9q5+WYtIPDiiyYWL7bmHwiGD3eRkOAlN1fguus8HD+uYdo0/xZiWRY4elTD\nrFkmunRxc+GCyNq1ygEiOxvmzDHx1FN24uO9pKZquPFGN2az6pyVJ6G0T4S9gxZqWCzw+uvG/A66\njz820r27FTHIyeb0dIH77zeTmqrUHkkF7vnERK96QgthXC4l4nrihIjNJmAyybRt6yUuTiY721fn\nYjDITJtmvyaplKgo6N49/J3yhASJdetyOH5cQ/XqMi1aeKldu/I7pCrBZ+VKHVu36mnb1sv69Tp2\n75Zo0EDimWfsvPlmBL//ruOXX7TcdptSmxYZCT16+O4pnc7LlCl2Zs40IsuF6x3//FPLoEGFm3N+\n/VXLV19ZyMkRaNhQ8mvuUalahL2DFkqaJqAUg65Z40u57NihISvLp24dLFas0JOS4vu6Cw6QeP55\nBzExQX37kCDUbKE47HbYt0/DggUGli/X43b7Fvnp06088oiLceOcbNigIzZWZv58K0lJ4e90lZS2\nbSXati18AKls9qDiz/nzAv/7n46ff9YxZIiLvn09funtknC5LVy4ADqdwOnTIqtW+afI33jDRlyc\nl1OnNDzzTATt21uKjOBGRyupzkGD3GzbpmXzZi2nTil1Z126eBg40M2LL14u0ifz+OMOmjSRAfUg\nURGE0roQ9g5aqHH2rEhBOYBq1WRMpuDeiGfOCHzwgf+Qw3r1lAWlbVsPnTtXXomFcCU7G5YsMfDi\niyYK2guAVivnazT16ePhl19yMJvlKtuS7/UqQrUul4AgyOh05EekVfHP8GXHDg1PP618wV99pWfY\nMCczZ9rzpSvKQkaGyOuvm7hwoXBqIyVF5JFHHPzzn2bOnxdZt07HhAnOImWKjEbo1MlLp05eHnrI\nid2uNAU4HOB2w7x5VlavVpzMZs28jB3rVA9ZKvmUSxenw+GgW7dudOzYkTZt2vD8888DkJmZycCB\nA2nRogWDBg0iOzs7/znTp0+nefPmtGrVim+//Tb/5zt27KBdu3Y0b96cJ598stj3DhVPOA+r1f9x\njx6eKyqdB/I9z53zrR4jRjjp1s1Lv34u3n/fWmVSPqFmC1fjf//T/3W69l/1IyNlli/PpVMnZRE3\nGpUi+armnGVlwdatGubNMzBiRCSDB0fTr18Ud94ZycqVem65JZJbb41k5UpdkcKiULnsQaUwJ074\nKyuvXm3g999LF3O43BbOnROLdM6qV5d44AEnAwe6iYxU7rlp00zXJG0jisqBITYW6teHRo2gc2cv\nr77qYM0aCx98YKNXL2+VOVSkpQn89psm5Jp1QmldKBcHzWg0smnTJnbt2sWePXvYtGkTycnJzJgx\ng4EDB3Lo0CH69+/PjBkzAEhJSeGLL74gJSWFDRs2MHHixPyU3IQJE5g/fz6HDx/m8OHDbNiwoTz+\nCQEjJsZ/I+3fP/gq+LVry7zwgp2bbnKxZImFN96w07KlxKJFVtq0UWvPQg2bDT77zD+tEhsr8fLL\nNr77Loc+fSq36n9ZuXgRXnghgptvjua55yJITtaxf7+GtDQN113nZeZME7t369i1S8eDD0bywQdG\nP0kElfCgefPCkaZly/RF/GXJadXKy+jRDjQaZb1WxGPtbNhgoW1biZYtZV591QYoY9KWLtXjLsNS\nHhERekLhweTQIZHbbotkyJBoPz3OUOTYMYFFi/S8846Bn37SculS+b13uaU4I/4KE7lcLrxeL9Wr\nV+frr79my5YtAPztb3+jb9++zJgxg9WrVzN69Gh0Oh2NGzemWbNm/PbbbzRq1AiLxULXrl0BGDdu\nHKtWrWLw4MFXfN9QyieDopdTv75ERobI0KFOkpKCn16MioLJk52Av6BOsCN3V+P8eYG9ezWkporo\ndIrsQ8uW3qDWwoWaLVyJiAh47z1b/qk8JkamceOqFyW7Eno9dOzoYfVqfaHxZNHRciFV9zffNDJ4\nsJuOHf039MpiDypFk5jopUsXN7//7utk1ukCU4PWoIHM66/bufdeFydPijRoINGpk5fISN9zBg50\n07Sph6NHtcyda+T229106FC50pMWizJVJDpaEeoNJG630vCwdKmeOnUk+vXz0KGDB4dDmfxx8qTi\nfhw/rqFnz9D53AraQmYmPPSQmT/+8NnYI484mDLl2pqxykq5OWiSJJGUlMTRo0eZMGECiYmJnD17\nljp16gBQp04dzp49C0BGRgbXX399/nMbNGjAqVOn0Ol0NGjQIP/ncXFxnDp1qrz+CQGhQQOZZcss\nHD+uoWNHD9WrV/QVlT9ZWfDiiyaWL/eX3x41ysnUqXbq1FEdkWbNJJo1U6ObRREVBQ884GLAAA/p\n6SKnTyuq7Xa7QHy8lzvvdLJ4sa/mUpYFjhwRCzloKpWbunVl/vtfKzNnmli+XE9MjMyECYFTdY2J\nUboyC3ZmFqR+fZk337Rz++1ReL0C77xj4O23bZUmRXn2rMAbbxhZsMBAy5Zevvgil/j4wK29x4+L\n3H57ZL6c09tvw/jxdoYM8fg51WWJPAab7GyBP/7wd5M++MBInz4eBg8O/oWXm4MmiiICRw2UAAAg\nAElEQVS7du3i0qVL3HTTTWzatMnv94IgIAQhxhuKJ+Q2baQqnVo8dUos5JwBfP65gREjXAwcGJyo\nYijagkrp0GqhaVOpyBFVLVtKbN6s49QpX+qkevXCG49qD5WfhASZWbNsPP20A5Op9FGg0tpCUpKH\nW25xsmaNgZUr9TzyiDMkRb8vR5bh6691LFigHGQOHtSyb5+G+PjArb2yrPxXkD17dGRl+VdWhdoU\nk4K2EBsrk5TkYedOf73J77/XhpeDlkdMTAw333wzO3bsoE6dOpw5c4a6dety+vRpateuDSiRsbS0\ntPznpKen06BBA+Li4khPT/f7eVxc3BXfa+LEicTHx+e/b7t27fI//LxxDurj8n9cv75E69bfs3+/\nFuiLwmYAdLrrKvz61MeV+3GLFhIvvbSerVu1HDnSn+HDXTgcW0hOlkPi+op6vGbNz5w5IxAf3xuD\nAXJytlC9euhebyg9NpvhzJkfAYiLK//3f+YZJ9988wtut8DChd1p397G77+HzudT1OOVK3/m5ZfN\nwI0obOaPP+wMGXJ9wN7P5YLHHx/AnDkm8tb3nj2vZ/58Q/5jo7EPTZp4K/zzuNrj2bNt3HzzDqxW\nkbz9ymzeRHKyp1Svl5yczJIlSwCIj49n0KBBXAlBli/3cQPPhQsX0Gq1VKtWDbvdzk033cTUqVP5\n5ptvqFGjBlOmTGHGjBlkZ2czY8YMUlJSuOeee9i2bRunTp1iwIABHDlyBEEQ6NatG3PmzKFr167c\nfPPNPPHEE0XWoG3cuJGkpCS1ziREOX5cZMUKPe+/byArS/hLANLB8OGuoM0EVW2h6uH1csWGilCw\nB6sVfvtNyzPPmDh+3Hde7tvXzfz5uVWyBKIiKIstSJLS1PPUU2ZEUWbTJgvt2gU2inbihMiCBXqy\nsgQmTnTSsmXZok7bt2sYNCja72crVljo1y9wETRQJJ7+/W8jH39sAASmTLHzxhum/N9PmmRn6lRH\n0IXaS0JRtnDwoMjPP2v57Tctffp46N/fHbBSnJ07d9K/f/8if1cuEbTTp0/zt7/9DUmSkCSJsWPH\n0r9/fzp16sRdd93F/Pnzady4McuWLQOgTZs23HXXXbRp0watVsvcuXPz059z587lvvvuw263M3To\n0Ks2CKiELk2aSDz9tIMxY5w4HIoKdyD0i1RUChLK3a5uNyxfrufvfy8sp3L8uIgkCYS7WKnDASkp\nGn77TZsvkTFqlJMbbvBUmlouUYQhQ9ysWOEmOVnHV1/paNPGGzDbczrhP/8x8umnSlnI9u1avvoq\nt0zySN7L/MfataUiu2LLSt26Mi+/bOfuu12kpGiIi5PQaGS8XoF69byMGeMKKefsSrRsKdGypYv7\n73eV6/uWSwStIsiLoKmoBBubDQ4c0LB7t4aLF0ViYiTi46X8cUwqKkVx5IhIjx7ReDz+zplGI7N0\naS4DBgQ2mlEW7HbFafR6lZqhQHRbnz0r8MknBt58s/AopO+/z6l0gq1//qnhppuikGXYvDmnzFGu\nPI4dU+zE5fJ9RmvX5pRpVFtamsCgQdGcPSui0cisWJFLnz7BtzeXC95918DmzTqmTbPRrl1o1Z9V\nBBUeQVNRCVc8HvjiCz2TJxeOgjRq5GHxYlVrLlSQZUXeRZYJiU5hrVbRKMzI8NlNhw4eZs60hVTH\naW4uvP22kdmzjciyMqboP/+xldmuly7VM3OmqdDPo6LkQnqRlYG2bb38+982Hn/czNatWlq2DEy0\nxWLBzzkDyMoqW0Ndw4aK4PUff2ho395DgwYSaWkCRiPUqCEHLaql18OECU4eftjpJ1miUjSVILhY\nNvKK81RUgmELubnw0UdGLnfOAE6e1LJoUeFuVZWKYcsWLX37RnPjjdF88omer7/+uUKvp3FjiTVr\nLHzxhYXPP7fw/fc5fPmlhS5dvOh0xT+/vDh5UmTWLNNfUS6B33/XMWaMmbS00jsJly7BF18Uvjdi\nYyWWLrUU2Z0bTAKxNggCDB7sYvhwJ7Nmmfymt5SFyEjQ6/0d1kCkf9u29TJkiDIndPDgaLp0iaFf\nv2gefTSCH37QkpNT9vcoCpOJkHbOQslnCHsHTUUlmFSrBrNmWalRo/CGEhEhc9tt5VuzoFI0NhtM\nm2bkzBmRM2dEJk82s3ChnosXK/a6GjeWGDjQw6BBHpKSvMTGVuz1FEVRRTAnTmhJSSl9kVVMDMyc\naaN1ay/Vq0u0beth+nQbGzZYrqg7VhmIjYWXXrITEyORmhqY7bVhQ4k77/StIzVqSEUOZy8Nv/2m\nZcoUM0ePanC5BE6dElmxwsAdd0Tx+uumoDlpKtdG2Kc4K7pLq7w5dUpg/34NEREyLVtK1KhR+VIF\npcXhUNJG2itYdbBs4frrvXz3nYUDB0TOnRNxOpWGhzZtvDRvrqY3QwGNBgyXBWw2bRrEH39YQqrW\nKxRp3Fhi1Cgnn38e2Ghwr14e1q/PwWYTiIqSK7QpIJBrQ5MmMgsWWDl7NjARNL0e/u//HEiS0k34\nxht2GjUKzLoSHy9hMsnY7YWvdd48I3ff7cqf+1tVCCWfIewdtKrGt9/qmDxZWekSEz188EH410Ad\nOybw1VcGvvlGS0SEzH33ueje3VOudUaNGwfuVKsSeAwGeOwxJ7/84p87XLlSrzpoxRAZCVOmONDp\nYMkSPV6vQL9+bhITy75xR0cr47nCjWbNJOrXD9zrJSRIzJ5tw+UioDJE7dp5Wb/ewmuvGdm0SZev\n+g8y48c7iYsLzJrm9cKPP2r57jsdvXp56NHDHdSxfuFC2Kc4QymfXB7k5PhOQvv2aRk2LIr9+8P3\na754UeDJJ81Mm2Zi+3YdP/6o5/77I5k504jN5v+3Vc0WVPzp1s3NAw84Cvxkc5ETBlQK06iRxBtv\n2EhOzmHTpkt89FFuWM2GDcbaEOhZxwZDYJ2zPNq39/LJJ1a2bs1h/focVq3K4eefc3jlFftVpTwy\nMgQyMoQiU+CXc+CAyKhRkbz/vpF7741k0SIDdnsA/xEBJJT2ifDduasoXbv6RwMuXhR59FEz588H\nfoxWKJCVJfDzz4UDwQsWGEhLU81bxUdsLLzwgp3Fi3Pp189F794uxo4N3OzGcMdoVPSgOnSQymVQ\ntEr5YTYrUb9u3bz07u2ldWvpqinns2cFhg6NokePaN54w8jeveJVHbVz50Tcbt8eNHWqiX37Qlik\nMEQI+x0slPLJ5UFiopfHHvM/mvz5p5ZDh8Lzq65fX2LYsMKF+PXrS0RG+q8YVc0WVApTvboiKvr5\n51a++qoLrVqpaWkVdW0oKVFRMs2aecnJEZk508TAgdGsXKnDYin67wunsQV27AjNCqtQsoXQ/IRU\nSk10tFJrY7UK+YNwATIzRaDiiz3dbkXw8tAhDYcPazh9WiAx0cvAgW7q1y95yiQiAl55xU5Skpf3\n3zditcL113v4xz/sxMXJnDolkJ4ucumSgMMh0KiRRIcOFf85qFQsV2okuVbsdrhwQcDrVTafUOy+\nVFEJFhER8MILDrZsUerWnE6Bhx6K5Ikn7Dz+uJOaNf3X8saNJdq18/Dnn74b7+DB8AwaBJKwd9BC\nYd5eeVO3rsw//mFn8GA3ixYZEARo1apinRK3G/bt07BkiZ6FCw1+4W5BkNmyJadUDhoooouTJjkZ\nNcqF2w2RkTLHjonMnGnkww8NXLyYtxBsZuDAHnzyiTXg9SEqlY/SrA12O2zbpuW99wxs2aLD41HG\nlj32mINbb3UX2phUKgdVcZ8oK+3be5k1y8ZTT/lEuufMMXHpkshLL9n8Di01asi8/baNYcOisFiU\nv+3RIzSbc0LJFsLeQauq1KgBgwZ56NfPgyhSofPOLl2CVasUtX1lvmBBZN54w0azZmVPNdWqJbNv\nn4YXXzSwerW+0PiYatUkXnrJrjpnKn7k5IDNJhATI2MqLGzvx6+/ahk5MpKCwsTHjmmYPNlMdHQu\nI0e6g3uxKiohglYLd9zhQqeTefxxc/56u3ChgR493Nx5p/+90LGjl7Vrc9iyRUdEhEyvXqHpoIUS\nYe+gFeUJezzKyBdBUDz7UFLtDjRlTeUEgpUr9fnSHwWpUUNizhwbffu6MRqLeGIJcLth0yYtDz4Y\nSW5u4YaIoUNd/Otf15W7QrlKaJKdDRERfXj/fS2ffmrgwgWBVasstG59dftQ0jJFN9xUhqHPKkUT\nKhGTykZEBIwc6SYuLpfx481kZSk3weTJZpKScgqtt23bSrRtG9qNOaFkCyGwfZcvp08LfPSRgU8+\nUUQXb7zRzaRJTtq396oLbBDIzBT44IOC3pdMUpKHiROddO7sIT6++JSQx6N0DXk8isNZo4ZcyKHb\ntUvD6NGRflEzUZS55RYXjzzipHVrr9p5pkJ2NuzZo2XaNCO//64lz9maNct6TaLCgwd7+PFHFxs2\n6PKfGxUlM3mynZ491YiAStVDr4fevT2sW2dh/Xod//mPCYtF4MIFgaZNK/rqKjeCLF+LiknlY+PG\njSQlJRXKJ69Zo2PcOP9BYHq9zJdfWrjhBrV4PBgcOyaSmiqi0ylDkOPjJaKjr/4cmw2OHBHZu1fL\n6tU6fv1V6RCKiIDhw10895zdT4dp924Nr71mxGoVaNfOS5cuHhITvTRuLOWnrUKptuBysrMhI0PE\nZFLUvTVqB3pAcThgzx4N06eb2LIlL2S+GY2mD++8Y+WWW9zXPB/QYoH0dJELFwR0OqhXT6ZhQ0k9\n4FViQnltqGykpgpYLAINGxa/zoci5W0LO3fupH///kX+rspF0AyGwv6oyyXw2msmvvoqt8ypNpXC\nJCRIJCRce2rx2DEl6vbhhwYuTyfZbPDDDzqefdZfSqRDBy9LllgBKl3K2u2G2bNNvPuuEaNRZupU\nOyNGuK4qEqlydRwOZXi1waA4+gsX6pk71+gXYY2Olli82EK3bt4SlQJERVFsKlRFpaqiZEXUtSsQ\nhL2Ddrkn3KGDl2HDnKxe7T9XTq8HSV1zK5wTJ0Ruv91MamrRptmli5tZs2xFpkaLc8xC9YR89qyS\ndgdwOASefz6C1FSB5593XHNUR0Xh5EmRTZu0fP65noQE7/+zd97xUVTr/3/PbN9kA4QSWiB0CF2q\ndKQ3USmigNiQr8qFq957RcXfVSwocrGgoqJXrwUEwQIqoCAgoBRFQKQTMEDoJdndbJ2Z3x9jslkS\nIGU32d3M+/XiZbJmk7Mzz5zzOc95CkOH+pg8OY5LlwLuLUFQmDrVzbhx11G/vuY114jcuUGj9Ikk\nW4h5gXY51aopzJ7t4pZbfHzwgZFTp3S0b+9j8mSPlt0XAZw9K3DmTPD5ntmsMGiQl9Gj1ca9seZZ\nsloV6tSROHAg8DjOm2fmxht9dOqkCYjCcviwyK23xpGWpqdvXx81aijccUd8UOZw794+HnvMRcuW\nUr7m6RoaGhqRRMwLtILOkytXVhg2zMegQT5cLrXNhRY/Ehm0by+xdm0WZ84I+HwCNptCtWoKNWvK\nJT66jNQ4k8REeOIJNxMm5HWXCWzZotcEWiHxeODFF82kpelp185Pw4YSL78cqJnRvr2PJ5900aqV\nlNukOVLtQaP00WxBI4dIsoWYF2hXQ68PT/NZjeIjCGq/vyZNynokpUu3bj6mTHHx2msBUXF5qyqN\nK3PhgsDq1aqCHznSy9NPW2jYUGLECA99+/pp0EDL4i1t/vhD5ORJEUFQM10TExUqVlT/q22IY5fN\nm3WsW2egUyc/rVpJVK6szWPFJeazODU0ogWHA7Zv17NkiYGaNRVuvdVLvXpaYGRhcDrhn/+08umn\nJvr29dGypZ8WLSR69fJRqVJZj6588vvvIhMnxuUe3QuCQs2aCq1a+Rk0yEejRhK1asnUrBlbgk1R\n4OJFte1eJNShLG2efNLMG2+oG8127Xy8/no2TZpo89iVuFoWpybQyjEul+qxMhq1I16N6OfsWYE9\ne3R4PJCcLNOwYcmPxWMJj0cVDKVZwuX4cYGNGw0895yFEyfyTzIVKsgMHOhj2DAvDRrI1KkjX7Ob\nQ6SzcKGR2bPNXHednzFjvLRr5y+099bnU0sGHTki0qWLn1q1om95XrVKz223BY6mkpJkPvvMTosW\nmkgriKsJtJhfljdu3FjWQ4g4Tp4U+M9/zAwZYmPIEBv33RfH558b+OMPEbe7rEcXPjRbiG2qVlXo\n2dNP//5+mjW7tjgrT/awZ4/IpElxfPyxEakUwxpr11YYM8bL999nsWSJnT59vOQtwZCZKbJokYlx\n42x065bA2LHxLF1q4OBBsVSz6kNpCz//rOPIER1Ll5oYNcrGo49aOXq04O4TecnKgk8+MTJggI1J\nk+I5eDA6iyG2bi3RuHGgaPPp0yK33RbPwYPRITciaV6IjiumEVJcLoG5c03s2KHnt9/0fP65kXvv\njadnzwQmToxjxw6dVnLkKpw4IbBzp8jx49eedDWiC69XrbUXSxw6JDJmTDzLlhmZNs1aoCcr3FSv\nrnDDDX7ef9/Jjz9mMX++gxtu8KLTBcSaJAmsW2dg4kR1Lnr6aTPbt+twOkt9uCVi9OhgEfrZZyYm\nTIjn0KGrX/fVqw08/HCgp2XeaxNusrMJmXCvXl3h3XedVKgQWEROnNAxd645ph0A4UA74iyn/PST\njgkT4jl/Pv+kYTAovP66kxtv9GmlCPJw8SJ8+62Rp5+2cO6cSLVqMkuWxK7rPi1NZOdOHRUrqnFD\nlSuX9YjCg9sNe/fq+P57A2vWGPB6YcoUN4MHR7/9yzI884yZV18NnBtu2ZJZqLZWALt3ixw4oMNk\nUrOpGzaUQhbT53JBerrI0aMiP/+sZ+lSUwHiUeGmm7w88oib5s2j4zlzOuH55y3Mmxdc9XzYMA9z\n52YXWF1/716R/v0TcDoD4mzz5kwaNAjv8nz+PKxcaWT+fBPVqslMnuzh+uv9IQkN2L5dx623BtYY\nQVBYuzaLVq2i4z6WFloMmkaBHDok8sknRt57z5yvwbggKKxZY6dNG63MA6jxO/PmmZgxI7hY3vz5\nDkaM8JXRqMKHwwH332/lm29UhXLHHR6mT3dRpUpsTRfp6QJvv23irbeCuwxUry6zdm0WSUnR/XkP\nHxbp0SMBl0v9bFarwk8/ZVGnzrUXSYcDhg61sWtXINK9VSs/jz3mokMHP4mJoR3r2bMCGRkCGRlq\n9ufWrXp+/13P6dMCSUkK773noGnTki3uFy7AqVMiigJ168phKwR9/jy8956ZF14wk7cbyjffZHH9\n9cFzqscDTz1lCepZPGWKiyeecIc9hnLhQiMPPhiX+70oKixbZqdLl9DM+3v2iDzzjIVVq9TetUuW\n2LnhBq1nbV60GDSNAmnYUOb//T8369ZlsWiRnYcfdtG7t5du3bw8/ribSpVia6dTElvYs0fHM8/k\nj15OTIzuBfxKXLggsmKFMff7Dz808f33sRVxv2zZJv7xjzjmzbMEiTOAv/3NTdWq0X9vjxwRc8UZ\nQN++PmrWLNxzHR8P998ffCa1a5caAD5+fDyHD4d2+ahaVaF1a5lBg/zcfbeXt97KZuXKLDZuzOKr\nr+xFahd3OQ4HrF2rZ/BgNdate/cE1q8PCM9QrxOVK8PkyW6WLnXQpElAkLjd+cMi/vxT/KutnYrN\npnDbbd5SSXBZvjz4j8iy2mYvVG6b1FSZd95xsmqVnYUL7TRtGvkb/kjSDOUwCVgjL4IQ6JXZr586\nkSiK+rpGgJMnhXyL+ODBXlq3js3doNmskJSkcPJk4DO//LKZgQO9MVO24tAhMbd2WgCZp592cfvt\n3pjIbD52LPhDjBvnKVLph0GDfDz7bDbTp1vI6wn6+WcD48bFsWCBM6ylYGw2VbCUhDNnBN55x8Sc\nOcEbrLzCNRxYrdC7t59vv7WTni7i8wk0bJhfoJw8KQZ1u3jjDWeplaVo2VJi5crg10wmJaTzv80G\nHTpEvjCLRGJgCro6kVIROJqIVXFWEluoU0fOLRwrigp33eXm+eezQ37MEylUrapwxx2eoNcOHxbJ\nzIwd42jXrjtGo3pPdTqZZ55x8tFH2Rw9quPuu+N49lkzaWmRP0VeuKD+K4i8XphWrdTacEUhIQEm\nTPDw7bd2OncOPsrfv1/P5s1XV3ter1oPbfVqPbt3i6WegOHzwf/+l1+cJSbKtG0buBbhXCcqVYLW\nrWXaty+4WLL/rz2eKCrMneukV6/SC5m49VYvDRoENplxcQoTJ3qu8o7YJ5I0g+ZB04g5fv9d5KOP\nTGRmCvTu7ad1az9Nm8olEp4tWsj88EMWJ06IVKki06CBjNl87fdFK4IAo0Z5+eILQ26h0bp1JeLi\nrvHGKKJrVz/r12fhdoPTKfDkkxZ++y2gaNauhTZtpBIdrYUTrxe+/dbAs89aUBR47DEXffv6gkRA\njnerVi2Jt992Ur160b1RcXHQubPEggUODhzQsWWLnh079JhMCi1bXt2D/MsvOoYNs6EoAoKgcOed\nHqZOdVOnTukcH+/bJzJrVvCDarMpfPihgwYNgu/r+fMCFotS6j2ZGzeWePttB/XqybRuLZVq7b76\n9WWWLnWwd6+O7GyBxo2lqEnGKCvcbrh4USA+Xgl7J6KYTxKIpL5aGuHH74cRI+LYsCEQP2U2K7z8\nspPExLX066fZQlE4dEhk4UIjv/+uY9o0N9ddFztHFTlzw65dIkOHJuRLlLFaFVauzIrYLN3du0V6\n9UoIOh57+WUnEyZ4c793OuGPP3RUry6XmijKy//+Z+Shh4JV/S23eHjppexSOSrfsEHH8OGBtMlu\n3Xw895yLli0Ddrx7t8i8eZvZuLEvvXr5mDnTVeoiTSNyuJpmOHRI5NlnLWzapKdOHYlnnnHRqZNU\nouLPV0sS0DxoGjGFXg9du0ps2BB4ze0WuP/+eCZP1tO3b+we4YaDhg1lnnwydosX+f3w4ouWfOLM\nbFb46CNHxIozgLNng2OXAJ591kLfvr7cCvRxcdCxY9mJ6oK8j59/buKuuzx07Rr+cTVrJvPRRw7s\ndqhdW6ZpUzk3E9nlgnXr9Nx7bzwulwnQsXOnHPU1II8fFzh8WEelSurnNRqv/R6Na2O3wz/+YeXH\nH1UX5/nzIjfdpOebb+xhi7GL/ACLEqJ5z8ofo0d7uf76/HEc//3vQK24rEYu3bp1w+cDiyXgWTIa\nFSZOdLN6dRa9ekV2AkitWjIGQ7BX7Px5IezB70WhbVs/kye78r1ut5fOGKtUURgyxMeYMT66dZNy\nxZnbDcuWGRg7Nv6v69ULgMmTPWErvVEanDghcM89cdx8s43evRP4/HNDboybRuG4kmbIyhL49ddg\nn5bfrxZXDhcxL9A0yh8pKTJvv+3k0UdduUHgoAbAamjkxWKBF15w8e23WXz7bRY//pjFc8+5SE0t\nWcxiaVC/vsycOU7yVq0fNqzwZTRKg/h4mDrVzdtvO0hJkQCFnj19Ja5nVlK2bNFz//1x5M1M7dTJ\nR7du0a1m/vhDx7ZtqmBQFIEpU+LYs6d4529ud+i6C8QClSopdO2af+OfkBC+dSXmjzi1GLTySe3a\nCv/4h5uRIz0cO6Y20M7MXE9ycteyHlrYcTjg6FGRP/8UsdsFTCZo1kwq80Ux0siZG6pUUahSJfpW\nIr0ebrnFR6NGdn7+WU9SkkKXLr6Ii5+qXBlGjfJxww1+srJUr1a4g6uvxpkzAo8+Glw2pFGj1cyb\n175YSRSRRHZ28K7C7xc4dEikVavC27ckqcknr79uxmxWExf69PHTpIkU9denMFxJM1it8OyzLk6f\nFtm5U5VObdr46dvXm+9nQ0XMCzSNonH+vMClS2pfvIoV1fYu0YpOBw0aKLlp5Bs3Ru9nKQzZ2WrW\n3CuvWFi3Tk/eBah2bYnVq+1RfT818mOxqDFmZRlnVlgqV1Yiol3Y8eNibmYywNixHnr3dpOSEv3P\nRrVq+TdhRU0DlGVVoG3bpl6jDRvg9dchOVli5sxsOnWK3bZv16JhQ5nFix0cPSoiSeppTThFa8wL\nNM17Vnj27BGZODGOvXtVs6hZU+bmm70MGuSlaVMp6mt+xbItZGbC+++bmDEj2DOQw9ixXipXjv4F\nKJTEsj2UJzIyBI4eFXG71UKw18pWrVxZZuJENxaLwsCBPpo1k6hQITY866mpEqNGefjsM7UzgcGg\n5Csnci0MBnjoITdbtug4ejQgEUQRjh3T8cMPBiZM8NCyZWx65K81L1StqlC1aulsiGK+zIZG4fnl\nFx39+9soaIEfNMjLjBmuIj/sGqXDunV6brkl/7mRICj8+99qZfxo76Mpy2qGWnq6iN0uYjQqNG0q\n5WYsapQ/Nm/WMXFifG6T9Vq1ZL780l6u56mMDIG1aw38+quO0aO9dOwoFasrRlqayPPPm/n8cyMg\n8PjjLmbPNuP1CvTu7eXNN50kJYV8+OUOrRenRqFo3lzinXec+TLDAFasMHL77XFkZER45PRViGVb\nqFhRoUaNnEVJoXFjiWeeyWbduizuu88T1eJMUdTiw88/b6Z79wrceGMCY8fGM2qUjccftxY7Sy2W\n7aE8sGuXjpEjbbniDODECZHjx4u+rMWSLdSsqTB2rJc5c1x07lw8cQZqEsqrr2bz3Xd2HnzQjU6n\n4PWq8//atUb27InNA7hIsoXYvMIaxcJigZtv9tGggZ0FC4x8/LEJjycgyI4c0XHmjEjNmpEf71Le\naNNGYs2aLLKyBAQBqlaVC2wrE214vbB6tZ67747PXRzycsMNviL1ltSIHVauNOQLijcYlALjsDSK\nR1wctG8v0a6di6VLg8tJpKfHvH+nzIn5qU2LMykaOh20bSvRsqWLBx7wcOyYyIULAnq9Qp06Cs2a\nRa84i3VbqF5dibksqx07dIwfH5+vUT0oPP64m6FDi59BFev2EOtc7ukXBIV585w0alR0gabZwtUR\nBNVLn5edO0tQPj+CiSRbiHmBplE89Hq1j19OL79Qc/CgyPr1evr08Yftb2hEP2uO9g4AACAASURB\nVKdOiUHizGhUuPlm719ByrHVG7SkHD4s8tNPehISFFJT1R6iJWlBU1YoCpw+LVC1qnLV8d94o4/0\ndDcbNxpo397PhAke2rSRNI9qmLjcM3nmjOZBCzcxf4Uj6TxZI8Aff+j417/iuPvuuFKr7q/ZQvTR\nu7ePFSuyWLTIzhdf2Nm0KZNXX82mc+eSi7NYs4e0NJGpU+O46654evRI4MMPjVy4UNajKjrbtuno\n1SuBd94xYrdf+ecaNJB56SUX332XxRtvqDZhNl/5569GrNlCOKhdW6Zdu0Ch1i5doruo75WIJFuI\neYGmEZnk5A7v3KnntdfMOJ1lOx6NyMRmg06dJPr189Ozp58GDZSY7i24Z4/IG2+YePNNE1u36nAX\noQ1qnToyVqv6YHk8Ao88Esf06VZOnoyexB63G557zsKZMyJPPBHH1q1Xd4fp9VCpEsUOhNcoPImJ\nMHOmC4NBQa9X6NQpNgVaJKGV2dAoE9as0TNqVE5ZCIXVq+1cd130xrdpaJSUtDSRfv1sXLyYozYU\n5szJZuxYL4ZCtPtTFPjwQyMPPRTsWhw+3MNLL7miIpP32DGBTp0q4HarorJdOx9ffunQjrIjBElS\nTz+8XjVWORqP0CONcl1mQyMySU6W0etzFgyBTz4x4svf5kxDo9xw+rSQR5wBCPzjH1Z+/71wq6Ag\nwLBhXh55JLg5+Vdfmdi4MToCswSBoB6oO3boOXUqejyAsY5OB61aSbRvr4mz0iDmBVoknSdrBEhJ\nkRk2LJCBt2CBiaNHw2uOmi1o5CXS7KFKFSX3iDIHWRaKVNcrMREefNDNyy870ekCv+u55yxREY+W\nkKCQkhIIRpckgUuXwr9MRZotaJQdkWQLMS/QSsKlS2qa/5o1evbuVXtvaYQGoxEmTAgINI9Hbeqr\noVFeadRI5u23HYhiQFgJgkLNmkXLcq5YUW3ttXKlnXvvdWOzKSQmygWUKok8EhJg+PDg0imyluSt\nUUgyMgTWrNHz3/8amTPHzPbt0e3m02LQrsAff4hMm2Zl0yY1+MNoVPj6azvt22sqLVRcuACjRsXz\n22/qNX7mmWwefNBTxqPS0Cg7fD61vtT69QZOnxYYPlxt1VOYGLSC8PvVo1Ozmajpxbp7t45+/Wx4\nPAJWq8JPP2VRp46m0jSuzPnzsGmTgccft5KREdjod+7s44svHJhMZTi4a3C1GLToCEwoZfbtExkx\nwhZU58XrFThxQtQEWghJTITZs10MGaLH7RY4eFDzoBWF7Gy4dEmgcmUlYiegixfB5RKQZfUIr7hl\nEMoLBoNauT1U84xeT9T1Kk1NlfjgAwdTp8bx//5fNrVra+JM48qcPCnwxBMWvvwy/yR4772eiJ0b\nC0PMr4jFOU9euNCYrwifwaBQv74mzkJNmzYS//2vA6NRoWHD4InY4YANG3RMm2bhnnvi2LGjZO7q\nSIotKAmyrDa2v/POOLp0SeCBB+LCHr9XFC5ehPXr9UyebKV//wSuv74CnTpV4NZb41m1Sk92dlmP\nUCVW7CGcKIoa5vHmmyYeftjCiy+aWbtWz5kz4TsuFUUYMMDPunVZjBjhK5USGpotlJzz5+GHH/R8\n9ZWB9PTSOU73eODtt00FiDOFxx5z0a9f0TPPIskWNA9aAaSlBQsBvV7h/fcdNG+u7eRCjSBAv35+\n1q7NCgqQPnNG4PXXTbz+uiX3tYoVZdq0cRX0a8oVv/yiY9gwGz6fOgl+8YWRvn19pKQUv+1RqDh/\nXuCxxywsWZJ/27phg4ENG/SsXGmnY0dts1McfD44ckTEYlFITg6/Z2znTh2DB9tyy17kcN11Pt56\nKzvfpiqUxFrbsljG6YTZsy28/bbqIu/Y0ceHHzqpVi289/D0aZF33gl2yzdu7OfFF120a+cnPj6s\nfz7sxLxAu1JfrexssFoLfs8//+ni0iU1e2rgQB+jR3tp2VLSiiGGCZ0OmjULTPRZWfDSS2beey/4\nwWvatGSLeiT1WCsumZkwfbolV5zlECleqSNHRJYsuXIl2T59/NStGxkbnWizB48Hli418Pe/x5Ga\nKvHpp46wi5jMTCGfOAPYvt3AZ58ZeeyxIlTSjWCizRYijd27dbz9dmBTtnWrgbQ0kWrVwrsRq1JF\n5v33HWzYoCclRaZRI5nmzaUS1fyLJFuIeYF2OadPC3zxhYHFi03cdpuHUaO8VKwY/DOtWsl8+qkD\nj0cgMVHbxZU2+/bp8okzm02he3etcnVmpshvvwU/tjqdQrt2keGRatZM4uOPHbz8spmdO/UoClSr\npnDddX7GjfPQrl3JJs/yzC+/6Pjb3+JQFIFdu/QcPSpSvfq177vPBwcOiGRkiNSoIdOkiVzopIPm\nzSXuusvN++/nDx6sXj0yhLZG2XPkiAhcvmkM/zGn1aoehw8YEJtrQ8wLtI0bN+YqYp9Prbf1zDPq\nsdmOHarq7tcv/82Ni4O4uPAtJD6fmoyQ4z0SIj8DvtTYuzf4iNlmU/jsMztNm5ZsQchrC9FK5coy\nvXv7WL1a9VKJosKbbzpp3jwyBFpcHAwe7KdXLwfnzokIgpKbQRhpHuhosgeXC9580xxUKsPpvPak\nkZ0NixYZefRRK36/gCgqfPqpg759C7egVami8O9/uxg1ysuPPxrYuVNH9eoyffr46dw5dipLR5Mt\nRCKXN6gXRYWkpOgU8JFkCzEv0PLy558iL7wQvBPctUtfoEDLi6IQcgH17bcG7r03DqMRPv/cTqdO\nkbHARgINGgS6DAwY4OOxx1ykpkbnwx5q4uJg1iwXv/7qxeMRaNnST9OmhfeIlBZWK8UqjZCZCSdP\nimRnC1SsKFO9unLFUITyREaGwHffBd/kwnj39+zR8cgjVnK8G7Is8NRTFjp0sFOhQuH+dkICdO4s\n0bmzNkdpFEyjRuqc7ferdvbQQ24aNdLm7JIS8wItrxK+cEHIF7tjMFx5kjt5UuDtt82kpYncfLOX\n9u39IQnMTU8XmTIlDkkScLlg1iwzCxY4ozodOJR07Ohn8+YsFAVq15ZDdl0iZVdUUlJS5KBq67HC\noUMiDz1kZdMmPaB6e66/3s/DD7vp2NEf8n6M0WQPZ8+KSFJg7kpOlqhV69o2oJauCZ7zPB5BK/56\nGdFkC5FIixYSy5bZWbLESJcufrp392O8cihqRBNJthDzAi0v6pGlQmDCUujY8cres+PHRV57TfW4\nff21kaZN/cyf7yxxNufRoyJ2e2DS/OUXA+fOCVFXryhcGI1Qv762gpQ3/vhDl1sYGlRvz6ZNBjZt\n0jNnTjYTJnijKhTA7VaPfi4//ikOZnPw3DBtmqtQGXIFFaedOtVNpUolH5OGRg46XY6XVcuyDyUR\nFhUSevLWNElJkZk4MVCp/tFH3bRqdWW3fdWqCgkJAaGwb5+eW26xsWdPyS6bwxH8vd+vHqNqhJdI\nqm+jkZ/UVIkaNQoS5gJPP23h5MnQqrNw2IPbrQbzv/KKieHD47nrrjgOHw6eL06eFNi8WcfGjTrS\n0go3l9SoodC0qbqZvP12zzXDMnJo1Upi3DgPoqhgNis8+WQ2AwfGTuxYqNDmBo0cIskWypkHDf75\nTzeDB/uwWhWaNZOuGt+SkiLz9NMuHnoocLZy9qzIk09a+eADBzZb8cZhswWrsXbt/Fq2qEa5p1Ej\nmWXL7Lz7rolPPzWSmamKF5NJ4amnXBH/jKSlCbz1lpn33jPlCeZXePTRgFfhwAGRMWPiOHpUnXpt\nNoXXXnMyYIDvql0WkpIU/vc/J2fPCjRpIlG5cuHGVL26wgsvZPO3v7nR66FuXTnikjWilQsX4Mcf\nVQ9v69YSHTr4adJE8/xrhA6tF+c1uHhRzZ76z38sQa+vWZNF27bFC5pNTxfo1y+Bs2fVmXLBAoe2\nq9XQ+AtFgRMnBM6fF/B4BKpWVUhOlkNyVBguduzQMW5cHBkZwRnIU6a4+Ne/3LkbwdmzzTz/vOWy\ndyusWmWnQwctCD+a+O47PWPGBHbpNpvCokV2LZlCo0hcrRentpe6BpUqwd/+5ubttx1UrKjujgRB\nKVEsTJ06CgsXOujVy8vrrzvo0kUTZxoaOQgC1K6t0Lq1TMeOEvXqRbY4O3hQZMyY+HzibPBgD5Mm\neYK89AWXHlCLYmtEF3njiHO+HzcunkOHtHupERpi3pJCcZ6ckACjRvlYvz6LZcuy+P57O6mpJdsl\nXXedxJIlTm6/3UdCQomHqFEIIim2QKPsCZU9LFkS3LvXYlGYM8fJK6+4qFEj+ICiRw8/HTsGb8gq\nVJBp3FjzupQlxbGFJk0krFaF4cO9TJ/u4vHHXQwb5uPgwSjKZNHIRyStExG8L408kpMVkpNDN5Fq\nsSAaGtGP0aj81RtTZsQIL8OGeWnSpODi03Xrynz4oZMdO3QcPKgjMVGmdWupwDp/sqwenR45IlKl\nikLLln4SE0vhA2kUihYtZBYtyuKTT8w8+6x6bN2hg5/bbivjgWnEDFoMmoaGhkYJcLnUJvHx8Uq+\ntnElYc8ekRtuSMDrVZVe794+/vMfJykpMTllRyV79oh065ZA3lpzM2ZkM3my58pv0tDIgxaDFgM4\nHHDsmMClS2U9Eg0NjbxYLGrMXCjFGcDp02KuOANYu9bA889bcDpD+3c0io/XC5cXAl682KjdI42Q\nEPMCLZLOk4vLrl0io0fH06VLAqNGxbF9u+7ab9LIRyzYgkboiHR7qFFDxmgM9pYtWWLkwAHt+Q81\nxbWF6tWVfE3jo6mYskZ+QjkvOBywebOO777Tc+BA0eVWzAu0aOfECYHx4+Np3VriwQc99OkjsX69\nnr17tVunoRFq/H61H2gkeEAaNZL5978vr8wuRMTYNFSqV1eYN8+JThcQ0lOnukPelkwj+lAU+PJL\nI4MHJzBmjI1+/RLYurVomystBi3C+fVXHf36JfDEEy6eey5QP6lRIz8zZ7ro2NFPfHwZDlBDI8qR\nZdi7V2T9egOrV+vJyNARHy8zZoyX/v191KlTdlPkxYuwfLmR6dOtOBwCLVv6+eQTB7Vrx+S0HZX4\n/fD77zoOHlSTObQ5WQPg1CmB7t0TOH8+4EypWVPmu++yqFkz8PxeLQZNy+KMcBITFaxWhYsXBerX\nl0hLUxX4wYN6Ro60cc89biZPdlO3bvmYsE+fFkhLEzGZFOLiYMECI7IsMGWKm6pVy8c1KG1kWV2E\norX58bVYuVLPPffE4/HkPZvSsX27ga1bPbz5ZnaZ1WGrVAnuuMNLjx5+Ll1SWz4lJWl2Hkno9dC2\nrVTswuUasYmi5G/hmJEhcuqUSM2ahbOVmD8ni/Q4k2uRkiLz3/86WLDAyKRJHipUCI53eO89M9Om\nWTl9OrYDH3w+WLdOT//+NoYMSWDdOgNjxsQxd66FN94ws2vXtV3H0W4LpU1mJqxdq+f++63cfHM8\nO3aUPPbp1CmBbdt0bNqklo8oSzZu3MjJkwJ/+1vcZeIsQLNmUkSUw0lJkWnTRtbEWZjQ5obSQ1HU\njfa5cwJyBHbGCpUtVKmiMHKk97JXFfT6wj/DETD1aFwNQYD+/f2sWmWnRQsfn33moHfv4EKXq1YZ\nWbnSUEYjDD8+H3zzjYGRI+M5dkxH8+Z+0tJ0/PlnwK1xeVVvjZJx4oTAjBkWRoyw8dlnJn7+2cDB\ng8WfLiQJfvpJPa4fMCCBYcMSuOEGW5knvFSqpDB9uguDIXjStNkUXn7Zydix3ogQaBoascKqVQZ6\n9kygd+8Exo6NY/FidW6RYswBaTDApEkeunULrNeTJ7tp0KDwqlSLQYtCzp8X2LZNz5NPmjl8WBUp\nAwZ4+fhjJ7oYTPDavFnHsGE2JEkVYdOmuZgzxxxUgmDJEjs33OAvqyHGFBkZAo8+auWbb/KeaSp8\n952d9u2LN4v+9puOAQNs+P3BQvq++9y88MLlgfCli88HR4+KnDghoiiQkKBQrZpMcnJMTo0aGmXK\nTz+p87miBOYCk0lh6lQ3N9/spXHjgos8RytnzggcPiyi00HjxlK+cjxaDFqMUbmywsCBPjp08HPy\npMClSwK1aikxKc4cDpg1y5IrzgBEUQkSZzabQv36RfeVHz8usGuXjvXrDWRnC9x2m4fOnSPjSKss\nWb7ceJk4gzFjvFitMgcOiCQny1gu7/d9DXbt0uUTZwBt25a9qDYY1IzJRo0i8LxFQ6OUOXtWQBQV\nKlcOz+9v107ivfecTJoUh8+nzgkej8CsWRbmzjXzzjtO+vTxYTaH5++XNtWqKVSrVryNbcwvRbEc\nW1C5skKLFjLduqkNpWOR8+cFfvwxsI+w2RRq1Aj+rNOnZ5OScu3Pn9cWfvtNx5AhNsaNszF/vplP\nPjExZoyNjIwY2roVg/R0gZkzg2fG/v291K0r0a1bRa6/PoGHHrJy9GjRrlNKiowgBHukxo/30KNH\n2Qm0WJ4bNIqGZgsqJ08KPPBAHK++asYVJse2yQTDhvlYvtxOu3bB4Toul8D48XF8+qkRn+8KvyDM\nRJItaB60GObYMYFjx9Rq5PXrS2VaLqC4VKigMH68h3XrDPTs6adRI4nMTAGDQcHnU71eQ4cW7Une\nvVvkppts+eLW6tWTiIuLvmsUSjweIfe66HQKjzzipkoVmX/9Sy3spCgCixebOHFC5H//cxS6N2Tn\nzn6WL7ezZYseiwVSUyVatfKHvPq+hoZG8fn1Vz1r1hhYu1bPuHHqcWM40OmgY0eJTz91smuXjnnz\nTKxebUDtyiDwz39a6dTJT7Nmsel4KCxaDFoMcv68wNdfG/j3vy1kZalO0jp1/Cxf7ojKuBqPR93Z\nPfSQlfXrjdSvL3HPPR48HrjxRi/16xftM73wgplZs4LP6Gw2hc8/t9OuXYxFqhYRj0edpC9ehAYN\nZOrVk3nsMQsffJD/vGHt2kxaty7fE6iGRqxgt8OYMfH8/LOacPbVV1l0714682F2Nhw6pJaguHhR\nwGZTaNdOKhdZy1oMWjni/HmYOdPMf/8bvKAeO6b7q5RA9Bm8yQQpKQqPP+5myxYDaWk6nnjCil6v\ncNNNPor6mS5vn9Ohg49Zs7I1sYF6rbt0CT52nDDBw9KlpiCPo9WqxEy19Oxs2LlTx9ateipVUmjX\nzk/z5gXbgqLAhQsCFouC1VrKA41CLl5Uaz8dOyZy8aLIuXNqeYWc2KMqVRQaNpSoXl0mJUWmWrXo\nm59ihbNnBbZsKZvMeKsVWrWSadVKm4PzEvMCbePGjXTr1q2sh1Fq/PabPp84AzXdt3bt6Db+9u0l\nvvnGzqOPWtixQ8/UqW5q1iz8Z8qxhfHjvbRtK+FwCNSoIVO/vlToo7rySOvWMt98Y+f9941s3myg\nWjWZxx93FSldvLi4XKp42rdPR4sWEq1bSxhCVFFm48aNdO7cjUWLjDzyiJWcptc2m8K332blE2lp\naQJvv21mxQoDtWvLTJ/uomNHqcyK2EYyTids3Kjn6act7Nun4/KG4gXRqpWf995z0KBB6Yu08rZO\nFERmpogsB+5TebXrSLKFcnoLYpczZ/JPhPfc42bKFHfUZ8UIglqx+7PPHGRlCSQmKsWqbl+1qkLv\n3mWfPRhNtGgh8dJLLpxOFwYDpWZLP/2kZ9SoeEDNLFu2zE6XLqE7dsnIEJk+PSDOQPUcbNxooHlz\nT+5rWVnw1FMWvv7aBMDx4zqGD9ezapWd664r38fiBZGVJfDuu2b27SvcElO3rsSDD7pJTNQ8aGWF\nwxH8vdms3YuyJuYFWqQo4dKic2d1otu2TU+3bj5uuMFPy5Z+bLayHlnoqFBBTR4oKpFsC5KkVtk/\nfVrkwgWBzEwBUYS4OIU6dWSaNCn72kCiSKnakdMJs2ebyRFPsizwxhtm2rVzYjKV/Pd369aNw4cV\nPJ78/69ixWDv2blzAl9/HbwbkCSBnTt1mkArgBo1FN55x8GRIzpOnRL4809dboa0TqcebVapIpOQ\noFC7tkzNmgpVqoROEMiyGreq06kNza9FWcwNp04JWK0KCQml/qcLJOfYOYeKFcunQIukdSLmBVp5\no359mWeeceH1xm7vxLLg1CmBixcFkpLkkB6HXroEf/yh54MPjKxebSAzM3/lG6tVYeXKLFq0iOwj\naodDXXyLWiPtSmRmCuzdG1zcb9cuPVlZQsj6rtaqpTBtmpvnnw8MumFDPx06BHtYK1SAevVkjhwJ\nHk/lyuVzESsMlSpBpUo54rX0PNY+H3z9tYG//z0Os1nh+eezGTrUFxJRHwoyM2HxYiMvvWShWTOJ\nWbOyadKk5M/24cMiZ88K1K9fvFg+kynwnooVZc22IwCtDlqMoomz/BTXFn79VUefPgl07VqBu+6K\nD1kPyT//FJk0KY5hw2wsXWoqUJwJgsLDD7uoUyeyxdmOHTpGj45n8mQrhw6F5vokJCikpgZ7p1JT\n/dhsoVk4Nm7ciNmshgAsXWpn1iwn77/vYOlSR77M4MqVFebNc1K1auA+DBzozSfkopXTpwXOn4+N\nGoD79olMnBiH3S5w9qzIfffFXbOPbGmuE1u36nn00TjOnRPZsMHA009byM4u2e88ckRkxIh4Bg9O\nYOLEOI4dK/q9rFZNya1V+H//56FWrfIp0CJJM2geNA2Nq5CeLnDHHfGcPKmKjg0bDCxbZmDq1ALO\nxYrI9u06vv++YCVdubLMqFFeRo/20rSpFNHxgydOCIwdG7hGOh3MnZtdYo9FfDz8859uRo7UoygC\ngqAwebIn5NeiUiXo3dtP795X/7mOHSVWrbKTni5gsUD9+lLYqq2XJr/+qmP8+HhMJoWXXsqmZ09/\nyBIxyoLTp4OD3RVFYMUKA506lf1RtCzDf/8b/GCsWWPg7FmRunWLvwnbt08kPV0VoRs2GFiyxMjU\nqZ4idUWpWVNmyBAf69cbGDLk8ibfGmVBzAu0SDpP1ihbimMLf/4p5gqPHDZs0DNliqfEMWG9e/tY\nvjyLM2dEHA4BoxESE2WqVlWoXl0mKUkp87izwpCWFnyNli0zMm2au1jtty6nSxc/335rZ/duHS1b\nSrRpE7pFtjj2kJIik5ISsiGUOX6/Gud36pR6/8aMiWfpUgc9e0avZ9Biye/5ydsariBKa53w+dQy\nLZdT0udcLaEU4JVXLIwY4S1ScfK4OHjqKRfZ2a4rlpkpD0SSZoh5gaahURIK6m/atGloAvYrVoSu\nXSWg7Hf2JSEzM/hieL1CiY9scjCZoFMnKSK8H7GIJAULBlkWeOghC6tWOUIW5xcuzpwR2LFDx8aN\neux2gREjvHToINGkiUz37j42bAi4AXv2LKO+QZdhMsHgwT62bQuMbcwYL0lJJRNElwf02+0CFy4I\nRe4eE4pNlUbo0GLQNMoNxbGFlBSZ+vUD3gSLReHWWzX3f14uXxzi4xUSEiJ7cQdtbgBVMAwYEOwt\nO3pUH/E9aY8dE5g61cqYMTZef93C//5n5sYbbezeraNKFYWXX3YyebKbtm39vPGGg86dr+4RLE1b\nGDrUS4cOqmBs3drP5MnuEocDNGwo5etRXJTjTY0AkTQvaB60a+DzqdXDtaD78knNmgoLFzr5/HMj\nsgyDBnkjPpuytKlXT6ZWLZkTJ9QV4e673eU2wDga6d/fy+zZZtzugCi7/MgsklAU+OQTE6tWXT4p\nC7kNvuvXV5gxw4XLFbqs4lDRoIHCJ584OX1aoEYNJSS132rXVnjzTScjR8YjSQKtW/upWVN7BqMd\nrRfnFTh2TODnn/V89JEJm01h2jSX1oZCQ+MK/P67yAsvWEhNlbjjDk9U9nwtrygKrF+vZ/z4eJxO\ngZYt/Sxe7IjYPohOJwwaZGP37mD/QqtWfj791FGoumexiN8Pu3bpOHJEpFUriUaNtPWqLDhyRGTL\nFj0//qjaZ58+Pnr29F+xzl+Je3GmpaXxxBNPsGPHDhx5yg0LgkB6enpRxx/xHDggctddcezdG7g8\nFgu8956zSL9HUeD4cbXxa8WKoR6lhkbk0LKlzIcfOhHFkgc8a5QuggAtWvhZvjwLu10gOVmJWHEG\najD7Pfd4eOihnBZSCgMG+HjuOVe5FWegtma67jpJK5xchmzfrmPMmHjOnQucL3/6qYmZM51MmlT0\n0JhCCbTbb7+dhg0bMmfOHCyR5i++BkXtq3XmjMDDD1uDxBlAnTpFM3q/H5YvNzB1ahzjx7uZNs0d\nU9X8o5FI6rEWixSUUBHJaPagcvCgWjfsyBEdb7zhCGkrrXAxerSXFi0kLl4UqFJFoX59qUQV+TVb\n0MihuLaQmQl//7s1SJzlcPp08QICCyXQ9uzZw6ZNm9BF2wxcDPbv1/HTT8FFgGw2hVGjiqZ+d+7U\nMWlSHH6/wLx5Zm67TYtd0tDQiDwWLjSya5e6FNxzTzzr1mXRrFno5qrTp9XYsPh4QtbOyWKBdu0i\nX0hqlB+8XiFfRjtAlSoyI0cWL7GsULKuR48e/Pbbb8X6A2VNUZWw/7Jkn4oVZRYutJOaWvgJS1HU\nVh5+f87NEjhzRkupKWu0HXJoOXlS4NAhkayssh5J8cixB79fbbnldhf8c2437N4tsmOHDm+MJfBm\nZsK33waC7X0+gX37QrMRP3VK4J13jPTuncB111Wgb18bmzdH5iZfmxs0ciiuLVStqvDRRw4GDPBS\nq5ZM48YS//53NitWFE0/5KVQHrS6desycOBAbrnlFpKSknJfFwSBGTNmFOsPRyotW0rMnetk0yY9\n3br56djRT8OGRbu4Z84ILFsWnGFUUPFEDY3CkJmp1jUyGilWj71Qc/EifPWVkZkzLZw9K9Cvn4+Z\nM7PztUeKdI4cEVm/Xs+KFQaOHtVhsyk0bChx/fV+WraUaNJEyq38PmOGGtqxapWd9u3ze26OHRP4\n4QcDR4+qG7GaNdVehgkJwf+qVlUiqkq/3x/IfMzh2LGSbyYvXIDHHrPw1VeB+hHp6Truvz+O1avt\nWp/HAjh/Hnbv1nP2rEByskzLlhJWa1mPSqMotGol88EHTux2AYNBoUKFS9RFgQAAIABJREFUkv2+\nQgk0p9PJ0KFD8Xq9HD9+HABFURCiIBq4qOfJVaoojB3rZezY4m+V7XaB06cD18ZgUKhWTTveLGui\nLc7k1Cl10X/jDTNpaSKVKyvMnu2kf39/mdY4WrnSyMMPx+V+//33Rnr08PPggyVvf1VaSBLcf/9W\ntm7tF/T69u16Fi82AQq33OJl3DgPTz8dWCX379cVKNCSkxW6dPFz6ZKBuXPNXLiQ/wYlJMi0bevn\nhhv8NGwoUa2aQtWqaseIsmrkXaGCOu5FiwKercvraRWHQ4d0QeIsh8REGaMx8sRZuOYGWYZt23Qs\nXmykTx8/Xbv6Cly0MzPh6aetfPxxzjVTeO21bMaO9WpJN6VMSW3BZApuPF8SCiXQPvjgg5D8sfKC\nwaDeJM9f69XAgT6t7IBGkUhPF5g8OY6NGwPuloyMnNeyyixb7dw5gZkz8zfDzKmBFi3odHDLLV4O\nHJC5dKmgsQt8/rmJ+vVlEhJksrLUn7Far3zdGzWSmTrVw4gRXg4fVivcL1hgym2DlZUlsn69kfXr\nA951i0WhXTs/gwf7aNxYLTaalCSTmBjSj3tF9Hq44w4PixYZAQGdTqFx45ILNDVcWUHNslSJj1eY\nOdNVrpKl9u0TGT7chtcr8P778MYbDm67LX9Xg5079XnEGYDA009b6NvXV64zU8s7hS5Ue+DAARYu\nXEhGRga1atVizJgxNG7cOJxjCwml5TFxu+GPP3RkZws0aeKnTx8f335rxGZTePRRl1boNgKIJu/Z\n998bgsRZDp06+cu0Sr8oFnREpzB0aPQFZ913Xxf69bOzdaue5csN7NypHi95vWoHiSFDfOj1kJWV\nIzIU6tS5tnipXVuhdm0/PXv6ufdeD+npIrt36/jqKyPbtulxuQKixeUS2Lgx771WSEmRuekmL927\n+0lJkUlOltGHsaR427YSixY5ePddExMnekhNLXnwfWqqxMKFjtwCuL16+bn1Vk/EJkqFa25ISxOD\n+oA+/riVbt2y8m3YL13K7yZzuYR8MdHh5vvv9WzZoqdFC4lGjSRSUmTi4q79vlgiktaJQj32y5cv\nZ+zYsQwdOpS6deuyb98+2rdvz0cffcTw4cPDPcao4JtvDNx3XxyKInDTTW4ef9xF//4+2raVih0g\nGE6cTnWXa87vDNGIAP78M79Xp21bP0895SrTuJTERHj++WzuuSee7GwBi0VhzhxnoWovyTKsWKHn\nxx8NDBrko0MHf5lP/vXqydSr52XUKC/nzwu43erxZ0KCwi+/6BkzJuDuGTrUS5MmRRMvSUkKSUkS\nHTpIjB3r5dQpgVOnRE6cENmwQc/atYa/7nUgoejoUR2vvGLhlVdUD9uAAV5GjFA9bCkpcshj2Mxm\n6NfPT79+oVMDFovaQqp7dweKAlZr+ayP5/MFf+jMTJFTp0SSk4PtqG5dGb1eyZNYBg895C71enSN\nGkk89ZSFOXMsCILC9df7uftuD61aSTRoEJoexBqFp1CdBFq0aMHcuXPp3bt37mvr1q1j8uTJ7N69\nO6wDLC45nQRKI+7oxAmBnj0TguJOvvrKTvfupbz9KSR//ikwc6aFkSO99O0bmWMMB9EUg5aWJjB/\nvplNm/QkJ6tp2p06RUb7FkVRa2ddvCiQlKRQt27hJu6jR0W6dk3I9SA9+2w2d9zhIT4+zAO+Atey\nhw0b9Awfrgq0unX9LF3qDHkz6QsXBM6dEzhzRuD0aZGtW/Vs3KgmG+T1tAEYjQoTJngYP95Dkyah\nF2rlmXDNDT//rGPIkOACbWvWZNK2bbAdSZL6szNmWHA6Re68082wYYHjzYwMgfPnBSpXVsI+B6Sn\ni8yebQ46co2PV3jkERcDB/po2FCOupqHRaG014kSdxI4ceIE3bt3D3qta9euuQkD5Z3z54V8QcEH\nD4pcdskiguxseOMNM4sXm0hMVMqVQIsm6tdX43WczsjzPggCxYpTkiQlqJTF9OlWGjeWItYGW7b0\nM2+eA0kS6NzZF5Ys1cREtRejGi0iMWKEj6wsF1lZAg6HQFaWkPt1draAKCocOaIjMTH8C7VGyUlN\nlejf38t336kxLnXq+KlRI/990+mgWzeJL7904PeTW3T31CmBL74wMmeOmfPnRRo39rNsmSOs2dx1\n6sg891w2Awb4ePBBK1lZIg6HwNNPW3nhBYW//c3NiBFeGjfWPGrhplAetF69ejFw4ECmTZsGqBmc\ns2bNYsWKFaxbty7cYywWJe3FWRT27xfp0iUBRQlY69y5zhJlgoaLTZt0DBtmAwTuu8/NI4+4qFq1\nrEelUR7IzobRo+ODCkE3bOhn5UpHSBpGa5Qd584J2O3q10ajmiRltSpamQjUcIVFi4zs3q3jX/9y\nFToO7+hRgSlTghOFbDaFn37KpFat0nle9u8X+eADE/Pnm5DlwPpmtSo8/riLQYO81KsXOc/u+fOw\nb5+O6tUVGjSIvNCigriaB61QAm3v3r0MGzYMp9NJcnIyx44dw2q1snz5clJTU0M+4FBQmgItOxvu\nvTeOlStzMgEUvvuu4HpJZcnZs/DAA3GsWaOO84EH3HTp4mPw4Mj0YGjEHmvW6Bk1ynbZa1m0bRtZ\nz4pG4Tl8WOTee+PYuVM997JaoVIlhSpVZDp29NO+vZ/q1WWqVVNISpLLbV9iRSm8J/zsWYFx4+LY\nti34HHv6dBd//7u7VMvseDywd6+OuXNNfPGFmu2bQ6VKMq+9lk337r4StdoKFd9/r+fWW21/FZh3\n0LGjFPFevqsJtELd5mbNmrF3714WL17MI488wuLFi9m7d2/EirO8bNy4Mex/w2qFp55y0auXj4oV\nZd56y0mLFuFZcE6dEvj6awMbNujJzCzae3ftUoOSc6hUSeHkyQi33hBSGragcXU6dvQzdWpwZdQr\nVfAPN5o9hIYGDdQ57+9/d2OxQHa2wIkTIjt36pk/38ykSfEMH57A9dcn0L9/AjNmmFmxQs+ePWK+\nIrllRWnYQlGEwvbtunzirGNHHyNGeEu9BqLJBG3aSLz2WjarVtkZMcKDWkIFLl4UGT8+nieesJKW\nVvZrSU7HnkuXRG6+2caePUW/WJE0LxQ6edtgMOSLQ9MI0LixzAcfOHA6BapXV8Km2vfv13HHHWpU\n9aBBXmbMcBXKlXvhAvz+uy6Pm1pBUYjIDFON2MVmgylT3NStKzN7toWUFIl69TQbjHaaNJGZPt3N\nuHFeDhwQ+fhjE6tWGZCkvBOhwKFDaoYqqCVbbrjBx4QJXpo1U+0g0r0dpcXOncFL85gxHqZNcxeq\nzEu4iIuDDh0kWrTI5oEHPCxcaOTjj0243QKffGJi7Vo9H35YuIzucJG3BJHbLfDKK2ZeeSW7zLPF\ni8sVjzibNm3Kvn37AEhOTi74zYJAenp6+EZXAgp7xHn0qMiWLTrS03V06eLjuuskLJZSGGAx2bZN\nx4ABAV9ymzZ+3n/fSd26V39wT56ERx4JHMO2betn5EgPY8d6I8I1rVH+OHNGbYdSqVJZj0Qj1Ljd\nanZ7RobI4cM6vv7awLZtBuz2ghWYzaYwfXo2N97oK/XSEpHIzp06Xn/dRPXqMn37+mnTxl/itkGh\nxu9X4+sOHhRZtMjEd98ZMBoVvv7aTvPmZSMk9+wR6dkzIc/GQOGHH+y0aRO5IRTFyuKcP39+7tcf\nffRRgT8TDa2ersbhwwKjR8dx5EjOZTCzbJmdbt0i92ampMjUrSvx559qvMeOHXpmzzbz7LPZV32A\nZVlgy5bA7b7tNg+DB2viTKPsiIS+ohrhwWyGBg0UGjSQ6N5d4vbbvZw7p5YUOXtWzK0Fl5EhcPy4\nWlLkjz90dO3qL7JAkyS1JMr+/ToGDvRSt27021Xr1hLz52eH9HdKkhpPFqrEDb1ePd5u0ECmTx8/\nGRkiWVmUqbeqYUOZu+7y8O67OQU+BfbtEyNaoF2NKwq0vMeZZ8+eZdSoUfl+ZsmSJeEZVQi5Wk2T\nFSuMecQZgMCqVYaIFmhVqyrMmZPNiBHx5ARrfvKJiREjvPTqdeVgf58PLl5Ufz4hQaZHDz81a5bG\niCOHaKqDphF+NHsoPYxGqFkzpzRIfu+KLFPs2KoDB0RGj47H7xfYtEnHq69mF9krG+u2cPSoyPz5\nJrZs0TNjRjZduoR2jTMYuOYpTmlgNMLdd3v49FMTDoe63p04oQPyt9e6EpFkC4V6JO6+++4CX584\ncWJIB1ParF6dX5+W5Rl/YenUyc8TTwRHVi9aZES6yjOnVqhWDXb27OyQ9NvT0NAoPS5ehLVr9Sxc\naGTpUgPbtum4cCH4Zy5cgL17RY4eFXN7AUcDJQl8P3FCzK3A//XXJnbsCGNfrCjE7YYXXzQzb56Z\n7dv1jB5tY//+6OqdWxSaNpX5/HM7iYnqGpeYKBOtJVuvaslpaWkoioKiKKSlpQX9v8OHD2OJ5GCt\nv7iaEh40yM+PPwaaZFasKEds9f+8WK1w111unE545RUzILB9ux67nSumsCckKNSuLdGtm5/evSP/\nM4aDSNkVaUQG0WYP779v4tlng8+nmjb189pr2bRrJ3H0qMiUKVY2bVJjgUaN8jJliptGjWJ7M+a9\nrNzkDz/oizzHRZstFIUjR0Q++yywzmVnC/z5p0iTJrFrF+3bSyxZ4mDdOj2//qrnyy+NvPmms1D1\n4yLJFq4q0Bo2bFjg1wBJSUk89dRTYRlUaTF0qJdLl9RKzR06+Jk0yU3TptFhtImJ8I9/uOnf38cX\nXxhp1066agxatWoKixY5qF5d1oKyQ8j+/SKHDok0aCBHje1oRCeBpu0B9u1T21F9/bWdEydENm1S\nSzN4vWpm3ebNOj791Bk1RTuLQ8WKwYvu+vUGnE531GbuFYczZ1TRZTQqNGwY3OD84kUhqMgsgMcT\n3fHjhcHvhxkzAhuar74y8sADUeRW5hpHnLIsI8sy3bp1y/0659/JkyeZNGlSaY2z2FytpkmtWgqP\nPupm1aosXn45u9AVniMFqxU6d5Z48UUXo0d7r5mi3qxZ+RZnoa5vc+iQyPDhNsaPtzFwoI3ff4/h\nBnUxSCTVOyoM48Z5ad06v2fI5RLYvl1HpUr556/Dh/Vs2BDbR341aypYLAGRdvasmBt/VFiizRby\nkpEhcOedcQwYkEDv3gnMnGnmzJnA569Q4XKvkULNmtG11hWHy9fDOXPMHD9+bbuIJFso1EH0jz/+\nGO5xlCkVKqgZKUVBUbhqzJdG7LN3ry63MGJWlshbb5miKu5HI7po2FDmf/9zMG+ek7Ztfeh0Cjqd\nQufOPrp29dOsmcSECfkNMDMztr0ltWrJTJoUiMlt2tRPpUrRn8lZWH77Tc/mzTlFbQXefNPC+vWB\nBS05WWbIkIBdjBzppXHj2F+81NOigBC9cEEkPT26Yu+uKEsGDBjAqlWrAK5YoFYQhIgXb6E+T/b7\nYccOHe+9Z+L4cZH+/X3cdJOX5OTyMyFEK6G2hby7VIAvvjDy6KMu6tTRbCEaKK1Yk/R0gWPHRCpU\nUGjcWMZovPZ7rkSdOgp16ngZMsTLmTMiogiVK8vY/uqe9dhjLtq39/Pqq2bS0kS6dvUzcGDhM9ii\nEYMB7rzTy7p1Bnbs0HH//Z4iX+NIijsqKk5n/teWLDFy880+9Hq18frzz7sYONCPyaRw/fX+XHuJ\nZWrWVLjvPg8vvhiIlb9w4dqblUiyhSsKtDvuuCP363vuuafAn4n2OmjFYetWHcOH23IL4W3aZODA\nAR0vvpitNQYuZ1SuHCzEPB7Nq6oRzNatOu68M55Tp0REUWHxYgc33FDyJJ34eIiPz39MVa2awtix\nXgYP9mK3i1SoIEdcgdNwUKeO2nsxI0MsF96hvNSvL6O2Xgqsx/HxoMsTcZGcrNpFeUIQ4MYbvbz1\nlonMTNVzFgV5jUFcUaCNHTs29+s777yzNMYSFkJd0+TDD02XtS9Rdyv/+pcLk0nhwAGRs2cFFEVd\nwGvWlElMDNmf1ygBobaFZs0kzGYFt1u1h3r1ysdiGCuEu97RoUMit94an7s4yLLArFlmunRxYDZf\n480lpFIlCoxJi2WSkhSSkoonziKp9lVRadFC4pVXsnn4YSuyLGC1KjzwgFtrm4Uad/3ZZw7uuise\ni0WmUaNr20ck2UKhIq8WLFhAmzZtSE1NZf/+/UycOBGdTse8efNo2rRpuMcYURiN+Y+v2rb1U7Gi\nwi+/qN41rzfQZqJRI5kHHnBz/fV+rfZYjNGokcy8eU4mTVJTpmbPziYxUTve1FDZu1eXK85ysFqV\nItX8unBB3fVH285fo/Qwm+G227y0aePn/HmRGjWiK6P85EkBr1cIW6Hb9u0lVq/OQpL4q1By9HDF\nXpx5qV+/Pj///DNJSUkMHTqUpk2bEhcXx4YNG/jhhx9KY5xFprC9OIvKnj0iI0faOHVKnWWbNPHz\n7rtOmjeXOXRIZMAAGxcv5p+BExJk3n3XSY8e/hLFoGhEFn4/pKWJSJLaMLokBTc1YovFiw383//F\nB7324YcOhg69dkzYkSMCy5YZ+fBDEw8+6Obuu8vX8VQs4fWqlfwvXRIwmxUqVFATG4qamBaLpKWJ\n3HlnHKdOiXz+uYMWLcrX8TQUsxdnXs6dO0dSUhIul4tNmzaxdOlSDAYDlStXDulAo4HUVJlVq7Jy\ns0Hq15epUUPVuA0byixfbmfy5Lh81ayzstTjjuXL7SFvs6FRduj1RIVnNGeBiNaedNFI8+YS8fHK\nXyUfFB55xE2XLtcWZ5dvAtetM2gCLYrZu1dHv3623G4HFovCkCFeRozw0ry5RO3a0eXVCSWrVxvY\nvVtdK+fPN/Kf/7g04ZqHQu33q1atysGDB1mxYgUdOnTAZDLhcrkohPOtzAlHTZPkZIWuXSW6dpVy\nxVkOqakyCxY4WLzYzpAhXszmwP8XBLh0SXOxlAbp6QKrVulZvNhAWpp6zSOpvk1psmuXyMCBNmbN\nCnPgU5QRbnto3lxm5cosFiyw8913dh5+2J0bj5qeLrBmjZ5t23RcvBh4z8GDal/JHHEGMGyYJs7C\nTThtITlZCrqHLpfAkiUmbrvNRp8+CXz0kTFfRnh54NIlePddU+73ixebOHmy7K9DJK0ThdKqTz75\nJO3bt0cURRYtWgTA6tWradOmTVgHF61Ur65QvbqfHj38ZGSInD6tGp3NplZ51ggfkgSbN+u46654\nzp1TF7n58x1/ZTqVP/bvFxk92saZMyL16pXPa1CWpKbKpKbmv+5Llhhz2za1b+/j1VezqVZN5rHH\nrGRkBNLvKleWadeufLZmixUSE9UyF9ddJ/Hvf1uCqvqfPSsydWocPXr4+M9/smO648PlOJ0Cp08H\nNiIej5CvbVckc+ECHDmiw2pVqF9fxmS69nuKSqFi0ACcTieCIGD9q5bEmTNnkGWZ6tWrh35UISBc\nMWgakYuiwJo1em6/PT73OAFg6VJ7xPUf9fnUf+EszXLypMCYMfH8/ru6D/v0Uzv9+0fWdShPSFKg\n9MFLL5mZOTMQ+Z+YqBahHTEikGQkigpffmmnWzftWDoW8Plgzx4dK1caePNNM3Z7sLeoXz8v8+c7\nSUgI3xguXQKfT6BKFaXMszwzMgSuv75C7nUQRYVff80KW7JAKPH71Qb0//mPBVFUeOwxN+PHe6hW\nreiniiWOQQPwer0sW7aMjIwMatWqxdChQ0nU6kdoRBA7dugYPz5YnNWr5yc1tXALnN0Of/yh4+JF\ngebNpbAVnFUUWLbMwIYNev71L3dYMosUBVauNOSKM6NRoUEDbaEvCzIy1ID/5csNtGolMXSolx49\nfMycaSandtWFCyL33x/H/fd7ePVVM6Ko8MEHTjp10u5ZrGAwQOvWEq1aSdx2m5e0NJFdu3QcPKgj\nM1Pgxhu9QbXLQoGiqPGnv/+u4/vvDWzerMftFnj1VWdI6vGVBKtVoWZNif371TkqOVkmPj7yw6ZA\nLVL+zjtqyIgsCzz3nAVF+f/snXd4U2X7xz/nZDRt0hYQaMveoyzZyB4CZYgiCCIvouJPBX3BAaiI\nIK4X9UVFECeiggJOlI0sEQQHILwgexQoe7RN0sxzzu+PYxtCC11pk6bnc11e0jTjNLnzPPdzj+8N\nY8c6A9oEmKeCqK1bt1K7dm0++OADdu/ezfvvv0+dOnX49ddfA3clRUQo5ZM1ig6nE+bMifAbAmyx\nKMydm0FcnPqlv5EtXLigalT17RvD8OHRLF5cBPHqfzhzRmDChCg+/9zEzz8bcn9AAThwQOD4cTFr\nRuG4cU5q1CgZi19xUVxrw7p1BiZNimLrVgMffGDittuiOXZMZPJkB6B29FWtKnHqlIjFotC8uYcf\nf7TSu7cHQ9GYh8Y1FOc+IQiqsG7Xrl7GjnUxa1YGn39uZ/BgT0AHvB8+LPL22xF07RrDffdZ+OKL\nCI4c0XH+vBASo7DKlIFHH/WNoHrySWc28e9gkBdbiIxUiIvzj/RNn27iyJHA1pjnKYI2btw45syZ\nw91335112+LFixk3bhx//PFHQC9IQ6MgnDsnsmSJ7+hy001qs0Zeuhbdbpg3L4J33/WlnLZvL7rB\n5+fPC1nNIq++Gkm3bh7i4wO3MJ05IzBrViSbNhl4/HEnb79tYuDAG5/OvV5IThaJi5OxWK5/P438\nk5FxbS5JYMwYMz/9lEZiosSaNQYkSaBGDdVR+/prpyZurVFg0tJg5UoDEyeasw2Nj45WmD/fRrNm\noRGZ7drVw8iRatSpe/eSM5KsbFn10Pvvf/s8allWD8UNGwYuRZsnd+/gwYMMGTLE77ZBgwZx6NCh\nPL/QyZMn6datG40aNaJx48a88847AFy+fJmePXtSr149evXqRWpqatZj/vOf/1C3bl0aNGjAmjVr\nsm7fvn07TZo0oW7duowbN+6GrxsqisAaRYvZrNCpk4f4eJlnnnGwbJmV1q39F6Hr2cK+fbpsHY5F\nGf6/uvYkJUUkJSWwp66VKw0sXBhBSoqIosDkyRk3lALxeFTNrvbtY9i8ufSEbIprbWjf3ptD6kbA\nahX5+OMIPv3UxPz5Ebz0UiQzZ5r8Ojg1iodw2ScyMwFjxliyOWe9erlZvtxK587ekNFrrFJFYfp0\nBy+95KBy5eBHzyDvttCjh4ekJP+uhkAfbvP0MdWtW5eFCxf63fb1119Tp06dPL+QwWDgrbfeYu/e\nvWzbto13332Xffv2MX36dHr27MnBgwfp0aMH06dPB+Dvv/9m8eLF/P3336xatYoxY8ZkyXqMHj2a\nuXPncujQIQ4dOsSqVavyfB0a4Un58mrNzsaN6UyY4KR+/byfYnbv1vl1VhkMCrfcUnSnuWtrFC5e\nDFy17qlTAi+/7IsEnjghMnCg+4YL8q5dOsaONePxCHz9taaiHGiaNJH4/nsrtWr5nP5y5WQqV1ao\nWtXfTvfu1TN0qIVDhwq3gyoKyKFfa60RYFasMPDee77vvyAo9OnjZunSdD780B5yQrBWq9pp/ttv\nOnbu1AV0LSxq4uMV3n47g1mz7HTp4mbKlAwSEwN7sM9TinPmzJn069ePWbNmUa1aNZKTkzl48CDL\nli3L8wvFx8dndXxaLBYaNmxISkoKP/74Iz///DMAI0eOpGvXrkyfPp0ffviBYcOGYTAYqFGjBnXq\n1OG3336jevXqWK1W2rRpA6hD3ZcsWUJSUlKOrxtKc7U0ipaYGIiJuf4p7Hq2cPLk1ZuhwowZGTlK\nIwSKqCj/a7y2m6swJCeLflp7Zcoo3KjR2ulUOwozHdTTp0W/bsNwpjjXhpYtJZYts3HihEhGhkC1\najK1ask8+KCLH34w+n1mKSk6VqwwMG6c6wbPmDNeL/zxh47Zs01ERqrdZaVJuqGghMs+Ub68Qs+e\nbmrUkGndWh0vWKeOVKTd4gXl779Fnnsuip9/1pPZLNOsmTqZJ5g2mx9bqFhRHUI/bNiND8EFJU8O\nWvv27Tly5AjLly/nzJkzDBgwgD59+hR4ksDx48fZuXMnbdu25dy5c8TFxQEQFxfHuXPnADh9+jTt\n2rXLekyVKlVISUnBYDBQpUqVrNsrV65MSkpKga5DQwOgUycPb75pwmyGGTPs9OnjKVIHpWxZBbNZ\nwW5XF6XM/weCM2f8V4lGjW58Yj5+XGT9el9aMyFBDnr7fbii6iP6fx6NGsl8952NBx6I4vhx33J8\ntT5Ufli3Ts+//mVBktQPsUULiTFj8u/oaZRM+vXz0K9f6NdynT8vcO+9Zo4e9XdBdu3Ss2xZwQ4n\nwaSoUsZ5ltkoV64c3bp1y5LZKKhzZrPZGDRoEDNnziQ6Otrvd4IgIARwdxgzZgzVqlVj8+bNxMbG\n0qRJkyzPOLNTQ/u5dP2cydW/b9tWYvbs5RgMMGhQhyK/nvLlFerXX8uOHQagK1FRSsCe32br/s9f\nuBGAatVa3PD+DkfXfzZz9f7du7dGFEPn8wqGPRT3zzffLPH886s4flzEau1G2bIKFSqsZ/Nm5YaP\nv3RJ4NKlbv9EPDcSGanwzDP9/D7PU6faBf3vKwk/Z94WKtcT7j+vX7+ZY8fMQDdUNv7z/67Ury8H\n9fo6duxYpM+/efNmvvzySwCqVatGr169uB55Eqo9ceIEw4cPZ+vWrZQrV47Lly9zyy23sGDBAqpX\nr57bw7PweDz079+fPn368PjjjwPQoEEDNm7cSHx8PGfOnKFbt27s378/qxbtmWeeASApKYlp06ZR\nvXp1unXrxr59+wBYuHAhP//8M++//77fa2lCtRqhzNq1eoYMUQ8oS5aohbuB4McfDdx3n1qpWrmy\nxKpV1hsW386da2TCBF8n0urV6dmaKzRCkz17RDp3js36ecAAF02bysyYYcLhUA+6n35qY8CA0I+o\naJQuPB74/nsD48aZs6SRypSRmTbNwYABbmJjc3mCMOJGQrV5Cszde++9tGzZkrS0NM6fP09qaiqt\nWrVi5MiReb4IRVEYNWoUiYmJWc4ZwIABA/jss88A+Oyzz7jjjjs/SfegAAAgAElEQVSybl+0aBFu\nt5tjx45x6NAh2rRpQ3x8PDExMfz2228oisL8+fOzHpMT156UNUovoWQLN98skZTkpk4db0AFZKtX\nlxFFBVCYOTMj186oq49nDRp4S9U4qM2bN3PokMjGjXoOHhQpAaOF/ahUSaZdO5/z9eOPEcydG8G0\naQ5iYmTi4+WQkVMIdUJpbSgNGAwweLCHzZvTWbEinZUr09m4MZ0RI4LvnIWSLejzcqcdO3awZs0a\njP+0n1ksFl577bV8pTm3bNnCggULaNq0Kc2bNwdUGY1nnnmGIUOGMHfuXGrUqMFXX30FQGJiIkOG\nDCExMRG9Xs+cOXOy0p9z5szhvvvuw+Fw0Ldv3+s2CGhohCrlyyu8+WYGGRlCQNvLExMlvv3WhiAo\neYqEVaigvrYgKDz4oItjx9QxMKWBixcFRo+OJiVFJCpKYe5cG927e0uMOGy5cvDKKw6SkvR4POra\neOaMyKuvmpgyxUHLlh6qVy8dn2WokpYGBw/qOHtWxGYDSRKIj5epU0emRo3ScxjKCVGE2rVlatcO\n9pWELnlKcfbq1YspU6b45eu3bNnCtGnT/PTJQgktxamhkTtHjwo88UQUSUleFiyIoGpViQUL7Ojz\ndHQr2ezYoePWW32DD0VRYelSK7fcUnKiTrIMmzer82evFsTt1MnDvHm2sBW8TU2FHTv0nDghUrmy\nTJMmUkDFngPBvn0izz4bxaZN2T3+cuVkvv/eRpMmJcfWNIqGQs/irFWrFn379qV///5UqVKFkydP\nsmLFCu655x6ef/55QC3wf/HFFwN31RoaGkWOLIPZDNOnR2K1CqSmCly5ImRF1sKZ2FiFiAglqwZG\nlgVeeCGSb76xcU3/UqFITVWlVBISlHw5vhcvCqSkCLhc6miehITsUx5EETp39rJsmZXRo6Oy5hr+\n8ouBgwd1tGsXfg6A1wtz50bwyis+7YjOnT3MmWMvkrm2BcFuh2eeieKXX3IOx16+LHLmjECTJsV8\nYRr55vJleOedSJxO+Ne/3MWqJZenGjSn08mdd96J0WjkwoULREREMHDgQJxOJ6dOneLkyZOcPHmy\nqK+1QIRSPlkjuGi2kJ3jx3WsWmXM0mIrW1bOmt8Z7pw8uYl77/Vv5//jDz2nTgWmZ/78eYEVKwz0\n7x9N27ax7N+vaszlhRMnBIYPN9OtWyxJSTHccksMgwdb+OEHA2fPZu90v/lmia++svHxxzbatvVQ\nu7aEyZTDE4cBFy8KfPCB/x+3aZOBDRsKnpsO9NpgMsHw4S4MhuzfpehohTfesNOqVWAagzQCy7W2\nkJIi8s47Jj780ERSUjSbNhVfeiFPr/Tpp58W8WVoaGgEg2vHTPXu7Sk1szj1enj4YScbNug5fFhd\nCkWRgOjAHTki8uSTvgiKyaRw+LCOZ56J4o473PTu7aFq1es7wi6XwO7dvuVZlgV+/93A778b6NrV\nw4wZdmrW9H981aoKVat6SEry4HKp8wLDEZNJoXx5mYsX/W13374QmV+EKvQ8cKCHZs3SOXZMFSfW\n69VOxSpVFGrVKt31ZyUJ9aCjAAIZGap+26pVVho0KPrPMN8WPWbMmKK4jiIjHNShNQKDZgvZiYjw\n/7lbt9Jzqu/YsSO1aiksWmTj4Yed1KghMXWqo9DF2/v2iQwaZPFLb/3f/zl5+eVIfv1VHWI9cWIU\nV40dzkatWjIff2zDaMzuxG3caODjj03XHeUUFRW+zhlAmTLw+usZ6HT+702HDgVPPRXF2mAwQP36\nMklJXu6808OAAR46d5Y05yzEudYWKlaUad7cty6mp4u8+66JjIyiv5Z8O2jz588viuvQ0CjVKIo6\nk27FCj0LFxo5cKB4ogHVq0uop0N46CEnzZqVHgctk1q1FF5+2cHatek88oirUKnBgwdF7r7bwokT\nvlEUDRt6EQSBo0d9t61ebeTAgeuPq9DpoE8fLytXWrn/ficREVc7Iwrlyvlv8g4HbNig56ef9CQn\nh04kqaho107V+Bs/3sFdd7lYvNhKx46a3ptG4ImNhRdecPjd9sUXRg4fLvrvWdj3al2tDq1RuglV\nW0hNhdWrDTzxhBmnU82vjRvnYOpUZ5G/drNmEvPn23A4BDp29Aa0OD7UudoedDoK3fF4+bJaGH7y\npM/xqlPHy3vv2enTJ/sbm9swc1GE5s0lmjRx8O9/uzh9WsDjgehoqF9f8hsv43bDpElRHDigo1w5\nmcmTHSQleUKuszFQ6PXqfNOWLQNTsB2qa4NG8ZOTLTRvLvHoow7efTdzEL3wzzg235dYktT//lEj\nCwh5cgEff/xxdu7cCcCkSZMC9+oaGqWcixcFZs40MXq0Jcs5A6hXr3jSIFFR0K+fl8GDw3czLy62\nb9ezcaMvrXnLLR4WLrTTuLHMq686yIxUAjRv7s1zqkuvhxo1ZNq3l+jSRaJFCwmz2f8+sbGqUw9q\nh+CTT5p56CEzBw+GfzRNQ6OosVjgkUdcPPCA79Cc6Yi53fD77zqeeCKSAQOi2bkzcIOc8xRBk2WZ\npKQkKlSowIgRIzh16pTfwPJQRjsVaWQSirawerWBmTMj/W6rVEmmQwctXZOJLMOJEyJHj4p4vdCk\niURCQuGdyUDbw8qVvoaA8eMdDB3qzhIhHjzYTe3aMjt36oiPl2nb1ktcXGAd4ltv9dK9u4f169Xr\n2LzZwIAB0Xz1lZWmTbW6pxsRimuDRmBITYUtWwyIokLDhrkLBF/PFipXVpg61cHAgW7S0wUSEyUc\nDvjhBwOPPmpGUdQD9q+/6mnePDCR3TwJ1QJ4vV5WrVrFggULWL58OW3btmXEiBEMGjQISwi2fWlC\ntRqhzokTAl26xJCW5otyVKoksWiRjcaNtQ0V4NIlVapi0qQo7HZ1AVy0yEqvXqFXK7d9u44zZ0Tq\n1JGoV0/2S0EWF0eOiDz4oJldu3xn75gYmR9+sNKsmWZTGqWPkycFWreOxe0WKFtW5qWXMkhK8gRE\nxHnlSgPDh5sBX/bjo49sDBqU9wN2oWdxAuj1evr378+iRYvYunUr58+f5/777ycuLo4HH3yQlJSU\nPF9QcaJpX2lkEmq2kJEhkJbm+2LfcYeLJUs05yyTU6cEnn46knHjzFnOmVogH5jIU6DtoWVLif79\nPTRoEBznDNTROfPm2eje3bdBpKeLPPKImZMnA6AfEqaE2tqgETgqVlQYPlzVO7xyReSxxyxMnRrF\nqVM5fx/yagtHjgg89JC/c1a+vIzXq4opB4I8LyNpaWl8/PHHdO3alc6dO9O2bVs2bdrE/v37sVgs\n2jxMDY18UqOGzLJlNj791Ma6dem8/XYGdepozhmoBfcTJ0bx3Xf+OiCjRrlITAw/dfyCcOmSwIED\nInv3ihw6JHL2rIDbDTVqKLz7rp3nnvPVvR04oGf16hIyZFRDI4BERMBDD7mwWHwHuy++iOCpp67v\npOWFQ4d0Vx0cwWhUmDDByUsvRXLuXGAOQ3lKcQ4ePJhVq1bRqVMnRo4cye23305kpK9uRpZlYmJi\nsNlsAbmoQFCUKc4zZwRMJiWstYY0NILJTz/pGTrUv/Oxb183r76aQbVqpbuZ4fJl+PFHIzNnmv6R\n1FA3g3LlZG6+2cuDD7po3lwiNlZhzx4d8+ZF8PXXRjp18rB4cemYs6qhcS2bNukZOtSSNdoN4M47\nXbz5ZgYxMTd44HVYssTAAw+o5V3R0QrPPedg9uwITp3S8fPPaTRpkrfDdqFncbZt25bZs2cTHx+f\n4+9FUeTcuXN5upiSjMMBP/5oYPLkKBo0kJg5M6PUiw6mpsLx4yI2m0B8vFLiIkCnTglIkkB0tBy2\ng6VLIitW+KI9gqDw3HNO7rnHpXWaAqdO6Rg/PgpZ9j+lX74ssn69kfXrjbRp4+Gjj+y0aiXRpEkG\nTz3lRK9Hc840Si2dOnn55hsr99wTnTXa7rvvIhg2zE2PHvnPSTZvLjF7tg2TCWJiFMaMMWdNt7DZ\nAhNBy1OKc8KECdd1zjIxX9v3HSIEsrZg1y4do0ebuXRJZMsWAz/8ULpTBocOiYwcaaF791gGDIih\nR48Y/vwzcC3GgeZaW1i+3ECHDrG0bBnDbbdF8+OPBi5c0Op0QoG77vJw110uXn01gzVrrDz2mDPg\nzllJrTtq2FBiwQIblSpd/zD09996UlPV5T0iQp1MUK1ayTo8FScl1RY08o4gqNMmli9Pp1Ejn0P2\nzjsm3G7f/fJqC9Wry9xzj4c77/RgMOA3eixvrZe5o52n8ogsw6efRnB1QeDPP+sZN84VtILgYHL2\nrDqT7MABnwlZrQKLFhlp1cpxg0eGDosW+YaE79un5777LLRp42HOHDu1ammRmmDSvr2X9u1Dr1Mz\nFDAYICnJS7Nm6ezfr+PsWZEDB0QuXhQxmRTatfOSmCiRmKg5ZOFIZiVRCIonlAgaN5b57jsbu3bp\nWLgwglq1JKRClrXWry9Rq5aXo0f1CIJC+fKB2T/C3kELlL6N1Ypf6zqoQ1QD5SmXNI4eFf2cs0zq\n1g3dTeFaWxgxwsXy5Qaudrp//93ACy9E8s47GZQpU8wXqBEw3G5IThZxOqFsWYXKlZVsQ9BLuvZV\nQoJCQkLJc2IVRf1sPB6IilKytOKCSW62YLUSElM20tPhqaeiOHxY5OmnXbRr59HWqQJQoYLCrbd6\nufXW7N+fgqwL8fEKb77p4K67LAwY4KZy5cDsg6Uw9lMwIiOhTBn/N33gQDe60M3oFSkWi4Io+i+s\nLVt66N275Aisdujg5ZVXMrL9HcuWRXD6tPbVKKk4nfD550bat4+hS5dYOnSI5b33IgLWWaVROFat\n0tOhQwxt28bSoUMMr75qYs8esdBRjBvhcKhD7Ddt0vHLLzp27xa5eDHv9vD665G8+qqJQ4eCuy5Y\nrQKrVxvZtcvAPfdYeOmlSC5d0uw6FOjY0cvatelMmeLINumjoIT9LhSo2gKjEf7v/1xZPzdoULpT\nMA0aqGHinj3d3Hqrm7fftjN3rj1XleZgcq0tmM0wapSbVausDBniwmBQAIUBA9wB09rSKH7Onxd4\n9tkoJEnduKxWgcmTo5gyJZLUVN/9tLqjvJOSIrBvn8iuXaqsx9GjAo4CVjIcPqzD4VA/m/R0kf/+\nN5IePWL47DMjdnsAL/ofTp8WeOqpKDp1iuGOO2K4/fYYunaNZeBAC7/+qkOWc7eFWrUk/vvfSPr2\njeaXX/R+NUuXL6s2VxxUqKDQpYvvEDxvnom5cyMK/FloZKeg64IoQpMmMlWr5rx3eL2we7fIzz/r\nOXYsb65X2Kc4A8mtt3pYtMhKWppAq1bSdT+I0oDRCJ07q06qIFBiI4lGI1mdbpMmOZAkdRHU6jtK\nLtHRCo0bS9lKEr7+OoJRo1y0aaPpqOWV/ftFFi40smBBBFeu+DYVUVTo3NnL6NFOOnTwEhWV9+dM\nSvLw4YcSKSm+RcPjERg/3kx0tMJddwU2Cr9zp45FiyKy3b53r54774xm7dr0XJ+jY0cvMTEyly6J\n3HGHhbffzmDQIDd//602jmVkCIwf72DAADc33RTQy/fDaFS1AJcv903knj7dRNu2Xrp0Kb0Bg5LA\nH3/oGDAgGkkSKFdO5vPPbbRvf+O1KM+jnkoa2qinvHP8uMjq1Xr27tVx771uWraUstXraGiUJPbs\nERk2zOLnBIDCmjVWWrXSHLS8cPasQO/e0Zw8eaPTl8KSJTY6d86fc7Bvn8jkyVFs2ODfCV+njsTq\n1ekB1Zg8elRg8GALx49nj0eYzQqrVqXTqFHukf+vvzbw8MOZJzeFmTMzWL9ezw8/+Jy/55/P4LHH\nXBiKsMHfZoNp0yKZO9eUdVvDhl6WL7dq9WghzNNPR/LRR77PzGxWWL06Hafzz+vqoOleeOGFF4rp\n+oqVY8eOkZCQEOzLCHkuXBAYPdrMvHkmdu/W89VXRvr0cVOxYlj67RqlAI9HLaBPSvLQsKGEwQA1\na0pMn+6gZUupSDfPcEKvhwoVZDZsMODx5Hxi69rVy5AhbsqUyd96UaGCQu/eqv6U0ajgdgtUqKDw\nzDMOGjeWAxqRL1sW+vb10LSphE4Her1ChQoyI0a4mDbNkWdB0YoVFfbv13H0qA4QWLXKwLBhbo4f\nF7MkTbZs0XPnnW5uuqno1k+jERITJXbv1mU5zxcvitx+u0fTCQxhdu/W88svvsXH4xG4+WaJChVO\nUatWrRwfE/YRtM2bN5f4bq2iZMMGPYMG+bcnffqpjQEDSk6xf17RbCHvZGRAerpQYhb8S5fUBfDH\nHw3s26fn7rtd3HGHOyuiIMtkk8MpCnuQJLXjLyNDwOtVX1cQVEmEcuWyd5KGOooCx46JHDkicvmy\nOjs2MlJNI1evLlOrlkRsbOFeQ5bBbldfqyCK7vlBUVTbVhR/mYq82sKxYwJDh1o4fFiNxun1Cq+8\n4uCVV0ykp6sG9sMP6XTqVPRR2uPHRWbNimDePFX+adWq9GJP30tSyS1vuR5FtU/88YeOpKRoFMW3\nCDz+uIP+/X8t3CQBjfAlpw4gOXTr/DWKgUOHRCZNimTvXj3ff2+lfv3QNojkZLV+ad063+n099/1\nNG/uzeq8LkqtwrQ0tfD9wAEdS5YYOH5cx7lzIjYbKIqAIChUqSLTvLnE4MFu2rTxlpgItSCoIrdF\nOTFFFItPwkIQKFSHXc2aCvPm2bn99mguXxbxegVefdXExIlOJk+OxGCgSKNnV1OjhsyLLzoYNsyN\n1SpQt27xOmdXrsDLL0cyYoSbm2/WygZyo2lTiVmzMhg3LrOBSaFTpxuXBoR9BC0/SBL89psq/Nig\ngUTDhnKJO/Hml2tnHhoMCmvXpuc57B/KXLmiLsZGY+731VA5ckRg0KBoTpxQj8Vz59oYODB0o6nn\nzws8+KCZzZv985axsTIbNliLvKs4OVlgypRIli7NXoSeEzqdwrJlVtq21Ta0ksxff+kYONBCWprq\n+ffq5aZ2bYkOHbz06uUN6kitixcFNm7Uc/GiSI8eniLTpty2TUffvjFUq+Zl5UobCQlh6UoEFI8H\n/vc/HceOiVSsqNCihZcDB64/izPsZTbyw5EjIoMGRfPggxZ69ozhl1/0YS9E27ixRPfu6gas0ynM\nmmUv8QrkbjcsW2agV68YRo40s2ePZuZ5QZbV2XSZzllJ4O+/ddmcM1FU+PDD4pF8EQSoVEnBZLrx\nQlGzpsSzzzpYs8ZKy5aac1bSuflmiW+/tVG+vGpja9YY6d7dS9++wXXOQB3i/dBDFiZNimLYMDMn\nTxZNlOHyZfV5T5zQs2dP4NaMjAz4808df/2lIyMjYE8bEhgM0KKFxKBBHjp18uYazQ37FGd+8slp\naULWpHuHQ+Duuy2sWWOlcePwXVATEhTefdfOkSMiZcoo1K0b2ALdYPD33zpGjjSjKAJHjuj4+28d\nS5daOXHiF60G7QYcPy4yc6bJ77b4+OA7606nGgXNKU157QEqIUHm3XftdOyYe1dhIGpNqlVTmDbN\nwSOPuLh4UeDKFQFJUq/VYFA7tSwWhbg4RdPWK2ZkWY2w6vXkOnqnILbQooXEsmVWJk2KYv16A2+8\nYaJtW1tQJXpSU+Hjj33f4aNH9ezcqadq1cBHwe12n+P32WcRdOsWGOd0xw5VjgLgmWecPPyws9B1\njvkhlGqVw95Byw/lyytERSlkZKiG53QKfPaZkddec4T1vM24OIW4uPBxQk+eFP0KMU+e1LF3ry4k\nRrWEMkeOiFm2D1C7tpc6dYLnoHk8sHSpgTlzTNx8s5eHH3ZlS9e0aOHl+++tnDsnULGiQt26UrGP\nDjIa1cHJ1asX68tq5MJvv+m4914LZrPC2LFO+vYNfJdjvXoyc+bY2bJFz5dfGklLE7BYgueIOxxC\ntokZ27bpi6Tp62pnbOtWPefPC1SqVPi/fdMm3/i96dMjqVVLYvDg0C2zKErC2O1QyfSE3W41N3+1\nAvS1VK0qM2qU0++2r76K4PTpMC9ECzP0+uyLhM0mhMypKFS5+kQM8PLLDipUCN5mc+CAyMMPm9mx\nQ88nn5gYMsTMkSP+S1ZsLHTp4mXIEA9du3rz5Zxp9hDebN1q4NIlkRMndIwfb2bsWDOnTuW8lhfG\nFipWVBg40MOCBfagzxWNiVGoV8//sB0VVTTXFBPje94rV8SAjZy6NtI8aVLUdT+3oiCU1oWwd9BA\nbRN/9tlIunWL4cEHzWzbpsOTg0Ou18PIkS5q1/alR2w2bujUaYQe9epJ2eamlpSuuWASG+t7j556\nykGbNsFVJr9wQcwa1wSQnKxn6VJNxCyTv/8WeeutCObONfL77zpt3M81JCb62+/atQZefTWStLT8\nPY/DAdu36/joIyMTJkSyfLkBmy37/SLy1idSpJjN8PjjLr/bWrcumu/xtY5UWlpgnKgGDfwdzIsX\nRVJS8uaqOJ0U6UzX4ibsHbTNmzezcqWBefNMpKSILFtmpH//aLZsyTm7W6uWwpdf2klKcgMKo0a5\ntO6UEkbt2gqff26nXDkZUBg92kHjxl5t9mIuNG4s8e67Nr7+2spjjzkDquZeEKKilGyD7L/7zpjj\n5lgQSro9zJgRyUsvRTFhgpmkpGhef93E2bNatD+Txo0l6tf3d04WLYrg0KHsRbbXs4WzZwWmTzfR\ns2c0Tz9tZu5cEyNGWLJFckOJ9u09vP66nSpVJCZOdBRZU0r58jJ9+rh57jkHzz3nyDHoURAaN5Zo\n1cr/ya4uvbgeZ84IjBljZt48I1ZrwV8/lNaFUlGDdvq0/5dJlgX+/W8z69al5xhZqVtX5sMP7Vy8\nKFCmjEJkZHFdqUag6NjRy88/p2O1ClSpImuzNfNAhQoKw4aFTq2HJMHQoW4WLvSFJvT6otU0K0nU\nqnX1xiswc2YkR4+KzJjhyLUovjRQpYrCJ5/YGTrUwqlTPqfs1CkxT+O+UlPh1VcjWbDAPzRmMin5\nmj1a3MTGwoMPurnjDg+xsUqRTc6oWFGhaVMvr7wShV6vMHOmhCxLhf5+li+vMGtWBnfdpX5u0dGq\njmBu7NqlY8kSI0uWGKlTR6Zr15I/mzTsl7qOHTvSr58bQfBfsE6fFrDbr/84iwVq1FC02WYlmMqV\nFRo08DlnoVRboJE7Fy+KmEwwZIgLQVAwGBSmTHEEbHMs6fZwxx3ubPIeS5dGsGNHCW/DDiANG8p8\n/72NBx90YjKpHbVVq2bf7HOyhb17ddmcM1B46y07tWsHv7s5N8qXLzrnDODKFSGrY9TrFXj8cTO7\ndwfG9urXl1m61MaiRVaWLLHmSctt3z7fa7/4oinfqexMQmldCHsHDaB5c4nZs+0YDL7FbPBgt3bK\n1NAIYWQZ5s2L4ORJkWefdbJsWXquytulicREmW+/tRIT4795rVmj1eldTe3aMv/5j4OtW9PZsiWN\nFi3ylvKz2fzTamazqq93222eYo/iejxqzeHly8X7ujfiwgWBxx930rWrGnX3eAR++ilwtle9ukyv\nXl6aN8/b53X+vO9D+esvPWfPlnz3JuxTnJmaJkOGeGjePJ1jx0QiI6FRI0mTXShlhJK+Tahz4YLA\nN98Y0OmgbVuJ+vUlTKbcHxdIKlZUHY+tWw1IEowa5QyoRl9JtwdBgFtukVi92sp770WwZIkRSRLo\n1i100tRFRVoabNtmQJYVmjWTcpV30OnUDf965GQLzZpJvP++jYMHdTRqJNGokUS9esGJnJ06JdKj\nRwzt23t580071asHN7hw+rTAqFFmDh/WM2GCg3371PFmW7cGL3rrL0wtcOGCQP36+X+e/K4Lu3fr\n+PFHAxcvCrRrJ9G+vYdq1QLz+YS9g5aJTgcNGsg0aBD6oelgkp6udr0mJ+tw/qM4EhEBlSurg5HL\nlQvu9WkUDw4HvPhiFC6XOkvy/vtdjB3rolq14vv+1KghU726l1OndEyZ4gh600KoUr++zIwZDiZO\ndCJJBESLKtT53//0DBum1i60aOHh44/t1KgR2L87Pl5hyBAPEHyH1+0Gl0tgwwYDTzxhZvZse1A/\n5337dFkD4+fOjWDECDczZ5qwWFTx6GCMSKxa1T/Sdm0EtCjYt0/kttuisVrV1/r8c6hXz8sXXwQm\nDR72DlpJPiEXN8ePi0ycGMnatT6hwKtp0sTLnDl2GjUqmU6uZgt5p1IlhUcfdfLmm5EoisAnn5jY\nvFnPvHl2GjYsns+/UiWFhQvtZGQING0a+E60cLIHna50OGaZXLjgW5927DAweXIk776bUWDF+VC3\nhbJlFRISZM6cEdm40cC33xp59FFX0Bpmrq41u3xZxGSSEQSFhx5yBW1+tdpIoJC5dxU02p4fWzhz\nRsxyzjI5eFDPunV6atcuvD5XyU/SagSMgwdF1q41kpNzBuqp9eqOOo3wRa+Hf/3LRUKCzxk7eFDP\nwIHRxTrbtEEDmRYtpKDPNyxu3G51JqHTCV6t7C4bmenvTFasiGDPnvA1kgoVFHr39m34r74ayb59\nwdu+09P994jERIl166xB1U6sU0dm+PDM90ghLq7oD5JVqshER2c/GJ05E5jPJuwdtFDSNAl12rTx\nMnu2nerVs0crLBaFRx5xZpu0UJLQbCF/1KihsHixlYQEnz2cPy9y333XV2QvSYSSPUgS7Nkj8t13\nBqZNM3HnnRb69o2mf/9obrstmgcfNPPSSyYWLzby22+6Uj/dpGZNmUqV/Dfg338veP1TKNlCTgiC\nKjmTicsl8O23RuQgJTOuFamNilIHyBuNwbmezGsYO9ZJkyZeRo50X1OTlndys4X0dFW4+MoVddTX\nN99Y/dKrlStLDBkSGHX78D1yaOSbMmXgnnvc9OrlISVFwOEQkGV11mCFCmp7uqZBVbpo3Fjm229t\njBlj5q+/1OXi6FE9y5cbefhhVy6P1sgre/eK9O4dg8uVN8erfHmZF15w0Levu1RKAVWqpDBzpp0h\nQyxZc3f37w9veZEGDSS6dvWwcaPaKfn++ybuvtsdlMaFa29beQEAACAASURBVBsurh77FEzq1pX5\n5hsbOp1CTEzgnz8jA2bONPHWW5G8+66NYcM8tG4tsWqV9Z8Z0GpULVAjvwRFUULjnQ0w69ato0WL\nFsG+DA2NsODUKYGFCyN4+20TDodAw4YSq1ala53QAcLphL/+0vHZZxGsXGkgPT23k5DCkCFupkxx\nlKras6txOmHpUgOPPWbG4xGYM8fO3XeH91y+P//U0bt3dJZT+uWXVpKSCpdWdDohOVnkwgWBmBiF\nGjXkXJ2bI0cEunWLxWYTqF/fy/LltmxRtXDkt9909OkTDQg0bepl+XIrZnPhnnPHjh306NEjx99p\nEbRSRGqq2n1z9KiOiAiF9u29pXZx18gfVaooPPWUk9tvd3P4sEhsrDZhI5CYTNCunUTr1hmcOSNw\n5oxIerpARobgN1/QZIKyZWXi4tSIdmE3h5KMyQR33umhUaN0UlOFbEPCC8rvv+tYvNjI7bd7aN3a\nG1J23rixxMSJTl57Tb2ow4d1QMEdtNRUNRL33/+akGUBUEhK8vDKKw5q1rx+ZE4dp2fj5ZcjeeON\njFLhnAEsXuyr0T50SMeVKwJmc9H97WHvoJV0raNAceiQyMsvm1i61Ffkv3ixlUqVSk8FsmYLhUMU\n1ZqLYGlBBZpQtAedTnWGq1QJo4nPAWb/fpGjR3W0aOElPl4hMbHw9phpC5IEb7xhYt06I/PmRfDy\nyw7uu88VMqOdTCYYNcpFSorIggURpKYWrhZx1y49r79+tQcqsGqVkebNJSZMuHG9cdeuXtq0sYbM\ne1NQLl4USE4W/5GokTl+/Jcc14Xz5wXWrPEV2ZnNSpE3L4W9g6YB//ufyLBhFk6f9tVoCIJSLJMU\ndu7UYTQqJVaaQ0NDI7Q4d07kX/+y0KmTh5kzA6t/Jopc5XAITJ4cSWKiFFJzHcuXV3j+eQe9enkK\nrUvovk5G+NChvBUbl3TnLDlZncu9ebNa11e+vMy4cTrat88+89dqxa85p2ZNidjYot1Dw77kO9RO\nyMXNmTMC//d/Zj/nDOCxx5w0bFi0p3S3W52JlpQUw19/Bd/USrstBJuzZwVWr9azcqWBK1eCfTWa\nPZRUEhJkDAaFX34x8MADFo4eLXxHa6YtCAJ07361MK3A449HcuZMaHXNVqig0L+/p9D6gI0bS3Tu\n7C/Ea7EojB5dOhqAtm/XZzlnoM7/femlPuzdm32/ysgQuFqC6rbbPEWe/g7+rqlRpPzvfzoOHvQP\nlD7wgJNHHnEVy+gep1PAbhcYM8ZMSkpoLXIaxce+fSJ3321h2LBohg+3cORIeHfcaRQdNWvKDBum\nOhB//aVn4kSzn3BtYenQwYvF4ouMnDih53//C097TUhQ+OADO99+a+XNN+3MnWtjzZr0PM+/LOnk\nNEze7RY4cSK7axQTQ9Y8b0FQuOWWoo+qhr2DFgh9G0mCbdt0TJtmYubMCDZt0ofU0NobcbWq8003\nycybZ2PyZAcJCUWf3jQayTrh7d+vZ+nSIIrkEPpaR+HKsWMiI0ea2b3bd1AIltr41Wj2UDIxGGDY\nMDeqajysX68q63sKMZHpaluoU0dmxgy73+/VYvzwJC5OoVs3L/fd52bgQE+pGofYrJmXZs38HS29\nfkOOzXMVK8r07q0a2dixTho1KnonVqtBywNHj4rcfns0Ho9vV+nWzcN//2unZs3Q7l5p3drL6tXp\ngDpPs7i7Nlu29PLRR+q/X3/dRFKSp8ACghr5w+VSx3dJElSrJmOxFP81ZGTAhx9GZM3tA7XO41qR\nUQ2N/NCkicSoUS7mzlXTAJMnR9KqlZdWrQKzad56q4cnn3Tw5psmQCA8xag0qlVTmD/fxrp1Blav\nNlCmjELz5hk0a5bdjiIjYcoUByNGuLj5ZqlYMlCaDloeOHZMpGPHGBwO/2N/8+YevvjCTnx8WL6F\nAeF//xPp0iWGzNz9vHk2br89+MOHSwOLFxsYM8aMosDdd7uZONFZ7M7xzp06evRQdYMymTvXxsCB\nmg1oFI7Dh0V6947myhU1EdSsmZdFi2zExQVmPbbb4c8/9ezYoaNvXw/162uHCo3AcyMdtLBPcQaC\n6tVlXn/dTmZIPZOdOw1hr15dWGrWlGnXzhdC/uijCOz2GzxAIyCcPi3w7LNR/whaCixaFMGkSZGk\npam/d7th926R7dt1XLpUdNeRnCxytXM2ZIiLLl0050yj8NSpI/Phh751edcuPb/+GrikkNkMXbp4\neeIJl+acaQSFsHfQAlFnIopwxx0ePvzQ7lc8CgoREVr07EZYLGq+PpNff9Vz7FhwzK601RxdGxtf\ntcqYVUuzbZuebt1i6Nkzhocf9nXCud2qWvnChQZ+/VWPzVa4a7i6LmjAABeTJjkoV65wzxkoSps9\nhCO33OL10+t67TUTly7lv8BRswWNTELJFrQatDxiNsPgwR6aN0/n6FGRK1cEqlWTc8xVa/jTtKlE\nQoLMmTNqNOX0aZHGjbUTaVGSkKDwwAMu3nrLvw/88mV18/rhB0PWuJj16w08/riZTz6xsXu3nrvu\n8s03nD3bxj33FDzi1bKlxHvv2YiPV2jWzFsq50ZqFB1RUXD//apw65dfRnDwoJ4DB0Tat9fWZY2S\nT1g7aHv2iFy+3I01axTq15ezDXgtCLVry9SurTkX+aFSJYUZMzK45x61Sv3SpeBE0EqT7pUgwIgR\nbn75Rc+ff6q95FFRSpaw5bXNIps3Gzh+XMeLL0ZmOWcAL7wQRdeu6QVuLqlVS6ZWrdD8vpQmewhn\n4uMVpkxxYLEofPihiZQUEcifg6bZgkYmoWQLYe2g3XprDG63utlUrizx3Xc26tYNzc2iOMnIgIMH\ndSQni3i9UKWKGgksyq6Ujh09PPSQkw8/NJGeHgIaC6WAGjVkPv/czvbtei5dEmjSRMoa09ShgwdQ\nO9QyuXRJ4MgRHcOHu6hXT2LHDj0//GDEalVn9GlohCoVKyo8+6yDPn08lCunrfEa4UFY16CpztlG\nAFJSdPz0Uw6qdKWM06cFXnvNRPfu0dx/v4X/+z8LffpEs2FD0frqmbVozzzjoGnT4IxNCaXaguIi\nPl6hXz8P997rpnlzKUt/rGlTdejy1ej1Cv36uShXTmHq1CgqVZLp2tVdLCPBgkFptIdwJjZWLepv\n0iT/DppmCxqZhJIthHUE7VqKerBpqKMoMG9eBLNmXTufQuDPP/X06VO0jlOlSgpPPeVEV4DGV7td\nrQPUCAxRUTB6tJP69SXefz+CevUk6taVePRRFyNHqqnozz6L4Ouvrdx0U3g6aBoaGhqhTClwWboC\nUK6cTKdOpbu9/8oV+Pbb7Gr+er1Cnz7F897k1zk7cUKViFi2zEDTphL33eeieXOpQE5eKNUWhAKx\nsTBwoIe+fT3o9epnc/CgKm4L6uy5K1fCNx2t2YNGJpotqNhs6vf//HkRu12dBlO9ulpHagzuIJhi\nI5RsIawdtE8/tfH77zpq1ZLp1Mlb6uvPypSBp55yMnZsVFYheL16XmbOzAjZ2WuffRaR1Ym4Z4+e\nr74y8uOPVtq1u/71nj8v8McfeqKj1c7B2NjiutqSSUSE79+yDFfXpakF1xrFQUYGpKYKWK3qfw6H\nOtYoLk6hZs3SvXZpFD0HDoi89pqJJUsi/G7X6xXmzLEzeHDpDnAEg7B20AYM8FCu3Iage8Rnz6rD\nV69cETAYICFB7SiNigrs67hc6onnenMORREGD3Zz881eUlMFoqLUEUChmsKSJNi61d9EvV6BqVMj\n+e4723VTnt99Z2DSJPWXTz/tYOxYJ5GRam1BsG0h1DEaFdSGANWIDh0KXyHmYNqDLMO5cwLnzomk\npIhs26b7p5NWJC3N5xS3aOFh1qyMoFxjaaK0rw3nzgmMHGnm4MHsLoHXK/DFFxH06+ch8trqmAJw\n7JjI3r0ikZHQqJEUcpN4QskWwtpBCwV27NBx//1mTp70bXSCoHDPPW4mTHBQrVrhjfPiRYGNG/V8\n8kkEdepIPPWUk+rVc37eiAho1KhknMZ1OtWh3LbNv7nj0iURtzvnmrT0dJg/39eO+tprJrp08dww\n4qbhw2JRGwvOnlUdNLWDUyMQXLmiRiSPHdOxcqWBn34yXEdyRqFFCy9PPumiRQtvyG1gGuGHLGdG\nz7NTvbqXadMyAuKcHTokMmiQhVOn1P2wc2cPH3xgD9h4rnAj7B20YHrCViuMHx/p55wBKIp6Irn5\nZi+jRrkL9Rrnzgk891wk332nhqW3bTPQq5eX6tXDIxzdr5+HHTtcfPml+vcJgsL48Q7Kls35/tmj\nhwJLlhhp184RMqeiUKZcOYV27bwsWaIWnCQklAxnviAUhz2kp6tRyC1b9CxYEMHhw/6jr66mbFmZ\nRx5x0b27hzp1JC01X4yU9rUhIUFh4UIbv/9uYMUKAzodNGwo0bSpl2bNpALrIF7Ltm36LOcMYNMm\nA9u36+nbN3T2q1CyhbB30IJJVBQMH+7mr79ykvdQAjK4+qefDFnOWSbXOwmVROLiFF59NYORI11c\nuCAQF6fQuPH1o2HR0dCpk4d9+3yLwM6detxuSk2Ra2HQ62HkSFeWg9a6dXAkUUo6x4+L7NqlY/bs\nCLZv15OTUyaKCq1bexk61E39+hLVqslUrqxFEjSCQ+3aCrVruxk2rHBBgxtx4kT2iPHJk1qd6/UI\newctmPlknQ6GDnVTr57MypUGNm/WIwiqA9G/v6fQY6LOnhV45RX/uHNEhEL9+uGVzouJgdat8/43\n3XWXm48/jkCW1U3RYpERxdCqLQhlmjTxMmKEi23bdDRqFF62dDVFYQ9XrsDatQYmTozyqyUD9bvZ\nqpWX225zU7euTJUqMpUrB74WVSP/5NUWjhwROX1aoH59mYoVS5Yzff68gNWqivpGRwfnGtq2zX7g\nq1EjtNaYUNonwt5BCzYWC3Tq5KVTJy92u3pboPS87HY1xXk1r72WQZ06YRRCKwBNm0q89VYGT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3n5mVKw1IWnBTI4wJewdNqy0omaSmqurOVyPLhdsti9sWmjWT+PJLOz17egutf3TsmMgrr1w9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\nq50iTiecOKESGiq8mgPK6YQVK9ynMe+5p5TERO3H17mzi5dfLsHlqrpV2Rs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+ "text": [ + "" + ] + } + ], + "prompt_number": 20 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Priors\n", + "\n", + "Each sky has one, two or three dark matter halos in it. Tim's solution details that his prior distribution of halo positions was uniform, i.e.\n", + "\n", + "\\begin{align}\n", + "& x_i \\sim \\text{Uniform}( 0, 4200)\\\\\\\\\n", + "& y_i \\sim \\text{Uniform}( 0, 4200), \\;\\; i=1,2,3\\\\\\\\\n", + "\\end{align}\n", + "\n", + "Tim and other competitors noted that most skies had one large halo and other halos, if present, were much smaller. Larger halos, having more mass, will influence the surrounding galaxies more. He decided that the large halos would have a mass distributed as a *log*-uniform random variable between 40 and 180 i.e.\n", + "\n", + "$$ m_{\\text{large} } = \\log \\text{Uniform}( 40, 180 ) $$\n", + "\n", + "and in PyMC, \n", + "\n", + " exp_mass_large = pm.Uniform(\"exp_mass_large\", 40, 180)\n", + " @pm.deterministic\n", + " def mass_large(u = exp_mass_large):\n", + " return np.log(u)\n", + "\n", + "(This is what we mean when we say *log*-uniform.) For smaller galaxies, Tim set the mass to be the logarithm of 20. Why did Tim not create a prior for the smaller mass, nor treat it as a unknown? I believe this decision was made to speed up convergence of the algorithm. This is not too restrictive, as by construction the smaller halos have less influence on the galaxies.\n", + "\n", + "Tim logically assumed that the ellipticity of each galaxy is dependent on the position of the halos, the distance between the galaxy and halo, and the mass of the halos. Thus the vector of ellipticity of each galaxy, $\\mathbf{e}_i$, are *children* variables of the vector of halo positions $(\\mathbf{x},\\mathbf{y})$, distance (which we will formalize), and halo masses.\n", + "\n", + "Tim conceived a relationship to connect positions and ellipticity by reading literature and forum posts. He supposed the following was a reasonable relationship:\n", + "\n", + "$$ e_i | ( \\mathbf{x}, \\mathbf{y} ) \\sim \\text{Normal}( \\sum_{j = \\text{halo positions} }d_{i,j} m_j f( r_{i,j} ), \\sigma^2 ) $$\n", + "\n", + "where $d_{i,j}$ is the *tangential direction* (the direction in which halo $j$ bends the light of galaxy $i$), $m_j$ is the mass of halo $j$, $f(r_{i,j})$ is a *decreasing function* of the Euclidean distance between halo $j$ and galaxy $i$. \n", + "\n", + "Tim's function $f$ was defined:\n", + "\n", + "$$ f( r_{i,j} ) = \\frac{1}{\\min( r_{i,j}, 240 ) } $$\n", + "\n", + "for large halos, and for small halos\n", + "\n", + "$$ f( r_{i,j} ) = \\frac{1}{\\min( r_{i,j}, 70 ) } $$\n", + "\n", + "This fully bridges our observations and unknown. This model is incredibly simple, and Tim mentions this simplicity was purposefully designed: it prevents the model from overfitting. \n", + "\n", + "\n", + "### Training & PyMC implementation\n", + "\n", + "For each sky, we run our Bayesian model to find the posteriors for the halo positions — we ignore the (known) halo position. This is slightly different than perhaps traditional approaches to Kaggle competitions, where this model uses no data from other skies nor the known halo location. That does not mean other data are not necessary — in fact, the model was created by comparing different skies. \n" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "def euclidean_distance(x, y):\n", + " return np.sqrt(((x - y) ** 2).sum(axis=1))\n", + "\n", + "\n", + "def f_distance(gxy_pos, halo_pos, c):\n", + " # foo_position should be a 2-d numpy array\n", + " return np.maximum(euclidean_distance(gxy_pos, halo_pos), c)[:, None]\n", + "\n", + "\n", + "def tangential_distance(glxy_position, halo_position):\n", + " # foo_position should be a 2-d numpy array\n", + " delta = glxy_position - halo_position\n", + " t = (2 * np.arctan(delta[:, 1] / delta[:, 0]))[:, None]\n", + " return np.concatenate([-np.cos(t), -np.sin(t)], axis=1)\n", + "\n", + "import pymc as pm\n", + "\n", + "# set the size of the halo's mass\n", + "mass_large = pm.Uniform(\"mass_large\", 40, 180, trace=False)\n", + "\n", + "# set the initial prior position of the halos, it's a 2-d Uniform dist.\n", + "halo_position = pm.Uniform(\"halo_position\", 0, 4200, size=(1, 2))\n", + "\n", + "\n", + "@pm.deterministic\n", + "def mean(mass=mass_large, h_pos=halo_position, glx_pos=data[:, :2]):\n", + " return mass / f_distance(glx_pos, h_pos, 240) *\\\n", + " tangential_distance(glx_pos, h_pos)" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 20 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "ellpty = pm.Normal(\"ellipcity\", mean, 1. / 0.05, observed=True,\n", + " value=data[:, 2:])\n", + "mcmc = pm.MCMC([ellpty, mean, halo_position, mass_large])\n", + "map_ = pm.MAP([ellpty, mean, halo_position, mass_large])\n", + "map_.fit()\n", + "mcmc.sample(200000, 140000, 3)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + " \r", + "[****************100%******************] 200000 of 200000 complete" + ] + }, + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "\n" + ] + } + ], + "prompt_number": 21 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Below we plot a \"heatmap\" of the posterior distribution. (Which is just a scatter plot of the posterior, but we can visualize it as a heatmap.)" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "t = mcmc.trace(\"halo_position\")[:].reshape(20000, 2)\n", + "\n", + "fig = draw_sky(data)\n", + "plt.title(\"Galaxy positions and ellipcities of sky %d.\" % n_sky)\n", + "plt.xlabel(\"x-position\")\n", + "plt.ylabel(\"y-position\")\n", + "scatter(t[:, 0], t[:, 1], alpha=0.015, c=\"r\")\n", + "plt.xlim(0, 4200)\n", + "plt.ylim(0, 4200);" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "display_data", + "png": 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ixAm2bdvGkCFDspiTMiphwcHBGI1GPvnkE06dOsWaNWt49tln3VZr0pSu/v3789BDDzFn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\n+CsAAAAASUVORK5CYII=\n" + } + ], + "prompt_number": 20 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The most probable position reveals itself like a lethal wound.\n", + "\n", + "Associated with each sky is another data point, located in `./data/Training_halos.csv` that holds the locations of up to three dark matter halos contained in the sky. For example, the night sky we trained on has halo locations:" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "halo_data = np.genfromtxt(\"data/Training_halos.csv\",\n", + " delimiter=\",\",\n", + " usecols=[1, 2, 3, 4, 5, 6, 7, 8, 9],\n", + " skip_header=1)\n", + "print halo_data[n_sky]" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "[ 3.00000000e+00 2.78145000e+03 1.40691000e+03 3.08163000e+03\n", + " 1.15611000e+03 2.28474000e+03 3.19597000e+03 1.80916000e+03\n", + " 8.45180000e+02]\n" + ] + } + ], + "prompt_number": 13 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The third and fourth column represent the true $x$ and $y$ position of the halo. It appears that the Bayesian method has located the halo within a tight vicinity. " + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "fig = draw_sky(data)\n", + "plt.title(\"Galaxy positions and ellipcities of sky %d.\" % n_sky)\n", + "plt.xlabel(\"x-position\")\n", + "plt.ylabel(\"y-position\")\n", + "plt.scatter(t[:, 0], t[:, 1], alpha=0.015, c=\"r\")\n", + "plt.scatter(halo_data[n_sky - 1][3], halo_data[n_sky - 1][4],\n", + " label=\"True halo position\",\n", + " c=\"k\", s=70)\n", + "plt.legend(scatterpoints=1, loc=\"lower left\")\n", + "plt.xlim(0, 4200)\n", + "plt.ylim(0, 4200);\n", + "\n", + "print \"True halo location:\", halo_data[n_sky][3], halo_data[n_sky][4]" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "True halo location: 1408.61 1685.86\n" + ] + }, + { + "metadata": {}, + "output_type": "display_data", + "png": 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ixAm2bdvGkCFDspiTMiphwcHBGI1GPvnkE06dOsWaNWt49tln3VZr0pSu/v3789BDDzFn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\nixKIWnlWGwAAAABJRU5ErkJggg==\n" + } + ], + "prompt_number": 24 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Perfect. Our next step is to use the loss function to optimize our location. A naive strategy would be to simply choose the mean:" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "mean_posterior = t.mean(axis=0).reshape(1, 2)\n", + "print mean_posterior" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "[[ 2324.07677813 1122.47097816]]\n" + ] + } + ], + "prompt_number": 25 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from DarkWorldsMetric import main_score\n", + "\n", + "_halo_data = halo_data[n_sky - 1]\n", + "\n", + "nhalo_all = _halo_data[0].reshape(1, 1)\n", + "x_true_all = _halo_data[3].reshape(1, 1)\n", + "y_true_all = _halo_data[4].reshape(1, 1)\n", + "x_ref_all = _halo_data[1].reshape(1, 1)\n", + "y_ref_all = _halo_data[2].reshape(1, 1)\n", + "sky_prediction = mean_posterior\n", + "\n", + "print \"Using the mean:\"\n", + "main_score(nhalo_all, x_true_all, y_true_all,\n", + " x_ref_all, y_ref_all, sky_prediction)\n", + "\n", + "# what's a bad score?\n", + "print\n", + "random_guess = np.random.randint(0, 4200, size=(1, 2))\n", + "print \"Using a random location:\", random_guess\n", + "main_score(nhalo_all, x_true_all, y_true_all,\n", + " x_ref_all, y_ref_all, random_guess)\n", + "print" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Using the mean:\n", + "Your average distance in pixels you are away from the true halo is" + ] + }, + { + "output_type": "stream", + "stream": "stdout", + "text": [ + " 31.1499201664\n", + "Your average angular vector is 1.0\n", + "Your score for the training data is 1.03114992017\n", + "\n" + ] + }, + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Using a random location: [[2755 53]]\n", + "Your average distance in pixels you are away from the true halo is" + ] + }, + { + "output_type": "stream", + "stream": "stdout", + "text": [ + " 1773.42717812\n", + "Your average angular vector is 1.0\n", + "Your score for the training data is 2.77342717812\n", + "\n" + ] + } + ], + "prompt_number": 25 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "This is a good guess, it is not very far from the true location, but it ignores the loss function that was provided to us. We also need to extend our code to allow for up to two additional, *smaller* halos: Let's create a function for automatizing our PyMC. " + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from pymc.Matplot import plot as mcplot\n", + "\n", + "\n", + "def halo_posteriors(n_halos_in_sky, galaxy_data,\n", + " samples=5e5, burn_in=34e4, thin=4):\n", + " # set the size of the halo's mass\n", + " \"\"\"\n", + " exp_mass_large = pm.Uniform(\"exp_mass_large\", 40, 180)\n", + " @pm.deterministic\n", + " def mass_large(exp_mass_large = exp_mass_large):\n", + " return np.log(exp_mass_large)\n", + " \"\"\"\n", + "\n", + " mass_large = pm.Uniform(\"mass_large\", 40, 180)\n", + "\n", + " mass_small_1 = 20\n", + " mass_small_2 = 20\n", + "\n", + " masses = np.array([mass_large, mass_small_1, mass_small_2], dtype=object)\n", + "\n", + " # set the initial prior positions of the halos, it's a 2-d Uniform dist.\n", + " halo_positions = pm.Uniform(\"halo_positions\", 0, 4200,\n", + " size=(n_halos_in_sky, 2)) # notice this size\n", + "\n", + " fdist_constants = np.array([240, 70, 70])\n", + "\n", + " @pm.deterministic\n", + " def mean(mass=masses, h_pos=halo_positions, glx_pos=data[:, :2],\n", + " n_halos_in_sky=n_halos_in_sky):\n", + "\n", + " _sum = 0\n", + " for i in range(n_halos_in_sky):\n", + " _sum += mass[i] / f_distance(glx_pos, h_pos[i, :], fdist_constants[i]) *\\\n", + " tangential_distance(glx_pos, h_pos[i, :])\n", + "\n", + " return _sum\n", + "\n", + " ellpty = pm.Normal(\"ellipcity\", mean, 1. / 0.05, observed=True,\n", + " value=data[:, 2:])\n", + "\n", + " map_ = pm.MAP([ellpty, mean, halo_positions, mass_large])\n", + " map_.fit(method=\"fmin_powell)\n", + "\n", + " mcmc = pm.MCMC([ellpty, mean, halo_positions, mass_large])\n", + " mcmc.sample(samples, burn_in, thin)\n", + " return mcmc.trace(\"halo_positions\")[:]" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 9 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "n_sky = 215\n", + "data = np.genfromtxt(\"data/Train_Skies/Train_Skies/\\\n", + "Training_Sky%d.csv\" % (n_sky),\n", + " dtype=None,\n", + " skip_header=1,\n", + " delimiter=\",\",\n", + " usecols=[1, 2, 3, 4])" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 10 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# there are 3 halos in this file.\n", + "samples = 10.5e5\n", + "traces = halo_posteriors(3, data, samples=samples,\n", + " burn_in=9.5e5,\n", + " thin=10)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + " \r", + "[****************100%******************] 1050000 of 1050000 complete" + ] + }, + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "\n" + ] + } + ], + "prompt_number": 11 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "fig = draw_sky(data)\n", + "plt.title(\"Galaxy positions and ellipcities of sky %d.\" % n_sky)\n", + "plt.xlabel(\"x-position\")\n", + "plt.ylabel(\"y-position\")\n", + "\n", + "colors = [\"#467821\", \"#A60628\", \"#7A68A6\"]\n", + "\n", + "for i in range(traces.shape[1]):\n", + " plt.scatter(traces[:, i, 0], traces[:, i, 1], c=colors[i], alpha=0.02)\n", + "\n", + "\n", + "for i in range(traces.shape[1]):\n", + " plt.scatter(halo_data[n_sky - 1][3 + 2 * i], halo_data[n_sky - 1][4 + 2 * i],\n", + " label=\"True halo position\",\n", + " c=\"k\", s=90)\n", + "\n", + "# plt.legend(scatterpoints = 1)\n", + "plt.xlim(0, 4200)\n", + "plt.ylim(0, 4200);" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "pyout", + "prompt_number": 14, + "text": [ + "(0, 4200)" + ] + }, + { + "metadata": {}, + "output_type": "display_data", + "png": 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P8/rrHo2NcPzxpV6Vu+5KMW/e7p2Qur04/vjjd8q4nTuXErX163fPDP1UCvr2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ZzorqSriOIqpMzYKVkpPSvqd5x4Mlcj5ebLHFICnVyOByASku14HvgRkdagJCKU+K5PlM9Rdhzb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\nqFAmKHSigwC0wRQVyoCT9XAcD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/vtXmr2uDWxerXgC19o4KSTmrnooibOO6+J445r5rTT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oLKK10+rillVFqMwYWq4+D1HD70fqEQ011WG3gpYoPlnMWLCyTiHx2JA7QTVyfjRnLeStWR9H\nLYoj1xazWq0ZJSWwc6dCu3aSLl3qDrXSHLUacOSRkhEjDM48U2fEiHSQ1hqwZYvC2rXWhbeiwuJe\nffJJYp7oCgokt93moW9fS/R3xIjWH6SBxWvr0iU2KPN46l8uJwdGjqw+B0OGBDj/fCuw0HWorKx+\nY1i82M7OnYftpaVOdO4sw/SD3r11Jk2y9Fy8Xnj33Ug9e+FCJ19/nc5W1IaQCXnVrsxQJ6ZQRIOE\nbK3skFovry16O6Gyn2K3h4MkoapB7poe9tCMzoUomhbcTvVyZ005k9A669RDCwZ86SCtZqxerTJ/\nvoN//MPJokV2vv1WpaIiuduUEr77TmXGjCzGjMnl3/9uGrUqfSWoA5s3K6xapdG7t8FJJ6VuObA2\nrFq1ilGjRrX0MBKG6pkzwR13ZDB4cHmd2Zt452Hy5ADjxwfIy2vSMGuFaVqlwk8+0XA4oHdvg2OP\nNTjyyOQltTt0kPz1r5VccEEoNfMxubn1u3YccYRk/nw3X3+tsX69iqbBCSdY5eBQSa5jR8mtt3r4\nwx9iOy5yc806O2VTAS11bvzqVwavvlrBli0Kp5yih/mMDoc1b9F46ikHJ52kx81HbCxS4TrREKeA\nmOxXEGGV/GAZszEoKiqKex6EoqDYNJChLJ6CiR50JpBhPpqp+y2pDruGEiyHEuzQrGmdMd2qdWXQ\nkpw9S4VjIhE4eBB+9zsXGzdGHxOSceN0brjBwwknGHWqPTR2Hr74QuXcc7PxehPzG6UDtRogpVUy\nuvjiLPbuVbj6ak+rDNTaGrp3N+nXT2fdushhu26dxt69SjVB2MbAZiNpQRpYGcFJk7Lx+yMnb48e\nOo8/Xsnxxyfv+DrpJJ0HH3Qzd24Gp5zij5s836WLpEuXABBR8a2shNJSyM215mv6dB+9ehk89JCT\nnTsV+vQxuOUWLz16pBZXL1WgaTBmjM6YMbHvCwETJwb46KNIVPbNNxqlpaJNcNXqQgzJHitoq1Pe\noirJPkjKb06EAkKp65EMnATD78MMmEjTwDRBs1vX8l7j0gAAIABJREFUKhHKAIYtp8zqXZaKErZs\nChnPW0K6ka7LmHKq2nA5jsMN7drB1Vd7ue666CdHwYcf2vjoI41//tPNuecmhj4Twtq1ChdckBUT\npDW1QnPYctTqwjffqEyaFImGn3yygilT2pavks8H69apbN6ssHevQvv2Jj17mvTpY5CV1dKjqx3f\nfGM9qZSXh7r3JCtWlLUKM/nt2xVGjYrV8ALIyJD897/lDB6c3IeBvXsF2dmyXsmR2vDDDwq33ZZJ\nRQU8/nglvXpF5tzrtUqqLlf8HalpxGL9eoUJEyLHR/v2JsuXlyU145oKiNE9g3q5ZVW/b8lbtIy8\nUnTgJKXE8AcsSyjdkuHQMp0oqmV5ZXWXRpat6j8agjQMaz1RPqWK3WYJ8zZgnpobMZpyKVSKLSuD\n11+3M2dOJoZRdUyS994rZ+jQxFx79+wRXHqpi88/j6TpxowJ8OSTFfVqWKY5ag3Ali2CSy5xhYM0\nVbUaDdoSTBP+8x8bY8dmc8UVWfzhD5nMmpXFuHHZ/PGPGZSUtPQIa8fxxxssXlzGzJleTj45wFNP\nVbSKIA0svtjDD7tRlNgbr8cjePTRpqm1x4PCwsYHadu3Cy64IJtVq2ysWWPj3Xdj6wVOp/X0mg7S\nGo++fU2eeKICTbOOjwsv9LX5bBoQo2UWfl3P9y2ifcsGaRDhqknDCHLSguKzqmLZfwYNRePhvYVQ\nrXs1vLHmCXzKy+Ff/7Jz7rkuFi60s3u3iNF/qy23E2qGqEtHriWQkwPTp/v5+OMybr7ZwxFHRO4X\nmmZdfxOFb77RYoK07GzJvfdWNlloPB2oRcHthgULnDEyDTfc4E2oDERzojYNmIMHBffdlxEW3YzA\nkl/4/vvUeUqrCccea/KXv3h4/fUKxo6tP6WcKlo4YJW3Xn+9gq5dY8ednS1pjmtbY+di5Uobu3ZF\nLherV6f2MVIfUumYiMbYsTpLlpTz0kvl/O//+hpLt2oQUmEuYgzH4yjnCUWpXYi1CuIJMqDh8yBN\n03rqldLKIAGmXydQXonhtsqW0jDDfpgxumNK7V2cQlVBDcpuVLWnCgaodXmINhXr16vceOMXLF9u\nZ84cF1de6aJ4V3BbtZjYN1Yapblgs0H//iY33+xl2bIyliwp4913y1i+vIyTTqr9HtKQY8Lng6ef\njjyp2mySF18sp1+/pscPrftqm2CsWaPy1FORzEbnzgbTp/vbXJagoMAigc+a5aKqvHRWlox54khV\nNIEz3KKw2WD0aJ3Fiy1C+f79CpmZkoEDjZTdH68XXngh9iRoDcdIa4SmwXHHGRx3XEuPJILwjbmJ\n5ayw1VEt2aVk8K1kyMcTwkFGSPsrHlJ+dDkvOjCSUWVIM6CDEJiGgaKqSJuKUFRQFKRJhJemxar/\nh+ejqj2TaaIoKqZWvXu1MTZRDUVZWTASDGLFChvvLrZz+aW1BzRCCGSU5lsquxYcdZTkqKMS/1Rc\nXi7YsMH6HTt2NHn88QpGjEjMdtIctSD8fpg9O5PXX7cCNbvd4g0NGZI6KdxEwuu12oc/+MDGihU2\nbDbJaafpTJgQYMCAtrnPaTQOJSUwblwO27ZFbiZPP13B2We3Ld5mcyIQsPSVAgHo1Cl1u2Tj9bys\nD1X1zRpSCmwKqnWIBvchejy1csWCgrXSMIMNCwLFbg92dloSHIFKTzBrpqBoVtem6fMjhIJUQdVs\nKHab1RRgjwRq1Xh2wTFIKTF9/uB71vnW3B6a69dbXFrTjGyzc2eDD5cc4oh8s9b5goimW1tpcghr\nCccx/boOq1ZplJcLBgww6NatYQ+zdXHU0hm1IHbsUHjrLStroCiSxx5zJ7UTr6XhdMLQoQZDhxr4\n/Zb3XlvLHKaRGDgckJdnAtaNo1Mng8GD24bOXHMjpK/0xBMOXn3Vjq5b9Io5c7wpef7V5HnZqKCh\nmcpiobxDaIxVMz1CiRKdDS1TW9doMMgz/NYDidBUhGFQvMfGunV2MhwK3btI8rMqMY0AEgUQKJlO\nhGkgVA1FVSBY5oyZtxqsn0KBoWmaCARS6g0OjE3TMjRoCrp3N7n2Wi8PPBBxJdm1S8HrUxFa3RnI\nthKggSWw/txzDnw+uPLK+vmioY7uZKDtzGoT4fGArgsKCkzeeKOCM84INPmAb2nEW1+329t2kJYK\nHJxUQWPmwuWCOXO8gCQ31+Spp9z1qmynOlrimJASPvxQY+LEbF580UEgIJBS8M47drxJ9imvC3XN\nhVCiWf412xjFg0StpyqszJRVQgwHOgEd3efDDJZsQyKzik0LS2DEjC34uuo8SCkxAjpmwLCycsEA\nb8kSG7/9bTZnT27HxLM7sGZDO6RUUYSCptnQ7DZsWVloGU6E3Rbm38XcUIK8tXBBK5RNC1iZPtMI\nWkk1wEPz669Vbrklg7Vrm3bjcjjguOOWctllkYNy6lQ/7ds3MkhvhdB1WLTIzn33fc4DD2SwenXL\n8lLSGbUgunQxeeedMjp2lA1OWaaRRlvHmDE6y5aVkZtLq+myTTWsWWNpM/p8sTe7iy/2pawzilV+\ni3DUmrQe0fSyWHRGL6YsKw2EEJgBHcPnBwTYTYTDXq3MammgKWHT9lpJ+SHTdAVABAOpAIqIPKQU\nFyucMyWPp59SGHtKJUgjnB1DmpbJOxJVi3QChtZj6iZCYI0xZBVFyI3AysY1ZK727hU8+aST11+3\n88Yb5QwY0PjztKBAcuedHqZO9eN2C445xiAjo/7l2go2b1aYNy+yw0VFGhMmtFwVIc1RSyONNNJI\nIHbtEixZYsNmg+OO0+nd28RuhzlzMli4MFZZc8IEPw88UNnmtdKailixWAOhqJiGjqJauQZT15GG\nju7TCcVRil1DdTpQ7XVIz9e2vWATQUjPTCLDQeJPmx2Mm5AfE3BrmuTdd0oZ1N+DYtOChutRwWFU\n0GXqOqZfj/lMdditbKBhhsui4Qxg1Hgi8xHqCI0EodG+vu3bm7z1VjnHHJN+qGoMPvpI47zzIka7\nF17o4+GHK5O6zSZz1LZs2cLtt9/OmjVrqIgyyRJCsH379sSMMo000kijDWDfPsHvf291B6iq5Prr\nvcya5UWPeiDXNMk113i57DJfOkiLQm2dkNGK/tKQSEwwTEzDD4qCGTCskqZuYkgDVVWRpowtuUbB\nymgZQZK/LRJEBSU3pCkxdB0MA1M3kIBR6SXg8VCoGSyYL7j8d+3CEke6Lnjo4QweeVgnQ1OrGbLH\n7GOV3Mi2HXa++NLO55+r5ORIxpwSYMCAAO07xBq2Iwm7FihaxL5KDXogdelicuSRJnv2WN3k8+Y5\neeCBSnJzG/VTHNY4cCD2uGlpia64ArVp06bRq1cv/vGPf5BxOOU/Wznail9bU5GehwhSaS6khO+/\nV3n3XRtffqnSubPJJZf4k+7QAMmdh6OOkhxzjM6GDRqGIfj73zP49FOVuXM9jB2rIyX06mXQs6eZ\nEtzQVDkmokuZloZYFMk/1BAQDHKkYSCEAtIM2zgBoApEMEZSVRHDR5NBzTOr9GiEdcoOlkjy8iVF\nK1cwYsiJYa6br9yD9PkwpIlpmOiVHswKD0YgwNBOlTy9sD+/u6pdWDB1+XIbB0s1MlyWBEkouKqq\nmaZoGmYw4Czea+fCadls2hS5FT/0UAZTp/r4872V5BfUrFFmmiYyoIf5fkJVKSyEa6/1ctttlqr1\nm286uPBCf6NKdqlyTLQUIu4xy4Ax9OvXss1TcQVqa9eupaioCDVVhZ7SSCONVoePP9aYPj2Ws/Xa\naw6WLClLiEhkS6FDB8lf/1rJ2WdnExKU+uQTO9deq/DUU+4WfzpvNYjKPAlFsbJUigIYCFNYQYpm\nA8Mi+5u6bgUvBHloihrhi0X5iRo+L7pXR1EE+8tczJiZy1lnBejZXWDoBr7SMvwHS/Hs3UfglwoC\n/kpwucjIzSbg9WIXGoppMLLnet55sw8fr8xg8WIHU6b4ycuLdJ2KWjo2hRCoDgdSSnYUazFBWgiv\nvOLgkku8DM31W52r0kQIq3xqGjr4I5p00rC4dhKYMN7HX/7i5NAhKzC8+eYMBgyooGPH5svalpQI\ncnIkKeRu1WAcdVTkHM3OlvTu3bLnbFxMxdGjR7N69epkjyWNBONwfiKKRnoeIkiVudi7V3D11a5q\nxPrKShEU3Ewukj0PJ5xgsGCBm+hUyLffaixc2LIdnjUhVY6JmG5MQbh5QQYNzYVQwkEOapRMhABU\nBdPvxzQNpARTN63ypt/6p/v9QS9OP7pPxwz4MQI6xbsUVq+2cc89maz5bhwluysp37yNgz9tpWL9\nFkq3/EzF1mJ8W3dQtnkn/uL9+H85REAPYApB366HuPYqN2/95xCz/tfTIIs2IQRdu5p06lQ9g+x0\nSrKyJKZft0q4QsGyolLQHA6ri1XTgmbw0uK9GSZHH+Vl7lx3eD0//6zxxRcNj5gac0x4vfDGGzbG\nj8/m7bdt1RRIWhN69zbp0MEETuHvf3fTp08rKH127dqViRMnMmXKFAoLC8PvCyG45557kja4NNJI\no23C56PGgGzwYL1NdJVmZMDkyQFyciq44oqscHnskUecnH9+gOOOa7sajSE01NEgLJ0hZWy3YxXd\nMzMQANMK3ix/TRPD60f3BoKZMz+aw4HhMcJ8Lqnr+H3lSL+O3+22TNOlgUpEafj++12cOCCXTvt/\npmzbLnS3GxHQsWc6MQ0DZ4YdbDaUTDuqzYZqd6BluRBCYLfJICeuYR2tXbpI/v3vCp5/3s4LLzjw\neASDBun84Q8e+vbyRQzfTdPKqpkmpmm5IoTmQbFpqE57uNR66mgvI0c6KSqyuGv/+peDCRMCSe/a\nXLVKY+ZMy+1mzpxMRowoa7X8yx49TP7zn3LKy0VKeH3HdVS53W4mTZqE3+9n586d7Ny5kx07drBj\nx45kjy+NJqA+rSjTtDIblcltZmlxHE46atu2KaxereJ21/x5qsxF586SJ5+sICfHCspsNsnll3t5\n8smKZrm4N8c8OJ1w+uk6ixeXMWWKD0WRSCk4dCi1tKiSMRdWABVr0B1W+o/uXozWEiNYMqwa7FQJ\n8gx/wJLhCBgYXh9SN5G6CYaOESyB6noAhILh8+MrLadyz368B0vxlB2k4ueduDdto2LDDpzGQRyO\n0PaXMe/+AmRWF2x+P4b0o9hVVLuGcNpRDIk9Lxebw4Vqs2PPy4qRLGmsxtgxx5jcdZeXoqIyvvyy\nlNdeK2fEMB+KanHPpGliGgYCgenXMX0BDI8H0xsAaWLqBrrXFy7t5ufp3DfPTfv21jwXFWkUFzcs\ngKzvmDAM+OEHhbVrFTwe+OUXwS23ZBAq9ZeUKJSXp9Zx3lD07Wvi8y1vUJY0WYgro/b0008neRhp\nNDcOHIAXX3Tw0ENOpk71c+ONHvLyWnpUaTQFJSVwzTWZFBVp3H23hyuu8OF01r9cS0BRYOJEnRUr\nyigvV8jIkHTunBrk+kRCCBg40OShhyq54QYvbregZ8+Wf0JPOmogv0cyY9Lin4VMy8FS76+FAx1y\nE4j25jSDwrYBtxvF4QRDx5QCRRHoho7wBfBJifQbSFPHqHQjFBuBg6XoB8qoPHgQs9yLzeflvMld\neGGRJcXw3fd29mr9KMj6hjzhQmS4ENl2cgsKMITEkZmF1BS0vFwUVbOyWjYNNU6D+NqgqkTxyARg\nSXzIQCDcBGF1t+qWCK/PT8DrwZaRieqwW3Okmiiq1cHa95gA//53Oeedl83+/UrC6QQ//ywYOzYH\nXYdLL/Vx1ll+tmyJhBNOp2xz53JLIm4dtZ9++omXXnqJXbt20alTJy644AL69OmT7PE1Cmkdtboh\nJTz/vJ3rrouk/RcvLmPYsMPgBtKG8f33CqecEurFl7z9djkjR6Z/0zSaH9W8PRUlxtsy3MUZhdo8\nLav6dRpB7pnh9WP4AoCJlKBXejAClk+mDBioGQ6MgI7U/RiH3KAJ3PsP4tlXQunuYswKD3Z7JuVD\nruCC3/UMr/9/Ly3jdyPexl9RiT0/m4zCIy1hWqcVECmKgup0kJGfZ3l/qkHeXIIR3QVrBKyyru71\nY/r8mAED3eNB2G3YMhyWE4LTFm5gCGUlf/pJ4ZtvVEaN0uncOXGZ6i1bFEaMyCEQEAghuf12D3/6\nUyT1NGZMgBdfrEjZB8VURF06anHlQ99++22GDBnChg0byM/PZ/369QwZMoQ333wzoQNNo3mwdasS\nbuEOIdXKMc2J0lJYtUpl+XKNPXta7zzEPjULnn7aEaPdlUYazQVF04KyFMFMWU22TfGeamYsZ1G1\naZYYrKqgOu0IoSKw1PyFqlpNBQE/nkNlVO7aS8XmnXh27aFk7SbKios5tKMY3/5f8Lg9GD43HeWP\nDB/mC69/+SculN4DaX/yibQfejzZvbuS1aMLziPycbbLw94uF0debiSDJqtroyUCEmJKxUJVUewa\nwmaz/nbYEEJBcTpQNBU0LeikELmt9+ljcsEFgYQGaWBptk2bZs2ZlBAIxP6Yl12Wutn81oi4ArVb\nb72VN998kxdffJG5c+fy4osv8tZbb3H77bcne3xpNAG18Qx27FBwu2NPrMzM1kn6jAf18S3ef9/G\n2WfncO652Vx4YRYbN7ZOk9ecnNjf8N137ezeHfs7pwpHraWRnocIkjUX4QAtHGgoMcGb9Xnwu0od\nZt9CWF2NAd3ivum6FaRlOIIBm0CxqdgznSiKCoaJUebGV+bGs+sXKn/eQ+nOXyjds5/SrbvwHTqI\nXhEA08DmykAp2c6dt5Rgt38MwJ49AiW3kKzC9tizs9AcDjS7DbsrEy3TiT3LhWpXIbQ/tWQCq6Iq\nH6++72LKYKdqICw7otjtKDYVwwigCNUS6xWgOO0oCTSnru+YsNng0kv9wfuGiJHiGDkywAkntI0n\nxFS5TsT1yxYXF3PyySfHvDdy5Eh27tyZlEGlkVxUlQfIzTU5+ui2G6jVBSnhhRciZIpvv9WYNcvV\nKjNrHTpIjjwykn3weEQ1he000mguhGyfpBkpXYYDNKysmqKFsmN18LuCXaASieH1YxoSQtQ21SpD\nKg4b2FQcmRkIpx00G8JbiZA6huFFryzFffAA/n37MNyl4LdKpqbDTnaXDvTtuIebb6rEZrO4kpku\ngeqwo9g1NIcN1W51emoOB6pNQ8vMRHM6UIKm6/XORVDrTepGpBuWOjJxMqLHpqgqKMISz5USqSpo\nNhuKTUVz2FE0W0KDtHgxcKDBk09WIIRk40aF6dN9XHCBj7vvrmxW3bbDAXH9uscddxx/+9vfwq+l\nlPzjH/9g0KBBSRtYGk1HbVo4+fmxJ9Hf/lbZJiQRakNdmkBCUM0Pb80ajXXrWp+4c2Gh5LLLfDHv\nVb1+p4xmVgsjPQ8RJG0uqgYhjSwPymCgpqhqTFlPGiamsNwHFFVFc2Wg5efizGuHvX0eDqcTNcOF\nZnPgr/Bg+jxWPXG3Fzw+MFU0ux17+wJsedlcefkgln54iAUPl5ObZ2mWqbagvZSiREq1Qc5ddJlR\nGkZYKqTGfTBlzN+hZoiQUG81hDXirP9Vmw2hKqAINNUKbkOCvkJLfJAW7zFx2mk6Tz7p5tVX7fzw\ng8rq1RobN7ZipdsqSJXrRFy/8COPPMKTTz5Jx44dGTp0KEcddRSPP/44CxYsSPb40kgC+vUzuOuu\nSo45xuChh9yMHx9o6SG1KM46q/r+b9rUOsufU6b4wlm17GxJu3bpJ9s0WghVy4GNlK8QwSBJKIol\ndKsoEZNy3UAAQlHDWSXVYbe6IXPbYXPYICcTM9OJ5nBABwe4nJCXTW77fFzZuajZ2SiKQNMU+vb0\n0q+X1wroguO1ArJg9s+uVWscCEmRIK3gscYsWdVdj/5ODRw3yxZKQdFUhBoqFVuBo6IqQcHbyHst\nBbsdzjwzwPvvl1NYaLJtm0JBQdt96G8pxHU36tevH+vWreOVV17hxhtv5JVXXmHdunUce+yxyR5f\nGk1AbfX1rCyYPdvHe++VMW2an5ycZh5YM6M+nsHgwTo33OCJea/1CjVKXnmlggsv9PH00xV06RK7\nH6nCuWhppOchgqRx1BQlwktTY0nuDV+PitBUbK5MFJtqaYzZbUGjcokpTSSgOR1oLieOXBcZR+Ti\n7NYRZ7tc8jt1wpGRCzggPwctw47m0BB2O5gmwmZj1SdFlg+oHmVJFQygQiXaeMqcNWUORVRGTqjx\nzUNov1WHI7JtIUBV0JxONFcGNldGrebvTUFDjgm7HYYMMVi40M0XX5Ry0kltg58GqXOdiDtHabPZ\nqvHU0mi90DTIza3/e4cDsrLgmmu8DBpk8Oyzdvr3N1o1GbZ/f4OHH27jKsZptAo0Njirtp6obJyw\n2TCFQFPBkJZTgaJpYXFdzeFAajZMw8QWCODIzUH4dWTgKJylmVRmm9hNE9XlIqMwH+n1h8uP0jSs\noFJVEAiLWxa1LzXtj+XFGfyWqHmfqy0rRKxpe5zZxpABO0bE+zPu7tkkw+UCl6t1PuCmOmrVUevb\nty/r168HoEuXLjUvLATbt29P3ugaibSOWhpppJFGakAaRkxmqsHLRwndRr8X0mUz/H5LrkJVMXUd\noVlq/np5OZ5SN3plJb49+/B7A+gHDkJAJ+D1ozrt2I8owNWxPa5OR6Jlu9AyHFbnaHg7BiLqda1a\nb6HO1iST+kNzQdD/FIINGo0sKycaa9cqrF+vkpcnGTDAoH37dOAWL+rSUav1rHniiSfCfz/33HM1\nfidVDo5kYPt2wdatCooiyMkxOfpok3btWnpUaaSRRhqtB5ajQBSR3jAapOAfI5wb5V4Q7QuqOuzh\n7yiahpQmGBJhc+DIlNicDiuY+aUUVbPh238A4TetBoGAQcDrQS9zozjs4LCDMEGEeHHxjTXZARrE\nzkWIM5dK2L9fMH16Fj//bM3Z0KEB5s+vbHFD87aAWo+u6DLn/v37GTNmTLV/+/fvb5ZBNjfKyuCy\ny1yce24O55yTzamn5nLGGdm89JKdrVtbD8k8VerrLY30PESQngsL6XmIoDnnoiHCsFLKGP5VdMAH\nEV/QsB6bCPK/Qtk7VbW8mUywOzOxZTtRhUDYBYYikbpE2GwoUsVUJJ9//ZW1LkUJc8KEEpWMEIlN\nToS9T4263UNCXp9hg3bDsNwZQuVaKS2duTq6ThuKxhwTFRWC7dsj98cvvrAxY4aL4uLWm9BJletE\nXFHHZZddVuP7V1xxRUIHkyrIyYEpU2I7ATds0LjqKhennZbNBx9o+Hy1LJxGGmmkkYaFKg4EDck8\nVQuKatXDDXZkVlHmF0qwa9JhQ9gs/TZvWQWePQcxDpbjLStHNw2UrEzszkyEWn0DoSYGi7eWOMme\niEF9rHF9VZi6bnWSGmbYpSDUYWoGdAyvD8Pnq7/rtBnQvr3JqafGcns3bND47LPUyvy1RtTp9bll\nyxaklBx33HF89913MZ9t3ryZGTNmsGvXrqQPsqFIBEftl18sC54//9lJ1SuEEJInnnBXC+bSSCON\nwwd+PyxbpvHGG3bOO8/P8OE6Llf9yzUWxcWCdetUvvpKo7hYoWdPg0GDDI47Tk8JWkY42AhmumI+\nq8qtsgTt6y3fhc3YaRgXy9R1ME0M08Tw+PDvO4jHXcbBtZvw79iDr9KPPctORtfOFPTtjbNjAbaM\nTEvuwmGPGVcoqIp3zPEgmmNn7Vz19Vb1OLXmwQrsLMcHiVBENf5fvE4JycDXX6uccUZ2jKXU5Ml+\nnnrK3SLjaU1oFEcNoFevXjX+DVBYWMhdd93V9NGlKI44QnLllV5OOknnn/908P77NkIBm5SCOXMy\nGT68jKOOSpMl00jjcMT336tceGEWUgoWLbLz/PNuzjgjOQ9v69Yp/M//uNi6tfol+/bbPVx3nZeW\npCxFG4hLQw9moSIBQyhwC5XwQnwrKaWVCaslsAhlyKzAxurArC9QCnO5FAVhWnw1bAqmT8cMmPgq\nvZg+HZlpQ8tworXLwZaRGSl1BscVHlMosISgHIjZZE5aaJ/CnLNa7bOIfCeY1bPKpSZSyPA+xnSd\ntiB3fPBgg0WLKrj8chclJdYcteYO+lRBnUebaZqYpsmoUaPCf4f+7d69m1mzZjXXOFsELhecdJKl\nvLx8eRmPPurmpps8XHmlh0cfdZOXl9pBWqrU11sa6XmIID0XFhIxD9u3K0gZkau//vpMdu5Mzk3y\nqaccNQZpAMuXN42KkYi5CAUK4XJeqFRXQ8FGVg18aij7RWfSrIxWcJlavh9eLorLhYRDpRrFJdmU\nGIUEXB1x5OVYAZlNRcnKwN6hAHuWCyEERZ9+ErbyaI5gR6iqFRgGs2LRum2hMYT4d6HmgRjbrWDm\nTGgqisMeFMhNTLTe2GNCUWDMGJ333y/n2WcreP75cs4915+QMbUEUuV6GdevumLFimSPI6XhcsGA\nASYDBrTeAy6NNNJILKrey3/5RaG4WKFz57rJ4Y3B2LEBnnrKERUYWujSxeDeeyuTWnKNByEtMSll\nkNgvgoGVjJmocCaJ2vXDYjo9qyxvvSVjyCghHhcEM0zBTzdv1bhwWg5btqhkZEgKC9sz7tSjGX3i\nSDrn/UI7uYPs/AJUp90yN1eVsCNADBQFZKT02dRsWjj7GCx3yqj9lYaBiAq2rECs+m1aKApqEjpN\nv/1WYf78DPr10xgwoOFam4cOQWWloGdPk549092eiUKtHLVf//rXvP/++wC1Ct0KIVIyiEvrqKWR\nRhrJxldfqUyYkE00h/XNN8s4+eTEB2o+H6xbp/LTTyrbtim0ayfp3dugTx8jYfSLujhmcS1vmkhd\nRxIMwOrgc4WDMRHLPavKywJQbFqsNEWUy4E0TUx/INIRKmRQc03B7VGZe5+Lxx7LqLb9zEzJ/0xz\nM+VcP/0H6GRmNY8NU1VumlBE9W7WODlmYRutRv5eNeHVV23MmpUFwEUX+bjlFk9cBuuGAWvWqNx0\nUwZbtqi8/XY5/funA7WGoFEctYsvvjj898zCxwyAAAAgAElEQVSZM2v8TlvWUUsjjTRSF4YBBw4I\npIT8fElL2B327WswfbqfF16wvB81TSZE4HPvXsG2bQqlpQK7Hbp3N+na1WTQIKt5IBmI5phZcvnx\nq+WHIBQFYbcHS5syXEasCbUFcEIIZBQvKxQDW84D1YVvIarsGtyuYreBEGRlw//9voITTtD5v/9z\nUVYWGU9lpeDxJ7N4YqHk+uu9zJjh4+ijm5/KYhnORwVrDeCYmboOwaDP8v5setkzPz8yB8895yAv\nz2TOHC9ZWXUvV1Skcf75WeEmgl27lHSglkDU2fXZWpHOqFlYtWoVo0aNaulhtDhSeR727xesWaPy\nxRcaBQWSYcN0Bg40SKASQAxSeS7iQSAAP/ygsnChg6VLbZgmnHpqgDlzvA0qtSRqHrZvFzz6qJP3\n3rNx550ezjwz0Oig0eOxbng33pjJjh2RA6BTJ4N//7uCY45Jzo1v1apVnDR8eIxmWVO8OZuKcKYI\napXECGXYhCKCpU+JNA0QlgaaEAKpB5DS+nzDT4IvPrfz0JMFYUHWaAwcqHP99e8xefLIpO5b9Nij\ns4n1ORtEZ+IsXpuC4fXFBLRahrPJY9uyRWH06BwqK5cDYwB4+eVyJkyovSFg40aF00/PDjcPAHzw\nQRlDhiTnoaI50ZzXy0Z3fYbw4osvMmjQII499lg2bNjAFVdcgaqqPPLII/Tt2zehg02jbcM0Yc8e\nESQ/C+x2Kwtht7f0yJof5eXwxz9m8PzzjvB7miZ5881yRoxo/Re5ZGDZMo1p07IwjEjW4ZVXHJgm\nPPpoZV1JnKTg6KMlf/qTh//7P29MNqIxWLFC48ILs6gqB1RcrLJ7t9KgQM3thq+/1nj2WSsrcsUV\nvjqXr+pXWY2A14wQQlDXk0p0w4A0JYrNhlRNkKqVmTJNTCnRvT6EouI9cJDsvZsYcHAdj119DKXO\nY9iyvwP/XVpAcbHCwYMC04SysubZZ8s9wdqBql2xtSG6XCpNiUjScd69u8m991by+99H3rv+ehfv\nvVdWY8bR74fnnrPHBGldu+p07pzOpiUScWXUevTowaeffkphYSGTJk2ib9++uFwuVq5cyUcffdQc\n42wQ0hm11IRpwr/+ZeeeezIpL7cuUNnZkoEDdcaNCzBwoMHRR1t2XS1RymoMdN2SadiyRaFbN5MB\nA4y4g841a1ROOy2W4wQwbpyfl15yJy2r1lpRUgITJljk8Kq46iovf/yjpwVGlRjoOpx/vovly6sf\nPMcfr/PMMxV06hRfIFhZCQsXOvh//y+D0LE1daqPhx6qrFPCI7pkmcq0lphmAyLZPyklpt+P1C1h\nWH+ll8DBQ5Rt3EnFgb3s+uYH9H0HEUIlt1s3Ok0+DVvH3hhKBi6XJK9d6rrOmIHYjJbQ1KSUPsF6\nkL7sMheffRa5CC9aVM748dWzahs3KowYkYNpRo6X+jJwadSMJmfUfvnlFwoLC/F4PBQVFfHaa69h\ns9koKChI6EDTaNtQFOuJzR/VPFteLigqslFUZF0U7HbJzJleLrjAT79+ZotqQ8WDzz5TmTIlG10X\nCCF54YUKJk6M7yJls0lU1eJbRaNbN7PZM0OtAapqqZ9XDdT69tWZMaN1W4VoGsye7ePzz214vZGH\nmN//3sOUKf64gzSwSsPRQRrA+vUqfj91nk+JLnWGJDbCMhMJQkhLLLoLU5omZiCAqZtgSjwlpfjd\nlXh37sGzZx8HNm7B9FaCL4DMd6IIP/q+fbTrfCSZhfYWK/NCyCqrbl6gUJWY0qcQAjWUSSSxv92R\nR0ruv7+Ss8/OZv9+a71ffqnVGKjt2SNigrRLL/UyfHhigjS323oIPnBA4fjj9biaGtoq4vp127dv\nz8aNG1m8eDEnnngiDocDj8fTYlYVacSHVNGAicaYMTpLlpQxa5YXVa0plS545JEMxo7N4aWX7Hga\nmCQxTdi8WWHdOiVEc0naPPj98MADTnQ9IoR8ww0udu+OLxvRp4/J3LmVCBGZh+7ddS67zJe0ylMq\nHhPxIjcXHn7Yze23exg71s+UKX7+9a8KXnutgl69GlZqScV5GDtWZ+XKMt57r4wlS8pYubKUa69t\nOMn9gw8i4twhnHeen8zMmr9f31xIs+G2RNHaZ3VZJAGsXq3y7LN2Nm6s/3YUCmoUTQtnkSwNMgNp\nSMxAAM++A/gOluLZsQvP3gN4yw/hd1diqiockY2Wm4E9JxfT0DF1f3jfWuKYiPh91q47B0E7LJul\nn0aMxEnNXEJpGBH/z0bcp/fvX8F//1vO+PGWgHN2dvV1bNqkcOCAws03e7jlFg8PPeRm9mwvOTkN\n3lw1uN1WVviMM7K56KKsoOB88yNVrhNx5SvuuOMOhgwZgqIoLFq0CIAPP/yQQYMGJXVwabQ9KAr0\n729yzz0eLrrIx5YtKu+/b+Pjj23s2hV0VgZ0XXDnnRmceKJO377x34Q//FDj0kuz0HV49dUKRo9O\nXgq+rEywcWNspmDPHoUDB0RcT382G/zP/1jWQzt2KGRmQu/eiZNbaIvo0UNy443elh5GUqAoBPWn\nmrYetzs2SOvY0WDiRH+9hPWaEFNmVBqQGasSHFTVPgth40aFc87JpqJC0L27zuuvu+natebzPUSo\nt7o/QQ1xDIIuAlKAaVhemIrdgenX8ZWUULJvH+bBQyBNsGvobtV6ovPr6JV+DJ8f4XC0TOKhivgv\nplk3Py+qqUCaZo3lzrAfaOh1FW22eNG7t8kjj1SwfbtCQUHs3CxfrnHRRVlUVMT+qieeGOChhyrp\n3btpHLXPP9e4665IVnjpUhuXXHL46pjG3fXpdrsRQpAZfCzbt28fpmly5JFHJnWAjUGao9a6IKXV\n/VhSIjh4UCClQFUlhYWSbt3iP+E3bxacdlpumP82YIDO22+XJ+QJryboOlx5ZSavvRZpBrDbJZ99\nVtagcaeRRiLx9ddWOb68HCZMCHDXXR769PJHdMjiDLji8aOsddlof0xq7yJ9/32NCy/MDr9++GE3\nF15Y8w3Z1HWLqxVap6ag2u0x2mu6x4PvYDm6z0/5z9txr93IwT37KNux17rQBAw4IosO7TuTP7gf\nrj5dyOnUEVtmRot0usbKotTfbVsbPy9mnU343eKBxwOTJmWzenXN65wxw8v99zeeL3rwoLX+desi\n67/+eg933tk2H9BCaDJHDcDv9/PWW2+xa9cuOnXqxKRJk8jPz0/YINM4fCEEdOgg6dChaU+0P/6o\nhYM0gI0bVcrKBDk5yXlSDvGK3n3XjsdjbffGG7106pQO0tJoOZxwgsGqVaVUVgo6djTJzjKRUZXH\n2rJb1dCE+ntIUT+kfSYNA8NrBWCKXQsHDpWVscstXGjnnHNqLtOapomhGyjhZgcR8eTUrCyZ5srE\nlBJ+OYQjLxdfp46oJRVo+VnoB8sgw4GGDSkNTN0LwbKuRLZIA4UVMBvh/WhwoFjDmKv5iCY4+MzI\ngDlzPFx0UWz3dQjDhjWtirFrlxITpAEJ4721VsT1C3766af07NmTxx57jO+++45HH32UXr168ckn\nnyR7fGk0AalSX28ubNsWezg7nRZZP5nzMGiQweLF5fzzn25eeaWcmTO9Kd2xergdE7Whrc9Dly6S\nY44xrWxyPQFIbXMRtlMKMhIak5URwaDK9EdutKZfD3tbZmbEPkRt2aJSWlp9vLrXi+n1Y1R6MXz+\nsP9lWN4i2LCgqCo2Vya23CwyjsgnMy+XzPbtyMzKQnU4cGTaceXnYMvLxtEuD0dONmowcCwqKmrw\n/iUCQrW4dtFZzgh3rYpLg6aFf4+Q5VVNCHH4hKbWnHGrp5BW3/kxdqzOBx+U8+c/VzJmjJ8RIwJc\nd52HN98sZ9KkQJ3L1oeqv3+vXjr9+7eMXFGqXCfiOvOuu+46FixYwAUXXBB+b9GiRVx33XV8+eWX\nSRtcGmk0BHl5sRefM88M0L69ZPPm5G1TCBg40GDgwLTuWVuBx2NRhVraPzNRsHTJlLg6MMMZqtCy\ntZDVmwwpQUKXLiaaJsMNOS4X1R50QoK2SFAd9ogGWXA/wrIiQeFYGdA56Mlm974clMxcsga0R3N9\nT3bHQoyKAGqmk7zeXXAefRT2vBw0pzMsOhuSwWhJwV+oohUn9ZggOd6AuV4f1Sbso80GgwcbDB5s\nMGuWD8Oou6O4IcjPlzgcEp9PkJ0tefJJ92HP242Lo5aXl0dJSQlK1I+q6zpHHHEEhw4dSuoAG4M0\nR+3wxOefq5x+uqVLZrdL3nuvPGmWO2m0TWzerPDnPzs5dEhh7txK+vQ5PMrYISmNkORFIjlNAKbf\nb0lnAIqmWGVRw0TX4Y9/zuLhhy0/zosv9vK3v3libvqmrmP4AhEPUEWgZTjCtlJhcr1hIIFt2+3M\nvCKH77/XAEmvXga33VjCgMINaN4D2HOzyO7cCTXTic3lRHM6q3uMJmEO4kVtfqcNWkcoExeliVfT\nPppomCYpJThumrBqlcbWrQpDh+r063d4nINN5qj17t2bl156ienTp4ffe/XVV+nVq1diRphGGgnA\nwIEGzz9fwfvv25g+3Z/OcqXRIHg8cN99Tt54w2oOeeABJw88UJlSN7FkIRSkhTpDpWImNKOk2O0o\n4SbNYNZOSjSb5H+v8CKl4NtvVWbP9lXLzCiaBqaJISVSShSHLZIVrJJnEMDOYjUYpFnvbNqkcdmV\nHZj9OxezL9lNbjurY1R12FFqyC4GdNi9R6N4l0ogIOjVy6Bz5+bL6FT1OxVKw7hzMVkzWXvH57oN\nNu6+O5NAQDBrlo9hwwK0a9f4cScKigKjR+uMHt3SI0kdxHUmPvjgg1x99dUMHz6cqVOnMmzYMGbP\nns2DDz4Y10Z27NjBqaeeyq9+9Sv69+/P/PnzASgpKWH8+PH06dOHCRMmxGTn5s6dS+/evenbty8f\nfPBB+P2vv/6aAQMG0Lt3b6677rqG7Othh1SprzcXMjLgjDN0HnzQw9ChRlg09nCbh7qQngsLNc3D\nzz8rvP56JCp75x07+/alrkJ/ohCaC6vEaGWoTD3x5G1pWuuVuqXxFeJmdTka7rrLw6JFFbVmMBW7\nHc2VgT3bhWa3R8p60eU9RQFF0K2rSceO1dez4FEXG3a2x57lQrXZgmXdCMdtxapP+HGdjdvvyGbk\nqDzOOiuHKVOyWbu2+S1ChKoGu3OVhosFy9i/o+2qojmH//mPgw8/tLN8uY1p07K4++5M9u+35iN9\nnbCQKvMQV6B20kknsXnzZq666iqGDBnCNddcw6ZNmxg5Mj4DW5vNxv3338+PP/7IZ599xsMPP8y6\ndeuYN28e48eP56effmLs2LHMmzcPgLVr17Jo0SLWrl3Le++9x+zZs8MH25VXXsnChQvZuHEjGzdu\n5L333mvkrqeRRhppRLB3b6zKenm5CHfztkWERFGlacYEAxZJX0m4rpisohkWyt6BxW+K7vSUwexZ\n6O/oAC8aQlGCfDKBoqmodjtdu0sWLSqnZ8/qwWbJQdUSjrVb4rGh/S4uFrzxHwdjx+Xy1FPO8O/e\nqZOR0PL3zz8rvPqqjXnznCxdqnHwYM3fC3EJG5rVlFLGah0LqnEOFc1qnsjIiF322Wcd/Pe/KdwJ\ndRgjbh01gJ07d4blOTp16tTojU6ePJmrr76aq6++muXLl1NYWMiePXsYM2YM69evZ+7cuSiKws03\n3wzAxIkTueuuu+jatSunnXYa69atA+Dll19m2bJlPProozHrT3PU0kij6SgthR9/VFm7VkXXBX37\nGgwYoNNWneOWL1c599yI6F5mpuTTT0vp0qXtEZmram0JNVbSISk8taoaYJpaI+E9WltMKEGz+Hq0\nw2rCjh2Cr77SWLzYxubNKhMnBvjtb6s7PWzYoDBjhoufford34ICkzfeKKd//8QEart3C6ZNy+Lb\nbyPbue46D3PmeGt1jYgXMbp14WSjqNO3dc0alXHjsmMeTrKzJStWlNUqOtzSKCmBJUtstG8vGTJE\nj9HIPHQI1q61LKe6drUCbKez5cbaUDSZo7Z9+3amT5/Op59+Sn5+PiUlJYwYMYLnn3+erl27Nmgw\n27ZtY/Xq1QwbNoy9e/dSWFgIQGFhIXv37gVg165dDB8+PLxM586dKS4uxmaz0blz5/D7nTp1ori4\nuMbtXHXVVRx99NEA5OTkMGDAAEaNGgVE0pnp1+nX6dc1v/Z44KOPxvPYY05gGRbGcMEFPs455wNc\nrtQabyJed+gwGiEkUi4H4De/Gc5RR8mUGV8iX0vTZOSIkwAsWQpFMOrkk8E0WVVUBEJw8sknN3l7\n0jRZtXIlSBg5aiQIKFplbe/kIAmp2vIrrdcjR45EmpKiT4qs5YMVnFUrVgCCkaNGIlQ1LKtR0/a7\ndAnQvv3H+P1w2mnVP9+yRXDeeV9RXKwCY7CwjOOP1/nnP0+kb1+DlStXIYRo8vx7vWOCQdqy4HbG\n8OCDTvr0+YguXczE/Z71zW/w9YknjuLeez3ceusX4fGUlwuWL19Fjx5NG0+yXn/3ncaVV34FwJ//\nPJSLL/bxzTfW5z/8cBq33eYKzq/k7ruHccklPr79NnXGH/0arHNv+/btAMycOZPaEFdGbcyYMQwa\nNIh7770Xl8tFRUUFd9xxB6tXr2bZsmX1LR5GRUUFp5xyCnfccQeTJ0+mXbt2HIzK/YaCwGuuuYbh\nw4eHmxcuv/xyTj/9dLp168Ytt9zCkiVLAFi5ciV/+ctfePvtt2O2k86oWVi1alX44DickZ6HCOKd\ni2++sZ62q3pGArz/fhknnti6GzVqmofKSrjrrgyefNKJyyV5550yBg5MzcxCUxGdUSsqKmLUKaOb\nLPgazYUKId4sWjRCEhnRy4SyRVKaCKGE9yHGSqoRuOceJw88EKoBLuOoo0Yzd24lI0cGyMuJjD0R\nch1Ll2qcf352tfeXLStt8nFW1eEg3oxoeTl8/LGNG2/M5MABhQEDdF55pYKNG1em5DXz1VftzJoV\n0s2RvPtuOcOHGxw4IBg7Npvt22P5fG+8Uc4ppzSeb9mc944mZ9S++eYbPvjgA+zBEyIrK4v77ruP\nggbUQAKBAL/5zW+46KKLmDx5MkC45HnkkUeye/duOnToAFiZsh07doSX3blzJ507d6ZTp07s3Lkz\n5v2mlGDTSCx27BBs2qRSUiJQVcu38le/aps3urYOl0uSmVldOT47W9KuXdsrBYLFkZozx8uECQE6\ndTLbtCyAUBSLiC+lpafV1CAtWiYjOkhoxKEiVCW8rpCoa6hzMbSdcAAorGCwMWVaXYejjrJKaEOH\n6hQUVHL++WV07iyD24ndv6YGar17G3TrprNtW2SsZ5/t4+ijm36cCVXFNANWsCZNFFXD8PutrtY6\nHA+ys+HsswOccEIZJSWC9u0t676NG5s8pKRA06IPKMHTTzs44YRKHA5JQYFZQ6Bma1KgliqIK6M2\nYcIE7rzzzpjIsqioiLvvvjumI7M2SCmZMWMGBQUF3H///eH3b7rpJgoKCrj55puZN28ehw4dYt68\neaxdu5Zp06bxxRdfUFxczLhx49i0aRNCCIYNG8b8+fMZOnQoZ555Jtdeey0TJ06M2V46o9a8CASg\nqEjjqqtc7N4duSBkZkreequc449v3dmXwxFSwsqVGtdfn8m2bdbF79hjdf7610pGjEj/nmnEoqYs\nWFhEVjfANBGqghJUsw1zqmi4qK6p62Gng1CmK55MXW3w+6vriDXFL9Pvh++/V9mxQ+GYY4yYgH/T\nJquz+KuvVMaPD/DrXweqceYag1Dgaho6QlFBSqRhRjKBigib1ze4izSF8PXXKuPHR4hpTqekqKiM\n7t1NPv5Y4ze/ySK6CjBnjodbb20dHqFNzqj16NGDM844g0mTJtG5c2d27NjBu+++y7Rp07jjjjsA\nK919zz331Lh8UVERzz//PAMHDmTw4MGAJb9xyy23MHXqVBYuXEi3bt145ZVXADj22GOZOnUqxx57\nLJqmsWDBgvBJuGDBAi655BI8Hg9nnHFGtSAthJ9/Vli6VKOgQHLGGYGUtvVp7VizRuW887JiSKkA\nlZWCPXvabtdcW4YQlpbRkiXl7NkjEAI6djRTQmcpjRRElO5X7PvCaghAASzPT6Gqscr7huUHGm+g\npWhauMFACFGts7GhqKlyKhTFCnaquCDUB12H//7XxhVXuJBS0KOHzttvV9Cxo7WeXr1MbrrJGzJS\nSAiqdtNixmbopJSgGwhFDXbTNi4DmQro0cNg4ECd776zxu/1CvbtE3TvDiNG6Lz0UgW33prBtm0a\nxx2nc+65/hYecWIQV0btkksuiSwgRDUuQkjA8F//+ldyRtlALF26lFtvHc2XX9rQNMnKlWUcc0zb\nLWPUhuaqr7/4op2rr67ut3PMMTovv+xu8Q6iNEctgvRcWEjPQwTLlllz0ZR7d3TXoaX/FbF3CpdE\npQzKaGhhzbZQxKLYbQ0KtmIycmrjs2nRSMQxsXq1yoQJ2TFm5UuXljJ4cPKugdI0Mf1W2VMiw/Iq\nSGkFxVJGhIGD86066ub1pfL58eGHGlOnRjJnVTmz+/cLDh0SHHFE0x8sWxVH7emnn07keJoFX35p\npdB0XVTj2aSRWAwZosc85WRnS2bP9vLb3/pbPEhLI400asYPPyi8956d117LpEsXF+ed52fUKL1R\nvorRPLIqH1g8soBVmpMiEjCES4tC0tAUU63ba2G8/bYtJkgDWU2vLJkQQoSzZWZAx/T7EJpmJTyN\nkORJdU/X1oQRI3TmzvVw660ZdOwoOfLI2HtM+/aS9u1Tk0e7fbtCZqbJpk0qy5bZqKyEvn1NBg6s\nm0fXIB01gNmzZ7NgwYImDTbZWLp0KePGhSJTq4bdlonBiYZhWCl8hyP+ZQ4cEOzeLZDSMkfv1EnS\ngp7GaaSRRh344QeFM87IoaIi9mY9bZqPefMqycqK/f769QpffaUxbJhO794Nu5aahoEM6Ji6EWxi\nCNoihbI+QYeA1sydAqvx5swzs2N00gYNCvD66xXk5SV+e6GMYlWdOWkaIBTMgJW1FMJq8FBttnBT\nhFCti3Nr5ay53fDTTypOp2w19/YlSzQuvzyLv/zFzVVXuWKoQna75N13P6o1o9bgW+lzzz3X+JG2\nAIYN0+nSpXX8kC0NKeGnnxQef9xBcXHDDo2CAkn//iYDBph06ZIO0tJII5WxZo1WLUgDePllOwcO\nxJ68mzcLJk/O5tprXVx6qYtffmlEJkaIKhmzoHVT6EJRT3ZHGoaVIQroMY4GqQRVtbqlI68l997r\nSUqQZupW4GsaQY/WsI5IkE8npcVVi6IphUrTZkDH8AeC7hCREnJrgssFgwcbrSZI27BBYebMLMrL\nBcXFajU+t99f9/Hf5m+nV1/tq/Z0eLigIT5lv/wiePZZO6edlkPv3gY9erSOEyAepIpfWyogPRcW\nWus8SNNMSKDSp4+BCJUhwwKsMHOmj8LC2PV/8omNffusW8XatRrbtsV/25BSginDXDWJDGZwJMFI\nIS6NsmiNsJhuTKxMlscT95BqRVOOia1bBfPnO5g504fDIcnPN3n++Yqk6A2auo7u8WF4vOgeL7rP\nh9QNpGlEZFeCfp4IQFEsmQ7FauwQmopAhI+jmopqrfX8SDQSNQ/ffBN5MNq6VWHixIY1OcRV5L/+\n+uuZMWMGgwcP5rbbbmv4KFsIgwbpnHBC8jVUdu0SfPGFxqpVVpfp2LEBBg40Wo19xfr1Crfdlsmy\nZTZuu83DSSe1ft2ZNNJoa4gWNZWm2aTOvUGDDN5+u5ynn3awapVJt24BLr3Ux+jResx1q7ISnnkm\nlnheVtaAjFowsBSqiqZpIC2RWkmUdlsDPUWlYSAVyx7p00817rgjA6cTbr3Vw/DhRpOaIhqDgwfh\n2mtdFBXZ6NrV4O67PYwdG6Bnz8Q/7ErDsDxPAwEMj98Kzmwa9uwskBDQfcFmAmHp4ylE5EvAavYA\nTKmHs5hN1Yc7nLFli0UJWLdOoaBAcsIJOscea5CbG/u95csjB+ULLzh47bUypk71M3++g3XrNOqr\nPsfFUbv22mtZtGgR7du356KLLmL69OkxVk6phqVLl3LDDaewcKE7KSdLNKyTNJN33okmdEkef9zN\neecFkrrtpsLjgU8+0bj8chelpQqzZnmZM8dDfn5LjyyNNNKoimoq/wlQyzdNyyMxI4MaSe979ghG\nj87hl18i22mI2rvh9yP1oHitYnV3IqVVcguV5wQodntYd836bux+RQvdhnTXthdrnHpqLqWl1ndV\nVfL66xWcfHLzPmj+8IPC6NGxd+bXXivn1FMTM45wgB6Kaw2TQFkFhl9HGjrCZkPNcCCEwDRMhDSR\nCFRNQ3XaY3TmpGEEu28jJefW2lTQ0ti+XXDeeVls2hT7ZDBjhpfbbvOGGxr8fpg0KZuvvop8L3R8\nlJdDaak1//v2fd00jtr8+fMpLi5m3rx5rF69mn79+jFu3DieeeYZKioqGrWTycYrr1QkPUgDq4sj\nNkgDEPzhD5ns3Zu6J8Du3YIHHnBy/vlZlJYqXHqplxtu8KaDtDTSaC1IwA1WUSA/v+YgDSySc1aW\njPq+pEOH+K6r0rTsnqzGAYJNBIq1UREdgCgWBy0o2WH9iy0ZCkVBsWkomhYOMg6WiHCQBmAYgttu\ny+DQoYbNQXi8QcmPmkrLW7YovPWWjZdesrFqlYbbHfmssrL677B9e2KyVFapO9QpGyl9m4ZhNWLY\nbBZXzRfA1A2kz480JNKvY9SwL0JVw3Mo6jBsT6N+7N2rVAvSAJ55xsn330dSZEJAu3aR30FVJR07\nWq+zs6FzZ0nnznXny+I+mjRNY9KkSbz88st8+umn7Nu3j0svvZTCwkIuv/zyWs3RWwodOjRPe25+\nvsVHqIrcXLPZU/BVUVt9ff16hRkzXPz1rxmAYMYMHzff7E3ZluamIs23iCA9FxZa4zxYN9igwGsC\nbJ9CqGsucnOthqwQTj89QLducT4Ah9IPZbMAACAASURBVEproeAgWN8JdRrGZHpMGctDM2u5FkXt\ncrt2Eqcz9ntr11oWdo3BqhUrguT62EDxxx8Vzjori0suyeKqq7I4++ws3njDHq7YFhTI/8/emcfJ\nVdVp/3vOXaqq14QASSCBsISwhE0DIRuyDWaCLAPIkhFEcQSFEQYRAQcElFcQERGMMAjqDJsKgmwC\nKgLZQRYxyB4CGEIka3dXV9W995zz/nFubb0kvXd1p57PJ9BdXXXr3HOX89zf8jwkEuXjKCW3fQ3h\nOHj1tciEh3Qkbk0StzaFFCA8t9BMYKK4+cLoDs8VHf9dR+0jf0Px+ugPbGoedtxRc8ABm8+aeR6c\ncELxfRddlO12EKnLRG3jxo387Gc/45BDDuHggw9m6tSpPPvss7z++uvU1dV16hAw3DF+vOGuu1rY\nccfiyT56tOanP21l1KjKIj5aw3PPORx9dD1/+YvVmTv99ByXXJIZMGJbRRVV9BylEZGBgOPAWWdl\nqa83jBunuOSSTJd1wSwhk4VoWmlNndX7KgrVirjQvfiGjreZJ6tCCsbvYLjkkvIugpEjTbdkhfJo\nJ3ERs7AwhOuuS7FqVWkRkeB730vx8cd2kBMmaP7rv4o2RY5j2HXXvsnm5OVM4q+1cyoEju/j1abw\nalO4qQRSSmTCx0n4SM9B+C6O7xU7QNvub4kzBIYh2fk52Nh2W8P//E8rV13VypgxGiEM222n+eEP\n0xxwQDn5nTEj5Iwzslx4YYa5c3PddkrqUo3aiSeeyOOPP86sWbP4/Oc/z7HHHkuq5GrVWtPQ0FAx\nadDB8Pr86CPB++9LpITtttM9Eo3sT2Qy8Kc/eXzpS7WFVuDPf75K0qqooorNY/lySSJh9RE3he46\nBpTWpHX22U35gq5da4uzr702hZTwi1+0cPjh3a8NK3VWsF9kSeGGDTB7dgNvvlle7b3PPhEPPdRM\nQ2w7+dFHgoce8nj0UZ/zzssya1bUp7aFpQK1ZYb0sSsBSuEkE0jXRUURJoiK+mgS3DadbaWNKVDu\nJlFF9/HPfwoyGUFNTediu0rZIHNnz1ibciboElG77rrrOO200xgzZkyn70mn09TWtrcRGgxUTdnL\nsW4d3H13gssvt6lOgG9+M8OXvpRl1KjBHVsVVVQxfFDW8NANI/OubNMYW1DvtGFAStnOeyFg++1N\nj0v3Cs0NlHt7/vznPl//enFtSyYN993XzPTp7aNQSrHZDr6+QJ645dKt6FwAxiAdF7c2aS26grBI\ngl2n3ZxBOeHrKxuuKnqOTRG1LsXPv/GNb2ySpAEVQ9KqKGLBggWsXCm46qoaLr+8BhAIYfjRj9Kc\nc86WQ9Kq9RZFDPRcNDfDggUuL77oUCEBd6B6TpSiT+fClP/cTeObTreZl6UwoUKF5XVBjmNLUMaN\n6zlJA1i4cKElLG2Y1vHHB9x9dzPnnpvhiitaefzxZqZN6zhVOGBBKa2JWlsJ1zcRbmxBteZQ2aDg\nnyo9t/ivDVk2xhTkXYQbp9LbTFz1+rColHmoPLO0KvoMq1YJfvCDWp591j5NeZ7h5z9Pc/jhYY/q\nOKqoortYt07yb/9Wh1Jw7LEB55+fY599VF80LJZh40Z46y2HjRsFqZRh/HjrkFHFwEJIUUypxTVV\nfbFNHZrCzwIxoF6VjY0we3bE7NmVoS9plEJFCh1qhM6nbTXCFwUHCCFEh3WMxhhMFFtPxfp2VVQ+\nuu31ORRQTX1ay4ozzqjljTeKRun33NPMQQepqr3TMIXWtqP3ww8lUWTNiceN04wePXiXeDoNZ59d\ny6OPWtHURMJwxx0tHHZY1GcPC83N8N3vprjttmIdTmOj5v/9vwxHHhlsMZHjSkFHWmi9JVYqtJZH\nheYDd8tN1eWJmsoGqHQrKgwLnaBebWqT6eZ2tWl9oMVXRd9gU6nPakRtGOLllx1OOaWuYPsyYULE\nL3+ZZu+9h48tVBXt8cILDsccU08uV1zAtttOc/75GT796XBQIky1tXDhhVmeeMIjigS5nOBzn6vj\nppvSHH982CfuHRs2CO68s5z1bdwoOeecWi69VHL++dlBl8rpKsIQXntNsny5Q0uLoL7esNNOil13\n1dTUDPbouoZ2YrUxOTD0nBhI1y1vKOgFScuLvua3O1Tw9tuSN9+U/POfPivelaRShm23HcGIEZqt\ntjJsOxp23NFQM3R2qYouonpIhxG0hkWLHObOrY99xZ7mU5+awfXXt/bKu1Nrm0ZtbRWMHq0LnU5D\nBQsWLGDmzJmDPYx+h+/bhb4UH34oueiiWv73fyNuvz3N6tXPDvhc7LWX4gc/aOX8820dqzGCc8+t\nJZFIc8wxYa+748aMMZx3XpZrrmmvG3HjjUlOOSXXTlCyUs+JRYtcTjyxDqWKREQIw8knB3zzm1l2\n3LHvH7b6cy6MaauPpntE1IQQCNcKzX7wgaSpSeD7hh120N0S6S4TkMWStnz6r1LPCYB33pEceWQ9\nGzZ0PndCGGbOjPiP/8jxyU9GjB3b/sFMOA7GRPH7O06PQmXPxUCiUuahGvMcJtAa/vxnlxNOqC+Y\nvx51VMC8eelekbRVqwQ33JBk5swGpk5t5EtfqmP58uppU4nYc0/FXXe1kEq1v0EvW+by4x8nGQy5\nJNeFE04I+O53W0teFZx9di3LlvW+Rsbz4Mwzs/zkJ2kaG8vP9S98IcuIEUOnuuP5590ykgaW2N57\nb4I77vDpQDR/i8Hf/uZw1lm1zJjRwOzZDRx2mL0fvfdeL6JrQ6TyZ4cdND//eZpddum8Ts4Ywfz5\nHqefXsfZZ9eyalXH8yJdt0yAuIrKR7VGbRggT9Lmzq0jDG1n57XXtnLiiQEjRvR8uy0tcPXVSW69\ntTxS8dOftnDyyZXtY7olY9kyyRNP+PzsZwlWr7akWgjDd76T4ayzcgPXmdYGzc3w4IM+559fgzF2\nEZkxI+R//7eFkSP75js++EDwj39IMhlBY6Nh4kQ1pCLAb7whOfXUWlasaJ/sOO20LDfckBlyNaal\nXpVtddC6ildflRx1VD1NTe0/e++9zRx5ZNcK/dvqpQ21Gq01awRvvy156SWHxYtdli1zWb3anu9g\nHRF23jniK18JOPLIoM+uqyr6H9UatWEMreHpp4skbeRIzc9+lmb69N4Xa7/zjuTWW9sXEZXWQFVR\neZg8WTN5cpZ///ccq1cLgkBQW2vYeWc9aCQNrK/dyScH7Lij5oILUixf7rJwoceKFQ4jR/ZNqG/8\neMP48QMTNty4EVascHjrLcmiRS4rV0p23VVx1FEhn/yk6tH1N2mS5sEHW3jxRZff/MZn+XKHxkbD\ncccFHHVUMORIGsQaXb0871591emQpNXV2fRnl8cSp1CN1kPOkNwoxVYjDAd80vCJPXOcfnyOjU0O\ngU4SiQQaSW0tjBhhqKplDS9UidoQhjHwzDMup55qSdohh4Rcc00ru+1mb1y9za+HYez9UoL6esOU\nKZXRpt5VVEqdwUBjzBjDmDGVVZvl+3DwwREPP9zCSy+5vPGGpL5+4IP6vZ2Hv/9dcsUVNfzxjy6l\n18gf/gC33JJkyZImJk7sWZ5yhx0MO+wQcvTRIem0NUzvS5X7thjsc6Ir2G03RX29obm5ONd77x1x\nww2t7L579+e5oyhaJcyDtbIy7RsySmrrTKTIrt9Abu16fCNI1daQHDUSv7GuQ2HbnqAS5qISUCnz\nUCVqQxhLljjMnVtHFMFVV7Vy0klBn9pB7bST5oQTctx/vw0NjB+vuO22NHvuuQUXylTRJxg71jB2\nbMicOYM9ku5jU2k4gC9/Ocf22/f+GnEchlTaFqyVThjasfu+YeRI+kQzb7/9NE8+2cS771rpmVGj\nrJ9mZ3Y93UUlVAAZra1gbfxzaUeq0RoVWEHbIN1KsD5N2NSKk0gg/YAg3YqT8DFhhIyN2YdSSreK\nTaNaozZEsWyZ5KijGmho0Nx6a5opUxS+3/ffkxcSBRg/fnA1uaqoohLw4IMeX/xiXbvXt9pKc/XV\nrRxxRLjFabcpZa2WfvjDFM3NgkTC0NBgOOCAiE99KmLCBMW4cZrttzeDmn5vi7KaNVEuA0IvZUC6\nizL7Lcrr56IgQGdDVBiSWb2G7Ecfo7M5BALZUEdqu23wUimkI3HranA8b8jV323pqNaoDTOsWiW4\n8MIazj47y9y5Qb+07OfR2AhTpgxCq2AVVVQoZsyIuPPOFl5+2WHNGsF++yl22kmz006qnQzIlgLH\ngX33VQQBpNOCdFqwbp2t4fvNb2xEvr7e8K//GjB3bsDee0eVUeiudZEcGVBBgBAxuTEKMYA6a0KI\nssieIZYzMQa0QTgSk1WWSEoQiQRKRwiTwxiDygbguegosl2dwy8Gs8WiSreHIHI5wfXXt/KNb2xa\nV6lSfMoGG9V5KKI6Fxa9mYdttjHMmRNy6aVZfvjDDKefHjBrVjRkSVpfnRMHHKB48slmrrsuzciR\n7e9Lzc2CX/86wXHH1XP88fUsXOgQBH3y1X2ChQsXlkW0TGR9Rc0AaaLYdKWwJY8C0BqdC1BBiABM\nZMeioxDheiAdvNoa3Jo6TC5E5XJoHSGkYwloL6Jp1fuERaXMQzWiNgQxYUK1RqyKKqqoPOy8s2bn\nnQOOOCLinXckS5a43Hefz4oVktKmi7/+1eXYY+t56KEWpk8fxOYkKcEoVBDG/4JCQb7WGikE2iik\nNzAdosJxLEeLIuvmEMXSJo4E1wHHIbntNuQ2NKHTrcjaJFI66EjhOS5OKonjOlu0xdZwRLVGrYoB\nxfvvC37/e5/tt9dMnRr1WTFwFVVUUZlYu1bw8ceCjz6SrFtnmw2iSDBihGGvvVSvHjxtN6S2shvd\nLH7L14QZrdBKI/JE0miMFNZbFIHRCuG5OCUisek0vPeeZJttzCbvYVprdBCABulKZBcLiY1SqDBC\nB2Gx29MootYAHYYgBCqKcHwPnc4S5jK4foLEViPwG2tx+8KbrYoBRbVGrYqKwXPPuVxyiTUtPOKI\nkOuvTw+KB2UVVQw3lBpuD1QhuVLw/PMOH3wgqauzpGXnnVWZrdOoUYZRo0yPZDQ2BdsIoAs/g+oy\nWTNtatPQBoOJLa4EQjroXIiKbLRPCoEwIJRifbPPzTcnufHGJL/8ZZqjj+5c/DtP0gB0pMHVyC4c\nF+E4iCjCCIGUBmNASBfpK1QuixQurusi0ZiEjysMbqoGYww6UETSRgarUbXhgWqN2jBGpeTXS5G3\ntwL44x89fvGLBNls/35nJc7DYKE6FxbDbR468tTsKnozF+k0XHJJirPOquPf/72eI49s4Jhj6nng\nAY8XX5R897sJnnvOaedB2ydokwzqcXJISoQjbI0asR+mspE6tEErgwltKrK5RfCTnyS58cYUIFi3\nrptESBflN0rN4du/TaO1RhjQxqC0JspkidI5iDTCd3GSCZQBx/fw62qtDIoxtlYtG6BaM+gg6NG8\nDLfro6eolHmoErUqBhRjxpQvID/6UZI33qigfv0qqqiiy2hogO9+N4PvF8nA3//ucuaZdZxxRh1b\nbQXf/naK++/3etQ4sGaN4Ne/9vnv/07xyivl9wkhZZked3eiR6WfFVIgEwmE7+EkEzYqZ0A6Drgu\nQmtMpNGR4pVlSX70o2JacZttNk2IS7XQkPZ3HUUxETRxFLSctOkoQqXT6CBCug7S9RBaIWwiFh0p\nwo1NRE1pQCCMIQojdBSA1jZAGEboSKEjbVO8JTBKxTVw1VrnoYJqjVoVA4oPPhAccUQDH39cfEa4\n6qpWzj03N4ijqqKKoY986tMYY8nHAElLaA3PPefw7/9ex/r1bZ/9DWefneOddyT/9V9ZDjqoe1I/\nt96aKJRKNDRonnyyueC8AkUlf+jYbWBzMMYUCF5p6thoVSjmV0ohpWB9S4rPnjKSZcvsvAphePrp\nJvbee9OER8eEKJ/y1GGROFmpjVivTdhIm86FqGwOrQwy4eEmfFSQQ4eaKBegsll0YCU5vJoahOfb\n1KzvWhkPIRCORPoe0rGNBdJzEUK012qrNh1UDDZVo1aNqFUxoBg/3nD99a1lr736ajWiVonIZGzB\n9PLlknR6sEfTdShltQY/+kh0OO7mZqugP9gwhrgz0uH1163ifm+Ql3cQwhbCt42k9BekhIMOstIc\nl1/eSjJZ+uwvuOWWJAcdpLjkkhSrV3d93j/8UHD99cXoVVOTbHevEEL02Og9//nCzzGpEa6D9H0c\n30O4Eq8mhZNM8vqbfoGkARxzTMCuu1oSpqMojmJF7VKNUsryurSSKTAUiSKmSBaF52EwoBRGGNz6\nOltDF9rtS8/HcTyEAbQCR+J4nh1zwkMmYpImRfGc6AjDL04zLFElasMYlZJfb4uZM0O+9a0M+Ue7\nnXfu3xB8pc7DYKArc5HNwoIFDqedVstBBzVwwAENXHhhDR99NPjkZnN46SWHc8+tYebMBmbObOCo\no+q57rokr79ub3XvvSf46ldrmT79Re6+2xtUAvrnP7scckgDc+Y0cPDBDdxzj08m07ttltapYfK1\na3qTdUp9dX3ssovma1/L8cwzTcybl2bKlJC6OoMQhpUrBVIKXn656w9lGzcK1qwpX6Lee693S5Yx\nptO5WLBggSV++X+Og5NMxtpmgnt/VdpJafjqV3OkUm1IWpzO3BSk6xYIlIwN4nVkP4+U9nhFCsd1\ncVIJ3GQSCfh1NXh1KRzXAyOQSR+RSOAkfKRvHRW0UggpcFNJnKRvo2rxd+S7YwsQnUchq/dMi0qZ\nh2rXZxUDjhEj4KtfzTJ9esjKlZL99686H1QK0mm4+26fb36zhtJH/1/9KsGZZ+YYM6Zyj9Xy5ZLj\njqsvM+5et07yyisuN92U5He/a+b55x0efdQHJOeeW8u4cS0cfPDA63itWCH5whfqSKftWKNIcN55\nNey5p+KTn+zFHAvKUls6imKJCW3TYf2YDtUxEZg4UTNxYsCxxwYsXOjywgsuL73k8NJLLvPnu3z6\n012b71QKkklDNls8nttt1/MIkFEKnY9IOV2TyhBCIFyXNWtg8eLi3J1xRo699lLxdosdpEYphOx4\njvMEsVRKRAAqyllXgvh90ndtelTa45X/m434uciEBxikdHHrUng1SUwUEWWySMe1DQhBaOvtStKd\nxhhrk5XvjK2mPIcMqhG1YYyZM2cO9hA6RSoF06YpTjwxZJdd+jeiVsnzMNDY3Fy88orTjqQBjB2r\nGT26souPa2pMp0SypUXw0EMey5blIzqHAIIf/zgxKOr4TU2UEUoL0euopXCcorK9sDpg+eJ1HUYd\nRnv64vqIslnbaZjNoePvSKVgv/0Ur78uefJJS4qWLXO6nG3bbjvNCScUD04iYdhrr56Tap0XjzV0\nWGS/qXnIZgWrV9vlcsqUkPPOy1FTE9e4SVmIXAIdSoQYpax4baTKjoExxnaZxjZRKDs+x/dxXLfY\n8FBIY4IUEsf3wREIrVC5EBVEGBU3EYRRLJQbX6+mSFJ1NkAFAYhNC/hW75kWlTIPVaJWRRVVFLBy\nZbmCPNjOtjvvbKl4vbsxYwz/939pPv/5LFKWj3X33SM++9mAtWvL9+2VV9zuSyz0Abbd1jBuXDlp\nktIwdmzv5lgIm06TsTirLbYv/j3fbJBPtW0uTdcVaKVAx2QgiFDZXCF6tPXWhu9/P8N3v9vK6NGa\nz30u6HIgx/fhv/4ry+c+l2OffUJ+/esW9tijNw8LPZ/bUaMMxx8f8IUvZLn11nTBuk+IWBBX2PRo\n23owYwwqtK4H+TkpTU+L+DMmsp2YWtmIn7Fqu4VUqo6N44XnYmTcoGAgzIboMIw/H6KzQSECZ6LI\nSnVEoSWpKk6B64GrXxwsDLfSuypRG8aolPz6YKM6D0Vsbi722Udx+OEhiYRhl10U3/pWhkceaR4y\n6enddtNcfXWGpUubeOyxJh58sJk//rGJRx5pYc89Nccck1+gngasUXiptMRAYcwYw513trDHHnY8\ntbWGW29Ns/fefTfP+e4/Yu4t4wiNiRd9q8pvmD9/fre33bbWy9ZA5fN/5XVa22xjOz+ffrqJo47q\nnqDazjtrrruulYcfbmHWrKhH9pX5sQrXLax4wpXtIl+bujZSKbjmmlauvTbDTjuV7LcxCFnSWSnL\nt2mUldXIR7U6gzYmrnOzkc9iY4GdVx3YeXMcF4yxj1JBDh2EqA3NmDDE8VxkwkW4EqU0YUsrUTYf\nbVMYFZWkXMWA1C12F6WRyZ5i0SKXuXNrefRRj40bezeeSlk7qjVqVVRRRQG77ab5+c9b2LBBUFtr\nGDlysEfUfdTU2ML2XXZp/7dp0yJ23FHx3nv29899Llemoj+Q2GcfzYMPtrBmjaCuzjBunOnzsiHp\nOHHUp5iW62oUzZiOy5jKJB4ciXQcTEwOkHRY+yUljB7dM0KcSNh/PUGp5AYC3GTSzsVmUn8dob6+\n/WtCCEycYs5/R/kA4pcdWYhoSbeczOkoQgpBpBQmDNHGgFYYIZGOLHTx5omVm0igZUgQKQhDlBDo\nXIgjBY7vY4S0JE5rhDJI3wM33pYUBQ25SpPlKJdH0T2up/yf/0nwxBM+Tzzh8+UvZ7noosygXeN9\nhaqOWh/hgw8Eb7/tsHq1RAjYdlvNHnsoxowZdtNbRT+ipQVee82hqUnQ0GAYP15Xz6E+xptvSp54\nwqO+3jB7drjFza8VWI2jFoJ2C+IHHwj+/GePJ57wuPLKTEGCAuKIR1RC9Eo+X0rgBsrCanMo1SyD\n/tENs+nEeI5iTTRrUWXTnvkoW2fadiqXI8rkMJHVScMYnKSPUdp2bjoOGIX0fMucjSFsbSXKRQil\nMLEQrkwk4u7PCJWLIP6L8D28VALhuYVGgko4Nm3RV8fq0ktT3HJLsUP35pvTnHpq11Pu3UE6DevX\nC0aPNnhe77ZV9frsZzzzjMuXvlTL2rXlJ/+UKSG33171sqyia9AabrstwXe+U1N4bexYzfe+18qn\nPhXS2DiIgxtG2G03zW67lQssf/CBYO1aQW0tbLWV9aYcrrARFbtqlS6EWsPSpQ7nnFPDihUuQhgu\nu6zreiHSdcs6GysCbbpg+2NcQggoSaPaGkBVIK46yNnUqCMxQhTrBmOSK10X6SkMEVI5NpRpTCFV\njTEgHYwQYDRRJrC+oQBCQhShpUDqCK0EKp1FSAcVBkjPxRWeTZfm6+gq5di0RZtj1VPMmBFxyy3F\n3y+6qIZPfjJi0qS+b4Z66imPc86p5bzzspx2Wo5tt+2f+0bl0eohhuXLJaefXteOpAH85S8e//jH\n4E1xpeTXBxtDZR60huefL392WrVKcsYZdfzkJ8k+0fyqhLnIZuGvf3W4+26fe+7xefvtgb9GSudh\nxQrJv/xLA4cd1sjUqY18+tN13HWXz/Llw/P2aD0si4vWggULUAqeesrluOPqWbHCnoMnnhgUiubz\nyBe/F7pKnQ4EaCuICJR2wQpn08ezt9eGUQoVBETpNFEm7oLNZItWUcqggrAYOYrr0ITjIF0HJ5mw\nQrWei3BtrZn0vJi72IaDKBsgpRW3RQiUMFbg1pEYjSVkjotBIx0PQRzFEzI2n+8aWSmdi3/8Q/DG\nG5ING3o1PZtF22PV0/No//0jdtihGPVtbbUR4p5gc+fEkiUuLS2Cq69O8c1vpvj44/4594fnnWgA\n4XmGkSM7PvmPOy5XZndSRc+wbh3Mn+/yq1953H+/x1//6nT1fjOk4Lrwn/+ZxXXbP5X94AdJ3nxz\n6Ds4rF0L8+YlOeywes49t5ZzzqnlW99KDYpERh719YZtty2eUMuXu/znf9ZyxBH1/PrXvS9IriTk\n0555e6R8BGz+fJe5c+sIQ7vQOI4VdPVElrCllaAlXahts8TCLWh8VTLKumD7Md1n/TMVOhcSZUKi\n1ixRa4YwnSVqaUXl4hPc5OVBIqJMhqi1lSiXAyHRWuP6Hk7Cw3El0nfjdGlJCtDYOjejNEIbHCSC\nWG/NkZaYeS7Cca1PaMJHK43WKj8h3TJpX7TI4ZBDGpg2rZFjjqnnqafcXosyd4a+OlbbbWe46aY0\nQhT387HHeuY1uznsuWeREP7udwkefdTrl7WpWqPWB3jjDckjj/g8/bRLc7Ng330jjjkmZL/91LBO\noQwE3n1XcOGFtWVPRJ5neOihZqZOHRqdiN2BUvDii1Zd/623itE1zzM8/vjQ6b7sCErBL37h841v\n1Ja9vsceit//vomGhkEaGPDaa5KTTqpj5cr2ZPgb38jw1a9mh0XquZ3XoyN55W8en/lMfUF8F2xd\nzwnHNCN0aC2NhEC6smhaXqHIy06UisoOBPI6ZSoXomKXAp3JYITE8T1wHbxUEjeZIEynUdkQE2nw\nZInVkyUnhc5RYZCeh44UUmA7MjDoSKNyIcZYRmCCCOm7tj7NxMEzrRHSEj0TRgjPxfHcguF8Phq6\nOaL95S/XcN99pZ0chttvT3PccWFF6+Vms/CrX/lccEENxggmT4547LFm6ur69nuef97h05+uJ99F\nkkwannqqid137z5bq9ao9TMmTdJMmpTla1+DMLRdZ1X0Df73fxPtwtZhKPjTn7xhSdQcBw44QPHw\nwy289ZZk9WrrATlpkmby5KG9vytWSP77v9tfHGedlR1Ukgawxx6a++9v4ZZbEvzylwmMKa5C112X\nYurUiMMOG/raU6JNRGX1Px3OOqumjKRddFGGzxyVQYQZwtYcKhfY1FxNApnw2zU2VgoKsiPkVfh1\nlyIz6TQ0NYneadgJAVKilcJoBdpghMDxPIS0KUzpOVYfLU5jqiiCrCLCEjInkUC4AseLuzKl1cHT\nQUikNVII/IZanKSLTFjNNKO09QA1YExJ9M2NpUMMiNic3SgNothFitZltXUdYeLEtoRDcM45tey1\nV1NFZ4uSSTj11IBJkxT33eczZ07Y5yQNbETtmGMCHnrIktlsVvDIIz67757t0++ppj77EJ5XWSSt\nEuqReoNcDp57rqNnCcO0aV1f0cbLKwAAIABJREFUNPtrHlavFjz/vMPjj7s88IDHQw95vPSS0yep\nsm23NcyYoTj++JCTTgrZd1+1uXtqlzCY50RLC+Ry5cv8UUflmD27e9pafYGO5iGvwfaHPzRzwQUZ\nttlGA4Zk0vTaML1SUFS4txprixa5vPlmcS4uuCDDf/xHFk+1EKRzZNZsILNmLdn1TQQtWcKS/JFN\n9+U1ulSfCej2FD1JDn3wgbXuOuywBu69d1GPv1tIiXAkTtLHSXi4NQn8+hpbz2dA5LXP4tRzFAQE\nLWkyrWmUUlboNp476cdixVphAitmK7RtUAiabQra9a2/p3AdZCIJwqDDEB0EtlYuG2BCZVOe2sR1\ncrroSxpGm9Qry18fxx4bsPXW5e+zLg2VSteL8H046CDFD36Q6fFD1ubul7W18PWv50iliufefff5\nfV4uUY2oVVGxSCTgsssynHyyW7Dbqa83/PCHaQ48cPBWzkzGiipefHGKd95pfwnNnZvjiisybL11\nNe1diu23N5x2Wpa7704wZozh4oszHHFE2G+dUj1BKgWf+IRi//0VX/pSjtZWkFIwblzlRg+6i3xK\nsLkZfvxjGwlIJAzf+14rxx0XUF8TEGywCzwotNIIDCqbQ6UzKM9DSlnQvMpbRuWtlEANSnpUSFkm\nO7K5aFpzM9x4Y5Lf/tbOwfvvd/5+k++a3NT3xxE06VqDdLSLchRgOziNsIbrmljUVdmUphQS10/Y\nejTPs7VmDuhAo3WEygYI17GyKEYTZXO4vraNBsbYY5ILka6LDhXKUZYYyng7josUtnbNGr/HRftd\niI3utpvm/vub+c//rOWVV+y9btQo3WsHjeGEyZMV8+alOfPMWrQWvP22ZONGSWNj390zqjVqVVQ8\nli+XrFplbyrbb2+YMGFwF81Fixw+85liXUJbNDZq/vzn5kEfZyUim4XVqyU1NYZtthl2t54hhQ0b\n4OKLa9hmG8NJJ+WYPFkjBKgwJGpuJWzNkFm3AZ3J4ng+MuWT3HZrErUpkAIhLLEpbTIA4mjd4NSx\nmVjaoispT1tfVMy533xzmrlz21ecF03NrVCulO1dDdq9F0vsVBAg4xSm0QYhBWG6lbAla62nEBij\nkQkf1/fxGusQYG2htE2Uhs1piG2kHM/HqU0hXWlr2Ywht64p9gyVVihXCgQSJ+FjVISTTOL4XqHr\ntXRupNe1WM3atYJ33pE0Nwt22kmz887Ve1spwhAWLrRNSDvsoLjnnpZul3NUa9SqGNLYeWfNzjsP\n9iiKSCRs5KWj7qfdd4+48cbWKknrBMkk7SQfqhgcjBgBN9/cSqkGq9EagU2/uSJFCjC5wAbXPK8Q\n0RGOLPiJ0lb2QsrY+qjohjBQ3aF5rbCuYOHC8uUvlWyfts3XvVmhX22L8xGURg0L6V4pC4K2Rlsr\nKCFkbNtl4o5PgXQkTspHaFBRhJfwwHNtlFKpmATnawkNXl0NKgghjJCOtJFOU2yckL6LDiKbZsXB\nSXg2takipJ9Aek5BUsVG++LjIrt+TEaNMowaNbRrZPsTngeHHBLx1FNNaE2f19xWidowxoIFC5g5\nc+ZgD2NQkMvB229L3njD4f33n+ULX5jWZ117n/yk4g9/aOLNNx3+/neH2lrDdtsZxoxR7L67ruhI\n0ZZ8TpSiq/PQ1NTE+vXrcRyHsWPH4lRwx2NP4LrFuSg6Fgik7yMTPtJ1rKG3VkSZHKqlFeN7OKkU\nRgU2UuMVyQnSmimZ2DQcYq2wHtoB9QR5kripzs/mZrj//nKrqzUfPwPYc0IHgbVgMgbheu1cvk1c\nc1bWRWuK+6lyQcnrxJZNltBKP4GXSFgDdd8KC+eJrFYaz0ugTYQR2n5GgjSxaG1cWygciYgbFvLp\nUqtBVmxgQAoc37MNBrJoH1UaUcvLiiCw24kJ4sKFC6v3Cbp/v+yve3+VqG1hWLVKsHSpywEHRGy/\nfeUSit5g3Tq4664EV12VQikB1DBzpsOUKX33RLjnnpo999Qcd9zAF8JX0f9oampiyZIl3HDDDTz3\n3HOkUilOP/105s6dy+TJkwd7eP2DEjKST9sJITEqtHZGrofSIISDzuUQrouT8K2Aq9Kx5Y+DjqKi\n9yX0idp8l3ehxB5rU52fGzYI3nijSOImTFCMGWMjVDqKCsr/BoEJA0vWZGl6N95m6b6V+HGWjUcD\nriy8VzoOSGHnTAqinI2WISTChTCTsRp3yiAcEJ6PwOAmEjZd6lrShSORIiZgwhq7G207PWXCErR8\nhC8fadRhVCZUrIKwMC6lczieV9TY013rmq2i/1GtUetHvPeepKUFGhttxKUSzvkHHvA488w65s7N\nce21rdTWbv4zQwkbN8L11ye5+eZU4TUhDM8808TkydWUWxWbRzqd5rbbbuOqq65q97f6+noefPBB\n9t9//0EYWf+ilORopVDZHBgbHVJBiJESoWwdGwIcz8OpSVh7ozCyZuOixKMxloIYyJq1MhN2Oq+X\nW7VKMGNGAxs22Jvyrbc089mTYqIWlFg0AdKVSN9H5x0dhCh4ZpZF1ETRRksHoe2CjbRNE3t5OyhA\nCqLWHKo1gw4ioiDArUniJHxQyprba4XwbEQTrUEbhOchXGvALh3HGq17rnUpwHpl6iC04/NcZCzL\nAR17tArHQWWKVmombnooTVN3tYatw+MQN2BUsu5eJWFTNWoVQB2GJ55+2uXggxuYNauR6dMbueaa\nJO+9N/jTPX++vfDuvtvn9deH3wX0hz94ZSQNYM6csFr8WkWX8eabb3ZI0gCam5u59NJLaWpqGuBR\n9T/yEhN5+Q6EtJZHQWhfN/k6K4NTk0KmkphIo7I5jNFW6DVUCBEXuudJ20Au1G2fhjupV9tqK8Nh\nh9lo+Ekn5Tj8iJIuctctXxnjmjtUnM41phA5syr6osxwXeSJkusgfRt1FFIWmhx0pDBRhAojVBRh\nwsjaTWUDokwWE1iCpzLZuM5NgFP0+UQbVKQIm1oJmltRmRy5dU2oTM5uW+lyo/gS5GVUdBRvt2Q/\n29k2FcwQdLekT2wU0dbRGW02KQNSRdcw+MxhmCCXs92JH38sCAK45ppUQVKipUXwgx+kOP30Wlas\nGLgpX7BgAU1N8NxzDrff7vP00w6vvpp/QhI8+WTP/M8qFR99JLjiinIhu9GjNXPm/KGi9O0GE0Nd\nW6+vsKl5eOaZZzb52aVLl/L222/39ZAGDaVzIfIdjSKuhZI2moQjcZMJ/MY6RDJhIzxCoKWwte2R\nIsrl0JR0XGpd0FgbKAghYnIo7f87SWMkEnDxxVnuv7+Zq67KsNVWxXmQ8T5nI48lL9byy/+r4Y9/\n9Fn9z5hwtvHMFE57Mpqft3yETQWBlc4IQ9AaFYYFUiQ9F1GIgLkIz6YsHSkLWmluIoHwLfkzUkKk\nrE5aEBI0txCkWwmzOXQY15xpYyNs+YYOYbtL8wTKprSVFdn1HITn4Ph+ocFg4aKFMamMLPGLunEc\n25K6fkjaaQ0D8axUKffLao1aH2D9erjjjiTf/36SOXMCfvSjVj71qbCdWOvf/ubypz+5nHnmwBgb\nrl8v+O53U/zsZ0kApk8Pqakp3mAee8zj3HOz1NcPyHD6HWvWCD78sHhj3mEHxZ13trBhQ/WJroqu\n45133tnse5qbmwdgJIMHIaUlLLUpMBoVqTgFp0BpwlyIikJc14XQSkIQGVRLKzqZKHZf5uu2uugS\n0Cdj72Ln5667anbdteN7g5SShYtdTj21jnxoaerUkJ/Oa2GHcVGXtm8dAhxMNhsTJAPazq2TTBAE\nLSCMrTVzHNyaJMaTqCA2avccHM8p1IshBcKV6FyIDnIYYZDSReVyBWImE0UrKmNA5wKIU6DSddGo\nOD2s0QocxymkTgFwHFsXF5P10ho8o23N3GYhrUxIyUR04UNdw/LlVqT5kUc83n/f4ZRTcpxxRm7Q\nnU36G9WIWh/gj3/0uPrqFGEo+N3vEqxYIZk7N+Dgg9sXmn/00cBMuVLwwQeHFUgawMqVkh13LF55\nr7/usHbt8DkFtt7acMIJOfbaK+L7309z//0tTJ6sq91LJajOhcWm5mHSpEmb/fyIESP6cjiDirZz\nke9oFK6NSknfx6tNIZPW4FsIcD0Hx3ExjgRHEuUCdBhgNJY4lHhXxhst+45ly4raiJWCtvNwzz0J\nSrUSly71+N1DiTJfzs3CGAxxTZsQqGyOKAgQgJdK4dXW4tamcJK2A1X6PtL3QAqkY9PP5HXYQoXj\nuEgBTiqFV1+PzuYQRiBjUVvH93BrUoXvUtkAlcnazlspweTTt3TY/NDZXEDZVGwSXY1qdgfr18OD\nD3ocfng9X/taLU8+aUt3rr++mLnqD1TK/bIaUesl3ntPctFF5Xm1IBDsuKPipz9NM3++xy9+4fPe\new5Tp0acdNLARNP+8Q/J1Ven2r22774RYJW4lRIMp8DAmDGGefNayWYZNlHCKvoeGzbYcgTHgREj\nDKnyy4RDDjmaSy7ZGa23AhqBCCGywEaiaDVR9BG77LLLIIx8YJDXDhNCWuFW14nJmyj8jLZOBfgu\nJpONu0B93ISDUQVFCouCobjFRx8JTj65nlGjNL/8ZZqddqrMiPcuu7RP9f3mNz5f/GKu6/cXY6wd\nlFI2MgZIbSyZzTddaDvHcacBjucWiK1NHVsNN2M0Bg8hHIRLLKshijIcCQ8nlUS4DqrVdo7igBYC\nFYa4hRStLkS5dBgWJDvaEipbGyfL9PC6iu7o2W0OLS1wyy1Jrrsu1e5vF12UYfToYdcP2Q5VotZL\nLF9u7SLyEMLQ2GhPnLFjDSedFHDssQEbNwoaGw2JxMCMKwwhk3kaOLTw2qxZETvvXH7zyWYr66m2\nt/A8+68UVe2wIrbkufjwQ8Hvfufzi18kePfdZ6mr+xQ776w49tiQI48MmTRJ8+GHgh/9aA9++9t9\n6SiE4HmGqVNDnnoqYL/9InbYYegvEqXnhDGmRBBVxj6RGhN3N0opQUqUCq11VEuIRoNrIzoFXTBj\nEJ5VzkeIQj2WMYaNGwWrVklWrZLccEOSq69urYgHq7bXxvHHB9x2W5KWluJ5sO++qnu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D4JlnEby46V/bfvDyilwG88Gepob4cPPrBYuFDS3CwYPVozaZLHlluqYso0PcI6WaNWRRU9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nnxy46qrtN7OVh8+y7IgbGcbIzMxK8uUpInRkB0Kbtnq1MDkpzM4q3va2DrffbviTPxmw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\n9NBDPProo+R5zpe//GXOOOOMF/q0atSoUaNGjRo1nnfsd6VPay2f+tS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+ } + ], + "prompt_number": 14 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "This looks pretty good, though it took a long time for the system to (sort of) converge. Our optimization step would look something like this:" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "_halo_data = halo_data[n_sky - 1]\n", + "print traces.shape\n", + "\n", + "mean_posterior = traces.mean(axis=0).reshape(1, 4)\n", + "print mean_posterior\n", + "\n", + "\n", + "nhalo_all = _halo_data[0].reshape(1, 1)\n", + "x_true_all = _halo_data[3].reshape(1, 1)\n", + "y_true_all = _halo_data[4].reshape(1, 1)\n", + "x_ref_all = _halo_data[1].reshape(1, 1)\n", + "y_ref_all = _halo_data[2].reshape(1, 1)\n", + "sky_prediction = mean_posterior\n", + "\n", + "\n", + "print \"Using the mean:\"\n", + "main_score([1], x_true_all, y_true_all,\n", + " x_ref_all, y_ref_all, sky_prediction)\n", + "\n", + "# what's a bad score?\n", + "print\n", + "random_guess = np.random.randint(0, 4200, size=(1, 2))\n", + "print \"Using a random location:\", random_guess\n", + "main_score([1], x_true_all, y_true_all,\n", + " x_ref_all, y_ref_all, random_guess)\n", + "print" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "(10000L, 2L, 2L)\n", + "[[ 48.55499317 1675.79569424 1876.46951857 3265.85341193]]" + ] + }, + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "\n", + "Using the mean:" + ] + }, + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "\n", + "Your average distance in pixels you are away from the true halo is" + ] + }, + { + "output_type": "stream", + "stream": "stdout", + "text": [ + " 37.3993004245\n", + "Your average angular vector is 1.0\n", + "Your score for the training data is 1.03739930042\n", + "\n" + ] + }, + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Using a random location: [[2930 4138]]\n", + "Your average distance in pixels you are away from the true halo is" + ] + }, + { + "output_type": "stream", + "stream": "stdout", + "text": [ + " 3756.54446887\n", + "Your average angular vector is 1.0\n", + "Your score for the training data is 4.75654446887\n", + "\n" + ] + } + ], + "prompt_number": 35 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## References\n", + "1. Antifragile: Things That Gain from Disorder. New York: Random House. 2012. ISBN 978-1-4000-6782-4.\n", + "1. [Tim Saliman's solution to the Dark World's Contest](http://www.timsalimans.com/observing-dark-worlds)\n", + "2. Silver, Nate. The Signal and the Noise: Why So Many Predictions Fail \u2014 but Some Don't. 1. Penguin Press HC, The, 2012. Print." + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from IPython.core.display import HTML\n", + "\n", + "\n", + "def css_styling():\n", + " styles = open(\"../styles/custom.css\", \"r\").read()\n", + " return HTML(styles)\n", + "css_styling()" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "html": [ + "\n", + "\n" + ], + "metadata": {}, + "output_type": "pyout", + "prompt_number": 1, + "text": [ + "" + ] + } + ], + "prompt_number": 1 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [], + "language": "python", + "metadata": {}, + "outputs": [] + } + ], + "metadata": {} + } + ] } \ No newline at end of file diff --git a/Chapter5_LossFunctions/README.md b/Chapter5_LossFunctions/README.md index db5d2880..b14d9815 100644 --- a/Chapter5_LossFunctions/README.md +++ b/Chapter5_LossFunctions/README.md @@ -1,4 +1,4 @@ -Chapter 5: Would you rather lose an arm or a leg? -==== - -### [Read it online here](http://nbviewer.ipython.org/urls/raw.github.com/CamDavidsonPilon/Probabilistic-Programming-and-Bayesian-Methods-for-Hackers/master/Chapter5_LossFunctions/LossFunctions.ipynb) +Chapter 5: Would you rather lose an arm or a leg? +==== + +### [Read it online here](http://nbviewer.ipython.org/urls/raw.github.com/CamDavidsonPilon/Probabilistic-Programming-and-Bayesian-Methods-for-Hackers/master/Chapter5_LossFunctions/LossFunctions.ipynb) diff --git a/Chapter5_LossFunctions/data/Test_haloCounts.csv b/Chapter5_LossFunctions/data/Test_haloCounts.csv index 138e53ac..5f4642a1 100644 --- a/Chapter5_LossFunctions/data/Test_haloCounts.csv +++ b/Chapter5_LossFunctions/data/Test_haloCounts.csv @@ -1,121 +1,121 @@ -SkyID,NumberHalos -Sky1,1 -Sky2,1 -Sky3,1 -Sky4,1 -Sky5,1 -Sky6,1 -Sky7,1 -Sky8,1 -Sky9,1 -Sky10,1 -Sky11,1 -Sky12,1 -Sky13,1 -Sky14,1 -Sky15,1 -Sky16,1 -Sky17,1 -Sky18,1 -Sky19,1 -Sky20,1 -Sky21,1 -Sky22,1 -Sky23,1 -Sky24,1 -Sky25,1 -Sky26,1 -Sky27,1 -Sky28,1 -Sky29,1 -Sky30,1 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-SkyId,numberHalos,x_ref,y_ref,halo_x1,halo_y1,halo_x2,halo_y2,halo_x3,halo_y3 -Sky1,1,1086.80,1114.61,1086.80,1114.61,0.00,0.00,0.00,0.00 -Sky2,1,3477.71,1907.33,3477.71,1907.33,0.00,0.00,0.00,0.00 -Sky3,1,2315.78,1081.95,2315.78,1081.95,0.00,0.00,0.00,0.00 -Sky4,1,1408.61,1685.86,1408.61,1685.86,0.00,0.00,0.00,0.00 -Sky5,1,3091.65,2001.08,3091.65,2001.08,0.00,0.00,0.00,0.00 -Sky6,1,4129.17,3097.58,4129.17,3097.58,0.00,0.00,0.00,0.00 -Sky7,1,3124.25,1787.56,3124.25,1787.56,0.00,0.00,0.00,0.00 -Sky8,1,942.51,2909.72,942.51,2909.72,0.00,0.00,0.00,0.00 -Sky9,1,2556.11,2645.23,2556.11,2645.23,0.00,0.00,0.00,0.00 -Sky10,1,3960.10,622.67,3960.10,622.67,0.00,0.00,0.00,0.00 -Sky11,1,3069.86,2090.57,3069.86,2090.57,0.00,0.00,0.00,0.00 -Sky12,1,599.75,3236.08,599.75,3236.08,0.00,0.00,0.00,0.00 -Sky13,1,3551.90,1429.02,3551.90,1429.02,0.00,0.00,0.00,0.00 -Sky14,1,1738.48,4000.01,1738.48,4000.01,0.00,0.00,0.00,0.00 -Sky15,1,1613.07,0.62,1613.07,0.62,0.00,0.00,0.00,0.00 -Sky16,1,2476.41,1550.01,2476.41,1550.01,0.00,0.00,0.00,0.00 -Sky17,1,2915.74,3655.42,2915.74,3655.42,0.00,0.00,0.00,0.00 -Sky18,1,1065.23,3784.81,1065.23,3784.81,0.00,0.00,0.00,0.00 -Sky19,1,3823.16,2237.95,3823.16,2237.95,0.00,0.00,0.00,0.00 -Sky20,1,31.42,4197.65,31.42,4197.65,0.00,0.00,0.00,0.00 -Sky21,1,2672.81,2115.98,2672.81,2115.98,0.00,0.00,0.00,0.00 -Sky22,1,2920.45,1352.51,2920.45,1352.51,0.00,0.00,0.00,0.00 -Sky23,1,3499.76,32.99,3499.76,32.99,0.00,0.00,0.00,0.00 -Sky24,1,763.57,2103.49,763.57,2103.49,0.00,0.00,0.00,0.00 -Sky25,1,2856.37,2567.43,2856.37,2567.43,0.00,0.00,0.00,0.00 -Sky26,1,1754.64,2964.13,1754.64,2964.13,0.00,0.00,0.00,0.00 -Sky27,1,723.33,2933.69,723.33,2933.69,0.00,0.00,0.00,0.00 -Sky28,1,1869.33,3540.80,1869.33,3540.80,0.00,0.00,0.00,0.00 -Sky29,1,257.63,860.01,257.63,860.01,0.00,0.00,0.00,0.00 -Sky30,1,3276.28,2791.57,3276.28,2791.57,0.00,0.00,0.00,0.00 -Sky31,1,27.72,4047.21,27.72,4047.21,0.00,0.00,0.00,0.00 -Sky32,1,2124.46,2690.81,2124.46,2690.81,0.00,0.00,0.00,0.00 -Sky33,1,2328.73,180.12,2328.73,180.12,0.00,0.00,0.00,0.00 -Sky34,1,1974.29,1250.80,1974.29,1250.80,0.00,0.00,0.00,0.00 -Sky35,1,2082.12,2303.05,2082.12,2303.05,0.00,0.00,0.00,0.00 -Sky36,1,1600.13,3561.65,1600.13,3561.65,0.00,0.00,0.00,0.00 -Sky37,1,1600.18,1596.77,1600.18,1596.77,0.00,0.00,0.00,0.00 -Sky38,1,96.97,2506.70,96.97,2506.70,0.00,0.00,0.00,0.00 -Sky39,1,4055.27,4036.97,4055.27,4036.97,0.00,0.00,0.00,0.00 -Sky40,1,1375.15,451.95,1375.15,451.95,0.00,0.00,0.00,0.00 -Sky41,1,1446.47,923.23,1446.47,923.23,0.00,0.00,0.00,0.00 -Sky42,1,2276.07,3782.16,2276.07,3782.16,0.00,0.00,0.00,0.00 -Sky43,1,1380.99,1823.89,1380.99,1823.89,0.00,0.00,0.00,0.00 -Sky44,1,3562.40,2992.25,3562.40,2992.25,0.00,0.00,0.00,0.00 -Sky45,1,730.51,3579.06,730.51,3579.06,0.00,0.00,0.00,0.00 -Sky46,1,3213.63,1925.18,3213.63,1925.18,0.00,0.00,0.00,0.00 -Sky47,1,3291.09,2155.31,3291.09,2155.31,0.00,0.00,0.00,0.00 -Sky48,1,2088.12,2931.84,2088.12,2931.84,0.00,0.00,0.00,0.00 -Sky49,1,2040.60,3795.89,2040.60,3795.89,0.00,0.00,0.00,0.00 -Sky50,1,2338.84,1039.43,2338.84,1039.43,0.00,0.00,0.00,0.00 -Sky51,1,545.50,969.24,545.50,969.24,0.00,0.00,0.00,0.00 -Sky52,1,1253.48,2143.11,1253.48,2143.11,0.00,0.00,0.00,0.00 -Sky53,1,2202.15,1456.83,2202.15,1456.83,0.00,0.00,0.00,0.00 -Sky54,1,1141.01,361.90,1141.01,361.90,0.00,0.00,0.00,0.00 -Sky55,1,2483.21,2926.96,2483.21,2926.96,0.00,0.00,0.00,0.00 -Sky56,1,77.60,4136.84,77.60,4136.84,0.00,0.00,0.00,0.00 -Sky57,1,126.29,1106.39,126.29,1106.39,0.00,0.00,0.00,0.00 -Sky58,1,2391.73,3569.88,2391.73,3569.88,0.00,0.00,0.00,0.00 -Sky59,1,739.60,3803.98,739.60,3803.98,0.00,0.00,0.00,0.00 -Sky60,1,2886.80,4170.15,2886.80,4170.15,0.00,0.00,0.00,0.00 -Sky61,1,3399.88,792.21,3399.88,792.21,0.00,0.00,0.00,0.00 -Sky62,1,1125.91,3082.58,1125.91,3082.58,0.00,0.00,0.00,0.00 -Sky63,1,472.99,2221.15,472.99,2221.15,0.00,0.00,0.00,0.00 -Sky64,1,3296.92,783.17,3296.92,783.17,0.00,0.00,0.00,0.00 -Sky65,1,2679.16,1743.54,2679.16,1743.54,0.00,0.00,0.00,0.00 -Sky66,1,4156.44,1563.79,4156.44,1563.79,0.00,0.00,0.00,0.00 -Sky67,1,1898.73,3827.57,1898.73,3827.57,0.00,0.00,0.00,0.00 -Sky68,1,3220.35,1084.54,3220.35,1084.54,0.00,0.00,0.00,0.00 -Sky69,1,2903.91,1720.97,2903.91,1720.97,0.00,0.00,0.00,0.00 -Sky70,1,2649.29,1443.47,2649.29,1443.47,0.00,0.00,0.00,0.00 -Sky71,1,3289.63,322.14,3289.63,322.14,0.00,0.00,0.00,0.00 -Sky72,1,3622.75,3445.56,3622.75,3445.56,0.00,0.00,0.00,0.00 -Sky73,1,1618.52,1332.46,1618.52,1332.46,0.00,0.00,0.00,0.00 -Sky74,1,2302.13,3181.16,2302.13,3181.16,0.00,0.00,0.00,0.00 -Sky75,1,304.10,621.62,304.10,621.62,0.00,0.00,0.00,0.00 -Sky76,1,1017.36,3671.04,1017.36,3671.04,0.00,0.00,0.00,0.00 -Sky77,1,1989.58,2110.15,1989.58,2110.15,0.00,0.00,0.00,0.00 -Sky78,1,557.80,1667.74,557.80,1667.74,0.00,0.00,0.00,0.00 -Sky79,1,3102.74,622.90,3102.74,622.90,0.00,0.00,0.00,0.00 -Sky80,1,2766.53,56.79,2766.53,56.79,0.00,0.00,0.00,0.00 -Sky81,1,570.98,1308.07,570.98,1308.07,0.00,0.00,0.00,0.00 -Sky82,1,3125.19,2592.45,3125.19,2592.45,0.00,0.00,0.00,0.00 -Sky83,1,2480.87,2357.96,2480.87,2357.96,0.00,0.00,0.00,0.00 -Sky84,1,3100.76,3962.21,3100.76,3962.21,0.00,0.00,0.00,0.00 -Sky85,1,1821.55,2503.15,1821.55,2503.15,0.00,0.00,0.00,0.00 -Sky86,1,240.33,3327.76,240.33,3327.76,0.00,0.00,0.00,0.00 -Sky87,1,3367.49,3146.58,3367.49,3146.58,0.00,0.00,0.00,0.00 -Sky88,1,1644.00,371.71,1644.00,371.71,0.00,0.00,0.00,0.00 -Sky89,1,3487.03,2272.38,3487.03,2272.38,0.00,0.00,0.00,0.00 -Sky90,1,552.31,1898.67,552.31,1898.67,0.00,0.00,0.00,0.00 -Sky91,1,782.08,2979.85,782.08,2979.85,0.00,0.00,0.00,0.00 -Sky92,1,2714.03,3423.92,2714.03,3423.92,0.00,0.00,0.00,0.00 -Sky93,1,1962.14,2337.37,1962.14,2337.37,0.00,0.00,0.00,0.00 -Sky94,1,4106.42,3601.96,4106.42,3601.96,0.00,0.00,0.00,0.00 -Sky95,1,3537.15,3426.49,3537.15,3426.49,0.00,0.00,0.00,0.00 -Sky96,1,3418.39,3075.62,3418.39,3075.62,0.00,0.00,0.00,0.00 -Sky97,1,569.53,66.86,569.53,66.86,0.00,0.00,0.00,0.00 -Sky98,1,2882.48,3847.19,2882.48,3847.19,0.00,0.00,0.00,0.00 -Sky99,1,3294.22,2646.39,3294.22,2646.39,0.00,0.00,0.00,0.00 -Sky100,1,3868.67,978.09,3868.67,978.09,0.00,0.00,0.00,0.00 -Sky101,2,3136.47,932.52,4093.96,345.65,1604.48,1871.51,0.00,0.00 -Sky102,2,266.16,721.01,19.77,790.82,2591.24,62.25,0.00,0.00 -Sky103,2,1797.30,2446.26,1775.04,2459.69,3644.59,1331.22,0.00,0.00 -Sky104,2,506.86,2603.82,527.74,2497.54,332.85,3489.45,0.00,0.00 -Sky105,2,1627.06,2360.39,1084.54,2839.79,3245.09,930.61,0.00,0.00 -Sky106,2,568.22,2776.89,432.88,3242.41,1372.96,8.92,0.00,0.00 -Sky107,2,3615.38,3140.73,3807.44,3159.73,1249.43,2906.70,0.00,0.00 -Sky108,2,1772.22,1110.77,1845.74,1104.40,97.65,1255.97,0.00,0.00 -Sky109,2,638.04,1439.74,416.27,1191.24,2957.72,4039.04,0.00,0.00 -Sky110,2,703.69,1692.32,540.85,1839.21,2532.82,42.36,0.00,0.00 -Sky111,2,4078.80,2509.88,4169.14,2423.06,3265.72,3291.30,0.00,0.00 -Sky112,2,694.03,755.78,736.14,660.02,96.87,2113.87,0.00,0.00 -Sky113,2,1213.36,705.78,1446.47,575.95,34.70,1362.23,0.00,0.00 -Sky114,2,1667.52,2000.22,1708.87,2108.82,1387.62,1265.10,0.00,0.00 -Sky115,2,3249.64,2587.52,3309.86,2319.44,2897.31,4156.06,0.00,0.00 -Sky116,2,3255.77,3508.18,3333.78,3487.48,1327.28,4020.02,0.00,0.00 -Sky117,2,2875.26,1251.41,2899.04,1274.66,2332.99,721.28,0.00,0.00 -Sky118,2,538.42,2366.11,10.24,2110.45,4016.69,4049.75,0.00,0.00 -Sky119,2,1876.66,1243.96,1909.03,1243.69,73.02,1258.72,0.00,0.00 -Sky120,2,696.50,1951.06,809.50,1628.21,274.63,3156.37,0.00,0.00 -Sky121,2,2664.78,3333.94,2773.89,3466.15,591.75,821.93,0.00,0.00 -Sky122,2,2306.45,1789.98,1660.05,2182.77,4102.01,698.89,0.00,0.00 -Sky123,2,3303.82,847.93,3427.54,611.64,2495.85,2391.03,0.00,0.00 -Sky124,2,2308.41,3639.78,2289.97,3673.73,3722.29,1036.86,0.00,0.00 -Sky125,2,1850.47,2038.79,2106.88,1933.46,1117.86,2339.75,0.00,0.00 -Sky126,2,328.15,2720.55,318.61,3071.32,374.54,1015.41,0.00,0.00 -Sky127,2,2522.29,3652.33,2500.67,3645.88,3711.19,4007.22,0.00,0.00 -Sky128,2,2694.58,1346.67,3127.35,1448.40,359.00,797.67,0.00,0.00 -Sky129,2,3519.06,1693.89,3600.12,1732.84,1467.27,707.98,0.00,0.00 -Sky130,2,1350.32,3256.02,1253.07,3233.34,3122.40,3669.26,0.00,0.00 -Sky131,2,2192.34,3819.21,2299.36,3828.22,1569.89,3766.82,0.00,0.00 -Sky132,2,4111.53,2083.12,4113.81,2086.62,4011.03,1928.51,0.00,0.00 -Sky133,2,2378.04,2505.98,2301.69,2380.04,3345.10,4101.27,0.00,0.00 -Sky134,2,2065.89,2681.17,2007.76,2865.47,2543.41,1167.29,0.00,0.00 -Sky135,2,865.45,3848.74,712.12,4109.68,2927.49,339.60,0.00,0.00 -Sky136,2,3060.85,3901.79,3085.09,3990.58,2812.11,2990.52,0.00,0.00 -Sky137,2,2741.31,1894.10,3298.15,1505.55,501.14,3457.23,0.00,0.00 -Sky138,2,2331.21,1774.16,2162.30,1978.52,3623.92,210.19,0.00,0.00 -Sky139,2,2290.21,2120.26,2263.88,2034.11,2897.32,4106.59,0.00,0.00 -Sky140,2,1953.44,3942.67,1922.59,4039.31,2438.88,2421.73,0.00,0.00 -Sky141,2,799.42,2439.84,831.69,2542.44,250.76,695.66,0.00,0.00 -Sky142,2,3405.75,2455.36,3373.83,2814.78,3584.81,439.11,0.00,0.00 -Sky143,2,1071.39,2575.42,773.65,2660.44,3728.13,1816.82,0.00,0.00 -Sky144,2,2391.80,767.03,2137.22,810.15,3426.04,591.87,0.00,0.00 -Sky145,2,3232.65,2410.52,3253.79,2392.59,2752.78,2817.57,0.00,0.00 -Sky146,2,2866.30,423.49,2983.76,231.55,1356.07,2891.23,0.00,0.00 -Sky147,2,1475.99,2794.07,1435.58,3045.90,1715.00,1304.74,0.00,0.00 -Sky148,2,3019.09,1753.90,3102.97,1447.23,2442.38,3862.22,0.00,0.00 -Sky149,2,1577.41,951.62,1371.82,725.77,2936.41,2444.52,0.00,0.00 -Sky150,2,2555.48,2403.51,2739.69,2800.20,1878.80,946.26,0.00,0.00 -Sky151,2,1025.61,3462.25,1134.57,3516.28,13.85,2960.50,0.00,0.00 -Sky152,2,271.53,3384.67,74.15,3601.08,2307.02,1152.97,0.00,0.00 -Sky153,2,1796.85,523.89,1762.36,420.43,2641.86,3058.57,0.00,0.00 -Sky154,2,1537.02,3081.44,1532.41,3148.23,1663.22,1251.99,0.00,0.00 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) - a = 1.0/ ( 1 - d ) - b = 1.0/( 1 + d) - theta = np.degrees( np.arctan2( _g[3], _g[2])*0.5 ) - - ax.add_patch( Ellipse(xy=(x, y), width=size_multiplier*a, height=size_multiplier*b, angle=theta) ) - ax.autoscale_view(tight=True) - +import matplotlib.pyplot as plt +from matplotlib.patches import Ellipse +import numpy as np + +def draw_sky( galaxies ): + """adapted from Vishal Goklani""" + size_multiplier = 45 + fig = plt.figure(figsize=(10,10)) + #fig.patch.set_facecolor("blue") + ax = fig.add_subplot(111, aspect='equal') + n = galaxies.shape[0] + for i in xrange(n): + _g = galaxies[i,:] + x,y = _g[0], _g[1] + d = np.sqrt( _g[2]**2 + _g[3]**2 ) + a = 1.0/ ( 1 - d ) + b = 1.0/( 1 + d) + theta = np.degrees( np.arctan2( _g[3], _g[2])*0.5 ) + + ax.add_patch( Ellipse(xy=(x, y), width=size_multiplier*a, height=size_multiplier*b, angle=theta) ) + ax.autoscale_view(tight=True) + return fig \ No newline at end of file diff --git a/Chapter6_Priorities/BanditsD3.html 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+ + diff --git a/Chapter6_Priorities/Priors.ipynb b/Chapter6_Priorities/Priors.ipynb index 20086567..1b76e3a4 100644 --- a/Chapter6_Priorities/Priors.ipynb +++ b/Chapter6_Priorities/Priors.ipynb @@ -1,1827 +1,1827 @@ -{ - "metadata": { - "name": "" - }, - "nbformat": 3, - "nbformat_minor": 0, - "worksheets": [ - { - "cells": [ - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "\n" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "#Chapter 6\n", - "\n", - "____\n", - "\n", - "This chapter of [Bayesian Methods for Hackers](https://github.com/CamDavidsonPilon/Probabilistic-Programming-and-Bayesian-Methods-for-Hackers) focuses on the most debated and discussed part of Bayesian methodologies: how to choose an appropriate prior distribution. We also present how the prior's influence changes as our dataset increases, and an interesting relationship between priors and penalties on linear regression." - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Getting our priorities straight\n", - "\n", - "\n", - "Up until now, we have mostly ignored our choice of priors. This is unfortunate as we can be very expressive with our priors, but we also must be careful about choosing them. This is especially true if we want to be objective, that is, not to express any personal beliefs in the priors. \n", - "\n", - "###Subjective vs Objective priors\n", - "\n", - "Bayesian priors can be classified into two classes: *objective* priors, which aim to allow the data to influence the posterior the most, and *subjective* priors, which allow the practitioner to express his or her views into the prior. \n", - "\n", - "What is an example of an objective prior? We have seen some already, including the *flat* prior, which is a uniform distribution over the entire possible range of the unknown. Using a flat prior implies that we give each possible value an equal weighting. Choosing this type of prior is invoking what is called \"The Principle of Indifference\", literally we have no prior reason to favor one value over another. Calling a flat prior over a restricted space an objective prior is not correct, though it seems similar. If we know $p$ in a Binomial model is greater than 0.5, then $\\text{Uniform}(0.5,1)$ is not an objective prior (since we have used prior knowledge) even though it is \"flat\" over [0.5, 1]. The flat prior must be flat along the *entire* range of possibilities. \n", - "\n", - "Aside from the flat prior, other examples of objective priors are less obvious, but they contain important characteristics that reflect objectivity. For now, it should be said that *rarely* is a objective prior *truly* objective. We will see this later. \n", - "\n", - "#### Subjective Priors\n", - "\n", - "On the other hand, if we added more probability mass to certain areas of the prior, and less elsewhere, we are biasing our inference towards the unknowns existing in the former area. This is known as a subjective, or *informative* prior. In the figure below, the subjective prior reflects a belief that the unknown likely lives around 0.5, and not around the extremes. The objective prior is insensitive to this." - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "%matplotlib inline\n", - "import numpy as np\n", - "from IPython.core.pylabtools import figsize\n", - "import matplotlib.pyplot as plt\n", - "import scipy.stats as stats\n", - "\n", - "figsize(12.5, 3)\n", - "colors = [\"#348ABD\", \"#A60628\", \"#7A68A6\", \"#467821\"]\n", - "\n", - "x = np.linspace(0, 1)\n", - "y1, y2 = stats.beta.pdf(x, 1, 1), stats.beta.pdf(x, 10, 10)\n", - "\n", - "p = plt.plot(x, y1,\n", - " label='An objective prior \\n(uninformative, \\n\"Principle of Indifference\" )')\n", - "plt.fill_between(x, 0, y1, color=p[0].get_color(), alpha=0.3)\n", - "\n", - "p = plt.plot(x, y2,\n", - " label=\"A subjective prior \\n(informative)\")\n", - "plt.fill_between(x, 0, y2, color=p[0].get_color(), alpha=0.3)\n", - "\n", - "p = plt.plot(x[25:], 2 * np.ones(25), label=\"another subjective prior\")\n", - "plt.fill_between(x[25:], 0, 2, color=p[0].get_color(), alpha=0.3)\n", - "\n", - "plt.ylim(0, 4)\n", - "\n", - "plt.ylim(0, 4)\n", - "leg = plt.legend(loc=\"upper left\")\n", - "leg.get_frame().set_alpha(0.4)\n", - "plt.title(\"Comparing objective vs. subjective priors for an unknown probability\");" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "metadata": {}, - "output_type": "display_data", - "png": 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gwL7+jo6OkJeXx9WrVxEREYFWrVrBy8sLsbGxyM3NxZUrV+Do6Agej8fWUdvjIs35sfzr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\nPGgV8ZTWXrFiBVevXuXTTz+1injupu3p6YmjoyM7d+4E4P777weoknb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- "text": [ - "" - ] - } - ], - "prompt_number": 2 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "The choice of a subjective prior does not always imply that we are using the practitioner's subjective opinion: more often the subjective prior was once a posterior to a previous problem, and now the practitioner is updating this posterior with new data. A subjective prior can also be used to inject *domain knowledge* of the problem into the model. We will see examples of these two situations later." - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### Decision, decisions...\n", - "\n", - "The choice, either *objective* or *subjective* mostly depends on the problem being solved, but there are a few cases where one is preferred over the other. In instances of scientific research, the choice of an objective prior is obvious. This eliminates any biases in the results, and two researchers who might have differing prior opinions would feel an objective prior is fair. Consider a more extreme situation:\n", - "\n", - "> A tobacco company publishes a report with a Bayesian methodology that retreated 60 years of medical research on tobacco use. Would you believe the results? Unlikely. The researchers probably chose a subjective prior that too strongly biased results in their favor.\n", - "\n", - "Unfortunately, choosing an objective prior is not as simple as selecting a flat prior, and even today the problem is still not completely solved. The problem with naively choosing the uniform prior is that pathological issues can arise. Some of these issues are pedantic, but we delay more serious issues to the Appendix of this Chapter (TODO)." - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "We must remember that choosing a prior, whether subjective or objective, is still part of the modeling process. To quote Gelman [5]:\n", - "\n", - ">...after the model has been \ufb01t, one should look at the posterior distribution\n", - "and see if it makes sense. If the posterior distribution does not make sense, this implies\n", - "that additional prior knowledge is available that has not been included in the model,\n", - "and that contradicts the assumptions of the prior distribution that has been used. It is\n", - "then appropriate to go back and alter the prior distribution to be more consistent with\n", - "this external knowledge.\n", - "\n", - "If the posterior does not make sense, then clearly one had an idea what the posterior *should* look like (not what one *hopes* it looks like), implying that the current prior does not contain all the prior information and should be updated. At this point, we can discard the current prior and choose a more reflective one.\n", - "\n", - "Gelman [4] suggests that using a uniform distribution with large bounds is often a good choice for objective priors. Although, one should be wary about using Uniform objective priors with large bounds, as they can assign too large of a prior probability to non-intuitive points. Ask yourself: do you really think the unknown could be incredibly large? Often quantities are naturally biased towards 0. A Normal random variable with large variance (small precision) might be a better choice, or an Exponential with a fat tail in the strictly positive (or negative) case. \n", - "\n", - "If using a particularly subjective prior, it is your responsibility to be able to explain the choice of that prior, else you are no better than the tobacco company's guilty parties. " - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### Empirical Bayes\n", - "\n", - "While not a true Bayesian method, *empirical Bayes* is a trick that combines frequentist and Bayesian inference. As mentioned previously, for (almost) every inference problem there is a Bayesian method and a frequentist method. The significant difference between the two is that Bayesian methods have a prior distribution, with hyperparameters $\\alpha$, while empirical methods do not have any notion of a prior. Empirical Bayes combines the two methods by using frequentist methods to select $\\alpha$, and then proceeds with Bayesian methods on the original problem. \n", - "\n", - "A very simple example follows: suppose we wish to estimate the parameter $\\mu$ of a Normal distribution, with $\\sigma = 5$. Since $\\mu$ could range over the whole real line, we can use a Normal distribution as a prior for $\\mu$. How to select the prior's hyperparameters, denoted ($\\mu_p, \\sigma_p^2$)? The $\\sigma_p^2$ parameter can be chosen to reflect the uncertainty we have. For $\\mu_p$, we have two options:\n", - "\n", - "1. Empirical Bayes suggests using the empirical sample mean, which will center the prior around the observed empirical mean:\n", - "\n", - "$$ \\mu_p = \\frac{1}{N} \\sum_{i=0}^N X_i $$\n", - "\n", - "2. Traditional Bayesian inference suggests using prior knowledge, or a more objective prior (zero mean and fat standard deviation).\n", - "\n", - "Empirical Bayes can be argued as being semi-objective, since while the choice of prior model is ours (hence subjective), the parameters are solely determined by the data.\n", - "\n", - "Personally, I feel that Empirical Bayes is *double-counting* the data. That is, we are using the data twice: once in the prior, which will influence our results towards the observed data, and again in the inferential engine of MCMC. This double-counting will understate our true uncertainty. To minimize this double-counting, I would only suggest using Empirical Bayes when you have *lots* of observations, else the prior will have too strong of an influence. I would also recommend, if possible, to maintain high uncertainty (either by setting a large $\\sigma_p^2$ or equivalent.)\n", - "\n", - "Empirical Bayes also violates a theoretical axiom in Bayesian inference. The textbook Bayesian algorithm of:\n", - "\n", - ">*prior* $\\Rightarrow$ *observed data* $\\Rightarrow$ *posterior* \n", - "\n", - "is violated by Empirical Bayes, which instead uses \n", - "\n", - ">*observed data* $\\Rightarrow$ *prior* $\\Rightarrow$ *observed data* $\\Rightarrow$ *posterior*\n", - "\n", - "Ideally, all priors should be specified *before* we observe the data, so that the data does not influence our prior opinions (see the volumes of research by Daniel Kahneman *et. al* about [anchoring](http://en.wikipedia.org/wiki/Anchoring_and_adjustment) )." - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Useful priors to know about\n", - "\n", - "### The Gamma distribution\n", - "\n", - "A Gamma random variable, denoted $X \\sim \\text{Gamma}(\\alpha, \\beta)$, is a random variable over the positive real numbers. It is in fact a generalization of the Exponential random variable, that is:\n", - "\n", - "$$ \\text{Exp}(\\beta) \\sim \\text{Gamma}(1, \\beta) $$\n", - "\n", - "This additional parameter allows the probability density function to have more flexibility, hence allowing the practitioner to express his or her subjective priors more accurately. The density function for a $\\text{Gamma}(\\alpha, \\beta)$ random variable is:\n", - "\n", - "$$ f(x \\mid \\alpha, \\beta) = \\frac{\\beta^{\\alpha}x^{\\alpha-1}e^{-\\beta x}}{\\Gamma(\\alpha)} $$\n", - "\n", - "where $\\Gamma(\\alpha)$ is the [Gamma function](http://en.wikipedia.org/wiki/Gamma_function), and for differing values of $(\\alpha, \\beta)$ looks like:" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "figsize(12.5, 5)\n", - "gamma = stats.gamma\n", - "\n", - "parameters = [(1, 0.5), (9, 2), (3, 0.5), (7, 0.5)]\n", - "x = np.linspace(0.001, 20, 150)\n", - "for alpha, beta in parameters:\n", - " y = gamma.pdf(x, alpha, scale=1. / beta)\n", - " lines = plt.plot(x, y, label=\"(%.1f,%.1f)\" % (alpha, beta), lw=3)\n", - " plt.fill_between(x, 0, y, alpha=0.2, color=lines[0].get_color())\n", - " plt.autoscale(tight=True)\n", - "\n", - "plt.legend(title=r\"$\\alpha, \\beta$ - parameters\");" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { 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RSa6YuyRHzNv+IS4uDrt374Zerwdg7glftGgRBg8ejHHjxqG4uBiffPKJOP/V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- "text": [ - "" - ] - } - ], - "prompt_number": 5 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### The Wishart distribution\n", - "\n", - "Until now, we have only seen random variables that are scalars. Of course, we can also have *random matrices*! Specifically, the Wishart distribution is a distribution over all [positive semi-definite matrices](http://en.wikipedia.org/wiki/Positive-definite_matrix). Why is this useful to have in our arsenal? (Proper) covariance matrices are positive-definite, hence the Wishart is an appropriate prior for covariance matrices. We can't really visualize a distribution of matrices, so I'll plot some realizations from the $5 \\times 5$ (above) and $20 \\times 20$ (below) Wishart distribution:" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "import pymc as pm\n", - "\n", - "n = 4\n", - "for i in range(10):\n", - " ax = plt.subplot(2, 5, i + 1)\n", - " if i >= 5:\n", - " n = 15\n", - " plt.imshow(pm.rwishart(n + 1, np.eye(n)), interpolation=\"none\",\n", - " cmap=plt.cm.hot)\n", - " ax.axis(\"off\")\n", - "\n", - "plt.suptitle(\"Random matrices from a Wishart Distribution\");" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "metadata": {}, - "output_type": "display_data", - "png": 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- "text": [ - "" - ] - } - ], - "prompt_number": 7 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "One thing to notice is the symmetry of these matrices. The Wishart distribution can be a little troubling to deal with, but we will use it in an example later." - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### The Beta distribution\n", - "\n", - "You may have seen the term `beta` in previous code in this book. Often, I was implementing a Beta distribution. The Beta distribution is very useful in Bayesian statistics. A random variable $X$ has a $\\text{Beta}$ distribution, with parameters $(\\alpha, \\beta)$, if its density function is:\n", - "\n", - "$$f_X(x | \\; \\alpha, \\beta ) = \\frac{ x^{(\\alpha - 1)}(1-x)^{ (\\beta - 1) } }{B(\\alpha, \\beta) }$$\n", - "\n", - "where $B$ is the [Beta function](http://en.wikipedia.org/wiki/Beta_function) (hence the name). The random variable $X$ is only allowed in [0,1], making the Beta distribution a popular distribution for decimal values, probabilities and proportions. The values of $\\alpha$ and $\\beta$, both positive values, provide great flexibility in the shape of the distribution. Below we plot some distributions:" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "figsize(12.5, 5)\n", - "\n", - "params = [(2, 5), (1, 1), (0.5, 0.5), (5, 5), (20, 4), (5, 1)]\n", - "\n", - "x = np.linspace(0.01, .99, 100)\n", - "beta = stats.beta\n", - "for a, b in params:\n", - " y = beta.pdf(x, a, b)\n", - " lines = plt.plot(x, y, label=\"(%.1f,%.1f)\" % (a, b), lw=3)\n", - " plt.fill_between(x, 0, y, alpha=0.2, color=lines[0].get_color())\n", - " plt.autoscale(tight=True)\n", - "plt.ylim(0)\n", - "plt.legend(loc='upper left', title=\"(a,b)-parameters\");" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "metadata": {}, - "output_type": "display_data", - "png": 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cuEs+i5Jo4lK0byvhg+KG8EFxQ/hqHTs2DxSOng1GJBZiSm5LGp4AiK37K5vu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\nIIzeeFTqSRrMOlaZ9dQZNdQaN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- "text": [ - "" - ] - } - ], - "prompt_number": 9 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "One thing I'd like the reader to notice is the presence of the flat distribution above, specified by parameters $(1,1)$. This is the Uniform distribution. Hence the Beta distribution is a generalization of the Uniform distribution, something we will revisit many times.\n", - "\n", - "There is an interesting connection between the Beta distribution and the Binomial distribution. Suppose we are interested in some unknown proportion or probability $p$. We assign a $\\text{Beta}(\\alpha, \\beta)$ prior to $p$. We observe some data generated by a Binomial process, say $X \\sim \\text{Binomial}(N, p)$, with $p$ still unknown. Then our posterior *is again a Beta distribution*, i.e. $p | X \\sim \\text{Beta}( \\alpha + X, \\beta + N -X )$. Succinctly, one can relate the two by \"a Beta prior with Binomial observations creates a Beta posterior\". This is a very useful property, both computationally and heuristically.\n", - "\n", - "In light of the above two paragraphs, if we start with a $\\text{Beta}(1,1)$ prior on $p$ (which is a Uniform), observe data $X \\sim \\text{Binomial}(N, p)$, then our posterior is $\\text{Beta}(1 + X, 1 + N - X)$. \n" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "#####Example: Bayesian Multi-Armed Bandits\n", - "*Adapted from an example by Ted Dunning of MapR Technologies*\n", - "\n", - "> Suppose you are faced with $N$ slot machines (colourfully called multi-armed bandits). Each bandit has an unknown probability of distributing a prize (assume for now the prizes are the same for each bandit, only the probabilities differ). Some bandits are very generous, others not so much. Of course, you don't know what these probabilities are. By only choosing one bandit per round, our task is devise a strategy to maximize our winnings.\n", - "\n", - "Of course, if we knew the bandit with the largest probability, then always picking this bandit would yield the maximum winnings. So our task can be phrased as \"Find the best bandit, and as quickly as possible\". \n", - "\n", - "The task is complicated by the stochastic nature of the bandits. A suboptimal bandit can return many winnings, purely by chance, which would make us believe that it is a very profitable bandit. Similarly, the best bandit can return many duds. Should we keep trying losers then, or give up? \n", - "\n", - "A more troublesome problem is, if we have a found a bandit that returns *pretty good* results, do we keep drawing from it to maintain our *pretty good score*, or do we try other bandits in hopes of finding an *even-better* bandit? This is the exploration vs. exploitation dilemma.\n", - "\n", - "### Applications\n", - "\n", - "\n", - "The Multi-Armed Bandit problem at first seems very artificial, something only a mathematician would love, but that is only before we address some applications:\n", - "\n", - "- Internet display advertising: companies have a suite of potential ads they can display to visitors, but the company is not sure which ad strategy to follow to maximize sales. This is similar to A/B testing, but has the added advantage of naturally minimizing strategies that do not work (and generalizes to A/B/C/D... strategies)\n", - "- Ecology: animals have a finite amount of energy to expend, and following certain behaviours has uncertain rewards. How does the animal maximize its fitness?\n", - "- Finance: which stock option gives the highest return, under time-varying return profiles.\n", - "- Clinical trials: a researcher would like to find the best treatment, out of many possible treatment, while minimizing losses. \n", - "- Psychology: how does punishment and reward affect our behaviour? How do humans learn?\n", - "\n", - "Many of these questions above are fundamental to the application's field.\n", - "\n", - "It turns out the *optimal solution* is incredibly difficult, and it took decades for an overall solution to develop. There are also many approximately-optimal solutions which are quite good. The one I wish to discuss is one of the few solutions that can scale incredibly well. The solution is known as *Bayesian Bandits*.\n", - "\n", - "\n", - "### A Proposed Solution\n", - "\n", - "\n", - "Any proposed strategy is called an *online algorithm* (not in the internet sense, but in the continuously-being-updated sense), and more specifically a reinforcement learning algorithm. The algorithm starts in an ignorant state, where it knows nothing, and begins to acquire data by testing the system. As it acquires data and results, it learns what the best and worst behaviours are (in this case, it learns which bandit is the best). With this in mind, perhaps we can add an additional application of the Multi-Armed Bandit problem:\n", - "\n", - "- Psychology: how does punishment and reward affect our behaviour? How do humans learn?\n", - "\n", - "\n", - "The Bayesian solution begins by assuming priors on the probability of winning for each bandit. In our vignette we assumed complete ignorance of these probabilities. So a very natural prior is the flat prior over 0 to 1. The algorithm proceeds as follows:\n", - "\n", - "For each round:\n", - "\n", - "1. Sample a random variable $X_b$ from the prior of bandit $b$, for all $b$.\n", - "2. Select the bandit with largest sample, i.e. select $B = \\text{argmax}\\;\\; X_b$.\n", - "3. Observe the result of pulling bandit $B$, and update your prior on bandit $B$.\n", - "4. Return to 1.\n", - "\n", - "That's it. Computationally, the algorithm involves sampling from $N$ distributions. Since the initial priors are $\\text{Beta}(\\alpha=1,\\beta=1)$ (a uniform distribution), and the observed result $X$ (a win or loss, encoded 1 and 0 respectfully) is Binomial, the posterior is a $\\text{Beta}(\\alpha=1+X,\\beta=1+1\u2212X)$.\n", - "\n", - "To answer our question from before, this algorithm suggests that we should not discard losers, but we should pick them at a decreasing rate as we gather confidence that there exist *better* bandits. This follows because there is always a non-zero chance that a loser will achieve the status of $B$, but the probability of this event decreases as we play more rounds (see figure below).\n", - "\n", - "Below we implement Bayesian Bandits using two classes, `Bandits` that defines the slot machines, and `BayesianStrategy` which implements the above learning strategy." - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "from pymc import rbeta\n", - "\n", - "rand = np.random.rand\n", - "\n", - "\n", - "class Bandits(object):\n", - "\n", - " \"\"\"\n", - " This class represents N bandits machines.\n", - "\n", - " parameters:\n", - " p_array: a (n,) Numpy array of probabilities >0, <1.\n", - "\n", - " methods:\n", - " pull( i ): return the results, 0 or 1, of pulling \n", - " the ith bandit.\n", - " \"\"\"\n", - "\n", - " def __init__(self, p_array):\n", - " self.p = p_array\n", - " self.optimal = np.argmax(p_array)\n", - "\n", - " def pull(self, i):\n", - " # i is which arm to pull\n", - " return np.random.rand() < self.p[i]\n", - "\n", - " def __len__(self):\n", - " return len(self.p)\n", - "\n", - "\n", - "class BayesianStrategy(object):\n", - "\n", - " \"\"\"\n", - " Implements a online, learning strategy to solve\n", - " the Multi-Armed Bandit problem.\n", - " \n", - " parameters:\n", - " bandits: a Bandit class with .pull method\n", - " \n", - " methods:\n", - " sample_bandits(n): sample and train on n pulls.\n", - "\n", - " attributes:\n", - " N: the cumulative number of samples\n", - " choices: the historical choices as a (N,) array\n", - " bb_score: the historical score as a (N,) array\n", - " \"\"\"\n", - "\n", - " def __init__(self, bandits):\n", - "\n", - " self.bandits = bandits\n", - " n_bandits = len(self.bandits)\n", - " self.wins = np.zeros(n_bandits)\n", - " self.trials = np.zeros(n_bandits)\n", - " self.N = 0\n", - " self.choices = []\n", - " self.bb_score = []\n", - "\n", - " def sample_bandits(self, n=1):\n", - "\n", - " bb_score = np.zeros(n)\n", - " choices = np.zeros(n)\n", - "\n", - " for k in range(n):\n", - " # sample from the bandits's priors, and select the largest sample\n", - " choice = np.argmax(rbeta(1 + self.wins, 1 + self.trials - self.wins))\n", - "\n", - " # sample the chosen bandit\n", - " result = self.bandits.pull(choice)\n", - "\n", - " # update priors and score\n", - " self.wins[choice] += result\n", - " self.trials[choice] += 1\n", - " bb_score[k] = result\n", - " self.N += 1\n", - " choices[k] = choice\n", - "\n", - " self.bb_score = np.r_[self.bb_score, bb_score]\n", - " self.choices = np.r_[self.choices, choices]\n", - " return" - ], - "language": "python", - "metadata": {}, - "outputs": [], - "prompt_number": 10 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Below we visualize the learning of the Bayesian Bandit solution." - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "figsize(11.0, 10)\n", - "\n", - "beta = stats.beta\n", - "x = np.linspace(0.001, .999, 200)\n", - "\n", - "\n", - "def plot_priors(bayesian_strategy, prob, lw=3, alpha=0.2, plt_vlines=True):\n", - " # plotting function\n", - " wins = bayesian_strategy.wins\n", - " trials = bayesian_strategy.trials\n", - " for i in range(prob.shape[0]):\n", - " y = beta(1 + wins[i], 1 + trials[i] - wins[i])\n", - " p = plt.plot(x, y.pdf(x), lw=lw)\n", - " c = p[0].get_markeredgecolor()\n", - " plt.fill_between(x, y.pdf(x), 0, color=c, alpha=alpha,\n", - " label=\"underlying probability: %.2f\" % prob[i])\n", - " if plt_vlines:\n", - " plt.vlines(prob[i], 0, y.pdf(prob[i]),\n", - " colors=c, linestyles=\"--\", lw=2)\n", - " plt.autoscale(tight=\"True\")\n", - " plt.title(\"Posteriors After %d pull\" % bayesian_strategy.N +\n", - " \"s\" * (bayesian_strategy.N > 1))\n", - " plt.autoscale(tight=True)\n", - " return" - ], - "language": "python", - "metadata": {}, - "outputs": [], - "prompt_number": 11 - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "hidden_prob = np.array([0.85, 0.60, 0.75])\n", - "bandits = Bandits(hidden_prob)\n", - "bayesian_strat = BayesianStrategy(bandits)\n", - "\n", - "draw_samples = [1, 1, 3, 10, 10, 25, 50, 100, 200, 600]\n", - "\n", - "for j, i in enumerate(draw_samples):\n", - " plt.subplot(5, 2, j + 1)\n", - " bayesian_strat.sample_bandits(i)\n", - " plot_priors(bayesian_strat, hidden_prob)\n", - " # plt.legend()\n", - " plt.autoscale(tight=True)\n", - "plt.tight_layout()" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "metadata": {}, - "output_type": "display_data", - "png": 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FRpirxEar1eJs4W3knL6BW8V3IKpVGh27MP6pzr+X0U4EYwxz5sxBYmIiFi9ebHCfqVOn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\n7+ViKInycyoR5WdriFsS41AuhsCCHkrE4ZJm2sw2PCbQszJaTP7/wSTnS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GfVtVv40U6H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FV8q0GBRYGt76LNGKAnPNKo4qONZoSGyuAhXBtyJAFxZC/O9+St7T/6QhwzmxYtF/PsKaV0Sf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\ns2+Q7t9+QOdr72G+UT9jH1W4iegHNhHz4FYiivMRlPMrmLZamE9OxATXb41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onOPxrB4P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n2wr8OUN4ijvEEc5Q3iKG+wjvKF3g1E3uC0QoS1iYXKy8v73GckXBBtiY25bdu2YcmSJYOR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\njru5AU9rUyGSlFZfx7MRFbdWTtbnp6PCw87KxWcyqhrKu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- "text": [ - "" - ] - } - ], - "prompt_number": 13 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Note that we don't really care how accurate we become about the inference of the hidden probabilities — for this problem we are more interested in choosing the best bandit (or more accurately, becoming *more confident* in choosing the best bandit). For this reason, the distribution of the red bandit is very wide (representing ignorance about what that hidden probability might be) but we are reasonably confident that it is not the best, so the algorithm chooses to ignore it.\n", - "\n", - "From the above, we can see that after 1000 pulls, the majority of the \"blue\" function leads the pack, hence we will almost always choose this arm. This is good, as this arm is indeed the best.\n", - "\n", - "Below is a D3 app that demonstrates our algorithm updating/learning three bandits. The first figure shows the raw counts of pulls and wins, and the second figure is a dynamically updating plot. I encourage you to try to guess which bandit is optimal, prior to revealing the true probabilities, by selecting the `arm buttons`." - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "from IPython.core.display import HTML\n", - "\n", - "# try executing the below command twice if the first time doesn't work\n", - "HTML(filename=\"BanditsD3.html\")" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "html": [ - "\n", - " \n", - " \n", - " \n", - "\n", - " \n", - "\n", - "\n", - " \n", - "
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\n", - "\n", - "\n" - ], - "metadata": {}, - "output_type": "pyout", - "prompt_number": 4, - "text": [ - "" - ] - } - ], - "prompt_number": 4 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Deviations of the observed ratio from the highest probability is a measure of performance. For example,in the long run, optimally we can attain the reward/pull ratio of the maximum bandit probability. Long-term realized ratios less than the maximum represent inefficiencies. (Realized ratios larger than the maximum probability is due to randomness, and will eventually fall below). \n", - "\n", - "### A Measure of *Good*\n", - "\n", - "We need a metric to calculate how well we are doing. Recall the absolute *best* we can do is to always pick the bandit with the largest probability of winning. Denote this best bandit's probability of $w_{opt}$. Our score should be relative to how well we would have done had we chosen the best bandit from the beginning. This motivates the *total regret* of a strategy, defined as:\n", - "\n", - "\\begin{align}\n", - "R_T & = \\sum_{i=1}^{T} \\left( w_{opt} - w_{B(i)} \\right)\\\\\\\\\n", - "& = Tw^* - \\sum_{i=1}^{T} \\; w_{B(i)} \n", - "\\end{align}\n", - "\n", - "\n", - "where $w_{B(i)}$ is the probability of a prize of the chosen bandit in the $i$th round. A total regret of 0 means the strategy is attaining the best possible score. This is likely not possible, as initially our algorithm will often make the wrong choice. Ideally, a strategy's total regret should flatten as it learns the best bandit. (Mathematically, we achieve $w_{B(i)}=w_{opt}$ often)\n", - "\n", - "\n", - "Below we plot the total regret of this simulation, including the scores of some other strategies:\n", - "\n", - "1. Random: randomly choose a bandit to pull. If you can't beat this, just stop. \n", - "2. Largest Bayesian credible bound: pick the bandit with the largest upper bound in its 95% credible region of the underlying probability. \n", - "3. Bayes-UCB algorithm: pick the bandit with the largest *score*, where score is a dynamic quantile of the posterior (see [4] )\n", - "3. Mean of posterior: choose the bandit with the largest posterior mean. This is what a human player (sans computer) would likely do. \n", - "3. Largest proportion: pick the bandit with the current largest observed proportion of winning. \n", - "\n", - "The code for these are in the `other_strats.py`, where you can implement your own strategy very easily." - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "figsize(12.5, 5)\n", - "from other_strats import *\n", - "\n", - "# define a harder problem\n", - "hidden_prob = np.array([0.15, 0.2, 0.1, 0.05])\n", - "bandits = Bandits(hidden_prob)\n", - "\n", - "# define regret\n", - "\n", - "\n", - "def regret(probabilities, choices):\n", - " w_opt = probabilities.max()\n", - " return (w_opt - probabilities[choices.astype(int)]).cumsum()\n", - "\n", - "# create new strategies\n", - "strategies = [upper_credible_choice,\n", - " bayesian_bandit_choice,\n", - " ucb_bayes,\n", - " max_mean,\n", - " random_choice]\n", - "algos = []\n", - "for strat in strategies:\n", - " algos.append(GeneralBanditStrat(bandits, strat))" - ], - "language": "python", - "metadata": {}, - "outputs": [], - "prompt_number": 14 - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "# train 10000 times\n", - "for strat in algos:\n", - " strat.sample_bandits(10000)\n", - "\n", - "#test and plot\n", - "for i, strat in enumerate(algos):\n", - " _regret = regret(hidden_prob, strat.choices)\n", - " plt.plot(_regret, label=strategies[i].__name__, lw=3)\n", - "\n", - "plt.title(\"Total Regret of Bayesian Bandits Strategy vs. Random guessing\")\n", - "plt.xlabel(\"Number of pulls\")\n", - "plt.ylabel(\"Regret after $n$ pulls\");\n", - "plt.legend(loc=\"upper left\");" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "metadata": {}, - "output_type": "display_data", - "png": 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TpkyBVCpF9+7dsXnzZtSpU0ccIEZEqFu3Lh49eoSvvvoKHh4eCAgIAACMHDkS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\n8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- "text": [ - "" - ] - } - ], - "prompt_number": 15 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Like we wanted, Bayesian bandits and other strategies have decreasing rates of regret, representing that we are achieving optimal choices. To be more scientific so as to remove any possible luck in the above simulation, we should instead look at the *expected total regret*:\n", - "\n", - "$$\\bar{R_T} = E[ R_T ] $$\n", - "\n", - "It can be shown that any *sub-optimal* strategy's expected total regret is bounded below logarithmically. Formally:\n", - "\n", - "$$ E[R_T] = \\Omega \\left( \\;\\log(T)\\; \\right)$$\n", - "\n", - "Thus, any strategy that matches logarithmic-growing regret is said to \"solve\" the Multi-Armed Bandit problem [3].\n", - "\n", - "Using the Law of Large Numbers, we can approximate Bayesian Bandit's expected total regret by performing the same experiment many times (500 times, to be fair):" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "# this can be slow, so I recommend NOT running it.\n", - "\n", - "trials = 500\n", - "expected_total_regret = np.zeros((10000, 3))\n", - "\n", - "for i_strat, strat in enumerate(strategies[:-2]):\n", - " for i in range(trials):\n", - " general_strat = GeneralBanditStrat(bandits, strat)\n", - " general_strat.sample_bandits(10000)\n", - " _regret = regret(hidden_prob, general_strat.choices)\n", - " expected_total_regret[:, i_strat] += _regret\n", - "\n", - " plot(expected_total_regret[:, i_strat] / trials, lw=3, label=strat.__name__)\n", - "\n", - "plt.title(\"Expected Total Regret of Multi-armed Bandit strategies\")\n", - "plt.xlabel(\"Number of pulls\")\n", - "plt.ylabel(\"Exepected Total Regret \\n after $n$ pulls\");\n", - "plt.legend(loc=\"upper left\");" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "0\n", - "1" - ] - }, - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "\n", - "2" - ] - }, - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "\n" - ] - }, - { - "metadata": {}, - "output_type": "pyout", - "prompt_number": 24, - "text": [ - "" - ] - }, - { - "metadata": {}, - "output_type": "display_data", - "png": 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Ro3Hp0iU899xzeOGFF/D888/XmZQAAHr16lXlvW+++QbffvstUlNToVarodfr6+zj0pBj\nXOXmcra2trUe4+pzjAgICMDzzz8PPz8/hISEIDg4GKGhoXB3d69z/SmqtaABA0U1Ej6fX2O77AqZ\nmZlISkqChYUFbt68Wa/5Vv5HaDQaMWTIEHz++edVprO2tgZgOgmu65/ng4xGIwDg/PnzVU6k6vqn\n3tBl1aU+81u6dCl+//13bN26FZ06dYJQKMTixYtRXFzc4OXZ2dmhffv2aN++Pfbu3YvOnTsjLCwM\nO3fuZLfLgQMH8NRTT1X5rq2tLfv8we304HowDMOeRFaepq792RDVbbtH3T9Tp05FWFgYFi9ejNDQ\nULOApELFyXDlZRkMBnb7NTY3NzezoKWi4/zmzZuxYcMGfPLJJwgKCoJEIsGWLVtw+PBhs+9XFywA\nqLZD7YPvMQzDrpfRaETnzp1x6NChKt+rWMbD/B4rq3xM6dKlC2JiYvD++++zAcNLL70ER0dHfPHF\nF/Dw8IClpSX69evHtumvUF0H+7r2T2P9tocOHYq0tDT8/fffiIyMxJQpU+Dv74/jx4/XmRjiwd/M\n/v37sWDBAmzcuBEDBw6EVCrFvn37EB4eXut86nuMq+54V9t2qM8xgsPh4K+//kJMTAz++ecfHDx4\nECtWrMD+/fsxfPjwWstNUa0F7fRMUY2krhNro9GIyZMnIygoCL/88gvWrVtX7ZX0yu/p9XpER0ej\nS5cuAICePXvi2rVrcHNzY09yKx4ymQyA6Sr28ePHa/wnx+PxzDrjVXwHMHVqfnC+FekJu3Tpgvz8\nfLMr3/n5+UhKSqpr01Sra9euAIBTp06ZvX/69Gn4+/uzZQVQpbxnzpzBlClTMGbMGPj7+8Pb2xs3\nb96ssg/qcwWzMh6Ph/DwcPz444+4d+8eunbtCj6fj+Tk5CrbpX379uBwOOy+OXfuHDsfvV5v1jG1\nJj169Khzf1Zsg7pO3vz8/JCQkAC5XM6+l5OTg6SkJPj5+TVoO1RmZ2eHMWPG4MSJEzWOt1GR1agi\now8AxMfHm5W5pn1Zl+q+x+VyzbZVRXKB06dP48UXX8SMGTMQEBCA9u3bIykpqcH1oL569uyJO3fu\nQCKRVNl/zs7OAEy/m+joaLOT87Nnzz70MhmGQUlJCQBTZ/sbN25gxYoVCAkJga+vL6ysrNg7B3XN\np0JFHa5cLp1OV6Xz9IOqO5bUxNbWFhMmTMBXX32Fw4cP49SpU7hx4wY7H71eX6/5nD59GkFBQVi0\naBGCgoLQoUMH3L17t85y1fcYl5eXhzt37rDfKywsrPUYV59jRIWePXsiLCwMp06dwsCBA7Fr1656\nrTNFtQY0YKCoRlJaWoqcnBxkZ2ebPSq8//77uHHjBn788UeEhoZi9uzZmDRpUpWr4hs3bsRff/2F\nGzduYO7cuZDL5Wxq0gULFsBgMGDkyJGIiopCSkoKoqKiEB4ezgYay5Ytw61btzB58mTExsYiOTkZ\n+/fvx4ULFwCYrlhmZ2fjwoULyM/Ph1arRceOHTFz5ky8/vrriIiIwO3bt3HlyhV899132LRpEwBT\nrvSAgABMmTIFMTExiI+Px+TJkxuU5pBUSnXaoUMHjB07FvPmzcPRo0eRmJiIhQsXIiEhAUuXLgVg\nahYiFovx999/Izs7G4WFhQCATp064dChQ4iJiUFCQgJmz56NrKysKifVdZ1kV/f5lClTYG9vj82b\nN0MsFmPlypVYuXIlvvjiC9y8eRPXr1/HL7/8ghUrVgAAfHx8MGLECMyfPx+nT59GQkIC/vOf/0Ch\nUJidlFVe9wr12Z8VJzO//fYb8vLyamwiMmnSJDg4OGD8+PG4fPkyYmNjMWHCBLi7u2P8+PG1boe6\nfPPNN8jLy0NwcHC1n/v4+MDT0xPvvPMObt68iaioKLz11ltm61/TvqyLp6cnOBwODh8+jNzc3Frv\nIvn6+uLkyZOIjIxEUlISVq1ahejo6CZLyTp58mR4e3tj+PDhOHbsGFJSUnDx4kV8+OGH+O233wCY\nxr3Iy8vD7NmzcePGDRw/frzOq+GVVRxTUlNTsW/fPkRERGDUqFEATCfhDg4O+Prrr3Hr1i2cP38e\nEydOhEAgqHO+letjx44d8fLLL2P+/PmIjIxEQkICZs2aBZVKVeu2a9++PRITE5GQkID8/PwqdzUq\nhIeH49dff8XNmzdx69YtREREQCKRsJmzvL29ERsbizt37iA/P7/W4MHX1xf//vsvfv/9dyQnJ+PT\nTz/Fr7/+WqVcD3OMCwkJQUBAAKZOnYpLly7hypUrmDp1KiwtLWv8LdfnGHHu3DmsX78e0dHRSEtL\nw/Hjx3H16lX2oglFtQlN302Coh5/M2bMIAzDVHlwOBwil8vJ2bNniaWlJfnzzz/Z75SUlJCAgAAy\nfvx4Qsj9zp5//PEHefrpp4mVlRXp2rWrWUdEQghJTU0lkydPJg4ODsTKyop4enqSqVOnmnWoi46O\nJkOGDCEikYhIJBLSt29fEhMTQwgxdcidNGkSsbOzIwzDkHfffZcQYuosuWnTJuLr60t4PB6xt7cn\nwcHB5MCBA+x8U1JSyNChQwmfzyceHh7ks88+q5IxpDYPTqtQKMh//vMfdl169uxJjh07ZvadH374\ngXh7exMLCwvi7e1NCDF1oH3++eeJSCQiLi4u5J133iGvvfYaGTRokNk+qdxhszpeXl7k/fffr/L+\nBx98QMRiMSkoKCCEmDoUBwYGEj6fT2xtbUmfPn3IV199xU4vl8vJmDFjiFAoJE5OTmTNmjVk7Nix\nZMSIETWue4X67M9FixYRR0dHwjBMlc6hld28eZMMGzaM7Sg7YsQIsw6chNSv0/M777xj1on0QSdP\nniQcDsesk/PFixfJ008/TQQCAQkMDCRnzpwx6/RMSPX7cteuXcTS0rLWeW/atIm4ubkRLpdrto8f\nVFxcTMaNG0ekUimRyWRkwYIFZPXq1eyyCKm5XlS3XR4sPyGE8Pl8NqsOIaZ9P3fuXOLm5kZ4PB5x\nc3MjoaGhJD4+np3m+PHjxN/fn1hZWRF/f39y4sSJOvfD999/b3YssbKyIh06dCBhYWFm2YhOnTpF\nAgICCJ/PJ76+vuTgwYOkY8eO7O+6pnV7sKOxXC4n48aNIyKRiDg4OJCVK1eaZUWqbtsVFBSwWYQY\nhqmyrSqsX7+e+Pn5EbFYTKytrUlwcDA5e/Ys+/mdO3fIgAEDiFgsJhwOh5w6dYrcvXuXcDgcs+kI\nMR2//vOf/xA7OzsilUrJ5MmTyeeff044HI7ZNA97jLt79y4JCQkhfD6ftGvXjnzxxRekV69eZp3f\nq/st13aMuH79Ohk2bBhxdnZmf+PLli0jZWVl1W4vimqNGEKa6NILRVENEhkZicGDByM9PR2urq4t\nXRzqERgMBvj6+uKVV17BRx991NLFoSjqISmVSri7u+ODDz7A/PnzW7o4FNVi2mynZy8vL0ilUnC5\nXFhaWiI6OpodeCY1NRVeXl7Yt28fHZGRoqgmd+bMGeTk5CAoKAhKpRJbt25FWloaZsyY0dJFoyiq\nAf744w9wuVx07twZubm5ePfdd8HlcjFu3LiWLhpFtag224eBYRhERkbi8uXLiI6OBgBs2LABISEh\nSEpKwnPPPVdlJEuKau2aqnMm1bQMBgPef/99BAYGYvDgwUhJScHJkydpG2WKamM0Gg2WLl0KPz8/\njBgxAgAQFRUFBweHFi4ZRbWsNtskydvbG5cuXWIziQCmzlCnTp2Ck5MTsrOzERwcjMTExBYsJUVR\nFEVRFEW1bW36DsOQIUPQo0cPfPPNNwBM2SScnJwAAE5OTsjJyWnJIlIURVEURVFUm9dm+zCcPXsW\nLi4uyMvLY/NPV8YwTLXNO44fP95cRaQoiqIoiqKoZvXcc881+jzbbMDg4uICAHBwcMCoUaMQHR3N\nNkVydnZGVlYWO5jQg7p3796cRaXasI0bN2L58uUtXQyqDaB1hWoIWl+o+qJ1hWqIuLi4Jplvm2yS\npNFooFQqAQBqtRpHjx6Fv78/Xn75ZezevRsAsHv3brzyyistWUzqMZCWltbSRaDaCFpXqIag9YWq\nL1pXqLqodQZcTCvGjgsZTbaMNnmHIScnhx3pUq/XY/LkyRg6dCh69OiBcePGYefOnWxaVYqiKIqi\nKIp6XJTqjUjIUSM+S4n4TCVu5mlgLE9h1LOJGtG0yYDB29sb8fHxVd63s7PDP//80wIloh5XEydO\nbOkiUG0ErStUQ9D6QtUXrSuU3khwM0+N+EwV4jOVSMhRo8zYvElO22xa1Yd1/Phx2oeBoiiKoiiK\napUMRoI7BVrEZyoRn6nCv9kqlOiNNU7PAOggEyDQVYIeljm003NTU6lUUCgUAOgAWpRJcXExrK2t\nW7oYj4QQAi6XC0dHR1qvm1BUVBT69evX0sWg2ghaX6j6onXl8UcIwb2iUraJ0ZUsFZSlhlq/086G\nj0BXMQJdJOjmIoaUbzqlj4trmiEFaMBQTi6XAzBlX6InVVSFimxcbZ1Go0Fubi47TglFURRFUS0n\nW1nKNjGKz1SiQKuvdXonMQ+BrmIEuUoQ4CqBTGjZTCU1oQFDudLSUri6urZ0MSiqSQiFQhQVFbV0\nMR5r9Aog1RC0vlD1RevK40GuKcOVTCXis0xBQrZSV+v0dgILBLpKyh9iOEusmqmk1aMBQzl6V4F6\n3NE6TlEURVHNQ1Gix9UsVXkzIxXSikpqnV5ixUU3F1MToyBXCTxsrOr9f9toJNCV6lGqLWuMoleL\nBgwURVGNgLYzphqC1heqvmhdaRu0ZQb8m6023UXIVOK2XIvasgrxLTjwdxab+iG4StDeTgAuxxQg\nECOBVlMGjaoUaqXO9FdV9W+JpgylJWUoLdWjYmGDx1Q/aPGjogED1eqNGDEC48aNw9SpU7F//37s\n3bsXBw4cAADIZDLExsbCy8uryvf27NmDiIgIHDlypNHLlJaWhqCgIOTl5YHDadj4h+fPn8eiRYtw\n8eLFRi8XRVEURVFNT6c34kaeGpczTM2MbuaqYaglQrBkgK4yAbrYWMFbZAmZBQclah3UmUW4nZSL\nq+VBgFpZCq1aB2Mzp02tCw0YqFaPYRj2ttzYsWMxduzYFi7Ro+nbty8NFh5D9Aog1RC0vlD1RetK\n62AwEiTla9hUp9dzVNAZCLhGAkGZHrYGI3iVHlYGI2y5DEQg4JYZUFaiB0kmyAeQ3wTl41lZgC9o\nutN6GjBQ9WY0Ght8Nf1Ber0eFha02lEURVEU1XoRQnC3sASxqcW4llqIlEwlmBI9BHoDBHoDAsoM\nEOoNsDLUPD4CABjKHw1lxbeASGwFoZgHocQKIjEPQrHpb8X7AiEPVgILWFlZgMM1nZ/FxcU9xNLq\n9mhnf1SzkMlkSElJYV/Pnz8fH3zwAQBT20Y/Pz9s3boVPj4+CAwMZJvrVEz79ttvY/To0fD09MSI\nESOQnp7Ofp6UlITQ0FB06NABvXv3xqFDh8y+u3jxYowbNw4eHh6IioqqsYxarRarVq1CQEAAvLy8\nMGzYMJSWliItLQ0ymQwRERHo1q0bRo0aBQCIiIhA37590b59e4wZM8asTCdPnkTv3r3h5eWF5cuX\no/LYgnv27MGwYcPMln306FF0794dPj4+WLt2LWoai7C2dW3oelXYt28funXrBh8fH2zZsoV9v7S0\nFCtXrkTXrl3RtWtXhIeHQ6czZUSo2GcVMjIyMG3aNDz11FPo2LEjli9fzn5W23aiWpfafh8U9SBa\nX6j6onWlaWk1OmSmFSLxahZO/nMLu36Mw6atUVi3/gR+2XIaqfvjIYlOhX96AfzyFehQpIarqgS2\npWV1BgsPsuJbwM5eBHcvWzzl74ygvu3QL8QHQ0d1xaip3TF5Xl/MXjYQi94NwRtrhmDm2/0xYXZv\nvDwxEM+N6IK+gzqgW08PdOjsCBcPG9jIhBAIeWyw0JTopd56Gvrt5Uad39FZQQ/93cpNdAAgNzcX\nBQUFSEhIQExMDMaPH4/AwEB07NgRAHDw4EHs3bsX3bt3xzvvvIPZs2fjyJEjUKvVCA0NRXh4OA4c\nOIDr168jNDQUnTt3RqdOndjv7t+/Hz179jQ7UX7QmjVrkJSUhL///huOjo6IjY01K+P58+dx8eJF\nMAyDI0ffXhpgAAAgAElEQVSO4JNPPsHPP/+MDh06YOvWrZg1axb+97//QS6XY8aMGfj8888xbNgw\nfP3119i1axfGjx9f47KPHDmCkydPQqVSYdSoUejYsSOmTp1qNk191vVh1uvixYuIiYnB7du3MWTI\nEIwYMYINHmJjY3H69GkAwOTJk7F582aEhYWZzd9gMGDChAkYOHAgduzYAQ6Hg/j4eHa9atpOFEVR\nFEXVjRBTB+LiAg2KC7QoLtSgqECLogIN8nNV0KqqpjflABDVc/4cLgNrGwGs7QT3r/yLyu8MiHj3\n/4p4sLDkNuq6NScaMLRRD15FX7lyJSwtLfHMM88gJCQEhw4dwpIlSwAAQ4cORZ8+fQAA4eHh8PLy\nQkZGBqKjo+Hp6YmJEycCAPz9/fHSSy/ht99+w7JlywAAw4cPR8+ePQEAVlbV5wA2Go3Ys2cPjh07\nBmdnZwBgv1Nh+fLlEAgEAIBdu3Zh0aJF8PHxAQC89dZb2Lp1K9LT0xEVFQVfX1+MGDECADB37lxs\n37691m3x5ptvwtraGtbW1pgzZw7++9//VgkYjh49Wue6Psx6LVu2DFZWVujatSv8/Pxw/fp1+Pj4\n4MCBA9i0aRNkMhk73dtvv10lYIiLi0NOTg7WrVvHNvfq3bt3rdspIyMDbm5utW4TqvnRdsZUQ9D6\nQtUXrSs1I4SgtEQPrVoHjVoHlbIUquISKIq0KC7QoqjQFCSU6R6mUVD5MhiAJ+TBxlYAe5kQUlsB\npDYC2NgJYSMTQmLNB4fz+KctpwHDY8DGxoY9GQcADw8P5OSYhgZnGMZsQDqRSARbW1tkZ2fj3r17\niI2Nhbe3N/u5wWBgr+Y/+N2ayOVylJSUVJupqELlE9z09HSsXLkSq1evNpsmKysLOTk5VZZZ18lx\n5c/d3d2RnZ1dZZq61rU69VmvyiMnCwQCqFQqAEB2djbc3d3rLFdGRgY8PDyq7RtS03bKzMykAQNF\nURT1WCNGApWyFEVyDQrlaqgUpVArS6FRmQIDtbIUamUJDLWlJqoHAwOoLS2gteBCx+PCzkaAdi4S\ndPG0gW87a0ikT0ZAUBcaMNTTozQhelRCoRBarZZ9nZ2dbXbCWFRUBI1GA6FQCMB0cty1a1cApug7\nIyODnValUqGwsBAuLi5wd3fHs88+i4MHDz5S+WQyGfh8Pu7evcsu90GVm/G4ublhyZIlGD16dJXp\nkpOTzcr7YPmrk56ezjYrSk9Ph4uLS5VpHmZd67NeNXF2dsa9e/fMylVxl6IyNzc3pKenw2AwgMvl\nVvmspu1EtT40VzrVELS+UPX1uNYVYiRQq0pNdwMKtVAUaqEoKjE9LzK91usb1kegJnqGgdaSC40F\nF1pLLrTlfzWWXLg5i9HdTYogNwm6OolhZUG791aHbpU2wM/PD/v374fBYMDx48dx/vz5KtNs2LAB\nZWVlOH/+PI4dO4aRI0eynx07dgwXL16ETqfDhx9+iJ49e8LV1RUhISG4ffs29u3bh7KyMpSVlSEu\nLg5JSUkAqjZ7qgmHw8HkyZOxatUqZGdnw2AwICYmhu3k+6BXX30VW7ZsQWJiIgBAoVCwHZBDQkJw\n8+ZN/Pnnn9Dr9dixYwdyc3NrXf727dtRXFyMjIwMfP3112zH6srqWtfGWK/KRo8ejY8//hhyuRxy\nuRwfffRRtXczunfvDicnJ7z77rvQaDQoKSlBdHR0nduJoiiKolozU98BHbLSi5F4NQsXI5Nx9Ndr\n2P9dDL7dfBqfrD2KrzZEYs9XF3F471WcOXoLV6LvIeVWPgry1PUOFiwsubAU82CU8lEg5uOeRIAk\nOzGuOFrjgqsdTno64ISXA867y3DF2Qaa9vYI6NMO/3mpE3a/GoTtozrjtV5u6O4mpcFCLegdhjbg\nww8/xLx587Bz504MGzYMw4cPN/vc0dERNjY26NKlC4RCIbZs2cJ2eGYYBmPGjMGmTZsQExODgIAA\n7NixAwAgkUhw8OBBrFq1CqtWrYLRaIS/vz/ee+899rv1HZZ83bp1WL9+PYYMGQKVSgV/f382W9OD\n8xg+fDjUajVmzZqFe/fuQSqVYtCgQXjllVcgk8nw3XffISwsDAsWLMD48ePZ/hc1lenFF1/EoEGD\noFAoMGnSJEyZMqXKtHWta2OsV2WLFy+GUqlE//79AQCvvPIKFi9ebLYeAMDlcvHzzz9jxYoV6Nat\nGxiGwdixY9GrV69atxPV+jyOVwCppkPrC1VfrbWu6Er1UBSXQFlUApWiBMriiocWyuJSKIu10JU+\nfN8BABAILWEjM/UVkNqYOhWXWXCQUWLALZUOVwtKkFdS+zIcRJYIdJUgyFWCAFcxHES8RyrTk4oh\n9b2M/Jg4fvw4unfvXuX9rKysapuytHZRUVGYM2cOrl27Vu3nCxYsgKurK1auXNnMJaNam7ZaxymK\noqjmVaYzQFneefh+IFD+UJiCBF2p/pGXwxdYwrq8E7GpMzHf7DVfYIlCbRk7WFp8phJZytrv8lvz\nLRDoKkagqwSBLhK4Snn1vvj5OIiLi8Nzzz3X6POldxgec09YPEhRLeZxbWdMNQ1aX6j6auy6UqbT\no7ioBIrC+30HVIoSqFU6qFWl0ChLodWUNcqyLHlcWNsJYGMrhLWdENa2pvSj1uUBAc+q6mmoWmfA\nv1kqXI7PweVMJVIKS2pdhojHRYCL2BQkuEjgact/ogKE5kIDhsdAbT+MhjQrqkvfvn2r7YC8devW\nNt0x93FdL4qiKOrJo9cboSwyjTNQXCkoqOhMrKlm3IGHYWHBgdiaD0l1DykfEhs++ALLOs9BSvVG\nJOSoEZ+lRHymEjfzNDDWcq3TisvAz7n8DoKrGB1lQnBpFqMmR5sklaPNNajHHa3jFEVRbZvBYISy\nqARFBRoUFWigUemgUZVCpSxlmww1RkDA4TAQW/MhtTad+EusBZCUv64IEgTCuoOB6uiNBEl5GlzO\nNAUICblqlNWSGtWCw6Czo7A8QJCgk4MQvGYY2bitok2SKIqiKIqiHlOEEGhUukp3BEx3CJTFJey4\nAxq1DnjEy7wcDgNJeV8Ba1vTQGQSKR8iiRVE4vKRicVWjTb2gJEQ3C3QIj5ThcuZSvybrYK2rOYM\nSAyAjjIBGyD4O4vAb8MjJD8uaMBAURTVCGibdKohaH15shBCoCvVQ6UshUapg1pZafyBSuMQVJdK\nNDUzAZ6uXeq9LIYBxFI+bGTlfQZsTf0FKjoTi5t4IDJCCNKLS00dlbNUuJKphKKObEkeNlYIKu+k\n3M1FDCmfnp62NnSPUBRFURRFPQJdqR7yXBUK8u+PSKxSlkKtuH93QF/LVfV6YwCxxAo2dqZUo2Ip\nH0KR6a5ARf8BscQKnGZuspOr0pVnMjJlM8qvo9O0o9jSFCCUBwkykWUzlZR6WDRgoCiKagT0ajHV\nELS+tC1lZQZ29GG2yVCRFopCU+pRtbK0UZbDF1ia7gbYmLIJSW0EkNoEQSzlQyy1glDEa/ZgoDpF\n2jJcyVKV90NQIVNR+/rb8C3YTspBrhI4S56sVKePAxowUBRFURT1RKs5IDC9boyOxBaWXIglVmxf\nAYkNH1IbQaW+BHxY8VvnlXY21Wn5XYS7daQ6FVpyEOAiQZAbTXX6uKABQxsQEBCAzz77DAMHDmzp\nouCZZ57Bxx9/jGeeeaZJ5r9nzx5ERETgyJEjTTL/2pbVrl07REVFoV27dk0y/4bYunUrUlJS8Omn\nnzZKWaimR9ukUw1B60vzMhqMUBSVoFCubpKAgMNhYGsvgsxRZBqRWGLFBgfi8g7FPCvuQ500t0Rd\nKdEbkZCjYjsq38qvO9Vp1/JUp0E01eljiQYMbUBjjqXwqM6dO9fSRWgyaWlp7PP58+fDzc2txUbI\nfuutt1pkuRRFUW0VIQQqRSkK89UolGtMf/PVKMzXoKhQA2MtqTvrwnAYSK359zsP294ffMzaVtAi\n/QYak95IcDNXjfgs02jKCTlqlNUSIXAZwNdRVN4PQQxfRxFNdfqYowEDRVFUI6BXi6mGoPXl4ZSV\nGUzjDRSVQFmshaLI1IegIE+N/BwVdKX6h5pvaw4ImqKuGAnBHbmW7YPwb7YKJdVkaKrwYKpTP2cR\nBDTV6ROFBgxtRFxcHJYvX46cnBwMHz4cH3/8MbRaLebMmYO4uDjo9Xr07t0bmzdvhqurKw4dOoTP\nPvsMJ06cYOfxxRdf4Ny5c4iIiEBpaSnee+89/Pbbb9DpdBg+fDjef/998Pl8yOVyzJ8/HxcvXgSH\nw4Gvry8OHz4MwNQ8atu2bRgwYABiY2MRFhaGW7duQSAQYMSIEXjvvfdgaWlqgymTybB582Zs374d\n+fn5GDt2LDZt2lTnuhJCsHz5cuzduxfOzs7YtGkTBgwYAAD46aef8PnnnyMzMxMymQwLFy7E9OnT\nAZhu286ZMwfz5s3Dp59+Ci6Xi1WrVmHSpEkAgIKCAixYsABnz57FU089hUGDBpktVyaT4dKlSzh9\n+jQOHDgAhmHw1VdfoX///vjpp59qLG9GRgbCwsJw4cIFGI1GjB49Ghs3bmQ/X7NmDSIiImBtbY2P\nP/6YHVAlKysLixcvxsWLF2Fra4uFCxdi6tSpAICNGzfi7t27+OqrrwAAFy5cwNq1a5GUlASxWIyV\nK1di4sSJte5HiqKotoQYCTRqnakvQXEJlEWmgEBZVAJFeXCgVT980yGRxAq2MlN2odYUEDQHQgju\nVaQ6zVTiSpYKyjpSnbaz4SPQVUxTnVIAaMBQb/9zbtw2+y9k179pDyEEBw4cwMGDByEUCjFx4kRs\n3rwZc+fOxZQpU/D9999Dr9fjjTfewPLly/Hjjz/ixRdfxOLFi5GUlISnnnoKALB3714sXboUALBu\n3TqkpqbizJkz4HK5mD17Nj766COsXr0a27dvh5ubG27fvg0AuHTpEluWyk2jLCws8OGHHyIoKAgZ\nGRkYN24cdu7ciTlz5rDTHD16FMePH4dSqcSgQYPw/PPP1zkCYWxsLEaOHInk5GT88ccfmDZtGuLj\n42FjYwNHR0f88ssv8PT0xLlz5zBu3DgEBQWhW7duAIDc3FwolUokJCTg5MmTmDFjBl566SVIpVIs\nXboUAoEAiYmJSE1NxZgxY+Dp6Wm2bIZhMH36dMTExMDNzQ1hYWG1ltVgMGDChAkYOHAgduzYAQ6H\ngytXrpity8SJE5GcnIzvv/8eb775Jq5fvw4AmDVrFrp27Yrvv/8eSUlJCA0NhZeXF/r372+2jHv3\n7mH8+PH45JNP8PLLL0OhUCAjI6PO/Ug1L9omnWqIJ7G+6Er17GjEiiJteSBw/7myWAvDIzQbAkxZ\nhmztRbC1F8LWXgQ7mRA29iLYyoTgWbXNU56HrSs5Sh3is5S4nKFEfJYSBZra7744iXmmAIGmOqWq\n0TZ/PU8YhmHw+uuvw9XVFQCwePFiLF++HCtXrsRLL73ETvf2229j5MiRAAArKyu88sor2L9/P8LD\nw5GYmIh79+7h+eefByEEP/zwA86cOQNra2sApjbzs2fPxurVq8Hj8ZCTk4O0tDR4e3ujd+/e1ZYr\nICCAfe7h4YFp06bh3LlzZgHDokWLIJVKIZVK0a9fP1y7dq3OgMHBwYGdxyuvvILt27fj6NGjGDdu\nHEJCQtjpnnnmGQwaNAjnz59nAwZLS0ssXboUHA4HQ4YMgUgkwq1btxAYGIg///wTZ8+ehUAggK+v\nLyZMmFBrnwxC6v7HFRcXh5ycHKxbtw4cjunqVK9evcy2S8Vdg/Hjx2PJkiXIy8uDTqdDdHQ09u3b\nBx6PBz8/P0ydOhV79+6tEjAcOHAAwcHBGDVqFADA1tYWtra2de5HiqKo5lJWZoCqIhgo/6ssMo1S\nrFSUQFVcihJt7bn564PhMJBI+ZDa8E1ZhqwF5aMWC+HgLIZIYtVq+vw1tyJtGeIzTX0QLmcqkaWs\n/W4MTXVKNQQNGNoINzc39rm7uzuys7Oh1WqxcuVKnDhxAkVFRQAAtVoNQggYhsGECRMwe/ZshIeH\nY+/evRg1ahQsLS2Rl5cHjUZj1iSHEMKeIC9YsAAbN27E6NGjAQDTp0/HwoULq5Tp9u3bWLVqFa5c\nuQKNRgODwYDAwECzaRwdHdnnQqEQarW6znV1cXExe+3u7o6cnBwAwD///INNmzYhOTkZRqMRWq0W\nXbt2Zae1tbVlT9wBQCAQQK1WIz8/H3q9vsp2fFQZGRnw8PAwW2ZlD64/ALY8tra2EIlEZuWJj4+v\ndhkP3gkBgPz8/Fr3I9W8nrSrxdSjaWv1pbSkDIVyDYryNVAUayv1IzDdIdDWMVBXffEFluWBAB8S\nGwGklYKCiuxDTTlKcWtUU11R6wy4mnU/QEipI9WpmMdFNxcxGyR42tBUp1T90YChnhrShKgppKen\nmz13dnbG9u3bkZycjH/++QcODg74999/ERwczAYMPXv2BI/Hw7lz53Dw4EF8++23AExt9QUCAc6f\nPw9nZ+cqyxKLxVi/fj3Wr1+PxMREjBw5Et27d69y5XvJkiUICAjAzp07IRKJ8OWXX+KPP/545HXN\nysqqsu7Dhg1DaWkppk+fjq+++grDhg0Dl8vF1KlT63WCbG9vDwsLC6Snp8PHx4edb03qexB1c3ND\neno6DAYDuNz6dwBzcXFBYWEhVCoVxGIxW56Ku0iVubu7Iy4ursr7de1HiqKo+iKEQKspu59VqKD8\nIdeguEDTKAEBl8tAbF0pAKgUFEhsBJBa89tss6HmUKo34npDUp1acODnJGJHVO4gE9BUp9RDo7/M\nNoAQgm+//RZDhw6FQCDA5s2bERoaCpVKBT6fD6lUisLCwmo7FI8bNw7Lli0Dj8djm8pwOBxMmzYN\nK1euxKZNm2Bvb4/MzEwkJiZi8ODBOHr0KDp27Ahvb29IJBJwudxqr6Cr1WqIxWIIhUIkJSVh165d\nsLe3r3U96iMvLw87duzAzJkzcfjwYSQlJSEkJAQ6nQ46nQ4ymQwcDgf//PMPTp48iS5dutQ5Ty6X\ni5deegkbN27Etm3bkJqail9++aXGMRccHByQkpJS53yffvppODk54d1338WKFSvA4XBw9epVs2ZJ\n1XFzc0OvXr2wfv16rFu3Drdv38ZPP/2Er7/+usq0Y8aMwdatW3Ho0CG89NJLUCgUyMzMhJ+fX637\nkWpeT2KbdOrhtVR90ZXqy+8UlKcelWtQkGdKP/ooTYZMTYWsILHmQ1I5ILDmQ2zNh0TKh1DEA0NP\nWOtNbyS4mafG/iMnoHbsXGeqUwsOg86OQjaTka+DEJaPcUduqnnRgKENYBgGY8eOxejRo5GdnY3h\nw4dj8eLFKCoqwuzZs+Hj4wMXFxfMmzcPf/31l9l3x48fjw8//JDt7Fxh7dq1+OijjzB06FDI5XK4\nurpi5syZGDx4MJKTk7Fs2TLI5XJYW1vjtddew7PPPlulXOvWrcNbb72Fbdu2wd/fH6GhoThz5oxZ\nuR9cj7qu3DMMgx49euDOnTvw8fGBk5MTdu/eDRsbGwDAhg0bMHPmTJSWluKFF17Aiy++WOX7Ndm0\naRMWLFgAX19fdOrUCZMnT0ZUVFS1350yZQpeffVVeHt7o3///vjhhx+qnSeHw8HPP/+MFStWoFu3\nbuy+6tWrV7XrW/n1N998g8WLF6NLly6wsbFBWFgYmw2q8rTu7u7Yu3cv1qxZg4ULF0IqlWLVqlXw\n8/OrdT9SFPXkKi0pg6KwBAX5auRlKZCXrURethKKotqbrdSEa8GBja0ANvYiWNsKILGuuENgChCe\nxKZCjc1ICO4WmKc61ZYZoUyWQ2JQVZmeAdDRXsDeQfBzEoFPU51STYQhT1iD5+PHj6N79+5V3s/K\nyqrSdv5xoNVq4evri8jISHh7e7d0cagW9LjWcYp60hj0RigVJVArS82yDikK749LUFrS8PEILHlc\nNsOQjV35Q2b6K5ZY0bsDjYwQggxFaXkWIxWuZCqhqEeq06DyTEbdXMSQ0CZc1APi4uLqTC7zMGhN\ne8zt2rUL3bt3p8ECRVFUG1Jaokeh3NRUqKhAi+ICDYoLTX+VxSV42Et9HC4DG1shbOyFsLMXwUZm\n+mtrL4JY+uRmGGouuSodOw7C5Qwl8uvoG2KW6tRVApmQpjqlWgYNGB5jAQEBYBgGERERLV0UM2+/\n/TYOHDhQ5f1x48bh448/boES1S49PR3PPFN1HA6GYXDu3DmzzEvUk4v2YaAaIioqCr179UGRXGsK\nDOQaU3Ag16AgXw2N6uEHKAMACwsOpDYCWNsJYO8sgaOzBA7OEtg6iMCl7dqbTXGJHlfKsxjFZ6qQ\noSitdfrqUp2ePXsW/TrSYwvVsmjA8BirPIBYa7JlyxZs2bKlpYtRb+7u7khLS2vpYlAU1YYYjQTK\n4hJT1iG5BsoiLdTKUqiUpVApSnEtIQ4XjlRtl14vDCCR8iGSWEEirehHYEo7Ki1PPyoU05z6LUFb\nZsC/2Wo21WmyXFvr9EJLDgJc7gcInrY01SnVOtGAgaIoqhHQuwtPngeDgiK5BoVyNZuKtLZRi13s\nn6p13lwuAxtZ+YjFMiGs7YSwthXC2k4AqY0AFhb0LkFrUGYwIjFPYwoQMpS4katGbYNV87gM/JzE\nCHSTINBFDB97YZ2pTumxhWoNaMBAURRFUbUwGIwolGuQn61Efo4K+dlKFOSr6wwK6sLhMrC2EcBG\nJjR1NpYJ2SBBaiOgWYdaoYpMRnEZSsRnKvFvtholemON03MYwNexYiwEMTo7isCjTcKoNogGDBRF\nUY2A9mF4PBiNBAV5KmSnK5CdUYzs9GLkZSthqOWksCZCMY8NAqztBGwzIrHUCv9ej8PgwQNp5qFW\njhCCTIWObWJ0JUuF4joyULW34yPQVYIgVwn8ncUQ8h4t1Sk9tlCtAQ0YKIqiqCdSmU6P/BwVO0ZB\nXpYSOZkKlOlqT21ZWeWgwFYmLH9uem3Fr/lfrFWyBQ0WWqkCTVl5J2VTkJCrqj2TkbOEh6DyACHQ\nVQwbAc1kRD1+aMBAURTVCOgVwNZLX2ZAQZ4a+bkq5OeoIM8xNS0qLtIC9WxRJLHmw95JDHtniemv\no7jOoKA2tL60HmqdAVezVLhc3g8htY7B7SoyGQW5ihHkJoGzxKpJy0frCtUa0IDhMTZixAiMGzcO\nU6dOrfd30tLSEBQUhLy8PHA4tJ0lRVFth0FvRGG+KTCQ55iCg/xcJYrkmgaNWyCSWMHZ3dr0cJPC\nyc0aQhGv6QpONSud3oiEXDUbICTla2CspX4ILDno5iJm7yJ40UxG1BOIBgyPMYZh6EGNopoJbWfc\nvEpL9MjJKEbWvSJkZyggz1GhqEADY21nfg9gOAxsZUI4lI9RYO8sgZOrFBJrfhOW3ITWl+ZjMBLc\nyi/PZJSpwvUcFXS1dFa35DDo7HS/o3InBxEsWrD5GK0rVGtAAwaKoiiqVdOodcjNVCA3U4GcLAVy\nMxQoLNDUuzkRGMDGVgiZk5htTmTvZBrEjKYnffwQQnCvqNR0ByFTiatZKqhq6ZfCAOhoL2DvIHR1\nFoNP6wVFmWnTAYPBYECPHj3g7u6OP/74AwUFBRg/fjxSU1Ph5eWFffv2wcbGpqWL+chkMhliY2Ph\n5eUFAJg/fz7c3NywcuVKAMCRI0ewYcMGpKamwt7eHh999BEGDx4MALh79y5CQkKQlJSE/v374/PP\nP6/XNomIiMDGjRtBCMH8+fMxf/58AEBsbCzCwsJw69YtCAQCjBgxAu+99x4sLS2xdOlS8Pl8rF+/\nnp3PpEmT0L9/f8ydOxdZWVlYsWIFzp8/D5FIhLlz52L27NnsfJcuXYrk5GQIBAKMGTMG7733XmNu\nRopqUvQK4KMjhEBRVILcLMX9ACFTAVUdo+NWJrXhQ+Z0v5+BzEkMmYMYlo+Yqaax0frSuHJV9zMZ\nxWeqINfU3lHZ3dqKDRC6uYghfci+KM2B1hWqNoQQGLWlKFMooS9+yMEg66H1/kLq4dNPP0WXLl2g\nVCoBABs2bEBISAiWLVuGjRs3YsOGDdiwYUOjLOvjlf9rlPlUWPLBCw/93cpNjWJjYzFv3jzs3r0b\nAwcORFZWFlQqU4UhhGDv3r04cOAA2rVrh3nz5mHFihX46quv6lxGVFQULl26hJSUFIwcORJ+fn4Y\nOHAgLCws8OGHHyIoKAgZGRkYN24cdu7ciTlz5mDixImYOnUq1q1bB4ZhIJfLcfr0aXz22WcwGo2Y\nNGkShg8fjp07dyIjIwOjRo1Cx44dMXjwYISFhWHu3LkYO3YsNBoNEhISHnr7UBTV+hkNRhTINcjL\nVCA3S4GcTCVyMxUo0dZ+oleB4TCwdxTDxcMaLh42cHCRwM5eBJ5Vm/63RtWTokSPK5U6KmfUEVTK\nhJYIchWbOiu7SeBA+6RQrQQhBAaNFvpiFXvSX6ZQQa8o/1usLP97//P7n5neI2X3U/06Hvm8ScrZ\nZo+s6enpOHLkCMLDw7FlyxYAwO+//45Tp04BAKZPn47g4OBGCxhaq4iICEyZMgUDBw4EALi4uLCf\nMQyD8ePHw9fXFwAQFhaGgQMH4ssvv6yzb8OyZcsgEAjQuXNnTJo0CQcPHsTAgQMREBDATuPh4YFp\n06bh3LlzmDNnDrp37w6pVIpTp04hODgY//3vf9GvXz/Y29vj0qVLkMvlWLJkCQDA09MTU6dOxa+/\n/orBgweDx+Phzp07kMvlkMlk6NGjR2NvKopqUrSdcc10pXrkZpkCgtwsBfKylZDnqKCv59gGFhYc\ntn+Bo6sUji6m/gaWlq3rrkFD0PrSMCVlBlzLMXVUjs9Q4rZcW2uLNDGPiwBXcXk/BAk8rK3abJ8+\nWldaN2I0wqDWoqxYaTqRL1ZBr1De/6tQV3qtMp9OaTrpJ4b6p3JuKW02YHjrrbfw0UcfQaFQsO/l\n5OTAyckJAODk5IScnJyWKl6zyczMxNChQ2v83M3NjX3u7u6OsrIyyOVy2Nvb1zrfB79XccX/9u3b\nWDi0qc8AACAASURBVLVqFa5cuQKNRgODwYDAwEB22vHjx2P//v0IDg7G/v37MXfuXACmAC87Oxve\n3t7stEajEX379gUAfPbZZ/jwww/Rp08feHp6YtmyZbWuF0VRrZNBb0RethLZGcXIuleM7IxiyHNV\n9e5vYMW3KA8KpHB0lcDJRQo7BxE4dHTcJ4reSHCzIpNRpgo3ctXQ19Khncdl4OckRqCbKd1pR5kQ\nXDrOBVVPhpJS04l8kelqflmx4v6V/iLl/Sv/xUrzE/5iBcoUasDY8IEdGxOHz4OlVAILqajJltEm\nA4Y///wTjo6OCAoKQmRkZLXT1JYhaP78+WjXrh0AQCqVwt/fHx06dKh1mY/ShOhRCYVCaLVa9nV2\ndjZ7Qu/m5oY7d+7U+N309HSz55aWlpDJZHUuMz09HT4+PuzzijsXS5YsQUBAAHbu3AmRSIQvv/wS\nf/zxB/u9sWPHol+/frh27RqSkpIwbNgwtpyenp6IiYmpdnnt27fHN998A8B0p2jGjBlsfwaq8URF\nRQG43yaWvm681/369WtV5WmO12dOn4GiWAsv967ITi/G6dNnUCTXwMO5MwAgNdN0ocHTtUu1r3OL\nbsFGJsKA/v3g6CrFnXvXIRLz0L9/L3Z5hbeBfs6tY31pfWm610ZCcPB/J3ArTwutU2dczVYhNzEO\nACDpYLoopUyOZ19zGMBanggfmRBjXhyMLo4iRF84Byiz0cmh5deHvm7e18RgwKljx2HQaNHzqc7Q\nK1Q4e/4CDBoNAp3bQa9Q4WLCvzCoNOhqZQ19sRJx6SnQqzXoVMLAWKJDglEDAOjCEQJAs77mCvhI\n5BnAFQvQ3aUdLKwluF5SBK5IgF6+frCwFiM+JwNcER/P9uoDC2sxLt1KBFckBFfIx/mYaKSlpQEA\nXkPTYAhpSHbq1mHlypX48ccfYWFhgZKSEigUCoSGhiImJgaRkZFwdnZGVlYWBg0ahMTERLPvHj9+\nHN27d68yz6ysLLPmPK3Jiy++iL59+yI8PByRkZGYNm0aFixYgLCwMMTFxWH06NHYvXs3+vXrh+zs\nbKjVavj4+GDEiBG4e/cuDh48CA8PD8yfPx88Hg87duyocVkV4zCMHTsWW7duRWpqKkaOHIkdO3Yg\nODgYISEhGDp0KJYsWYJbt25hypQpsLe3x5EjR9h5hIaGIi8vD0FBQfjss88AmO4mPPfccxg1ahRe\nf/118Hg8JCUloaSkBEFBQdi3bx8GDx4Me3t7REZGYvLkybhz5w6srJp2QJwnSWuu41TrZTQYoSgq\nQaFcjSK5BkUFWhQVaFBUoEGxXFOvZkUMA9g5iuFc3qTIwVkCBxcJBELajvxJlqW4n8koPlOF4hJ9\nrdN72fLZjsr+LmKIWllHdurREKMReqUaZUUKlBUpy/9Wel6sRFmhAmWFxeWvTU189AoV9Ep1i5b9\n/+zdeVib55U//K920C4hgVjEvhlvGMfY8W6nTrO4aVbH00mcjp02bbYm6UzTNs2vbSZtkplOpm/S\n6XQ6cTx2mqZZ2iROmsWO7Xh3vOAdbHYECARol9Cu5/1DQoABWWBAAs7nuriQHm03yW14znOfcx9O\nchK4cknoKr9MDJ5UDK5MEvou7bsvHvD4gOdJxWDzx687eFVVFW644YZxe78+U3KF4de//jV+/etf\nAwD279+P3/zmN3jjjTfwox/9CNu3b8fTTz+N7du34/bbb4/zSMfHCy+8gIcffhhbt27FLbfcgltv\nvTXyWEVFBX73u9/hmWeegU6ng1qtxr//+7+jqKgILBYLGzduxKOPPora2losX748Uu8RDYvFwrJl\ny3DdddchGAzisccew+rVqwEAzz33HJ588km8+uqrmDt3Lu68804cPHhw0Os3btyI73//+4PqR9hs\nNt566y08++yzqKiogMfjQVFREZ555hkAwN69e/Hss8/C5XJBq9Xitddeo2CBTClTPc/Y4/bB2OWA\nqbsXpm4HTD1OmLqdod4GUfasH45MkQyNVgZNpgzpWhlS06VUjHyFqT5fxsLU68PZjlCK0el2OwwO\nb9Tnp4n5KB9Qh6AUjt9J1VQy1eZKwOWBzzrgBN9ig99qh9cc+t53LPK41R4JAOKV2sPiccGTScCT\nS8CTSQef9Mv6T/IH3ubKxKH7UjHYvOn/+21KrjAMtH//fvzHf/wHdu7cCZPJhA0bNkCn0424repU\nXGGYao4ePYqHHnoI586di/dQyAA0xyfWVPqj7nb5oNdZYGi3oktvR1eHDVaz6+ovHIZYKkBqhjTc\nFTnUHZm6Il/dVJovY2X3+HGuw4EzegfO6O1osbijPl+WxEV5el8dggTpEv6ULVQeT/GYK3079/hM\ntsiVfq/Z2n+yb7ENeixy4m+1IeiOHghOFK5EBG7fFX2ZGFypBDypCNxwbj9PJg0FBHJpJDjgyiTg\nKaTgJE+f7t20wjCCVatWRXYIUiqV+OKLL+I8opnN5/PhD3/4AzZt2hTvoRAyqRL15I8JMjB2OaBv\ntUCvC32Zuke3fC+SCKBIEULe96UUQqYUQq5MprSiMUrU+XIt+nYyOhNOMao39iJa4+0kLhtzNWJU\nZIZWEPKUSWBPk5O28XQtc4UJBkMFusOl9vRd2Tfb+gMBczgwsNgGbdU5WThiYf9JvXzgCb4UPIUk\n/D38NTCtRyICi0MpahNpygcMZPTeffdd/PCHPxxyXKvV4vDhw2N+38uXL+NrX/sa5syZg+9973vX\nMkRCyBi5XT50tFrR0WqBXmdGR6sVnqvkhgMAm8OCUi1CiloMpUoEhVoEpVpEvQ3IiHyBIGq6enG2\nw44zejtqunqj7mTEY7MwK00UWkXIkKBELQSPdr+KCcMwoRN/sxVesw0+kxVeowVekyV88m+Dz9wX\nEIRu+63hNJ9JTiRhcTn9J/hXnvhfcZsrl4Af/s6TSWdEas9URf9nZqB77rkH99xzz7i/b0lJCVpb\nW8f9fQmZCuKRNuDzBtBjsKOrw47ONiv0rZaYtjBls1lITZcgPVse6m2QLoUyVQwul07eJstUTEkK\nBBk0GF3hImU7LnQ64IlS38JmAUUqIcozJCjPEGN2mhhJNMcQ9Pvht9jhNVlDAYDJGj7xD932maz9\nV/pNFpzubEOJizXpe/WzkwXgyaXgK2ShE/y+K/vh25Hj4SCAG07z4QiTp016D+lHAQMhhCQ4hmHg\ntHvQ1WFHd2eo5qBbb4fZ6Izp4qFQzEdGtjzylZYhA492mCFXwTAMWizuSIrR2Q4HnN7oJ619OxmV\nZ0gwVyOCeBqvTjEMg4CjN3Rib7SGc/ytg1YBIrcH5P+Pdkcff7AXTHgrzrHgSkSRq/p9OfsD8/h5\nCtnQoEAmBSeZNh4h/abvv+RRmuK134RcFc3xiTWeV4ttFhc6dBZ0toc6I3d12OFyxlZIyGKzkKoJ\nrR5kZMuRmS2HVEFX/BJNIq4uMAyDTrsXZ8LN0s7o7bBcJZ0tQ8oPryBIMD9dDEXy1N3JKOjzh670\nm6zwGs2hlB9j+H5P+H74MZ/ZBq/JMil5/n379nNEQvCV4ZP9FDn4Sjn4Shl4Cln4JF/Sn/Ij6w8Q\nKM2HjAeaRWECgQBGoxFKpZL+sJJpp7e3FxwqCEtIPq8fne02dLRaIrUHDpsnpteyWIBSJYI6QxoJ\nEjSZUvD49KudxMbo9OFMuAbhjN5x1a1OU4S8yFan89MlSJMkZtF7wO0ZVNDbV8jbt7vPkMDAZIXf\nap+cwbFY4MnE4PWd8CvloSv8KeEr/Qpp/1V/pRR8pRw8uXRc9+onZLTor0pYSkoKHA4HOjo6AICC\nBgIAsFqtkMlk8R7GNWEYBhwOB6mpqfEeyrQWS046wzAw9Tihb7GEAoQ2K3oMDjDRtpIJ4/E5SE2X\nQJ0ujXxXpYoptWiKilcNg80d3uq0I9QwrdUSPTiVCDgoT5dgfjhIyJIJJv3vIxMMwmexh67y930Z\nLZEUoL5jnm5TpAB4srb25CQngaeUDbjSLwNfIQVPOeC2Qha6L5eCr5COekefqVjvQqYfChgGEIvF\nEIvF8R4GSSANDQ0oLS2N9zDIFOX3B2Fot6K9xYz2Fgv0LWa4en1XfR2Pz0G6VoZ0bagoWZ0ugVwh\nBItNFzLI6Lh8AZzvdOJsuKNyg9EVtSY+mRfa6rRvFSFPmTzuW5327fjjNVoGBwA95tAV/x4zPAOO\n+UzWySn4ZbPBV8jAT5GHrvanyMFPUYS+K2XgDbjNV8rBU8goz5/MGFO+cdtojdS4jRBCrlWv0wu9\nzhIKEJrNMLRbEbhal2QWkJIqRnpWKEBI18qgShWDTdtNkjHwBoK41OXEGb0Dp/V2XOpyItoU5HFY\nKEsVRXYyKlGLwB1lYNrX5OvKk39Pjxk+oyV88j94dWCic/9ZPG7/Dj8Ddvbpux1KAZKHA4DQd55c\nQnv5kymPGrcRQkgCYYLh9KJwgKBvscDUc/XdT5KSecjICRUkp2fJocmSQZBEv4rJ2ASCDBpMLpxp\nD60gxLLVaYk6vNVpugRlaSIIhtnqNOD29F/17zb1BwHGAUHAgEBgolOAuDJJ6ORepYBApYgU/fLk\nUgjUitBKgEoRTgWaXp17CUkE9FeKkCgod5T0CQYZdOlt0DUa0dpkRofOArerP72oRV+NnIyyIa9T\npAiRkaNAZo4cmTkKKFUiSi0iY/7dwjAMWq2ecJGyHWc7HLB7oqfr5CuTUJ4uxnwZB0VcHzgWKzyG\nDngvmNAazv33dpv6g4Bu06i3/hwtjkgIvkoRCQL4KXIIVIorjoXvK2VgCxKzuHoy0N8hkghiChi+\n+uorLF68eMjx48ePo7KyctwHRQgh8cYEGXQb7GhtNEHXaEJbk+mqHZPZHBbSMmSR4CAjWw6RhHKc\nybXpdnpxur1/J6OevjoYhoHA7YLCYYPIYYfQYYPQYUearxeZAReUHieEdhsCplB6kNXlwckJGiM7\niR86uQ+f6Av6TvgHBAQDH6fcf0KmlphqGCQSCez2oduNKRQKmM3mmD9s7969yM3NRX5+Pjo6OvD0\n00+Dw+HghRdegEajGd3Ix4hqGAghw2EYBqZuJ3SNJrQ2GNHaZLpqgXKykBdqhhZeQUjLlIHHoxxo\ncm2sLh/O1hlQU92Kprp2uDp7ILZbIbZZILZZIbJbIbZZIXTYwA1MTC0Ai8PpP8FXDwgChpz8h25T\nd19CEkNcahiCwWCk2VMwGBz0WENDA3i80e0J/PDDD2PXrl0AgKeeegosFgtcLhff/e53sXPnzlG9\nFyGEXCuLqRe6BmMoSGg0wWmPvsWkWCpAdn4KtPlKZOUqIE8R0kkSGZVArxtuQw88nT3wGLrh7uyB\ns70LXS2dsLV3w9/VA4HFAp7PixwAOeP42ewkPgRqJfgqJfhqZei2WhH+roRApQwHCErwZGKw2FR4\nTwgJiRowcLncYW8DAJvNxjPPPDOqD9Pr9cjOzobP58Pnn3+OlpYWCAQCpKenj+p9CJkslDs6vTAM\nA0O7DXXVBtRfNMDYHT1PO1nER3a+Etp8JbILUqCIEiDQXJnZgj4/PIYeeAw9cHeGvns6e+Du7A4F\nB509cBt6Is3BqoO9kQ6+fZLG8LkcsTB05T8SAIS/DzmmAEdEAe5URL9bSCKIGjA0NjYCAFauXImD\nBw9GVhtYLBbUajWEQmG0lw8hlUrR2dmJixcvYvbs2ZBIJPB4PPD5rr4vOSGEjEXAH0Rbsxn1NQbU\nV3fBbnWP+FxBEjcUHOSnIDtfiZQ0MZ1gzXBMMAhvj3lQEOAx9MDd0R0OAkLfvT2xp+fGws/nA6oU\nCNPVUGhTkZyRiqQ0FQQaFQRpKiRpVBCkqsARjiXMIISQ0YkaMOTm5gIAdDodgFBaksFgGPOKwGOP\nPYbKykp4PB789re/BQAcPnwYs2bNGtP7ETLR6KrO1OSwudFU24PGS91oru+Bzzv8LjJcHhvavNDq\nQXa+Eup0Kdhj3MGI5srUwjAM/FZ7/wpA38rAwFUBQw88XUYw/vFrGhbgcOCQyCCX5KFWKoNTIodd\nKoNQo0JWQQaKSrMwZ3Y2pClSClYJAPrdQhJDTLskmc1mPPLII3jvvffA5XLR29uLnTt34vjx43j+\n+edj/rCnn34at99+OzgcDgoLCwEAWVlZeO2118Y2ekIIQWhHI32rBXUXDWiq7YGxyzHic5OSeSiY\nlYrCslTkFqrA41OR8nTj73WF04C6I0FAZFUgkjLUPb69A1gsQClHr0wOY7IEJqEUTqkMDokcDqkM\nDokMTqkMrmQRwGZDI+FjQYYE12dIMD9DDEXy6GoCCSFkMsUUMHzve9+DQqFAS0sLyspC+4xff/31\neOqpp0YVMABASUnJoPvFxcWjej0hk4lyRxOX2+VDS4MRzbU9aLzcHbVgWaZMRn6JGkVlacjKVUxI\nF2WaKxMv6PXBYzAOWAHojqQK9QUDns6ece8hwFNIQ2lA6WoIwmlBrBQl2vli1CEZZ3w81AcEYKJ0\nCZYncbEkU4IF4Y7K9WdPYPny2eM6TjI90e8WkghiChj27NmDjo6OQbsiqdVqdHV1xfTaWJZV165d\nG8tQCCEzVDAQREebFS31RjTV9qCzzYKRNoXmcFjIyFEgv0SN/FJ1qFkapXckNIZhQrUCbQa42jvh\nbjfA1dYJt74rfL8L3m7TuH4mR5gMQbo6VBvQ910T+uo7JkhNASdJAH+QwaUuJ6ra7TjVbsPl7l4E\nB5bfXRErCHlszEsXY0FGKEjIUQzuPFw/rj8JIYRMrJgCBrlcju7ubmRkZESO6XS6QfdHsmXLlpj+\nUDc1NcUyFEImFV3ViS+r2YXmuh601PWgpcEYtXFasoiPorJUFJalQZunAI8/uY3saa5EF3B74NZ3\nwa03hIOBcEDQ1glXe+hY0DM+KUIsPm/wyb9G3R8EDLjPFYtGfA+GYdBm9aCqwYaqdjvOdtjR6wuO\n+Hweh4XZaaLwCoIExSohOFHqYWi+kFjRXCGJIKa/qA8++CDuvvtuPP/88wgGgzh69Ch++tOf4qGH\nHrrqa5ubm691jISQGSAYCELfaoG+xYKONis626xRdzQCC9BkypBXpEJOkQoZ2fIxFyyTaxdweeBu\n74SrtROu1o7+r7bQMY+h59o/hM2GIFUZPvlXDzr5j+wcpFGDpxhbwbDV7cdpvR1V7XZUtdvQ5Rh5\nBz8WgCKVEBXhNKOyNBEEXOpbQAiZnmIKGJ5++mkkJyfj0Ucfhc/nwz/90z/he9/7Hn7wgx9c9bV7\n9+6NaSCUkkQSEeWOTqxepzdUg1DbjabL3VFXEABAIktCTmEK8opUyC5MQbKQP0kjvbrpPlcCve7Q\nyX/bwICg//Z4pAtxZRIkZ6YhKUsT+p6ZiqTM8O2MVAg0KrC547dy5A0EUW1w4lQ4QKjvcWGELDcA\nQJqYj4pMCRZmhlYRpEljH8t0ny9k/NBcIYngqr/t/H4/tmzZgv/5n/+JKUC40ubNmykliRACoH8V\nobm2B7pGE/StFkQ7Q+PyONDmKZAbXkVIUVMtwkTx97rgjgQAVwYGHdfeZ4DNRlK6GkmZaeEAIA3J\nWg2StelIykpDckYauJKRU4TGA8MwaDG7IwHCuQ4HPIGRJ6CQx0Z5hiQSJGRIBTT/CCEzEothRiob\n7Jeeng6dTjeo6Hmq2rNnDyoqKuI9DEJmDK/Hj+a6HjTUdKHxcjdcvSOneUhkScgtUiFdK4MmSwZV\nqnhCdjSaiYJeH1w6PZzNbZGVgYEBgtd4bQEBi8NBUkZqJAgIffXfFmjUYPMmt64EAEy9vkiKUZXe\nDlPvyKtYbBZQmirCwkwJKjIkKEkVgUtpboSQKaSqqgo33HDDuL9vTL+9n3zySfy///f/8Mtf/hJ8\nfuKkABBCEpPD5kZ9TRcaarqgazAiMMJVXBYLSNfKkV+qRn6JGmqNhK7gXoOgzw9Xawd6G1vR29wG\nZ2Mbepta4Wxsg6u1AwiOXLR7NSwOJ7Q6oE1HcpbmisAgHYL08U0XGiu3P4gLnQ6cagsFCU3mKHUw\nADKlAlRkhlYRyjMkEFFfDkIIGSKm3+6vvPIKDAYDXn75ZajV6sgfdBaLFekCHYtnn30WLBYLfYsa\nA08MnnvuudGMm5BJQbmjsWEYBj0GRyhIqDags9024nNFEgEKStXIKVQhu0CZUHUI12Ky5goTCMDV\nbkBvQyucTa3obWyFs6kNvY2tcLV2jLkrMYvLCdULDAwEsjSRlYLxrh8YL0GGQYPRFdnu9GKnE77g\nyAvnEgEHC8JpRhWZEmgkgkkcbT/63UJiRXOFJIKYfvv/6U9/GpcPa21tHRQkdHR04MCBA7jjjjvG\n5f0JIZMnGGTQ3mJGQ00X6mu6YDH2jvhctUaCwlmpKJiVirQMKViU5hEVwzDwGs1w1uvgbAh9RQKE\n5nYw3pHTuqJJykyDMDcLwpyMSCCQFA4KkjQqsKI0HkskXQ5vJEA4o3fAGqVYnssObXfaFyAUpkTf\n7pQQQshQMdUwTKTPPvsMf/7zn7Fjx45J+TyqYSBk7IKBINqazbh8vhN11Qb0OobfN5/NZiErTxkJ\nEmSK5Eke6dTg73Wht6EVjvoW9Dbo4GxshbNRh97GNvhtjjG9p0CjgihfC2GeFsL8LIjC34U5WeAk\nx+dq+rXq9QZwrsMRKVZutY7c1RsAcuRJWJgVChDmasRI5k2NQIgQQq5VXGsY+lKJrsTn86HVanHT\nTTchLS1tTANYt24dNmzYMKbXEkImXjAQRGuTKRwkdMHlHD5I4PE5yC9Vo3BWKvKK1UhKnvqbJIwH\nhmHg6eiGo7YJjroWOOtbQisGTW1wtxvG9J6C1JRQEJCnDQcHWRDla5GcmwmucOoHZ4Egg9qe3tAq\nQpsNNV1ORNnMCPIkbmQFoSJTApVoeqS5EUJIoogpYKitrcUHH3yAyspKaLVa6HQ6nDhxAuvXr8dH\nH32Ehx9+GO+99x5uvvnmqO/T2Ng46H5vby/efPNNZGdnj/0nIGQCzdTc0UAgiNbGUJBQX20YcWcj\noZiPorI0FMxKRXa+EtwZfCX34IEDWJidD0dtMxx1zXDWNkduBxwjp2uNhCMSQlSghaggO/RVmB0J\nECZ6+9F40Ns8kd2MTusdcHpHrsXgc1iYoxGHdjPKlCJPmQT2FCuWn6m/W8jo0VwhiSCmgIFhGPzl\nL38ZVGvw4Ycf4s0338RXX32F7du34yc/+clVA4bCwsJB94VCIcrLy7F9+/YxDJ0QMp4C/iB0jcZw\nkNAFt2v4IEEkEaB4ThqK52iQmaOYcd2Vg14fepvaBgQGoZWDU5cvwukf3ZVtFpcDYW4mRIU5EOVn\nQ1igDX3Pz4IgNWVa7xhl9/hxRu8IbXfabkeHffiVqz4FKcmRfgiz08TUVZkQQiZRTDUMUqkUZrMZ\nnAEFcX6/HwqFAna7fdDtREc1DIT0C/iDaGkIBQkNNSMHCWKpAMVzNCiek4bMbMWMKFoOen1wNurg\nuNQI+6XG0IpBXTN6G9vABEa3ExFXJoG4KAfi4jyIinIhKswOpRBlZ8SlN0E8+AJB1HT1RgKE2p5e\nRNnMCCohb1CakZxS3Agh5KriWsNQUFCA3//+93jssccix/7whz9EVgx6enogEl19idzj8eD555/H\nW2+9Bb1ej8zMTNx777342c9+hqSkpDH+CISQ0fD7g2ip70Ht+U7U13TBM8IOMxJZUmQlIUMrn7ZB\nAhMMwqXTw36pEY6aUHDguNQIZ0PLqLco5auVEBfnQVyUA1FJ+HtR7rRfLRgOwzBotXpQ1W7DqXY7\nznU44PKN3AciicvG/HRxJEDIlifNuP9mhBCSqGIKGLZu3Yo77rgDL730EjIzM9He3g4Oh4O//e1v\nAEI1Dv/6r/961ff5/ve/j9raWrz66qvIzs6GTqfDr371K7S3t2Pbtm3X9pMQMgGmS+6o3x9Ec11/\nkOD1DB8kSOVJkZWE9KzpFSQwDAOPoSe0YlATCgrslxvgvNyMgCt6c68rJWs1EBXlQlycG/6eh7PG\nDqy+6cYJGv3UYHH5cFpvD9ci2NHtHHn7VxaAYrUwXIcgwaxUEXgzqKv3dPndQiYezRWSCGIKGCoq\nKlBXV4djx45Br9cjPT0dS5cuBY8XWiJeuXIlVq5cedX3+eCDD9DQ0ACFQgEAmD17NhYvXoyCggIK\nGAgZZwzDwKC34cKpdlw62zFiupFUnoySuaGVBE2WbFpc1fWabXBcDgcFlxrgCK8a+CyjS5tMzs6A\nuDQfktL8SHAgKsoZdici7iHreA1/yvD6g7hocOJUOM2o3uiK+vw0MT+y3Wl5ugTSpJmRjkUIIVNd\nzL+tB3Z3XrVqFRwOBzweD8Riccwflp6ejt7e3kjAAAAulwsZGRmjGDIhk2cqXtXp6XKg7kInLp3v\nhNEw/F7+MkUyiudqQkFCpnTKBgn+XleotuByI+w1DZF0Ik9nz6jeh69WQjKroD84CAcIXHHsuxFN\nxbkyWgzDoMnsDqUZtdlxodMBT5T9ToU8NhZkSlCREdrNKEPKn7JzbbzNhPlCxgfNFZIIYgoYzp8/\nj9tuuw0CgQBtbW249957sX//fuzYsQNvv/12zB92//334+abb8ajjz4a2Z7197//PTZt2oS9e/dG\nnrd27drR/ySEzFAMw6Cn04HaC52ovdAJY7dz2OdJ5UkonZeO4rmaULflKXTiFvT5IwXIoZSi0KpB\nb4seGEXvSa5EBPGsgkhQEFo5yANfpbj6i2coo9OHKr09Uqxsdo3cVZnNAmaliiLbnZaoqasyIYRM\nBzHtkrRs2TI89NBD2LRpExQKBcxmM5xOJ4qKiqDX62P+sNzc3NCHDjhRYRhmyIlLU1NTzO85WrRL\nEhmNRM0dZYIMOtutqK/uQu2FTpiNw+/zz+WxUTxHgzkVmdDmKadETYKnxwT7xXrYqxtgr6mHvboe\njtpmMN6R8+GvxBbwIS7ODQUHJeEVg9J8JGWkTliglKhzZbTcvgDOdTojxcot5uj1HVkyQXi71dFN\nwAAAIABJREFUUynmpYsh4s/cXhyjMV3mC5l4NFfIaMR1l6Tq6mrcf//9g44JhUK4XNHzVa/U3Nw8\nqucTQvoFgwxaG424dK4TDZe60OsYft96Lo+D/BIVimdrkF+qBl+QmHniQb8fzgYd7OdrYauuDwcJ\n9fB2m2J+DxaHA2F+FiSlBZGgQFKaD2FuJlgcOnGNRZBhUN/jigQI1QYnfFH2O5UKOFiQIcHCLCkq\nMiVIFVNXZUIIme5iOpPIycnByZMnsWjRosixEydOoKioaMIGRkgiiPdVnYA/CH2rBfXVBlw61wmn\n3TPs83h8DgpKU1E8Nw15RWrwEuwqb8Dtgb26HrbztbBdqIX9Qh3sNfUIuqM36xooKSsNkpICiGfl\nR+oNRAXZ4CQJJnDksYv3XBkNg90bSTE6rbfD5hl5+1gem4WytHCaUZYUhSnJU66rciKaSvOFxBfN\nFZIIYgoYnn/+eaxfvx4PPfQQvF4vfv3rX+MPf/gD/vd//3eix0fIjGO3ulF30YDmuh60Npng8w5/\nMpcs4iO/RI2islTkFqnA5SVGkMAEg3A2tMJ6uhrWqouwnKmG/WI9GN/Iue8DcZKTQqlEZQWQzC6C\nZFYBJLMKwJNJJnjk05fTG8DZjv7tTtuswweefXIVSeF+CFLM04iQlCBzixBCSHzEFDCsX78en332\nGf74xz9i1apV0Ol0eP/997Fw4cKJHh8hcTVZuaMetx+1FzpRfUaP1iYTMEJGiFDMR+m8dJTM1SBd\nKwc7AWoSPF1GWE9Xw1JVHQoSztTAbxt+d6YrCdLVkM4phnRuMSRlhZCUFYbSidhTbz/+RMozDgQZ\n1PX04kRbaBWhpssZtauyIpkbCRAqMiRIEVFX5YmWSPOFJDaaKyQRxJzcvGDBAvz3f/935H5bWxue\neuopvPzyyxMyMEKmu2AgiNYmM6rP6HH5fCf8vuFXEmSKZOQUpqB4jgbZBSlxDRL8zl7YztVGVg6s\np6vhbjPE9FphvhayeSWQzC0OBQmzi2h3onFkdvlwqs2OE202nGqzRU0z4nNYmBfpqixFnoK6KhNC\nCBlZ1IDB7/fjj3/8I6qrq1FZWYlNmzahpaUFv/jFL/DWW2+Ny/ann332GZRKJSorK6/5vQgZb+N9\nVcfvD0LXYETdRcPIhcssIDs/BcVz0pBbqII8RTiuY4hV0O+Hs7YZlqqLsJ6ugaXqIhyXm4Bg8Kqv\n5acoIKsog2xBGeQLyiAtnwW+QjoJo46fyb4CGAgyuNTlxIk2G0602VDXE30TisKU5Mh2p7PTROBz\np94qznRCV4xJrGiukEQQNWB46qmn8Le//Q3Lli3Dj3/8Y5w8eRI7duzA+vXrcfLkScyZM2dMH7p5\n82bs378fixYtwne+8x00NDRQwECmLa/Hj6baHtRdNKDxche8I1z5VWnEmFORhdJ5GoilSZM6RoZh\n4G43wFpVHVo5qLoI29nLCLiib6kJAOxkAWTzSiFbMCsUIFTMRlKWhq5YTwBjrw+n2mw40WpDld4O\ne5RVBGUyF9dlSXFdlhTlGWLIkynNiBBCyNhEDRj++te/4sCBAygoKMClS5dQVlaGt99+G/fcc881\nfeitt96KrVu34ujRo9ixYwdEIhH+4R/+4Zrek5CJMNbc0WCQga7BiItV7airNsDvG/6qvEgiQPGc\nNJSVZ0CTJZu0k2yf1Q7rmZpQzUF49SCm7UxZLIhL8iIrB7KKMohL8sHmJebWrZNpIvKM/UEG1QYn\nToZXERqMI68isFnA7DQRFmVJsUgrRb4ymYK2BEZ56SRWNFdIIoj6V95ms6GgoAAAUFpaCqFQeM3B\nAgBwOBywWCwsXboUS5cuveb3IyRRGLscuFjVjuozejhsw+9EI1Mmo6gsDUWz0yalcJlhGDhrm2E6\ndgaWUxdgrboIZ70uptcmZaRCFg4M5AvKIJ1XAq5YNKHjnem6nV6cbLXhZJsdp9pt6B0h2AQAlZCH\n67RSLAr3RKCmaYQQQiZC1ICBYRg0NjZGbnM4nMj9Pvn5+aP+0JMnT2L79u24//77ccMNN0Amk43q\n9W63G6tWrYLH44HX68U3v/lNvPDCCzCZTLj33nvR0tKC3NxcvPPOO5DL5aMeHyF9Yrmq4/X4UXO2\nA+dPtqGzzTrsc1RpYhTP0aBodhpUaeIJvfIb6HXDeqYa5hPnYa2qhvnkefiMlqu+jiMWQlY+C/KK\n2aEgYcEsJGnUEzbO6WasVwB9gSAuGkK1CCdbbWiK0lmZwwLmaMSRVYRcKlaesuiKMYkVzRWSCFgM\nw4y42R77KlsbslgsBAIj59CO5Pe//z1KS0uxe/du7Nu3D3K5HJ999tmo3qO3txdCoRB+vx/Lly/H\nb37zG+zcuRMqlQo/+tGP8NJLL8FsNuPFF18c9Lo9e/agoqJi1GMm5Ep2qxtVR1tw7ngrPO6hPQaS\nRXyUladj9oJMpGZMXMGv12iB+fg5mI+fhfnYWdjOXwbjj/7vksXlQFJWGFk5kJWXQVSUMyW3M52K\nuhxenGgNpRmd1tvhirKKoBbxsCi8ilCeQasIhBBCRlZVVYUbbrhh3N836gpDMIbdUMZiyZIl6Orq\nwgsvvAAgdPI/WkJhaOcYr9eLQCAAhUKBnTt3Yv/+/QCABx54AKtXrx4SMBAyGsPljpp6nDi+vxHV\np/UIXrG5PYfDQsGsVMyuyERukQoczvifgHt6TDAdOgXj4SqYvzoLZ23zVV/DU8qgXFIOeeU8yBfO\ngXROMTjJidEhebqIlmfsDQRxodOBk212nGi1ocUy8ioCj80KrSJoJViUJUW2nFYRpiPKSyexorlC\nEkFcKhWvvMLfd/I/GsFgEBUVFWhoaMD3v/99zJ49GwaDAWlpaQCAtLQ0GAzD7w//yCOPIDs7GwAg\nlUoxd+7cyD/GQ4cOAQDdp/sAgPPnzwMAll6/FHXVXXj3rY9h0NuQk1EGAGjRVwMAyudehwXX58Ds\naoJA4ERBaeq4jSfg9mAWkmA8cBJffvo5XC16lLFD/2aqg6Fg+8r7laWzIa+cizopB+KiXKy99y6w\n2GwcOnQI7R4rloeDhXj/953O97scXuz4cDdqunvRLS+G2x+EveEMAEBSUA4AkfuF8ytRqZVC0FmN\ngpRk3LC6PPJ+rQny89B9uk/343O/T6KMh+4n1n0AOHz4MHS6UG3ili1bMBGipiRNBVarFV//+tfx\nwgsv4M4774TZbI48plQqYTIN3vmFUpLIaHjcPpw/2YaqIzrYLEN3qMnMUWDRyjwUlKjBGqfiZSYQ\ngPXsJRj3n0DPgeOwnLwAxucf8fksLgey+bOgWDwfisXzIF80D3zl6OqCyLXzBxlcNDhwvNWG4602\ntESpReBxWJinEUdSjbJkAlpFIIQQcs3ikpI0FchkMtx66604deoU0tLS0NnZCY1Gg46ODqSmpsZ7\neGSKspp6UXW0BedPtg3pm8BiAXklalSuzENWrnJcPs/TZUTPvq/Qs+8YevYfh89sG/G5LC4H8oVz\nkLLiOiiXLoCsvAwc4eT2bSAhRqcv1Dit1XbVHY0ypPxIsfK8dAmSqHEaIYSQKWJSA4ZgMHjVQupY\n9PT0gMvlQi6Xw+VyYffu3fj5z3+O2267Ddu3b8fTTz+N7du34/bbbx+HUZOZgmEY6HUWnDzUjPpq\nAxgmlHLUl36ULOShfHE25lVqIZFd2wl60OOF+cS50CrCl1/Bdr426vMlZYVIWbUIKcuvg2LJfHBF\n8en+PNMN7K58vNWG+gF9EewNZyKpRkD/KkKlVopKrRSZ1zhnyPRy6BDlpZPY0FwhiWDSAga/3w+J\nRAKLxQKB4NqKLTs6OvDAAw8gGAwiGAxGtmddsGABNmzYgK1bt0a2VSXkapggg7pqA44faBp2W9QU\ntQgLl+diVnkGeLyx71DT29yG7i+OoHvvMZiOnkbQNXyfBgAQpKZAtWYxUlYuQsqK6yBITRnz55Jr\n4/IFcLLNjmM6K77SWWGL0l05TcxHpTa0ilCeLkbSNcwXQgghJFGMWMOg1Wqv/mIWK1JkEYt58+bh\n008/RWZmZuwjHGdUw0D6BIMMas934uiXDTAaHEMezy1SoWJpDvKKVGOqTwj6/DAfPxsKEr44Amdd\ny4jPZXE5UFTOg2rtEqjWLIGkrJBy2uPI6PThmM6KIy1WnNHb4QsOX+rFYQFz00N9ESq1tKMRIYSQ\n+Jr0GoY33nhj3D/svvvuwze+8Q08/vjj0Gq1g/6wrl27dtw/j5DhBAJB1JzpwFf7G2DuGbylL4fL\nRll5BhYuy4EqTTLq9/aabejefRhduw/B+OVx+O3OEZ8rzNdCtXJRZBWBK6EOyvHCMAyazW4cabHi\nmM6Ky90jb/WsFHKxWCtDpZb6IhBCCJkZJnWXpNzc3NCHDnMFrqmpaVLGQCsMM5ffF8CFqnYc3980\nZMcjHp+DBdfnYOHSHIgk/SlzseSOutoN6Pr8IAyf7If56BkwIzQzZCcLkLL8Oqi/thTqtUuQrE2/\n9h+KjJk/yOBCpwNHW6w4qrOi0+4d8bn5yiQsyZZhaY4chapksIf5HUZ5xmQ0aL6QWNFcIaMR912S\nTp8+jYMHD8JoNGJgjPHcc8/F/GHNzc2jGhwh48Hn9ePs8TacPNQEh21w3QBfwEXF0hwsXJaDZCE/\n5vd0NrXB8PE+dP59H2xnLo34vGStBuoblkL9taVQLltIzdLizOkN4GSbDUdbrDjeaoPDO0JwxwLm\npYuxNEeGJdkyaCT0/40QQsjMFVPA8Mc//hFPPvkkbrzxRnzyySe45ZZbsGvXLnzzm98c9Qfu2rUL\nf/nLX9DV1YWPP/4YJ0+ehM1mo5QkMu48bj/OHGvByUPNcPX6Bj2WLORh4fJcLFiSDUESb8T3GHhV\nx1HXEgoSPt4H+8W6EV8jXzgHqTevQOq65RAV51JOe5x1Obw4prPiaIsVZzsc8I9QjyDksbFIK8X1\n2TIs0kohEYxuTwi6AkhGg+YLiRXNFZIIYvqL+NJLL+HTTz/FypUroVAo8P777+PTTz/FW2+9NaoP\ne/XVV/Hb3/4WDz74IN577z0AQFJSEh5//HEcOXJk9KMnZBiuXi+qDreg6mgLPO7BDc9EEgEWrcjF\nvEVa8K9yQsgwDBy1TTB8tA+dH+2D43LjsM9jcTlQLluItJtXIvWmFUjSqMftZyGjxzAMGk0uHGkJ\nBQkDtz69klrEw/U5MlyfI8M8jRg8DvVGIIQQQq4UUw2DVCqFzRZqJJWSkoKuri6w2WwolcpBnZWv\nJj8/H3v27EFeXh4UCgXMZjMCgQDUavWQjswThWoYpi+f14+Th5px/EATfFekmkjlSahclY85FZng\nRtnqkmEYOGoa0PnRXnR+vA8nLtegjD205wFbwIdqzWKk3boGqTcuA082+gJpMn4CQQbnOx2RIMHg\nGLkeoTAlORQkZMtQkJI8bitAlGdMRoPmC4kVzRUyGnGtYcjKykJTUxPy8vJQVFSEDz/8ECqVatT9\nFBwOx5DtWr1e7zX3ZSAzWzAQxIWqdhz+oh5O++AaBUWKEItX52NWeQY4I1w9ZhgGtvO1kXSj3sbW\nYZ/HTuJDfcNSpK1fg9SvLaVdjeLMHe6PcKTFgq9abbCP0B+By2ZhfroY14frEVLFsdeqEEIIISTG\ngOFf/uVfUFNTg7y8PPz85z/HXXfdBa/Xi1deeWVUH7ZixQq8+OKL+NnPfhY59uqrr2LNmjWjGzUh\nCKeeXO7Ggc9qYewa3EchJVWM69cUoHiuBuxheigwDAPbucvo3BlaSXC1tA/7GXNFSqjXLYNm/Rqo\nblhCHZbjzOkN4JjOioNNFpxss8EbGH6BVMTnoFIrxfU5MizKkk7K1qd0BZCMBs0XEiuaKyQRjGlb\nVY/HA6/XC4lkdGkYer0e3/jGN9DT0wO9Xo+8vDxIJBJ8/PHHSE+fnC0mKSVpeuhst2L/p5fR2jg4\nlU0sFWDZ14owuyJz2EDBbehBx3ufo/2dT0esSeCIhEi9cRnS1q+Bes0ScIRJE/IzkNhY3X4cbQkF\nCaf19hGLllVCHpbmUj0CIYSQmSuuKUkLFizA6dOnI/cFAgEEAgGuu+46nDx5MuYPy8jIwIkTJ3Di\nxAm0tLQgOzsblZWVYLPpDzuJjd3qxqHddbh4uh0YcN7IF3BQuTIfC5flgMcfPK0Dbg+6dh1C+9uf\noGffV0AwOOR9uRIRUr++HGnr10C1ejE4SaE0OcodjQ9jrw+Hmy041GzBuQ4HRogRkKNIwrKcUH+E\nItX41SOMBc0VMho0X0isaK6QRBBTwFBfXz/kGMMwaGwc/grtSH7zm9/gn//5n7F48WIsXrw4cvzl\nl1/GU089Nar3IjOLz+vHiYOhgma/rz9Xnc1mYf5iLa5fUwChuL8WhmEYWI6fQ/vbn6Dz71/Cb7UP\neU9OchLS1q+G5ps3QLViEdgCym2PJ4Pdi0PhIKHa4MRIS59FqmSsyJVjWa4cWjmt/hBCCCETLWpK\n0v333w8AePvtt7Fx48ZBDdv6mrAdPHgw5g+TSCSw24eeuPXtmDQZKCVpavH7Ajh/sg3HvmwcUtCc\nX6rG6ltKoVT1Fx/7LDa0v/sZWne8D2ddy7DvqVy6AJn33oK0W1eDK6bC5Xhqt7pxsNmKQ00W1Pb0\njvi8sjRROEigJmqEEELISOKSklRQUAAAYLFYKCgoiAQMLBYLy5cvxz333BPTh+zduxcMwyAQCGDv\n3r2DHmtoaIBUKh3L2Mk05vMGcPZ4K04cbBoSKKg1Eqy+pQQ5hSoAodUE6+lqtG7/AB0f7kbQPXRL\nzeTsDGRuuBkZG26GMDtjUn4GMhTDMGgxu3Gw2YJDTRY0md3DPo/NAuZqxFiRJ8eyHDlSRCM31yOE\nEELIxIoaMPziF78AACxZsgQ33XTTmD9k8+bNYLFY8Hg82LJlS+Q4i8VCWloaXn311TG/N5l+6qoN\n2PtRDezWwSeTVxY0+x1OdPxtN3Q73of9wtDOyxyREOl3rkPmvbdAvnDOmPLbKXf02jEMgzqjC4ea\nQulGbVbPsM/jsllYkCHG8lw5rs+RQZ48tYIEmitkNGi+kFjRXCGJIKYahptuugn79u3Djh070N7e\njqysLNx3331Yu3btVV/7u9/9LpK+9K1vfQt//vOfr2nAZPrqaLXg0O46tNQbBx0XSwVYtCIP8yq1\n4PE4sF2sQ+uOD6B/73MEnEPTWKRzi6HddAfS71xH26DGSZBhUNPlxKEmKw41W0ZspMbjsLAoS4rl\nuXIsyZZCfJXu24QQQgiZfDFtq/raa6/hpz/9KR588EFkZ2dDp9Ph9ddfx3PPPYfvfve7UV87sEv0\nSDUMk4lqGBKPQW/D4S/q0Hipe9DxZBEfS28oxNyFmWD5/ejcuQetOz6A5dSFIe/BThYg/Ztfg/aB\nOyArnxXX3XJmqr5uy4eaLTjcbIWx1zfs85K4bCzWSrE8T45KrRTJUTpvE0IIISR2cd1W9aWXXsLu\n3bsxf/78yLGNGzfizjvvvGrAkJ+fjx/+8IcoKyuD3+/H66+/DoZhIid0fbc3b958DT8GmYp6Ou04\nvKcedRcNg46z2CzMXZiJFV8vBstmReN/vIbWHR/AZ7IOeQ9RcS6yN92OjLtvAk9OtTCTzR9kcLrd\njkPNFhxpscLq9g/7PBGfg+uzQ0HCwkwpBFzaSpkQQgiZKmIKGEwmE2bNmjXoWElJSUw7G7399tv4\nt3/7N7z11lvw+Xx44403hn0eBQwzh9PuwYHPa4f0UgALKJ2XjqVrC8Hr6UTd0y+i44MvwPgGn4Sy\neFxo1q+BdtMdUCyZP6GrCZQ7OpQ/yOCs3o79TRYcbrbA7gkM+zxZEhdLc2RYnitHecb0b6RGc4WM\nBs0XEiuaKyQRRA0Y2trakJWVhWXLluGpp57CSy+9BJFIBIfDgZ/85CdYunTpVT+gpKQEW7duBQCs\nXbt2yC5JZOYIBoI481UrDu2ug9czOAgomp2GpTcUgN1Qh8YfPIuevceGvD5Zq4H2gTuQufFWCFTK\nyRo2QX+60ZcNZhxqtsA2QpCgFHKxPFeO5blyzNWIwRmm2zYhhBBCppaoNQx99Qd6vR4bN27EkSNH\noFQqYTKZsHTpUrz11lvIzMyczPFeM6phiI+2ZhP27KxBd+fgGpa8EjWWrskDzpxG0+/fhO3MpSGv\nVSyej5zvbEDqTSvA5lJR7GRhGAaXu3uxr8GM/U1mmHqHTzdSi3hYmafA8jwZZqWKwKb6EUIIISQu\n4lLD0BdLZGRk4MCBA2htbYVer0dGRga0Wu2YPrCzsxPHjx+H0Wgc1AiOUpKmJ7fLh31/v4SLVe2D\njitUQqxeVwjeyWOovedFuFoGPw4WC2m3rkLew/8IecXsSRwxaTa5sK/RjH0NZnTah9/dSCXkYWW+\nHKvyFShVC6nInBBCCJnGrnq5NhgMRm5nZmZGVhT6jrPZseclf/DBB7jvvvtQVFSECxcuYM6cObhw\n4QKWL19OAcM01FzXg8/+eh4OW/+++1weB5VLMpFy4SiaN74In9Ey6DVsAR+ZG29F7kMbIcofW1A6\nnmZK7miHzYN9DWZ82WhG8wjN1ORJXKwKBwllabSScKWZMlfI+KD5QmJFc4UkgqgBg9PpBDdKCgiL\nxUIgMHwu83CeeeYZvP7669iwYQMUCgVOnz6Nbdu24cKFodtkkqnL4/bhy08u4/zJtkHHCwoVyNVV\noeeRF2HrdQ16jCeXIHvz3cjefBfVJ0wSY68P+8MrCZe7h/azAEK7Gy3PlWF1gQLl6RKqSSCEEEJm\noKg1DGKxGBcvXkS0Vg25ubkxf9jAngwKhQImkwnBYBAajQbd3d1XefX4oBqGidV4uRu73r8waFUh\nWcjFnEA7PP/3fwi6Bnf5TdZqkPvQRmT+w3pqsjYJbG4/DjVbsK/BjHMdDgz3L1vAYWFJdihIWKSV\ngj/NdzcihBBCpou41DCwWCzk5OSM24elpqais7MTGo0Gubm5OHr0KFQq1aC0JzI1uV0+7Pu4BhdP\n6wcdz0zyQPHuH+AydA06Lp5VgPzH7ofmtrVUyDzBXL4AjrZYsa/RjFNtdviDQ8MEDgu4LkuK1QUK\nLM2RUTM1QgghhERM6pnagw8+iEOHDuHuu+/Gk08+ibVr14LFYuGHP/zhZA6DjLP6mi7s/uAinPb+\n1QMBh0HmiV0Qnvlq0HOlc4tR+M9boL5x+ZQolJ2quaPeQBAn22zY12DGMZ0NHv/QoJwFYF66GKsL\nFFiRK4c0iQK3azFV5wqJD5ovJFY0V0giiHqG8Mknn4zrh/34xz+O3N60aRNWrVoFp9OJsrKycf0c\nMjm8Hj/2/f3SkFqFlK5GqHf/FVxPf52CMC8LRT95CJr1a8AaRaE8iV0gyOBshx37Gsw43GyFwzt8\nfVGJWojV+QqsypdDJeJP8igJIYQQMtVErWGYjqiGYXx0tFrw93fOwWLsL5bl+dxI3/8hpLrLkWOC\n1BQU/HAzsr71DbB5dAV7vDEMg5quUK+EA01mmF3D90rIkSdhdYECq/MVyJQJJnmUhBBCCJkMcalh\nIORKwSCD4/sbcXhPPZgBufDSxovIOPJ3cL2hLTm5EhHyHr0POd/ZAK4wOV7DnZYYhkGT2R3aBrXB\nDINj+F4JaWI+1hQosKZAgVxF0pRIASOEEEJI4qGAgcTManbhk3fOob3FHDnG9nqQcfQTyBrOg4VQ\nH4XszXch/7FN4Ctl8RvsOEmk3FF9X6+EBjNaLMP3SlAkc7EqPxQkUEO1yZVIc4UkPpovJFY0V0gi\noICBxKTmrB67P6iG19Of8iI06JC1/wPwHRaAzUbmhptR+M9bkJylieNIpxeD3Yv9TWbsbzSjrsc1\n7HPEfA6W58mxJl+Beeli6pVACCGEkHE1Yg3DihUrBj+RxRrUj6HvyuWBAwcmcHjjj2oYRsfj9uGL\nndWoOdPRfzAYROrp/VCfOwQWwyD15pUo/vFDEJfkxW+g04jR6cOBplDX5Zqu4RuqCbhsXJ8tw5oC\nBRZmSahXAiGEEEImv4Zhy5YtkdsNDQ3Ytm0bHnjgAWRnZ0On02H79u3YvHnzuA+IJI62ZjM+eecc\nbJb+K9t8mwlZ+9+HsLsdsorZKH3ucSiumxvHUU4PFpcPB5os2N9owYXO4RuqcdksXJclwZoCBa7P\nliGJeiUQQgghZBKMGDB8+9vfjtxevHgxPv/8c8yePTty7B//8R+xefNmPPfccxM6QDL5goEgju5t\nwLEvGzBw/Uleewbpxz6DUCVF8f/3M2Tcc9O03yJ1InNH+7ou72+04GyHHcP0UwOHBVRkSrAqP9RQ\nTSygLMJERXnGZDRovpBY0VwhiSCms49Lly4hPz9/0LG8vDzU1NRMyKBI/PQ6vfjorTNobTRFjrE9\nLmQe/hjy9jrkPfwt5P9gE7giYRxHOXXZPX4cabFif6MZVe3DBwlsVrihWr4Cy6mhGiGEEELiLKY+\nDLfddhuEQiGee+45aLVa6HQ6/OIXv4DD4cBHH300GeMcN1TDMLKeTjv+9n8nYLP1b9Mp6mhG1oEP\noKkoRtkLP4SoMCd+A5yinN4Ajums+LLRjFNtdviHiRJYAOZoRFiVr8CKPDkUybzJHyghhBBCprS4\n9mHYtm0bHnnkEcyZMwd+vx9cLhd33nkntm3bNu4DIvFRX2PAx29WwR8M77DDMEit+hIZbRdQ9tIT\nSL/r67RF5yi4/UEcawkFCSfabPAFho/LZ6UKsSpfgZV51HWZEEIIIYkppoAhJSUFf/nLXxAIBNDT\n0wOVSgUOhwoupwOGYXD004s4crAVCAcEbK8H2i//ipKlRSj985vgp8jjPMr4GU3uKMMwuGhwYled\nCQcazej1BYd9XrFKiFX5cqzMUyBNQkHCdEF5xmQ0aL6QWNFcIYkg5uTompoavPvuuzAYDPiv//ov\nXLp0CV6vF/PmzZvI8ZEJ5PcHsfN3e9DYFYgECzybGSUX9+C6lx+DauWiOI9wajDYvfjtWGa9AAAg\nAElEQVSi3oTddUbobcN3Xc5XJmN1vhwr8xXIkAomeYSEEEIIIWMXUw3Du+++i4cffhh33nkn/vzn\nP8Nut+PEiRP4yU9+gi+++GIyxjluqIYhxGYw452X98DCEUeOCTtbcL3Gjbk/+y64wuQ4ji7xuX0B\nHGq2YledEWf0jmGfkyUTYG2BAqvyFdDKkyZ5hIQQQgiZaeJaw/Dss89i9+7dKC8vxzvvvAMAKC8v\nx5kzZ8Z9QGTiNR+8gJ1/q4E3WRI5pmq7hFseXIZUWlUYEcMwON/pxO46Iw40WeAaJuVIxOdgVb4c\nNxalYFaqkOo+CCGEEDLlxRQwdHd3D5t6xJ7me/BPNwzD4Kv/+hBHWlgI9gULDINitw43vbIZfLk0\nvgNMQIcOHUJxeSV215mwq9aIDvvQlCN2uFfCjUUpuD5HBgGX/l3MRJRnTEaD5guJFc0VkghiChgq\nKirwxhtv4IEHHogce/vtt1FZWTlhAyPjy2u149Nnd6BOlA/wwsXNPg9WzBJg0eaH4jy6xOMLBHFM\nZ8PW4+3ovHxx2H4JWrkANxal4IZCBe1wRAghhJBpK6YahkuXLmHdunXIy8vDV199hVWrVqG2tha7\ndu1CcXHxZIxz3MzEGgbb5WZ88Ov30ZU5K3JM4Hbg9m/Ng/a6qfX/b6K1Wtz45JIRX9SbYHX7hzwu\n4nOwpkCBG4uUKFFTyhEhhBBCEkdcaxhKS0tx6dIlfPzxx1i/fj2ys7Oxfv16iMXiq7+YxJXur7vw\n6ccNsA8IFhSMExue+TokKZIor5w5vIEgjrRY8feaHpztGL6AeUGGBDeVKLEsRw4+pRwRQgghZAaJ\nKWB4/PHH8corr+Dee+8ddPyJJ57Ab3/72wkZGLk2TDCI87/6Iw60JcGdnhc5nqNk4Y4f3A4ub2b3\n0WAYBnVGF3bXGrG3wQy7JzDkOWoRD/muBjxyz03QSGgrVBId5RmT0aD5QmJFc4Ukgpg7Pb/yyitD\nju/YsYMChgTkdzhx/NEXcEpYAk+KOnK8Yq4CazZWzug0GlOvD3sbTNhVa0Kz2T3kcTYLWJItwy2l\nKizMlODoEQsFC4QQQgiZ0aIGDFu3bgUA+P1+vP7662AYJnKy2dDQALVaHe3lE6a1tRWbNm1CV1cX\nWCwWvvvd7+Lxxx+HyWTCvffei5aWFuTm5uKdd96BXD6zuhT36vQ48p1f4mLRavikitBBhsG69cWY\nv6wgvoOLE28giK90NuyqM+JEq23YAuY0MR9fL1bippKUQQXMdFWHxIrmChkNmi8kVjRXSCKIGjC8\n8cYbYLFY8Pl8eOONNyLHWSwW0tLSsH379gkf4HB4PB7+8z//E+Xl5XA4HFi4cCHWrVuHbdu2Yd26\ndfjRj36El156CS+++CJefPHFuIwxHkxHTuPoE/+GuuvvgF8U2iKVBQa3bpyP0vkZcR7d5GIYBvVG\nF3ZFSTkScNlYmSfHuiIl5qWLwZ7BKy+EEEIIISOJGjB8+eWXAIBnnnkGv/rVryZjPDHRaDTQaDQA\nALFYjFmzZqG9vR07d+7E/v37AQAPPPAAVq9ePWMChtY/fYjTv9qKxq/fD78wVMzMZjG4/f6FyC9N\njfPoJo/Z5cPeejN21RrRNEzKEQDM1YhxY7ESK3LlEPKj13JQ7iiJFc0VMho0X0isaK6QRBBTDcPK\nlStx+fJllJSURI5dvnwZOp0O69atm7DBxaK5uRmnT5/G4sWLYTAYkJaWBgBIS0uDwWAY9jWPPPII\nsrOzAQBSqRRz586N/GM8dOgQAEyZ+wcPHIDu//4GyYHLaLrl22iwtAIWoEA7G3d+exF0HTXQH6pN\nmPFOxP0gwyA5dz4+udyDz/fuB8MAkoJyAIC9IdSNvGD+IqwrSoHceAkpQieWFxfF9P7nz5+P+89H\n9+k+3af7dH/m3u+TKOOh+4l1HwAOHz4MnU4HANiyZQsmQkx9GAoLC3HgwAFkZPSntbS3t2P16tWo\nq6ubkIHFwuFwYNWqVXj22Wdx++23Q6FQwGw2Rx5XKpUwmUyDXjOd+jAEPV6cfeQXaNt7Ck23PACv\nVAkA4HLZuHvzdcjKVcZ5hBPL6PThs1ojPrtshMExtAOzgMPCijw5bixOoZQjQgghhEx7ce3D0N3d\nPShYAID09PQRr+BPBp/Ph7vuugv3338/br/9dgChVYXOzk5oNBp0dHQgNXX6puIE3B6c3vJTdB4+\nNyhY4HBYuGNTxbQNFgJBBqfabfjkkhHHdNZhC5hnp4nw9eIUrMiTQ3SVlCNCCCGEEBJdTB2o8vLy\nsGfPnkHHvvzyS+Tl5Y3wionFMAy2bNmCsrIyPPHEE5Hjt912W6QQe/v27ZFAYroJ9LpR9cDT6Dx4\nGk033QevXAUAYLNZuO0fFyCnUBXnEY6/bqcXf6rqwKa3L+JnnzfiSMvgYEEq4OCuOal47e5Z+M9v\nFOOmkpRxCRauXBImZCQ0V8ho0HwhsaK5QhJBTCsMv/zlL3HXXXdhy5YtKCgoQH19PbZt24Zt27ZN\n9PiGdfjwYfzpT3/CvHnzsGDBAgDACy+8gB//+MfYsGEDtm7dGtlWdbrx97pQdf+P0P3VObTcvAke\nZahmg8UCbr13PgqmUYFzIMjgRJsNn1zqwfERtkOdny7GLaUp1IGZEEIIIWSCxFTDAADHjx/H1q1b\n0dbWBq1Wiy1btmDRokUTPb5xN5VrGPwOJ07d/y8wHTsL3Q33wp5dHHqABdx891zMXpAZ3wGOk067\nB5/XmrCr1ohup2/I47IkLm4sUuLm0hRkyZLiMEJCCCGEkMQT1xoGAKisrERlZeW4D4DExm934uS3\nnoL5xHnol97SHywA+NptZVM+WAgEGRzTWfFxTQ+q2u0YLootzxDjllIVlubIwOfQagIhhBBCyGSI\n6azL7Xbjpz/9KfLz8yGVhhqC7dq1C7/73e8mdHAkxGe148SGH8By4jy6FqyCufS6yGOLV+WjfHF2\nHEd3bWxuP945a8C336nGL79owqkrggVZEhcb5qVi2z2z8G+3FGF1vmJSgwXKHSWxorlCRoPmC4kV\nzRWSCGJaYXjyySfR3t6ON998EzfffDMAYPbs2XjiiSfw6KOPTugAZzqv2YaTG5+A7ewlGGctQveC\nVZHHZs1Px/J1RXEc3dg1GF34sLobe+tN8AYGryewACzMkuDmEhWWZEvBo9UEQgghhJC4iamGQaPR\noL6+HmKxeFCvA5lMBqvVOuGDHE9TqYbBZ7Hh+N2PwX6hDpa82WhbfWeouhlAXrEKt99XAc4UKvT1\nBxkcabbgw+punO90DnlcKuDg5lIV1peqkCbhx2GEhBBCCCFTV1xrGAQCAfz/f3t3HhdVvf8P/DXD\nsC+yyCIDyL4ICOKKG25YlltuaWVq1u/e0jbrmt57tbRr6a1baXW738zM1KRrtvhN4mtqlmlihpXl\nBsoOsgoCwz6f3x+TB0cBzyg4A/N6Ph738eCcM2fOe3i8bs6b8z7nNDXprSspKUHPnt3v9p2mollT\nh58eeBZVv6WjyicYeQlTpWahl68zJt8X22WahYraRiSfKcOXp0tRqrn+IuZgN1tMiXTHqEAXWHeR\nz0RERERkLmR9O5s5cybmz5+PCxcuAAAKCwuxePFizJ49u1OLM1fapib8/KcVqDj+G2o8fJEzZiag\n1D1TwM3DAdPmxcHSSvb16kZzrkSDV77Nxv07fscHPxXqNQsWCiAh0BmvTwzB21PDcEeom0k2C5wd\nJbmYFTIE80JyMStkCmR961yzZg2WLVuGvn37QqPRIDg4GI888ghWrlzZ2fWZHSEETv/tdZR8fRh1\nLh7ITpwDobIEADi52GLGggGwtTPdcZ3GZi0OZerGjk4Xa67b7myjwt0RurEjN3tLI1RIRERERIaQ\n/RwGQPdltrS0FD179oTij/GYrsbUr2HI2vhfnFnxBhrtHHF+0kI02evuSmXnYIU5fxoMFzd7I1fY\nujJNI5LPlGLP6VKU1zZdtz3M3Q5TI90xIsCZt0QlIiIi6gRGfw7DuXPn8N///heFhYXw9vbGzJkz\nERoaeuMdSbbifYdx5vkNaLa0Rtb4+6RmwcpahRkLBphks3CuVINPTxbju8wKNF3zKGaVUoGEQGdM\n6eOOcA/Tq52IiIiIbkzWn3o/+ugjxMXF4eTJk7C3t8evv/6KuLg4bN++vbPrMxtVp8/jlz89Dy2A\nnDEzUe/qCQBQWigw9YF+8OjlZNwCr6IVuoesPbsnHYs/P4sD5y/pNQuudirM698L2+dE4rlR/l26\nWeDsKMnFrJAhmBeSi1khUyDrDMPf/vY3JCcnY+TIkdK6Q4cOYe7cubj//vs7rThzUV9Sjp/mPovm\nGg2KBo9HjTpQ2nbHtCj4BbkZsboWDU1afJ1Rjk9PFiO3sv667ZGe9pgS6Y7h/s5QKbvmyBoRERER\n6ZPVMFRXVyM+Pl5v3ZAhQ1BTc/299MkwzbX1SJv3HOryinDZLwxlkUOkbcPGBSOyn9qI1ek0NGmR\nfLYMSb9cRLlG//oEpQIYFeiCadEeCO1pZ6QKO8/w4cONXQJ1EcwKGYJ5IbmYFTIFshqGJUuWYPny\n5XjxxRdha2sLjUaD559/Hk8//XRn19etCSHw+9J1qEz7HQ32PZA3YrK0LSjCA0NGBxmxuvYbBTtL\nJe4O74kpke7wcDDduzYRERER0a2R1TC8/fbbKCoqwvr16/We9Ozl5YV33nkHAKBQKJCTk9N5lXZD\n2e9+jIKdKRAKJXJHT4PW2hYA4ORsgzunRxntTlTtNQqudirMjPbEnWFusLeyMEp9t9P333/Pv+6Q\nLMwKGYJ5IbmYFTIFshqGbdu2dXYdZqfs++M4s+otAEDRgDGo9fAFACiVCkycHWOUZy3cqFGYHeOJ\nCWE9TfIBa0RERETUOQx6DkN3YArPYagrLMGRcfPRUHYJVT7ByB5/n7Rt5J1hGDQy4LbWw0aBiIiI\nqOsz6nMY6urqsHr1aiQlJaG0tBSXL1/G3r17ce7cOSxevLjDi+rORHMzfl20Cg1ll9BkZYP8kVOk\nbQFh7hg43P/21SIEvr1QgY3H8lFS06i3jY0CEREREQEyn8Pw9NNP47fffsP27duhVOp2iYyMxL//\n/e9OLa47Or/+Q5QfSQMAFMZPQJON7hkF9o7WmDAjGorbdDvSc6UaLPkyHS99k6XXLLjaqfBYvBpb\nZkViaqSH2TcLvP81ycWskCGYF5KLWSFTIOsMw2effYaMjAw4ODhIF+Kq1Wrk5+d3anHdzaXjJ5Hx\n6iYAwOXeYagMipa2JU6NhJ1951+3UK5pxObjBdh7rhxXz6L1sFHhvlhP3BXOMwpERERE1EJWw2Bt\nbY2mJv3Z9pKSEvTs2bNTiuqOmmo0OLl4NaDVosnaFoUJLaNIkf28ERzh0anHb2jW4rPfSvDRzxdR\n26iV1lsogHuiPHB/Py+zuOuRoXhnCpKLWSFDMC8kF7NCpkBWwzBz5kzMnz8fr732GgCgsLAQTz31\nFGbPnt2pxXUnZ1e9BU2W7ozMxZGT0KiyAQA4OFlj9MSITjuuEAJHsivxbmo+Cqsa9LYN9nPCnwar\n4dPDptOOT0RERERdm6zZkzVr1iAgIAB9+/ZFZWUlgoOD0atXL6xcubKz6+sWSvYdQe6HnwMAKv37\noMI3XNo2/p4o2NhadspxL5TXYmlyBlbty9RrFno72+DlO4Pw4vggNgs3wNlRkotZIUMwLyQXs0Km\nQPZI0uuvv47XXntNGkVSKpVobGy88c5mrqGsAr8teRkA0GRjj4ujWkaRovqrERjm3uHHrKhtxJaf\nCvHV2TJor7pQwdHaAnPjemFiRE+obtPF1URERETUtck6wzBu3DgUFBRAoVDAw8MDSqUSv/zyC/r3\n79/Z9XV5p5a9ivriMggAF0dPRaNSdzbBsYcNRt8d3v7OBmps1mLXyWIs2Hkae860NAtKBTClT09s\nntkHUyPd2SwYgLOjJBezQoZgXkguZoVMgayGoX///oiJicHHH38MrVaLtWvXYvTo0Xjsscc6u74u\nrWTfEVz83wMAgMrASFT0CpK23TEtCtY2HTeK9NvFajz62Vn8T2o+ahqapfVxakf8Z1o4Fg31hZON\nrBNKREREREQSWQ3DunXr8Omnn+K5555DYGAgdu/ejWPHjuHPf/5zZ9fXZTXX1eP031/X/WxljeKE\nydK2vgN94B/SMXeYqmloxobDuVjyZTpyKuqk9d5O1lidGIiX7wyCv4tthxzLHHF2lORiVsgQzAvJ\nxayQKZD9J+cLFy7g8uXLCAwMRHV1NWprazuzri4v898fSXdFKhkyHg2KllGkUXd1zCjS4awKvHUk\nD2WalmtJbC2VeKCfF6ZGusPSgs9TICIiIqJbI6thmDFjBk6ePImUlBQMGjQIb7/9NhISErBs2TIs\nXbq0s2vscjQ5BbiwYQsAoM7FA2XBsdK2UXeFw8r61kaDKuuasOFwLg5lVuitH+znhMeH+sLDofMf\nAGcuODtKcjErZAjmheRiVsgUyPoTtLu7O37++WcMGjQIALBo0SIcPXoUu3bt6tTiuqozK9dDW9cA\nAaB43DQI6C4y9gtyQ2iU5y29d2pOJf7frtN6zYKLrQp/G+OP1YmBbBaIiIiIqEPJahjeeecd2Nrq\nz8GHhobiyJEjnVJUV1a87zCKUw4BACoDo3DZUfcEZ6VSgbGTIqBQ3NwdiuqatNhwOBcr9l7ApdqW\np27fEeqK92ZEICHQ5abfm9rG2VGSi1khQzAvJBezQqag3YbhiSee0FvetGmT3vKsWbM6vqIurLmu\nHqf/9obuZ0srlCRMkrb1H9Ybbh4ON/W+6aUaLPrsDL48XSqtc7VV4R93BOKZkb3heIsjTkRERERE\nbVEIIURbGx0dHVFVVSUtu7i44NKlS21u7wr279+PuLi4TnnvjH+9j4xX3gMAFA+/C8WhAwAA9o7W\nWLhkhMHXLmiFwK6Txdh8vBBNVz2BbYS/M54Y7osevE0qEREREf0hLS0NY8eO7fD35TfODlKbW4gL\nb34IAKhz7omS0JaH2o2aEGZws1CmacQr32YjLb+lIbNRKbFoqA/Gh7hy/IiIiIiIbgved7ODpP9z\no3Shc8m46dKFzj7+LgiP6WXQex3NqcSfPz2j1yyEudvhnXvCcUeoG5uF24izoyQXs0KGYF5ILmaF\nTEG7f/Zubm7GgQO6JxULIdDU1KS33Nzc3N7uZqPq7AUUfPJ/AIDL/hGodNLdCUmhVGDspD6yv+A3\nNGmx8Vg+vjjVcq2CAsC9MZ54sH8vqJRsFIiIiIjo9mr3GgZ/f3+9L7tCiOu+/GZmZnZedZ2gM65h\nOLHwryjacxDNKktcuO9p1KtsAABxQ3tjzMQIWe9RVNWA1fsvIL205YF4Pe0ssXRUb8R6O3ZovURE\nRETU/RjlGoasrKwOP2B3U/nzaRTtOQgAKIkZLjULdg5WGDo2WNZ7/FxQhX/sz8Tl+pYzNkN798CS\nEX5w4oXNRERERGREvIbhFqWvexcAUO/kirK+w6T1I+8Ig42tZbv7CiHw+e8lWP5VhtQsWCiAx+J9\n8Py4ADYLJoCzoyQXs0KGYF5ILmaFTAG/kd6C8h9+Ruk3qRAACuMnQCh0/Ze3nzMi+3m3u299kxbr\nv8/BvoyW29S62qqwYlwAIj1v7nkNREREREQdjQ3DTRJCIH3t/wAAqtVBqFYH6TYooHuiczsXKJdp\nGvHC1xdwtkQjrQvtaYfnEwPgbm/VqXWTYYYPH27sEqiLYFbIEMwLycWskClgw3CTSr9JxaXUXyAA\nFA8YI62PGegLT3WPNve7UF6LFf93HiU1jdK6O8PcsDjeB1YqTogRERERkWnhN9SbdP6NDwAAVX5h\nqHXTPWdBpVIifkxQm/tcKK/FX/akS82CUgEsivfB08N92SyYKM6OklzMChmCeSG5mBUyBTzDcBMu\npf6CimO/QgAo6j9aWh87xA8OTjat7pN9qRbPJWeg6o+Lm+2tLPD3Mf7o7+N0O0omIiIiIropbBhu\nwoU3twLQPaSt3sUDAGBpZYFBCYGtvj6vsg7PJWegsq4JAGBnqcS6CcEIdbe7PQXTTePsKMnFrJAh\nmBeSi1khU8A5GANVncpAyb4jEABKYkdK6/vF94ZdKxcsF1yux9I9GSiv1TULtpZKvMxmgYiIiIi6\nCDYMBrrw9nYAQJVvKOpcPQEAKksLDBjuf91rL1bVY2lyOko1umsWrFVK/OOOIER42N+2eunWcHaU\n5GJWyBDMC8nFrJAp6JINw0MPPQRPT09ER0dL68rLy5GYmIjQ0FCMHz8eFRUVHX5cTU4BLn6+T3d2\nIablIW2xg32vO7tQXN2ApckZKK7WNQtWFgq8OD4Q0V58xgIRERERdR1dsmFYsGABUlJS9NatXbsW\niYmJOHfuHMaOHYu1a9d2+HGzN/4XorkZGq/eqPXwBQBYWCiuO7tQVtOIpckZuFjVAACwtFBgVWIg\nYr0dO7wm6lycHSW5mBUyBPNCcjErZAq6ZMMwYsQIuLi46K3bvXs35s2bBwCYN28ePv/88w49ZlN1\nDfJ2fAkAKOnbcnYhMk6td2ekS7WNWJqcjoLL9QAAlVKB58cF8G5IRERERNQldcmGoTVFRUXw9NRd\nU+Dp6YmioqIOff/8nSlortag1tUL1T7BAACFAhg4MkB6TUWt7sxCbqWuWbBQAH8f649Bvm0/yI1M\nG2dHSS5mhQzBvJBczAqZgm55W1WFQgGFQtHm9kWLFsHPzw8A4OTkhOjoaOmU35X/Y169LIQA3v8E\nAJDqo0ZNwSn09u6D0Ggv/H76BACg74AhWPbVefx2/CgAoEdwLJaP8Yc29zd8n4t235/Lprt88uRJ\nk6qHy1zmMpe5bF7LV5hKPVw2rWUAOHz4MHJycgAACxcuRGdQCCFEp7xzJ8vKysKkSZOkL3Th4eE4\nePAgvLy8UFhYiNGjR+PMmTPX7bd//37ExcUZdKzS737E8VlPot7RBenTFwFK3YmZuYuHwtPbCY3N\nWiz76jxOXqwGoHuC89KE3hgT7HqLn5KIiIiISJ60tDSMHTu2w9+324wkTZ48GVu2bAEAbNmyBVOn\nTu2w987ZpDu7UBo9VGoWAkJ7wtPbCUIIvHkkT2oWFACWjPBjs0BERERE3UKXbBjmzJmDoUOH4uzZ\ns/D19cXmzZuxbNkyfP311wgNDcWBAwewbNmyDjlWXVEpir8+jEZbB1SExEjrrzzV+YtTpUg5Wyat\nf2igN8aHunXIscn4rj0lTNQWZoUMwbyQXMwKmQKVsQu4GTt27Gh1/b59+zr8WAWfpABaLcoiB0NY\n6H5d3n7O8PF3QfalWmxMzZdemxjiill9PTq8BiIiIiIiY+mSZxhuFyEE8pP2oNnKBuURA6T1gxIC\noRXAq9/loFGruwQkpKctnhzm2+7F1tT1XLm4iOhGmBUyBPNCcjErZArYMLSjMu131KRnoyxiALSW\n1gAANw8HBIW5Y+fJYpwt0QAALJUK/CWhN6xU/HUSERERUffCb7jtyEvaA62FCmV9BkvrBiUEILuy\nDlt/KpTWzY3zgr+LrTFKpE7G2VGSi1khQzAvJBezQqaADUMbmjV1uPj5PlwK7YdmW3sAgJOzLUKi\nvPDqty2jSGHudpjZ19OYpRIRERERdRo2DG0oSvkOjdW1KI2Kl9YNHOGPT38vwbnSllGkZ0f6wULJ\n6xa6K86OklzMChmCeSG5mBUyBWwY2pCftAeVgZFodHQGANjaWcIxyA1b0y5Kr5nbvxd6cxSJiIiI\niLoxNgytqM27iNJDx1ESPVRa129ob7xxJF9/FCmat1Dt7jg7SnIxK2QI5oXkYlbIFLBhaMXF//0G\ntW69UO+quzZBZWmBLAcbjiIRERERkdlhw9CKouSDek919glzx/bfSqVljiKZD86OklzMChmCeSG5\nmBUyBWwYrlFXVIrytFOoCIyS1qVByVEkIiIiIjJLbBiuUfzVd7jsFw6tte4MgpWjNY7XNAEAlApg\nyQiOIpkTzo6SXMwKGYJ5IbmYFTIFbBiuUZT8LSpCYqXlTFsrQKFrEKZGuiPAlaNIRERERGQ+2DBc\npeHSZVw8kY5qdaC07ryNNQDA1U6FuXG9jFUaGQlnR0kuZoUMwbyQXMwKmQI2DFcp2fs9KgKipDMK\nl+ysUKeyAAAsGOANeysLY5ZHRERERHTbsWG4SlHyt6gIarnYOdfBBgAQ4GKDccGuxiqLjIizoyQX\ns0KGYF5ILmaFTAEbhj801WiQd+I86l10d0DSAiix0zUMCwepeaEzEREREZklNgx/KN1/FBXqEGm5\n2N4azUoFwt3tMNDH0YiVkTFxdpTkYlbIEMwLycWskClgw/CHouSDqPSPaFm2151duDfGEwoFzy4Q\nERERkXliwwBA29SEnOPpV40jCZTaWcPP2QbxvXsYuToyJs6OklzMChmCeSG5mBUyBWwYAFSmncIl\nd39pudjeBs1KBWb19YCSZxeIiIiIyIyxYQBQ+s3R68aR3O0tMTrIxYhVkSng7CjJxayQIZgXkotZ\nIVPAhgFA3uGTLeNIQjeONLOvBywt+OshIiIiIvNm9t+IG8oqUHC5ZeyowkYFO1sV7gx1M2JVZCo4\nO0pyMStkCOaF5GJWyBSYfcNQduhHVPsES8tFDna4M8wNNpZ8qjMRERERkdk3DEXf/Ihq7wBpuczO\nChPDexqxIjIlnB0luZgVMgTzQnIxK2QKzL5hyDlbBKGyBADUQ4uoQFf0crI2clVERERERKbBrBuG\nuoJilFm33AmpyNGOZxdID2dHSS5mhQzBvJBczAqZArNuGC4d+wVVPiHSco2zHQb4OhmxIiIiIiIi\n02LWDUNe6hk09NDdDUlom9E30hMqJR/URi04O0pyMStkCOaF5GJWyBSYdcOQlV0p/VytaMboEN5K\nlYiIiIjoambbMDRWVqFM5SwtX/ZwQZSXvRErIlPE2VGSi1khQzAvJBezQqbAbKzjDB4AAA6mSURB\nVBuGktSTqPHyl5ZDY3ygVHAciYiIiIjoambbMGQcTYdQqQAA2roajOzjbuSKyBRxdpTkYlbIEMwL\nycWskCkw24YhK6fl+oU6KyDCk+NIRERERETXMsuGQVvfgMtKB2m5R4Qvx5GoVZwdJbmYFTIE80Jy\nMStkCsyyYSj56TTqXL10C0KLgcOCjVsQEREREZGJMsuG4fR3pwDlHx+9thpxvXsYtyAyWZwdJbmY\nFTIE80JyMStkCsyyYcg5X9qyYKuEjaWF8YohIiIiIjJhZtkwVDdbSj+7hHgZsRIydZwdJbmYFTIE\n80JyMStkCsyyYahzaWkSYoaFGbESIiIiIiLTZpYNg9baBgCgaKhDbLCbkashU8bZUZKLWSFDMC8k\nF7NCpsAsG4YrlNp6qCzM+ldARERERNQus/62bOdiY+wSyMRxdpTkYlbIEMwLycWskCkw64bBO8Lb\n2CUQEREREZk0s24Y+g7hA9uofZwdJbmYFTIE80JyMStkCsy2YVA01sNP7WzsMoiIiIiITJrZNgyq\nJg0UCoWxyyATx9lRkotZIUMwLyQXs0KmoNs1DCkpKQgPD0dISAjWrVvX5uts7C3b3EZ0xcmTJ41d\nAnURzAoZgnkhuZgVMgXdqmFobm7G4sWLkZKSglOnTmHHjh04ffp0q6/t6c/nL9CNXb582dglUBfB\nrJAhmBeSi1khU9CtGoZjx44hODgY/v7+sLS0xOzZs/HFF1+0+trw+NDbXB0RERERUdfTrRqG/Px8\n+Pr6Sss+Pj7Iz8+/7nWKxnqEh/e6naVRF5WTk2PsEqiLYFbIEMwLycWskClQCCGEsYvoKLt27UJK\nSgo2btwIANi2bRtSU1Px5ptvSq/Zv3+/scojIiIiIupUY8eO7fD3VHX4OxqRWq1Gbm6utJybmwsf\nHx+913TGL5GIiIiIqLvqViNJAwYMQHp6OrKystDQ0ICPP/4YkydPNnZZRERERERdVrc6w6BSqfDW\nW2/hjjvuQHNzMxYuXIiIiAhjl0VERERE1GV1qzMMADBhwgScPXsWGRkZWL58ud42uc9ooO4rNzcX\no0ePRmRkJKKiorBhwwYAQHl5ORITExEaGorx48ejoqJC2ufll19GSEgIwsPDsXfvXmn9Tz/9hOjo\naISEhODJJ5+87Z+Fbo/m5mb069cPkyZNAsCsUNsqKiowY8YMREREoE+fPkhNTWVeqFUvv/wyIiMj\nER0djfvuuw/19fXMCkkeeugheHp6Ijo6WlrXkfmor6/Hvffei5CQEAwZMgTZ2dk3LkqYiaamJhEU\nFCQyMzNFQ0ODiImJEadOnTJ2WXSbFRYWihMnTgghhKiqqhKhoaHi1KlT4i9/+YtYt26dEEKItWvX\niueee04IIcTvv/8uYmJiRENDg8jMzBRBQUFCq9UKIYQYOHCgSE1NFUIIMWHCBPHVV18Z4RNRZ/vX\nv/4l7rvvPjFp0iQhhGBWqE0PPvig2LRpkxBCiMbGRlFRUcG80HUyMzNFQECAqKurE0IIMWvWLPHB\nBx8wKyT57rvvRFpamoiKipLWdWQ+3n77bfHoo48KIYRISkoS99577w1r6nZnGNpiyDMaqPvy8vJC\nbGwsAMDBwQERERHIz8/H7t27MW/ePADAvHnz8PnnnwMAvvjiC8yZMweWlpbw9/dHcHAwUlNTUVhY\niKqqKgwaNAgA8OCDD0r7UPeRl5eH5ORkPPzwwxB/3FCOWaHWVFZW4tChQ3jooYcA6EZke/TowbzQ\ndZycnGBpaQmNRoOmpiZoNBp4e3szKyQZMWIEXFxc9NZ1ZD6ufq/p06fLuoOo2TQMcp/RQOYjKysL\nJ06cwODBg1FUVARPT08AgKenJ4qKigAABQUFenfaupKba9er1WrmqRt6+umn8corr0CpbPlPJbNC\nrcnMzIS7uzsWLFiAuLg4PPLII6ipqWFe6Dqurq545pln4OfnB29vbzg7OyMxMZFZoXZ1ZD6u/k58\n5Y8b5eXl7R7fbBoGhUJh7BLIhFRXV2P69OlYv349HB0d9bYpFArmhfDll1/Cw8MD/fr1k84uXItZ\noSuampqQlpaGxx57DGlpabC3t8fatWv1XsO8EACcP38eb7zxBrKyslBQUIDq6mps27ZN7zXMCrXH\nGPkwm4ZBzjMayDw0NjZi+vTpmDt3LqZOnQpA161fvHgRAFBYWAgPDw8A1+cmLy8PPj4+UKvVyMvL\n01uvVqtv46egznbkyBHs3r0bAQEBmDNnDg4cOIC5c+cyK9QqHx8f+Pj4YODAgQCAGTNmIC0tDV5e\nXswL6Tl+/DiGDh0KNzc3qFQqTJs2DT/88AOzQu3qiH97rnzvVavV0hPEm5qaUFlZCVdX13aPbzYN\nA5/RQAAghMDChQvRp08fPPXUU9L6yZMnY8uWLQCALVu2SI3E5MmTkZSUhIaGBmRmZiI9PR2DBg2C\nl5cXnJyckJqaCiEEtm7dKu1D3cNLL72E3NxcZGZmIikpCWPGjMHWrVuZFWqVl5cXfH19ce7cOQDA\nvn37EBkZiUmTJjEvpCc8PBxHjx5FbW0thBDYt28f+vTpw6xQuzri354pU6Zc916ffPKJvIca3/Kl\n3F1IcnKyCA0NFUFBQeKll14ydjlkBIcOHRIKhULExMSI2NhYERsbK7766itRVlYmxo4dK0JCQkRi\nYqK4dOmStM+aNWtEUFCQCAsLEykpKdL648ePi6ioKBEUFCQef/xxY3wcuk0OHjwo3SWJWaG2/Pzz\nz2LAgAGib9++4p577hEVFRXMC7Vq3bp1ok+fPiIqKko8+OCDoqGhgVkhyezZs0WvXr2EpaWl8PHx\nEe+//36H5qOurk7MnDlTBAcHi8GDB4vMzMwb1qQQoo3hXCIiIiIiMntmM5JERERERESGY8NARERE\nRERtYsNARERERERtYsNARERERERtYsNARER65s+fjxUrVhjt+AsWLICrqyuGDBnSoe+blZUFpVIJ\nrVYLABg1ahQ2bdrUoccgIuqO2DAQEZk4f39/eHp6QqPRSOvee+89jB49ulOOZ8ynzB46dAj79u1D\nQUEBjh492qnH4tN0iYjkYcNARNQFaLVarF+//rYdr6PuuH3lr/lyZWdnw9/fHzY2Nh1yfCIiunVs\nGIiITJxCocCzzz6LV199FZWVlddtv3bUBtAft/nggw8wbNgwLFmyBC4uLggODsaRI0ewefNm+Pn5\nwdPTEx9++KHee5aWlmL8+PFwcnLCqFGjkJOTI207c+YMEhMT4ebmhvDwcOzcuVPaNn/+fDz66KO4\n66674ODggIMHD15Xb0FBASZPngw3NzeEhITgvffeAwBs2rQJjzzyCH744Qc4Ojpi1apV1+175bM8\n/vjjcHZ2RkREBA4cOCBt9/f3x/79+6XlF154AXPnzr3RrxgZGRlISEiAs7Mz3N3dMXv27BvuQ0Rk\nLtgwEBF1AQMGDMCoUaPw6quvynr9teM2x44dQ0xMDMrLyzFnzhzMmjULaWlpOH/+PLZt24bFixdL\nI09CCGzfvh0rV65EaWkpYmNjcf/99wMAampqkJiYiAceeAAlJSVISkrCY489htOnT0vH2rFjB1as\nWIHq6moMGzbsutpmz54NPz8/FBYW4pNPPsFf//pXfPPNN1i4cCH+85//ID4+HlVVVXj++edb/WzH\njh1DcHAwysrKsGrVK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- } - ], - "prompt_number": 24 - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "plt.figure()\n", - "[pl1, pl2, pl3] = plt.plot(expected_total_regret[:, [0, 1, 2]], lw=3)\n", - "plt.xscale(\"log\")\n", - "plt.legend([pl1, pl2, pl3],\n", - " [\"Upper Credible Bound\", \"Bayesian Bandit\", \"UCB-Bayes\"],\n", - " loc=\"upper left\")\n", - "plt.ylabel(\"Exepected Total Regret \\n after $\\log{n}$ pulls\");\n", - "plt.title(\"log-scale of above\");\n", - "plt.ylabel(\"Exepected Total Regret \\n after $\\log{n}$ pulls\");" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "metadata": {}, - "output_type": "display_data", - "png": 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w119/8eKLL+Y6NldXV3bt2kVERASTJk1i1KhR3Lx5Uz0eGBiIp6cnV69e5d13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- } - ], - "prompt_number": 25 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### Extending the algorithm \n", - "\n", - "\n", - "Because of the Bayesian Bandits algorithm's simplicity, it is easy to extend. Some possibilities are:\n", - "\n", - "- If interested in the *minimum* probability (eg: where prizes are a bad thing), simply choose $B = \\text{argmin} \\; X_b$ and proceed.\n", - "\n", - "- Adding learning rates: Suppose the underlying environment may change over time. Technically the standard Bayesian Bandit algorithm would self-update itself (awesome) by noting that what it thought was the best is starting to fail more often. We can motivate the algorithm to learn changing environments quicker by simply adding a *rate* term upon updating:\n", - "\n", - " self.wins[ choice ] = rate*self.wins[ choice ] + result\n", - " self.trials[ choice ] = rate*self.trials[ choice ] + 1\n", - "\n", - " If `rate < 1`, the algorithm will *forget* its previous wins quicker and there will be a downward pressure towards ignorance. Conversely, setting `rate > 1` implies your algorithm will act more risky, and bet on earlier winners more often and be more resistant to changing environments. \n", - "\n", - "- Hierarchical algorithms: We can setup a Bayesian Bandit algorithm on top of smaller bandit algorithms. Suppose we have $N$ Bayesian Bandit models, each varying in some behavior (for example different `rate` parameters, representing varying sensitivity to changing environments). On top of these $N$ models is another Bayesian Bandit learner that will select a sub-Bayesian Bandit. This chosen Bayesian Bandit will then make an internal choice as to which machine to pull. The super-Bayesian Bandit updates itself depending on whether the sub-Bayesian Bandit was correct or not. \n", - "\n", - "- Extending the rewards, denoted $y_a$ for bandit $a$, to random variables from a distribution $f_{y_a}(y)$ is straightforward. More generally, this problem can be rephrased as \"Find the bandit with the largest expected value\", as playing the bandit with the largest expected value is optimal. In the case above, $f_{y_a}$ was Bernoulli with probability $p_a$, hence the expected value for a bandit is equal to $p_a$, which is why it looks like we are aiming to maximize the probability of winning. If $f$ is not Bernoulli, and it is non-negative, which can be accomplished apriori by shifting the distribution (we assume we know $f$), then the algorithm behaves as before:\n", - "\n", - " For each round, \n", - " \n", - " 1. Sample a random variable $X_b$ from the prior of bandit $b$, for all $b$.\n", - " 2. Select the bandit with largest sample, i.e. select bandit $B = \\text{argmax}\\;\\; X_b$.\n", - " 3. Observe the result,$R \\sim f_{y_b}$, of pulling bandit $B$, and update your prior on bandit $B$.\n", - " 4. Return to 1\n", - "\n", - " The issue is in the sampling of the $X_b$ drawing phase. With Beta priors and Bernoulli observations, we have a Beta posterior — this is easy to sample from. But now, with arbitrary distributions $f$, we have a non-trivial posterior. Sampling from these can be difficult.\n", - "\n", - "- There has been some interest in extending the Bayesian Bandit algorithm to commenting systems. Recall in Chapter 4, we developed a ranking algorithm based on the Bayesian lower-bound of the proportion of upvotes to the total number of votes. One problem with this approach is that it will bias the top rankings towards older comments, since older comments naturally have more votes (and hence the lower-bound is tighter to the true proportion). This creates a positive feedback cycle where older comments gain more votes, hence are displayed more often, hence gain more votes, etc. This pushes any new, potentially better comments, towards the bottom. J. Neufeld proposes a system to remedy this that uses a Bayesian Bandit solution.\n", - "\n", - "His proposal is to consider each comment as a Bandit, with the number of pulls equal to the number of votes cast, and number of rewards as the number of upvotes, hence creating a $\\text{Beta}(1+U,1+D)$ posterior. As visitors visit the page, samples are drawn from each bandit/comment, but instead of displaying the comment with the $\\max$ sample, the comments are ranked according to the ranking of their respective samples. From J. Neufeld's blog [7]:\n", - "\n", - " > [The] resulting ranking algorithm is quite straightforward, each new time the comments page is loaded, the score for each comment is sampled from a $\\text{Beta}(1+U,1+D)$, comments are then ranked by this score in descending order... This randomization has a unique benefit in that even untouched comments $(U=0,D=0)$ have some chance of being seen even in threads with 5000+ comments (something that is not happening now), but, at the same time, the user is not likely to be inundated with rating these new comments. " - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Just for fun, though the colors explode, we watch the Bayesian Bandit algorithm learn 35 different options. " - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "figsize(12.0, 8)\n", - "beta = stats.beta\n", - "hidden_prob = beta.rvs(1, 13, size=35)\n", - "print hidden_prob\n", - "bandits = Bandits(hidden_prob)\n", - "bayesian_strat = BayesianStrategy(bandits)\n", - "\n", - "for j, i in enumerate([100, 200, 500, 1300]):\n", - " plt.subplot(2, 2, j + 1)\n", - " bayesian_strat.sample_bandits(i)\n", - " plot_priors(bayesian_strat, hidden_prob, lw=2, alpha=0.0, plt_vlines=False)\n", - " # plt.legend()\n", - " plt.xlim(0, 0.5)" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "[ 0.01086616 0.20672538 0.00137644 0.02843378 0.00809559 0.09709516\n", - " 0.00540949 0.02886983 0.1670677 0.01158008 0.06498409 0.15652432\n", - " 0.17674427 0.0351021 0.11126791 0.00988438 0.24309639 0.02708666\n", - " 0.04342859 0.00825645 0.01890499 0.24829156 0.15444239 0.03984653\n", - " 0.00785845 0.00758847 0.08759903 0.02189288 0.0228888 0.18814637\n", - " 0.04898048 0.01136161 0.02290211 0.17823588 0.17785098]\n" - ] - }, - { - "metadata": {}, - "output_type": "display_data", - "png": 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1a5g7dy6bNm0qtD8iIoIWDT5m0ebaDB/06R3rGLDgD/LyfdDrklg/qm+hY5d+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\nFcoPhgJwc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/Lr2T3F/AYRBjniNOXbU7QaJT64pS/3XYVDhLapgc1vj2J4Uz4K5IQ4u5nL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8zts9AG/K+yU8D9q1B/dz/ZQETNbsYWreHH925m5n1fIh6nws/ijAXIyFw08Cqm3307latS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bmnjv4c/Q+CWAKKJtb8I9qow7rzuASaPQ6Nby0aFU5maOw4xK56iy+LNl6EjmpAYzL7rn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\nFxNu30PM2kJg34vEhvsZ2DyEp6GdnBtXkzR/xpj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bITb5J0Lwja003Pk/IATTHroP78TR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- "text": [ - "" - ] - } - ], - "prompt_number": 17 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Eliciting expert prior\n", - "\n", - "Specifying a subjective prior is how practitioners incorporate domain knowledge about the problem into our mathematical framework. Allowing domain knowledge is useful for many reasons, for example:\n", - "\n", - "- Aids the speed of MCMC convergence. For example, if we know the unknown parameter is strictly positive, then we can restrict our attention there, hence saving time that would otherwise be spent exploring negative values.\n", - "- More accurate inference. By weighing prior values near the true unknown value higher, we are narrowing our eventual inference (by making the posterior tighter around the unknown) \n", - "- Express our uncertainty better. See the *Price is Right* problem in Chapter 5.\n", - "\n", - "Of course, practitioners of Bayesian methods are not experts in every field, so we must turn to domain experts to craft our priors. We must be careful with how we elicit these priors though. Some things to consider:\n", - "\n", - "1. From experience, I would avoid introducing Betas, Gammas, etc. to non-Bayesian practitioners. Furthermore, non-statisticians can get tripped up by how a continuous probability function can have a value exceeding one.\n", - "\n", - "2. Individuals often neglect the rare *tail-events* and put too much weight around the mean of distribution. \n", - "\n", - "3. Related to above is that almost always individuals will under-emphasize the uncertainty in their guesses.\n", - "\n", - "Eliciting priors from non-technical experts is especially difficult. Rather than introduce the notion of probability distributions, priors, etc. that may scare an expert, there is a much simpler solution. \n", - "\n", - "###Trial roulette method \n", - "\n", - "\n", - "The *trial roulette method* [8] focuses on building a prior distribution by placing counters (think casino chips) on what the expert thinks are possible outcomes. The expert is given $N$ counters (say $N=20$) and is asked to place them on a pre-printed grid, with bins representing intervals. Each column would represent their belief of the probability of getting the corresponding bin result. Each chip would represent an $\\frac{1}{N} = 0.05$ increase in the probability of the outcome being in that interval. For example [9]:\n", - "\n", - "> A student is asked to predict the mark in a future exam. The figure below shows a completed grid for the elicitation of a subjective probability distribution. The horizontal axis of the grid shows the possible bins (or mark intervals) that the student was asked to consider. The numbers in top row record the number of chips per bin. The completed grid (using a total of 20 chips) shows that the student believes there is a 30% chance that the mark will be between 60 and 64.9.\n", - "\n", - "\n", - "\n", - "\n", - "From this, we can fit a distribution that captures the expert's choice. Some reasons in favor of using this technique are:\n", - "\n", - "1. Many questions about the shape of the expert's subjective probability distribution can be answered without the need to pose a long series of questions to the expert - the statistician can simply read off the density above or below any given point, or that between any two points.\n", - "\n", - "2. During the elicitation process, the experts can move around the chips if unsatisfied with the way they placed them initially - thus they can be sure of the final result to be submitted.\n", - "\n", - "3. It forces the expert to be coherent in the set of probabilities that are provided. If all the chips are used, the probabilities must sum to one.\n", - "\n", - "4. Graphical methods seem to provide more accurate results, especially for participants with modest levels of statistical sophistication." - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "##### Example: Stock Returns\n", - "\n", - "\n", - "Take note stock brokers: you're doing it wrong. When choosing which stocks to pick, an analyst will often look at the *daily return* of the stock. Suppose $S_t$ is the price of the stock on day $t$, then the daily return on day $t$ is :\n", - "\n", - "$$r_t = \\frac{ S_t - S_{t-1} }{ S_{t-1} } $$\n", - "\n", - "The *expected daily return* of a stock is denoted $\\mu = E[ r_t ] $. Obviously, stocks with high expected returns are desirable. Unfortunately, stock returns are so filled with noise that it is very hard to estimate this parameter. Furthermore, the parameter might change over time (consider the rises and falls of AAPL stock), hence it is unwise to use a large historical dataset. \n", - "\n", - "Historically, the expected return has been estimated by using the sample mean. This is a bad idea. As mentioned, the sample mean of a small sized dataset has enormous potential to be very wrong (again, see Chapter 4 for full details). Thus Bayesian inference is the correct procedure here, since we are able to see our uncertainty along with probable values.\n", - "\n", - "For this exercise, we will be examining the daily returns of the AAPL, GOOG, MSFT and AMZN. Before we pull in the data, suppose we ask our a stock fund manager (an expert in finance, but see [10] ), \n", - "\n", - "> What do you think the return profile looks like for each of these companies?\n", - "\n", - "Our stock broker, without needing to know the language of Normal distributions, or priors, or variances, etc. creates four distributions using the trial roulette method above. Suppose they look enough like Normals, so we fit Normals to them. They may look like: " - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "figsize(11., 5)\n", - "colors = [\"#348ABD\", \"#A60628\", \"#7A68A6\", \"#467821\"]\n", - "\n", - "normal = stats.norm\n", - "x = np.linspace(-0.15, 0.15, 100)\n", - "\n", - "expert_prior_params = {\"AAPL\": (0.05, 0.03),\n", - " \"GOOG\": (-0.03, 0.04),\n", - " \"TSLA\": (-0.02, 0.01),\n", - " \"AMZN\": (0.03, 0.02),\n", - " }\n", - "\n", - "for i, (name, params) in enumerate(expert_prior_params.iteritems()):\n", - " plt.subplot(2, 2, i)\n", - " y = normal.pdf(x, params[0], scale=params[1])\n", - " #plt.plot( x, y, c = colors[i] )\n", - " plt.fill_between(x, 0, y, color=colors[i], linewidth=2,\n", - " edgecolor=colors[i], alpha=0.6)\n", - " plt.title(name + \" prior\")\n", - " plt.vlines(0, 0, y.max(), \"k\", \"--\", linewidth=0.5)\n", - " plt.xlim(-0.15, 0.15)\n", - "plt.tight_layout()" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "metadata": {}, - "output_type": "display_data", - "png": 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ByJXbGcRHOy/A7QygYmLmTSTh7Q0BAGpvqMLMuZUSR0NSKS2DqC/v6/ryyy9j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\nW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- "text": [ - "" - ] - } - ], - "prompt_number": 18 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Note that these are subjective priors: the expert has a personal opinion on the stock returns of each of these companies, and is expressing them in a distribution. He's not wishful thinking -- he's introducing domain knowledge.\n", - "\n", - "In order to better model these returns, we should investigate the *covariance matrix* of the returns. For example, it would be unwise to invest in two stocks that are highly correlated, since they are likely to tank together (hence why fund managers suggest a diversification strategy). We will use the *Wishart distribution* for this, introduced earlier." - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "import pymc as pm\n", - "\n", - "n_observations = 100 # we will truncate the the most recent 100 days.\n", - "\n", - "prior_mu = np.array([x[0] for x in expert_prior_params.values()])\n", - "prior_std = np.array([x[1] for x in expert_prior_params.values()])\n", - "\n", - "inv_cov_matrix = pm.Wishart(\"inv_cov_matrix\", n_observations, np.diag(prior_std ** 2))\n", - "mu = pm.Normal(\"returns\", prior_mu, 1, size=4)" - ], - "language": "python", - "metadata": {}, - "outputs": [], - "prompt_number": 33 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Next we pull historical data for these stocks:" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "# I wish I could have used Pandas as a prereq for this book, but oh well.\n", - "import datetime\n", - "import ystockquote as ysq\n", - "\n", - "stocks = [\"AAPL\", \"GOOG\", \"TSLA\", \"AMZN\"]\n", - "\n", - "enddate = datetime.datetime.now().strftime(\"%Y-%m-%d\") # today's date.\n", - "startdate = \"2012-09-01\"\n", - "\n", - "stock_closes = {}\n", - "stock_returns = {}\n", - "CLOSE = 6\n", - "\n", - "for stock in stocks:\n", - " x = np.array(ysq.get_historical_prices(stock, startdate, enddate))\n", - " stock_closes[stock] = x[1:, CLOSE].astype(float)\n", - "\n", - "# create returns:\n", - "\n", - "for stock in stocks:\n", - " _previous_day = np.roll(stock_closes[stock], -1)\n", - " stock_returns[stock] = ((stock_closes[stock] - _previous_day) / _previous_day)[:n_observations]\n", - "\n", - "dates = map(lambda x: datetime.datetime.strptime(x, \"%Y-%m-%d\"), x[1:n_observations + 1, 0])" - ], - "language": "python", - "metadata": {}, - "outputs": [], - "prompt_number": 34 - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "figsize(12.5, 4)\n", - "\n", - "for _stock, _returns in stock_returns.iteritems():\n", - " p = plt.plot((1 + _returns)[::-1].cumprod() - 1, '-o', label=\"%s\" % _stock,\n", - " markersize=4, markeredgecolor=\"none\")\n", - "\n", - "plt.xticks(np.arange(100)[::-8],\n", - " map(lambda x: datetime.datetime.strftime(x, \"%Y-%m-%d\"), dates[::8]),\n", - " rotation=60);\n", - "\n", - "plt.legend(loc=\"upper left\")\n", - "plt.title(\"Return space\")\n", - "plt.ylabel(\"Return of $1 on first date, x100%\");" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "metadata": {}, - "output_type": "display_data", - "png": 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IJvJkGt4+zjzy54G1HtssZT/ffPMN8+bNw9HREW9vb2xtbSkqKiIpKYn+/fsT\nFBTU4AYABAQEkJCQwOXLl3Fzc2Pz5s1s2rSpyjFJSUnGn+fPn8/DDz9cLfEXBEEQhLagpKicLV+d\nJC/7Go4uHXh0YWCNM6zERV7ltx3nqVAbBkCeOHSJwSPFk+y6kPUyu7capm20dbBg2mMD2nziD9C9\nd0ee692xWa5lKAlq+NjOhurVt5Px7wBAUkjMe3pwrbMStRX3P9iDuMirJMVnc+lCNl17Ojf5NWv9\nK+jSpQvh4eFERkby3nvvsXjxYt59913OnTtHeHg4Xl5ejdIIlUrFhg0bGD9+PL1792bOnDn4+vqy\nceNGNm7c2CjXEO5NlY/Z2isRX9vWnuNrz7FBw+IrLixn85cnyMu+hlPHDjy6qObEHwxJz9K3xzFl\nbj+Q4PDeC0SeTL3ra9dVa//+LsZksn71Ptav3kfM2Ss1HhO2L4GE85mYmat45MmBVabJbO3xNVR7\njE+pNDzxSk6Pwdxc1S4SfwCrDmYMGd0dgD9+jePQoUNNfs1ae/4r9ezZk549ezZpQyZOnMjEiROr\nbHv66adrPPabb75p0ra0lIcffpjz588TFxeHqWnVEfTJyckMGDCA+fPns3bt2ir7HB0dsbS0RJIk\nrK2tmTFjBqtXr0ahUNCvXz/Wr1/PyJEjmzMUQRAEoQZFBWVs+fIkBXmlOHeyZvaCwDrNmNKrbyfK\nSzXs2xXD7z+fx9zChJ59XJuhxXWTGJvFnuAokGBiEw9MLswvZddPEcaxEbu3RnJobzwu1wdJ6/Qy\nEcdSDDO8SPDwvP71XqRLaH0mzPQnZHv09TUMWs+A7MYwYJgXp8MukZd9jR3fxeHu3KtJ/4bu+Pxr\n48aNDB06FBsbGxQKBTY2NgwbNox///vfTdaoe1FKSgpnzpzB2dmZPXv2VNsfFBSEr68vO3bsoKKi\notr+w4cPk5KSws8//8y2bdv47rvvAMNg6nu5PrRyYE17JeJr29pzfO05Nqh/fImxWWx4J5T/fHiQ\ngrxSXNxseHRh3RL/Sv2HeDJsbHdkGX7dfI6UxNz6NvuOLpzPYP3qfZzdX86F8xl3PF6v05NwPpOd\nP56lvExDeamG3VsjG71dYJi6MfJkKv/9+Ei16TlLitQkxWdz7EASJw9dMk7taGKipEsPp2rnEr+f\nbU9lCdLaL5a2+HS44cmFzP4hitk/RBGeXFjnfbejUinQaPQAuLv0Mk7921Rq7flfsWIFv/zyCy+9\n9BJ9+/aHxUmmAAAgAElEQVTFxsaGwsJCzp07x7p160hKSjLOyd9WZf0WRtSy9wHw/+g1XB6q/x9M\nY5wjKCiIkSNHMnDgQIKCgpg2bZpxnyzLbNmyhZUrV7J69WpCQkJuO96hR48eDBkyhLi4uHq3QRAE\nQWgau7dGGlculRQSjy4MrNO83rcaOqYbZdcqOHsshR3fn2HOXwbh6l51ikNZb0iSD4bEAxJjpvSi\nz0CP255T1sukXc4nLvIq507cKCna9WMEPft0xLuXC117OmHV4UaZRUlROZEn04g8mWqc+72SulxL\n1Kk0/ANuf836Ki4sZ+/2aC4n5ADQydOO/JxrSJLEQzP8cHTpQNaVIrKvFnMy7JJxsa7K1XsFoTGt\nO5xC4fW/5/f2X2Kwpy0lah3XKnRczC2l8t703dBLLAh0w6+jFd2dLFEpbt8ZW1nWBKCvff3dBqs1\n+f/yyy+JjIysNttLQEAAEyZMoG/fvm0++Y9a9j6aPMOcuWeefKXB54v+6/uMOb+73u/bvHkzK1as\nYMCAAaxZs4bs7GycnQ2DPo4dO0Z2djYPPvgg586dIygoqFryXzkTUlxcHMeOHeONN95ocCztQVhY\n+5qr+lYivratPcfXnmODuscnyzKnwi4bE38Ac3PVXSX+YHiaO2aKL2WlGuIir/LDp+GYmqno3b+T\nYdGijGKyM4qrrGIbsi2asN8T6ORhh6uHDXo9nD56GVkv07mrA5lXiqrM5w6Gumov995ciM7kQnQm\nSIbZVUqKypH1Mnq9bJx5xd7JEo8u9iTEZKGt0KHV6tm7PZqMtELGTPFFeZeDbCsXP9Nq9ciyjFaj\nx9zCxLDKbV/Xak+1HZys6NW3E26edlVmqKmJ+P1su1o6trxSDaU3/X1V6GQOXyqo8ViNXmbj8XQA\nzJQSnWzMuFqkxkSp4OWRXgz1unHjPmGmP3u2RXE57TzPvjC3SWOoU81/Te7lUpLGduzYMa5evcqE\nCROwtrbGx8eH4OBgnn32WQA2bdrE+PHjMTc3Z9q0aXzyySfk5OTg5HTjUeaoUaNQKpXY29vzxBNP\n8Nhjj7VUOIIgCAJQXqYhJDiKi7FZgGGqThNTJRMeaVi9sqSQmDjLnwvnM9DrZCrUWiKO3zIIWAJu\n6jwsKVKTEJNJQkxmlcMq22ZjZ45vPzesrM0I/yMRMwsVD87wQ6fVkxSfTWpSHgU3TTsKhkWK+g/2\nxLObA5IkMf76eqDRp9P4fWcM506kkp1RzNQ/9aeDjXm9YpRlucrTEjCUfTw03e+OAz1byww1QusX\nnlzIusPJyMDyB6om47fSyzK/xubw9amraK537ZspJR7q6UjfTh2wMlXSwVTJxdxS/nvqKjIwtrs9\nZRo95zOvkVao5nK+4SZbrdPx4cFktj/Z13j+br4uPPfGWMLCzJq8rKnW5H/hwoWMGTOGl156iX79\n+hmn+oyIiGDdunWNtthAS/L/6DWi/2oo2enzr7sv+7n5HPW1adMmRo8ejbW1NQDTpk0jKCiIZ599\nlrKyMnbt2sWGDRsM7fX3x9PTk+DgYJ555hnjOQ4ePEiXLl3qfe32rr32fFQS8bVt7Tm+9hwb3Dm+\njPRCfvkpgsL8MszMVUyc5U/3RpyeUalSYGqmMq4MrFQpGP5gD1w62eDcyZqrKQXG3u/xM/ywd7Ii\nI62QjLRCIk6kIl9PXlQqBY8uCqRTZztjp96AYV7AjeR5wFAvKiq0fPH3A8apFs0tTZj22H01tq3P\nQA+cOlqz88ezXEkp4JuPw0AGhUK64yrFWo2O2MirnA1PqZL4m5opmf74fY3W8Xiv/362ZY0VW3qh\nmvf/uIRaa/hbWB2axGP3dWKguzU9nSxR3lSik5hbysdhqcRlG26AB3W2YckwDzrVcCPay8WKKb7V\np+ssKNPw1JYYSq/X9pdpdOhlGcUtv9PN8d3VusgXGAb8fvvtt8TExFBSUkKHDh3w8/PjySefvO1s\nPC2prS3yVVZWRq9evZBl2biQmlqtpqioiIMHDxIbG8vTTz+No6MjSqWhdrGwsJCePXty4MABwDDb\nz+nTp2tM/vv378/69esZMWLEXbWvtX5ugiAIrc3NZSo6rQ69Hjq62/DwvP7YOTT+QkR3uwCT4X1R\nQP0Wiarv9a6VqPllUwRpl/KN20xMlUye0w9bewtsHSxITcwjZFsUsgydvR1Iu5RH2fUbGlNTJXpZ\nRmWibPIZhIS2zdCDnwLAiw94VunBv3nf04PdKNXoCb2YR2xWaY3nArAyVdLZ1ozL+eXoZRmNTkYG\nHCxVLB7qwQNd7O7qRrTySUNRuQ4ZeHmkJw/2cKzz+xtrka87Jv9tTVtL/rdt28Yrr7zCoUOHjNN7\nyrLMggUL6N+/P7GxsXh4eFSp4b9y5Qpjx47l0KFD9O7d+47J/9q1a6vcSZqYmBhvJO6ktX5uddXS\ntYFNTcTXtrXn+NpzbFBzfBveDTX2xAP0H+zJqEk+bXLQaWN9fzqdnk9W7UOr1df5PR3dbLhvqCe9\n+nZqss/uXvz9bC9qim32D1HGAbhKCfp2ssZMJWGmUnA0uRCNrnqqa2GioKeTJRdzS1FKEhN9nLim\n0XEmvZgrtwxiB5jW24mnAtywMm347+S+hDzWHEzGwULF17N7Y3nTOWv77pplhd87SUlJwdPTs8GN\nuJcFBQXx2GOP4e7uXmX7okWLjE9WDhw4YBz8C+Ds7MzYsWPZvHkzq1atuuM15syZU+X18uXLee21\n+pcnCYIgCDW7GJtVJfE3NVMyblrvFmxR66BUKnh4Xn92b41Er5fx6GoPMhTklVKUX4bupqRMqTSU\nILl53l2vqnDv0upv3FzqZDh7pfi2xw7ubMOY7vYM8bTF4jY3lxnFap7eFkfZ9ZvWDqZKlgzr3Gjt\nHdPdnl9is4nNKuWniAwWDXK/85sa0V33/JeXl2NlZYVOp7vzwc2orfX8t3bicxMEQbi98jIN+/8X\na1xlVqGQMDUz1PiLMpXa6fUy58+kcWB3vGEQsyjtaTfCkwv556FkAJaPqH0gbUPdnKibKiWeGOBK\nd0dL1Do9aq1MbFYJe+PzQILnh3kwro5lNrWVEjWG+OxrLN15AaVC4t8ze+Fhe+dB8c3S83/w4MHb\n3n2r1WraWcWQIAiCINRZUnw2v+2IpqRIjUql4IHxPRkw1Auplrm8hRsUCgn/gM74BzRej6rQfCoT\nfI1e5v4utliolORc05B9rYLE3DLjZFPvhl7isxk+eNlbNHobyrV6Vu27RJlWT6CHDasf8q4yUBdg\ndDd7Fg+t/+/YUC9btno13UrCPs5WPNTTgb0X8th4LJ13xndrsmvdqtbkf/To0bi6ut62Plw8lhNa\nu/Zc9wgivrauPcfXXmNLjM1iz7YoEpIi6ezqC4Cbpx0TZvnj4GTVwq1rPO31+6sk4mu4fx5Kpkht\nqP7Yl5B/2+M0epn/2xbH2O72PD6gE242tU/VeieVscmyzL8Op5CYW4abjSkrRntVS/xbuwUBbhy+\nVMDx1CJOpBYyqLNts3x3tSb/Xl5e/PDDD9x///3V9pWXl2Np2fizFwiCIAhCayTLMr9uOUeFWmdc\nQXbkRB8G3t8FRRtLOgShIUorDKvZVjJTSiwIdMPJyhRnKxNSCsr5z4kryLKMj7MlZ9KL2Xcxnz8S\n85ng48if7nPF2cq0QW3YFp3NH4n5mKsUvD3OG2uzBg1jbRH2liY8PqAT/z6ezufh6dznZt0s1621\n5n/WrFmMGDGCpUuXVtunVqvx8fHh8uXLTdm+ehM1/41LfG6CIAiGAaqhv8RyKT7buM3cwoTn3mx4\n/a0gtCVlGh2v700kOuMaEtDBTMlLd6jrv1qs5oczGYRezOP6EhOYKiWGedniaXe91l2SSCso50hy\nIRKGaTkn1zBfPsCZ9CJeC0lEL8NbY7syvKtd4wbZjDQ6Pc9sjyO1UM2iQW482vf264E0y1SfGo1h\n5gITk7tbhrwliOS/cYnPTRCEe5lOq+dU2CXC/0hEq9GjMlEgSRIqE2W95sgXhPagXKvnzb2JnLta\ngpOlCR9O7oG7bd3LeFLyy3l2R5xxhdw76e5owShve0Z42+F6fUGtq8Vqnvs5nmK1jnn9OzI/oO3n\nKKfSDDczFiYKvp7dG0fLmvPuZhnwe6ekX6PRtKkbA+HeI+o62zYRX9vVlmOrXKxLr5cxMVVScn3O\nb9/+nRg1sRdW1maEhYW168S/LX9/dSHiqz+1Vs/bvyVx7moJDpYq1kzuXq/EH8DT3hxLU6VxTn4z\nlYJZ/i7IsmERre1RWahvmv71Ym4ZF3PL+PLkFdxtTMkt1ZJz4QwdvPszqLMNTw7o1JghtpgADxt8\nnCyIzylj2ns/8uH/zWjSGZIUdTlo3LhxXLlypcq2c+fOMXDgwCZplCAIgiC0lN3BkZSValCXaykp\nUmPvZMnsBYFMfrQfVtYNG6woCHURnlzI7B+imP1DFOHJhXV+38GkfKZ/e463fkus1/vupEKrZ9W+\nJM5eKcbeQsWaST3qNDVlTV58wBNbcxW25ipeG92FPw/sxFMBbswPcOO1MV2N+94c24W3x3VllLcd\nZioF6UUVlGv16GVQSLBiVNsb4Fub9KIKALR6mQ8PJjfpteo0z/+rr77K119/zYYNG5g9ezZr1qxh\nzZo1vP/++zzzzDNN2sD6EmU/jUt8boIg3Csy0gs5/kcSCTGZxm0mJkqWvDkWlapOfWXCPehu54M/\nkJjPx2EpyMD4ng642ZhTrtVTptERHJVFxfUecFtzFVsfr33KSY1Oz+64XD4LTzNOsalSSCwf4ckw\nr9svZlWX2P55KJlSjR6tXsbWXMWHk7vTpQmm7axNuVbP3B+jKNUYFt2yNlOy7Ym+zdqGpnbzKsU2\n5kqCH68eX7PU/N/s8OHDPPHEEwC4ubnx3Xff0b179wY3oLGJ5L9xic9NEITmUFlqAzChmRd7Sruc\nz7EDiVy+kAMY5p9XKCRUpkqx8JRwR7O+jzROednBVMlXs32xM1dVmw5do9MTl13K2fRizqQXE5N1\nrU7nV0iwaJA743s6VJvRRqeX+SMxn29PXyWzpKLG95urFPR0tuBiThkqpcTyB+q+6Nb0b88ZE24J\n+OKRXnR1aN7Ev1JTL7rV0uoSX7PU/N8sKSmJoqIivL29KSkpoaysrMEXF6p6+OGHOX/+PHFxcZia\nGqbAWrJkCUFBQfzwww9MnDjReOxrr73Gxo0b+fTTT5k7dy5Dhw4lPT29yvkqKirQarXk5OQQFhbG\ntGnTWLBgAR9++KHxmIkTJ/Lkk08yb9685gmymYm6zrZNxNd21Se2stIKft0SSYXa0Ou1e2skz70x\ntkkXy0qMzWL31kg0FTr01wcfmpgq6T/Yk4DhXe5Y3tOevzsQ8dXV6bQiitU3prwsqdAx58dorM2U\neNiaYaZUEJt1DZ1sSJ5vN9DVRCkxoacj5ioFFiYKMosrOHCpgAqdoczl38fT+fbUFcZ0d6CrvTk/\nRmSg0clYmyrJvGaYnMXLzpxhXWzZHZdL3oUzTH1oNJfyyonJukbk1es3Ghp4f/8lNkyvfdGt9EI1\nG4+nGRN/ACtTZYsl/nBj0a2wsLB2l/hD88ZXp+R/1qxZREVFERISwqBBg/j0008ZOXIkK1as4JVX\nXmmUhoSEhLBs2TJ0Oh2LFi3i1VdfrbJ/586dvPXWWygUChQKBR9++CFjxoxplGu3BikpKZw5cwYP\nDw/27NnDtGnTjPu6d+9OUFCQMfnXarXs3LkTb29v4zHh4eFVznft2jXGjh3LjBkzjNusrKzYsmUL\nS5cupXNnw2p3kiSJxdoEQWgWlb37MtBvUGe0Gh0pSXlkZxTDTTmRulzLV/86zH1DPOkz0B0z88af\nWKJyvv5KQ0Z3Y+D9XlhYNmzuceHeUKbR8dXJK+yKMTwtUkqGJ0YuVibkl2kpVuuIzSqt9j4vO3Pu\nc7fmPjdr1Fo9n4anATX39C4f6YVOL3MitYidMdmcSS9mT3xulWNKNXpcOpjw5IBOjO3ugFIhMT/A\njbCwQoYP9wTgSpGap7fHodYaEnm1TuYv2+LwdbFkfE9HRnrbY2VqKAsqrdCxKSKD7dHZaPQypkoJ\nhSRhplLw4gOejfshCi2mTmU/zz77LOvWrcPC4sYd34ULF3jiiSc4fvx4gxuh0+nw8fFh3759uLu7\nExgYyKZNm/D19TUec+3aNaysDKsnRkVFMWPGDC5evFjtXPUt+2mMR82NcY41a9YQERHBwIEDOXXq\nFJs2bQIMPf+Ojo5s2bKF48ePY2try969e/nqq68oKSnhiSeeqLHXfuHChRQWFhIcHAwYejmeeeYZ\npkyZQklJCRs2bABg0qRJPPnkk8ydO7fGdomyH0EQGsun74ZSVqqptl2plLBzsqQwrwwJCZWpgrLr\nvZkmpkrcu9hzNbUAhSQ1SknQmfBk9v8Sa3xtYWnCkjfEfP1C3ZzPLOHDgylcKVKjlOCJAZ2Y06+j\ncfCpLMvkl2lJLSjnzd+SKL+edNuYKQluQJ16SkE5v8TksDPmprUmVAqCH/fH9A5jUipLSnR6w6Jb\nsVnXjL36KoWEJIFSklApoKTCsP3BHg4sCHS77bSTQvNr1rKfzz//vNq2nj17cuTIkQY3AODEiRN0\n796dLl26ADB37lx27txZJfmvTPwBSkpKcHJyapRrh2yLMv5jtOP7Mw0/3/Zolrxe/ycSmzdvZsWK\nFQwYMIA1a9aQk5NjjNHMzIyJEyeyfft25s+fT1BQEHPmzOGrr76qsdd+48aNnDp1igMHDlTb9+KL\nLxIYGMiyZcta5ZgNQRDaL/1NJQ8KhcSgkd54ejvQydMOk5sGJOr1MolxWZw5mkxqUp6xFh/gl6AI\nxk3tjZOrNY4uHUi5mFvnzhdZljnyewLHDiQBhsG8KlPDfP2CUJvKga9qrZ4KnWFayi725rw6yotu\njpZVjpUkCQdLExwsTfjb6C5V6rgbwtPOnCXDPPDraMXHR1JRKmD5A153TPzhRklJpXKtnrBLBYTE\n5xKZUQKA5vrjNx9nSxYP9cDXxarGcwltX4OmL1CpGmcp5fT0dGMZCoCHh0e1+nWAn3/+GV9fXyZO\nnMj69esb5dqtwbFjx7h69SoTJkygW7du+Pj4sHXr1irHzJkzh6CgIIqKiggPD2fy5Mk1nuvkyZO8\n9957fP3119jb21fb7+Liwvz58/n73//eJLG0NmFhYS3dhCYl4mu9EmOz+PTdUD59N5TE2Kwaj2nL\n8d3JrbHpdXrMr/cgqkwUTHvsPoY/2APPbo5VEn8w3Bj06N2ROYsG8dQL96O8KbnRavSEbIvmh0/D\nWb/yd37+4QxlpRrKSjXsCY66bXv0Oj2/7TjPsQNJSAqJ8TP78MKqB1ny+pi7epLQnr87EPHd6sOD\nyRSpdaivJ/5z+rqwYbpPtcT/VkO9bNn6uD9bH/dvtDruUd3s2fFkX4If73vbc94pPnOVgnE9HFg7\npQcdTG/8/VmYKPh4as9WnfiL382Ga5zsvYHqWnM+ffp0pk+fbpx5KD4+vsbjFi9ejKen4Q7b1tYW\nf3//KvXxN5sw05+Q7dGGn+9ytcbE2Kwq56ivTZs2MXr0aKytrQGYNm0aQUFBPPvss4Dh8xkyZAi5\nubmsXbuW8ePHY25efX7d3Nxc5s+fz1tvvVXrGgxLly5l4MCBnD9//o5tKywsJCkpyTgwqvKXsq28\njoqKalXtEfG1XHyJsVl8/lEQAM8um0s3X5cma//9w+7n1y2RJCRFAsB2iSWvj7nnvr+bX58JTyYy\n6jSWHUx5Z90zmJqp6vz+qfP6E7ItiovJ0bh72uHTvR/ZGcVERJ5C1st4ufcGIP7iOd58MYEpUx/E\nx78T0bGGp7mDBw3lf5vPsX/fAZQqiedffoxuvZru+xev289rvV4mzboHJRU6ihIjAHDzHcjCQe6t\non2N8frlkf6sO5xCfsJZJvXtiELq16rad+vrSq2lPU0ZX1RUFIWFhvUaUlJSWLRoEY2hzlN9NqVj\nx46xcuVKQkJCAPj73/+OQqGoNuj3Zt26dePEiRM4OjpW2d7WpvosKyujV69eyLJsLG1Sq9UUFRVx\n8OBBPvvsM9zd3Xnttdf4xz/+wYcffsgvv/zC0KFDq9Tr6/V6Zs2ahaOjI//5z3+qXScszFDzHx1t\nuEn5xz/+wblz5ygoKLjtuAFovZ+bINTXJ+/sQ12mBcDCyoQlr9etbjIhJpOQ4CgkSWLirNrLStTl\nGqJPpxNxPIX8nBuD/UxMlSx9a1yTzl7TmhXml/HNR2FoNTpmPDmAbr0aZ+pMrUZHxIlUju5LQKeT\nkQCt9sbsJHYOFlwrrkCn06PXy5hbmPDInwfg5ln9qagg3CqloJwPDyYTn234WzZVSliYKHixHlNl\nCkJjavapPptSQEAACQkJXL58GTc3NzZv3mwc8FopMTERb29vJEnizBlDb86tiX9btHv3blQqFYcO\nHTJO7ynLMgsWLCAoKMj4GuDpp59m2LBhDB06tNp5PvjgA65cucL3339fp+suXryYAQMGIMuymO1H\nuCfobkoKy8u05GWX4ODcodb35GQW88tPEcZa9Z9/OEPPPq64e9nh5mVPcUEZv+04j14v06mzHenJ\n+WgqDDPIWFiaUKHWotPJaCp0BP/3FBNn+dPB5u5WxWyrZFkm9JcYtBodPft0bLTEH0BloiTg/i4E\n3N8FMCT+yQk5xEVd5WJMFgV5N6akliSY9/RgHF1q/84FQS/L7IjO5ptTV6jQyThZmbD8AU8Geti0\ndNMEoVHcdc3/qlWrCA0NbZRGqFQqNmzYwPjx4+nduzdz5szB19eXjRs3snHjRgC2bduGv78/9913\nHy+88IIxMW7rgoKCeOyxx3B3d8fZ2RlnZ2dcXFxYtGgRwcHB6PV6Y3JuZ2fHAw88UON51q1bR0pK\nCr6+vnh6elb5r3L8xM1JvrW1Nc8//zwFBQVNH2QLuvUxWnsj4qs7B6cbNayyXub7T8OJOXulxmN1\nWj1HQy/y3YajVQapyjLER2Ww/39x/PBpODt/jKCsVIO6XMvlhBw0FTo8vR2Y+qf+PPu30fz1nfFM\nf2IAFpYmJF/M5dv1R6rU/7fn768ytgvRmSTFZWNqpmLMFN87vKthVCoF3XxdmPxoPxa/PgbTmxZE\nMrMwadTEvz1/d9B+4wtPLmT2D1GMe/s7wpMLq+2b+X0kk7+OYOPxdCp0Mg/1cOA/M33bXOLfXr8/\naN+xQfPEd9c9/3/88Qfff/89rq6ujdLQiRMnVlnECgw93ZVeeeWVRltToDW5dWBvpcrxDbXZvXu3\n8eecnJxajgR3d3djfXGlpUuXsnTp0jq2VBDaLlkvG3uB5y8bTvj+ROIir7J7ayQpSbmMfbg3JtcH\nvV1NLSBkWzS5WYYZMLr0cCIzvRAkiWFjuqFQKkhPzudKcgEFeTdKe1QqBY8vGYZTx6oJZndfF1yX\n3s+e4CiSL+ay4/szdO3pREZaIZdSz9PJsWedxhq15Aq4d0tdrmH//wxTao4Y37NZn3qYmCiZ/Gjf\nBo3HEuouJD6Xz8PTkCRYPsKTB7q2ztKqfx4yDNwtqdDxbugl+rtZU6zWUlKhI71QbVxuQgJWPugt\nynuEdqnBNf9paWl4eHg0VnsarK3V/Ld24nMT2oPsjGK+XX8Eaztznn5lFLIsE3Uqjf2/xKLV6rG2\nNTeU6Gj1xppxO0dLxs/oQ2dvh9ue9/yZdPb/LxaF4s7zz8t6mdNHL3No7wX0uhv/21WZKBh4fxdM\nTJQU5JUSH5UBgN8AdxxdOqDX6dHpZI6GXkSrMZQUmVmoeP7NcY3x0TSp33ee59zxVNw87Zj3f4Pv\n2TEP7ZEsyyTllXE0uZDw5EIu5pZV2T+uhwOjve0Z4G5tnP++pV3IKWXpznhus8huFQ2dk18QmkKL\n1PynpqaSnp7OkCFDjNtaU+IvCIJQkysphvI2d087wFAC1zewM5062/HLpgjysq9VOX7QiK4MHdu9\n2hSUt/Ib4I7fAPc6tUFSSAQM70pnb0d++PQold0uWo2e49fnnb9ZxLGU255LXabluw1H8R/ojm9/\nN8wtWt8iPFdS8jl3IhWFQuLB6X4i8W8HjiYX8OHBZDQ6GUsTJQXl2tseuy8hj30Jediaq+jpZEFM\nVikqBS0yWFanl9kSmcl3p6+il0EhgalSwSQfR+5zt6aDmRJrMxUXsq+x8bihFFCsZiu0Z3VK/lNS\nUpg3bx4REYZprq5du8bWrVvZu3cvX375ZZM2UBAaIiwszDiNVnsk4qubKyn5ALhdT/4rObta8/ji\noXz63n7jgGAzCxUjJvg0+Jq309HNhilz+7N3ezSXUqN5aMJY7Bws0Wp0nD5y2fjkQalS0GeAO0ql\nAoVSojC/jEsXskE23EhkXSki9EoRB/bE4+phS3ZGMco6PIFoapXlSfEXz+Hp1puAEV1wdrVusfY0\nlXvpby/3mobfEnL59nryDFCh0+JgoWKIly1DPW2p0OlZfyQNgD8PdCW/TMsfifmkFao5mVZsPO/7\n+y+x7uGedHe0aNBkE5Ur1oIhUb/dDUVGsZo1B5KJzjTc4M/wc2ZBoBsnjx1l+NB+VY71tDNnXI+2\nP5EItO/fz/YcGzRPfHVK/v/v//6PSZMmcfjwYeMMOw899BDLly9v0sYJgiA0hsqe/5qmeDQ1UzF1\nXn/2bItCkmDCI/7VjmlsPv6u+Pi7EhZmzvDhN67n5mlXp3VHtBodF2OziDqVRnJiLumX84379gRH\n8dybDX8sfLcqV02XZcMMO0PHdG+xtgj1V5lU5yUk8oS5N0l5ZZxILapWKtPBVMlPf+qD4qYE/tY6\n/8fvcyUxt4xlv1yg4nqpm1ons+TneDxszRjlbY+dhYrvzxhK3WpL4m+19lAyxWpDGdwHBy7zzkPe\nuNua42Ch4lhKEesOJ1Ohk9HpZSp0Mg6WKl4a4UVAGxu4KwhNoU41/w4ODuTk5KBQKLC3tyc/3/AP\njUgmYdQAACAASURBVK2trXHxgdZC1Pw3LvG5CW1d6bUKPntvPyoTBc+/NQ6lskELm7c6hjn0D6PV\nGJ4YKBQSf33noQZP4Xs3A4xlWebjlb8b22JmruL5t1r/2AThhlnfR1J0PamupJRgWBc7utibsyvG\nMLlEfRL1yhsKnV6md0dL4rPLKKyhZMjGXEnw47XX2au1erZGZfHd6as17rcwUaDW6qvcrAzvYsuy\n4Z7YmLeK2c0F4a41a82/q6srCQkJ+PjceBQeExODl5dXgxsgCILQlK5e7/V3dbdtd4k/gK29BQ/P\n7W/scdfrZRLOZ9Kzj2uDzrsnOJLy64ui/S/oHM+/PQ5FLXX7sl5m/6+xxsTf1EzJpNliwGRbIcsy\nB5IKjL3pYKiNXxjoxrgeDthfH1fyxIBO9T73UC9btnrdeMKl08tEXCnmQFI+ey/kGbcXlev49Gga\n0/2ccLetOjOULMsculTAlyeukFlSAYCJQkKpkPBxtqBCJ5NWqK7SfjDcDLw5tqtYz0YQblKn5P+l\nl15iypQp/O1vf0Or1bJp0ybef//9WlfgFYTWQNQGtm2NEZ+x5MfL7g5HNr/G+v66+bqw5I2xnD2W\nQuiuGA7tvUC3Xi4oVfW/2VGXazl2INGY+ANoNDqC/n2cSbP7YudoWe09er3MbzuiiT6djlIp8fC8\n/mTkJbSJ6UjvVn2/u/0X81h/JBWABQGdmOTrjKqVDIJOyi3js/A0IjMM09sqJSi/HMn7i6YxtAn+\nbpQKiYEeNgz0sGFQZxv+eSiFCp2MVi+zMyabXTHZDOpsg4+zJTtjstHpwcFSRUqBGgBvB3OeHeJB\nP7fqY0mKyrXsvZDLj2czUCkklo/wqjHxF//vbLvac2zQimr+FyxYgKOjI1988QWdO3fm22+/5Z13\n3rnjPPSCIAgtLf36YF/3Gur925u+gR6cDU8mL/saEcdTGHh95du6kPUy0WfTObz3AqXXe1aVKoVh\nwLHCcBP17SdHGDWpF30DPYwJlU6nZ/eWSOKjMlCZKJj++AC69HAiIyyhKUJs1SrLW2RkHr/PFROl\ngtjMa8RkXSOtUG08bkN4Ol8cv4K7rRleduYoJDiRWoRCknh5pGejJNx1GRBbrNby3ekMfonN/n/2\nzjysirL945+Zs7JvgiIIuKAB4r6v5ZJL21tm669Ne7PSSivrLVvUrMxsz8qyrLTUynLJJcMlxdw3\nUFAQZFHZdzjAWWZ+fxw5iCCCLALO57q4rjNzZp557plzDvfzPN/7vpFkcNGrmdTHmzFdPPh3d1GD\nOP6XMrS9my1WIC7LwJoTGWyLy2Ffcj77kvNtxxUaLbjo1Tzax5uxnT0umz7UWa9mYrfWTOzWusH7\nrqDQXKmR5n/fvn3079+/0v79+/fTr1+/BunY1aJo/usX5b4pNGcsFonP5m7FbLLw9KsjsHfUXusu\nNThx0en8sewwejsNj784rNo0oGW6fkmSsbPX2AqhebdzYcRtwXj7Wh3GYoORreuiOBlhDcxs38WT\nMXeGoLfTsH7FUeJOZqDVqbjr4d74tr98XYSWzoRlEZVkJ1UhCHC5/7wCMKy9K6HejoS2cSSloJSP\ndllXDGqiszdZJE5nFfPyxtOUXMgcpRYFBvu7oFOL6NQiWQYTh87mY7TIyFjlPbcFefJw7zY46a69\nLj632MTGk9bsQmW3SacSWPFAVxybQP8UFK4Vjar5HzVqFAUFBZX2jxkzxhb8q3B1tGvXzjaDVlRU\nhF6vR6Wy5hb/6KOPGDVqFLNmzWLr1q0UFRXRpk0bHnzwQZ577jkAPDw8OHToEAEBAVW2X1hYSFBQ\nEAMHDuSXX35pFJsUFJoKGakFmE0W3DzsrwvHH6DDDZ606+BOcnw2e7fHceP4Gy57bFmcAFjlPo7O\nOoaN7UJQd+8KUgk7ey233teDTkEphK2L4sypDL6avwNRFJAkGb2dhgmP9bENFq43jBaJ1ZHpFRx/\nQbA68cFeDgR5OZBZZOSTC6kwnx/qR4+2jiTnlpKYW8yn4cmUXsiGIwP/nMnlnzNWuZpwYR/Au9sT\neKK/Dw5aFQ5akTPZxaw6lo4ky/TxcSa3xMzJjCJbZp0yzJJsa+9SVKLAoju60MHDrl7vSV1wtdPw\nQM82+LvpWbgzCVGAF4f5K46/gkI9Ue03SZIkyhYGJEmq8F5cXBwaTdMrLNPcSE5Otr3u0aMHn376\nKcOGDbPtmzp1KiUlJezbtw9nZ2diY2OJjo6ucfvr16/Hx8eH3bt3k56ejpdXy9XgVoWiDWze1NW+\n84lNV+8PDfP8BEHgxnFdWPbFHo7sSaTHAD9c3Svr9GVJxmQsd1bVGpFJM4aircbBuqG7Nz4Bbnyz\n8B8ki4x0IaXKvY/3w9O7ov76evls7kvK48u95zifb5X1aEQBvUbkxWGXFrNyYMglqTA7e9rT2dMe\nR63aJtF5qFcbVKJAZEohkamFZBSZbMeXmCVb3MCl7Ewod+7buejwdNASnVGEKMAdwZ4EuNlRapEo\nNUss2X/etirgqFVV6fg3hec3OMCVwQEN891tCvY1JC3ZvpZsGzQBzb9ara7yNYAoisyaNathetWI\nHDq9k682zQHgyXFv0rvTsCuc0TBtXI6jR48ya9YsnJ2tuYkDAwMJDAys8fkrV67koYceIiwsjF9+\n+YVp06bVW98UFJo6tmDfdk3T+W8oWvu4ENyjLVFHzrNzcwy3P9CjwvuSJPP3mhO2gmJanZpb7ulW\nreNfhpOLHp1ObVsx0NtpKjn+LZkyLX3mqThCMlsRk2mVSvm56nl6oA+9fGqfR/7SbDgAt9zQCoBN\nJ7NYvO8skgy9fJxw0asxGC0UmSwcOVdA2SS/TiXw6oj2BLd2wOUKKS09HbQV4gEUFBSuL6rV/Cck\nJAAwbNgwdu3aZVsFEAQBT09P7O0rzyZda2qr+f/vZyMpKK56OfRqcLZ34+tpYVd1blUz/8899xwH\nDhxg2rRp9O/fn44dO1Y4pzrZT3JyMr169eLo0aOEhYWxZMkSdu3aVas+KZp/hebM1wt2kJ9bwiPP\nDm6RVWaroyCvhG8/2InZLPHAk/1tBc4ki8Sm1ZFEH02pEKBbG+Ki02tUjKwlcmkefHuNyEO9vLkj\npPGz99S0yq2CgkLLoFE0/2UOZVJSUp0vpHB1vPfee3z55ZcsWbKEGTNm0K5dO+bPn8+oUVcunLNq\n1Sp69eqFj48Pt912GzNnziQyMpLQ0IavYKqgcK0pzC8hP7cErU6Nh5fjte5Oo+PkoqfPkAD27ohn\n+4aTPPDkACSLzJ+rjhF7Ig2N1hqg265D7QN0OwZ5MXXWiAboddPmVEYRhRdJpTQqgaUTg3GzvzYS\n2KpWDBQUFBSuRI2jZ9auXcs///xDVlYWkiTZgsF+/PHHButcY/DkuDdZvHkuAFPGvnHVsp+L26hP\n9Ho9M2bMYMaMGRQUFPDJJ58wadIkIiMjcXGpfpZn1apVPPbYY4C1SvPgwYNZsWLFdeX8K9rA5k1d\n7CuT/Hi3c6m2ONWVaMjZ1YZ+fv2GdyDiwFlSkvOIOnqeUxGpxJ/KQKdXM+HRPrT1azg5VEv6bBrN\nEsuOpPJrRBqSbM2OU5oQwZzH/3PNHP+GpiU9v6pQ7Gu+tGTboHHsq1EFmDlz5jBlyhQkSeKXX36h\nVatW/PXXX7i6Nn8dbe9Ow/h6WhhfTwu7aq1+fbRRE5ycnJg+fTpFRUUkJiZWe+y+ffuIj4/ngw8+\nICgoiKCgIA4ePMjq1auxWK6cik5BoblzrkzvX0cH94OdieSVmMkrMfPBzuq/d00NrU5N567WfOeb\nfo0k/lQGdvYa7pnct0Ed/8vxb2IuE5ZFcNePEfwVk4XRXJ5IYk9iHhOXRzJxeSR7EvMavC81vV50\nehFPrznFqmNpANwd6sXaR7rz1piOisxGQUGhWVKjPP9+fn5s2LCB0NBQXF1dyc3NZf/+/bz11lus\nX7++MfpZY5pznv+qNP/vv/8+o0aNIiQkBEmSWLRoEV988QWRkZHY29vj4eHBv//+i7+/v+0cjUbD\niy++SHJyMl9++aVtf3FxMUOGDOGbb75hzJgxNepTc7hvCtcXNZ2J/+nLPaQk53H3Y31qrWkvo6DU\nzD3LI7k4c2KwlwO9fZ3o4+tMtsHEx+FV52BvKnrsRfO22oJzEeDRZwfTqnXDxT/sSczjg52JmCWZ\nwQGu6NQiqQWlpBYYKxS6KsNOI+KsU5NZZKwQvPpon7a426txs9OQlFvCj4dSEAR4fuilWXSujotz\n8qtFgbFdPGhlr8HDQUN6oZE/jmdgtEiYLuTCb+ei48Xh/gR5OdT52goKCgpXQ6Pm+c/Ly7NJRbRa\nLUajkX79+vHPP//UuQMK1SOKItOmTePs2bOo1Wq6du3KypUrKwRbDxo0yPZaEATmz5/P2rVr+eqr\nr/D09KzQ3r333svKlStr7PwrKDQ13v8n0aa7fnd7AgtvCaRTKzvEi/LSm00W0s/ng2CV/VwNhaVm\nXtkUh0W25mwXBZAliEq3Vmxddji1wvHztp1hWHtXJBlkWWZ3Qh6mC6kw39uRwAe3BtLORY9WXaMF\n1wZBr9c0qOMPsHBnos2p/js2+7LHCVhzzBebJIpNxgrvlVpkFu87V+V587ae4flhfvT1dcb5Cllt\nqqLEXDknv1mS+TM687Ln3NvNi4d6eV/TZ6egoKBQX9Ro5r9nz54sX76ckJAQbrrpJv7zn//g5ubG\nG2+8YcsI1FRozjP/TZHmft8UbWDz5lL70guNPLTyBJf+aLno1fTyccJVryLsdA7OxUZCEjJp1dqR\nR5+r/f0pLDXzv01xxGQaaOOkZeEtgXg5aikyWohIKeTg2XwOnSuw5XavKaIAbZx0OOlUJGQXkxd3\njAljbyLIywG9RiQhu5g/TmQiADOGtmPoJXnhr4bGzMyTbTDxwIrjSDLkxx2lVeeeTO7bljZOOto4\naUnKLeHzf8sLXQ3wc8ZgksgrMbM7IZefj6QiAYP8XXDSqckxmMgqNhGVVoR0yUMXBQhu7YC3k449\niXmoxOpXBSRZJiw2m+8PppB5YSVELQro1AK33uCJu72abIOJTIOJHfE5WC4okhy1Kn5/uFul9q63\n715LQ7Gv+dKSbYPq7WvUmf958+aRmWmdFZk/fz4PPPAAhYWFfPHFF3XuQBmbN29m+vTpWCwWHn/8\ncV5++eUK7//0008sWLAAWZZxcnLiyy+/pFu3yj/ICgoKLZMio4VZf8UhY3XatCqBIC8HzuaVklZo\nZHtcebVx9/wS4Or0/oWlZl7ZXNnxB3DQqhjo72JzMDeezOTrfeeQgbGd3Qls5WBbJTidWcyGk5lY\nZOjgrqeg1ML5/NIKAwajRWLDySw2nMyq1I+3tibQxTOdIC8HbvC0p8QssfTgeUCoQmKUywc7rRKj\nFy4pLtVYmXkyi4y8tPG0LSDWQSMya0T7Cn1p727H8A4VBzTWarUqJnZrzcRuratsu0xCJckyQwJc\nSC0wEpFSyPHUIo6nFtmOe2vrGcZ0dsfbWUdbJx0ZRUZ+OpKKRZJx0qtJLbCuMHTysOOJ/j70aFv1\nKsiw9m5KHnwFBYUWS41m/hsai8VCly5dCAsLw8fHh759+7JixQqCgoJsx+zZs4fg4GBcXFzYvHkz\ns2fPZu/evZXaUmb+6xflvik0BUwWidf+iuPI+UL8XfV8dFsgjhcKUsmyzNm8Ug6ezeeb/ecxSzLd\nU3NpbSglP9CTCWM6083b0ZahrDrKHP9TGZUd//rAaJE4m1vKjD9jKDZdKLClEhjW3pUSs8TepHzM\nl05xV4FaFAhw01NktFBktFTIO69VCax+qBu6RpSopBcaeWljLOfzjXRwt2P+uI642jVsFpwio4WD\nZ/NZsCPRJq+6Eq0cNEzq05YRndwqyMQUFBQUmgMNPvMfHx9fowY6dOhQ507s37+fTp062eoK3Hff\nfaxdu7aC8z9w4EDb6/79+3P27Nk6X1dBQaHpI8syn+5O5sj5Qtzs1Lw1poPN8QdrnEs7Vz3tXPW0\ncdLxwT8JuJZaZR0RxRJ7N56ma2sHevo4sS4qg6pnzq1BqkVGCxYZWjtqeX98/Tr+AFqVSAcPO/53\nY0CVwcAXBwlPHeiLs17FyXQD0elF7E/Ot8mdzJLM6aziKq9htMhMXXOKl2/0J7BV9YUY6yMoObWg\nlJkbTpNWaCSwlR3vju10VVr82uKgVTG8gxtalWhbFbg9qBXOejUpBUZS8ks5cDbfJhfSq0WWTgxu\n1EGRgoKCQlPksr/QnTp1uuLJgiDUS9rIc+fO0a5dO9u2r68v+/btu+zx3377LePHj6/zdRVaPtez\nNrAlEB4eToJDJ/6KyUanFnnr5o60cdJd9viB/i4suTWQJQtT0NtpmNDfhzVRmRxPK+J4Wrk85O1t\nZxjXxQNBEBAE2BCdidFSVsEcFt4SSGun+nX8L+3nr/6hhIeHV3C4qyra1MvHGbBKexbuTEKSZO7u\n1pq+vs44aEXstSqOpxby6e6zWCQZvVogKbeE59bF8FCvNtzTrTWqKuocyLLMgn+sAx6wBizPGOJH\n97aOeDrUzPbz+aXM3BBLRpGJGzzteWdsR9vArLE+m9UVurp0cFOfjv/18N1T7Gu+tGT7WrJt0Dj2\nXdb5l6Ty/MvfffcdYWFhzJkzBz8/P5KSkpgzZ069LD0ANVqOL2P79u1899137N69+7LHPP300/j5\nWXWaLi4uhIaG1ssKxfVIbm4u8fHxtg9ieHg4QLPZjoyMbFL9ud7sW7z6L1YeTcUtsCczh/tjSa5d\nf1dv28ue4lhcOvbg1ZsCSD91mPRT1Z+feDoT0OPj74pncTxP+Upkundm6YEU8uKOAuDcsQdrozLJ\nv2gbrEGq9hqR1k49G+X+1Ob5DfR3ZUZ7a+DukJ7dK7w/dMgQhrZ3Izw8HKNFIlrTnrVRmXyyahPr\ntuj58Km78HbSER4eTn6JmQLPIP6KySIl+pDNfpNF5rXv1gIQ1LM/3k5a/v13N6IAz98/ns6tHNi9\nO5wSswQ+IWw6lU3GqcPIwICBg3l7bEeO7N/ToPerttuW5EieC2g6/VG2lW1lu+7bZTSV/jSkfZGR\nkeTlWeuQJCUl8fjjj1Mf1Ejz7+vrS0xMTIX0kgaDgc6dO9eL/Gbv3r3Mnj2bzZs3A/Duu+8iimKl\noN+IiAjuuusuNm/efNmVictp/tPS0nBycqpgg0L1GAwGCgoKaN266iA8BYUrcdePEba0nCoRZgzx\nY2h7V+w0qmrP25OYx4J/EigyWichnhrgw51da5alJmxdFEf3JjH05kD639jRtv+f+Bw+2pWELMOI\nTm74u9khyTKSDAnZxew8k4tWJVQKmG2uHDybz8KdiWQbzADo1CL+rjpOZxXbpDCOWhGTRUatEhkS\n4EJusZnI1EIMJqmaliuiEgV+fyj0is9UQUFBQaFuNGq2H0mSSEhIIDg42LYvMTGx3irF9unTh9jY\nWBISEmjbti2rVq1ixYoVFY5JSkrirrvuYvny5TWSJF2Kl5cX6enp5Obm1kufrwdUKhVeXg2XFlCh\n5WO5KBDTIsHCnUks2nOW4e3d8HHR8ltkOiDw3GBf2jrrOZNTTEJOCasj022Br1qVUGPHH+C8rbJv\nxawywzu4Vco0czEvDve/7HvNkT6+znx9VxD3/XwcsyRTapaIySxGJcBgfxfGdPGgr69zJUmQRZKJ\nyTTw8sbT1ll+rNl7Orjb4aBVYa9VcTA53xZk66gVFcdfQUFBoRlRI+d/xowZjBgxgkmTJtGuXTuS\nkpL4/vvvmT59ev10Qq3m888/Z8yYMVgsFiZPnkxQUBCLFy8GYMqUKcydO5ecnByeeuopwFrFdv/+\n/TW+hiAIVz2DHR7ecvVlLdk2UOy71nTzdmRfcj46tcjYzu6czirmRFoRm2MqpracuzWhwrZnUQld\nM/JJPBeFpd/gGl/vZESKtbgXYCgyXuHoa09DPz9nvRoHrUheiXWiRq8W+eHeYNyqycSjEq0pVF+5\nqeqgZKispa+Kpv7ZrCuKfc0bxb7mS0u2DRrHvho5/zNnziQ0NJRffvmFI0eO4O3tzdKlSxk7dmy9\ndWTcuHGMGzeuwr4pU6bYXi9ZsoQlS5bU2/UUFBQanrKZ49dHBtDvQqXd5NwStsRk8UtEeoViXT7O\nOtq76/F30ZGx9jhIMhpJpktaXo2v99eFYlZglf90CW1TL3Y0Z54f6l/BUa/O8b+Y6gJpq3tPQeF6\nI31LOJHT3wEg9ONX8bq55TqmCi2DJpHnvz65nOZfQUGh8Zm4PJK8EjPL7wuplDZzd4I1e40ATB/a\njmHt3SgpNrHupyMkxWdXOHb8xG4E97x8vQmTycLWdVEcP3TOts/OQdsoxa0UFBSub7YGj8OUbZ2k\n0Lg6M+LEBgSVIoVTqH8aVfOvoKCgUFtyik1os4q4KTOfXz/exdgJoXQMKtfuDw5wZXBAeQXevJxi\nfv/hEFnphWj1agTAYpYwmyU2/hpBRloBQ2/ujHiJRj0328C6n4+Sfj4fURRQa0RUahVj7+raWKYq\nKDQr0jbvJPK5txFEgdBPXlNmquuIxVBie23KzSes02icugbi3K0Lgihy7pdNCCqVsiqg0GRQqp3U\ngEvTL7UkWrJtoNh3LUnILiEkIw+NRaLYYGLjrxFcbqEx9VweP3+1l6z0Qtw9HXjkmUE888Yo+txs\nz6jbgxFEgQM7z7Bm2WFKS8y28+JOprPs839JP5+Pq7s9/zd1IM++OZqps0ZUGGg0VZry86srLdk2\naBr2pW8JJ6zLGMICR5PwzSqMWbm271j6lnC2Bo9na/B4UjfsIOdgJPGfL+fQ/73IkcdewZxXgCkn\nn2NPvYlcRfKOquxL27yTsMDR/N1xFDHvfUPOgUgKTydizMolbdNO2/XSt1z7e3Ml6uv5GRLPIZmt\nv0mCRoPGwxVLcQm5ByJJ+vY3Er/5xXqvs3M5+sRrZO7Yh2Q01cu1q6MpfD4bipZsGzSOfcrMv4KC\nQoOQkFOMeJGvX1pi5tsPdnFDd2+Cunvj4eUIWB349SuOYTZZaNfBnTse7In+Il16jwF+uHs6sO7n\no8SfymDpx7swmyyYzRLmCykpOwZ5Me7u0ArnKSi0dCKemYs5rxCAk69/wsnXP0HUadG1aUXJuTRk\ns9WpPzr51cu2YSkqZt8dT9H1w1dx7BxQ5TGyLJO5Yx9HJ8+yDRTiP1pK/EdLqzz+2FOzGX5gNVr3\n5p8y90qcmrsIzBba3j2Wbp+/AYAxK5f8yFPkHTvJ6Q++Q77g7EslRg7eNwO1kwOtRg5E39aLcys2\ngCAoqwIKjUqNNP8LFy7kxRdfrLT/ww8/5Pnnn2+Qjl0tiuZfQaFp8NGuJAr+Pom9WUJUCWi0KkqL\ny2ftXd3tKMgvxXIhKDi4Z1vG3NkV1WWqsOZmGfhj2WGy0gsr7B86pjP9hrZHqKKKrYJCS6U0I5vt\n3W+jrGiDoBJROTpgziuo8niHwADcB/bArX93LKVGYt/+0joDrRIx5xYgaDV0ev4x2k/9P0RN+bxg\nzsFIYt7+ipw9Ryq0J2jUOId2wZSTZ/3LrXhdQa2i1fB+eN85Gq+xQ1E7OtTzHbj2ZO0+zIEJ01DZ\n6Rn67yr03p6VjknfEs7xGe8gmS20Gt6PwtgECqPjKh2ncrBn6L8r0bdu1RhdV2im1Jfmv0bOv5OT\nEwUFlX9Q3NzcyMnJqXMn6hPF+VdQaBq8uCKCNpHnUevUTHv1JkSVSHJ8FtHHUog5noaxtHwgoNao\neG72qCtW+y4tMbPo7a1IFuvPlk6v5pk3RjWoHQoKTQ3JaOLAPc+Ss/cYglqF2sWJ0I+sM8fmIgMl\nKRmkrd9G/KKfEASB4HdfpO3dY6psy5RXwKm3FnF2+ToA7Py8MeUVAAIOHXzJOxINgMbVCa8xQ0kP\n+xcB6PpRxZnqtE07Of7Cu0hGE/YBPhRGx9tWCQSNGgQBUa3C5/7b8BjSC42LMxpXJ3KPnSTmrUVA\n85r9li0W/h39GAVRpwl8+b90nPFYjc81JJwlbfMuYuZ9YVudAUAQcO0dQutxw1E5ORA7/2ugdhmE\nUjfs4PiMdxDUKkI/ntVs7qdCzWgU53/btm3Issxtt93Gn3/+WeG9uLg45s2bR2JiYp07UZ80hPPf\nknPKtmTbQLHvWiHJMi++v4u2uQaC+/oy/s6Kwbcmk4Uv39mGsdT6j+9ymXmqsi82Ko3Nv0UiiALj\nLgkibm401edXH7Rk2+Da2hf1ygckLV2Nrk0rBm1Zis7Lo85tZoUf5Pjz8ylOOm+9hlREsOiAyk6P\n/5R7af/UA2hcnGrcXmlGNml/bidlTRg5+47V6By1swMjT2254iRAfVDX55f04xqiXlqA3rcNQ3et\nQGWnq3Ub1hShbyMZTTh08qcwOg6ptHJ9Eo27KyOjNlbblixJpKwNI2LqXJAkoqQiurm1YdSpv2rd\nr6bO9fzb0ijZfiZNmoQgCJSWljJ58mTb/rKCWZ999lmdO6CgoNDySMktxjO/GIA+/SsXgdJoVNxy\nT3c2X8jLX5vMPIHBrQl84+oK9ikoNHfO/vwnSUtXI2g19Pzu3Xpx/AE8hvRh8PZlbAsZj1RSCoCo\n1zFs369XdQ2dpzt+j03A77EJbL1hLKZca/E9Uael1Y39MOUWYMrNpzAmAS7MQZrzi9h7yxN0enEy\nrW7qX+0goGyGmwsZi1qPGVp7o68SU16BbVa+y+tTr8rxB/C6eQgjozbZts1FBjK37SVt805Sft9C\nWSEUU04ese99g9+kCeg83Su0IcsyWf/sJ+btL8mPjKnwnjmvgJNzPidw5uOo7PVX1ceWQNkgC0mm\n6yezGvWzUnVfrn1NiBrJfh566CGWLVvWGP2pM4rsR0Hh2rN+axyntsZictDxyqybrnV3FBSaNOlb\nwomYNtfmnLS55cYqj8s9fIJ9/3ka2Wii64ev4vvArQ3Sl8hn51mDUD+pH9lIme4dKsuF0reEWITO\n3QAAIABJREFUEznjHaTiUgSViLmgCADXPl3p9OJkPIb3QxAEJJOZ/IiTZO0+TPbuQ2T9c6D8AoKA\nx/C+uPQIwqVHkFXKNGcR0DAO1sk3PyVh8UrcBnSn3x9fNMhKReqGHRyf/jaW4hKbNEjUa/G55xac\nugYSO/9rZLMZvU9rWwyBvq0XXuOGk/LH31gMxdZVBFnGvr0vXT94BfdBPeu9n82BrUFjMeVYB58I\nAt53jsZjSG/cB/fCzq9to6w02fpyUU0IrYcrI05Uv6JzKY2q+ZdlucLN2b59O6IoMnz48Dp3oL5R\nnH8FgEOnd/LFhjewyBZu7fsQfQNvxNneDSc7Vzbv3MTK/QsBuK/fi9x60+3XuLctj88+Cac0rRBt\nqDfP3t/9WndHQaHJIssyYR1HlueKFwTaP/0Avv93Bw7tfW3HlaZn8e/Nj1Gamonfo3cRPL9yEo7m\njrmomOTvfyd+0U+YsnMBa+AwgoAgilVKYq6E2tmREVEbEdX1k9ywKC6J8OEPIlskBv71HS7dutRL\nu5dDlmVy90cQv+gnMi6TQlXt4kTHZx/Gb9LdFVYh8o5EETnjHQpPxgPWVReVvV29DeqaA4bEc+wc\neC9IUpXvazxcsRQaEDUaQhe90WCrAgXRcZz9eT2JS361rXQJWg0jozejdrCrcTuN6vwPGzaMd999\nl8GDB/Pee+/x4YcfolKpmDp1KrNmzapzJ+oTRfNfO1qibXlF2Uz76hZMFiPZicW4+1/yxZKBC2NZ\nteTAhLYfobPToNOrMRQaiT+ZgagSGD+xW5PXkzfF55ebbWDJwp1YBAi5rye3hl69RKcp2leftGT7\nWrJtUD/2SaVGjr/4Hud/3VTl++5DeuPc7QbOrfwTc34hstmCW//u9P31U0Rtw6a1vZbPz1xkIOm7\n34h5Z7HNUQKw7+iHx+BeuA/qhWQycWq2VXocOOspNM6O5B2NJu9oNNm7D9kkMwDaVm60uWMk3neO\nxrV3VwRBuGr7Dj00k4y/d+P7wG10/fCVOttaGwpjEjjz5c+cW1Eegyna6bjpyFo0rs4Vji2zTzKa\niPvkB+I++M72ntrFqVnHAtT02eUfj+HQAy9Qmp6FoFKhdnak08zHQZbJ3n2I7H8PV8hSpbLXMzp+\nW537Z5P2yDJt7hhJ/oXPZRmCSoUsWUAG525d6PXDggqZoq655r+MEydOMGDAAAC+/vprtm3bhrOz\nM4MGDWpyzr/C9YvZYmLLkV/5bfdiTJbyGSKVqKatuz95hmwKDLnIQvl/BRkLcSczKjdmgvUrj/Lc\nm6NrlEIyLjqdzasjASpVsr3eOH7oHABpDnpub+14jXujoNA0Kc3I5sjkV8ndH4Go1SDqtIhaDe2n\nPkhhTAIpa8PIDj9Edvih8pNEgR5L3m5wx/9ao3awp8MzD3PmixWYcqwSCY2bC8N2r6xwnM/EcRW2\n29xqlRimbd5plcyUmlA7O2JMyyTp299I+vY3tK3cMBcaOCmW0vmrBbWaAc/YvpeMv3ejcrQn8JUp\ndbSy9jh2DiD0o1dxG9Cd6FkfWWerP5lVyfG/GFGrIXDm4yQu+dWWBtacX0Du4ShcewU3Vtcbnazd\nhzny6MuYC4pwH9KbXkvno3YqTzfrP/luZIuFrcHjbLUyLIYSzq74E9/7r05OV5KaQX7EKY5OeQOp\n2LqSl/z974B1Bcr7ztH4PnAbzt26UBSbyKGHXiQ/4hR7xk6m1/fzcenZeM+jRjP/bm5uZGZmkpCQ\nwM0330xcXByyLOPk5ERhYeGVTm9UFNlPy6KmTnVEwl5+2LqQc1lnAAhofQOZeecRRRVTxr5B707D\nADh+OJnla5eTaL8GWTDj59ydJ4a9S0mJmdJiE7u2xNgKRwF0uMGTW+7pjk5f/Tj5s7lhtsqzdvYa\npr5W95F5c0SSZL5e8A+F+SUc8HZj6ZQ+2GtV17pbCgpNioLoOA49NJOSs6no23rR64f3cA6tKB8x\n5Rdy/re/iH79I7BYf5Oa+4xtbakuVqCmyLJMfsQpUn7fQsq6rZSmlE/2iHotw/b8WmV+/ktJWRPG\nsamzwSLR9p7xdPv0tVr35VpSFlthKShCMloHRX1WftwiBwCp67dxbOocZKOJNrePpNtnryPqtFUe\nW/YZs5SUYikqRlCp6PXjAjxHDqz2Gulbwol45i0kownHLu0pTcmgNC2z0nGCRk3ox7NoPf7GSoHh\nxuw8jkx+lZw9RxD1WkI/fg3v/1SfurpRZT+33nor7dq1IyUlhU6dOrFw4UJOnz7N6NGjOXPmTJ07\nUZ8ozn/L4vO3tlJSbK2OqFIJjPpPCB26eOLgqLPq+je+SampGLPFekxrV18eHvECvToOrRTEczYh\nh1+/3Y/FIhM6wp6lh2fgqHfhq6l/oVZZZ9LiotPZ/PtxJIuEJMmYjBbcPR248+FeuHlULlJTcmHA\ncGxfsm2fSi0yfc7oRg0iaiqciclg9feHMKhVxAZ5s+z+mmfxUVBoyZRJAWSTCcloQio14tIrhF7f\nz682m07aX7uIfHYegiAQ+ulr141WuyGQJYmtN4zFnF8+aSnqtfg9OoEOzzyE1sO10vHZuw9zduWf\npKzeYtuv8XBlZC0DNZsKksnMsafeJO3P7aidHem76uNGnXFuKMq+X1Kp1YkH8Jt0N0HzpiOIVReO\nvJSYd74i/tMfUdnp6ff755e9L7LFQljg6PI4nQuonR1xDu2MxsWJrF0HrbUWPqn+OysZTUS9+oGt\nzoZop0dlp79soHqjOv9ZWVksXLgQrVbLzJkzcXR0ZMOGDcTGxjJ9+vQ6d6I+UTT/taO2tsVFp7Np\ndSSyJDe4Jj45PptVS/ZXfkMA97YiWw1vYJFNtt33D5vG+D4PolGXj/DL7MvNNvDTF3soNpjoOcCP\nkbcHM/O7e0jOjGPmXR/ZVgYu5uKKsno7Dbfd3x3/Ttbqi7IsE3XkPDs2naK4yIgggEolYr5QrXbU\n7cH0GFA5xWV909Q+m+t+PkLM8TRi3Rxo3b0tc2/uWKf2mpp99U1Ltq8l2wa1t29r8HhbECuA952j\n6frhq1edJrKhaanPr2ym93hxLv1CQsk9YF1ZVjnY4zlqEFk7D4As4TGsH7mHjlNyLq1SG1eTpaWx\nqe75SSYzx558g7QNO5rlAKAq2y79fgX+7wk6PPdIrSbhZFkm8tl5nP91E1oPV/r/+XWFoHsAQ1IK\nkc/OJWdvee0KlaM9g7YsxT7Ap8YDjUuvm/jNL5x84xPAWmOju6dPlQPMRtP8m81mnn/+eRYvXoxe\nX54n9pZbbqnzxRWaF7Is8+eqY5iM1rRj61Yc5elXb0Knr1/9qSzLHAxPYOdf1pzFoiig1anoHOpN\ndnYOB86v43DhLiSh3PFXy/bc0ucR1OrKX7zSEhO//3CIYoOJgM6tuOmWGwAYHDyWlTsXsTt6c5XO\nv6uHPQ88OYCNvxwj7mQGvy49iEajQhQFHJ11ZKVbU9L5Brgx6o5gWrV2IvrYeTasimDbhmi82jrT\n1s+1UrstFUOhkdPR6QCcd7Kjv1vNMxgoKLR0pJLyWUKVvZ5uX8y+LlcHrzVeNw9hxImNaMPDGTBk\nCHkRp4id/zWZ2/aQujbMdlzquq0A6H3b4HPvePTensS+uxiwSpCaM6JGTfev5toGAAfunU7fXz7B\npUdQpWNT12/j+AvzkS0WOs96Gv9JE2p0DVtufVm+4ux3XZGMJixFBtu2ytGejtMfrXU7giDQ9cNX\nMGZmk7l9H4fun0H/9YvRebojyzLnVm4g+vWPsRQaULs4gSwhajR0/ehVHDq0u+r+C4JAwBP3cvr9\nJbZUt7LJfNXt1eiaNZn59/b2JikpCY2m6QcZKbKfhiEzrYCwtVGcTcipsN/JRc+4u0Px61h9EZia\naveNpWY2/RZJ7AnrbItXj2x2pX0LQN/Amzh4egf5BmsfHCw+lAjZCIgEGO7E174HfYe2J7SvL1qt\ndVwrWSR+//EQCbFZeHg58sCT/W2DlfTcczz79e3oNHoWTw1Dr63aWZUlmd1hsezdEV9hv72DluHj\nuxDco2Ke4G3rozm8JxFHZx0PTRuEg2PTnNmrbw6GJ7Bj40nM7g5sc3Xkfzf6M6KT+5VPVFBo4ST9\n8AdRL78PWB2T7l/MVuQ7TYycfcfYP2FaeU59nZbeP32A+6CeVzWb2xy4eAUAQUDt7EDIgpdQOzuS\ns+co2XuPkrs/osI5DoH+tB4/nNbjb8S5W5dKA1hDUgqZ2/cS/dpHNgdW0GgYsmMZDh3rfzXcXFDE\nkcmvWldsALWTA90WvVmn75e5sIj9d00jP+KUNUuQkwP2HXzJOxwFQOtbbiRkwUuVZGJ1pazGhmQ2\nX/Y3olFlPwsWLCAnJ4c5c+ag1VYdNNFUUJz/+sVYambPtjgO7U5AkmS0OjUgI4oiensNuVnW0Xbv\nwf4MubkzGk3l4M7cbAPffxJuC6QVBIGQXm3x9nWhTTtX8nIM/P3HCSRZRqNWUVhQilanZtzEUBZs\nfYCC4twK7XX26c4Dw59BU+DD5t+PYzFL6OzUFORaZ9bs7DUEdG7FmZhMTEYLFrOEnYOWB58agKu7\nfYW2Xl/+GLHnI3jm1rcZHDy22nvx6Zy/MZZa/zGo1SJPvnITervKA2KLWWLVkv2cT8qlXQd3Jj7W\nB1HVMv95lCHLMt9/spus9EKSAlpxUlTx1Z030MFDmf1XuL45u3IDx6e/DUDwuy/g91jNZk4VGp+0\nv3ZZn5UgXtPqq42JZDLzd8eRyEbTlQ8WhAqpVzUertYgWbUK98G9MMQnUxSbWPWpGjX+k+6m4/OP\noXFxqpe+l6RkcOjBFyiIOo22lRu9ly+scvXiaihNz2J7jzsq1AdQOzkQ9M7ztL177DVbtWtU59/X\n15e0tDREUcTT09NmtCAIJCUl1bkT9Ymi+a8ZZTPxZ5JP8NT0++gY5IUsyyDD6ZPpbPn9OBaLjEol\nUGwwgQDd+7Vj6M2dbQ6vZJHYuyOePdvjkCUZd08Hxt/TjTY+LhhLzcScSOPEoXMkn8muVd9atXbk\n9gd74uqu59GPh2I0Xyg1L4g8/5+F9O40rNIXT5Zk4k5lsHd7HKln82z7E89F4e8TzP1T+uPj71bp\nWpsPr+L7sAX06jiUlyZ8fMV7tml1JMgw7u7q03kW5pfw4+f/Yig00m9Ye4aNbZhCME3ls5mSnMtP\nX+7FzkHLei9XEAXWPdodbR0HPU3FvoaiJdvXkm2DmtmXsuZvjj09BySJLrOfof2T9zdS7+qO8vya\nN7Wx7+KqswAuvUJwH9ADtwE9MBcZOPnaRwAEv/8yGicH0jbsIG3Tziqz26idHPAY1hedlwcpa/4G\nBJxCO5O96yDIMhp3VwJf/i/t/u92BNXVZYILDw+ne6u2HHrwBUrOpWHf0Y8+P3+Avb/PVbV3OcJu\nGIP5Qh0AQa1m2J5V2LXzrtdrVEWTyfO/fPnyOl/oSmzevJnp06djsVh4/PHHefnllyu8f/LkSR57\n7DGOHDnC22+/zQsvvNDgfWrJbF4dSbHBRGmJmT+WHa722NY+zoy6IwRvX5cK+0WVyKCRnejQxZON\nv0aQnVHE8kV7EFUCgiBguRD8qtaItPF1ISOlAFEU6DusPWq1SMrZPFKT88jJukirpxZ54KkBGCUD\n762ebnP8dRo7pt06jz6BVVeVFkSBTkFedLzBk6S4bFZ/fxBJso5rtTpVlY4/wIAuo/hx6wccO/Mv\nBcW5ONldfhmvY5AX02qYwtPRWc9t9/Xgl+8OsH/nGbzbuRIYcvXFrmpDdRKrhqhHEBedzroVRwFw\nbeOEJAv4u+jr7PgrKDRn0jb+Q8TUuSBJBP7viWbl+CtcX4R+PIvjM95BMlsIef8lvG+v+H+u7Z2j\nK2x7DO1D0DvPV8icJNrp6fPzB7j2CUXUWF3L4HfL/bS8iFOcfONjcvYeI+rl94l69QPU9naEfl7z\nqrplGX2OG7IxCPZIxSW49g2l1w8L0Lq7XLmBWtLt09eJfG4estlC6GevN4rj31jUaOa/obFYLHTp\n0oWwsDB8fHzo27cvK1asICiofPkmIyODxMRE1qxZg5ub22Wdf0X2UzM+fvNvzCbLFY/TaFU888Yo\nxCsUujKZLCx6a6st2w2Aj78rIb186BLaptqg4Kij59m6zqqlG3d3KDqvQj74/QVSc5NxsnNh+u3v\nEeLft4aWWYmLTmfjbxEgc8WsRO/+Oo1jZ/bw+M2vMqpH/S7JH9h1hn82nQJAb6dm3N0NXzX44vSo\ngijQuq0zKpWISi1yNiEbyWL9yts5aJg6q2aDmZgTqWz+NRJJlmnf2RMnZz0mkwWzycKp46m2NlVa\nFZt8WzG8vSuzRrZvGAMVFJo4GWH/cvix/yGbzHSY/gid/9f4BaEUFBqa2tZhkGWZtPXbOfrk63Bh\ncg5RoN3/3YHnqMF4DOmNyl5f5bkl59PZNewBLIXlk4Wtb7mRbp+/2WQzZjUEDT7zP2/ePF57zVrE\n4vXXX0cQBMrGCWWvBUFg7ty5de7E/v376dSpEwEBAQDcd999rF27toLz7+npiaenJxs2bKjz9a53\nThw5Z3P8tTo14ydaZ4DLpDRlue4Bxt7V9YqOP4BGo0KjVdmcf72dhvunDKhRf4J7tCW4R1sADsRu\nZ9GyNygxGQjw6sLzdy7Ey6VtrW3sGOTFM69XXyyjjEFBYzh2Zg+7o/+qd+e/z5AAwrfEYLHIlBSb\n2bQ6ssarB1fDucQcm+MPVjnUxTKoiykxmDmXmHPZVZEyEmIzWf/zUZvUsywYuyrKhn7+7orWX+H6\nI31LOBFT59gydgRMuY/Al5+4xr1SUGgYyjIn1RRBEGhz+wg0/3u/XGYkyST/uIbkH9cg6rU4dm5P\nUVwSgkpFmztGYSksImd/RKWUq6JeR4+v37pq6dD1zmWd/3PnztleJycnV9ZYX3D+64Nz587Rrl15\nmiRfX1/27dtXL23XBy1JG5gQm8lfq62O/U233ECxfJZOwRXlKB2DvJg6a0St2x47IbTCoKGmHDq9\nk682zaHUVILRbA3aHRQ0hiljX0enqZsTWZNn1zfwJpao3uFk8mEy81Np5dymTte8GEEQ0OjUWAxW\nh7y02ERBXglOLlXPbtSWi+2LPHiWv9eeAMrTow4Y0Ym27VyxmCUsFomzZ7I5vCcRk9GCLMusWLyP\nrr19GDa2C/YOFYP5c7MMbN94krgL6TvL0GhUDLk5EI1WhVqjIiutkKP7khBFgfT2raBYIsCt/u1r\nibRk+1qybVC1fceeetNWYEjUa+ky+5lmm87zenx+LYmmbF+ZzAig/bOPYCksIuPv3eQdjSY/4pTt\nuLPL1theq50csAvwwRCXRJRczP2LW67j3xjP7rLOf3BwecGHWbNmERgY2GCdqO8fx6effho/P2tK\nKRcXF0JDQ203Mjw8HKBW25GRkXU6v6lsp53L45P3lmM2SUy4bzy9Bwfw5Zeb6q39jkFedB9udSDL\npC01Of/91S9g522dM85OLGZUjwk8c+tcBEGos/2RkZE1Or5Xp6HsO7WV71YtYlDQmHq9/17tDaSf\nsae0xExC8gnefi2OV+ZOwsXNrl7skyQJU24rjuxNIvFcFIEhrZn2wv2IKpHw8HDik87ajj+bdpJe\nI+3o338g+3bE8+uKP0lcF8XpqHSGje1MXnECZouEytiGQ+EJxCedQK0RGT1mBGdiMjiTfIJ+Q9vT\ne3CArT+CAzzzhnWVZcycZeSXmGk/Mahe7l9Nn1/Z9vqPvuTM58sJ0bkQ+vGrxFxI7tQUvn/1YZ+y\n3TS3B/XtR9SsD4kssAZABosOqB3s2b17d5Pon7KtbDep7QsrBuHh4Zy78H6nFyaxff1Gjk2dzQ1G\nNQDRqlL8HpvAzQ/cg2OX9uzeswc7oDfgNWRI07GnnrfLCA+3+p95edZVkqSkJB5//HHqg8tq/p2d\nncnPz6/0uiHYu3cvs2fPZvPmzQC8++67iKJYKegXYM6cOTg6Oiqa/1qSm23g5y/3YigyEtTDm/F3\nd0OogZynodl78m8+XvcKYP0Y2usc+e65fxq9H/tjtvHhmpkEeHVh/qM/N8g1ig1Gflt6kLRz+Ti5\n6rl3cj9cPeyvfOIV2lz381GS47MRVQKj7wghtI9vjc/PzigkbF00SXFZ5KqjSbD/HYAAw124moMI\n7tmWYWM64+h85Zn8wlIzdy2LRKcSWPNId1TX4PMV1vlmWwCaxt2VkVE1W5IuCyQDrpsUf9eC9C3h\ntgC6oHeex2fiuGvdpTpTkprBkcmvknfoBIJGjajTotJpa6SBVlBQqEht4wiuNxpc89+hQwdeeOEF\ngoODMZlMfPfddxWkPmWvJ02aVOdO9OnTh9jYWBISEmjbti2rVq1ixYoVVR7bBOKTmx2GQqvTaSgy\n4t/Jg7F3hV61418m0QF4ctybVVbGrQmFJfl8H7aA8CjryoNaVKPXOvDU+NlX1V5d6dFhMHZaBxLS\nT3Eu6ww+HvUfrGpnr+WeyX1Z/f0hziflsvKbfdwzuS/uno61bisuOp2Nv0ZgLDUjy2DvqOWOB3te\nUb9/Ke6ejkyc1IdTEam8tWkeFtEqWYhzWMHAwPEUeXmzJy6GzPxU/j76K6Kg4qnxs6t87ok5VsmW\nn5ve5vjX1+flShiSUoh5a5HN8Qcw5eQR9/H3+E26G43z5e+xZDRV0Gkfn/FOrXSsCjVDMps59uSb\nWAzWz1jkM29xZtFPeAztg8fQPlgMJUS9+iHQfAZgOfsjOPr4LErTs9D7tKbnd+/i0v2Ga90tBYVm\nS23jCBSujsvO/J86dYoFCxaQmJjIjh07GDq06lRM27dvr5eObNq0yZbqc/LkybzyyissXmwtpT1l\nyhRSU1Pp27cv+fn5iKKIk5MTUVFRODpW/Keu5PkvpywvfWmJGVmS8fJ24t7/9kenLx/z1da2/342\n0lZ0S6+159tnt6MSLzuGrJKIhL18tXEO2YXp6DR6HrxxOqN73N0g2tja2PfVpjnsiFzHhEH/ZeKQ\nJ+utDwdj/+GLjW8iCPD0+LmEthvE7z8c4mxCDvaOWiZO6otnm9oVPflsbhilJWYSz0UR0C6EJ2YO\nr1McQb4hhyc+Gw3ClQfXAgJdA/rh5xmIv2cghSX5/LHnW4xmiWz1OLr6+NLPu4S03GR2ndiARbIG\nlzvbu/H1tLBa9etKz89cWET8Z8tI+GolUqkRQatGEFXIZrOtUqfaxQn/yRPx/+89aN2cAbAYSsjc\nsY+0jTtI37K7wqBB4+rMyJOba9XPq+VS+1rSCsTFtuUdjebESwsq6HmrQ+PuwsgLEwNNjbJnFFmY\nyQ1mLUgS7oN70WPxW2hb1W7w3ZRprv/3aopiX/OlJdsG1dvX4DP/Xbp04dtvvwVgxIgRbNu2rc4X\nq45x48YxblzFJeApU8rTo7Vp04bk5OQG7UNLY/PqSEouBJoKAkx4tE8Fx/9qMFvKM8mUGA28vPR+\n7hs2rcrCWxdjnQGeTYmpBNOF3P2BbUN5evxcvN3rv+T31TA4aCw7ItexO2ozdw+eUufBiCzLRCTs\n5aO1M20O8FebZvPNM9uY8Ggf1iw/TOLpLH74dDc6vfqKKUnLSD6TTWmJ2batt1PX2fGft+pJq+Mv\nC6jQMajTrXQMaE+eIZu8oix2Ht+AWbI+exmZyIR9RCZUDsp3MK3izGk4c7rydepr1a7M+ZJKSxHU\nasx51iIsbe8eQ+dXn0Lf1lqwLjv8EKc/XErOniPEffgdZ75YDgjIkoSAdca/DL1Pa0pTM5EtFlCJ\nlKRkoPf2rHFfoH6c9cjpb9uyYBx5fBa+99+K3tsTXRtPSs6nk7B4JYIoEvrJrGYxMDAXFBEzfzFJ\nS38HSULj7opsMiFqNQQveAmtmwtZuw6SFX6Q3AORtvNMOXmcXvgtAVPuQ+3kcA0tqIi5oIhjT8/G\nUmhAkkpBVOM/5V66vD4VUV2331YFBQWFxqJJ5PmvTxTNvxVZlvn4zb9thbb0dhqmvV630eL57ET+\n9/39GM2laFRa7HWO5Bms1Xu7+HTngeHP0sW3R4Vz0nLPciR+N8u2fYhFKndY7xs2ldv6PVzrVYOG\nRJIsPPXlOPKKsnj7oR/p6B1yVe3IssyxM3tY/e/XxJ6PrPCeVq3jx+f/BcBssvDp3DBbjnytzlpT\nobpBR1J8Fr//cBizyYJKLaLVqRl7V9errh1Q5vgnZZymrXsAb9y3GFfHVpWOO3R6J4s3W9P63jt0\nGi72biRlxJKUEcv+mG1IsvVzJiMS6DuIG7zb08atHfmGHFb/+w0WyczNPScyafT/rqqfZUilRraG\njK+Q69mldwhBb03HtVfVzyt771HiPlpK1j8HKux36RFE61uG03r8jTh09MNcZODA3c+SdyQKx87t\n6bf2S9tKweW4OMZA5WBP318+xvGGDqgdahfLIcsymVv3cOiRl8AiXfkEQcAppBN2vm2w822D2VBM\n6rptCCoVoZ++VuuiOVC7wUt159kGZ0YjglqFObcAQaXC/7/30Gnm5Mvem5S1YZx48T0sJaXIJutv\nhcbdhQ7PPozfI3fVey7v9C3hRD47D9liodNL/6XthDFo3JwRBKGCfUHzpiMZTaRt2EHmP/uRLxo0\nqhztGX26dqtZCgoK1y91lcLW18y/4vy3UA6GJ7Bj40mAWs0qX44SYzGvL3+E5Mw4BnQZxXO3z8ds\nMRF2bDW//7vEJgVSixo0ai3Bfn1IyU7gfHZipbYc9M58+2z9yMXqmwWrp3M4bhdatY7nbp9f4y9m\n2RfabDHh4uBBak4SAE52LvTsMISDp3diKC1AJar5bMqfuDtZZ5UXzdtKsaHcmQgMac3Nd4ZgZ6+t\ndI3E01n8sewQZpNESC8fxtSwBsPlqKnjfyXKbM8vtVBo/wjfP/IgnhelDd15YgNfbHiDjt4hvP3Q\nj7b9tXE8i8+mkrxsDWd/Wo8xM8e2X+Voz6jYv2u0SlMhGNjNmZHRlaU9xuw89v/naQp/Nh1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3+eWsnwTpMKS9zsef4/+eQTatasyahRowpDpjyRmec/s+o8kiShTTHg7xvG8b3+GA0Szm42PI5M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\nnDnC2dlZtGvXTomy8sWFCxfEG2+8IZo0aSJGjRolunTpIlq1aqV0WXnK/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- "text": [ - "" - ] - } - ], - "prompt_number": 37 - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "figsize(11., 5)\n", - "returns = np.zeros((n_observations, 4))\n", - "\n", - "for i, (_stock, _returns) in enumerate(stock_returns.iteritems()):\n", - " returns[:, i] = _returns\n", - " plt.subplot(2, 2, i)\n", - " plt.hist(_returns, bins=20,\n", - " normed=True, histtype=\"stepfilled\",\n", - " color=colors[i], alpha=0.7)\n", - " plt.title(_stock + \" returns\")\n", - " plt.xlim(-0.15, 0.15)\n", - "\n", - "plt.tight_layout()\n", - "plt.suptitle(\"Histogram of daily returns\", size=14);" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "metadata": {}, - "output_type": "display_data", - "png": 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27Thw4AAAIDw8HH369JF9I0JOfefkmmtuwkmU/F2gvoJCgmO3IFg62tdxZLon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\ndPO28p89mLaGU2IGEGzD9jhz8QZu9wz9a2QHgBmx4zFmlD13yQx6AHH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- "text": [ - "" - ] - } - ], - "prompt_number": 38 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Below we perform the inference on the posterior mean return and posterior covariance matrix. " - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "obs = pm.MvNormal(\"observed returns\", mu, inv_cov_matrix, observed=True, value=returns)\n", - "\n", - "model = pm.Model([obs, mu, inv_cov_matrix])\n", - "mcmc = pm.MCMC()\n", - "\n", - "mcmc.sample(150000, 100000, 3)" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "output_type": "stream", - "stream": "stdout", - "text": [ - " \r", - "[****************100%******************] 150000 of 150000 complete" - ] - }, - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "\n" - ] - } - ], - "prompt_number": 39 - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "figsize(12.5, 4)\n", - "\n", - "# examine the mean return first.\n", - "mu_samples = mcmc.trace(\"returns\")[:]\n", - "\n", - "for i in range(4):\n", - " plt.hist(mu_samples[:, i], alpha=0.8 - 0.05 * i, bins=30,\n", - " histtype=\"stepfilled\", normed=True,\n", - " label=\"%s\" % stock_returns.keys()[i])\n", - "\n", - "plt.vlines(mu_samples.mean(axis=0), 0, 500, linestyle=\"--\", linewidth=.5)\n", - "\n", - "plt.title(\"Posterior distribution of $\\mu$, daily stock returns\")\n", - "plt.legend();" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "metadata": {}, - "output_type": "display_data", - "png": 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GYPfu3YiLi8O5c+cwefJkFBUVYcWKFdDpdLY/Y86cORPPP/88rrvuOnFHQUREivjTn/4E\nPz8//O53v/N2V1yWnJyM6upqPPLII3jppZe83R0iIkU5rVkvKSlBnz59sHjxYhw6dAjXXHMN/vzn\nP6OiogJxcXEAWuvu2uZYLSsrsxuYJyUltbvqnIiI1MkXz0yfPHnS210gIhLG6d8vzWYz8vPzkZmZ\nifz8fISGhtpdeAU4v/BJyemgiIiIiIh6Cqdn1pOSkpCUlIRrr70WQOv0WCtWrEB8fDzOnTuH+Ph4\nlJeX26biSkxMxJkzZ2yPP3v2LBITE+3a/Pjjj21n5YmIiIiItKKhoQFz5sxRrD2ng/X4+Hj069cP\nxcXFGDRoELZt24arrroKV111FXJycrBs2TLk5ORg7ty5AIDZs2fjjjvuwOOPP47S0lIcPXoUY8eO\ntWszLi4Oo0ePVuwg6GfZ2dm2+XxJecxXHGYrDrMVh9mKw2zFYbZi5efnK9qeS/Os/+Uvf8Gdd94J\no9GIK6+8Eh988AEsFgsyMjLw3nvv2aZuBFq/wS0jIwNpaWnw8/PD6tWrWQbjQadPn/Z2FzSN+YrD\nbMVhtuIwW3GYrTjM1re4NFgfMWIE9u/f3+72jr4Vr+2b1YiIiIiIqOv0zz///POe3mlJSQn69u3r\n6d32CBERER1+myB1H/MVh9mKw2zFYbbiMFtxmK1Y5eXlSElJUaw9l77BVGnbt29nzToRERERaU5+\nfj7S09MVa8+lMhjyHXl5eZgwYYK3u6FZzFccZisOsxWH2YrDbMW5NFtZllFZWQmLxeLlXvkOWZYR\nERGBsLAwj+yPg3UiIiKiHqqyshLh4eEICQnxdld8hizLqK6uhsFgQExMjPD9sQyGiIiIqIcqKytD\nQkKCt7vhkzrKTukyGKffYEpERERERN7BwbrG5OXlebsLmsZ8xWG24jBbcZitOMxWHGbrWzhYJyIi\nIiJSKdasExEREfVQjuquz9UbUNlgFLbP2LAAxIcHurTtP/7xD7z11lv46aefEBISgv79+2PBggW4\n9957AQB79+7FK6+8ggMHDkCn0+H666/Hc889h8GDB9vaqK2txYsvvojNmzejvr4eycnJyMzMxB13\n3OHWvi7nqZp1zgZDRERERDaVDUa8vbdUWPv3j0t0abD+xhtv4I033sCrr76KX/ziFwgNDUVBQQHe\neOMN3HXXXTh48CBuu+02PPPMM/j4449hMpnw5ptv4qabbsLOnTtxxRVXwGg0Yt68eYiNjcXWrVuR\nkJCAXbt24aGHHkJNTQ0yMzNd2ldAQICwPJxhGYzGsA5NLOYrDrMVh9mKw2zFYbbi+EK2dXV1WLly\nJV577TXMmjULoaGhAIBhw4bh7bffRkBAAJ5//nncfvvt+O1vf4vQ0FBERkbi97//PcaMGYOVK1cC\nANauXYvS0lJ88MEH6NevH/R6PdLT07FixQpkZ2ejoaHBpX15EwfrRERERKQq+/btg8FgwM033+zw\n/qamJuzfvx9z5sxpd9/cuXOxa9cuAMCuXbswdepUBAcH220za9YstLS0YP/+/U735W0crGsMv+1N\nLOYrDrMVh9mKw2zFYbbi+EK21dXViImJgU7381B1xowZGDBgABITE3Ho0CFYrVbExcW1e2xsbCyq\nqqps7cTHx7fbxs/PDzExMaiurna6r2+//VbAEbqOg3UiIiIiUpWoqChUVVXBarXabvvyyy9RUlKC\nqKgoNDQ0QKfT4dy5c+0eW1FRgd69ewMAYmJiHG5jNptRVVWF6Ohop/vywlwsdjhY1xhfqEPzZcxX\nHGYrDrMVh9mKw2zF8YVsx44di8DAQPz73/92eH9ISAiuvfZabNy4sd19GzZswMSJEwEAkyZNwrZt\n29DU1GS3zaZNmxAYGIgxY8Y43Ze3cbBORERERKoSERGBJ598Ek8++SQ2bdqE+vp6WK1WFBQUoKmp\nCZIk4dlnn0Vubi7WrFmD+vp61NTU4OWXX8b333+Pp556CgAwf/58JCQkYPHixThz5gxMJhO2b9+O\nrKwsLFu2DOHh4U735W2cZ52IiIioh1L7POvr16/HX//6VxQVFSEkJARXXHEF7r77bixYsAD+/v7Y\ns2cPXnnlFRw8eBCSJNnmWR8yZIitjZqamnbzrD/44IO466673NrX5Tw1zzoH60REREQ9VEcDTnLO\nU4N1lsFojC/Uofky5isOsxWH2YrDbMVhtuIwW9/CwToRERERkUqxDIaIiIioh2IZTNexDIaIiIiI\nqIfjYF1jWIcmFvMVh9mKw2zFYbbiMFtxmK1v4WCdiIiIiEilWLNORERE1EOxZr3rWLNORERERNTD\ncbCuMaxDE4v5isNsxWG24jBbcZitOMzWt/h5uwNEREREpB5NZ8rRUlYprP2ghFiE9Ovr8vazZs3C\n4cOHUVRUhICAALv7Tp06hdGjR2Px4sV47bXX7O6LiYlBSEgIJElCeHg45s2bhxdffBE6nQ4jRozA\nqlWrMGnSJEWOSSSXBuvJycno1asX9Ho9/P39sW/fPlRXV2P+/Pk4deoUkpOTsW7dOkRGRgIAVqxY\ngffffx96vR6rVq3C9OnThR4E/WzChAne7oKmMV9xmK04zFYcZisOsxXHWbYtZZU4tvIdYfsfuOw+\nlwfrp0+fRn5+PpKSkvDFF19gzpw5dvfn5uZi6NCh+Ne//oVXXnml3WD+66+/RnJyMo4ePYrZs2dj\n4MCBWLRoESRJgiRJih2TSC6VwUiShF27duHAgQPYt28fACA7OxvTpk1DcXEx0tPTkZ2dDQAoLCzE\n2rVrUVhYiC1btiAzMxNWq1XcERARERGRJuXm5mLSpEnIyMhAbm6u3X2yLGPdunVYtmwZoqOjsWXL\nlg7bSU1NxXXXXYeioiLRXVacyzXrl08as2nTJixcuBAAsHDhQmzYsAEAsHHjRixYsAD+/v5ITk7G\nwIEDbQN8Eo91aGIxX3GYrTjMVhxmKw6zFceXsl27di3mzZuHuXPnYseOHTh//rztvj179uD8+fOY\nNm0a5syZ024wD/w8fi0qKsKePXswbNgwj/VdKS6fWZ86dSrGjBmDd95p/bNIRUUF4uLiAABxcXGo\nqKgA0DqNTVJSku2xSUlJKC0tVbrfRERERKRhe/bsQXl5OWbOnIkrr7wSgwcPxvr16233f/LJJ5gx\nYwaCgoIwZ84cbN++HRcuXLBrY/LkyUhJScGdd96Ju+++G3feeaenD6PbXBqsf/PNNzhw4AC++OIL\nvPnmm/j666/t7ndW9+MrNUFawBo/sZivOFrPtry83OGyJ6gtW6WO39M5OqK2bLWE2YrjK9l+8skn\nmDJlCsLDwwHA7ux5c3MzNm3aZKthHzZsGPr37283mAeA3bt348SJE/j++++RlZXl2QNQiEsXmPbt\n23oRQJ8+fTBv3jzs27cPcXFxOHfuHOLj41FeXo7Y2FgAQGJiIs6cOWN77NmzZ5GYmNiuzczMTPTv\n3x8AEBERgWHDhtmePG1/nuE617nOda2s5+XlYfny5cjLy8PHH3+M1atXq6p/nlxX6vhzcnJst6vp\n+LjOdV9aj4mJUeWXIjU3N2PDhg2QZRlDhw4FABgMBtTV1eHw4cM4cuQI6uvr8fjjj+PJJ58EANTW\n1iI3NxcPPPCAR/pYW1uLEydOAGjN8vTp0wCAJUuWKLofp99g2tTUBIvFgvDwcDQ2NmL69Ol47rnn\nsG3bNsTExGDZsmXIzs5GTU0NsrOzUVhYiDvuuAP79u1DaWkppk6dimPHjtmdXec3mIqTl5dnexGS\n8pivOFrPNjs7G8uXL2+37Alqy1ap4/d0jo6oLVstYbbiXJqto2/hrN57SPhsMNHjRnS6zT/+8Q88\n9dRT+Oqrr2wzvMiyjHvvvRcjR47EkSNHkJSUhGeeecb2mLKyMqSnp+Orr75CWloaYmJi8P333yM5\nObld+yNHjsRrr71m9xzz9/eHXq93+Tg89Q2mfs42qKiowLx58wAAZrMZd955J6ZPn44xY8YgIyMD\n7733nm3qRgBIS0tDRkYG0tLS4Ofnh9WrV7MMhoiIiMhHBCXEYuCy+4S270xubi7uvPPOdtUZS5Ys\nwf333w8A2LVrF/r06WO7r0+fPkhPT8fatWvxwgsvON3H/Pnz7dafeOIJVZbKOB2sDxgwAAcPHmx3\ne3R0NLZt2+bwMVlZWao82J6AZyHEYr7iMFtxmK04zFYcZiuOs2xD+vV160uLRPj0008d3j537lzM\nnTu3w8etXbvWtlxVVdXhdo7Gtmrl8tSNRERERETkWRysa0zbxSMkBvMVR+vZxsfHO1z2BLVlq9Tx\nezpHR9SWrZYwW3GYrW/hYJ2IyAMWLVrkcLknUur4e3qORNQzOJ0NRgTOBkNERETkfR3NaELOeWo2\nGJ5ZJyIiIiJSKQ7WNYZ1aGIxX3GYrTjMVhxmKw6zFYfZ+hYO1omIiIiIVIqDdY3hvLRiMV9xtJ5t\neXm5w2VPUFu2Sh2/p3N0RG3ZagmzFYfZ+hYO1omIPCAnJ8fhck+k1PH39ByJqGfgYF1jWIcmFvMV\nh9mKw2zFYbbiMFtxnGVbe7EZpScvCvtXe7HZrf7OmjULKSkpMBqNttseeughxMTE4IsvvrDbNisr\nCzExMcjNzQUAjB8/Hv3797f7Fx8fj969e9uyiImJwZNPPmnXzk033YRPPvnErX6K4uftDhARERGR\nejTUtmDvVyeEtT9uYgoiooJd2vb06dPIz89HUlISvvjiC8yZM8d238CBA5Gbm4ubbroJAGA2m7Fx\n40akpKTYtvn222/t2mtsbER6ejrmzZtnuy00NBTr1q3D0qVL0a9fPwCAJEmQJKnLx6gknlnXGNah\nicV8xWG24jBbcZitOMxWHF/KNjc3F5MmTUJGRobtbHmbGTNmYO/evaitrQXQ+j0+V111Ffr06YOO\nvkZo6dKlSEpKwrJly2y39erVCwsWLMDKlSvFHUg3cLBORERERKq0du1azJs3D3PnzsWOHTtw4cIF\n232BgYG46aab8M9//hNA68B+/vz5AODwrPjbb7+N7777Du+88067+x5//HF89tlnOHbsmKAj6ToO\n1jWGNX5iMV9xtJ5tfHy8w2VPUFu2Sh2/p3N0RG3ZagmzFcdXst2zZw/Ky8sxc+ZMXHnllRg8eDA+\n/fRTu23mz5+P3Nxc1NXV4dtvv8Utt9zisK39+/fj5Zdfxvvvv4+oqKh298fGxmLx4sVYsWKFkGPp\nDg7WiYg8YNGiRQ6XeyKljr+n50ikdZ988gmmTJmC8PBwAMCcOXPsSmEkScJ1112HqqoqvPbaa5gx\nYwaCgoLatVNVVYXFixfj2WefxTXXXNPh/pYuXYodO3bg8OHDyh9MN/ACU43xpTo0X8R8xWG24jBb\ncZitOMxWHF/Itrm5GRs2bIAsyxg6dCgAwGAwoK6urt1g+rbbbsOrr76Kzz77rF07VqsV9913H8aP\nH48lS5Z0us/o6Gg88MADePnllwGgw7p3T+NgnYiIiIhUZfPmzfDz88NXX32FgIAAAK2D53vvvdd2\ndr1tMH3//ffj+uuvx/jx49u1k52djbKyMnz44Ycu7TczMxOjR4+GLMuqmQ2Gg3WNycvL84lPzL6K\n+YrDbMVhtuIwW3GYrTjOsg2LCMK4iSkd3t9dYRHtS1Uul5ubizvvvBOJiYl2ty9ZsgRPP/00Jk+e\nbBtMR0ZG4sYbb3TYzv/7f/8PAQEBtrPzl2qb1vHSQXl4eDh+97vf4cUXX3T5eETjYJ2IiIiIbCKi\ngl2eB12Uyy8kbTN37lzMnTu308du3rzZtnzp7DGOJCYmoqCgwO62pUuXYunSpS72VDxeYKoxPAsh\nFvMVR+vZlpeXO1z2BLVlq9TxezpHR9SWrZYwW3GYrW/hYJ2IyANycnIcLvdESh1/T8+RiHoGDtY1\nxlfmTvVVzFccZisOsxWH2YrDbMVhtr6Fg3UiIiIiIpXiYF1jWIcmFvMVh9mKw2zFYbbiMFtxmK1v\n4WCdiIiIiEilOFjXGNahicV8xdF6tvHx8Q6XPUFt2Sp1/J7O0RG1ZaslzFYcZutbOFgnIvKARYsW\nOVzuiZQ6/p6eIxH1DJLc9l2tHrR9+3aMHj3a07slIiIiokuUlZUhISHB293wSR1ll5+fj/T0dMX2\nw28wJSLDXm1QAAAgAElEQVQiIiKbC3XnUF1fKaz96PBY9O7VeRlbv379IEkSAKCxsRFBQUHQ6/UA\ngD/96U+YOnUqfv/732P79u1obGxEfHw87rzzTjzyyCMAgJiYGHz//fdITk522H5DQwOGDh2K8ePH\nY926dcodnAAuDdYtFgvGjBmDpKQkfPbZZ6iursb8+fNx6tQpJCcnY926dYiMjAQArFixAu+//z70\nej1WrVqF6dOnCz0AspeXl8ervAVivuIwW3GYrTjMVhxmK46zbKvrK7ElP1fY/meOvt3pYP3MmTO2\n5ZEjR2LVqlWYOHGi7baHHnoILS0t2Lt3L3r16oWjR4/iyJEjLvfhs88+Q2JiIr755htUVlYiNjbW\n/QPxEJdq1l9//XWkpaXZPuFkZ2dj2rRpKC4uRnp6OrKzswEAhYWFWLt2LQoLC7FlyxZkZmbCarWK\n6z0RERER9TgHDx7Er371K/Tq1QsAkJqaitmzZ7v8+NzcXNx9990YO3as6s+sOx2snz17Fps3b8aS\nJUvQVt6+adMmLFy4EACwcOFCbNiwAQCwceNGLFiwAP7+/khOTsbAgQOxb98+gd2ny/EshFjMVxyt\nZ1teXu5w2RO8mW1pbQv2nK61+/fv74rb3XampsXttj2doyNaf956E7MVRwvZjhkzBn/4wx/w8ccf\n4/jx42499syZM/jvf/+LuXPnYu7cuVi7dq2gXirD6WD9sccew6uvvgqd7udNKyoqEBcXBwCIi4tD\nRUUFgNZC+6SkJNt2SUlJKC0tVbrPREQ+Jycnx+Gy1lU1mfBhfrndv5VvrGl32/lGo9tt96Qcicje\nypUrcdttt+Hdd9/F9ddfjzFjxmDbtm0uPXbt2rUYPXo0EhMTMWvWLPz0008oKCgQ3OOu67Rm/fPP\nP0dsbCxGjRqFXbt2OdxGkiRbeUxH9zuSmZmJ/v37AwAiIiIwbNgw2ye9tvk/ue7++qVzp6qhP1pb\nZ77i1ttuU0t/RBxf2/rp06ft1kXvv6CgAA8++KBXjv/Avm9RUXQBcUNaZwCrKMpHw4Wfz4hXFOW3\nLlyb4JX+dXf9rbfe4u8vQet8v/XM+21MTIxPzgYTFBSExx57DI899hjq6+vx+uuv495770VBQQEi\nIiI6fezatWuxePFiAEB0dDRuuOEGfPLJJxg2bJhbfaitrcWJEycA2L+3L1mypAtH1LFOp27MysrC\nhx9+CD8/P7S0tKCurg6//OUvsX//fuzatQvx8fEoLy/HlClTUFRUZKtdX758OQBg5syZeOGFFzBu\n3Di7djl1ozh5ebwgRyTmK46vZmu8WAvZZHa63Wt/WYX/73dLAQB/em8Nlj/9tOiu2Xgz2x/K6/H2\nXvu/sBZseBfD5tr/MvvNtQkYndjLrbazs7Ntv2+8xVeft76A2YpzabaOph8sLv1B+AWmgxKHu7y9\nowtML9fQ0IArrrgCO3fuxPDhwzucDWbv3r24+eabERkZiYCAANtjQ0JCUFhYaJtxxhWqmLrxlVde\nwSuvvAIA2L17N1577TV8+OGHeOqpp5CTk4Nly5YhJycHc+fOBQDMnj0bd9xxBx5//HGUlpbi6NGj\nGDt2rGKdJef4xiYW8xXHV7O9sGMvyv651el2FUfzUXCiEcEJsZAjPfv1Fr6QrSwDF5tNTrfz1+sQ\nFuD6L1PRfCFbX8VsxdFCtq+++iqmTp2Kq666ClarFW+//TYiIyMxcOBA2zYGgwEtLT9fD+Pv74/c\n3FxMmTIFb731lu325uZmTJgwAdu2bcOMGTM8ehyu6HSwfrm2kpbly5cjIyMD7733nm3qRgBIS0tD\nRkYG0tLS4Ofnh9WrV3daIkNE5OtkiwXWZucXR8omM6zNLbC0GACoZ7CpFh8eKEeAzvnvi4wR8RiT\n5N4ZeCJyT3R4LGaOvl1o+92l0+nw8MMP4+zZs/Dz88PVV1+N3NxchISE2La5/vrrbcuSJCE7Oxsb\nN27EX//6V/Tp08euvfnz5yM3N9e3B+uTJk3CpEmTALTW93RUxJ+VlYWsrCxlekdu458NxWK+4mg9\n2+jAYNty2wX6nqK2bIMje7e7zWSRYbI4/4uD9ZLKzfj4zudp9gS1ZaslzFYcZ9n27hXvdB50Tzp4\n8GC725544gk88cQTHT6mqqrK4e0d1ZO/+uqrXeucB7g0zzoREXXPLQmptuVF99zjxZ5438DJcxVp\nZ9GiRYq0Q0SkZhysawzPQojFfMVhtuIwW3GYrTjMVhxm61vcqlknIqLuMVbXomz9l4Abl/OEJCci\nevwocZ3yIU1Gi0tfoBTsr0Pv0AAP9IiISCwO1jWGNX5iMV9xekq21uYWlK3f4tZjYmfe2K3Bupay\n/bSg0qXt7hwZ75HBupayVRtmKw6z9S0sgyEiIiIiUimeWdcYflIWi/mKo/VsqwxNiAkMabfsCSKy\nPVPTgrI6g9Ptyh1s03TxPEKi+jjY2j1KtdMdWn/eehOzFefSbPV6PZqamuymPKTOybKM6upqBAYG\nemR/HKwTEf2fhmOn0Hy6zL3H/HTCpe02lx3D3QOGt1v2Vecbjfh7fnmXHnt898Z232DqzXaIerLY\n2FhUVlaipqbG213xGbIsIyIiAmFhYR7ZHwfrGsM6NLGYrzhqyLaltAIlb3zk1T6IoIZstYrZisNs\nxbk0W0mSPP7dD+Qe1qwTEREREakUB+saw7MQYjFfcZitOMxWHGYrDrMVh9n6Fg7WiYiIiIhUioN1\njcnLy/N2FzSN+Yqj9WyjA4MdLnuC2rINjuytqna6Q23ZagmzFYfZ+hYO1omIPOCWhFSHyz3RwMlz\nVdUOEZGacbCuMaxDE4v5isNsxWG24jBbcZitOMzWt3DqRiIisjld04xz9UYXtmvxQG+IiIiDdY3h\nvLRiMV9xmK047mR7rt6InO+79mVHPRGft+IwW3GYrW/hYJ2ISOVayitxcX8BIMsuPyagdxRCU/oJ\n7BUREXkCB+saw0/KYjFfcbSebZWhCTGBIe2WXVF36CfUHfrJrf0lP3C7bbCutmybLp5HSFQf1bTT\nHWrLVkuYrTjM1rfwAlMiIg/YXHbM4XJPdHz3RuHt6CRFdkFE5HU8s64xrEMTi/mKw2zF6YnZbv6p\nCt+V1jvd7oYrIjEqMbzL++mJ2XoKsxWH2foWDtaJiEhzqppMqGoyOd1ueHyYB3pDRNR1LIPRGH5S\nFov5isNsxXEnW1aPuIfPW3GYrTjM1rfwzDoRUQ9QVNmIH8qdl4WcrTV4oDdEROQqnlnXmLy8PG93\nQdOYrzhazzY6MNjhsifk5eWhusmE3SU1Tv8dr24W3p/gyN6qaqc7tP689SZmKw6z9S0crBMRecAt\nCakOl3uigZPnqqodIiI142BdY1iHJhbzFYfZisNsxWG24jBbcZitb2HNOhFpUnNpBRqKTrj1mPri\nEkG9ISIi6hoO1jWGc6eKxXzFUTpbU209St78SLH2fFleXh50SVd7uxuaxPcEcZitOMzWt3RaBtPS\n0oJx48Zh5MiRSEtLw9NPPw0AqK6uxrRp0zBo0CBMnz4dNTU1tsesWLECqampGDJkCLZu3Sq290RE\nREREGtbpYD0oKAg7d+7EwYMH8cMPP2Dnzp3Iy8tDdnY2pk2bhuLiYqSnpyM7OxsAUFhYiLVr16Kw\nsBBbtmxBZmYmrFarRw6EWvGTsljMVxytZ1tlaHK47Alqy7bp4nlVtdMdastWS5itOMzWtzi9wDQk\nJAQAYDQaYbFYEBUVhU2bNmHhwoUAgIULF2LDhg0AgI0bN2LBggXw9/dHcnIyBg4ciH379gnsPhGR\nb9hcdszhck90fPdGVbVDRKRmTgfrVqsVI0eORFxcHKZMmYKrrroKFRUViIuLAwDExcWhoqICAFBW\nVoakpCTbY5OSklBaWiqo6+QI504Vi/mKw2zFYbbiMFtxmK04zNa3OL3AVKfT4eDBg6itrcWMGTOw\nc+dOu/slSYIkdfwF1R3dl5mZif79+wMAIiIiMGzYMNufZdqeRFznOtd7znobpdobHh0PADh0sfVk\nwoioOK+utzl0sQIVLQ126yL2l/x/7efl5aGgoAAj/u8C04qifABA3JDRXltvuFBuO35v96fguz3Q\nlYV3+flWUFDg1vZc57oa1tuopT++vt62fPr0aQDAkiVLoCRJlmXZ1Y1feuklBAcH491338WuXbsQ\nHx+P8vJyTJkyBUVFRbba9eXLlwMAZs6ciRdeeAHjxo2za2f79u0YPXq0godBRGSvrvAYip75s7e7\nYfNhyQ+4e8DwdsuiJD9wO2KnT7Ct//dkDT46eE7oPl1VsOFdDJvb/V9mSrQzf3gcJqZEdbsvRERt\n8vPzkZ6erlh7nZbBXLhwwTbTS3NzM/7zn/9g1KhRmD17NnJycgAAOTk5mDu39VvkZs+ejdzcXBiN\nRpSUlODo0aMYO3asYp0lIiIiIupJ/Dq7s7y8HAsXLoTVaoXVasXdd9+N9PR0jBo1ChkZGXjvvfeQ\nnJyMdevWAQDS0tKQkZGBtLQ0+Pn5YfXq1Z2WyJDy8vI4d6pIzFccrWcbHRjscNkT8vLUNc96cGRv\np9skh/sjMkDf6TYtifEYGRNkd1uTWUZxraFb/XOH1p+33sRsxWG2vqXTwfqwYcOQn5/f7vbo6Ghs\n27bN4WOysrKQlZWlTO+IiDTiloRUh8ta1ytQjwC9/R9xe998m9PHpQTqUbz/TKfbDOw9Dhe+s99m\n4IgEFLvfTSIi1ep0sE6+h5+UxWK+4jBbZdUXHYfk3/oWPxh+uFDwA2bVt3T+mNh47GoOULQf43sF\noKKk2u3HlTabYDK5/z0dklXGuD4hLm8fIcuou9gMvZ8OoeGBbu+Pz1txmK04zNa3cLBORKRBVbv2\no2rXftt6bYsZFxqMnT6m16O/AXQxivajqdmM8rI6RdvsTGG+e9MFG8MDcTzUH2kjEzBkeF9BvSIi\n6jqn86yTb7l8WiZSFvMVh9mKc/n0kaQcPm/FYbbiMFvfwjPrRETU48lWGQaD2e3HmUwWAb0hIvoZ\nB+sawzo0sZivOFrPtsrQhJjAkHbLnjAiKg61Le4PREVpqK9GWHi0atoBgOLCCpw8fsHtxyUkDVBk\n/9Se1t8TvInZ+haWwRARecDmsmMOl3uigoNbVdUOAFjMVjQ3mtz+xzPrRCQaB+sawzo0sZivOMxW\nHNasi3Oo4Dtvd0Gz+J4gDrP1LSyDISIip6KC/eCnc/9L7vRdeAwREf2Mg3WNYR2aWMxXHGYrjhI1\n6zeE+eNsF+ZLP1vvuW8T9YYRw8Z4uwuaxfcEcZitb+FgnYjIh5mtMgDZ6XayC9t0pr7R6NH50omI\nqBVr1jWGdWhiMV9xtJ5tdGCww+XuajRacKqmpdN//zl7BucbTIrts7tCw6JU1U53sGZdHK2/J3gT\ns/UtPLNOROQBtySkOlzuLhkyLNbOt7FaXTn37jnDR81QVTtERGrGwbrGsA5NLOYrDrMVJzWsj7e7\noFoyAKvV+UcZCYDk4GJZ1qyLw/cEcZitb+FgnYiIeqzKBiOqm5yXCPUO9UdUiL8HekREZI816xrD\nOjSxmK84zFacow3nvd0F1bLIMgwWq9N/lg5OvrNmXRy+J4jDbH0Lz6wTkepZjSaYauvdeozsrJCb\niIjIB3CwrjGsQxOL+YrTWbammloc+f2fYWl2fc5u2aKur4GvMjQhJjCk3bInqK1mvaG+GmHh0app\npztYsy4O32/FYba+hWUwROQTzE0tsDQ1u/zPajB6u8t2Npcdc7jcExUc3KqqdoiI1IyDdY1hHZpY\nzFccZisOa9bFYc26OHxPEIfZ+hYO1omIiIiIVIqDdY1hHZpYzFccZiuO2mrWtYQ16+LwPUEcZutb\neIEpEVEPoQ8MQL+502EymB3eHxAVhet1AQ7va7rQKLJrRETUAQ7WNSYvL4+fmAVivuJoPdvowGCH\ny55wtOE8UsP6QB/oj+oWP5w6WuNwOz9TKc5LjgfrSgoNi1JVO92xd98eJF4RBVl2/i2ol5J0Evom\nRQrqlTZo/T3Bm5itb+FgnYjIA25JSHW43BMNHzVDVe10R+3FZny787jbj4uKDuFgnYhcwsG6xvCT\nsljMVxxma6/ZbIHJ7PxsbbPJ+Zc/sWZdnCGpI7zdBc3ie4I4zNa3cLBORKRCLSYrzjeavN0NIiLy\nMs4GozGcO1Us5isOsxWH86yLU3T0kLe7oFl8TxCH2foWnlknIiIAgE6nQ5DevXM4JosMi5sXV/oi\nWZZhtrQ/Tou1/e1+eslT3SKiHsDpYP3MmTO45557UFlZCUmS8Nvf/hZLly5FdXU15s+fj1OnTiE5\nORnr1q1DZGTrxTIrVqzA+++/D71ej1WrVmH69OnCD4RasQ5NLOYrjtazrTI0ISYwpN2yJ7has245\nW4Zwvd6ttq2JCaiyuDc4baivRlh4tFuPEdmOKyobjKhqal+WpI9KxbGqJtt679AA9A71d9peXV0L\n9nThwlT/AD2uviYRgUHO9+HrtP6e4E3M1rc4PYXi7++PP/3pTzh8+DD27NmDN998E0eOHEF2djam\nTZuG4uJipKenIzs7GwBQWFiItWvXorCwEFu2bEFmZiasVucXQBERadnmsmMOl9XEYjDB3NTi1r+u\nKDi4VZH+KtWOK2QAZqvs9J+rUzhazFaUnalx+19FWZ3YAyUi1XE6WI+Pj8fIkSMBAGFhYRg6dChK\nS0uxadMmLFy4EACwcOFCbNiwAQCwceNGLFiwAP7+/khOTsbAgQOxb98+gYdAl2IdmljMVxxmKw5r\n1sU5c+pHb3dBs/ieIA6z9S1uFSeePHkSBw4cwLhx41BRUYG4uDgAQFxcHCoqKgAAZWVlSEpKsj0m\nKSkJpaWlCnaZiIiIiKhncPkC04aGBvzqV7/C66+/jvDwcLv7JEmCJHVcs+jovszMTPTv3x8AEBER\ngWHDhtlqqNo+8XHd/fUJEyaoqj9aW2e+3lk3XaxF27vOoYutJwZGRMX51HqbQxcrUNHSYLfuaPv+\nQa212G1nxdvqzru63ubIqSOoqKzFgNiBAICSytaSnC6vn/oRtRYJ/a64GsDPZ5o7W6+rrbT1x5Xt\n1bzedlvb+okTP6Aq2N82/3rbbDFKrRf+dADBMdWY8ovJANTx+hS1zvdbrvvKetvy6dOnAQBLliyB\nkiTZhQI7k8mEW2+9FTfddBMeffRRAMCQIUOwa9cuxMfHo7y8HFOmTEFRUZGtdn358uUAgJkzZ+KF\nF17AuHHjbO1t374do0ePVvRAiEi7DJUXUPBYNqzNXauRVoMPS37A3QOGt1vuyMVmk+LzrAf0CkXQ\nlGk4dfSCYm3qUlPcvsD0269zMf7G27u9b6XaUVJcWAD6hAUIaz8o2B/ps4b2iAtMiXxVfn4+0tPT\nFWvPaRmMLMv4zW9+g7S0NNtAHQBmz56NnJwcAEBOTg7mzp1ruz03NxdGoxElJSU4evQoxo4dq1iH\nqXOsQxOL+Yqj9WyjA4MdLnuC2mrWQ8OiVNVOd7BmXRytvyd4E7P1LX7ONvjmm2/wv//7vxg+fDhG\njRoFoHVqxuXLlyMjIwPvvfeebepGAEhLS0NGRgbS0tLg5+eH1atXd1oiQ0TUE9ySkOpwuScaPmqG\nqtohIlIzl8pglMYyGCJyhxbKYNyl5TIYLWMZDBF5vAyGiIiIiIi8g4N1jWEdmljMVxkt5efb/dux\n8XOHt7eUn4el2QDwy9W6TG0161rCmnVx+H4rDrP1LU5r1omIlHbiLx+i8dhp+9uqzyE8ehsAQB8S\nDMPNg1FXd8kgc0p8t/Yp6XToUybBdLCkW+0QERF5EgfrGtM29yeJwXyVIVsskM1mu9uG9+r9822y\nFSWVR/DT6QOK7VOSdBgzaDL0Cf0UaxMA4mtCYfpvkdPtqgxNiAkMabfsCW1zrqtFQ301wsKjVdNO\nd1w63zopi++34jBb38LBOhH1CLJsxf6fdije7qzE2S5tt7nsmG1u9UuXe6KCg1sVmR9dqXaIiNSM\nNesawzo0sZivOJd/0ycphzXr4rBmXRy+34rDbH0LB+tERERERCrFwbrGsA5NLOYrzoioOG93QbPU\nVrOuJaxZF4fvt+IwW9/CwToRERERkUpxsK4xrEMTi/mKo/Wa9ejAYIfLnqC2mvXQsChVtdMdrFkX\nh++34jBb38LZYIiIPOCWhFQAQIvZism9U9BotHS6vcHS8ZdAhcbHIPaWGWiub3Zp31UlRxA/YCgk\nSUJpWaPrnRZk+KgZqmqHiEjNOFjXGNahicV8FSIBkCS7m0ZEX/KlRzoJgOzRLnlKo9GCqiZTt9rQ\nBwbg9Jl6XDh70aXtdeiNIz+q6+y6VrBmXRy+34rDbH0LB+tE1G2HSr5FY0u9y9vXjgyE5cqETrcp\nP/dDd7tFRETk8zhY15i8vDx+YhaI+Tp2tOwHlFWfcnn72qNHYK63L8c4W1aHpIReSndNuNKQWgTe\n1N/l7Y1mKwI6KXEBgIjaEJz/UrkPKyWVxzAgdqBi7dHPzpz6kWfXBeH7rTjM1rdwsE5E1A35R3e7\ntb3RLHdajw4A6Qk3d6dLHhWkB6LdLFmqtUqwaLPKCRcaTag3dH49AgD0CvJD71B/t9uXZRlGgxkm\nU+fPIUcCg/zg7693+3FE5F0crGsMPymLxXzF8cWz6u5oaDQiLDQAANDUZEJIiPsDta4SeVa9qajE\nre39ggNhjAiBPqT7M7k01FcjLDy62+10x+Vn1S2yjCaT88F6iH/XJmMztJix4/Mj7a75cEaSgCk3\nD4V/hO8M1vl+Kw6z9S2cupGIyAMOF/18gedPRy94sSdKk937J8s4cOBLRfZccHCrIu34GotFhsVs\ndfsfEfkmDtY1hnOnisV8xTlbVuftLmhWSeUxb3dBszjPujh8vxWH2foWDtaJiIiIiFSKNesawzo0\nsXw9X6tsRXnVKcgKzmGuk3Qwmlq63Y7Wa9a9iTPBiMOZYMTx9fdbNWO2voWDdaIexGq1YNuhf6C2\nqVqxNs019bAYjK4/QAKsxu59KRAREVFPwcG6xnDuVLGYb3vGmjo0nynvdju+Os+6q0JDAmzLIcGt\nM8FIkgRdQPu3Yb/gIATHRHTYVmCvMDR2eG97aptnPSxMmRlcQsO6P6NMd3GedXH4fisOs/UtHKwT\nEXnA1UP72JYHD+oNAAiI7AX0img3U4eufzL045M6bKsZQG1prZB+esLo0TPQpMBE68NHzXBpu76J\nfggMVfYC5uCAMBz5kTOsEJF4HKxrDD8pi8V8xdHyWfXONDeaYDaZ7W6rrW5G+QnlBpdqOqvuDcGh\nZnxV/A9F27w2dTIkqR/PqgvE91txmK1v4WCdiIioBzAazKi92OT244KC/REY5Lkv8SIiexysawzr\n0MRivuJovWbdm9RWs64lvlKzLsvA7i0/demxk2YO9spgne+34jBb38J51omIiIiIVIqDdY3hJ2Wx\nmK84Wj+r3tD48/SWTU2enbpSbWfV6+uVmTq0QaF2usMXzqr7Kr7fisNsfYvTwfq9996LuLg4DBs2\nzHZbdXU1pk2bhkGDBmH69Omoqamx3bdixQqkpqZiyJAh2Lp1q5heExH5mMNF523LPx294MWeeN+B\nA18q0k7BQf6OISLtc1qzvnjxYvzud7/DPffcY7stOzsb06ZNw1NPPYWVK1ciOzsb2dnZKCwsxNq1\na1FYWIjS0lJMnToVxcXF0Ol4At9TWIcmlifzNRhbcLKyCFZZuenhJEkHo9mgWHtKYs26OGqqWbda\nrAiUregDs/ON2+gkXJD1kJX74l3F+ErNui/i7zNxmK1vcTpYv/HGG3Hy5Em72zZt2oTdu3cDABYu\nXIjJkycjOzsbGzduxIIFC+Dv74/k5GQMHDgQ+/btw3XXXSek80RaZpHN+OrwZjQbG7zdFXKBxSp3\nOpi0yoDZIsOixhFnF/kH+sHPwZc6OSM1NsD/fIXD+ywmC4wt9mVCAb2joIuIgQXayY6IyFVdmg2m\noqICcXFxAIC4uDhUVLS+6ZaVldkNzJOSklBaWqpAN8lV/KQsFvMVx5fPqusjekEOCoHF2slgMqwO\niI+HPwD/4/UITkqAzk8Pa52x3abBvQIRN1S5b+eMG3otmmuMqCt353tPnes7rhdONxS6/TjzyRo0\np550eF9MeDx0hkC72/TBFgQH1rcbqh8pNOKKQc4/zMp+4q4R4Fl1cfh+Kw6z9S3dnrpRkiRIktTp\n/UREWiYFBKC2ztTpWfMWgwW19abLlh0PIrcXrYefXtmZda++chz6XBGiaJtVplL8dPYHtx93oa6i\nk8e1v10XGACDfyDky4brp6uO4Jvif7m9f6X4+em6XJrTaJZxrqH9z99isS97C/HXISqEc5wT9WRd\n+m0QFxeHc+fOIT4+HuXl5YiNjQUAJCYm4syZM7btzp49i8TERIdtZGZmon///gCAiIgIDBs2zPZJ\nLy8vDwC43oX1tmW19Edr657Md/S1IwEAJUda/zo1YGiiKtdPl1yAofLnevOzZa3fvOnuetttXX28\nN9f1TRKCY6IBABVnW2coiUuyXw8ODbStm4w/12t3tL2S6xfP16FpVKPH9uds3d3jlwL8EJXS+nyr\nPNV6oW7sFX0QHBZkt375/SLXT/QqRL9+RnyzbTf69ktEyuDWawJO/HQMALq0HhfZF9s/PwmTyWo7\nY19ScgS9QwMwJHUEAKDo6CEA8Oh6UFQ1bp41DYB232972nrbbWrpj6+vty2fPn0aALBkyRIoSZJl\n5+cFTp48iVmzZqGgoAAA8NRTTyEmJgbLli1DdnY2ampqbBeY3nHHHdi3b5/tAtNjx461O7u+fft2\njB49WtEDoVa8aEQsT+bbZGjAR7tWqb5mvelkKZrPlHe7HV++wNSvT29caFBvPXrF2Wrb4NcXdXRm\nXQ0qT523DeS766r+16ClYhgMBovttqhgfyRGBHbyKPEmzRyMmNgwj++Xv8/EYbZi5efnIz09XbH2\nnMJxCUcAABJ+SURBVJ5ZX7BgAXbv3o0LFy6gX79+ePHFF7F8+XJkZGTgvffeQ3JyMtatWwcASEtL\nQ0ZGBtLS0uDn54fVq1ezDMbD+OITy5P5SuhZrx1fHaj7Al8eqKudUgN1ao+/z8Rhtr7F6WD9k08+\ncXj7tm3bHN6elZWFrKys7vWKyMfUN9Vgb/EOWGWL841dZJWtMJiaFGuPiIiIfI+yVzCR1/FPW2J1\nlK9FtqC47BDMFs9+M6WW+HIZjNr5ehmMmilZBkP2+PtMHGbrW/htRUREREREKsXBusbwk7JYzFcc\nrZ9Vb2pocbjsCWo7q67U8TfXNyvSTnfwrLo4fL8Vh9n6Fg7WiYg84Njhsw6XeyKljv/EwRJF2iEi\nUjMO1jXm0jk/SXnMV5xL51snZbXNXU7Ka5t3nZTH91txmK1v4QWm1ONYrRaYunghqMlshMHU/k/4\nLnxdgU+wGoyQL/sGRWfc3V7N9FGRkAOD3H6c7O8PuYEz95A2VVU2oLHe4PbjIqKCERGt7LfmEvVE\nHKxrDOvQnKuqr8Tn+z/s8uNP7v6u3W2ybNXETDCmmno0FHuntEANNetSQCCq67ryczShy9877wFq\nq1nXkp5Qs/5jfmmXHnfd5Cu7NVjn7zNxmK1v4WCdeqT65hpvd4GIiIjIKdasawzr0MQqOdK1M0zk\nnGpr1uXWk+ad/YMLJ9WDQwMdLnuC2mrWlTr+4DD3S5aUxpp1cfj7TBxm61t4Zp2IqBNWWYYSVfmp\nV/dzuNwTKXX8KaNSFGmHiEjNOFjXGNahiTVgaKK3u6BZaqhZ1yqfr1m3WBHob3XvugCdDi0euIxA\nyZr1JmM9rkgxwmyx2G4L0psRFGhy/tcbCdBL7W/28/NH47lgmE2+dyE4f5+Jw2x9CwfrRESkalaz\nGWgwu/UYXXAwoNcL6pEYJeeKUXKuuN3tEhyMwi/jp5MQGtD+eJPjUzHAf6pPDtaJqBVr1jWGdWhi\nsWZdHNXWrGuA2mrWtcQTNeuyC/9pEX+ficNsfQvPrJOq1TXV4EJdmaJtGk3uzxdMRERE5A0crGuM\n1urQ6ptr8Pn+//V2N2xYsy6O1mvWmxpaEPJ/s5dcuuwJaqtZV+r4PZ2jIz1hnnVv0drvMzVhtr6F\nZTBERB5w7PBZh8s9kVLH39NzVDudToLVKrv9T7Zqs6yHqKt4Zl1j8vLy+IlZoJIjpTy7LsjZsjrF\nzq7ro6OAgAC3Hyf7BwBw70JGX1Bxtlp1Z9e1ovLUeZ5d70D+t6fg7+CiV2eGDOuLfinR/H0mELP1\nLRysE5H2BASius7U6SZWWXYwHV77x/AcH1F7ks75DDUGgxkGg+sfftvOqFssnLmG6FIcrGsMPymL\n5Utn1WWTGVaTe2eJZS/+kvR0zbrDsbpG8ay6OGo/q17bUA1zv7PQhyv32vbz06PZXAezWbm/QgUG\nBCK8JRX1F39uk7/PxGG2voWDdSKNsjQ2o7bgJ293g4g8wGKVYTBb2t1+rqYS52o22NYlSUKAXn2X\nq4WF9MLUtFTogwCTrh4XG5T5KB0WFAF/P/dL4ojUhIN1jWEdmlisWRdHyZp1NQoODXS47Alqq1lX\n6vg7a0eCDHf3YoWjQqjOqaVm3QoZzWbnA1w/lQ7WG5rqsCl/DQAg6kIIQsMDu/1+G+AfhNtvfIiD\ndQc4VvAtHKwTkWr5JyXC1P5koVMGi/oKXFKv7udwuSdS6vg7a8fS3OJ2e/rQEJgk9Q1kewqrtbVU\nxypbYTZbYLG0/t9VkmRfS2+1duHNg0iFOFjXGH5SFotn1cVxdFbdbLGittboVjuy+sbpXqems+pa\no4az6lpTU92EuovNCA4PRUVprcuPC48MRlgvz/7VyldxrOBbOFgn0irJ+WwNWmSVtfrl60TdZ5Fl\nNLgwQ4tOkhAcoIc33kVkK2DpwquY87OTVnGwrjGu1qGdOX8MxWUFiu47OrwPAv1CFG2zyVCnaHvd\n5a2adavBiOYz5yBbXZ/RQTa6W33rXVqvWfcmtdWsa4laatZdJQMwu/DnJ50MmCxW51MmSYC/ToIk\n4ORAWUklEgbEKt4usWbd13Cw3kM1G5tw+PR+b3eDXGWVYai44NZgnYjcI0kS/N0cc2q1wt0KGU0u\nXDCik6QuffGRJ8iyDKPZgNrGakXbDfAPhKTwT95P7wc/vb+ibZJ2cLCuMfykLBZr1sXR+ln1poYW\nhIQFtVv2BLWdVVfq+JXO0drYBJ2bhR+JyX1gYPWFEN09q26yGPFp3l8V6s3PAvyDIClcIHTrtXch\nNtJzv184VvAtHKwT+QIfLz/375cEk9n9vwoYXZiKzlccO3wWw8cNbLfcEyl1/ErnKMsy3P2qLB9/\naWqKLMuwXPY+YzE7nxVIAqDzc/1Mucni3kXvrth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- "text": [ - "" - ] - } - ], - "prompt_number": 41 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "(Plots like these are what inspired the book's cover.)\n", - "\n", - "What can we say about the results above? Clearly TSLA has been a strong performer, and our analysis suggests that it has an almost 1% daily return! Similarly, most of the distribution of AAPL is negative, suggesting that it's *true daily return* is negative.\n", - "\n", - "\n", - "You may not have immediately noticed, but these variables are a whole order of magnitude *less* than our priors on them. For example, to put these one the same scale as the above prior distributions:" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "figsize(11.0, 3)\n", - "for i in range(4):\n", - " plt.subplot(2, 2, i + 1)\n", - " plt.hist(mu_samples[:, i], alpha=0.8 - 0.05 * i, bins=30,\n", - " histtype=\"stepfilled\", normed=True, color=colors[i],\n", - " label=\"%s\" % stock_returns.keys()[i])\n", - " plt.title(\"%s\" % stock_returns.keys()[i])\n", - " plt.xlim(-0.15, 0.15)\n", - "\n", - "plt.suptitle(\"Posterior distribution of daily stock returns\")\n", - "plt.tight_layout()" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "metadata": {}, - "output_type": "display_data", - "png": 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NzJkzK71Wy8NbtXLvaSFPLeQIkqeoqMqvTwMCAti5cydZWVkVxrpGRkbStGnT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\n5Gmrnair4ufnR7NmzXB2dsbV1ZWDBw+Sk5PDmDF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- "text": [ - "" - ] - } - ], - "prompt_number": 43 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Why did this occur? Recall how I mentioned that finance has a very very low signal to noise ratio. This implies an environment where inference is much more difficult. One should be careful about over-interpreting these results: notice (in the first figure) that each distribution is positive at 0, implying that the stock may return nothing. Furthermore, the subjective priors influenced the results. From the fund managers point of view, this is good as it reflects his updated beliefs about the stocks, whereas from a neutral viewpoint this can be too subjective of a result. \n", - "\n", - "Below we show the posterior correlation matrix, and posterior standard deviations. An important caveat to know is that the Wishart distribution models the *inverse covariance matrix*, so we must invert it to get the covariance matrix. We also normalize the matrix to acquire the *correlation matrix*. Since we cannot plot hundreds of matrices effectively, we settle by summarizing the posterior distribution of correlation matrices by showing the *mean posterior correlation matrix* (defined on line 2)." - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "inv_cov_samples = mcmc.trace(\"inv_cov_matrix\")[:]\n", - "mean_covariance_matrix = np.linalg.inv(inv_cov_samples.mean(axis=0))\n", - "\n", - "\n", - "def cov2corr(A):\n", - " \"\"\"\n", - " covariance matrix to correlation matrix.\n", - " \"\"\"\n", - " d = np.sqrt(A.diagonal())\n", - " A = ((A.T / d).T) / d\n", - " #A[ np.diag_indices(A.shape[0]) ] = np.ones( A.shape[0] )\n", - " return A\n", - "\n", - "\n", - "plt.subplot(1, 2, 1)\n", - "plt.imshow(cov2corr(mean_covariance_matrix), interpolation=\"none\",\n", - " cmap=plt.cm.hot)\n", - "plt.xticks(np.arange(4), stock_returns.keys())\n", - "plt.yticks(np.arange(4), stock_returns.keys())\n", - "plt.colorbar(orientation=\"vertical\")\n", - "plt.title(\"(mean posterior) Correlation Matrix\")\n", - "\n", - "plt.subplot(1, 2, 2)\n", - "plt.bar(np.arange(4), np.sqrt(np.diag(mean_covariance_matrix)),\n", - " color=\"#348ABD\", alpha=0.7)\n", - "plt.xticks(np.arange(4) + 0.5, stock_returns.keys());\n", - "plt.title(\"(mean posterior) variances of daily stock returns\")\n", - "\n", - "plt.tight_layout();" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "metadata": {}, - "output_type": "display_data", - "png": 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6i3xJwpX9LSwN2Oov3fpsvpFuXSr3AFhKuL6JkyYhRMtTScR68OABhg59OBRK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\nVFZWYtOmTQ7nWiwWbN++HR999BG8vLzs9qlUKuzatQsHDhw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- "text": [ - "" - ] - } - ], - "prompt_number": 47 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Looking at the above figures, we can say that it is likely that TSLA has an above-average volatility (looking at the return graph this is quite clear). The correlation matrix shows that there are no strong correlations present, but perhaps GOOG and AMZN express a higher correlation (about 0.30). \n", - "\n", - "With this Bayesian analysis of the stock market, we can throw it into a Mean-Variance optimizer (which I cannot stress enough to not use with frequentist point estimates) and find the minimum. This optimizer balances the tradeoff between a high return and high variance.\n", - "\n", - "$$ w_{opt} = \\min_{w} \\frac{1}{N}\\left( \\sum_{i=0}^N \\mu_i^T w - \\frac{\\lambda}{2}w^T\\Sigma_i w \\right)$$\n", - "\n", - "where $\\mu_i$ and $\\Sigma_i$ are the $i$th posterior estimate of the mean returns and the covariance matrix. This is another example of loss function optimization." - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### Protips for the Wishart distribution\n", - "\n", - "If you plan to be using the Wishart distribution, read on. Else, feel free to skip this. \n", - "\n", - "In the problem above, the Wishart distribution behaves pretty nicely. Unfortunately, this is rarely the case. The problem is that estimating an $NxN$ covariance matrix involves estimating $\\frac{1}{2}N(N-1)$ unknowns. This is a large number even for a modest $N$. Personally, I've tried performing a similar simulation as above with $N = 23$ stocks, and ended up giving considering that I was requesting my MCMC simulation to estimate at least $\\frac{1}{2}23*22 = 253$ additional unknowns (plus the other interesting unknowns in the problem). This is not easy for MCMC. Essentially, you are asking you MCMC to traverse a 250+ dimensional space. And the problem seemed so innocent initially! Below are some tips, in order of supremacy:\n", - "\n", - "1. Use conjugancy if it applies. See section below.\n", - "\n", - "2. Use a good starting value. What might be a good starting value? Why, the data's sample covariance matrix is! Note that this is not empirical Bayes: we are not touching the prior's parameters, we are modifying the starting value of the MCMC. Due to numerical instability, it is best to truncate the floats in the sample covariance matrix down a few degrees of precision (e.g. instability can cause unsymmetrical matrices, which can cause PyMC to cry.). \n", - "\n", - "3. Provide as much domain knowledge in the form of priors, if possible. I stress *if possible*. It is likely impossible to have an estimate about each $\\frac{1}{2}N(N-1)$ unknown. In this case, see number 4.\n", - "\n", - "4. Use empirical Bayes, i.e. use the sample covariance matrix as the prior's parameter.\n", - "\n", - "5. For problems where $N$ is very large, nothing is going to help. Instead, ask, do I really care about *every* correlation? Probably not. Furthermore ask yourself, do I really really care about correlations? Possibly not. In finance, we can set an informal hierarchy of what we might be interested in the most: first a good estimate of $\\mu$, the variances along the diagonal of the covariance matrix are secondly important, and finally the correlations are least important. So, it might be better to ignore the $\\frac{1}{2}(N-1)(N-2)$ correlations and instead focus on the more important unknowns.\n" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Conjugate Priors\n", - "\n", - "Recall that a $\\text{Beta}$ prior with $\\text{Binomial}$ data implies a $\\text{Beta}$ posterior. Graphically:\n", - "\n", - "$$ \\underbrace{\\text{Beta}}_{\\text{prior}} \\cdot \\overbrace{\\text{Binomial}}^{\\text{data}} = \\overbrace{\\text{Beta}}^{\\text{posterior} } $$ \n", - "\n", - "Notice the $\\text{Beta}$ on both sides of this equation (no, you cannot cancel them, this is not a *real* equation). This is a really useful property. It allows us to avoid using MCMC, since the posterior is known in closed form. Hence inference and analytics are easy to derive. This shortcut was the heart of the Bayesian Bandit algorithm above. Fortunately, there is an entire family of distributions that have similar behaviour. \n", - "\n", - "Suppose $X$ comes from, or is believed to come from, a well-known distribution, call it $f_{\\alpha}$, where $\\alpha$ are possibly unknown parameters of $f$. $f$ could be a Normal distribution, or Binomial distribution, etc. For particular distributions $f_{\\alpha}$, there may exist a prior distribution $p_{\\beta}$, such that:\n", - "\n", - "$$ \\overbrace{p_{\\beta}}^{\\text{prior}} \\cdot \\overbrace{f_{\\alpha}(X)}^{\\text{data}} = \\overbrace{p_{\\beta'}}^{\\text{posterior} } $$ \n", - "\n", - "where $\\beta'$ is a different set of parameters *but $p$ is the same distribution as the prior*. A prior $p$ that satisfies this relationship is called a *conjugate prior*. As I mentioned, they are useful computationally, as we can avoided approximate inference using MCMC and go directly to the posterior. This sounds great, right?\n", - "\n", - "Unfortunately, not quite. There are a few issues with conjugate priors.\n", - "\n", - "1. The conjugate prior is not objective. Hence it is only useful when a subjective prior is required. It is not guaranteed that the conjugate prior can accommodate the practitioner's subjective opinion.\n", - "\n", - "2. There typically exist conjugate priors for simple, one dimensional problems. For larger problems, involving more complicated structures, hope is lost to find a conjugate prior. For smaller models, Wikipedia has a nice [table of conjugate priors](http://en.wikipedia.org/wiki/Conjugate_prior#Table_of_conjugate_distributions).\n", - "\n", - "Really, conjugate priors are only useful for their mathematical convenience: it is simple to go from prior to posterior. I personally see conjugate priors as only a neat mathematical trick, and offer little insight into the problem at hand. " - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Jefferys Priors\n", - "\n", - "Earlier, we talked about objective priors rarely being *objective*. Partly what we mean by this is that we want a prior that doesn't bias our posterior estimates. The flat prior seems like a reasonable choice as it assigns equal probability to all values. \n", - "\n", - "But the flat prior is not transformation invariant. What does this mean? Suppose we have a random variable $ \\bf X $ from Bernoulli($\\theta$). We define the prior on $p(\\theta) = 1$. " - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "figsize(12.5, 5)\n", - "\n", - "x = np.linspace(0.000, 1, 150)\n", - "y = np.linspace(1.0, 1.0, 150)\n", - "lines = plt.plot(x, y, color=\"#A60628\", lw=3)\n", - "plt.fill_between(x, 0, y, alpha=0.2, color=lines[0].get_color())\n", - "plt.autoscale(tight=True)\n", - "plt.ylim(0, 2);" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "metadata": {}, - "output_type": "display_data", - "png": 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ykhVSyAtZ5X1i5rjvhDc3N0d/f3/ceuutMTY2Fhs3boxFixbFtm3bIiJi06ZNsWPHjti6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\nRU5ErkJggg==\n", - "text": [ - "" - ] - } - ], - "prompt_number": 48 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Now, let's transform $\\theta$ with the function $\\psi = log \\frac{\\theta}{1-\\theta}$. This is just a function to stretch $\\theta$ across the real line. Now how likely are different values of $\\psi$ under our transformation." - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "figsize(12.5, 5)\n", - "\n", - "psi = np.linspace(-10, 10, 150)\n", - "y = np.exp(psi) / (1 + np.exp(psi)) ** 2\n", - "lines = plt.plot(psi, y, color=\"#A60628\", lw=3)\n", - "plt.fill_between(psi, 0, y, alpha=0.2, color=lines[0].get_color())\n", - "plt.autoscale(tight=True)\n", - "plt.ylim(0, 1);" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "metadata": {}, - "output_type": "display_data", - "png": 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- "text": [ - "" - ] - } - ], - "prompt_number": 49 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Oh no! Our function is no longer flat. It turns out flat priors do carry information in them after all. The point of Jeffreys Priors is to create priors that don't accidentally become informative when you transform the variables you placed them originally on.\n", - "\n", - "Jeffreys Priors are defined as:\n", - "\n", - "$$p_J(\\theta) \\propto \\mathbf{I}(\\theta)^\\frac{1}{2}$$\n", - "$$\\mathbf{I}(\\theta) = - \\mathbb{E}\\bigg[\\frac{d^2 \\text{ log } p(X|\\theta)}{d\\theta^2}\\bigg]$$\n", - "\n", - "$\\mathbf{I}$ being the *Fisher information*" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "##Effect of the prior as $N$ increases\n", - "\n", - "In the first chapter, I proposed that as the amount of observations, or data, that we posses, the less the prior matters. This is intuitive. After all, our prior is based on previous information, and eventually enough new information will shadow our previous information's value. The smothering of the prior by enough data is also helpful: if our prior is significantly wrong, then the self-correcting nature of the data will present to us a *less wrong*, and eventually *correct*, posterior. \n", - "\n", - "We can see this mathematically. First, recall Bayes Theorem from Chapter 1 that relates the prior to the posterior. The following is a sample from [What is the relationship between sample size and the influence of prior on posterior?](http://stats.stackexchange.com/questions/30387/what-is-the-relationship-between-sample-size-and-the-influence-of-prior-on-poste)[1] on CrossValidated.\n", - "\n", - ">The posterior distribution for a parameter $\\theta$, given a data set ${\\bf X}$ can be written as \n", - "\n", - "$$p(\\theta | {\\bf X}) \\propto \\underbrace{p({\\bf X} | \\theta)}_{{\\rm likelihood}} \\cdot \\overbrace{ p(\\theta) }^{ {\\rm prior} } $$\n", - "\n", - "\n", - "\n", - ">or, as is more commonly displayed on the log scale, \n", - "\n", - "$$ \\log( p(\\theta | {\\bf X}) ) = c + L(\\theta;{\\bf X}) + \\log(p(\\theta)) $$\n", - "\n", - ">The log-likelihood, $L(\\theta;{\\bf X}) = \\log \\left( p({\\bf X}|\\theta) \\right)$, **scales with the sample size**, since it is a function of the data, while the prior density does not. Therefore, as the sample size increases, the absolute value of $L(\\theta;{\\bf X})$ is getting larger while $\\log(p(\\theta))$ stays fixed (for a fixed value of $\\theta$), thus the sum $L(\\theta;{\\bf X}) + \\log(p(\\theta))$ becomes more heavily influenced by $L(\\theta;{\\bf X})$ as the sample size increases. \n", - "\n", - "There is an interesting consequence not immediately apparent. As the sample size increases, the chosen prior has less influence. Hence inference converges regardless of chosen prior, so long as the areas of non-zero probabilities are the same. \n", - "\n", - "Below we visualize this. We examine the convergence of two posteriors of a Binomial's parameter $\\theta$, one with a flat prior and the other with a biased prior towards 0. As the sample size increases, the posteriors, and hence the inference, converge." - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "figsize(12.5, 15)\n", - "\n", - "p = 0.6\n", - "beta1_params = np.array([1., 1.])\n", - "beta2_params = np.array([2, 10])\n", - "beta = stats.beta\n", - "\n", - "x = np.linspace(0.00, 1, 125)\n", - "data = pm.rbernoulli(p, size=500)\n", - "\n", - "plt.figure()\n", - "for i, N in enumerate([0, 4, 8, 32, 64, 128, 500]):\n", - " s = data[:N].sum()\n", - " plt.subplot(8, 1, i + 1)\n", - " params1 = beta1_params + np.array([s, N - s])\n", - " params2 = beta2_params + np.array([s, N - s])\n", - " y1, y2 = beta.pdf(x, *params1), beta.pdf(x, *params2)\n", - " plt.plot(x, y1, label=r\"flat prior\", lw=3)\n", - " plt.plot(x, y2, label=\"biased prior\", lw=3)\n", - " plt.fill_between(x, 0, y1, color=\"#348ABD\", alpha=0.15)\n", - " plt.fill_between(x, 0, y2, color=\"#A60628\", alpha=0.15)\n", - " plt.legend(title=\"N=%d\" % N)\n", - " plt.vlines(p, 0.0, 7.5, linestyles=\"--\", linewidth=1)\n", - " #plt.ylim( 0, 10)#" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "metadata": {}, - "output_type": "display_data", - "png": 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/LJvcZWsB8GkTSWi/JEL6JxLaL4nAHp1Ru+ldshBCCCGaB5fN852dnc2wYcM4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PGEXTgGdbAYwCX0HnaXTHGdg8JaO0V1dgprHRTV2imtb90AYa1KIslkoH+4gdRwo/cRbuz5M7AI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MtaqaqqMptmD7wFEqDhzFknf+N0bW0jKqjpZRdfRE/fIzGtC6u6H1cEfr4YbWxYjGaETjYkTr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\n6/26RqWdnD9/nsGDB9OzZ0/69evH3XffXSvwFkII0XqZLpdw8q0FWjn2d+O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- "text": [ - "" - ] - } - ], - "prompt_number": 50 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Keep in mind, not all posteriors will \"forget\" the prior this quickly. This example was just to show that *eventually* the prior is forgotten. The \"forgetfulness\" of the prior as we become awash in more and more data is the reason why Bayesian and Frequentist inference eventually converge as well." - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### Bayesian perspective of Penalized Linear Regressions\n", - "\n", - "There is a very interesting relationship between a penalized least-squares regression and Bayesian priors. A penalized linear regression is a optimization problem of the form:\n", - "\n", - "$$ \\text{argmin}_{\\beta} \\;\\; (Y - X\\beta)^T(Y - X\\beta) + f(\\beta)$$\n", - "\n", - "for some function $f$ (typically a norm like $|| \\cdot ||_p^p$). \n", - "\n", - "We will first describe the probabilistic interpretation of least-squares linear regression. Denote our response variable $Y$, and features are contained in the data matrix $X$. The standard linear model is:\n", - "\n", - "\\begin{equation}\n", - "Y = X\\beta + \\epsilon\n", - "\\end{equation}\n", - "\n", - "where $\\epsilon \\sim \\text{Normal}( {\\bf 0}, \\sigma{\\bf I })$. Simply, the observed $Y$ is a linear function of $X$ (with coefficients $\\beta$) plus some noise term. Our unknown to be determined is $\\beta$. We use the following property of Normal random variables:\n", - "\n", - "$$ \\mu' + \\text{Normal}( \\mu, \\sigma ) \\sim \\text{Normal}( \\mu' + \\mu , \\sigma ) $$\n", - "\n", - "to rewrite the above linear model as:\n", - "\n", - "\\begin{align}\n", - "& Y = X\\beta + \\text{Normal}( {\\bf 0}, \\sigma{\\bf I }) \\\\\\\\\n", - "& Y = \\text{Normal}( X\\beta , \\sigma{\\bf I }) \\\\\\\\\n", - "\\end{align}\n", - "\n", - "In probabilistic notation, denote $f_Y(y \\; | \\; \\beta )$ the probability distribution of $Y$, and recalling the density function for a Normal random variable (see [here](http://en.wikipedia.org/wiki/Normal_distribution) ):\n", - "\n", - "$$ f_Y( Y \\; |\\; \\beta, X) = L(\\beta|\\; X,Y)= \\frac{1}{\\sqrt{ 2\\pi\\sigma} } \\exp \\left( \\frac{1}{2\\sigma^2} (Y - X\\beta)^T(Y - X\\beta) \\right) $$\n", - "\n", - "This is the likelihood function for $\\beta$. Taking the $\\log$:\n", - "\n", - "$$ \\ell(\\beta) = K - c(Y - X\\beta)^T(Y - X\\beta) $$\n", - "\n", - "where $K$ and $c>0$ are constants. Maximum likelihood techniques wish to maximize this for $\\beta$, \n", - "\n", - "$$\\hat{ \\beta } = \\text{argmax}_{\\beta} \\;\\; - (Y - X\\beta)^T(Y - X\\beta) $$\n", - "\n", - "Equivalently we can *minimize the negative* of the above:\n", - "\n", - "$$\\hat{ \\beta } = \\text{argmin}_{\\beta} \\;\\; (Y - X\\beta)^T(Y - X\\beta) $$\n", - "\n", - "This is the familiar least-squares linear regression equation. Therefore we showed that the solution to a linear least-squares is the same as the maximum likelihood assuming Normal noise. Next we extend this to show how we can arrive at penalized linear regression by a suitable choice of prior on $\\beta$. \n", - "\n", - "#### Penalized least-squares\n", - "\n", - "In the above, once we have the likelihood, we can include a prior distribution on $\\beta$ to derive to the equation for the posterior distribution:\n", - "\n", - "$$P( \\beta | Y, X ) = L(\\beta|\\;X,Y)p( \\beta )$$\n", - "\n", - "where $p(\\beta)$ is a prior on the elements of $\\beta$. What are some interesting priors? \n", - "\n", - "1\\. If we include *no explicit* prior term, we are actually including an uninformative prior, $P( \\beta ) \\propto 1$, think of it as uniform over all numbers. \n", - "\n", - "2\\. If we have reason to believe the elements of $\\beta$ are not too large, we can suppose that *a priori*:\n", - "\n", - "$$ \\beta \\sim \\text{Normal}({\\bf 0 }, \\lambda {\\bf I } ) $$\n", - "\n", - "The resulting posterior density function for $\\beta$ is *proportional to*:\n", - "\n", - "$$ \\exp \\left( \\frac{1}{2\\sigma^2} (Y - X\\beta)^T(Y - X\\beta) \\right) \\exp \\left( \\frac{1}{2\\lambda^2} \\beta^T\\beta \\right) $$\n", - "\n", - "and taking the $\\log$ of this, and combining and redefining constants, we arrive at:\n", - "\n", - "$$ \\ell(\\beta) \\propto K - (Y - X\\beta)^T(Y - X\\beta) - \\alpha \\beta^T\\beta $$\n", - "\n", - "we arrive at the function we wish to maximize (recall the point that maximizes the posterior distribution is the MAP, or *maximum a posterior*):\n", - "\n", - "$$\\hat{ \\beta } = \\text{argmax}_{\\beta} \\;\\; -(Y - X\\beta)^T(Y - X\\beta) - \\alpha \\;\\beta^T\\beta $$\n", - "\n", - "Equivalently, we can minimize the negative of the above, and rewriting $\\beta^T \\beta = ||\\beta||_2^2$:\n", - "\n", - "$$\\hat{ \\beta } = \\text{argmin}_{\\beta} \\;\\; (Y - X\\beta)^T(Y - X\\beta) + \\alpha \\;||\\beta||_2^2$$\n", - "\n", - "This above term is exactly Ridge Regression. Thus we can see that ridge regression corresponds to the MAP of a linear model with Normal errors and a Normal prior on $\\beta$.\n", - "\n", - "3\\. Similarly, if we assume a *Laplace* prior on $\\beta$, ie. \n", - "\n", - "$$ f_\\beta( \\beta) \\propto \\exp \\left(- \\lambda ||\\beta||_1 \\right)$$\n", - "\n", - "and following the same steps as above, we recover:\n", - "\n", - "$$\\hat{ \\beta } = \\text{argmin}_{\\beta} \\;\\; (Y - X\\beta)^T(Y - X\\beta) + \\alpha \\;||\\beta||_1$$\n", - "\n", - "which is LASSO regression. Some important notes about this equivalence. The sparsity that is a result of using a LASSO regularization is not a result of the prior assigning high probability to sparsity. Quite the opposite actually. It is the combination of the $|| \\cdot ||_1$ function and using the MAP that creates sparsity on $\\beta$: [purely a geometric argument](http://camdp.com/blogs/least-squares-regression-l1-penalty). The prior does contribute to an overall shrinking of the coefficients towards 0 though. An interesting discussion of this can be found in [2].\n", - "\n", - "For an example of Bayesian linear regression, see Chapter 4's example on financial losses." - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "##### References\n", - "\n", - "1. Macro, . \"What is the relationship between sample size and the influence of prior on posterior?.\" 13 Jun 2013. StackOverflow, Online Posting to Cross-Validated. Web. 25 Apr. 2013.\n", - "\n", - "2. Starck, J.-L., , et al. \"Sparsity and the Bayesian Perspective.\" Astronomy & Astrophysics. (2013): n. page. Print.\n", - "\n", - "3. Kuleshov, Volodymyr, and Doina Precup. \"Algorithms for the multi-armed bandit problem.\" Journal of Machine Learning Research. (2000): 1-49. Print.\n", - "\n", - "4. Gelman, Andrew. \"Prior distributions for variance parameters in hierarchical models.\" Bayesian Analysis. 1.3 (2006): 515-533. Print.\n", - "\n", - "5. Gelman, Andrew, and Cosma R. Shalizi. \"Philosophy and the practice of Bayesian statistics.\" British Journal of Mathematical and Statistical Psychology. (2012): n. page. Web. 17 Apr. 2013.\n", - "\n", - "6. http://jmlr.csail.mit.edu/proceedings/papers/v22/kaufmann12/kaufmann12.pdf\n", - "\n", - "7. James, Neufeld. \"Reddit's \"best\" comment scoring algorithm as a multi-armed bandit task.\" Simple ML Hacks. Blogger, 09 Apr 2013. Web. 25 Apr. 2013.\n", - "\n", - "8. Oakley, J. E., Daneshkhah, A. and O\u2019Hagan, A. Nonparametric elicitation using the roulette method. Submitted to Bayesian Analysis.\n", - "\n", - "9. \"Eliciting priors from experts.\" 19 Jul 2010. StackOverflow, Online Posting to Cross-Validated. Web. 1 May. 2013. .\n", - "\n", - "10. Taleb, Nassim Nicholas (2007), The Black Swan: The Impact of the Highly Improbable, Random House, ISBN 978-1400063512" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "from IPython.core.display import HTML\n", - "\n", - "\n", - "def css_styling():\n", - " styles = open(\"../styles/custom.css\", \"r\").read()\n", - " return HTML(styles)\n", - "css_styling()" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "html": [ - "\n", - "\n" - ], - "metadata": {}, - "output_type": "pyout", - "prompt_number": 1, - "text": [ - "" - ] - } - ], - "prompt_number": 1 - }, - { - "cell_type": "code", - "collapsed": false, - "input": [], - "language": "python", - "metadata": {}, - "outputs": [] - } - ], - "metadata": {} - } - ] +{ + "metadata": { + "name": "" + }, + "nbformat": 3, + "nbformat_minor": 0, + "worksheets": [ + { + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "#Chapter 6\n", + "\n", + "____\n", + "\n", + "This chapter of [Bayesian Methods for Hackers](https://github.com/CamDavidsonPilon/Probabilistic-Programming-and-Bayesian-Methods-for-Hackers) focuses on the most debated and discussed part of Bayesian methodologies: how to choose an appropriate prior distribution. We also present how the prior's influence changes as our dataset increases, and an interesting relationship between priors and penalties on linear regression." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Getting our priorities straight\n", + "\n", + "\n", + "Up until now, we have mostly ignored our choice of priors. This is unfortunate as we can be very expressive with our priors, but we also must be careful about choosing them. This is especially true if we want to be objective, that is, not to express any personal beliefs in the priors. \n", + "\n", + "###Subjective vs Objective priors\n", + "\n", + "Bayesian priors can be classified into two classes: *objective* priors, which aim to allow the data to influence the posterior the most, and *subjective* priors, which allow the practitioner to express his or her views into the prior. \n", + "\n", + "What is an example of an objective prior? We have seen some already, including the *flat* prior, which is a uniform distribution over the entire possible range of the unknown. Using a flat prior implies that we give each possible value an equal weighting. Choosing this type of prior is invoking what is called \"The Principle of Indifference\", literally we have no prior reason to favor one value over another. Calling a flat prior over a restricted space an objective prior is not correct, though it seems similar. If we know $p$ in a Binomial model is greater than 0.5, then $\\text{Uniform}(0.5,1)$ is not an objective prior (since we have used prior knowledge) even though it is \"flat\" over [0.5, 1]. The flat prior must be flat along the *entire* range of possibilities. \n", + "\n", + "Aside from the flat prior, other examples of objective priors are less obvious, but they contain important characteristics that reflect objectivity. For now, it should be said that *rarely* is a objective prior *truly* objective. We will see this later. \n", + "\n", + "#### Subjective Priors\n", + "\n", + "On the other hand, if we added more probability mass to certain areas of the prior, and less elsewhere, we are biasing our inference towards the unknowns existing in the former area. This is known as a subjective, or *informative* prior. In the figure below, the subjective prior reflects a belief that the unknown likely lives around 0.5, and not around the extremes. The objective prior is insensitive to this." + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "%matplotlib inline\n", + "import numpy as np\n", + "from IPython.core.pylabtools import figsize\n", + "import matplotlib.pyplot as plt\n", + "import scipy.stats as stats\n", + "\n", + "figsize(12.5, 3)\n", + "colors = [\"#348ABD\", \"#A60628\", \"#7A68A6\", \"#467821\"]\n", + "\n", + "x = np.linspace(0, 1)\n", + "y1, y2 = stats.beta.pdf(x, 1, 1), stats.beta.pdf(x, 10, 10)\n", + "\n", + "p = plt.plot(x, y1,\n", + " label='An objective prior \\n(uninformative, \\n\"Principle of Indifference\" )')\n", + "plt.fill_between(x, 0, y1, color=p[0].get_color(), alpha=0.3)\n", + "\n", + "p = plt.plot(x, y2,\n", + " label=\"A subjective prior \\n(informative)\")\n", + "plt.fill_between(x, 0, y2, color=p[0].get_color(), alpha=0.3)\n", + "\n", + "p = plt.plot(x[25:], 2 * np.ones(25), label=\"another subjective prior\")\n", + "plt.fill_between(x[25:], 0, 2, color=p[0].get_color(), alpha=0.3)\n", + "\n", + "plt.ylim(0, 4)\n", + "\n", + "plt.ylim(0, 4)\n", + "leg = plt.legend(loc=\"upper left\")\n", + "leg.get_frame().set_alpha(0.4)\n", + "plt.title(\"Comparing objective vs. subjective priors for an unknown probability\");" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "display_data", + "png": 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gwL7+jo6OkJeXx9WrVxEREYFWrVrBy8sLsbGxyM3NxZUrV+Do6Agej8fWUdvjIs35sfzr\nFxcXhy5dukBe/t/b3Dp06AA1NTWxNlxZO4+PjwcAfPr0Cb6+vmjXrh20tLSgqqqK4ODgCq95Tc7h\nX2LatGm4fv06nj59CqCkPQ4ePBjNmzev0+1QskOT8CbM3NwcHA6n0gSjNiQNu1R+HsMw7I1dlSn7\nBeHWrVsYMWIEevbsiaCgINy9exd79+4FIUSsf6acnJxUN+hwOByxE2jp/6Ux1fdoA9J++QH+jWn7\n9u24f/8++/fgwQMkJiaiXbt2dRrbuHHjcPHiRbx69QoXLlzAx48fMWrUqC+Opap6AWDZsmVISEjA\niBEj8OjRI3Tp0gXLly+XOm4Oh4OQkBBcuXIF9vb2OHXqFFq3bo0LFy6wywHxY19cXFxtOyy/Tnki\nkQhqampix+P+/ft4/PgxQkJCpKpDWhoaGnB3d2f7sB86dAiDBw9Gs2bNahRLbdXVTaIMw1Soq7rX\nry5J2r4kf/zxB2bOnInRo0cjJCQE9+7dw4oVK8TOOQAqnHPKn08k4XA4FdpEYWFhhXKSzp3l11NX\nV4eTkxPOnDmD58+fS9yepBilOQeX7guPx0PXrl0RGhqKsLAw9OrVCy1atECbNm0QHh6OK1eusPcy\nVLVNoOrjUrrdqkh6/SQdl9pYuHAhjh49ilWrVuHq1au4d+8eBgwYINbfW5oY64qlpSW6d++O/fv3\n4+XLlzh37hymTp36VbZNfR00CW/CNDU10b9/f+zcuVPsJsdShYWF+PTpE8zMzMDj8RAeHi62PDw8\nHO3bt6+TWMrfcHbjxg1YWVkBKBnCrXnz5lizZg3s7e1hZmaG9PT0OtmuJJaWlrhz547Yh0VUVFS1\n61lZWUk8RqU3dZUqX/eNGzfA4/HEypTS0dFBy5Yt8eTJE5iYmFT44/F47M2Yly5dqjQ2Lpcr1XCT\nffv2haamJgICAnDo0CG4u7tDTU1N6lhqU28pY2NjeHt7448//sDq1auxZ8+eauMtz97eHkuWLEF4\neDicnZ1x4MABAP+OaFI2Sbl3757ED9Oq2mJ5nTp1wtu3b5GXl1fheJReNe7UqRPi4+OrTZCkeX3G\njx+P4OBgJCQkICQkROzXBHt7+2pjqUxOTg5SUlLY6YSEBLx69QqWlpbVxlSWtO+BylT2+n2t7Zd1\n7do12NjYYM6cObCxsYGpqSmEQmGN6qiMtrZ2hfYQGxtb4QKANBcEuFwuTp8+jfbt28PZ2bnCVdvq\nWFlZ4fXr13j8+DE7Lz8/H7du3RL7Yu3i4oIrV67gypUrcHV1BQD06tULgYGBuH//foUkvLZqcn4s\nuw9RUVFiX2Tu37+Pd+/eie1Dde382rVr8PLygoeHB9q3bw9jY2M8ffq0wutQmxirUnoOkHQ+mjZt\nGg4dOoT9+/fD0NAQvXv3rtU2qIaJJuFN3O7du6GgoAA7OzscP34c8fHxSEpKwpEjR2Bvb4+kpCQo\nKSlh9uzZWL58OQIDA5GQkIANGzbg7Nmz7N3wX+q3337D8ePHkZCQgBUrViAqKgrz5s0DUPKTbE5O\nDn777TekpKTg0KFDtUrQpDVjxgy8ePEC3t7eePz4McLCwrB06VIAVX8oLlmyBKdOncLGjRuRkJCA\nkydPYvXq1Zg/f77Yz6SvX7+Gj48Pnjx5ggsXLmDFihWYPn06+Hy+xHrXr1+P7du3Y8OGDXj06BGe\nPn2KoKAgTJ8+HQCgoqKC+fPnY9WqVdi9ezcSEhJw//59+Pv7s3UYGxsjMjIS6enpePXqVaVXcuTl\n5eHp6Yndu3cjODgY48ePr1Eslamq3o8fP8LHxwdhYWEQCoW4e/cuLl68KJb4jhs3rkIsZd28eRNr\n167F7du3kZaWhtDQUDx48ICtw8zMDEZGRli1ahWePn2KyMhIzJ07V+LrWVVbLM/V1RW9e/fG0KFD\n8eeffyIlJQUxMTHYsWMHfv31VwDA6NGjYWRkhEGDBiE0NBRCoRChoaE4efIkAMDIyAgcDgcXLlzA\ny5cv8e7du0r3083NDRoaGhg5ciQ0NTXh5ubGLuvVq1e1sVRGSUkJEydORExMDKKjozF+/HjY2NjU\nOLGS5j1ASu5FEluvutevvrcviYWFBR4+fIizZ88iOTkZ27Ztq3akGWn17t0bly9fRmBgIJKSkuDv\n74/IyMgKcUkTJyEEcnJyOHnyJDp16gRnZ+dqvyyUrdfV1RWdO3eGp6cnbty4gUePHmHcuHEoKCiA\nt7c3W65Xr1548OAB7t+/DxcXF3bekSNHwOfzpeqyJ43qzo+SXr+ZM2fi/fv3mDBhAuLi4hAZGYmx\nY8fCyckJ3bp1Y8tV184tLCwQFBSEO3fuID4+HlOnTkVWVlaF7dX0HF6d0lFx/vzzT+Tk5ODjx4/s\nstJRrtatW4fJkyfXqn6qAfsqPc+pBi0nJ4csWLCAtG7dmigqKhJtbW3i5ORE9u7dy44YUlhYSHx9\nfYmBgQHhcrnEysqKHD9+XKweSTculr3xrZSioiL53//+Rwj598ahI0eOkJ49exJFRUViYmJSoe7l\ny5cTHR0doqysTAYOHEiOHz9OOBwOezPbgQMHiIKCQoV9Kz9fUrn09HTC4XBIeHg4O+/y5cukXbt2\nhMfjkY4dO5KQkBDCMAw5ffp0lcfy4MGDpG3btoTL5RIDAwOybNkyUlxczC7v2bMnmTRpElm4cCHR\n0tIiqqqqZMqUKewNTYRUvKmHEEKCgoKIo6MjUVJSIs2aNSPW1tZk7dq1YmW2bdtG2rRpQ7hcLtHR\n0SEjRoxgl0VHRxNbW1vC5/PZ4yYUCgmHw2FvzCxVekOTjo6OWOw1iUWSyur9/Pkz8fT0JMbGxmz7\nGzVqFMnIyBA7bi4uLpXWHRcXRwYMGEB0dXUJj8cjRkZGZNGiRWI3at26dYvY2dkRPp9PrK2tSURE\nRIUbMzkcTrVtsXw7z8vLI76+vsTY2JhwuVyiq6tL+vfvLzaiQnZ2Nhk3bhxp3rw5UVRUJG3bthV7\nX2zatIkYGBgQOTk5dj9XrVoldhNgqblz5xIOh0PmzZtXYZk0sZRXetPY0aNHSatWrYiioiLp3bu3\n2E2SlcUiab4074HyNyVK8/qVFxYWRjgcToUbXmuzfUkKCwvJtGnTiKamJmnWrBkZM2YM2blzJ+Fw\nOFXuf0REhNi5qbK658yZQ7S1tYm6ujqZOXMmWbFiBTE2NmbLlB9hg5CSG/iq2n5xcTHx8vIiLVu2\nJElJSZW+x8vfqJ2VlUVGjRpF1NXVCZ/PJz179iQxMTEVYlZVVSXW1tbsvLdv3xJ5eXni5uYmVra2\nx0Wa82Nlr19UVBRxcnIifD6fqKurkzFjxojdwFgaU1XtPD09nfTr148oKysTPT09smrVKjJp0iSx\nc480MZZ/7cofD0mfQ6XtgWEYMnHixArLuFwuyc7OrvTYUY0TQ0j1X7WLi4vRqVMnGBoa4ty5cxWW\nz549GyEhIVBSUsLvv/8OGxubevnCQH17UlNTYWJigsjISHTt2lXW4VTq2rVr6NmzJx4+fFjjq3M1\nNXr0aOTn54uNp041DPn5+eDz+QgKCsKgQYNkHU6dWLVqFY4ePYrExERZh0I1cS4uLjA3N8f+/ftl\nHUqDMmLECBQXF+PUqVOyDoWqY1I9MXPbtm2wtLTEhw8fKiwLDg5GUlISEhMTcevWLXh7e0vVf5ai\nGrI9e/agY8eO0NfXR3x8PObOnYsuXbrUawJeWFiIhIQEREVFVdn1gpKNt2/f4syZM2AYps5viKUo\nSvquQk3FmzdvcPv2bQQFBeHKlSuyDoeqB9X2Cc/IyEBwcDAmT54s8c1x9uxZNmFwcHDA27dvKwyh\nRFFVqe/RSGojLS2NfYLojBkz4OzsXC8jNZR1/fp1ODg4oF27dvjxxx/rdVtUzc2dOxd+fn7YuHGj\n2DBnjR3DMA3yPUg1PbQtirOxscHw4cOxePFidO/eXdbhUPWg2u4ow4cPh5+fH96/f4/NmzdX6I7i\n7u6OJUuWsF0JevfujY0bN0o9DitFURRFURRFNTVVdkc5f/48tLW1YWNjg6tXr1ZarnweL+mb7LFj\nx6Cjo1O7KCmKoiiKoiiqgcrNzcXgwYNrtE6VSfiNGzdw9uxZBAcH4/Pnz3j//j3GjRvHPiwCAAwM\nDMTGbM7IyICBgUGFunR0dGBra1uj4Kimy9/fH76+vrIOg2oEaFuhaoK2F0patK1QNREbG1vjdars\nE75hwwakp6dDKBQiICAAvXr1EkvAAWDQoEHsvKioKKirq9Mr3hRFURRFURRVBalGRylV2s1k3759\nAEqe5DRgwAAEBwfDzMwMysrKNX7CGUVJUtOnvlFNF20rVE3Q9kJJi7YVqr5JnYQ7OzvD2dkZQEny\nXdbOnTvrNiqqyWvfvr2sQ6AaCdpWqJqg7YWSFm0rVH2T6mE9dSE0NJT2CacoiqIoiqK+ObGxsXB1\nda3ROjXqjlJfPn/+jOLiYjo+KEVVghACRUVFyMnJyToUiqIoiqLqgMyT8MLCQgCAsrKyjCOhGpLE\nxESYm5vLOowGgxCCjx8/gs/n00S8nMjISPogC0pqtL1Q0qJthapv1T4xs74VFBRAUVFR1mFQVIPG\nMAyUlZXx+fNnWYdCURRFUVQdkHkSTrugUJLQq+AV0Uc6S0avVFE1QdsLJS3aVqj6JvMknKIoiqIo\niqKaGpqEUw1SYmKirEOgGonIyEhZh0A1IrS9UNKibYWqbzQJbyA6duyI8PBwictu3rwJBweHOt9m\nfdVbG127dsWNGzdkHQZFURRFUdRXQZNwKbi7u8PExAQFBQX1to2q+vs6Ojri1q1bX7wNLS0tpKam\n1nm9deHGjRvo2rUrO037hFPSov02qZqg7YWSFm0rVH2jSXg10tLSEBsbixYtWiAkJETW4Xyxr/Rs\nJqkVFRXJdH2KoiiKoihZoEl4NQICAuDs7IwRI0YgICBAbJmPjw8WLlyIUaNGQSAQoE+fPmJXmssL\nCQmBo6MjjI2NMWjQICQkJIgtj42NhaOjI0xMTDBz5kzk5+cDKOmX1q5dO7ZcVlYWxo0bh9atW8PG\nxgb79+9nl4lEImzZsgV2dnYQCARwdXXF8+fPMXDgQACAk5MTBAIBgoKCxOrdtm0bJkyYIBaPr68v\nfH19AQDv37/HrFmzYGlpCSsrK6xfvx4ikUjifvr7+2P8+PGYNGkSBAIBXFxcEBcXxy7v2LEjtm/f\nju7du0MgEKC4uFisO05+fj68vb1hZWUFKysr+Pn5sb9CREZGwsrKCtu3b0fbtm0xe/bsSo831TTQ\nfptUTdD2QkmLthWqvtEkvBonTpzA999/jyFDhuDKlSvIyckRW37mzBksXrwYQqEQJiYmWLduncR6\nkpKSMHXqVPj7+yMpKQm9e/eGp6cneyWXEILAwECcOnUKsbGxSE5OxubNmyvUIxKJ4OnpiQ4dOiA+\nPh5BQUHYu3cvrly5AgDYuXMnTp8+jZMnTyItLQ3bt2+HkpISLly4AACIiIhAWloahgwZIlbv0KFD\ncfnyZeTm5gIAiouLcfbsWQwfPhxAyRcOLpeLmJgYhIeHIywsDIcOHar0uF28eBFDhgyBUCjEsGHD\n4OXlheLiYnZ5aYxCoRBycnJi3XF+/vlnxMfH49q1a7h27RpiY2PFjkVOTg7evn2LBw8eYMuWLZXG\nQFEURVEU1VBVm4R//vwZDg4OsLa2hqWlJZYsWVKhzNWrV6GmpgYbGxvY2NhUmog2NlFRUcjKyoKb\nmxtMTU3Rpk0bBAYGipX57rvvYGNjAzk5OXh4eODhw4cS6zpz5gz69u0LZ2dnyMnJYdasWcjLy8Pt\n27cBlPQJnzx5MvT19aGuro558+bh9OnTFeqJjY3F69evsWDBAsjLy8PIyAhjx45lyx45cgTLli2D\nqakpAMDKygoaGhrV7mvLli3RoUMHNlm/du0a+Hw+7Ozs8PLlS1y+fBnr168Hn89H8+bN4e3tjTNn\nzlRan7W1Ndzd3SEnJwcfHx/k5+fjzp077L5OnToV+vr64PF4FdY9deoUli9fDi0tLWhpaWHRokU4\nefIku5zD4cDX1xcKCgr0QU8U7bdJ1QhtL5S0aFuh6lu1j61XVFREWFgYlJSUUFRUhO7du0t8lKuz\nszPOnj2CWQanAAAgAElEQVRbb4HKwvHjx+Hi4gJVVVUAwODBgxEQEABvb2+2TIsWLdj/+Xw+Pn78\nKLGuFy9ewNDQkJ1mGAYGBgbIyspi5xkYGLD/GxoaIjs7u0I96enpyM7OhrGxMTuvuLiYvakxMzMT\nrVq1quGelvDw8MCpU6cwcuRIBAYGwsPDg91mYWEh2rZty5YViURi+1Oevr4++z/DMNDX1xfbn7L7\nWl52djZatmzJTpc/FlpaWuByuTXbOYqiKIqiqAak2iQcAJSUlACUPGK+uLgYmpqaFco0tBv+vlRe\nXh6CgoJACGGTz/z8fLx79w5xcXGwsrKqUX26urqIj49npwkheP78OfT09Nh5z58/Z//PyMiArq5u\nhXoMDAxgZGTEXlWWtFwoFMLCwqJG8QHAoEGDsHz5cmRmZiI4OBh//fUXWyePx0NycjI4HOl6MJXd\nF5FIhMzMTLH9qerJj7q6uoiKikKbNm0AVDwW9KmRVFmSLgo0Bfk5/6A4L79W6yrqaIHDa5pfZJtq\ne6FqjrYVqr5JlYSLRCLY2toiOTkZ3t7esLS0FFvOMAxu3LiBjh07wsDAAJs3b65QprEJDg6GvLw8\nrl27xl51JYTghx9+QEBAANauXVuj+oYMGYJt27bh2rVrcHR0xN69e6GoqIjOnTuzdf/666/o27cv\n+Hw+tmzZgqFDh1aox87ODioqKti+fTumTJkCLpeLp0+fIj8/HzY2NvDy8sKGDRvQpk0bGBsbIz4+\nHvr6+tDQ0IC2tjaEQmGlV8qbN2+Obt26wcfHB61atWKHCdTV1YWLiwuWLl0KPz8/KCsr49mzZ8jK\nyhIbVrCs+/fv4/z583Bzc8O+ffvA4/Fgb28v1bEaOnQoDhw4gO+++w4A8NNPP2HEiBFSrUtR3yoi\nEuHdvcd4eSkCLy9GIPepsNZ1ySkponlPB2j364EWvbuCq6Veh5FSFEVR0pAqCedwOLh37x7evXuH\nfv364erVq+jZsye73NbWFunp6VBSUkJISAiGDBlSYeQPAJgxYwYEAgEAQE1NDe3bt4etrS2Af5+Q\nWJr4yXr6t99+w4ABA9huE6XLJ0+eDD8/P4wZMwbv378XW56RkcFepS1fHyEEK1euxOLFi5GVlQUz\nMzP85z//gbx8yUtQVFQEFxcXDBs2DNnZ2ejevTsGDx7MHruioiIkJibC3Nwcx48fx5w5c7Bjxw4U\nFxfD3NwcEyZMgIqKCnx8fFBQUIBBgwbh7du3sLCwwOHDh5GYmIgJEybAx8cHeXl5WLx4MTQ0NCrE\n6+HhAW9vb8yaNYvdHgDMnz8fu3fvhqOjI3Jzc6Gnp4dx48axSXjZ/WUYBj169MChQ4cwY8YMmJqa\nYt26dUhJSWHre/78uVj9hYWF7NXzBQsWID09HY6OjpCXl8fgwYMxZMgQdhsMw8i8fchqurS9ld61\nX3qVpilPl3aRayjx1OW0o509XkdE49LBo3hz5yFavy+5uTle9BGMggI6qGsDAOLy3wEArHhq1U+L\nRLj/Ogs4HwzL4HCAw0GamTY0OnfAAO8foGwqaDD7T9sLnabTdLqhTpf+n5aWBqAkP6wphtSwH8na\ntWvB5/OxYMGCSssYGxsjJiZGrNtKaGgom3CX9enTJ7a7CyXZtWvXMGfOHMTGxso6FKls3LgRQqEQ\ne/fulXUo3xz6fvn25ef8g5zLN/Dyr0i8unoLojJdThQ01aFuawk1W0uoWJiAIy/VdZQKCl6/xbu7\n8Xh7Nx658ckgZUYuUjIVQKdfD2i79YC6nRUYObkv3ieKoqhvXWxsLFxdXWu0TrVn8FevXkFeXh7q\n6urIy8vD33//jZUrV4qVefHiBbS1tcEwDG7fvg1CiMR+41TtPH78GEZGRrIOQ2p1cX9A2avkFFWV\nxt5vkxCCj0nP8PJSJF5eisDb6EdAmfcQv5UB1G2toGZrCX5LvTq5J4KrpY4WvbuiRe+uKM77jPcP\nE/AuNh7v7j3Gp+Q0CHcfhXD3UShoqkG7Tzdo9+sBLefOkFfmf/G2Za2xtxfq66Fthapv1SbhWVlZ\nGD9+PEQiEUQiEcaOHQtXV1fs27cPADBt2jQEBgZiz549kJeXh5KSUoWH2lC15+vri7/++gu7d++W\ndShSKzvmN0VRkpHiYqQfPYfUvcfxKSWdnc/Iy0HV0gxqtpZQs24Lrmb99teW4ytCo3MHaHTuAFJc\njNzEVLyLjcfb2DgUvPwHz08E4/mJYHC4CmjRpxta+02HsqmgXmOiKIpqCmrcHaW2aHcUivpy9P3y\nbXhz6z7i/bbgQ1xJX385ZT7UrEu6mTRrZw45vuzHvyeE4HPmy5Ir5Hfj8DE5HSAEjLw8Wk0bCdO5\nEyCvoizrMCmKohqEeumOQlEURdWNz1k5eLpuF7JOlQz/qaCpDsPRA6HeqV2D63vNMAz4BjrgG+hA\n190FBW/eIev0X3h9LRrCXUfx/I+LsFjhA71h/egvXxRFUbVAH1tfjTVr1tTZDYYCgYC9i7Y6UVFR\n6NSpEwQCAUJCQupk+3VpxIgROHHiRL3VXzoaCEVVp+yd6g2VKL8AKTsOIaLbSGSd+guMgjx0h/SG\n1cYF0HDo2OAScEm4GmowmjQcbVbOhJJJSxS8fI0HM9fglvs0vLv/RNbhSa0xtBeqYaBthapv9Ep4\nFV69eoUTJ07U2agk0ibgAODv74+pU6di6tSpdbLtL+Hv74/U1FSxLyNlHyNPUVTlXv51HY+Xb0Xe\ns5IhONU6tYPh6O/Aa9E4b15XNmmJNit88M/1WDw/EYy30Y9w020SDMe4o7XvNHCba8g6RIqiqEaB\nJuFVOHbsGPr27Qsej/fVt52RkcE+MbKmiouLIdcIrqxVhY6MQkmroY5e8DE5DY9XbMOr0JsAAEU9\nbRiOHYxm7Rp/22Y4HGj16AT1Tu2QFXQZLy9FIuPIWWSfvQLzRVPQcsL3tR4+sb411PZCNTy0rVD1\njXZHqcKVK1fQrVs3dvrYsWMYMGCAWBktLS2kpqYCAHx8fLBw4UKMGjUKAoEAffr0YZfVpKytrS1S\nU1Ph6ekJgUCAwsJCZGVlwdPTE6ampujUqRMOHTrE1uvv74/x48dj+vTpMDIywrFjx+Du7o7169fD\nzc0NAoEAnp6eeP36NaZOnQojIyP07t0b6en/jsjg6+uL9u3bw8jICL169UJUVBQA4PLly9i6dSvO\nnDkDgUAAZ2dnAIC7uzsOHz6M/Px8tGrVCo8fP2brevXqFQwMDPD69WsAwKVLl+Dk5ARjY2O4ubkh\nPj7+y14YimrAinI/4unaXYh09sKr0JvgKPJg6OmOtuvnfhMJeFlyfEUYjv4OlhvmQbWdOYre5+Lx\nsv/ihut4vI6MkXV4FEVRDRpNwqsQHx8PMzOzGq1z5swZLF68GEKhECYmJli3bl2Ny8bGxsLQ0BDH\njx9HWloaFBQUMHnyZBgaGuLx48f4/fffsW7dOkRERLB1Xbx4EYMHD8azZ88wfPhwAEBQUBD27duH\nR48eQSgUol+/fvDy8kJKSgpat26NjRs3suvb2dkhIiICQqEQw4YNw8SJE1FQUIDevXtj7ty5GDp0\nKNLS0hAeHg7g32EIeTwe3N3dcfr0abauoKAgdOvWDVpaWnjw4AFmz56NrVu3IiUlBRMmTICnpycK\nCgqqPI60TzglrYbSb5MQgszAi7jWdRSEu46CFBdDy9keVpsXQ9utBxj5xv3rVFUU9bVhtnAyTOaM\nB7eFJnKfCnHHYxbuTVmGvIxsWYcnpqG0F6rho22Fqm80Ca/Cu3fvoKKiUqN1vvvuO9jY2EBOTg4e\nHh54+PDhF5fNyMjA7du3sXLlSnC5XLRr1w5jx44VG4+9c+fO6N+/PwBAUVERDMPA09MTRkZGaNas\nGXr37g1TU1M4OTlBTk4OgwcPFtve8OHDoa6uDg6HAx8fH+Tn5yMpKQlASXJR1UiWHh4eYkl4YGAg\nPDw8AAAHDx7E+PHjYWtrC4ZhMGrUKPB4PERHR0txNCmqcfgQn4Rb7tPxYOYaFLx8DSWTlmizciaM\nJg2HQrOanUMaK4ZhoG5rBcv/zIeeRz9wuArIPncFEd1HI+nn3yAqLJJ1iBRFUQ1Kw+y09//6/nq3\nzur6a7JNjddRV1dHbm5ujdZp0aIF+z+fz8fHjx+/uGx2djY0NDSgrPzvmLyGhoa4e/ff46Ovr19l\n/YqKimjevDk7zePxxLa3Y8cOHD16FNnZ2WAYBh8+fGC7k1Sne/fuyMvLQ0xMDFq0aIG4uDgMHDgQ\nAJCeno4TJ07gl19+YcsXFRUhO7vqq2O0TzglLVn328wK+hsPf1wPUX4B5JupwGDkAGh2swXDaZrX\nODhcBegNcoVWNzs8D7iAN7fuI+mnX/E6Mho2v24AV6t+Hz5UHVm3F6rxoG2Fqm8NOgmXNUtLSyQl\nJcHa2hoAoKSkhLy8PHb5ixcvvkocurq6ePPmDXJzc9kr8xkZGWKJ95eM03vz5k3s3LkTQUFBaNu2\nLQDAxMSEvfpdXd2lV9ZPnTqFFi1aoF+/fuwXBkNDQ8ybNw/z5s2rdXwU1RARkQiJG/cjZVvJ/Rla\nPTrBcIw75JQa/6Pd6wJXSx3GPmPQ3MUBwj3H8ebmPdx0mwTbQ5ug2tZU1uFRFEXJXINOwmtz9bou\n9enTB9evX2e7VrRr1w5PnjzBo0ePYGZmJtanuj4ZGhqic+fOWLt2LdasWYOkpCQcPXoU+/fvr3I9\naR+GmpubC3l5eWhpaaGgoABbt27Fhw8f2OU6OjoIDw8HIUQsIS9bv4eHB7y8vKCpqYnly5ez88eN\nG4exY8fC2dkZtra2+PTpE65fv46uXbtCRUUFPj4+AIBdu3aJxZSYmEivhlNSiYyM/OpXrIpyP+KB\nzxq8vBQBMAwMx7ijRZ9u9KE1EqhamsFi9WykbDuIT8IMRA2cig67V0LHzUkm8ciivVCNE20rVH1r\nmr+XSmnUqFH4+++/8fnzZwCAmZkZFi5ciO+//x6dO3eGo6NjhQ/dqqZrUra8X375BWlpabC0tMS4\ncePg6+sLJycndj1J60q7PVdXV/Tq1Qv29vawtraGoqIiDA0N2XKDBw8GAJiamqJXr14S67Ozs4Oy\nsjJevHiB3r17s/Otra2xdetWLF68GCYmJrC3t0dAQAC77vPnz9GlS5dK95uiGppPzzIRNXAqXl6K\ngJySIswWToJ23+40Aa8CV1MNrZd6Q6OLNYo/5eHuxCVI3n5I6gsFFEVR3yKGfKWzYGhoKGxtbSvM\n//TpE5SUlL5GCLWybt06NG/eHNOnT5d1KN+cgoICODs7IzIystGPa/61NPT3y7funxt3cXeyHwr/\neQeebnOYzp0IRb0W1a9IASj59ezF+TBkBl4CCIHe933Qbosf5Phf/1kMFEVRdSk2Nhaurq41WqfK\nK+GfP3+Gg4MDrK2tYWlpiSVLlkgsN3v2bJibm6Njx45iNwt+C5YtW0YT8HrC5XJx8+ZNmoBTjUL6\n4SDcGTEbhf+8g2r71rBYNYsm4DXEMAx03XvB5Mdx4PC4yDrzN24N8cbnrBxZh0ZRFPXVVZmEKyoq\nIiwsDPfu3cODBw8QFhZWYdzM4OBgJCUlITExEfv374e3t3e9Bkw1DXSccEpa9T2Wr6iwCPF+WxC3\ncBNIUTG0+zvBbP4P9AbML6Bua4U2K2eC21wD7+8/wY1+P+Bt7Nd5iBcd+5mSFm0rVH2rtk946U/f\nBQUFKC4uhqamptjys2fPYvz48QAABwcHvH379quNGkJRFFWfCt68R/TouUj7LRCMvByMpoyA4ejv\nmuzwg3WJb6gLi9WzoWJhgoKXr3F7iDcyAy/KOiyKoqivptpPEpFIBGtra+jo6MDFxQWWlpZiy58/\nf46WLVuy04aGhsjIyKj7SKkmhY6MQkmrvkYvyH0qxE23SfgnMgbyzVRgvmQ6tHp0qpdtNVXyqsow\nXzQFzXt1gaigEA9mrsHTtbtAiovrbZt0tAtKWrStUPWt2iScw+Hg3r17yMjIwLVr13D16tUKZcrf\n21nZKAEzZsyAv78//P39sWfPHrGfehITE8W6IHwr0//973/x448/fnF9hoaG7CPjqyuvpaWFq1ev\n1vn+/PLLL2jXrh0EAgEuXLhQp/WPHTsW8+fPB1AybrmNjQ27PDExEQ4ODjA0NMQvv/yCz58/Y9Cg\nQRAIBPjhhx/qbP9kPR0XFwcHBwe8fv262vKRkZFi7x86XbfT57buxa99RiHv2XPwBfr4MKYP4gre\ns8tvxT3ErbiHdLoOphl5OWTZm+NVbxuAw4Fw11Ec+G4cwv+6zJaXdXug03SaTtPp8tORkZHw9/fH\njBkzMGPGDNRGjUZHWbt2Lfh8PhYsWMDOmz59Onr27IlRo0YBACwsLBAeHg4dHR2xdRvj6CjW1tY4\nd+4c/P390b17d4wePRrHjh3D7NmzoaSkBIZh0KpVKyxduhR9+/aVdbgsLS0txMTEoFWrVnVar62t\nLTZs2AA3N7c6366Pjw8MDAzg5+cHQHyc8FmzZkFNTQ3r1q0DAPYJnH/99Rc4jaRbwLFjx3D9+nX4\n+vrC3d0d9+7dk1hu+/btyMnJwdq1ayUub8jvF1mJjKy7sXwJIUjdfQxP1+0GCIF65w4wmjICcjxu\nndRPVe1DfBJSdhxG8cc8KLduBbtDm6DUyrD6FWugLtsL9W2jbYWqiTofHeXVq1d4+/YtACAvLw9/\n//03bGzEH6AzaNAgHDpU8sS4qKgoqKurV0jAvzUODg5IS0tDamoqvLy88MMPP+D9+/cVyhXX40+q\nXxshBBkZGWjTpk29bkOS8ttNT0+HmZlZrRLwoqKiWsf3NQwbNgwBAQEoLCyUdShNjqioCA9/XI+n\na3eVDJ83tC+MfcbQBPwrUrU0g8Wq2VDU18bHhFTccJuEf6Ikf2GlKIpq7KrMYrKystCrVy9YW1vD\nwcEB7u7ucHV1xb59+7Bv3z4AwIABA2BiYgIzMzNMmzYNu3fv/iqBfw2VPWin7OPcPT09kZeXh5SU\nFPj7+2P8+PGYPn06jIyMcOzYMfj7+7NDHKalpUFLSwsBAQHo0KEDzM3NsWXLFrZekUiELVu2wM7O\nDgKBAL169UJmZiaAkqvMqampAEquGs+bNw9Dhw6FQCCAu7t7pf3w8/PzsXz5cnTo0AEWFhaYP38+\n+/Ch8ggh2Lx5Mzp27Ig2bdpgxowZeP/+PfLz8yEQCFBcXAwnJyd06lR9v1h/f39MnDgRM2bMgEAg\nQNeuXcWu/j548AA9e/aEQCDApEmTkJ+fzy6LjIzE999/D6DkQUGRkZFYvHgxBAIBpkyZgs2bN+PM\nmTMQCAQ4evQoAODIkSPo0qULTExM4OHhIXY8tLS08L///Q+dOnVC586dAQCXLl2Ck5MTjI2N4ebm\nhvj4f0dm6NixI3bu3IkePXqgVatWFeILDg6Gk5MTjIyMYGdnh9DQUADA+/fvMWvWLFhaWsLKygrr\n16+HSCQCIP5Apaoe6mJgYAB1dXXcuXOn2mNMlaiLK1WioiI88F6FzJPB4HAVYDxrLPSG9KYP4JEB\nno4W2qyciWbWbVH09gOiR8/FPzfrbuhbemWTkhZtK1R9qzIJb9++PWJjY9khChcuXAgAmDZtGqZN\nm8aW27lzJ5KSknD//n2JXU4aq7t376Jly5bYtWsX292mrKKiIhw+fBgqKiowNTUFAFy8eBGDBw/G\ns2fPMHz4cIkf4rdu3cKdO3cQFBSEn376ie3ru3PnTpw+fRonT55EWloaduzYAT5f8jBogYGBWLRo\nEZKSktCuXTtMnTpVYrnVq1dDKBQiIiIC0dHRyMrKwk8//SSx7NGjRxEQEIBz584hNjYWubm5WLx4\nMXg8HtLT0wGArUcaly5dwtChQ/Hs2TP0798fixYtAlAy0o6XlxdGjRoFoVCIwYMH49y5cxKP1Z9/\n/glHR0ds2rQJaWlp+OWXXzB37lwMHToUaWlpGDNmDIKDg7F161YcPnwYSUlJcHR0xOTJk8XqCQ4O\nRmhoKG7evIkHDx5g9uzZ2Lp1K1JSUjBhwgR4enqyV58ZhsGff/6JwMBA3Lt3D3FxcTh+/DgAICYm\nBjNmzMDatWvx7NkznD9/HgKBAEDJlyMul4uYmBiEh4cjLCyM/ZVo9OjR2LlzJ1q2bFntWPqtW7fG\no0ePpDrG1JcTFZYk4NnnroCjyIP5kmnQsG8v67CaNDm+IkznjIdmdzuI8vIR7TkP/9z4tp5BQVEU\n1Tg61DYw0dHRMDY2Rtu2bXHmzBkcPnwYqqqqAIDOnTujf//+AErGWZfUxWLRokXg8XiwsrKClZUV\nm3AdOXIEy5YtYxN6KysraGhoSIyhX79+6NKlC7hcLpYtW4Y7d+6wV81LEUJw+PBhrFu3DmpqalBR\nUcGcOXNw+vRpiXUGBgbCx8cHAoEAysrKWLFiBU6fPs1eza2pLl26oHfvkquJw4cPR1xcHICS41dc\nXIzp06dDTk4OgwYNqtDNqXy3kbLHkRAiNn3gwAHMmTMH5ubm4HA4mDt3Lh49eiR2NXzu3LlQU1MD\nj8fDwYMHMX78eNja2oJhGIwaNQo8Hk/sy8W0adOgo6MDdXV1uLm54eHDkpvIjhw5Ai8vLzg7OwMA\n9PT0YG5ujpcvX+Ly5ctYv349+Hw+mjdvDm9vb5w5c6bGx01FRQXv3r2r8XpNVdkbZmpKVFiEBzP+\nPwHn82C+eAqUTQV1GB1VWwyHA6PJw/9NxMfUTSL+Je2FalpoW6Hqm7ysA2iMOnXqhODgYInL9PX1\nq12/bJ95JSUlfPz4EQCQmZkp9U2NZbejrKwMDQ0NZGdni81/9eoVPn36BBcXF3YeIaTSpDo7OxuG\nhv/eBGVoaIiioiK8fPkSurq6UsVVlra2Nvu/kpISPn/+DJFIhKysLOjp6YmVLTvMpSRVdQtIT0+H\nn58fli9fLjY/KyuL3R8DAwOx8qU3d5YqKipCVlaWxNgVFRXZse8zMzMl3oSbnp6OwsJCtG3blp0n\nEonEjqe0cnNzoa6uXuP1qJoRFRbhvvdKvDgfVpKAL6IJeENTmoiDYfBPRDSix8yD3ZGfodXt2/nF\nlaKoposm4XWobL/fsvOkZWBgAKFQCAsLi2rLPn/+nP0/NzcXb968qZAoa2lpgc/n4+bNm1Il0Xp6\nemy3E6Dkhkh5eXmxhLQu6OrqiiW8QEkSa2xszE7Ly1feNMsfU0NDQyxcuBDDhg2Tah1DQ0PMmzcP\n8+bNq2noMDAwQEpKisT5PB4PycnJXzxiS0JCAmbOnPlFdTQltem3SRPwxoPhcGA0yQMA8E9ENGK8\n5n9RIk77+VLSom2Fqm+0O0odktT1pAYjQMLLywsbNmxASkoKCCGIi4vDmzdvJJb9+++/ERUVhYKC\nAmzYsAH29vYVrsJzOByMHTsWfn5+ePXqFYCSK7lXrlyRWOfQoUOxZ88epKWlITc3F2vXrsXQoUPr\nfBhAe3t7yMnJYd++fSgsLMS5c+eq7SddvjtKWRMnTsSWLVvw5MkTACU3SAYFBVVa17hx43DgwAHE\nxMSAEIKPHz/ir7/+Qm5ubrXb9/LywrFjx3Dt2jWIRCJkZmYiMTERurq6cHFxwdKlS/HhwweIRCII\nhULcuHGj2uNRVmZmJt68eSPVza9U7YgKi3B/+or/T8AVaQLeCJQm4lo9OkGUl48Yr/l4fT1W1mFR\nFEV9EZqE15Ckq91VLSs/r6or4z4+PhgyZAiGDRsGIyMj/Pjjj+xIJuXX8/DwwKZNm2BmZoaHDx+y\no9WUL7tq1SqYmJigb9++MDIywtChQ5GcnCxx+15eXhgxYgQGDhwIW1tbKCkpYePGjVLFXn55Vb8K\ncLlcHDp0CMePH4epqSmCgoLg7u4uVrb88I5V1T1w4ED8+OOPmDx5MoyMjNCtWzexLxrl47C2tsbW\nrVuxePFimJiYwN7eHgEBAVK9rra2tti5cyeWLl2KVq1aYdCgQWzf8927d6OwsBCOjo4wMTHBxIkT\n2W4s0goMDMTo0aOhoKBQo/Waspr022QT8AtX/z8Bn0wT8EaC4XAgKJuIj6ldIk77+VLSom2Fqm81\neljPl2iMD+tpqHx8fKCvr4+lS5fKOpR6U/ZhPU1Ffn4+nJycEBwcDC0tLYll6PulImkfqFEhAV88\nBcomVd+LQDU8RCRC2v8C8ToiGhxFHuyObIZWdzup16cPYKGkRdsKVRN1/rAeipKVppaAAwCPx8Ot\nW7cqTcApyaRNwO9NW04T8G+A2BXxz/mI8VqA15ExUq9PkypKWrStUPWNJuGNFH2ICEVJpzQBfxkc\nThPwbwSbiDvZl0nEpXt+AUVRVENBk/BGaNeuXfDz85N1GPWq9AFGFFWdqvptigqLcG/qMpqAf4MY\nDgeCH4aVScQXSpWI036+lLRoW6HqG03CKYr6JokKCksS8JBrkFOiCfi3iE3Encsk4hH0ijhFUY0D\nTcKpBqkp9gmnakdSv01RQWFJF5T/T8DNFtEE/FvFcDgQTCyTiI+tOhGn/XwpadG2QtU3moRTFPVN\nYfuAs1fAp9IE/Bv3byLe+d8+4vSKOEVRDVy1SXh6ejpcXFxgZWWFdu3aYfv27RXKXL16FWpqarCx\nsYGNjQ3WrVtXL8FSTQftE05Jq2y/TSIS4dHc9WIJuJKxoQyjo76WkkR8aEkinl+A2PGL8O5ufIVy\ntJ8vJS3aVqj6Vu1j6xUUFPDf//4X1tbWyM3NhZ2dHfr06YO2bduKlXN2dsbZs2frLVCKoqjqPF2z\nC5mBl8DhcWG2aApNwJuY0kScFBXhn+uxiB4zHw5n90LFzEjWoVEURVVQ7ZVwXV1dWFtbAwBUVFTQ\ntm1bZGZmVij3lZ75801yd3fH4cOHJS7LyMiAQCCo8+NbX/XWxogRI3DixAmxebRPOCWt0n6bwt3H\nkLr3OBg5OZjMHke7oDRRJY+4H45mHdqg8J93iB41B5+zc9jltJ8vJS3aVqj6VqM+4ampqbh79y4c\nHNWT7toAACAASURBVBzE5jMMgxs3bqBjx44YMGAA4uMr/gTYmLm7u8PExAQFBQX1Ur+kR7yXMjQ0\nRFpa2hePC96xY0dcu3atzuutCydPnsTIkSNlHQbViD0/GYKna3YCAIymjkCz9q1lHBElS4y8HIxn\njYWSSUt8zniB6FFzUfjug6zDoiiKElNtd5RSubm58PDwwLZt26CioiK2zNbWFunp6VBSUkJISAiG\nDBmChISECnXMmDEDAoEAAKCmpob27duzj7Iv7QNcegW0oUzzeDzExsZCW1sbv/32G6ZPn14v23vx\n4oXYo9rruv6ioiJkZGSgVEM4voQQmJubg2GYCsuvXr0KAwODKtcvKipiu0U1hP35GtMGBgYA/u2r\nWHqlpilPn9+2Fwn/2QeIROg7djQ0HW1wK+4hAMDBqj0A0OkmOm03/wc8Xbcbt+Mf4vGgCfjh4jHc\njLmDUg2h/dLphjtdOq+hxEOnG9Z06f9paWkAgMmTJ6OmGCJFf4TCwkJ899136N+/P+bMmVNtpcbG\nxoiJiYGmpiY7LzQ0lE24y/r06ROUlJRqGPbXs2nTJty7dw92dnaIjo7G8ePHKy177NgxbN68Ga9e\nvYKWlhaWLl0KDw8P+Pv7IzU1FXv37gUApKWlwcbGBjk5OeBwOBg0aBDs7e0RHh6OxMRE9OjRAzt3\n7oS6unqFsu/fv8fSpUsRGhoKhmHg6emJJUuWgMMp+VHj4MGD2LNnDzIzM2FgYIB9+/Zh9+7dCAwM\nBI/Hg5ycHBYuXIjBgwez9QYFBWHXrl0IDQ1l92X37t24fv06jh49ivz8fKxbtw5//vknCgoKMHDg\nQKxfvx6KiooSj8GhQ4fQsWNHnDhxAjo6Ovjpp5/g5OQEoORXhS5duiAiIgKPHj1CREQEZs+ejREj\nRmDs2LEghODnn3/GgQMHUFRUBFdXV/j7+6NZs2bssdi2bRs2bdoEIyMjnDt3ri5f7gavob9fvra3\nMY9wYMhEtC1UgM53LjAY0V/WIVENTMGrN3i6dhcK37yHtpsTPv4wAD3+/3xEUVWJjIykXVIoqcXG\nxsLV1bVG61TbHYUQgkmTJsHS0rLSBPzFixds3+Lbt2+DECKWgDdmJ06cwPfff48hQ4bgypUryMnJ\nkVju48ePWLJkCf744w+kpaXh0qVLaNeuHYDqHzFPCEFAQAB27tyJx48fQ05ODr6+vhLL+vj4gMvl\nIiYmBuHh4QgLC8OhQ4cAAEFBQdi0aRP27t2LtLQ0HDt2DJqamti7dy8MDQ1x/PhxpKWlYdasWWJ1\nurm5ITExESkpKey8U6dOwcPDAwCwevVqCIVCREREIDo6GllZWfjpp58q3Z/Y2FgYGxsjOTkZvr6+\nGDduHN69e8cuP3nyJLZt24a0tDS0bNlSrDvO0aNHERAQgJCQEMTGxiI3NxeLFy8Wq//mzZu4desW\nAgMDqzyu1LctNyEV0WPmo22hArR6dIL+cDdZh0Q1QNzmGjBbOBlySop4efEaNM7eaBD3wlANH03A\nqfpWbRJ+/fp1HDlyBGFhYewQhCEhIdi3bx/27dsHAAgMDET79u1hbW2NOXPmICAgoN4D/xqioqKQ\nlZUFNzc3mJqaok2bNlUmfhwOB/Hx8cjLy4O2tjYsLCwAVH/TKsMwGDVqFCwsLKCkpAQ/Pz8EBQVV\nWO/ly5e4fPky1q9fDz6fj/9r787DoizXB45/35lhR1ERQdkEQcUN18zMXXNLTXBNzTRNPXZMK9O0\n5ddmtpdZVMeW0+ox1PQoWmlHzQUXNPcUFWRREBRkFYaZ9/fHyCiCAgbMAPfnuriYZ95l7nd8wJtn\n7vd5GjZsyKxZs1i7di0A3377LU8++aT5Rlo/Pz+8vEqfHcLR0ZEhQ4awevVqAM6ePUt0dDSDBw9G\nVVW+/fZbXnvtNVxcXHB2dmbu3LmsWbPmtudzc3Nj5syZaLVaRo4cSUBAAL/88ov5WsePH0+LFi3Q\naDTodEUrosLDw5k9ezY+Pj44OTnx4osvsmbNGoxGo3mfBQsW4ODggJ2dXanXJmqmaxcucWDcXArS\nM6nbPgifqaFWcX+DsE4OXh40e2oqio2OhO/Wc+atFZYOSQghSq8Jv//++4skQCWZPXs2s2fPrrCg\nrMWPP/5Inz59qFOnDgAjRoxg5cqVzJo1q9i+Tk5OfPHFFyxfvpw5c+bQtWtXXn311TLP8lFY6wum\nmyb1ej2XL18usk98fDx6vb7I9JBGo9GcaF+4cAE/P79yXydAaGgoL7zwAvPnzyc8PJwHH3wQe3t7\nUlJSyMnJoU+fPuZ9VVW9Y59o3Lhxkba3tzdJSUklXuutkpKS8PLyMtfHe3l5UVBQwKVLl8p0vKj5\n8tMy2D9uLtcuXMIpwJfUvsEEaLWWDktYOefmTfF7YiIb3guD97/C1q0BvlNDLR2WsGJSjiIqW5lv\nzKxtcnNzzaPRhUlvXl4eV69e5fjx47Ru3brYMX379qVv377mGuq5c+eyceNGHB0dycnJMe+XnJxc\n7Nibb5pMSEjAxsYGV1fXIsd5enpiZ2fH2bNnzTXgN/P09CxSUnKz0kYJe/fuzeXLlzl27Bhr1qxh\nyZIlALi6uuLg4MCePXvw8PC44zkKXbx4sUg7Pj6eIUOGlCmWxo0bEx8fT9OmTQHTe6HT6WjUqJH5\nPZIRz9rLkHONg4/MJ/t0LPZNGtHsqSlEnT9r6bBENVGvQysaDe4Jm/dzcvF72DWsj8fwvpYOSwhR\nS8my9bcRERGBTqdjz5497Nixgx07dhAZGUm3bt1KLLdJSUkhIiKC7OxsbGxscHR0RHt9dK5t27bs\n2bOHhIQEMjIy+OCDD4ocq6oqq1at4tSpU+Tk5PDGG28wYsSIYsmmh4cHffr0YfHixWRmZmI0GomJ\niWH37t0ATJo0ieXLl3P48GFUVeXcuXPmxNXNzY2YmJjbXq+NjQ0jRozghRde4OrVq+aRb41Gw6RJ\nk1i0aBGpqamAacT9999/v+25UlJS+Oyzz9Dr9fz8889ER0czYMCAItd7OyEhIYSFhWFnZ0dWVhav\nvvoqISEhJf7RIWoXY0EBf858gfT9R7Fp4ELAs9PQOTuaZ8QQoiweeHg0TUYPBlXl8Oz/4/JOWd5e\nlExGwUVlk8zmNlauXMmECRPw9PTEzc0NNzc3GjVqxLRp01i9enWxcgyj0UhYWBitW7emWbNmREZG\n8s477wDQp08fRo4cSY8ePejXrx8DBw4skmAX1oTPnj2boKAg9Ho9S5cuLTGuTz75BL1eT7du3fD3\n92fKlCnmkfURI0bw9NNP8/jjj+Pr68sjjzxCeno6APPmzePdd9/Fz8+Pjz/+2Py6Nxs1ahQ7duxg\nxIgRRZLe//u//8Pf358HHngAX19fQkJCOHv29qOPnTp14ty5cwQGBvLGG2/w73//m3r16hW53tuZ\nOHEiY8aMYejQoXTs2BFHR0fefPPNMh0rai5VVTk+/y1Sft2F1smBgPnTsG1Qr/QDhSiB+4O9cXvg\nflR9AQcnLyTj6ClLhySEqIXKNEVhRaiuUxRaWmxsLPfcc0+Rmmhr9sMPP/Ddd98RERHxt85z85zp\n4oba+vNyesmnnFv2DYqNDYELH8c58MYy5HuPH5XRcFFmhf1FNRqJ/XQlaZF/Yutaj3s3fo5j09Jv\nZBe1h9SEi/KolCkKhWWdPHnSvMCRELVR7L/+w7ll34BGg/+ciUUScCHulqLR4Pv4GOq0DiT/cjr7\nx8wlL+WKpcMSQtQikoRbsY8//pinnnqKF1980dKhlNnNc37/HTIKLgAu/vwbf73wIQC+00bjEhxU\nbB8ZBRflcXN/0eh0+M+ZhKOfF7lxFzgwfh4FmdkWjE5YExkFF5XNqstRNnvcV2GvPyhpd4WdSwhL\nqU3lKKk79hP18NOoBQV4jh2C+9Delg5J1FD6jCxOv/oxecmXaXB/Jzp//y4aO1tLhyWEqEakHEXU\nGNHR0ZYOQVhQxvFoDk15DrWggEYDe9BoSK/b7rv3+NEqjExUdyX1F5u6zgQ8Ox2dSx2u7Izi6FNL\nUEtZH0PUfDt37rR0CKKGs+p5wi09ev3KK6/QqFEjZs6cyZ49e5g7dy579+4t07Fffvklb775Jrm5\nuRw5cqTI7CDWwMfHh507d/6tevNLly4xfPhwduzYga2tjBqJipGbkETUw09jyM6hftdgPMcPlVlx\nRKWzc2tAwNNTOf16GBdX/4p9E3daLC6+MJsQQlQUqy5HsaTU1FR69erFwYMHy708ul6vp2nTpvz2\n22+0atWqkiIsu2HDhjFmzBgmTZpU4eeeP38+zZs3Z/r06RV+blGctf68VBR9egaRw2eSfToW5xZ+\nBDw7HY2NVY8ViBom4+hpzrz7JRiNtHrjaXymyKqaQojSSTlKBfrhhx944IEHyp2Ag2lFzGvXrtGi\nRYtyH6uq6h0Xs7kblTmKOGrUKL7++utKO7+oPYx5+RycstC8Gqb/3MmSgIsqV7dtc3wfGwXAicXv\nk7x5h4UjEkLUVJKE38bvv/9O9+7dze2dO3fSpk0bczs4OJjly5fTo0cPmjZtymOPPUZeXh5nzpyh\nW7duAPj5+TFy5EgA9u7dS79+/WjatCn9+/dn37595nMNGzaM119/nUGDBuHt7U1sbCyurq58+eWX\ndO7cGR8fH5YsWUJMTAwPPPCA+fX0ej0AV69eZdy4cTRv3hx/f3/Gjx/PhQsXAHjttdfYs2cPCxYs\nwMfHh4ULFwKm5ehjY2M5cOAAQUFBRRL/DRs20KNHD8C0CNEHH3xAp06dCAgIYOrUqeYFgMC0MM/5\n8+fNK3NWFKkJr11Uo5EjT75G2p4/0bnUIeCZx9A5lW3EX2rCRXmUpb+49uhM45AHwGjk8MyXSI86\nVgWRCWsjNeGispWahMfHx9OnTx9at25NmzZtWLZsWYn7zZkzh8DAQIKDgzl06FCFB1rVTpw4QUBA\nwG23K4rCunXrCA8P588//+T48eP8+OOPBAQEmJeRj42NZe3ataSlpTFu3DhmzpzJuXPnmDVrFuPG\njSuSzK5atYoPP/yQuLg4vLxMC0b873//Y9u2bfz6668sW7aMuXPnsmLFCo4cOcKJEydYvXo1YEqU\nJ06cyJEjRzhy5Aj29vYsWLAAgOeff55u3brx1ltvERcXV2wlzs6dO+Po6Mj27dvNz4WHhzN69GgA\nPv/8czZt2sSGDRs4efIk9erVY/78+eZ9dTodfn5+HDsm/0mJu3f6tTCSft6Cxt6OgGcew7ZhfUuH\nJGo5jxH9cO11D8ZreURNmk92TMUONAghRKlJuI2NDe+//z7Hjx8nMjKSjz/+mJMnTxbZJyIigjNn\nzhAdHc3nn3/OrFnV/2aWq1ev4uzsfMd9ZsyYgbu7O/Xq1WPQoEEcPWoaYbm1nOTXX38lICCA0aNH\no9FoCA0NJTAwkE2bNgGmhH78+PG0aNECjUaDjY0NAP/85z9xdnamZcuWtGrVin79+uHj40PdunXp\n378/R44cAaB+/fo8+OCD2Nvb4+zszFNPPcWuXbuKxHCnEpeQkBBzQp+ZmcnWrVsJCQkB4Ouvv2bx\n4sU0btwYGxsbnn32WdavX4/xppkDnJ2dycjIKPU9LQ+ZJ7z2OP9FODGffH99MZ5JOPo2KdfxMk+4\nKI+y9hdFUfCZPJK67Vqgv3KVA+PmkZ+aVsnRCWsi84SLylZqEu7h4UH79u0BU7IVFBRkLnUotH79\neiZPngxA165dSU9PJzk5uRLCrTr16tUjKyvrjvs0atTI/Nje3p7s7JIXeUhKSjKPbhfy9vYmKSnJ\n3Pb09Cz1/Ld7vZycHObNm0dwcDC+vr48+OCDZGRkFEm871QXHhoayoYNG8jPz2fDhg0EBweb442P\nj2fSpEn4+fnh5+dHt27d0Ol0XLp0yXx8VlYWLi4utz2/ELeTHLGdk8+/D4DvY6Oo26a5hSMS4gZF\np8XviYk4+HqSez6RqEnPYMi5ZumwhBA1RLnueoqNjeXQoUN07dq1yPOJiYl4e3ub215eXiQkJODu\n7l4xUVpAq1atOHPmjPkPkNLcKclt3Lgx//3vf4s8Fx8fT//+/ct0fGk+/vhjzp49y5YtW3Bzc+Po\n0aP07t0bVVXLtIJly5Yt8fb2ZsuWLYSHhzNq1CjzNi8vLz766CPuueeeEo8tKCggJiaG1q1b33X8\nJYmOjpbR8Bou7cBRDs96CVSVxqEDce3R+a7Os/f4URkNL4dvtt15cKGmO594Al/Pcs5a1e8x88Nd\nr22r2ICE1bqrviJqrb6jGpW+0y3KfGNmVlYWo0aN4sMPPyyxTOPWcoeSEr9//OMfLF26lKVLlxIW\nFlbkpofo6OgiN+NZut2hQwciIiLM7YSEBAoKCsxtvV5PYmKiuX358uViJRmF5xswYADR0dEsX76c\ngoIC1qxZw6lTp4rUnCcnJxe7GTE2Ntb8ODc3t8jI+ZUrV8yvl52djcFg4NKlS6SlpfHWW28VeX03\nNzcOHjx4x/P37t2b9957j8jISEaMGGF+Px599FFee+01/vjjD6Kjo0lNTWXTpk3m7VFRUXh7e5Ob\nm1uh739iYqJV9Qdra+/cubPIz091a29ZtZpvx87AmJePa+97iAtwK3LD3N7jR6Vdie3ziSc4n3hC\n2tKWtrSlfZft84kn2LE/nP/+HsZ/fw/jbpRpnnC9Xs+DDz7I4MGDmTt3brHtM2fOpHfv3owbNw4w\njaxu3769yEh4dZsn/MqVK/Ts2ZMDBw5gb2/Pzp07mTVrlrnuu3379ixbtoyePXsC8OabbxIbG0tY\nWBhxcXF07NiRS5cuodGY/s6JjIxk0aJFnDt3jmbNmrFkyRLzJwrDhw9nzJgxTJw40fz6DRs25MCB\nAzRt2hSAIUOG8Mgjj5jf49dff52UlBQ++OADkpKSePzxx/nzzz9p3Lgxs2bN4plnnjG//v79+5k9\nezapqamMHTuWN954A1dXV6KiosznT0hIoH379gwYMIAff/zRHIeqqoSFhfHvf/+bixcv4ubmRkhI\nCIsXLwZknvCqZq0/L+WRl3KFyKGPkxt3gbrBLWk2dzKKVmvpsGqNjBwDV7KMaDWyAFJ56c/Fkv7p\nl1BQgOv0STR4WOYQF0KARquQlhVf7nnCS03CVVVl8uTJuLq68v7775e4T0REBMuXLyciIoLIyEjm\nzp1LZGRkkX2qWxIOpun9GjZsyMyZMy0dilVKSUlh2LBhsmJmFbLmn5eyKMjOZV/oE2T8eRJHPy8C\nn5uB1r78c/GLuydJ+N+Td/gYGd/8ACq4L5pH3QG9LB2SEMLC7jYJL7UmfNeuXXz33Xe0a9eODh06\nALBkyRLi4uIA0wwhQ4YMISIigoCAAJycnPjqq6/u4hKsz/PPP2/pEKyam5tbsT+2KorUhNc8xoIC\nDs98kYw/T2LbsD7NnppSIQm41ISL8jh8+hjBzduUvuNt2AW3wWnEULJ/3kjyW8vQudbHsWO7CoxQ\nWIuog3vp1LFr6TsKcZdKTcLvv//+ItPR3c7y5csrJCAhRM2jqionnnuXlN92oXVyIGD+Y9i41LF0\nWELcFcee3TGmpZO7fRcXXngD74/ewM6/qaXDEkJUM7JiprBKMgpes5xb9g0J365DsdHR7Kkp2Dcu\n/13ktyOj4KI8/s4o+M2chg3GLrgNak4uiQteQZ+SWiHnFdZDRsFFZZMkXAhRqRJXbSL6jc9AUWg6\nczzOgU0tHZIQf5ui0VDn4dHo/HwxpF7hwrOvYChlbQkhhLiZJOHCKt06naKonlK27uHYU0sA8Jow\nnPpdKn7U+uap94QozeHTxyrsXIqNDS5TJ6Ft5EZ+bBwXFi/BmJdXYecXlhV1cK+lQxA1nCThQohK\nkR51jEPTFqEWGHAf2ptGD3S3dEhCVDiNkyMujz+KxqUu146cIOnV91ANBkuHJYSoBiQJF1ZJasKr\nt6zTsRyY8DTG3Dxce3SmyZjBlfZaUhMuyqOiasJvpm1QH5fHH0VxsCd7114uvf9psQXsRPUjNeGi\nskkSLoSoULmJyewf+yQF6ZnUbR+Ez9TQElfQFaIm0TX2wGXaZNDpyNj4G5e//MHSIQkhrJwk4VZi\n2LBhfPvtt5YOo5jg4GC2b99e4rY9e/aYV/2sSHv27DHPSW9p9913H7t377Z0GNVG/pWrHBj7JHkX\nU3AK9MV/9oRKXw1TasJFeVRkTfitbPx8qTv5YdBoSPvuJ9JXb6i01xKVT2rCRWWTJNwCli5dWmwV\nTkVRrHK08E5xdevWjb17//4vKVdXV2JjY4ucd9WqVX/7vBVh9+7d3HfffZYOo1ooyM4lasLTZJ+J\nw97TnWZPTUFjJyupitrFrnVL6owZCUDK8hVkbt1h4YiEENZKkvAaRlXValmLeGvMlq4JLygosOjx\n1Y1RX8Cf0xdz9dAJbFzrETB/Gjonxyp5bakJF+VRGTXht7K/pxNODw4CIGnph2TvP1TprykqntSE\ni8omSfgdfPDBB3Tq1AkfHx+6devGxo0bzdt++OEHBg8ezIsvvoi/vz8dOnRgy5Yt5u0XL17k4Ycf\nplmzZnTu3JlvvvkGgC1btvDBBx+wdu1afHx86NWrl/mYuLg4Bg8ejI+PD6GhoVy5csW8bf/+/Qwc\nOBA/Pz969uzJrl27zNuGDRvG66+/zqBBg/Dy8uL8+fPFruXDDz+kdevW+Pj40LVrV/744w8AZs+e\nzeuvv27eb+fOnbRpU/Q/qYMHD9KtWzf8/f154oknyLs+Bdet+168eJFHHnmE5s2b06FDBz7//HPz\nNqPRyHvvvWd+P/v160diYiJDhw4FoGfPnvj4+PDzzz8XOe+HH37Io48+WiSehQsXsnDhQgAyMjL4\n5z//SatWrWjdujWvv/76bVd4Xbp0KZMnT+axxx7Dx8eHPn36cPz4cfP24OBgli1bxv3334+Pjw8G\ng6FIOU5eXh7PPfccrVu3pnXr1ixatIj8/Hzze9G6dWuWLVtGUFAQc+bMKTGGmkg1Gjk273VSf49E\n6+xI4LPTsG3gYumwhLAohz49cOh9PxQYuPjiUq6dPG3pkIQQVqbUZest6Z1FmyvsXM8sGVTuY/z8\n/IiIiMDd3Z21a9cyc+ZMoqKiaNTItNrfwYMHefjhhzl79ixff/01Tz75pDmpmzZtGq1bt+brr7/m\n9OnThISE4OfnR//+/Zk3bx6xsbGEhYWZX0tVVVavXs1PP/1EkyZNGDNmDMuXL+fFF1/kwoULjB8/\nnk8//ZT+/fuzbds2Jk+ezL59+2jQoAEAq1atYtWqVQQGBhZLQqOjo1mxYgW///477u7uJCQkFBmp\nvVMZjKqqhIeHs3r1ahwdHRk/fjzvvPMOixcvLrKf0Wjk4YcfZujQoXz55ZckJiYycuRIAgIC6Nu3\nL8uXL2fNmjWsWrWKZs2acfz4cRwdHdm4cSOurq788ccfNG3aFDAltIXxhYSE8Pbbb5OVlYWzszMG\ng4H169eb6+dnz55No0aNiIqKIjs7m3HjxuHp6VkscS+0efNmVqxYweeff05YWBgTJ07kwIEDaK/X\nLRfG6OrqilarLVKO8+6773Lw4EF27DB9vDxhwgTeeecdFi1aBEBKSgrp6ekcOXIEQy2ZokxVVU69\nvJwL4b+gsbMl4JnHKnQ1zLLYe/yojIaLMjt8+liVjIYrioLTg4MwZmWTd+AQiQtfxfujpdj6eFb6\na4uKEXVwr4yGi0olI+F3MGLECNzd3QEYOXIk/v7+REVFmbd7e3szadIkFEVh7NixJCUlkZKSQkJC\nAvv27eOll17C1taWNm3aMGnSJFauXAmUXDKiKAoTJkzA398fe3t7HnroIY4eNd1w9tNPPzFgwAD6\n9+8PQO/evWnfvj2//vqr+djx48fTokULNBoNOl3Rv620Wi35+fn89ddf6PV6vLy8zAlvYTy3oygK\n06ZNo0mTJtSrV4+nnnqKNWvWFNvv4MGDXL58mWeeeQadToevry+TJk0y7/vdd9/x/PPP06xZMwBa\nt25N/fr1S/038Pb2pl27duZPIXbs2IGDgwOdOnXi0qVLbNmyhddffx0HBwcaNmzIrFmzWLt27W3P\n1759e4YNG4ZWq2X27Nnk5eWxf/9+87U+/vjjNGnSBDs7u2LHrl69mvnz5+Pq6oqrqyvPPvtskdp1\njUbDwoULsbGxwd7evtRrqwliPv6e2M9Womi1+D/5CE7+3pYOSQiroWg01Bkbgk1Qc4wZmSTOf4mC\nlMuWDksIYSVKHQmfOnUqGzdupFGjRuak8Gbbtm1jxIgR+Pv7AxAaGsrzzz9fIcHdzeh1RVq5ciVh\nYWHExcUBkJ2dXaREpHBEHMDR0dG8T2pqKvXr18fJycm83cvLi0OH7lwXePP57O3tyc7OBiA+Pp51\n69axefONTwYMBgM9e/Y0tz09bz+64u/vz5IlS3jzzTf566+/6Nu3L6+99hoeHh53jKekc3t5eZGU\nlFRsn/j4eJKSkvDz8ysSY+FNjRcuXCiS+Jfm5j8kRo0axerVqxk7dizh4eGMGjXK/Jp6vZ6goCDz\nvkajES8vr9uet0mTJubHiqLQpEmTItdzp/cxKSkJb+8bSeat74Wrqyu2trXnRsSElRs5/donoCj4\nzhhL3TbNLRKHjIKL8qiKUfCbKVotLo88TPqnX1BwPp7EZ1/Ga9kStHWcqzQOUX4yCi4qW6kj4VOm\nTCmS/JWkV69eHDp0iEOHDlVYAm5p8fHxzJs3j7feeotz584RExNDUFBQmW569PDwIC0tjaysLPNz\nCQkJ5gSwvLOgeHl5MWbMGGJiYsxfcXFxReqOSztnaGgoERERHD58GEVRePnllwFwcnIiNzfXvF9y\ncnKxYxMTE4tcR0nJu6enJ76+vsViLBz99/T0JCYmplzXXWj48OHs2rWLCxcuEBERYU7CPT09sbOz\n4+zZs+bXPH/+fJF6+Ttdi9Fo5MKFC0Wu507vo4eHh/kPMij+Xljj7DaV5dKvOzn29BuAaTn6hZMr\nhQAAH9NJREFUBve2t3BEQlgvxc4Wl2mTbyxvv+g1jNdkeXshartSk/AePXqUWjZQHWfjKE12djaK\nouDq6orRaOT777/n5MmTZTrWy8uLe+65h1dffZW8vDyOHz/O999/z5gxYwBwd3cnLi6u2Pt2u/dx\n9OjR/PLLL/z+++8YDAauXbvGzp07uXDhQqnHApw5c4YdO3aQl5eHnZ0ddnZ2aDSmf/o2bdrw22+/\nkZ6eTnJyMp9++mmxmFasWMGFCxdIS0vjvffeIyQkpNhrdOrUCWdnZ5YtW0Zubi4Gg4ETJ06YR/8n\nTpzIkiVLOHfuHKqqcvz4cdLS0gDTJwC3Jug316w3bNiQ7t27M3v2bJo2bWqeOcXDw4M+ffqwePFi\nMjMzMRqNxMTE3HFe78OHD7NhwwYKCgoICwvDzs6OLl263Hb/m4WEhPDuu+9y+fJlLl++zNtvv23+\nN61N0vYe5s/pz4PBiMfwvhZfjl7mCRflUZnzhN+JxskRlxlTTMvbH/uLiy+/jVrLZlGqbmSecFHZ\n/nZNuKIo7N69m+DgYIYMGcKJEycqIi6La9myJbNnz2bgwIG0bNmSkydPcu+995q3lzR/9s3tf/3r\nX8TFxdGqVSseeeQRFi5caC4fGTFiBADNmjWjb9++JR5/8/k9PT357rvveP/992nevDnt2rXj448/\nLpJ432kUNj8/n1deeYXAwECCgoK4cuUKL774IgBjx46lTZs2BAcHM3r0aEJCQorFMXr0aEJDQ+nY\nsSP+/v48/fTTxV5Dq9Xy448/cvToUTp27EhgYCDz5s0jMzMTMN1A+dBDDxEaGoqvry9PPvkk165d\nA2DBggXMnj0bPz8/1q1bV+J7O2rUKHbs2EFoaGiR5z/55BP0er159pYpU6aUOJpfeC2DBw9m7dq1\n+Pv7Ex4ezjfffGO+KbM0zzzzDO3bt6dHjx706NGD9u3b88wzzxQ5f02XefIsUZPmY8zLx7X3PTQO\nHWjpkISoNrT16+EycyqKowM5kQdIfveTGjmIJYQoG0Utw2+A2NhYhg0bVmJNeGZmJlqtFkdHRzZt\n2sSTTz7J6dPFp2LaunUrK1aswMfHBwAXFxfatm1Lx44dcXR0JDo6GrgxP7S0rb994MAB3n77bQ4e\nPGgV8ZTWXrFiBVevXuXTTz+1injupu3p6YmjoyM7d+4E4P777weoknb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+ "text": [ + "" + ] + } + ], + "prompt_number": 2 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The choice of a subjective prior does not always imply that we are using the practitioner's subjective opinion: more often the subjective prior was once a posterior to a previous problem, and now the practitioner is updating this posterior with new data. A subjective prior can also be used to inject *domain knowledge* of the problem into the model. We will see examples of these two situations later." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Decision, decisions...\n", + "\n", + "The choice, either *objective* or *subjective* mostly depends on the problem being solved, but there are a few cases where one is preferred over the other. In instances of scientific research, the choice of an objective prior is obvious. This eliminates any biases in the results, and two researchers who might have differing prior opinions would feel an objective prior is fair. Consider a more extreme situation:\n", + "\n", + "> A tobacco company publishes a report with a Bayesian methodology that retreated 60 years of medical research on tobacco use. Would you believe the results? Unlikely. The researchers probably chose a subjective prior that too strongly biased results in their favor.\n", + "\n", + "Unfortunately, choosing an objective prior is not as simple as selecting a flat prior, and even today the problem is still not completely solved. The problem with naively choosing the uniform prior is that pathological issues can arise. Some of these issues are pedantic, but we delay more serious issues to the Appendix of this Chapter (TODO)." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We must remember that choosing a prior, whether subjective or objective, is still part of the modeling process. To quote Gelman [5]:\n", + "\n", + ">...after the model has been \ufb01t, one should look at the posterior distribution\n", + "and see if it makes sense. If the posterior distribution does not make sense, this implies\n", + "that additional prior knowledge is available that has not been included in the model,\n", + "and that contradicts the assumptions of the prior distribution that has been used. It is\n", + "then appropriate to go back and alter the prior distribution to be more consistent with\n", + "this external knowledge.\n", + "\n", + "If the posterior does not make sense, then clearly one had an idea what the posterior *should* look like (not what one *hopes* it looks like), implying that the current prior does not contain all the prior information and should be updated. At this point, we can discard the current prior and choose a more reflective one.\n", + "\n", + "Gelman [4] suggests that using a uniform distribution with large bounds is often a good choice for objective priors. Although, one should be wary about using Uniform objective priors with large bounds, as they can assign too large of a prior probability to non-intuitive points. Ask yourself: do you really think the unknown could be incredibly large? Often quantities are naturally biased towards 0. A Normal random variable with large variance (small precision) might be a better choice, or an Exponential with a fat tail in the strictly positive (or negative) case. \n", + "\n", + "If using a particularly subjective prior, it is your responsibility to be able to explain the choice of that prior, else you are no better than the tobacco company's guilty parties. " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Empirical Bayes\n", + "\n", + "While not a true Bayesian method, *empirical Bayes* is a trick that combines frequentist and Bayesian inference. As mentioned previously, for (almost) every inference problem there is a Bayesian method and a frequentist method. The significant difference between the two is that Bayesian methods have a prior distribution, with hyperparameters $\\alpha$, while empirical methods do not have any notion of a prior. Empirical Bayes combines the two methods by using frequentist methods to select $\\alpha$, and then proceeds with Bayesian methods on the original problem. \n", + "\n", + "A very simple example follows: suppose we wish to estimate the parameter $\\mu$ of a Normal distribution, with $\\sigma = 5$. Since $\\mu$ could range over the whole real line, we can use a Normal distribution as a prior for $\\mu$. How to select the prior's hyperparameters, denoted ($\\mu_p, \\sigma_p^2$)? The $\\sigma_p^2$ parameter can be chosen to reflect the uncertainty we have. For $\\mu_p$, we have two options:\n", + "\n", + "1. Empirical Bayes suggests using the empirical sample mean, which will center the prior around the observed empirical mean:\n", + "\n", + "$$ \\mu_p = \\frac{1}{N} \\sum_{i=0}^N X_i $$\n", + "\n", + "2. Traditional Bayesian inference suggests using prior knowledge, or a more objective prior (zero mean and fat standard deviation).\n", + "\n", + "Empirical Bayes can be argued as being semi-objective, since while the choice of prior model is ours (hence subjective), the parameters are solely determined by the data.\n", + "\n", + "Personally, I feel that Empirical Bayes is *double-counting* the data. That is, we are using the data twice: once in the prior, which will influence our results towards the observed data, and again in the inferential engine of MCMC. This double-counting will understate our true uncertainty. To minimize this double-counting, I would only suggest using Empirical Bayes when you have *lots* of observations, else the prior will have too strong of an influence. I would also recommend, if possible, to maintain high uncertainty (either by setting a large $\\sigma_p^2$ or equivalent.)\n", + "\n", + "Empirical Bayes also violates a theoretical axiom in Bayesian inference. The textbook Bayesian algorithm of:\n", + "\n", + ">*prior* $\\Rightarrow$ *observed data* $\\Rightarrow$ *posterior* \n", + "\n", + "is violated by Empirical Bayes, which instead uses \n", + "\n", + ">*observed data* $\\Rightarrow$ *prior* $\\Rightarrow$ *observed data* $\\Rightarrow$ *posterior*\n", + "\n", + "Ideally, all priors should be specified *before* we observe the data, so that the data does not influence our prior opinions (see the volumes of research by Daniel Kahneman *et. al* about [anchoring](http://en.wikipedia.org/wiki/Anchoring_and_adjustment) )." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Useful priors to know about\n", + "\n", + "### The Gamma distribution\n", + "\n", + "A Gamma random variable, denoted $X \\sim \\text{Gamma}(\\alpha, \\beta)$, is a random variable over the positive real numbers. It is in fact a generalization of the Exponential random variable, that is:\n", + "\n", + "$$ \\text{Exp}(\\beta) \\sim \\text{Gamma}(1, \\beta) $$\n", + "\n", + "This additional parameter allows the probability density function to have more flexibility, hence allowing the practitioner to express his or her subjective priors more accurately. The density function for a $\\text{Gamma}(\\alpha, \\beta)$ random variable is:\n", + "\n", + "$$ f(x \\mid \\alpha, \\beta) = \\frac{\\beta^{\\alpha}x^{\\alpha-1}e^{-\\beta x}}{\\Gamma(\\alpha)} $$\n", + "\n", + "where $\\Gamma(\\alpha)$ is the [Gamma function](http://en.wikipedia.org/wiki/Gamma_function), and for differing values of $(\\alpha, \\beta)$ looks like:" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "figsize(12.5, 5)\n", + "gamma = stats.gamma\n", + "\n", + "parameters = [(1, 0.5), (9, 2), (3, 0.5), (7, 0.5)]\n", + "x = np.linspace(0.001, 20, 150)\n", + "for alpha, beta in parameters:\n", + " y = gamma.pdf(x, alpha, scale=1. / beta)\n", + " lines = plt.plot(x, y, label=\"(%.1f,%.1f)\" % (alpha, beta), lw=3)\n", + " plt.fill_between(x, 0, y, alpha=0.2, color=lines[0].get_color())\n", + " plt.autoscale(tight=True)\n", + "\n", + "plt.legend(title=r\"$\\alpha, \\beta$ - parameters\");" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { 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RSa6YuyRHzNv+IS4uDrt374Zerwdg7glftGgRBg8ejHHjxqG4uBiffPKJOP/V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+ "text": [ + "" + ] + } + ], + "prompt_number": 5 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### The Wishart distribution\n", + "\n", + "Until now, we have only seen random variables that are scalars. Of course, we can also have *random matrices*! Specifically, the Wishart distribution is a distribution over all [positive semi-definite matrices](http://en.wikipedia.org/wiki/Positive-definite_matrix). Why is this useful to have in our arsenal? (Proper) covariance matrices are positive-definite, hence the Wishart is an appropriate prior for covariance matrices. We can't really visualize a distribution of matrices, so I'll plot some realizations from the $5 \\times 5$ (above) and $20 \\times 20$ (below) Wishart distribution:" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import pymc as pm\n", + "\n", + "n = 4\n", + "for i in range(10):\n", + " ax = plt.subplot(2, 5, i + 1)\n", + " if i >= 5:\n", + " n = 15\n", + " plt.imshow(pm.rwishart(n + 1, np.eye(n)), interpolation=\"none\",\n", + " cmap=plt.cm.hot)\n", + " ax.axis(\"off\")\n", + "\n", + "plt.suptitle(\"Random matrices from a Wishart Distribution\");" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "display_data", + "png": 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+ "text": [ + "" + ] + } + ], + "prompt_number": 7 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "One thing to notice is the symmetry of these matrices. The Wishart distribution can be a little troubling to deal with, but we will use it in an example later." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### The Beta distribution\n", + "\n", + "You may have seen the term `beta` in previous code in this book. Often, I was implementing a Beta distribution. The Beta distribution is very useful in Bayesian statistics. A random variable $X$ has a $\\text{Beta}$ distribution, with parameters $(\\alpha, \\beta)$, if its density function is:\n", + "\n", + "$$f_X(x | \\; \\alpha, \\beta ) = \\frac{ x^{(\\alpha - 1)}(1-x)^{ (\\beta - 1) } }{B(\\alpha, \\beta) }$$\n", + "\n", + "where $B$ is the [Beta function](http://en.wikipedia.org/wiki/Beta_function) (hence the name). The random variable $X$ is only allowed in [0,1], making the Beta distribution a popular distribution for decimal values, probabilities and proportions. The values of $\\alpha$ and $\\beta$, both positive values, provide great flexibility in the shape of the distribution. Below we plot some distributions:" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "figsize(12.5, 5)\n", + "\n", + "params = [(2, 5), (1, 1), (0.5, 0.5), (5, 5), (20, 4), (5, 1)]\n", + "\n", + "x = np.linspace(0.01, .99, 100)\n", + "beta = stats.beta\n", + "for a, b in params:\n", + " y = beta.pdf(x, a, b)\n", + " lines = plt.plot(x, y, label=\"(%.1f,%.1f)\" % (a, b), lw=3)\n", + " plt.fill_between(x, 0, y, alpha=0.2, color=lines[0].get_color())\n", + " plt.autoscale(tight=True)\n", + "plt.ylim(0)\n", + "plt.legend(loc='upper left', title=\"(a,b)-parameters\");" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "display_data", + "png": 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cuEs+i5Jo4lK0byvhg+KG8EFxQ/hqHTs2DxSOng1GJBZiSm5LGp4AiK37K5vu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\nIIzeeFTqSRrMOlaZ9dQZNdQaN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+ "text": [ + "" + ] + } + ], + "prompt_number": 9 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "One thing I'd like the reader to notice is the presence of the flat distribution above, specified by parameters $(1,1)$. This is the Uniform distribution. Hence the Beta distribution is a generalization of the Uniform distribution, something we will revisit many times.\n", + "\n", + "There is an interesting connection between the Beta distribution and the Binomial distribution. Suppose we are interested in some unknown proportion or probability $p$. We assign a $\\text{Beta}(\\alpha, \\beta)$ prior to $p$. We observe some data generated by a Binomial process, say $X \\sim \\text{Binomial}(N, p)$, with $p$ still unknown. Then our posterior *is again a Beta distribution*, i.e. $p | X \\sim \\text{Beta}( \\alpha + X, \\beta + N -X )$. Succinctly, one can relate the two by \"a Beta prior with Binomial observations creates a Beta posterior\". This is a very useful property, both computationally and heuristically.\n", + "\n", + "In light of the above two paragraphs, if we start with a $\\text{Beta}(1,1)$ prior on $p$ (which is a Uniform), observe data $X \\sim \\text{Binomial}(N, p)$, then our posterior is $\\text{Beta}(1 + X, 1 + N - X)$. \n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "#####Example: Bayesian Multi-Armed Bandits\n", + "*Adapted from an example by Ted Dunning of MapR Technologies*\n", + "\n", + "> Suppose you are faced with $N$ slot machines (colourfully called multi-armed bandits). Each bandit has an unknown probability of distributing a prize (assume for now the prizes are the same for each bandit, only the probabilities differ). Some bandits are very generous, others not so much. Of course, you don't know what these probabilities are. By only choosing one bandit per round, our task is devise a strategy to maximize our winnings.\n", + "\n", + "Of course, if we knew the bandit with the largest probability, then always picking this bandit would yield the maximum winnings. So our task can be phrased as \"Find the best bandit, and as quickly as possible\". \n", + "\n", + "The task is complicated by the stochastic nature of the bandits. A suboptimal bandit can return many winnings, purely by chance, which would make us believe that it is a very profitable bandit. Similarly, the best bandit can return many duds. Should we keep trying losers then, or give up? \n", + "\n", + "A more troublesome problem is, if we have a found a bandit that returns *pretty good* results, do we keep drawing from it to maintain our *pretty good score*, or do we try other bandits in hopes of finding an *even-better* bandit? This is the exploration vs. exploitation dilemma.\n", + "\n", + "### Applications\n", + "\n", + "\n", + "The Multi-Armed Bandit problem at first seems very artificial, something only a mathematician would love, but that is only before we address some applications:\n", + "\n", + "- Internet display advertising: companies have a suite of potential ads they can display to visitors, but the company is not sure which ad strategy to follow to maximize sales. This is similar to A/B testing, but has the added advantage of naturally minimizing strategies that do not work (and generalizes to A/B/C/D... strategies)\n", + "- Ecology: animals have a finite amount of energy to expend, and following certain behaviours has uncertain rewards. How does the animal maximize its fitness?\n", + "- Finance: which stock option gives the highest return, under time-varying return profiles.\n", + "- Clinical trials: a researcher would like to find the best treatment, out of many possible treatment, while minimizing losses. \n", + "- Psychology: how does punishment and reward affect our behaviour? How do humans learn?\n", + "\n", + "Many of these questions above are fundamental to the application's field.\n", + "\n", + "It turns out the *optimal solution* is incredibly difficult, and it took decades for an overall solution to develop. There are also many approximately-optimal solutions which are quite good. The one I wish to discuss is one of the few solutions that can scale incredibly well. The solution is known as *Bayesian Bandits*.\n", + "\n", + "\n", + "### A Proposed Solution\n", + "\n", + "\n", + "Any proposed strategy is called an *online algorithm* (not in the internet sense, but in the continuously-being-updated sense), and more specifically a reinforcement learning algorithm. The algorithm starts in an ignorant state, where it knows nothing, and begins to acquire data by testing the system. As it acquires data and results, it learns what the best and worst behaviours are (in this case, it learns which bandit is the best). With this in mind, perhaps we can add an additional application of the Multi-Armed Bandit problem:\n", + "\n", + "- Psychology: how does punishment and reward affect our behaviour? How do humans learn?\n", + "\n", + "\n", + "The Bayesian solution begins by assuming priors on the probability of winning for each bandit. In our vignette we assumed complete ignorance of these probabilities. So a very natural prior is the flat prior over 0 to 1. The algorithm proceeds as follows:\n", + "\n", + "For each round:\n", + "\n", + "1. Sample a random variable $X_b$ from the prior of bandit $b$, for all $b$.\n", + "2. Select the bandit with largest sample, i.e. select $B = \\text{argmax}\\;\\; X_b$.\n", + "3. Observe the result of pulling bandit $B$, and update your prior on bandit $B$.\n", + "4. Return to 1.\n", + "\n", + "That's it. Computationally, the algorithm involves sampling from $N$ distributions. Since the initial priors are $\\text{Beta}(\\alpha=1,\\beta=1)$ (a uniform distribution), and the observed result $X$ (a win or loss, encoded 1 and 0 respectfully) is Binomial, the posterior is a $\\text{Beta}(\\alpha=1+X,\\beta=1+1\u2212X)$.\n", + "\n", + "To answer our question from before, this algorithm suggests that we should not discard losers, but we should pick them at a decreasing rate as we gather confidence that there exist *better* bandits. This follows because there is always a non-zero chance that a loser will achieve the status of $B$, but the probability of this event decreases as we play more rounds (see figure below).\n", + "\n", + "Below we implement Bayesian Bandits using two classes, `Bandits` that defines the slot machines, and `BayesianStrategy` which implements the above learning strategy." + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from pymc import rbeta\n", + "\n", + "rand = np.random.rand\n", + "\n", + "\n", + "class Bandits(object):\n", + "\n", + " \"\"\"\n", + " This class represents N bandits machines.\n", + "\n", + " parameters:\n", + " p_array: a (n,) Numpy array of probabilities >0, <1.\n", + "\n", + " methods:\n", + " pull( i ): return the results, 0 or 1, of pulling \n", + " the ith bandit.\n", + " \"\"\"\n", + "\n", + " def __init__(self, p_array):\n", + " self.p = p_array\n", + " self.optimal = np.argmax(p_array)\n", + "\n", + " def pull(self, i):\n", + " # i is which arm to pull\n", + " return np.random.rand() < self.p[i]\n", + "\n", + " def __len__(self):\n", + " return len(self.p)\n", + "\n", + "\n", + "class BayesianStrategy(object):\n", + "\n", + " \"\"\"\n", + " Implements a online, learning strategy to solve\n", + " the Multi-Armed Bandit problem.\n", + " \n", + " parameters:\n", + " bandits: a Bandit class with .pull method\n", + " \n", + " methods:\n", + " sample_bandits(n): sample and train on n pulls.\n", + "\n", + " attributes:\n", + " N: the cumulative number of samples\n", + " choices: the historical choices as a (N,) array\n", + " bb_score: the historical score as a (N,) array\n", + " \"\"\"\n", + "\n", + " def __init__(self, bandits):\n", + "\n", + " self.bandits = bandits\n", + " n_bandits = len(self.bandits)\n", + " self.wins = np.zeros(n_bandits)\n", + " self.trials = np.zeros(n_bandits)\n", + " self.N = 0\n", + " self.choices = []\n", + " self.bb_score = []\n", + "\n", + " def sample_bandits(self, n=1):\n", + "\n", + " bb_score = np.zeros(n)\n", + " choices = np.zeros(n)\n", + "\n", + " for k in range(n):\n", + " # sample from the bandits's priors, and select the largest sample\n", + " choice = np.argmax(rbeta(1 + self.wins, 1 + self.trials - self.wins))\n", + "\n", + " # sample the chosen bandit\n", + " result = self.bandits.pull(choice)\n", + "\n", + " # update priors and score\n", + " self.wins[choice] += result\n", + " self.trials[choice] += 1\n", + " bb_score[k] = result\n", + " self.N += 1\n", + " choices[k] = choice\n", + "\n", + " self.bb_score = np.r_[self.bb_score, bb_score]\n", + " self.choices = np.r_[self.choices, choices]\n", + " return" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 10 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Below we visualize the learning of the Bayesian Bandit solution." + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "figsize(11.0, 10)\n", + "\n", + "beta = stats.beta\n", + "x = np.linspace(0.001, .999, 200)\n", + "\n", + "\n", + "def plot_priors(bayesian_strategy, prob, lw=3, alpha=0.2, plt_vlines=True):\n", + " # plotting function\n", + " wins = bayesian_strategy.wins\n", + " trials = bayesian_strategy.trials\n", + " for i in range(prob.shape[0]):\n", + " y = beta(1 + wins[i], 1 + trials[i] - wins[i])\n", + " p = plt.plot(x, y.pdf(x), lw=lw)\n", + " c = p[0].get_markeredgecolor()\n", + " plt.fill_between(x, y.pdf(x), 0, color=c, alpha=alpha,\n", + " label=\"underlying probability: %.2f\" % prob[i])\n", + " if plt_vlines:\n", + " plt.vlines(prob[i], 0, y.pdf(prob[i]),\n", + " colors=c, linestyles=\"--\", lw=2)\n", + " plt.autoscale(tight=\"True\")\n", + " plt.title(\"Posteriors After %d pull\" % bayesian_strategy.N +\n", + " \"s\" * (bayesian_strategy.N > 1))\n", + " plt.autoscale(tight=True)\n", + " return" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 11 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "hidden_prob = np.array([0.85, 0.60, 0.75])\n", + "bandits = Bandits(hidden_prob)\n", + "bayesian_strat = BayesianStrategy(bandits)\n", + "\n", + "draw_samples = [1, 1, 3, 10, 10, 25, 50, 100, 200, 600]\n", + "\n", + "for j, i in enumerate(draw_samples):\n", + " plt.subplot(5, 2, j + 1)\n", + " bayesian_strat.sample_bandits(i)\n", + " plot_priors(bayesian_strat, hidden_prob)\n", + " # plt.legend()\n", + " plt.autoscale(tight=True)\n", + "plt.tight_layout()" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "display_data", + "png": 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sjY1ay5B+pQoeIp46EQIoL9ieo33/ORJHi41QtcGSsQ2d5Wz3/d+4XAl1owaR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\n7+ViKInycyoR5WdriFsS41AuhsCCHkrE4ZJm2sw2PCbQszJaTP7/wSTnS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GfVtVv40U6H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FV8q0GBRYGt76LNGKAnPNKo4qONZoSGyuAhXBtyJAFxZC/O9+St7T/6QhwzmxYtF/PsKaV0Sf\nP/wUjdHgc7+i481ExgRRXFCNwyHYuzWTa28eevENu5Dzk5WWlpaSmJjIH//4RxYuXNjV3ZJ0EfUF\nxZx7azXn/rsKa3GZ+0qNQvjV44i7+wYCB/X33EAvotZiZ8OOYgpLGlzLzIE6Jo0Ow+ThJZWttIzc\n3/8VXVgICX/4uWt5kU2wPF+Q32zy4wEGlbuCVQzdX+Vy+HAFdrtg5MhgdK1M1Nae6IYORvu7x2j4\nYCX2HU6XJFFdQ+0zL3Dyf+uo/u5iJo9tu+41BRlJHB5NdmO2vfStmcQkhWMK8hxkPSImgFizgfwq\nK/V2lVVpxdw3NvbSD6wDaNWI2LNnDwMGDKBfv34AzJs3j9WrV7cwIjrJI6pH0t2HrG1VNeS+/znZ\nb6yk7sy5FutNibHE3X0DETMmuk0Sdx6HEGwrdfBhnp3CBvfzJEIPt0TA8AA8PngfOHqw27gzVVfb\nOH26hsLCBrflGg3Ex/sTG+uHppNSz4qqGtJKchhjaz3f9JWE3S6wWlUcjsu/l7SHO1OlqmBQfOuL\nVoE7zCpKFaQ1GhJbq5zn/vxI0AYGEP+rhyl44TXq9jvfxles24KtqIT+f/0tulDf0vcpisKIcfFs\n/Mz55vbw3nNcNS2JAC8KqDvgy2SlEs90d93gK0IIKvYc5uzrH1H4+SaE3d0wVwx6omZfTdwds/GL\n85xa80J6ujtTbqGFjbuKsdQ3OfvGRhkZMzwEvbcHaVVgLykjraGS89OZHakVvFnknM/mPONMKrMD\nVa6AAX8ArFYVu11c+N7ykmiLblD8Tfg9cC/28WNpePt9RKnT6I0/dRzHr/8PywPz8LtrbpuD+/sM\nj6b4bDmWqgbsVgdHvj7F+LnDPD4DaRSF2YPCeXOfcyR75dEibh0eSXAHjEZcKq32JDc3l8TERFc5\nISGB3bvd/RYVRWHHjh2kpqYSHx/Ps88+y7BhPX+q+Z6MEILKA8fIWfEZ+R9/1SK9HkDIuBHE3HIt\nIRNGenTLcAjBjjIHH+XZyat3v/oDtHBdKEwOAV03EUMcIQAAIABJREFUH6quqnIaD0VFDS3WRUUZ\nSUjwx2CQ48G9HY0CtzcaEkcbDYkd1VDjECyKBoOfkdiffp+S/3xI5VebAKg9dIyMRT8l6fk/Ykz0\nPqTdnLg+IYRFBlBWXIvdprJvexbTbhjcUYclkVwytqoaClavJ/s//6P6aEaL9YaIUKJvmk70nGkt\n5grqrdjtKnuPVHD0pPsEY8MHBjGgb4DPo9xWVbCyVLClWTNaBDcFqYwyyZe+bUE3fAja3z+G9ZM1\nWNdvQhECrdWK5V9vYf16GwE/XYZuULLP7Wm0GgZO6MPh9c5rouB0KeeOFdJneIzH+mPig1h7opSC\nait1NpX3DhbwvYntP7v2pdKqEeHLCTtmzBjOnTuHv78/a9as4bbbbuPkyZMe68osHN27bCuvol92\nObnvf8Ge486sAcM0AYAzS4bGz8iMm24k+pZrOVScSyUqExsNiPNZJFJTRvN1sYO3tu2jwi4wJztH\nEqpOH8SowO3jRzElBNKPHeJILq6RhgONWSQuLJ/H2/qOKAsh2LpzHwWF9QT7DwTgbK7TF71v/DBC\nQ/VU1Z2itkGLwdA1WSYAjmZnMGr4kC7Zf3uXT2YepbSkgcTEsZfdXsrQ1MvuT9Xpg+gVAZEpbdr+\ntiGpaKtha9phAA4nj+KFfMHE0oP4aRTGPHAP+ugItrz1FgjBsOxcTj7wCGWLb8M0sD8Txk8EYM/e\nXQAeyyPGxfPff68CQLdTy9jJfTl4eB/QsVk4JJ3LlTgKIVSVsp0HyV3xGQWfb0S1tHz5EpQyiNi5\nMwmdPBqN7tLeqPbEUYjisgY27S6hoqrJ78ig1zB+ZIjHAGpvhPUZxp9zBEXN3JfMGsHdwQ7ifQ+j\n6JFc6gi1YjRivPs2jo0YS/CKFUQVOOMUHKfOULXs5xjnzMK0aAGaEN9GlUOiA4kdGEF+hjMhzdGN\npwlPCCYguKUrr0ZRuGVoBK/uyQPgk/QSbh8RRVSg766wHUmrgdW7du3i97//PWvXrgXgySefRKPR\ntAiubk7//v355ptvCAsLc1suA+i6J6rVRtG67eS+9zklX+9COFr6gJv6xRM7dyYR105Ea/IcyFlu\nFXxRaGddsZ3aC5rw08C0EJgaAqZuPIaqqoL8/HrOnq2lurqlq1BoqJ6EBP8OSdnaFix/fwlH+gn8\nHl6KrtGIuNLJzq4jL89CYqKJ+PiuTV3aoMJfSnQYFMFjka3HRHhCCFhfq2FnXdMIVZwBlsYohOud\n53/NngMUvviGa1I6tFoSfrGUiLtu8qF9wRcfHKa8xJlSOPWqRGbd6lumpq4IrG4NqRd6BpbcQvI+\n+IKc9z7HcjavxXqN0UDEtROJueVaApL7dEEPuy9Wm8o3RytIy6hyc9mJjjAyelgwfkbf3GVqikr5\n4It97J98LWozF5vBBpWbzSoBV+iA+b59ZdjtgrFjQ9Hru/YgdtQqfF0Ft+9ZT9+v1oCtyVJTAgMw\nPTAf49wbfHJxctgd7P/iBJZqp6EdGmtmyj0j0XiYDVsIwbNbsjnbmKlpRnIov5zRr12OCTowsHrc\nuHFkZGSQlZVFXFwc77//fgsf18LCQqKiolAUhT179iCEaGFASLzTFX6vwuGgbOcB8ldvoPDzTdjK\nKlvU0fgZCZ86jqjZVxM0YpDHUSkhBGnVKuuLHewqd3ChO3uAFqYEO40H/0swHjorJsJicZCbW8e5\ncxasVrXF+tBQAwkJpi43HppzTK1FPnp5pqvT3yoKzApUCdQI1tU4lUmeFf6SI3gwBgaaFAInjEb3\nm2Dyn30ZR1UNOBzkPPkilhOnif/FUjR6768MFUVh9MQ+fN0YG3Fkbw7jru5HaHhApxyfpHPo7jER\ntooqCr/YQv6qdZRu3dci2QaAf/8EomZPJWLmJPTmS5tl3RM9ISZCCMHp7Fp2Hyynrr7pZYVWq5Ay\nyEzfeJNP3iBCCA7Wwoc1wVRMnUXV6YOYk0dhUASzA1VG+Qm6uddwp9EeukHVasmbOYuhE1NoeH8l\njqPpAIiaWupe/DcNn3+F/w8Wox89stV2tDotgyf35eBXJ0FAeX4Vx7ZkMmJGS9coRVG4dVgkz293\nxqVuPF3OTUPCGRkbdFnH0h60+lSk0+l48cUXmT17Ng6Hg8WLFzN06FCWL18OwPe+9z0++ugjXn75\nZXQ6Hf7+/rz33nud0nFJ2xAOB+V7j1CwegMFn21smRmjkaARg4i6fgrh14z3OupQaRNsLrGzvthB\nfkNLxRGhd448jDODoZOCjduKwyEoLKwnL89Caam1xXqNBiIijMTE+OHv332MBwDj4m9jTB+JdmBS\nV3el3YiL8yM62oi2G4xUGRR4KNzO5fZkkr8gUONgdZUGFYUaFZ7LE9wTAVPN4DcwiYQnfknB316h\nIdOpHEpXrsFyKot+f34MQ6z3INPYPiFEx5spzK1CVQWb15zgtm9f2Q9Vku6PvbaOoi+3kb9qPSUb\ndyE8JHfQBvoTMWMiUbOnEjCgT69O0eqN/KJ69h4up7DU3d0rItTA6GHBBPioc7LqBZ+UCY5bAJre\nYPfRC241OwjtAZnGU1KcLkI6XdefR2NMgmF+dowKaAKjMD30feyH02j4YCWiyOma5MjMpvpnv0M/\nfjSmRfe2Gi9hjgigf2ocmQedo3dnDuQSEhNIwtDoFnUHRfozJj6I/bnOdL8v7sjhpduHoOviZyw5\n2VwPxlFXT+nWvRSu3Urxuu1YSzxP4W6ICCVy1hQiZ03BFN/y5AVoUAX7K1S2l9n5pkLF7uGs6esH\n00NhRIDTj6+7oaqC8nIr+fn1FBTUe8wEZDBoiI72IyrK2OVDp5KeQbYVPqzUUiuarolJQXB3hIKf\nRkFtsFL06tvUbN/rWq8NDqLP739C8DUTvbZbUljN2o+Ousp3LRxHv4ERrfZFujNJ2kpDcRlFX22j\naO1WSrfuRa1v+dIFRSF49DCiZl9N2OQxHjP1SaCotIF9R8rJLax3W+5n0DBikJl4HycozWsQfFou\nOOQ+TRMBiuC6QJWRcvShUxE2O7YNm7B+/iU0uF8f+qmT8F84H23fRM/bCsGxLZmuSeg0WoVJd6YQ\nntByYrtyi43H12dibXx2uW9MDN8ec/kpXzt0srn2QiqLzqEuO5/SLXsoXredki17PQa2AehDzYRP\nHU/4tPEEDRvgMcOSXRUcqVLZVuZgb7nDLU3cefw0MCYIJgV3z3keVFVQWmqlsLCeoqJ6t5mlmxMc\nrCcqykhoqKHTUrVKeg+VDvigUku+vencitTDwiiFfn6KMw3m5+spXbEK1KYLLfLe24n90UKv7k07\nNpzizPFiAMIiA7j/R1PQtpJLXRoRkoshhKDm+BmKN+yk6MutVOw76tFVCSBgUH8ipk8g/JrxGCOl\nG7MnhBBk51s4cqKK/CJ340FRICkxgCHJgd5TtzZr51Q9bKgQHKmD5r+IgmCcSTAjQMVPvvvqMtSK\nSqyrPse+c4/7NaPRYJg1HdO9d6GNb/nQb7c6OPjlSeqqnOeH3qhjyj2pmCNbuqiuzyhjVZrznq9R\n4Pm5gxkUeXlxhNKIuIK5XL9Xe3UtZTv2U7JpDyWb93icy+E8+hAzoZNHEzFtAuaUwSgeAniq7YKD\nlQ6+qVA5WOloESR9nj5+MNEMo4LA2EEP3ZcaE1Ff76C0tIGSEislJQ3YPQ2bAH5+GiIjjUREGDH6\nGLzWXehqv//uTHeVjU3AZxfMbq0BbgpTuD4EtIqC5fgpCl94HXtZ06ih34B+9Pn9T/Ef2nJyI0ut\nlU/eOYjN5rxQp1w3gEnXep8ESRoRVw6dGRNhLSmnZMteSjbtoXTzHhoKS7zW9e+fQPi0CURMm+Dz\nvA7tzZUQE1Hf4OB0di3HMqqpqLa1WN8nzsTgpEACTK27LllV50zTmyoF2R7eCQ4zqkwPUIlobKa7\n3v+6A50lGzW/gIbVa3Dsd88yiUaDYepE/Obd0cLNqb6mgQNfnsRW73QRNJj0TL57JOYId0NCFYLn\ntp3jdKkz9X5CsJEXbh1MgOHSn2E6LLBa0v2wllZQvucQZbsOUr7rEFVHTrq9ubwQU584QieNImzS\naAIH928x4uAQgqw6wdEqp+FwvEbFm1UZoYfRQc5PdDea6tJmU6mosFFa2kBpqZWaGu+TsOn1CmFh\nBiIijAQG6qS/rqTT0Ctwm1klqV6wpkaDVSiowKdlgm9q4J4IGDRkAIlP/YrCV95yTUxXfyqLk/c/\nTPTCbxG9ZL7bqIQpwEDKhAT2bz8LwM6NpxkwNJrIbhBwJ+m+NBSVUr6rUY/sPkR1Wst5HFxoFIKG\nDyRs0mjCJo3uMsPhSkBVBbmF9ZzMrCYrt66FalYUiI/2Y3BSEEGtJOpQhSCzHnZWC/bXQL0HpTzQ\noDIjQCVGeo51OzSxMZi+vxDH2XNYV32GI82ZBANVxbp5B9bNO9CNGoHfbXPQT56AotXiF2hkxPRk\nDm/IwGFTsVps7PjwMBNuHU5YXNM8KhpF4TtjYnhyYxYNdkFOZQNPbsziD7OS0HaBF4UciejGOOob\nqD52msqD6VQdSqfyQDo1JzNb3UZjNGAeOZjgMcMJvSq1RYyDQwjO1gnSqh2kVakcq1GxtJLFMlgH\nowKdhkOC0be5QzoSIQQWi4OKChvl5VYqKmytGg0ARqOGsDADYWEGaThIugXlDlhVpeWczf1cHBcI\nd4QrBGuh8suNlK5YhbA2vcX0S+5L/M++R9CE0a5lqir4auVRSgprAIiKDWLB9yei07d8MyVHInof\nqtVGdbpTj1QeOEb5nsOtjliDc5b1kNFDCbkqldAJI9EHS6PUG3a7Sm5hPZk5tWTnWWjwkOFPp1Po\nF+9PUmIA/ibPb4wdQpBhgYO1gsO1UOFBL+sQjPQTXOWvEilfAV8xOE6ewrpmPY609BbrlIhw/G6+\nHsPsa9FGRVBVUsuRDadw2J3nkUarYfQNg4gf7G6878upcs1kDXDrsEiWTYq/pOcb6c7UA7BV1VBz\nMpOa9NNUHjpO1aHjVKefRtgvkqdeUQhITiR4zHBCxo4gaNgAV1CbEILCBsGpWpVTtSqnawWZdSoN\n3gcuUIBEPxgW4PzEGbrOcFBVQV2dnaoqO1VVNqqrnf+9uSedR1EgKEhPSIie4GA9/v7aHmU41L/2\nFo6MM/gt+jbaQd5dV64k8vIsFBTUExfnR0xMywl3OpMGFV4p02JQYGl42+eJ8BVVwK46hc11GmzN\ngq51CkwOglkhCkElxRQtf4v6E6fdtjVPm0j8j5dg7BMPQGW5hS/eP+RKFpAyLoHrbx/e4ryXRkTP\nxl5dS/WJM9QcP0N12ikqD6ZTfewUaoOHYOjmaDQEDU0mZOxwgseOIHBgP4/urpLGOLsKK7mFFnIL\n6iksqcfhRaeGmPX0iTORGGtqEfOgCkGBFY5b4ITFaUB4GnEACNcKUv1URpuE1/ke1LJyLE8/hxIa\ngv+jP76MI+xeHD5cgd0uGDkyGN1F4kY6mm8sCttqNYwxqUwNaPujs+NcDrYvN2Dfe6BlnJGioEsd\njvG6adQPH8WxPfnYGppekPZNiWH49GS3l0Or04pZl9GUafP24ZF8f2LbDQnpznSFIITAWlxGXWaO\n02A4mcX2XTtJLqmnIb/YpzYUrZaAQf0wjxiEOWUQQcMHog0wUWGHbIvKuXLBOYuVcxZBtqX1UYbz\nmLWQ7A+DTDA0AII6MZWaEAKrVaW21kFdnZ3aWrvre3rGEfrEDfOpnYAArctwCArSd4tUoR2FqKoh\nrSSHMR7SK16p2O3O88BTxqy20h5+r5WqgkHp2PcrGgUmBwhG+DlYV6MhrTFWwi5gSxVsqxJMCIrg\n6l88QvimTZR98CmiwekUXbV5F9Xb9xE2dxZR37mT4D7xjJncl71bswA4si+HqNggRk/q26HHIOk4\nvMVECCGwlpRTdzaXujM5ToPh+BlqTpyhPrfQp7YVvY7AwUmYUxr1yNBktP5da7y3hc6KiRBCUF1r\np7isgaJSK8VlDZSUW1u9T5n8NMRFmegTZyI4qOmFXqlNcLYBzjYIztY7s7bVt/JCz6QIhhoFqSaV\nBB0Xz7akqoiyco5Zqxh/CcfaXbFaVex24S22v01crm5oUJ26oV4o4NXx2zvaxAS0S+5HvWMuti07\nsG/dgah2jiAjBPaDR7EfPAo6HQMmTCBz6HTqhfMx/eyRAoqyyhk+LYnYgREoisItwyIoqbVyIM/Z\nxv/Siim32Hhkah9MHkaiO4KLGhFr167lxz/+MQ6HgyVLlnicrfqhhx5izZo1+Pv78+abbzJ69GgP\nLfV8VKuNhuIyGgpLqc8vwpKdhyU7H0t2HnXZ+Vhy8ltkSzpsLyVBF+61Tb/4aAIG9kOb3Bdbv37U\n9O1DnmLgQL2gsEGlMEtQ2FDf6s3oQoJ1kOQHA/wh2eSMdeiIN/XnDQSbTaW+XqW+3tH4cf/u7YZc\nUJzl0YjQahUCA3UEBekICtITGKjr0UaDJ7LUejnZnBfOZJ++ogILzVq4M1hljFWwoUZDXmMGJxXY\nVQ27qhWiR8xg8tAxDPriE2zbdgEg7HZKV66h9H9rCb52MvELbqdkUASZJ51BsRs+TUej1ZA6wXNq\nwc7AF/0hcUe12mgoKmXPF+sYWO2gPreIuuw8LGdzqTubh+VsHg5L/cUbaoYxOoLAQf0IGNyfoCHJ\nBA7uf0WnYT126mS7GRFCCBqsKrV1dipr7FRU2aistlFRZaOi+uIj3wBBATpiIo2ERPjhMOkosSvs\nsEFhoUqRDQpteMxueCHBGsFgo2CIUdBHL7gUF/csW22PMiLak+6iGzRhoRhvuwnDzbOx7z+Efftu\nHMdPNo1O2O1od+yg/95vyJtyE5VJIwCwVDew77N0zFEBDByXSMyACB4YFwf78lyGxKYzFZwqtfCj\nKYmMjut4N8RWjQiHw8EPf/hD1q9fT3x8POPHj2fu3LkMHTrUVeeLL77g1KlTZGRksHv3bpYuXcqu\nXbs6vOMdiRACtd6Ko86CvboGW0U1toqqxk/j9/IqrKUVNBSX0lBYSkNRqceZny9GHc47i9DpcMRE\nUx8TQ3ViH0oS+pAbk0ihzp8Ku2iaDToboGWmB2+YNE73pD5+kGh0/jf7ONKgqgJVFTgczo/dLrDb\n1cb/ApvNaQDYbM7lNpuK1dr08ZZO1VfqrXUYDBoCArT4++tc/41GTY9yT7oUzp83kpbU1tVevFI3\npL9BsDjUQaZNYWuthrPN4iUKbfA/guGG7zBw1DVM++JjzGcaXZyEoHLDdio3bCekf1+CZnyLapwT\nRa5blUZlWR2TZw7wGCPRkfiiP3oywuHAUVePvbbO+b+qBmt5ZaP+qMbm+l6FtbTc+fKpoARbWQUA\nx+zFHHh9XZv2qei0mBJjMfWNx79vHAED+xI4sB/6EPPFN76CqKqp8bpOVRv1k12lwapSb3XQ0KBS\n3+D8Xt+gUt/goM7ioKbOTq3F0fYRUIMGNcCAJcBAqclAqUZLhR1sLs8S39rzVwR9DYL+BkF/vSBM\n68OIw0WoEz1nhLq96W66QdHp0E8Yi37CWNSKSux792PfvQ81OwcAra2BhE0rCcw5RcH4WThMzkxN\nVUW1fPPFcXQ4iAiC6QlmzAEmNlcroNGQU9nAo1+cYmx8EDcNiWB8ohljB7mCtWpE7NmzhwEDBtCv\nXz8A5s2bx+rVq92UwCeffML9998PwFVXXUVFRQWFhYVER7ectOzdP3/cZGmJ5sNTAuH2TCSa1Wus\n2+x7U51ml6oQrmWoKjhU53/VAQ4V0VhWVIfTGdmhgsMONjuKzQb2xu+Ny5ztXXA1K54KWtBFQVwU\nxLWo5H4rURTsOj31Jn/qAoOoCwji7MlNrJl6L/X+/ojGzEkuL4oyFTM1mD23htJYVwH0OH0l/TXO\n/yaNczhUB1DrPBybKjjVKFohhFM8zQwF53dc3zsnWsY5suDnp8Fk0uLn5/yYTFpO55kYMya0czoh\nkXQDFAWSDIIkg4NzNjhg0XCsQcHaLGYiI6YvGQsfISHrFOO2riPpZJprnS3zLPG5z3N29r1YIp3x\nEnu2ZHJgy0nMRhupt/TrtGPxRX8ArGimF4T7H/dbnhCude73fU/fPbQhmm/X7MuFNzohnDpCdSAc\nolGHOFBUAQ5Ho345r0ealW12sFkb/9tR7I0Pcx6eCj3fWsMhJhxinKW6/IOUxHlKca0gDHpEQAAi\nKADVHIwabEYNDkYEBUKjHnHtI8MBNJ9otGnvPt/jPdRri3pwq+tlp+K8rldx/dZCCOeQ3Pnnhcb/\nB0/X8MaaPIQqnL+RQyBU1fm9nfWWTaNQadRTZdRTadRTadRh1TUzyB2Nn4tgVASxOkGcHuJ1gji9\nwKy5fKNB0jPQhARjmDUDw6wZqGXlOA4fxX7oKI4TGYSeOow5+yRFo66hbMhYhM45imhHS0E1FKTX\nYqSWGxssaCy1YKtHdVhxINiuKGzTKPj56TGajBiMTs8NjaJBq1VQFIUhNyZdcr9bNSJyc3NJTGwa\nCk9ISGD37t0XrZOTk+PRiMiraTlxRrujANrGTzfHBFhrq0i0Ata6dmvXAdQ0froarRZ0Og16vYLB\noMFw/r9BQa/XYDBo0Go9uVMJCovzsVl9H3XpLahCUCxsOOx2t8w9VzKqw6mFHQ71sn/zgqK8y2rD\nOYCmA0GXnn8xwI1+cJ0RTti0pFu1ZNs1WFFAUcjpP5Cc/gOJKMhl9M5NDDq6H2NDPTprPf3Wvk32\nzLupjXMqBxt6Shs6133FF/0BkNsZeqEtNNchXejxk/v1GQqumu1bZTtQKqC0ukP71F0oK8rHXnWR\nYPE2YFcU6nUaLDottQYdtXottXodtQYdNo3i85O+AUGQRhCiEYRpBeEalTCNIFyrEnBhMw64WN6U\ntiAaY+SK7PU9Sm+6PHxsNhCX9zb9cnWDw6EDtKgOBzZrB474BAbC5InoJk9Ea7Uhss6iPXWGuIzT\nRK7eS1n/FMoHpmILcn/J6jCacBjdY5vOPwrbGz+1HozeIZfR1VaNCF9dRi5M8ORtu2vvkvmlL+Ta\nu37X1V3otvz68V91dRe6J397iN/xUFf3ol0JTvLDtxD6i9Me581TrteZfpfdVnsQAUxxlS581RoH\ncxYAC9yWtpwXtXPxVX9IveAZqRu80/myacvwhoKbp0JnkRQHX7xITztrpiW13z34cnXDbGA2Auej\nc2flJfKDISOAEa4lcZ20Z19oVQrx8fGcO9eUT/rcuXMkJCS0WicnJ4f4+PgWbXWntIISiUQi6Vh8\n0R9SL0gkEsmVS6tjQ+PGjSMjI4OsrCysVivvv/8+c+fOdaszd+5c3nrrLQB27dpFSEiIR1cmiUQi\nkfQefNEfEolEIrlyaXUkQqfT8eKLLzJ79mwcDgeLFy9m6NChLF++HIDvfe97zJkzhy+++IIBAwYQ\nEBDAG2+80Skdl0gkEkn3xZv+kEgkEknPoNNmrJZIJBKJRCKRSCQ9g3ZNHLt27VqGDBnCwIED+ctf\n/uKxzkMPPcTAgQNJTU3lwIED7bn7bs3FZPPOO++QmprKyJEjmTJlCocPH+6CXnYNvpw3AHv37kWn\n07Fy5cpO7F3X4otsNm3axOjRoxkxYgTTp0/v3A52IReTTUlJCTfccAOjRo1ixIgRvPnmm53fyS5g\n0aJFREdHk5KS4rVOZ9+HpW7wjtQN3pG6wTtSN3hG6gXvdIhuEO2E3W4XycnJIjMzU1itVpGamiqO\nHTvmVufzzz8XN954oxBCiF27domrrrqqvXbfrfFFNjt27BAVFRVCCCHWrFkjZeOh3owZM8RNN90k\nPvrooy7oaefji2zKy8vFsGHDxLlz54QQQhQXF3dFVzsdX2Tzu9/9Tjz22GNCCKdcwsLChM1m64ru\ndipbtmwR+/fvFyNGjPC4vrPvw1I3eEfqBu9I3eAdqRs8I/VC63SEbmi3kYjmEwvp9XrXxELN8TYx\nXU/HF9lMmjSJ4OBgwCmbnJycruhqp+OLbABeeOEF7rrrLiIjI7ugl12DL7J59913ufPOO11ZbyIi\nIrqiq52OL7KJjY2lqqoKgKqqKsLDw9HpOistX9cxdepUQkO9T9LY2fdhqRu8I3WDd6Ru8I7UDZ6R\neqF1OkI3tJsR4Wliodzc3IvW6Q03RF9k05zXXnuNOXPmdEbXuhxfz5vVq1ezdOlSwPf881c6vsgm\nIyODsrIyZsyYwbhx4/jvf//b2d3sEnyRzYMPPkhaWhpxcXGkpqby3HPPdXY3uyWdfR+WusE7Ujd4\nR+oG70jd4BmpFy6PS7kPt5v51d4T0/Uk2nKMGzdu5PXXX2f79u0d2KPugy+y+fGPf8xTTz2FoigI\nIVqcQz0VX2Rjs9nYv38/GzZsoK6ujkmTJjFx4kQGDhzYCT3sOnyRzZ///GdGjRrFpk2bOH36NLNm\nzeLQoUMEBQV1Qg+7N515H5a6wTtSN3hH6gbvSN3gGakXLp+23ofbzYhoz4npehq+yAbg8OHDPPjg\ng6xdu7bVIaeehC+y+eabb5g3bx7gDIpas2YNer2+x+ec90U2iYmJREREYDKZMJlMXHPNNRw6dKhH\nKwrwTTY7duzg//7v/wBITk6mf//+nDhxgnHjxnVqX7sbnX0flrrBO1I3eEfqBu9I3eAZqRcuj0u6\nD7dLtIYQwmaziaSkJJGZmSkaGhouGjy3c+fOXhMg5otszp49K5KTk8XOnTu7qJddgy+yac4DDzwg\nPv74407sYdfhi2zS09PFzJkzhd1uF7W1tWLEiBEiLS2ti3rcefgim0ceeUT8/ve/F0IIUVBQIOLj\n40VpaWlXdLfTyczM9Cl4rjPuw1I3eEfqBu9I3eAdqRs8I/XCxWlv3dBuIxFyYjrv+CKbP/7xj5SX\nl7t8O/V6PXv27OnKbncKvsimt+KLbIYMGcINN9zAyJEj0Wg0PPjggwwbNqyLe97x+CKbX/3qVyxc\nuJDU1FRUVeXpp58mLCysi3ve8cyfP5/Nmze4UFDMAAAgAElEQVRTUlJCYmIif/jDH7DZbEDX3Iel\nbvCO1A3ekbrBO1I3eEbqhdbpCN0gJ5uTSCQSiUQikUgkbaJdJ5uTSCQSiUQikUgkPR9pREgkEolE\nIpFIJJI2IY0IiUQikUgkEolE0iakESGRSCQSiUQikUjahDQiJBKJRCKRSCQSSZuQRoREIpFIJBKJ\nRCJpE9KIkEgkEolEIpFIJG1CGhESiUQikUgkEomkTUgjQiKRSCQSiUQikbQJaURIJBKJRCKRSCSS\nNiGNCIlEIpFIJBKJRNImpBEhkUgkEolEIpFI2oQ0IiRdxvTp0/nud7/b1d1olQ8//JDk5GR0Oh2L\nFi3q6u5cUbz55pvo9XpXedOmTWg0GvLy8rqwVxKJpDsj9ULPRuqFnoU0InoIDzzwABqNBo1Gg16v\np1+/fixdupSysrJ2aX/btm1oNBqys7PbpT2AVatW8be//a3d2rsUdu/ejUajYcKECS3WORwOFi1a\nxLx58zh37hz/+Mc/WLJkCTNmzOjQPqWlpXH33XczaNAgtFotDz74oMd6J0+eZPbs2QQEBBAZGcnS\npUupq6tzq5Ofn88999xDcHAwwcHBzJ8/n+Li4g7tv0Qi6R5IvXBpdEe98PrrrzNjxgwiIyMxm82M\nGzeOd999t0U9qRcknYk0InoQ11xzDQUFBZw9e5bnn3+elStXct9997XrPoQQl92G1WoFICQkhMDA\nwHZp61JZvnw548ePZ//+/Rw6dMhtXV5eHrW1tdx4443ExsZiNpsva18XYrPZPC63WCz069eP3/72\nt6SmpqIoSos6NTU1zJw5E4PBwM6dO/nggw9Yu3YtixcvdtVRVZWbb76Zs2fPsn79er766itOnjzJ\nbbfd1q7HIZFIui9SL7Sd7qgXNm7cyO23387atWs5dOgQCxYs4L777uODDz5w1ZF6QdLpCEmP4P77\n7xfXXXed27InnnhCaLVaUV9fL1RVFc8884zo37+/MBgMIjk5WfzjH/9wq79q1SoxatQo4e/vL0JC\nQsSECRPEgQMHRGZmplAUxe0zY8YM13YrVqwQqampws/PT/Tr10/85Cc/EbW1ta7106ZNE4sXLxa/\n/vWvRUxMjIiNjXUtX7Jkiaue1WoVjz76qIiPjxcGg0EMGzZMvPvuu259VBRFPP/882L+/PkiODhY\nzJs3z3WsSUlJwmg0isjISDF79mxhsVhalVlFRYUICAgQa9asETfffLNYunSpa90bb7zR4pinT5/e\nYtl//vMfIYQQ1dXV4qGHHhLx8fHC399fjB49WqxcudLV3nkZvvPOO+LGG28UAQEB4rHHHmu1f0II\nMX36dPHggw+2WL58+XJhMplEVVWVa9nnn38uFEURWVlZQgghvvzyS6Eoijh58qSrTlpamlAURWza\ntMnrPs+fS3/7299EXFyc8Pf3F3fffbcoKytrUac5//3vf4WiKG4y1Ol0rvLGjRuFoigiNzdXCOH8\nvR955BGRkJAgjEajiI2Ndf2eEonk8pF6oWfqhfPMnTtX3Hnnna6y1AuSzkYaET2E+++/X8yaNctt\n2V//+lehKIqoqakRL774ojCZTOLVV18Vp06dEq+88orw8/MTr732mhBCiPz8fKHX68UzzzwjsrKy\nxPHjx8WKFSvEkSNHhMPhEJ988olQFEXs27dPFBYWivLyciGE84YQGhoq3n77bZGZmSm2bNkiRo4c\nKb7zne+4+jFt2jQRFBQkli5dKtLT08XRo0eFEC0fkH/2s5+J8PBw8dFHH4mMjAzx5z//WWg0GrFh\nwwZXHUVRRHh4uPjnP/8pzpw5IzIyMsTHH38szGaz+Oyzz8S5c+fEwYMHxXPPPXdRZfHiiy+KpKQk\nIYQQn376qTCbzS4lZ7FYxN69e4WiKOLTTz8VhYWFoqqqStx7771iypQporCwUBQWFgqLxSJUVRXT\np08XM2bMENu3bxeZmZniX//6lzAYDK6+n1cWCQkJ4t133xVZWVkiMzPzor+rNyPivvvuEzNnznRb\nZrVahVarFe+8844QQojf/va3Ijk5ucW2iYmJ4k9/+pPXfd5///3CbDaLW2+9VRw9elRs2rRJDBw4\nUNx+++2uOg888ECL862tyuKvf/2rSEhIEJs3bxbnzp0Te/fuFc8991xr4pBIJG1A6oWeqRfOM3Xq\nVHH//fe7ylIvSDobaUT0EC58A5CWliaSkpLEpEmThBBCJCQkiEcffdRtm0ceecR1s9y/f7/b24oL\n2bp1q1AURZw9e9Zted++fcXy5cvdlm3evFkoiiIqKiqEEE5lMXjw4BZtNlcWtbW1wmg0ipdfftmt\nzu233y6uvfZaV1lRFLe3VEII8be//U0MGjRI2Gw2j333RmpqqnjyySeFEEI4HA7Rp08f8e9//9u1\n/vwNfvv27a5lixcvFtOnT3drZ+PGjcLPz09UVla6LV+4cKG47bbb3Npq7SbtCW9GxKxZs8S9997b\nYnlkZKR49tlnhRBCPPjgg2LKlCkt6owfP1788Ic/9LrP+++/XwQFBbm9zfrqq6+Eoiji9OnTrjqX\n+8bp4YcfdvttJRJJ+yL1Qs/UC0I477cGg0EcOHDAtUzqBUlnI2MiehCbNm0iKCgIf39/UlJSGDBg\nAO+88w5VVVXk5uZyzTXXuNW/5ppryMrKor6+ntTUVGbPns2IESO44447eP7558nJyWl1f8XFxWRn\nZ/PII48QFBTk+syZMwdFUTh16pSr7tixY1tt69SpU1itVo99TEtLc1t2YbDbt771LWw2G3379mXh\nwoW8/fbb1NTUtLq/3bt3k56e7sqsodFoWLx4McuXL291O0/s3bsXq9VKfHy8mxzeeecdNxl46vul\n4ilOwhPiEn2Vhw0bRlBQkKs8efJkAI4dO3ZJ7Xli4cKFHDlyhAEDBrB06VJWrlzp1R9YIpFcGlIv\n9Dy9sHr1ar773e/y+uuvM2rUKNdyqRcknY2uqzsgaT8mTpzIf/7zH3Q6HXFxceh0zp+3qqrqottq\nNBrWrFnD3r17Wb9+PR9//DGPPfYYH374ITfddJPHbVRVBeD555/3mJkiPj4ecN7YAgICLvWwWnBh\nW3FxcRw/fpyNGzfy9ddf8/jjj/Poo4+ye/duEhISPLaxfPlybDabq4/gvLEKITh06BCpqak+90dV\nVYKDg9m3b1+LdQaDodW+XyqxsbGcO3fObZnNZqOsrIzY2FhXnQ0bNrTYtqCgwFXHGxdTMhqNpkWd\ntt7oU1NTyczMZN26dWzcuJGHH36Y3/zmN+zatctNUUkkkktH6oWepRfee+89Fi5cyL///W/uvfde\nt3VSL0g6GzkS0YPw8/MjKSmJPn36uBQFgNlsJiEhgc2bN7vV37x5M0lJSfj5+bmWjR8/nl/+8pds\n3ryZadOm8cYbbwBNNz2Hw+GqGx0dTWJiIsePHycpKanFx2g0+tz3AQMGYDQaPfYxJSXlotsbDAZm\nz57NX/7yF44cOUJdXR2rV6/2WLeyspIPPviAl156iUOHDrl9pk6d2upbJ4PB4CYDcMqsoqICi8XS\nQgbelNXlMmXKFHbu3El1dbVr2bp161BVlSlTpgBw9dVXk5mZ6fbW69ixY+Tk5HD11Ve32n56erpb\n2zt27ACcb6IAoqKiWuT13r9/f5uPIyAggNtuu43nnnuOffv2kZ6ezpYtW9rcjkQi8YzUCz1HL7z6\n6qssXLiQt956q4UBAVIvSDofORLRS/jlL3/JT3/6UwYOHMi0adP4+uuveeWVV3jppZcA581gw4YN\nzJ49m5iYGDIyMjh8+DBLliwBoG/fvmg0Gj7//HPuuecejEYjwcHBPPHEEyxevJjQ0FDmzp2LXq8n\nPT2dtWvX8sorrwBNb3IupPlyf39/HnroIX7zm98QGRnJyJEj+eijj/jkk09Yv359q8f22muvIYRg\n/PjxhISEsGHDBqqrq103tgt5++230Wg0LFy4sIVCu/fee/nZz37Gs88+63HbpKQkPvroI44dO0ZU\nVBRms5lrr72W6667jjvuuIOnn36alJQUysvL2bFjByaTySVDX7HZbK6h+urqakpLSzl48CAGg8F1\nTAsWLODxxx9nwYIFPPHEE5SWlvKDH/yAefPm0bdvXwCuu+46xowZw7e//W1eeOEFVFXlBz/4AZMm\nTWrhHnAhiqJw33338ac//cnV9q233kpSUhIAs2bN4umnn+all15i9uzZfP3113z44YdtOs5nnnmG\n+Ph4UlNT8ff3Z8WKFeh0OgYNGtSmdiQSyaUh9UIT3V0v/P3vf+cXv/gF//znP5k6dSoFBQWA04AJ\nCwsDpF6QdAGdG4Ih6Sg8ZUW4kPOp/PR6vUhOTnbLeJCWlibmzJkjYmJihNFoFH379hW/+MUv3ILS\nnn76aREfHy+0Wq1bKr9Vq1aJSZMmCX9/f2E2m8WoUaPE448/7lrvLTj4wuU2m0089thjrlR+w4cP\nFytWrHDb5nw6vOasXLlSTJ48WYSGhgp/f3+RkpIiXn/9da9yGDVqlFiwYIHHdcXFxUKv14vXXntN\nZGZmCo1G4xZAV1ZWJubMmSOCg4PdUvlZLBbx2GOPuVIlxsTEiBtvvFFs3LhRCCE8tuWN5qkTNRqN\n63v//v3d6p04cUJcf/31wt/fX4SHh4vvf//7oq6uzq1Ofn6+uPvuu0VQUJAwm81i3rx5ori4uNX9\nnw+Oe/bZZ0VsbKzw9/cXd911l1sqPyGc6RPj4+NFYGCgWLBggfjnP/8pNBqNa/0bb7wh9Hq9q7xx\n40ah0WhcAXTLly8XY8eOFWazWQQGBooJEyaITz755KLykUgkviH1Qs/RC/369XPTB57S6goh9YKk\nc1GEaIdZYiQSSY/hgQceIDc3l3Xr1nV1VyQSiUTSDZB6QeIJGRMhkUgkEolEIpFI2oQ0IiQSiRuK\novicKlAikUgkPR+pFySekO5MEolEIpFIJBKJpE10WnamXbt2UVtb21m7k0gkEskFhISEXHSCr85E\n6gWJRCLpWi5HL3SaEVFbW8uYMWM6a3dXDMuWLXOl05O4I2Xjnd4qG4cq+M1Xp9mX05SrfEC4iVFx\nQZRbbGzLqiD9nadI+tajGLUKz986mP5hpi7scffiUnK2dyRSL3int17jviBl4x0pG++0VTZ/35rN\nmhOlAAQZtfjrtRTWWAGIDTLwrzuHYtRd+VEBl6MXrvyjv8Lp06dPV3eh2yJl453eKptXduW4GRC3\nDovgoasTmZ4cyu0jovjZNX0JjYoDoMEheHxDJnVWh7fmJJJuS2+9xn1BysY7UjbeaYtsSmttfHmy\n1FX+Vmo0o+OaZszOr7ayNbOiXft3JdIuRsSJEycYPXq06xMcHMzzzz/fHk1LJBIJAPtzq1h9rMRV\nvmFwOLMGhaNpFuwXazYyLsGMQetcllPZwKt7cju9rxKJRCK5ctmcWY7aGDF8frTbT+/+yLw9SxoR\n7WJEDB48mAMHDnDgwAG++eYb/P39uf3229uj6R5PcHBwV3eh2yJl453eJpt6u8pz2865yqmxgdw0\nJNxj3ZjIUOaNinaV15wo5Wy5pcP7KJG0J73tGm8LUjbekbLxTltks/F0uev7+EQzABoFmnsv7cup\nwmLr3SPd7e7OtH79epKTk0lMTGzvpnskKSkpXd2FbouUjXd6m2zeOVBAfrXTF9Wk1/Ct1Giv6QYH\nDR3OhMRghkT6A6AK+PeevE7ra29k0aJFREdHu52XP//5zxk6dCipqanccccdVFZWdmEPrzx62zXe\nFqRsvCNl4x1fZZNbWc+J4joAtAqManRjunZAGP+YO5jYIAPgdJlt7l7bG2l3I+K9995jwYIF7d1s\nj+Xqq6/u6i50W6RsvNObZFNaa+N/R4tc5TtGRGH2854TYuxVkwG4bUQk582M3eeqOJTXu2/2HcnC\nhQtZu3at27Lrr7+etLQ0Dh06xKBBg3jyySe7qHdXJr3pGm8rUjbekbLxjq+y2XimyU1pWHQgAQat\n2/rUZrER23q5S1O7ZmeyWq18+umn/OUvf/G4ftmyZa7AluDgYFJSUlw/6rZt2wBkWZZlWZbdyu8c\nLKDk5AEAho+9iol9zHyzewfQZDB4K0/o05/d2VVUnT7IP97P4I1H7uny4+nM8vnv2dnZACxZsoSO\nYOrUqWRlZbktmzVrluv7VVddxccff9wh+5ZIJJL2ZFuzgOlxCUEt1o+KC2RtY9am3dmV2Bwqem3v\nzFPUrpPNrV69mpdffrnFGymADRs2yFR+Hti2bZt8c+AFKRvv9BbZ5Fc1sOjDYzga71LLJiUwLDqg\n1W2+2b3DZUwU1Vh5fH0m529yr901lMQQvw7scfdm//79zJw5s0PazsrK4pZbbuHIkSMt1t1yyy3M\nnz+/xSi11Ave6S3X+KUgZeMdKRvv+CKbyno7d7/tvIdpFHh6zsAWAdVCCH731RnKLHYAnps7iKFR\nreul7szl6IV2HYlYsWIF8+fPb88mJRJJL+aDw4UuAyI53MTQKP82bR8VaGB4TABHC5wTmq1KK+ZH\nU2S8VmfyxBNPYDAYvLq5yhFqWb6UEbbu1J/uVD5y5Ei36k93Kp9/wdFa/UP51UAMAKbCY6TtL/U4\n4p0cbiJr81YA0oviGRoV0OXH1xUj1O02ElFbW0vfvn3JzMwkKKjl8I984ySRSNpChcXGt99Lw9po\nRTw0JZFBkW0zIgBOFNfywvYcAIw6De/OH06QsV3fn1wxdPZIxJtvvsmrr77Khg0b8PNrOQIk9YJE\nIulOvLD9HJ+mO1OJzx4Uxi3DIl3rHKrAoQo0GoXtWRV8eNgZqzetfwj/N7N/l/S3PbgcvdBuTlwB\nAQGUlJR4NCAkEomkrXyaXuIyIBJDjAyMuLSZpwdF+BNvNgLQYFfdUvdJOo61a9fyzDPPsHr1ao8G\nhEQikXQ3DjZLwHHhS6uNp8v5yWcZfHqsmKSwJn10rKi20/rX3eidkSDdiAuHZyVNSNl4p6fLpsGu\n8kmzieVmDgjzmtL1Qs4POZ9HURQm92vKD74+o6x9OilxMX/+fCZPnsyJEydITEzk9ddf50c/+hE1\nNTXMmjWL0aNHs2zZsq7u5hVFT7/GLwcpG+9I2XjnYrIprbVxrrIBAJ1GoX+Y9xdXcWaja1LT4lob\nxbXW9uvoFUTvHNOXSCTdms1nyqmsdwathZp0jI67vBHOsQlmVh4pwiHgeHEd5yrqe3WAdXuzYsWK\nFssWLVrUBT2RSCSSS8MZD+Gkf5gfhlYyLmk1Cn1D/cgocU5kml5YS2SSocP72N2QIxFdjMyi4B0p\nG+/0dNl8frxpFOKapBC0Gt9GIaApzWtzAg1aRsQEusrr5GiEpJvT06/xy0HKxjtSNt65mGwOF9S4\nvg+KuHj8XX/p0iSNCIlE0r04XVpHepFztlCdRmFin+CLbOEbExLNru/rT5Whtl92a4lEIpFc4Rxv\nZggkhV88Bq9/aFOddGlESLoC6b/oHSkb7/Rk2XyeXur6nhoX2OZMShfGRJxneEzTzKMltTaONxoq\nEkl3pCdf45eLlI13pGy805psLDYHWeX1AChAHw/urhoF9FrFNTLeL6ypzplSCw61972YajcjoqKi\ngrvuuouhQ4cybNgwdu3a1V5NSySSXoLF5mDD6SZXo6v7hbRb2zqNwsjYJpemrZkyS5NEIpFIIKOk\njvM2QEyQAZNe26LOtQPC+Pstg5jbmPY1yKjDbHTWa3AI8qsbOq2/3YV2MyIefvhh5syZQ3p6OocP\nH2bo0KHt1XSPRvovekfKxjs9VTa7siux2FQAogMNDPBhSPlCPMVEnKd5gPa2rEraaZociaTd6anX\neHsgZeMdKRvvtCab5iPT/UJ91ztxwUbX9zNllkvr2BVMuxgRlZWVbN261ZWNQ6fTERzcPn7MEomk\n9/D1qabRgfGJZp/TuvrKoEh/TDrnba+wxurKrCGRSCSS3svx4qaYhr5hvmfuSzA3GRGZZfXt2qcr\ngXYxIjIzM4mMjGThwoWMGTOGBx98kLo66W/sC9J/0TtSNt7pibKpqrezL6fKVR6bcGlpXb3FRIDT\npSmluUtTVsUl7UPizqJFi4iOjiYlJcW1rKysjFmzZjFo0CCuv/56KiqkrNtCT7zG2wspG+9I2Xin\nNdm4j0T4bkTIkYh2wG63s3//fpYtW8b+/fsJCAjgqaeealFv2bJlPPXUUzz11FO8/PLLbj/otm3b\nZFmW3cpHjhzpVv3pTuUjR450q/60R3n5x1/SOEE1/kXHyD66z7X+m9073IyDyymPigui6vRBqk4f\nZHujEdEdjr8jytu2beOpp55i2bJlHTrZ28KFC1m7dq3bsqeeeopZs2Zx8uRJZs6c6VEnSCQSSVdT\nUmulpM4GgEGrEBtkvMgWTcS7jUT0PiNCEe3gFFxQUMCkSZPIzMwEcCmuzz77zFVnw4YNjBkz5nJ3\nJZFIeig//SyDI415uu9KiWJ6cmiH7MfmUHn0i1NYGy2WN+4eRnyw70rjSmb//v3MnDmzQ9rOysri\nlltucRn/Q4YMYfPmzURHR1NQUMD06dM5fvy42zZSL0gkkq5mW2YFf9zgfH4dEG7ix1P7eKznUAUO\nVaDRKOgaMzTZVcFPPj3pCsr+330jXVkArxQuRy+0y0hETEwMiYmJnDx5EoD169czfPjw9mhaIpH0\nAopqrC4DQgHGxF/eDNWtoddqGBwZ4CrvPlfZYfvqzRQWFhIdHQ1AdHQ0hYWFXdwjiUQiaUlGaZMr\nU59WXJk2ni7nJ59l8OmxYtcynUYhJqhppuqsXjYa0bYE7K3wwgsvcO+992K1WklOTuaNN95or6Z7\nNNu2bZPZFLwgZeOdniabTaebAqoHR/lj9rv0W9M3u3e0mqEJYHhMgMto2Z1dyR0joi55f5KLoyiK\n1yD5ZcuW0aeP881fcHAwKSkprnP7vItWbyw3d0/rDv3pTuULZdTV/elO5SNHjrB06dJu05/uVH75\n5Zc93l9O1cQCUHX6IPW6cBhxHdAUX3den5w5vJeqrAoYMMNtfby5H3lVVqpOH+Tz9bkM//bN3eJ4\nW7t+tm3bRnZ2NgBLlizhUmkXdyZfkMPWnulpD4PtiZSNd3qabL6/8rgrKO3bY2Iua5ZqX4yICouN\nX395BgCtAh9958obgr4UOtudadOmTcTExJCfn8+MGTOkO1Mb6GnXeHsiZeMdKRvveJKNEIJvvXOU\nino7AL+Z2Z/oZiMLzVmfUcaqtGJmDgjl9mYvns4vB7h5SAQPXZ3YQUfQMXS5O5Pk0pEXu3ekbLzT\nk2STVW7hTJkFRQiCbXYSHQ4Kz5Tx/+y9d3xc13Xv+z3TG3rvAAGikSDAXkSKIqlCWqLcZDu2b+Qn\nW/F78efakWPHiZObdxPnxfaNHSeKE6fYcSzJjiRLsi2JkiiKFHsDSRSCAInee8f0ds77Y4ABQGKI\nNgAG5Pl+Pvhg9sw+ZzYWZs4+a++1fmu0z4Lb6Zn3+WZzIAAi9WpSx/MgvBJc6xyb5QiZ+fLkk0/y\nwgsvAPDCCy/wsY99bIVHtLq4l77jwUa2TWBk2wRmJtsM2Tx+B0KjFIgzqed93qTwSaejdeT+knkN\nWjiTjIyMzHwRvSJHz7SwsWeYKLsblSRxrX1wsoMA0cnhJK+NI70oEdUMVUQXyvpEEx2jvgqjpW1j\nPJi1NInc9wOf/exnOX36NAMDA6SlpfGd73yHP/uzP+PTn/40//mf/0lmZia//vWvV3qYMjIyMtNo\nmJIPkRqhQ7GA2kSJpklhjrb7zImQdyJWmKkxajLTkW0TmNVuG0mSqK3q4Wc/OovlcitxNheqmSIr\nJRjqHOPGqUaO/6yUxrIOJPHuEZh3qxMxlcKEyeTqsk6zXL16Ebz88st0dXXhcrlob2/nmWeeITo6\nmuPHj1NXV8exY8eIjIxc6WGuKlb7d3wpkW0TGNk2gZnJNvWDk4nQaZF3V+lTCKBWCigV0x2NKIMK\njdL33KjDw4jdHYTRrg7knQgZGZllxTzq4L3Xq2hrHLzjNY1ejc6kQaFU4LK5sY1Nruq47G6qTzXR\nXT/AxsfyMEbqFzWOjEgdepUCu0dkwOambcRBRtTizikjIyMjs3poGJjciUiLuHuRuf050ezPib7j\neYUgkGDS0D6+s9024iRSP/+wqNVI0JyIzMxMwsPDUSqVqNVqSktLg3Xqexo5fjEwsm0Cs1pt01Tb\nz7u/vo5jykqNSyHQEW4gKjOKJwtjp6n4uBxuBtpGaK/uxTleDGioc4wz/13Oto+uIyblzgTsueRE\nACgVArlxBiq7fSpN1zrNshMhEzKs1u/4ciDbJjCybQIzk22mhTPNshNxNxLDtFOcCAcbkkwLPtdq\nImjhTIIgcOrUKcrLy2UHQkZG5g7KL7by2xev+R0IQYCuKCPn0mJpiDaxPjX8DhlQjU5Ncm4cW58s\nJGNDoq+IBOB2eLj4+nW6GwYWNaaC+MmQpmsd5kWdS0ZGRkZm9TDm8NBn8c1HKsX8KlXfztRaEfdT\nXkRQcyLkmOL5I8cvBka2TWBWk20kSeLcsTpOvH2TiUuEwaQh66FsbkSZ8CgVhKkVZIXPLKsHoFAq\nyChKouTRXNTjNSREr8TVIzfpax6a1neuOREA+fEG/+Pr3WZcXnEef5mMzNKxmr7jy41sm8DItgnM\n7baZuguRHK69I9dhPshOxCIRBIGHH36YLVu28NOf/jRYp5WRkVnFSJLE2WN1XDrV5H8uJt7ERz61\ngaop6q1Fsfo5qWKExxopeSwX/fiKkSRKlL5Vw1DXwqpOxxo1xBl9satOr0R1r3VB55GRkZGRWV00\nDMw9qXo2EsPuT4WmoOVEnD9/nqSkJPr7+3nkkUfIz89nz5490/rIlUnl9kIqK4bSeEKlPfFcqIwn\nUFvlSaL0dDOtnTUA7Nq1iz2P5XL52mVOlPWiyyoGQNNeRfmAiuJN21EoBCrLfSGRxRu3AUxr601a\niB2mq7WD5OhcRK/Iq//yGsUHcti1/3mKuqEAACAASURBVCE2b991R6XRu7Xz4400Hj8FQFlHPBuT\nw0LGfqFUmVRmeZFj2wMj2yYwsm0Cc7tt6m+Td50NryjhFSUUCgHVbbsWsUY1SsFXd2jA6sbq8t4X\nBUyXpGL1X//1X2MymfjGN77hf06uTCojc39xs7KLd1697m+nZEbx4MFclEoFpd0W/rmiD4BYnZIn\n8dJR00tmcRLp6xPndH672UnF+3X+gnQR8SYe+EzxvGtJXO828x+XuwDIidHzk4/nz+v41cRSVqxe\nCPK8ICMjs1J88bUaf62gb+5NJ3MWYY1AFasn+NsTzXSbXQD805O55E/JuQtlVrxitc1mw2z2JSVa\nrVaOHTtGUVFRME59zyPHLwZGtk1gQt02Hc1DHH29yt9OSAn3OxAAF7os/tc2xBpYQH0f9GFaCvZk\n+o8d7bNQc6ZpXjkRAGtjDUwsKjUM2hm+jzS+l5rvfe97rFu3jqKiIj73uc/hdDpXekirhlD/jq8k\nsm0CI9smMFNtY3V5/Q6EQvDlRCyW+zEvIihORG9vL3v27KGkpITt27fzxBNP8Oijjwbj1DIyMquM\noX4Lv/tlOV6vb5MzIkrP3kN5fgfC6vZS2T+5jbwhduGyqpEJYWRvSfW3Wyq7GeqcX36EXq0kK3py\nDBVdskpTMGhpaeGnP/0pZWVlVFVV4fV6eeWVV1Z6WDIyMjI0DU3mQySGadAoF387nHAf5kUEJSci\nKyuLioqKYJzqvkOOXwyMbJvAhKptnA43v3mxzC/jqtOr2fdEPhrt5KXmSo+Vcf+CFKOaWL2Kxdy2\nJ62NZaTHzEC7z3nw9ETgsLrQGQOrPd1OfpyBxvHKpdc6zOzLvrOgkMz8CA8PR61WY7PZUCqV2Gw2\nUlJSVnpYq4ZQ/Y6HArJtAiPbJjBTbTO1yNxc8iHmgrwTISMjI7NAJEni6Bs3GBlPVlOqFDz0eD6m\n8OkX6IvTQpkWX9xNEATWbk9Ha/CpLLkdHqo+bJjXOabVi+g0y3LVQSA6OppvfOMbpKenk5ycTGRk\nJA8//PBKD0tGRkaGhsGpykyyE7FQgqbOJLMwpirsyExHtk1gQtE2ZRdaqa/u9bd37c8mNmF61c4h\nh4dbQ76Lq4BP2hVAUAgolMIdxebmilqrIndHOlUfNo4rQRXSVddPcm7cnI5Pj9KhVyuwu0UGbW5a\nhh3TQpxk5k9jYyP/+I//SEtLCxEREXzqU5/iV7/6FZ///Oen9ZNV+2ZuT43fDoXxhFL7dhut9HhC\nqV1VVcUf/uEfhsx4Qqn9r//6r/7rS8OAjbFGXwRN2u7DwN1V/ABaqq5gax1Fmbtvxtc7a65hbuwg\nLLuEHrOLk6fPoFYqQubvXwrVviVRZ5oJWYVjZkLxZjBUkG0TmFCzTXf7CC//+2VE0Xc5yStKZOuD\nWXf0e695hJdv+YrDrYnQ8MXC2KCOo+5SG5fPnCUjpRCtUcOBZ7ag0sxtreRnpZ1UjO+S/D87UvjE\nDOobq53lVGd69dVX+eCDD/jZz34GwEsvvcSlS5f4l3/5F38feV4ITKh9x0MJ2TaBkW0TmAnbODwi\nH3uhElHyLWb93eM56Oep6heIv/qgiQGrL5z3Xz+eR3aMYZYjVp4VV2eSWTjylz0wsm0CE0q2sdtc\nvPVyhd+BiI43sumBjBn7Tg1lKo4N/sV1zaZk1uZsAMBpdVF3uX3Ox+bHTYY0lXXKydWLJT8/n0uX\nLmG325EkiePHj1NYWLjSw1o1hNJ3PNSQbRMY2TaBmbBN06Cd8emKeJMmaA4EQKJpakjTva9GF1Qn\nwuv1snHjRg4fPhzM08rIyIQokiRx7LfVmMfjPzVaJQ8+NinlOpUui4uWMZ+GtlKAwujgxKFORaVR\nkbVxMnm3qawDy7D9LkdMkh8/6dRc77bg9opBH9/9RHFxMU8//TRbtmxhwwafY/flL395hUclIyNz\nv1M/Jak6fZGVqm8nMfz+UmgKqhPx/PPPU1hYuOC45vsRWdM5MLJtAhMqtrlV2T0tD2Ln/pw7Eqkn\nuNQ9uQuRF6VDr1qajdCe4XrCY327CqJXovp045yOizVqiBlPznZ4RG722WY5QmY2vvWtb1FdXU1V\nVRUvvPACarV6pYe0agiV73goItsmMLJtAjNhm7ppTkRwF7Om70TITsSc6ejo4N133+XZZ5+VlU1k\nZO4DzKMOjr9V42+vXZdA2pqZpVElSQq6KlNABGFa7YjepiF6m4fmdOjU3YiyzrGgD01GRkZGZmWZ\n5kREBdmJCJediAXx9a9/nR/84AcoFHKaxXyQ4xcDI9smMCttG0mSeP+3N3A6PACYwrVs2jVzHgRA\n86iTXpuvr1YpkHfb6o/oFfF6RH9exWIo3riNsBgDidkx/udunGpEnEN40tS8iHK56JzMCrLS3/FQ\nRrZNYGTbBGb37t3Y3V7aRyYVAudTI8IrSrg8Ip67zFMJU3YiOkedeIMwp4UyQbnjP3LkCPHx8Wzc\nuFHehZCRuQ+4fqWDlroBf3vngRzUmsDJaRenhDIVRutQK6eHPLZW9XD+1Uo6anpvP3TBZJYkoVSP\nV8kettNc2TXrMblxBiZGVttvw+L0BG08MjIyMjIry9Sk6oQwDdp5hNWebBzmj4/U83ZNf8A+erWS\nSL1PEdAjSnSN3dvJ1UGpE3HhwgXeeust3n33XRwOB2NjYzz99NO8+OKL0/rJeuCy3rWsdx18vevl\nfv+RIRu/+I838LhFMlIKKShOorWzhtZO2LZ1BwClVy4BvrZXlHj39DmsHpHw7BI2xOqpLC8FfLsG\nAHX1FfR1DpNZnARwx+vzaU88BsgoyqSprJPWzho6X6/jD9b/X6g0qrvqgadF6rhxzTf+iu4sdmdG\nrvj/OxT0wGWWF1mqMzCybQIj2yYw586doz8y198Odj7EBIkmDSN23wJU64gjaMXsQpGg14k4ffo0\nP/zhD3n77benPS/rgc+M/IUPjGybwKyUbSRR4tWfldLRMgxARJSeQ58uQqUKvAtR2Wfj76/1ABCm\nVvAnmxNQ3Ca+0FzRRXt1L5nFSaSvT1zUGCvLS/3OhegVufL2TZxWnypU3s4M8nYGDrsC+O2NPk40\n+P6+wwWxfPWBtEWNJ5RYzjoRc0GeFwIjX/8CI9smMLJtAnPu3DkueFI5Pn59f6oonoeyo+Z8/PH6\nIX5X3c+BnCg+fpc6Qq9f7+VU0wgAz2xJ4rMli5vTlpqQqxMhqzPNHfnLHhjZNoFZKdtcu9DqdyAE\nwRfGdDcHAuDclNyC4jj9HQ5EsJlwIAAUSgUZRZMX8MZrHTjt7rsenxMzmfQt14uQWSnk619gZNsE\nRrZNYHbv3k3dwKTk95LtRITdPzKvQQlnmsrevXvZu3dvsE8rIyOzwgz2WTh7rM7fXr85hdgE012P\nsbq9lPVOKmFsjFv+6p0JWdF03OzDNurA4/JSX9rG+r3ZAftnRk06EZ1jTnrNLhLCNAH7ywRmZGSE\nZ599lurqagRB4Oc//zk7duxY6WHJyMisIHabi9aGQTpbhxkbceCwuVBrVBhMGhJTI0hfEzPr3LIQ\nbK7bk6qDWyNigsQp80Xr8L3tRMhSSiuMrOkcGNk2gVlu24hekfder8Lr8SkcRcUaWT9FRjUQpT1W\n3ONZbElGNQmGmesECAoBhVIIyi7m1JyIiXNP5FoAtFR0YTcHvrCrlAJTR1EmqzQtmD/6oz/iIx/5\nCDdv3uT69esUFBSs9JBWDfL1LzCybQITyrZpbx7izV+V85PvnuTIK5WUX2yj8WYfna0jtNQPUFPe\nxYdv3+QXz5/jlz+5SE15F1IQ1Y1eP/ohE2dLDNegmWetIoUAaqWAUnH3eWqqE9E+6kS8hwWHgr4T\nISMjc+9x+XQzPR2jACgUArsezp6xKvXtnO+cVGXaGBe4NkTmhiQyNyQFfH2xxKRGEBZjwDxoQ/RK\n1F5opeSxvBn76tVKPrYujt9W+xQ4yjrHOJQXM2NfmcCMjo5y9uxZXnjhBQBUKhURERErPCoZGZnl\nZrDPwqn3ammuDaxqdDs9HaO8+9p1rpxr5sDhQlIz5567EIiOKaFFCwll2p8Tzf6cmWshTcWkVWHS\nKLG4vDg9In0W17QQp3sJeSdihZHjFwMj2yYwy2mb3q4xLn7Y4G8Xb08jKsZ4lyPGj7O6qRvfylUA\nG2KWsMDcFKbmREwgCAKZJcn+dltNL5bhwBWp86YUnavostzTK0lLRXNzM3FxcTzzzDNs2rSJP/iD\nP8Bmk6uAzxX5+hcY2TaBCSXbiKJE6ZkmXvzx+TsciNgEE0VbUtnzWC4Pf6yQfY/ns2V3JmlrolFM\nWenv7zbz6k8vc+5YHd451Pq5G0Jakf/xUuVDTDA1BPZezouQdyJkZGQC4vGIvPfadX8RuNhEEwVT\nbsbvxoUpFarXRmox3aWOxHIQlRhGZKKJkR4LSFB7sZXNH5k5vCY5XEuYVonZ6WXU4aFp0E5O7PLn\nc6xmPB4PZWVl/PM//zNbt27lueee4/vf/z7f+c53pvWTpb/ltty+99o2i4u//9sX6Osyk5FSCEBr\nZw3J6ZF8/NOHiIw2UHrlEr3DsC1nUhpcHwuf3LeZW5XdvHvkOKJXIiOlkEunmjh58jQPPLyW/Qce\nWtD4Lpw/x5jVTXh2CemRurtKfS+2nRimobz0IgBtw8lsS4sImf/PxONgSH8HXeI1ELKU38zIcmyB\nkW0TmOWyzZmjtZSeaQZAqVLw+Gc2EB45+46CJEn8yel2+sa1sj+zNoqi2OXZiZgq8Xo7Y/1WKqYk\nhz/09GbCY2feVfnF1S6udvjyIZ7dmsynixOCP9hlZjklXnt6eti5cyfNzb7Pz7lz5/j+97/PkSNH\n/H3keSEw8vUvMLJtAhMKtunvNvPbl64xNmUFPjreyI6HsomOm30XewKr2cnFEw30dI5NnifOyFPP\nbJnTPDTtXC4vB/73i4Rnl6AQ4IdPrEUzh5DchXKycZg3qvoAOJgbwx8/mL5k77VYVlzi1eFwsH37\ndkpKSigsLOTb3/52ME4rIyOzgnS2DnPlbLO/vWln+pwv3HXDDr8DoVMK5EeHRrGd8DgjUcnh/nbt\nxdaAffOmTHZycvX8SUxMJC0tjbo6n9N2/Phx1q1bt8KjkpGRWUq62oZ55aeXpzkQRVtSOfiJ9fNy\nIACMYVoOfLSQDdsma/UM9Vv59c+uMDZiv8uRd9IwMBlKmRSmXVIHAqYnV8vhTLOg0+k4efIkBoMB\nj8fD7t27Q8IbXg3INgqMbJvALLVtXC4P771excQ+ZWJqBLlFcy+Yc7J98qZ7fYwe9SxqFqJXRJLG\nVZpm6TsbgXYhJsjckMRwl29lq7t+gNE+CxHxk3KCkiTh9kpkT3F8bvRYcHnEeat53O/8+Mc/5vOf\n/zwul4vs7Gz+67/+a6WHtGqQr3+BkW0TmJW0TVvjIL99qQy3ywuAWq3kgUfXLiop2usRKSxJIixC\ny8UTjYiixMiQjVd/Vsrn/u8dGOeYsFw3YCM8uwRYeD6EV5TwihIKhYBqHgpNbSMOJEm6J2uoBW1G\nNBh88cIulwuv10t09OwZ7DIyMqHJmffqGBn0rdyo1Up27s+e8wXQ7PJS2j2ZD7EtYfZcgtaqHs6/\nWklHTe/CBjwPwmIMxKROqgTdvhvh8Ij88ZF6/u50Gwkm30Tg8krc6LUgMz+Ki4u5cuUKlZWV/OY3\nv5HVmWRk7lEab/XxxgvX/A6EVq/ikY+vW7Sq0m9fLOOV/yglKS2SBw/m+heZRofsvPHCNZwOz5zO\nU9Nr9T/OiFqYE3GycZg/PlLP2zWzq0xF6lToxhedLC4vw/a5jXO1ETQnQhRFSkpKSEhIYN++fRQW\nFgbr1Pc0oazpvNLItgnMUtqmqbafistt/vaWPZlzXu0BONNhxjO+g5FqUpNsWt5CbbfXiZiJjCly\nsj2Ngwz3zByulDelON5EfoSMzHIgX/8CI9smMCthm6baft78Zbm/jpDBqOHRj88/fGk2UrOi2XMw\nl4n1rL6uMd5+uRxxFtUmSZKo7rUy1lgBwJplUAoUBGGaQlPrPRrSFDR1JoVCQUVFBaOjozz22GOc\nOnWKhx56aFofWYVj5iz5UBpPKLWrqqpCajyh1K6qqlqS82/etI33f3OD1s4a3+t7drMmP47SK5cA\n2LZ1UkVjpvaWLds52T7mv1hvffQhYPLGfiLU6PZ2XX0FfZ3D/qJws/VfbLuxpYpRTzcRKt/16MhL\nb1H4YJZfZWOssQKHUkHhlkOcaR5hrLGCd/s0fHn754Nq79WkwiEjIyNzO52tw7z13+V+BT9TuJaH\nP1qIKXxp8uDSsqLZ/tAaLp1sAqClfpBzH9Tz4MGZ6/4AdI25GBnfsdCrFdNCjZaSRJPGX7G6fcTB\nxuSwZXnf5WRJ1Jn+5m/+Br1ezze/+U3/c7IKh4xMaCNJEm/9dwX11b6QIp1ezROfLUann7nK9Ezc\nGLDxd1d6fMcrBb61OWFOCWzNFV20V/eSWZxE+vq5514sBtuog6vv3GSihOkDnykmJiUCu9vLn7zT\ngE6l4LsHs/nWuw14xifIlz6zbtrq0mpjOdWZ5oI8L8jIrF76e8y88h+X/SFFxjAtj35iHUZT8Aqr\nvfafV3A6PDz1xS3T5qKKy23cuNrpbz/5uRJyA8wdH9QP8oPTvoWUwgQjX9mZuqCxHK8f4nfV/RzI\nieLj6+Nn7f9B/SBvVg8AcLgglq8+kDbLESvDiqszDQwMMDIyAoDdbueDDz5g48aNwTi1jIzMMlFT\n0eV3IAB27M+elwMB8GHbpBTfxjjDkitgLAZDhI74KfG6tRda7uijUSnInVIf4krH2B19ZGRkZO43\nRoZsvP5fV/0OhE6v5sCTBUF1IO5G8bY0kjMi/e33Xq9isG/mvLXqKfkQa6KXR2ocIHGKLe5Vhaag\nzPDd3d3s37+fkpIStm/fzuHDh0NqtSuUkWM7A7PabeO1OXB092Nt7sBc08BIWTWD567R/+ElBk6X\nMnjuGkOXKhi+WsVoxU0s9S04+4cQ3bMnYAXbNqPDdk68ddPfXrsuYd4JccMOD2V9kzJ6W+eQUD2B\noBBQKIWgqFfMJSdigoyiJBh/y4H2UQbafIshaqWAWul7oTBhMq63tH100eOTkZkLq/36t5TItgnM\nctjGbnPxxi+uYjU7AZ/4xv7DBfOu3TAXlCoFyhlU8QRB4IGH12IK992ou11e3vxl+YyJ1hNOxFhj\nxaKcCIXgmxuUc1QQnBo21X6POhFByYkoKiqirKwsGKeSkVkVeG0ObK2d2Fo6sLV0YmvpxNk3iKt/\nCGf/EK7+Yby2+elYT0VpMqCODEcTE4k+NRF9WtKUn0REtztof4skSrz3+nVcTt/FNyxCx6ZdGfM+\nz+l2M+NRP2SGa4g3zH0XI3NDEplTkp2XC32YlsQ1MfQ0DgJw60ILD3ymmH84nOvvsy7ByOu+FBTK\nu2SpVxkZmfsXr0fkrV9VMDxed0GhFNj7eF7Qk6gn+MQXNgd8TatTsfdQHkffuIHXIzI0YOWD393g\n8c8U+xekLE6PPy9BISxcmQlgf040+3PmrjwaY1SjUgh4RIkhuwez00OYNmipyCHBvfXXrEJkvevA\nhIJtRI8Ha0Mb5poGzDfqGaupx3KrCWfPwJK+r9diw2ux4ejoYazy1h2vC0olZ9ekEVaQTVjBGkwF\n2YQX5aFPmX9V5SvnmuloHvadV4BdD+eg1ijndQ6PKHGyfTLUZ1vC0kwoc2G2OhG3k74+kd7mISRR\nYqhrjP7WYeIzJyeKOJOGOKOafqsbp0ekstvC1rTwu5xRZiper5ctW7aQmprK22+/vdLDWTWEwvUv\nVJFtE5iltI0kSXzwZjXtzUP+5x54eC2JKSsn3RwVa2THvjWc/6ABgFvXe8jKi2PdxhRgeihTwabt\naJdxAUghCCSYNHSO+XZs2kYcrEswzXLU6kJ2ImRkpuDoHWCk9DrDV6sYuXIDc3U9otO1oHMJKiWq\ncBMKrcb3o9Gg1GkQ1CoQJSSviOT1IokikseD1+bAY7bisVjxL+kHQPJ6sda3YK1voeetE/7ntUlx\nRG0pInLLeiK3rCd8fS4KbeBE4K62Yc4dq/e3129OIS5x/goSl7stDDt9+uAmtYLCEKlQPRd0Jg2J\n2TF01/scw1vnW4nLiJoWWrU+0cTJRp+jdbF1VHYi5sHzzz9PYWEhZrMskSsjs5opPd3EjWuTycwl\nO9LJyIlZwRH5yMqNo6djlMabvvoNJ96qISUjishoA+Vdk9edtbFzD7ENFolhU5yIYdmJkAkycmXv\nwCyHbewdPQyevcrguauMlFZhb++e24EKBdqEWHTJceiS49ElxaONi0YdFY460vejNBkWFOMvieK4\nQ2HBNTiCs28QZ8+A73fvII6uXsq7WilU3Lna7+zup+ftD+l5+0PfMHUaorYXE/vgNmL2biWsMAdB\n4VuJsdtcvP1KpV+aLzbBRNGW+atWSJLEu82TuQI7Eo2zVvNcSirLSxewG5FAT+Mgkigx0mumt2mI\nxOzJybE4aYoT0TbK/5RSUdyD1UeDTUdHB++++y5/8Rd/wY9+9KOVHs6qQp4bAiPbJjBLZZvaqh7O\nTllwys6PY92m5KC/z0LZsjuLvi4z5lEHLqeXd399nd/7g21UdE0mW0sdVbB+efN1b69cfa8hOxEy\n9xXuMQuDZ68ydPYqA2evYmtsm/UYTWwUhjVpGNekYcxOx5CVijYpDoVqab4+gkKBymRAZTKgS5pZ\nRs5++RLrI+KwNY/nZTR1YKlvRrQ7p/UTHS4GT19h8PQV+BvQxEQSvWcLcQd2cdkchXn8oqbRKtn9\n6FoUC1BTqh6002727daoFcKKhjItFK1BQ3JuLJ23fCtZty60kLAm2u8EZkXrMWqUWF1eBm1u6gds\n5C1RDPC9xNe//nV+8IMfMDYmq1rJyKxWutpGeO+16/52Qko42x5aExQhjGCh1ih54JG1vP+bG0ii\nRFfbCCc/qKdpyJebqBAgZYlqV9yNxCmFWu/FgnNBuQtqb2/n6aefpq+vD0EQ+PKXv8zXvva1YJz6\nnkdeTQlMsGxja+2i74Nz9B87z9CFMiSPN2BfQaPGlJdFeOFawgqzMeWvQR0ZWqErosvNjuKNKNRq\nwvKz/c9LXi+2lk7MNY2YbzZgrmnE2d037VjX4Ag9vzvOjTozPTse8z+/dWPsgosDHWma3IXYHG/A\noJ6/IyJ6RSRpXKVpkbsY892FmCCtMIHu+kFEr8hYv5X2W/2kF/icOKVCYH2CkcvjeR8XWkZlJ2IW\njhw5Qnx8PBs3buTUqVMB+8lFSGdu7969O6TGI7dXT3uCYJzPanbQWKbA4xFp7azBYNLwqS99FqVS\nMecipItpez1etm7ZgVKl4MrVy3ft39R2A1VYP+7RWAB+98o7iDFhKAq2kBmlR60UuHb5gr+o6LXL\nFwDm3L5y8QKiJLF5xy5UCmFOxw/bPIAvV7H04gXOGrvZs2dP0P4/C2lPPA5GEdKgFJvr6emhp6eH\nkpISLBYLmzdv5ne/+x0FBQX+PnJRIZnlQhJFRstr6Dt2jr73z2G51RSwr6BRE74+l4iNhYRvyMOY\nnY5CHdobdDXf/ntGy6op+O4fE7l5/V37OvsGGS2vYaSsmtHyGjyjFqzxabQcehpJ6Uuejqm+RNLl\nY+jzc4h6bC+Rj+1FkxA3p7HUDzv4m0tdgE8v+rmN8UTr5m+/lSg2NxNN5Z101PgcL6tGxe99ZSfC\nuFNT2WXmp6W+vzUjSsdPP1kQ8DyhynIWm/vzP/9zXnrpJVQqFQ6Hg7GxMT75yU/y4osv+vvI84KM\nTOjisLt5+d8v++svaHUqDj5VRFjE8q3oByo2FwhRlDj+ZjV947kQNpWSi6nRPFIQxxMFsYsay3yL\nzQGIksS33mnA4REB+NVn1xFnDK2CpYuZF4Jyt5SYmEhiom/iN5lMFBQU0NXVNc2JkJkZObYzMPOx\njSSKjFyrpufN4/QcOXlX9SRjTgaRW9YTsbGQsMIcFJr5FVQLBWpEK3P5dmnjY4h/bA/xj+1BEkUG\nbrXx7nU3kuBzIPT9nSRcOQ6A/VYD9lsNdP3TzzFuXEfUwX1EHtiN6i47MW+O5wkAbIjTL8iBCDYL\nyYmYIK0wga66AUSPiNHlobO2n9Tx3YiCeCNqhYBblGgddtA24iA9cvUkkC833/3ud/nud78LwOnT\np/nhD384zYGQuTvy3BAY2TaBCZZtvF6Rt/67wu9AKBQCew/lLasDsRAUCoFdB9byzquVuF1eDB4v\neYMW8uIypu1CLNt4BIHUCC0Ng76wqrp+W8g5EYsh6DN+S0sL5eXlbN++PdinlpGZhiRJjJZV0/3W\nCXrfPomjq2/GfoJaRcTGQqK2FxO1vRht3Nx1nu8lvBKc69DgGo8W0qigJM6FtygfW3UdeMaL9EgS\n1rIbWMtu0PF/fkL4zs1EHXyIiH27UOgm4zubRp1c7/ddGAVgb8r8VZ1CDbVWRWJuHF01vsrdtRdb\nSc6LQ6EQ0KgUFCYYqez2Taqnm4b5/U3LX9titRJK8dMyMjKBkSSJ42/W0DZePwdg54Ec4pNDK7Q3\nEKZwLbnb06k+2wxAqtmOftjKSmVmpUfpJp2IARsPZEbOcsTqIahOhMVi4amnnuL555/HZLpTxkqO\nfZXbwYjtNN9s5MiP/pXB89fIGfIlEteIPi3oCcWiWr1IWEEODz1xiMhN67hSW8MokDjuQFyq8BVH\n3FGyaVW2Aa421PLweDjTbP0vll+j8uYoSuUaANq6aliXG0bCzl3wyC6uXL2E/VYD2a2D2KtrqfH6\nbpQLMTJ2rpRLZ06iMOjZffhJoj/6KFXmAV6pHYJY335ITP9Num51EDe+AzBRNbp4ju26+gr6OofJ\nLE5a0PFT28Ubty3q+MS8OM6eOIVKlMigkI6aXvqtvpC4zanrqey2MNZYwWs9av7Hxs8jCELIfF+W\nMvZ1Mezdu5e9e/euyHuvVuSV/7OVrgAAIABJREFU9sDItglMMGxTeqaZqqsd/nbx9jSychcXCrTc\n9Jh09Bi1JFp99wg3jjew7wtbVmQsU3es68eL9N0rBCUnAsDtdvPEE09w6NAhnnvuuTtel2NfZRaD\ns2+Q7t9+QOdr72G+UT9jH1W4iegHNhHz4FYiivMRlPMrmLZamE9OxATXb41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onOPxrB4P\nrlPncJ06hyI9Fd0Tj6J5eC+KiNk/T8HehZhKRlEiQ11j42FNEk0fNrA+J4Gqfp+6ya/Ke/j2vswl\ne//VisVi4amnnuL555/HZJqu/PKVr3yF9PR0ACIiIigqKvJfF8+dOwdwX7Z3794dUuMJhfbp4yew\nNrVT4NVQ8dJfcv7CBZy9A/48gBrRd8GaqS2oVTTG6tAlxbNr23YM2encsAziMegoHJ9rLlWUAQ52\nxEZNaU/ORaHerhGtqJm8KZ14PTk+nxMX+mls80mpZ6UVsnl9JD39tfQPweb1JWgzUrlhHoDITDZ/\n9mMAXLl2GXfvAIWCHmdTK9eqK/EMDVMoGKbb12PEdqOWq9fL/PbWJCfQmByONjuT3U8+iT4niyvl\nVwDYtnUHAKVXLs3abm6/RXJc3qz9328ZZayxAoAHH9yNRqmgsrwUmD4nTOxGCAoBj6mfzuo2UmLz\ncDs9vPz8yxQdWMvOvQ8CcO3yBQA2b98FQNP1K4y1jEDOvhlfn0vb0DcCumwAfvX2cdzFCcv+fZp4\n3NbmK6b67LPPslAESZLmF5twF1paWjh8+PCM4UwnTpxg0yb5pnC1IYkiI1eq6H7rBL1HTuHsHZix\nnzYhhtj9O4nbvxN9upznsJRc/av/oCaxBGfUZExmVISaHSVRaIMkGVdqlvhF3+SlYZte5GDY0hWU\nbGuz0d1mJsvcgOn6FcTG5js7qVWod25Fe/AA6i0lSxZO4PCId+RETMU6Yqf8aC3iePhYVHYMr4pK\nEAQE4N8+kU9W9PyroS4HZWVlHDhwYFnf0+1288QTT3Do0CGee+65aa/J84JMIES3B/PNxmm7DJba\nZn9O1d1QGnQYczIxrs3AuCYNQ3Y6+rREFKp7Nw3U0TNA+Re+hTYhhk0v/gAAUZSouDnKtRuT2txq\ntcCOkmhiIhe2Wy3a7Dhb2nE0teFsasXZ3Iq7p3/W4xQGPYb1ef6dCuOGfJSmwEngE7z2n1dmzYlo\nHHHw1xd9whcKAb65MYFw7dzmB/OQjcoP6hHHK3VHxJt44NPFqGaYS4/XDy0qJwKgZcjOD8/4bt7D\ntEpe/XzRgpK0g8li5oVl/UbJK04ze4ShtuIkuj0c/ekLDJVWklLRgrNnYMYVHlWYiQcP7Cfmwa1U\nu8foUihIH3cggrHCUtNQxxef+r2gnW+1tyVJIio8l8q8/VyqOkaCLZOMlELSkvR4xWZu1HWweX0J\nANdu+FZkFtKuskr888VyRCA8u4RMtUhSRzlVQFFBMQBVNyshiO36lhsMDjpJ274Fw6EHqDxzAk/l\nDfLqOsHp9H3+nFB45iLuMxe5aVKi3lrC5i88gzItZdqK08TjiTZwx4rUbG1bUyVupQDjTsTU142R\netymfjpq+shIKWS4cZAUsYObgpLw7BJeuNbNw3rfhLbS3+eJx8FYcVoIkiTxpS99icLCwjscCJm7\ncz/lREiiiLWpnbGKm4yMOwzm6npEh2vG/jWi1T8XCWoVxjVpGHOzMOX5fvSpiXPKu7uXEARQaDVU\neyxsAuwOLycv99PZ4/D3CcZutcKgR1+Yi74w1/+cd8yCo6EZR10j9tomnI0tSO7puZGizY6ltAJL\nacX4iRTocjIxFRdiLFmHsbgQTdKdN+ZKlQKlKvD/UpIkXrk1uSNfFKMP6EDMlC8XFm2gcHcmN043\ngQSjfRauvXOTrR9dd4dSoEIAtVJAuYib/owoHVF6FcN2D2anl8ouM5tTV28unbwTscKEykThHjUz\ncPISfe+fo//ExYDydurIcKJ3byZm7zbC162dJjEabOTE6klGzG7OXR2ku883IbR21rAmrZAN+RGk\nJ+uDFrt73Srxsx6JCdHAeKXEF6K86FdoPpYcDjyXr+G+cBmxuXXGPqrCPDQHHkTz4C4U0ZFLklh9\nx7gkibpLbfQ2jU9eApQlRDJg8CWz/91HcigJwSrWy70Tce7cOR588EE2bNjg/4x+73vf4+DBg4A8\nL9yNUJkbgo0/8Xk8f2G04iZj12vnJqkqCOjTk2mM0fLArl2Y8rIwZKai0IR+vZnl4lJFGelJBZy6\nPOCX+waIidKwtSgS3RxX6BeD5PHgbO3AUdeEo64Je10j3qGRWY9TJ8RhLCn05VaUrEOfkznrjvO1\nXivPl/ny1BQCfK04ntgAhVXvNjd01w9QXzopRZ+cG8emj+QvWnJ8Jt6o6uNko0+l6SP5MTy3Oz3o\n7zEfFjMvyE7EfYokSVgbWhk4XUr/sfMMXShD8sxcWVMVYSLmgS3E7N1KeFFuyKhS3A94vCJVtWOU\nV4/gnbKLbzIq2bYhinBT8CbPy2aJl/okJt4mUiHxTJSXsBD5d4tdPbgvXMZz6QrS2MyJ/KqSIrT7\ndqPeswNF2NJWXfV6RK4fr8c8Xu1VUgpcTohiTKcmNULLv30iH80SOtkLYSXCme6GPC/c+7gGhqc5\nDKMVN3ENDM/pWG1CLKbcTIx5WZjy1mDKSUdpCM1QwVDA6fJyuXKY2qbpDllulpH8NWFLckM8FyRJ\nwjM4jKO20edU1DbgauuEWW4/FUY9xqKCcaeiEMP6/Gn/f5dX5H+d76TH6tv12JFo5ImshScqN1d0\n+YUzAJJzY9l0KB9FkK/jjYM2/uGsz2GJ0Kl4+XPrVzSkKSTCmT772c9y+vRpBgcHSUtL4zvf+Q7P\nPPNMsE4vEwRcQ6MMnr3K4OlSBk6X3lXyThMfQ/TOEqJ2lBBRnC87DsuMKErUt1i4Vj2C1Tbp3AkC\nZKcbyc8OQ7UYmaSp7yVJvDUkcWzKQlGUUuL3I0PHgQBQJCeifeqjaD72BN7qm7jPX8J7vXoyRloU\n8ZRV4imrhOf/HfXWjWgeegD1ji0o5hB7O1+UKgXr9q6h/GgtTpsbwSuxuWeYq0lRdIzCKxW9PL1Z\nzg+SuX9wj4wxdqOescpbjI6HJjk6euZ0rCoizBeOlJvpcxhyMxclzHE/IUkSzR02LpQNYXdMzhdq\ntcCW9ZEkxK6sYpwgCKhjo1HHRhP2wFbAF97kaGjBXtuAo64RR30LktM57TjRasd8qQzzJV94L0oF\n+txsjCWFmIrX8b4xiR6r7wZfqxTYl7q4haPM4iS8HpGuWl+OR1fdAC7HDbYeLkQ9Q82JhZIVrSdC\np2LU4WHU4eFU4zAPr11eNatgEdSdiLshrzjNzFJuWXvMVoavVDF8qYLBM1cYrbx1V8/fmJtJ9A6f\n42BYk7bi8nb3YziTKPomg7LqEUbGpseURoapKSmMIDJczbUbFf58hsUw7JH4Ra9E/WTYLPFKic+H\nmAMRCMlswVNWgbu0DLGhCSRpWrw0AEolquL1aHZtRb1rK8qEhSXEBcI6YqfyeD0ep2/ydisEyhIj\nMes1/J9DORSHUFiTvBOxegjlcCZJkrC3dftrMJirx2sxzNFhUBp0GNdmYprIY8jNRBM/94rv9+Pc\nEIiuPjtXro/QN+i7AW/trCEjpZCkeB0b8sLR61bBhRyf+qMvBKoRR61vt8I7PDrrcSNRMXSlryFm\n83rW7ipGmZEWMB9mLqGukiTReK3T70iAT95765PrMEUFbxfsaO0gR276hGqyonT82yfyV+yeKyR2\nImRWHmffIMOXKhm6XMHw5UrMNY13VbJQGvSEl+QTuXk9UduL0S6zrrPMJE6Xl1uNFqobxqbtPABo\nNQryskxkphqCth0tShIXzPC7QQnblI/IWo3IJ8JFtKEVhRMQIcyEeu9u1Ht3Iw6P4LlajnD6OPRN\n2c73eid3KP75ZyhzslBv3YR6czGqdfkIi4ynNkbq2bA/h+snGvC4vKhFiS3dw9yIi+BvP2zhJx/P\nI9Yo10iRWZ14rHasDa2Yaxr8zoK5pmFuOQyMJz7nZPh2GHKzMOVmoUtNuO8Sn4OJJEn0DDgprxmZ\nljgNoFELbNsQSXLC6gr7EpRKdGsy0K3JgIP7fSFQA0M4aht9uxW1Tbg6uu5YCI0cHiRyeBAqrzD2\ncxBMRlQFuShzs1HlZqNcm40iPnbON+iCIJC9OQW1VkXr9W4AzIM2zvx3GSWP5pG8NjYof++erEiO\n1Q3i8ko0Dzu42mFma9rq23mTdyJWKe5RM2NVtYxV1jJ6/RZjlbewtXTe/SCFgClvDZGb1hGxeR2m\nvKx7WvIu1BFFiY4eOw2tVlo6bXi907+KKqXA2kwj2elGVFPUKUSXGyQJQa1a0ERca5N4c0iiZcrO\nsYDEboPEXqPISoRmiqKEJI0rjARhAGLfAJ6rZXjKryO2tgfuqNOi3rDO51Bs3IAyMw0UCtyi738x\nn5wG86CNGycbcTs9/udaIgy41sTyd0+sJTKAPOFyIu9EyATCY7ZiqW/BUtuMpa4Fa53vt729e87n\nENQqDBkpPqchz+c06DNT5HkmSHg8Ig2tVqobxhgamb5TrRAgM1lHXqYereHeKXjpGZ8XlQpfCFT/\nzSbOlTUS09xIYmcL6ttUoGZCiAgfdyjWoMrLmbNj0dM0SP3ldiRxcm5Ozo+ncO8aDEFYGHr9eh+n\nmnz5QflxBv7hcO6ilJ8WSsgkVt8NebJYGJIoYm/vwVrfgvlWk89xuF6Lrblj9oMFAcOaNMLXryW8\nKI+IkgJUYcGPDZeZOy63SGevnfZuO62dNhzOO3eKNGoFWWkG1qQZ0WruvInt/O4/Ya+6SfK3v4ph\nQ+Gc3tcrSVRZ4cSoROP0hSsiFRIfDfeSsYKL5W1tNrq67KSl6UlJCW7FUHF4BG/lDTyVVXhv1YN3\nZgEBAMFoQMjP5WxkKv1Z2TzzsR0I+rlPyHazk6qTjTjMkx6aWa1iODuW//eThSu+IyE7Efc3HosV\nW0vnlJ8O3++mdhxdffM6lyrMiCE73Sevmp1+X9RiWAm8XonOXjvN7TZaOq243HfesqUn68mO9ND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n2wr8OUN4ijvEEc5Q3iKG+wjvKF3g1E3uC0QoS1iYXKy8v73GckXBBtiY25bdu2YcmSJYOR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\njru5AU9rUyGSlFZfx7MRFbdWTtbnp6PCw87KxWcyqhrKu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+ "text": [ + "" + ] + } + ], + "prompt_number": 13 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Note that we don't really care how accurate we become about the inference of the hidden probabilities — for this problem we are more interested in choosing the best bandit (or more accurately, becoming *more confident* in choosing the best bandit). For this reason, the distribution of the red bandit is very wide (representing ignorance about what that hidden probability might be) but we are reasonably confident that it is not the best, so the algorithm chooses to ignore it.\n", + "\n", + "From the above, we can see that after 1000 pulls, the majority of the \"blue\" function leads the pack, hence we will almost always choose this arm. This is good, as this arm is indeed the best.\n", + "\n", + "Below is a D3 app that demonstrates our algorithm updating/learning three bandits. The first figure shows the raw counts of pulls and wins, and the second figure is a dynamically updating plot. I encourage you to try to guess which bandit is optimal, prior to revealing the true probabilities, by selecting the `arm buttons`." + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from IPython.core.display import HTML\n", + "\n", + "# try executing the below command twice if the first time doesn't work\n", + "HTML(filename=\"BanditsD3.html\")" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "html": [ + "\n", + " \n", + " \n", + " \n", + "\n", + " \n", + "\n", + "\n", + " \n", + "
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\n", + "\n", + "\n" + ], + "metadata": {}, + "output_type": "pyout", + "prompt_number": 4, + "text": [ + "" + ] + } + ], + "prompt_number": 4 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Deviations of the observed ratio from the highest probability is a measure of performance. For example,in the long run, optimally we can attain the reward/pull ratio of the maximum bandit probability. Long-term realized ratios less than the maximum represent inefficiencies. (Realized ratios larger than the maximum probability is due to randomness, and will eventually fall below). \n", + "\n", + "### A Measure of *Good*\n", + "\n", + "We need a metric to calculate how well we are doing. Recall the absolute *best* we can do is to always pick the bandit with the largest probability of winning. Denote this best bandit's probability of $w_{opt}$. Our score should be relative to how well we would have done had we chosen the best bandit from the beginning. This motivates the *total regret* of a strategy, defined as:\n", + "\n", + "\\begin{align}\n", + "R_T & = \\sum_{i=1}^{T} \\left( w_{opt} - w_{B(i)} \\right)\\\\\\\\\n", + "& = Tw^* - \\sum_{i=1}^{T} \\; w_{B(i)} \n", + "\\end{align}\n", + "\n", + "\n", + "where $w_{B(i)}$ is the probability of a prize of the chosen bandit in the $i$th round. A total regret of 0 means the strategy is attaining the best possible score. This is likely not possible, as initially our algorithm will often make the wrong choice. Ideally, a strategy's total regret should flatten as it learns the best bandit. (Mathematically, we achieve $w_{B(i)}=w_{opt}$ often)\n", + "\n", + "\n", + "Below we plot the total regret of this simulation, including the scores of some other strategies:\n", + "\n", + "1. Random: randomly choose a bandit to pull. If you can't beat this, just stop. \n", + "2. Largest Bayesian credible bound: pick the bandit with the largest upper bound in its 95% credible region of the underlying probability. \n", + "3. Bayes-UCB algorithm: pick the bandit with the largest *score*, where score is a dynamic quantile of the posterior (see [4] )\n", + "3. Mean of posterior: choose the bandit with the largest posterior mean. This is what a human player (sans computer) would likely do. \n", + "3. Largest proportion: pick the bandit with the current largest observed proportion of winning. \n", + "\n", + "The code for these are in the `other_strats.py`, where you can implement your own strategy very easily." + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "figsize(12.5, 5)\n", + "from other_strats import *\n", + "\n", + "# define a harder problem\n", + "hidden_prob = np.array([0.15, 0.2, 0.1, 0.05])\n", + "bandits = Bandits(hidden_prob)\n", + "\n", + "# define regret\n", + "\n", + "\n", + "def regret(probabilities, choices):\n", + " w_opt = probabilities.max()\n", + " return (w_opt - probabilities[choices.astype(int)]).cumsum()\n", + "\n", + "# create new strategies\n", + "strategies = [upper_credible_choice,\n", + " bayesian_bandit_choice,\n", + " ucb_bayes,\n", + " max_mean,\n", + " random_choice]\n", + "algos = []\n", + "for strat in strategies:\n", + " algos.append(GeneralBanditStrat(bandits, strat))" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 14 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# train 10000 times\n", + "for strat in algos:\n", + " strat.sample_bandits(10000)\n", + "\n", + "#test and plot\n", + "for i, strat in enumerate(algos):\n", + " _regret = regret(hidden_prob, strat.choices)\n", + " plt.plot(_regret, label=strategies[i].__name__, lw=3)\n", + "\n", + "plt.title(\"Total Regret of Bayesian Bandits Strategy vs. Random guessing\")\n", + "plt.xlabel(\"Number of pulls\")\n", + "plt.ylabel(\"Regret after $n$ pulls\");\n", + "plt.legend(loc=\"upper left\");" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "display_data", + "png": 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TpkyBVCpF9+7dsXnzZtSpU0ccIEZEqFu3Lh49eoSvvvoKHh4eCAgIAACMHDkS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\n8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+ "text": [ + "" + ] + } + ], + "prompt_number": 15 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Like we wanted, Bayesian bandits and other strategies have decreasing rates of regret, representing that we are achieving optimal choices. To be more scientific so as to remove any possible luck in the above simulation, we should instead look at the *expected total regret*:\n", + "\n", + "$$\\bar{R_T} = E[ R_T ] $$\n", + "\n", + "It can be shown that any *sub-optimal* strategy's expected total regret is bounded below logarithmically. Formally:\n", + "\n", + "$$ E[R_T] = \\Omega \\left( \\;\\log(T)\\; \\right)$$\n", + "\n", + "Thus, any strategy that matches logarithmic-growing regret is said to \"solve\" the Multi-Armed Bandit problem [3].\n", + "\n", + "Using the Law of Large Numbers, we can approximate Bayesian Bandit's expected total regret by performing the same experiment many times (500 times, to be fair):" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# this can be slow, so I recommend NOT running it.\n", + "\n", + "trials = 500\n", + "expected_total_regret = np.zeros((10000, 3))\n", + "\n", + "for i_strat, strat in enumerate(strategies[:-2]):\n", + " for i in range(trials):\n", + " general_strat = GeneralBanditStrat(bandits, strat)\n", + " general_strat.sample_bandits(10000)\n", + " _regret = regret(hidden_prob, general_strat.choices)\n", + " expected_total_regret[:, i_strat] += _regret\n", + "\n", + " plot(expected_total_regret[:, i_strat] / trials, lw=3, label=strat.__name__)\n", + "\n", + "plt.title(\"Expected Total Regret of Multi-armed Bandit strategies\")\n", + "plt.xlabel(\"Number of pulls\")\n", + "plt.ylabel(\"Exepected Total Regret \\n after $n$ pulls\");\n", + "plt.legend(loc=\"upper left\");" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "0\n", + "1" + ] + }, + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "\n", + "2" + ] + }, + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "\n" + ] + }, + { + "metadata": {}, + "output_type": "pyout", + "prompt_number": 24, + "text": [ + "" + ] + }, + { + "metadata": {}, + "output_type": "display_data", + "png": 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Ro3Hp0iU899xzeOGFF/D888/XmZQAAHr16lXlvW+++QbffvstUlNToVarodfr6+zj0pBj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\nRK5CYII=\n" + } + ], + "prompt_number": 24 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "plt.figure()\n", + "[pl1, pl2, pl3] = plt.plot(expected_total_regret[:, [0, 1, 2]], lw=3)\n", + "plt.xscale(\"log\")\n", + "plt.legend([pl1, pl2, pl3],\n", + " [\"Upper Credible Bound\", \"Bayesian Bandit\", \"UCB-Bayes\"],\n", + " loc=\"upper left\")\n", + "plt.ylabel(\"Exepected Total Regret \\n after $\\log{n}$ pulls\");\n", + "plt.title(\"log-scale of above\");\n", + "plt.ylabel(\"Exepected Total Regret \\n after $\\log{n}$ pulls\");" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "display_data", + "png": 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w119/8eKLL+Y6NldXV3bt2kVERASTJk1i1KhR3Lx5Uz0eGBiIp6cnV69e5d13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+ } + ], + "prompt_number": 25 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Extending the algorithm \n", + "\n", + "\n", + "Because of the Bayesian Bandits algorithm's simplicity, it is easy to extend. Some possibilities are:\n", + "\n", + "- If interested in the *minimum* probability (eg: where prizes are a bad thing), simply choose $B = \\text{argmin} \\; X_b$ and proceed.\n", + "\n", + "- Adding learning rates: Suppose the underlying environment may change over time. Technically the standard Bayesian Bandit algorithm would self-update itself (awesome) by noting that what it thought was the best is starting to fail more often. We can motivate the algorithm to learn changing environments quicker by simply adding a *rate* term upon updating:\n", + "\n", + " self.wins[ choice ] = rate*self.wins[ choice ] + result\n", + " self.trials[ choice ] = rate*self.trials[ choice ] + 1\n", + "\n", + " If `rate < 1`, the algorithm will *forget* its previous wins quicker and there will be a downward pressure towards ignorance. Conversely, setting `rate > 1` implies your algorithm will act more risky, and bet on earlier winners more often and be more resistant to changing environments. \n", + "\n", + "- Hierarchical algorithms: We can setup a Bayesian Bandit algorithm on top of smaller bandit algorithms. Suppose we have $N$ Bayesian Bandit models, each varying in some behavior (for example different `rate` parameters, representing varying sensitivity to changing environments). On top of these $N$ models is another Bayesian Bandit learner that will select a sub-Bayesian Bandit. This chosen Bayesian Bandit will then make an internal choice as to which machine to pull. The super-Bayesian Bandit updates itself depending on whether the sub-Bayesian Bandit was correct or not. \n", + "\n", + "- Extending the rewards, denoted $y_a$ for bandit $a$, to random variables from a distribution $f_{y_a}(y)$ is straightforward. More generally, this problem can be rephrased as \"Find the bandit with the largest expected value\", as playing the bandit with the largest expected value is optimal. In the case above, $f_{y_a}$ was Bernoulli with probability $p_a$, hence the expected value for a bandit is equal to $p_a$, which is why it looks like we are aiming to maximize the probability of winning. If $f$ is not Bernoulli, and it is non-negative, which can be accomplished apriori by shifting the distribution (we assume we know $f$), then the algorithm behaves as before:\n", + "\n", + " For each round, \n", + " \n", + " 1. Sample a random variable $X_b$ from the prior of bandit $b$, for all $b$.\n", + " 2. Select the bandit with largest sample, i.e. select bandit $B = \\text{argmax}\\;\\; X_b$.\n", + " 3. Observe the result,$R \\sim f_{y_b}$, of pulling bandit $B$, and update your prior on bandit $B$.\n", + " 4. Return to 1\n", + "\n", + " The issue is in the sampling of the $X_b$ drawing phase. With Beta priors and Bernoulli observations, we have a Beta posterior — this is easy to sample from. But now, with arbitrary distributions $f$, we have a non-trivial posterior. Sampling from these can be difficult.\n", + "\n", + "- There has been some interest in extending the Bayesian Bandit algorithm to commenting systems. Recall in Chapter 4, we developed a ranking algorithm based on the Bayesian lower-bound of the proportion of upvotes to the total number of votes. One problem with this approach is that it will bias the top rankings towards older comments, since older comments naturally have more votes (and hence the lower-bound is tighter to the true proportion). This creates a positive feedback cycle where older comments gain more votes, hence are displayed more often, hence gain more votes, etc. This pushes any new, potentially better comments, towards the bottom. J. Neufeld proposes a system to remedy this that uses a Bayesian Bandit solution.\n", + "\n", + "His proposal is to consider each comment as a Bandit, with the number of pulls equal to the number of votes cast, and number of rewards as the number of upvotes, hence creating a $\\text{Beta}(1+U,1+D)$ posterior. As visitors visit the page, samples are drawn from each bandit/comment, but instead of displaying the comment with the $\\max$ sample, the comments are ranked according to the ranking of their respective samples. From J. Neufeld's blog [7]:\n", + "\n", + " > [The] resulting ranking algorithm is quite straightforward, each new time the comments page is loaded, the score for each comment is sampled from a $\\text{Beta}(1+U,1+D)$, comments are then ranked by this score in descending order... This randomization has a unique benefit in that even untouched comments $(U=0,D=0)$ have some chance of being seen even in threads with 5000+ comments (something that is not happening now), but, at the same time, the user is not likely to be inundated with rating these new comments. " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Just for fun, though the colors explode, we watch the Bayesian Bandit algorithm learn 35 different options. " + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "figsize(12.0, 8)\n", + "beta = stats.beta\n", + "hidden_prob = beta.rvs(1, 13, size=35)\n", + "print hidden_prob\n", + "bandits = Bandits(hidden_prob)\n", + "bayesian_strat = BayesianStrategy(bandits)\n", + "\n", + "for j, i in enumerate([100, 200, 500, 1300]):\n", + " plt.subplot(2, 2, j + 1)\n", + " bayesian_strat.sample_bandits(i)\n", + " plot_priors(bayesian_strat, hidden_prob, lw=2, alpha=0.0, plt_vlines=False)\n", + " # plt.legend()\n", + " plt.xlim(0, 0.5)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "[ 0.01086616 0.20672538 0.00137644 0.02843378 0.00809559 0.09709516\n", + " 0.00540949 0.02886983 0.1670677 0.01158008 0.06498409 0.15652432\n", + " 0.17674427 0.0351021 0.11126791 0.00988438 0.24309639 0.02708666\n", + " 0.04342859 0.00825645 0.01890499 0.24829156 0.15444239 0.03984653\n", + " 0.00785845 0.00758847 0.08759903 0.02189288 0.0228888 0.18814637\n", + " 0.04898048 0.01136161 0.02290211 0.17823588 0.17785098]\n" + ] + }, + { + "metadata": {}, + "output_type": "display_data", + "png": 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1a5g7dy6bNm0qtD8iIoIWDT5m0ebaDB/06R3rGLDgD/LyfdDrklg/qm+hY5d+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\nFcoPhgJwc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/Lr2T3F/AYRBjniNOXbU7QaJT64pS/3XYVDhLapgc1vj2J4Uz4K5IQ4u5nL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8zts9AG/K+yU8D9q1B/dz/ZQETNbsYWreHH925m5n1fIh6nws/ijAXIyFw08Cqm3307latS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bmnjv4c/Q+CWAKKJtb8I9qow7rzuASaPQ6Nby0aFU5maOw4xK56iy+LNl6EjmpAYzL7rn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\nFxNu30PM2kJg34vEhvsZ2DyEp6GdnBtXkzR/xpj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bITb5J0Lwja003Pk/IATTHroP78TR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+ "text": [ + "" + ] + } + ], + "prompt_number": 17 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Eliciting expert prior\n", + "\n", + "Specifying a subjective prior is how practitioners incorporate domain knowledge about the problem into our mathematical framework. Allowing domain knowledge is useful for many reasons, for example:\n", + "\n", + "- Aids the speed of MCMC convergence. For example, if we know the unknown parameter is strictly positive, then we can restrict our attention there, hence saving time that would otherwise be spent exploring negative values.\n", + "- More accurate inference. By weighing prior values near the true unknown value higher, we are narrowing our eventual inference (by making the posterior tighter around the unknown) \n", + "- Express our uncertainty better. See the *Price is Right* problem in Chapter 5.\n", + "\n", + "Of course, practitioners of Bayesian methods are not experts in every field, so we must turn to domain experts to craft our priors. We must be careful with how we elicit these priors though. Some things to consider:\n", + "\n", + "1. From experience, I would avoid introducing Betas, Gammas, etc. to non-Bayesian practitioners. Furthermore, non-statisticians can get tripped up by how a continuous probability function can have a value exceeding one.\n", + "\n", + "2. Individuals often neglect the rare *tail-events* and put too much weight around the mean of distribution. \n", + "\n", + "3. Related to above is that almost always individuals will under-emphasize the uncertainty in their guesses.\n", + "\n", + "Eliciting priors from non-technical experts is especially difficult. Rather than introduce the notion of probability distributions, priors, etc. that may scare an expert, there is a much simpler solution. \n", + "\n", + "###Trial roulette method \n", + "\n", + "\n", + "The *trial roulette method* [8] focuses on building a prior distribution by placing counters (think casino chips) on what the expert thinks are possible outcomes. The expert is given $N$ counters (say $N=20$) and is asked to place them on a pre-printed grid, with bins representing intervals. Each column would represent their belief of the probability of getting the corresponding bin result. Each chip would represent an $\\frac{1}{N} = 0.05$ increase in the probability of the outcome being in that interval. For example [9]:\n", + "\n", + "> A student is asked to predict the mark in a future exam. The figure below shows a completed grid for the elicitation of a subjective probability distribution. The horizontal axis of the grid shows the possible bins (or mark intervals) that the student was asked to consider. The numbers in top row record the number of chips per bin. The completed grid (using a total of 20 chips) shows that the student believes there is a 30% chance that the mark will be between 60 and 64.9.\n", + "\n", + "\n", + "\n", + "\n", + "From this, we can fit a distribution that captures the expert's choice. Some reasons in favor of using this technique are:\n", + "\n", + "1. Many questions about the shape of the expert's subjective probability distribution can be answered without the need to pose a long series of questions to the expert - the statistician can simply read off the density above or below any given point, or that between any two points.\n", + "\n", + "2. During the elicitation process, the experts can move around the chips if unsatisfied with the way they placed them initially - thus they can be sure of the final result to be submitted.\n", + "\n", + "3. It forces the expert to be coherent in the set of probabilities that are provided. If all the chips are used, the probabilities must sum to one.\n", + "\n", + "4. Graphical methods seem to provide more accurate results, especially for participants with modest levels of statistical sophistication." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "##### Example: Stock Returns\n", + "\n", + "\n", + "Take note stock brokers: you're doing it wrong. When choosing which stocks to pick, an analyst will often look at the *daily return* of the stock. Suppose $S_t$ is the price of the stock on day $t$, then the daily return on day $t$ is :\n", + "\n", + "$$r_t = \\frac{ S_t - S_{t-1} }{ S_{t-1} } $$\n", + "\n", + "The *expected daily return* of a stock is denoted $\\mu = E[ r_t ] $. Obviously, stocks with high expected returns are desirable. Unfortunately, stock returns are so filled with noise that it is very hard to estimate this parameter. Furthermore, the parameter might change over time (consider the rises and falls of AAPL stock), hence it is unwise to use a large historical dataset. \n", + "\n", + "Historically, the expected return has been estimated by using the sample mean. This is a bad idea. As mentioned, the sample mean of a small sized dataset has enormous potential to be very wrong (again, see Chapter 4 for full details). Thus Bayesian inference is the correct procedure here, since we are able to see our uncertainty along with probable values.\n", + "\n", + "For this exercise, we will be examining the daily returns of the AAPL, GOOG, MSFT and AMZN. Before we pull in the data, suppose we ask our a stock fund manager (an expert in finance, but see [10] ), \n", + "\n", + "> What do you think the return profile looks like for each of these companies?\n", + "\n", + "Our stock broker, without needing to know the language of Normal distributions, or priors, or variances, etc. creates four distributions using the trial roulette method above. Suppose they look enough like Normals, so we fit Normals to them. They may look like: " + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "figsize(11., 5)\n", + "colors = [\"#348ABD\", \"#A60628\", \"#7A68A6\", \"#467821\"]\n", + "\n", + "normal = stats.norm\n", + "x = np.linspace(-0.15, 0.15, 100)\n", + "\n", + "expert_prior_params = {\"AAPL\": (0.05, 0.03),\n", + " \"GOOG\": (-0.03, 0.04),\n", + " \"TSLA\": (-0.02, 0.01),\n", + " \"AMZN\": (0.03, 0.02),\n", + " }\n", + "\n", + "for i, (name, params) in enumerate(expert_prior_params.iteritems()):\n", + " plt.subplot(2, 2, i)\n", + " y = normal.pdf(x, params[0], scale=params[1])\n", + " #plt.plot( x, y, c = colors[i] )\n", + " plt.fill_between(x, 0, y, color=colors[i], linewidth=2,\n", + " edgecolor=colors[i], alpha=0.6)\n", + " plt.title(name + \" prior\")\n", + " plt.vlines(0, 0, y.max(), \"k\", \"--\", linewidth=0.5)\n", + " plt.xlim(-0.15, 0.15)\n", + "plt.tight_layout()" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "display_data", + "png": 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ByJXbGcRHOy/A7QygYmLmTSTh7Q0BAGpvqMLMuZUSR0NSKS2DqC/v6/ryyy9j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\nW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+ "text": [ + "" + ] + } + ], + "prompt_number": 18 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Note that these are subjective priors: the expert has a personal opinion on the stock returns of each of these companies, and is expressing them in a distribution. He's not wishful thinking -- he's introducing domain knowledge.\n", + "\n", + "In order to better model these returns, we should investigate the *covariance matrix* of the returns. For example, it would be unwise to invest in two stocks that are highly correlated, since they are likely to tank together (hence why fund managers suggest a diversification strategy). We will use the *Wishart distribution* for this, introduced earlier." + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import pymc as pm\n", + "\n", + "n_observations = 100 # we will truncate the the most recent 100 days.\n", + "\n", + "prior_mu = np.array([x[0] for x in expert_prior_params.values()])\n", + "prior_std = np.array([x[1] for x in expert_prior_params.values()])\n", + "\n", + "inv_cov_matrix = pm.Wishart(\"inv_cov_matrix\", n_observations, np.diag(prior_std ** 2))\n", + "mu = pm.Normal(\"returns\", prior_mu, 1, size=4)" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 33 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Next we pull historical data for these stocks:" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# I wish I could have used Pandas as a prereq for this book, but oh well.\n", + "import datetime\n", + "import ystockquote as ysq\n", + "\n", + "stocks = [\"AAPL\", \"GOOG\", \"TSLA\", \"AMZN\"]\n", + "\n", + "enddate = datetime.datetime.now().strftime(\"%Y-%m-%d\") # today's date.\n", + "startdate = \"2012-09-01\"\n", + "\n", + "stock_closes = {}\n", + "stock_returns = {}\n", + "CLOSE = 6\n", + "\n", + "for stock in stocks:\n", + " x = np.array(ysq.get_historical_prices(stock, startdate, enddate))\n", + " stock_closes[stock] = x[1:, CLOSE].astype(float)\n", + "\n", + "# create returns:\n", + "\n", + "for stock in stocks:\n", + " _previous_day = np.roll(stock_closes[stock], -1)\n", + " stock_returns[stock] = ((stock_closes[stock] - _previous_day) / _previous_day)[:n_observations]\n", + "\n", + "dates = map(lambda x: datetime.datetime.strptime(x, \"%Y-%m-%d\"), x[1:n_observations + 1, 0])" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 34 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "figsize(12.5, 4)\n", + "\n", + "for _stock, _returns in stock_returns.iteritems():\n", + " p = plt.plot((1 + _returns)[::-1].cumprod() - 1, '-o', label=\"%s\" % _stock,\n", + " markersize=4, markeredgecolor=\"none\")\n", + "\n", + "plt.xticks(np.arange(100)[::-8],\n", + " map(lambda x: datetime.datetime.strftime(x, \"%Y-%m-%d\"), dates[::8]),\n", + " rotation=60);\n", + "\n", + "plt.legend(loc=\"upper left\")\n", + "plt.title(\"Return space\")\n", + "plt.ylabel(\"Return of $1 on first date, x100%\");" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "display_data", + "png": 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IJvJkGt4+zjzy54G1HtssZT/ffPMN8+bNw9HREW9vb2xtbSkqKiIpKYn+/fsT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3+eWsnwTpMKS9zsef4/+eQTatasyahRowpDpjyRmec/s+o8kiShTTHg7xvG8b3+GA0Szm42PI5M\nzDR5N22d/Fc2XCPuyRilKFDd1RqtwYjOIHE/NjlD8QxRgCYe9lRwtOBQYDQgmBcNccl6QuJS+Gxv\nIJonYRWikHUBDnsLBbZqEQdJopxvKMonj1AnClQd3BB7SyX2FkruxyTzv6uP0BmNpOhNYzpWceKj\nthWwzMJDn7ZyjbWFLasnHn++MMCdKA2zDt8hNE6LAFiqRN5o6E6tsjYYjBJ6o8SNRwlsuR6BIAh8\n2r4CLb1fXIawoDhzL5b5x+9hMEp0qOJIWVsLNHojyToDe/yj0D1ZqdkrorCImobRaGDO8A1UerL7\nk0pYdDAfr34FoyTx7Vu/U6FM9ksZ/rR7Bif8dtOxXn/e7Tkj33Rbc+g79l/ahCiI2Fja56qOMMDV\n0HjmHg0iWqPH0VLJ5x0r0sjD5NGXJIkroQlsuR7OufvpdxgcLJX8OexpSIzJ8zobfXwikk7P6f4i\nAVU02QqnkklPbutDF6fYfRkZGZnSQOrfY0mSqOv9En7B54nXmAqe2Fk5otWnoFZavPBv9Z2H/zJt\nw3AEBOaO2Ii3W/Us71uoYT9t2rTh/PnzeHt74+7+NPxBEAR8fHzyLER+kpnxv2TWIXNHVEEwGfLJ\nyfoMSbupOLpY41XJGQtLJdcvhSAIAj0G1sVYxpY9NyPZfTMqW7IoBBjbwpN2lR1xssrojU/LswmV\n9cvZcjdaw+0oDavOh5gN0mcpk5hCnQjTC+dXxoEIm+d73Ue/VJ5X67m9cAfnr1Or+OvUSkRBZNKA\n72larX2W4wESUvQM/u06+myUDRQFk44dqjihziQvoSAJjklm3Jab6LJZ3rCZ3W5u39tKnQrNmP7a\n8nTfXWrpzg71+jM2hwZ8WHQwk399xTTP6L/zJdv/wq2jLNj6MQpRydfD1lL5mcXKizC9g/dI1kto\n9UYkoL67LZ93qoiLdebvb0hsMu9uuWlOHn/W+D9Uo7u5Ay+CQNm/p/Ptyek42riwdOxulIqsfxcy\nJpK1SYz9qTvJOtMOi7WFHasnHitaoWRkZGT+ozxb3huginsdejcbxkvVO+bo37ZUp1218vX56o1f\ns8wbLNSwn9GjRzN69OgMnxf3MCCD3sjpI4Fmwx9MlVNSK++o1Ap02qdefoVKwehJbbFzsARMxtCx\nKC0R/pe5cK0sofEhAFS+6Uu3LRsRBNB9PIE6AzuiUoioFQJ+DxNZ808oAJPbeWdZPz8tLb0d+NM7\nfRJhXXdb6rrb4marNi8MJrb2pK67LYlaAwlaAxfux/GXbzgS0MrbAUdLJbEpBuKS9VxME25koxYZ\nXD9jYmVmsWWPYh4AMLDVmGwZ/gC2Fkps1CKxyabvUyFALTcbFKKAKAj4PkwwLwyMEnzvE8zqf0IZ\nUKcMfWq6YmtRMPHHqfo9itey8XIYB29Fp9tVUSsEBtV1w1IlYqVSEBqXzIGAaLQG047FP7HtcRIP\n4Bd8gct3TtK4iqlzqn/IVc4HHEattGBwm7E5lquccwXa1e3NMd8dbDnzC+N7fZUn/SLjHrJiryk0\n6fX2E3Js+IcnaJl3NAiN/ml32aENyjK8STlznkdmeDhYMq1TpXQL1+SwCMK2HiT0r31PDX9A5WBL\nw5Y9KH/jF0Kjg7hy5xRNq3XIln6llaz0kySJgJCrHPXdwdmbB82GP4DeoM30muLEf/nZlQZk/Uo2\npVm/4qCbwfjUdlQqVHzx2gqqezTIlV38WttxnPM/xK3Qaxy7th11fJkC1y9bFtdbb71VoEIUBBEP\n49nz5zUiwkzGh1IlolCItO1enep13FFbKLj1OJl5m3yp8eiJ59zZjlM7AsxzxKcYkIAUg5HQeC12\nFgq6VHOm6ve/Y0gyxUHbfr+IOuP6mq+p6GRF71p5q5n+LJktDByf7CTUKGPDsMaZx04/u5uQHZK1\nGs4HmCrAtKndM0dyTmrr/dxykGll6VTFkSuhCdx9nMzqC2FsvGRKJlUrRIY2LEs1V2uS9UY0OiN+\njxI4EBANQO+aLjTzssfBUomjpYqbEYksOnk/y/tFBdymdWI5LobEozdKKARo5mGHf2QSgiBkWrZy\nfEuTF/5SSByrzoUQmtIba81m5u+YT7KzLUpRgaf2e5NMzYbhbJe7ngwvtxyFz/Vd+FzfxcVAH8b3\n+ipXIToGo56lu6aTmBxHo8qt6dn09eeOTZuT0r9OGRK1Bi4+iOdeTHK6cTZqkbebZd4j4lmq+Psy\ndvZsjFodRu/yHPv3trk+qcLGCslgQGFpSb3F0xEEgU71B7Dx2CKOXNv2QuP/v0bqVrJWn4y12o7H\niRHmc+WdKxIRF4ZOn4K7U/Z+zzIyMjIy+YveoMPawpaklHjUSksm9ptLDc+GuZ7P2sKONztOYsmu\nafx+fAmv1i74nkjZCvuRJIk1a9awYcMGQkJC8PT0ZNiwYbz99tvFzvt/+PBh9AlOnDoYgMEg4eBs\nRc9X6uNZ0QmAiEQth25Fc/BWNA9is9/EyVolsumNeiScvcSFwR+aa3QDVJsyhsofvlXsvovccNJv\nD0t3f0G18vX5etiaAruPJElcDInnL99wLoXEv/iCFyAK4O1oiVIhoBJF/CMS0yVZC0Cnqk682bgc\n5e2zn5BsMErsvfmQjXvfBkMEidbDMYo22CUsx8rCkU8Hb6aqmxP/PIjPsg7+83hzQUtzgzB7aydW\nvZ+9jsJp+fPkCv4+/TNONq58+/b/sLd2SnfeKEmExaVwK1LDAp97pGQSQmalEqngYElwTDIqhfDC\nXStJkki4eYfIo+cImLMCSZ+mW6pahVvX1pR/tQdlOrVM1x0XIDYxmvHLe2KUjPw0dneuF0+lkWe3\nkh1tXGhXtw8d6vajvEtFwmNC+GBVP5xsXFn+3v4ilFRGRkbmv8m2s6v5n89PlHX0ZP7bm1CrLPM8\npyRJTFk7lOCIW6gUaj7s/22mzsBCDfuZM2cO69evZ/LkyVSoUIHg4GDmz59PaGgo06dPz7MQ+Y3P\nPn8A6jfzpEOvmlwIS+C9dVfRPQnlSMXJSkktNxuuhSUgCjC2hQdNPU0dNgVB4J8HcSw/+wABgY8a\nuXDrs++edsVUKBAtVBiSkrn17c/o45Oo/sX4Er8AOPGkMkbbOr0K9D6CINDU056mnvYMXH+NBO3T\ncKE6ZW2xVIlYKkXOBMea8x1UokDtsjbEJOuJ1eiJSRPOZZTg7uPkTO+lFAV+GlCDSs5WmZ7PCoUo\n0Kd2OWwNH7Ji7zSsNNuQBNPiIVLRm4m7g1EIwUg8TdL+3ucef79ZP1vzW6gszca/3pD9RnCp+AX/\nw5YzvyIg8F6fr7FUO7DFN5x1l8IwGCXK2VkQkag11+hPp5sAr9YvS1NPO2q52aSr2/8s4QdO4jvx\nG4w6PQ4Na5EYeI+Uh5EZ57SxpsOlragcnt8YzcHGmabV2nPO/zDHr+/k5ZbFv5BAUWCpsuancXvM\nHbIBXB3KoVZa8DgxkoTkOGwtn98RWEZGRkYmfwmLDubvUz8DMLrb1Hwx/MFkE0XFm5pb6gxalu2e\nwa8FmNeVLeP/559/5vjx43h7e5s/6969O23bti2Wxj+CqeRlxequ+NyJYdPynYzYshGAAwOH4dmz\nLd2qO9PEwz7LeObOVZ3pXNWZnQtXkDJsLw/CIkxdMT96i0rvv4moUhK27RDX3v+Ku8t+Q5+QRO15\nkxHE4lXrPivSxs7FJERyLegcClFJy5pdC02GT9pnL1zo2XOngmJYeMJkeI9oXI467jbon1QXuhaa\nwGbfR8QGXuGrUQNyZfinpX3d7vzvxHJiEh6ABEqVM02q9yEoRk9YXAppfenxKQbGbrlJK28HWld0\noLKz1XMXheN6fcXinVNJ0WkQEIhLepzBc58Zv53ey45Tc4kOisLF25Iy7oNYeN6WkLir6XIaUsN5\nXKxVVHWxwkolcv5+HEoxo3f/aU10qPX1RNQujsRe8yfu6k0e7fUx73ZFn7wIgIWbCy4dmqN2dSTk\nf7sRBIG6C6dmafin0qn+AM75H+bote30b/H2cxOcchrbmduKOEXFs/oNajWGtYfnP1nMzUpn+IOp\nK7OHSyXuPrpJSNRdang0KGyRs01xiMstSGT9SjayfiWXotJNkiR+OTAHnUFLuzq9s13eO7uk/jsY\nfU+DXc2CrYiYLeM/KSkJV9f0cewuLi4kJ2fuaS1qLK1URNtY8P02fwKjNIz/ax2WyaZa+j3/Xk/f\neS9ucGNITiFo1SZuf/8rt5JjqC3a4NC4DvUWTsW2RiXzuHIDuqCwseLK6GncX78VQ1ISdRdNK/AG\nOgXBqX/3I0lGGlVpi51V4ZXizCynITvnWld0pHXFzOWsU9aWoY3cOXkyPtshOFkhCAJa3dNwDJWg\nZWY3U0kujc7A7puRbLj0EL1BQhDgTrSGO9EaNl5+iKOlkiSdAbVC5JP26Q3uJlXbsWbicb7+31j+\nfXCJlfu+5uOXF2S5g6TRGdhxah6ClIiAhIQC/5RuoE1BFNKXirVRi6x+pTZOz6nWA2BISib22k2u\njp2BIcn0m7723vMTkBXWVrTYtRLbWlXMctackbOynfUqtsDOyonw2BBGL+7Ie72/zhdDfdnuGSSm\nmMLIVuydxc8Tch5GVZSklorrWL8/zap1zHSMp2sVk/EfeadYG/8yMjIypQkfv134BV/AzsqRYR0/\nyvf5x/b8kpX7ZpFsqWRszy/zff60ZMtC7dGjB8OGDWPu3Ll4e3sTFBTEtGnT6N69e4EKl1tul3Nk\nx77bADS6dQ2LJ4Y/gIUmiSN1euParhmuHVuAKOA/6yeQJLxHv4JRp+fx2SvEXLqB9KQtfG3RxmTw\n7FyBoMjY1deta2ua/LaAS8M/JfSv/egTNTRcMQvRImdNlYqCtKvnk09CftoUcMhPYZKf3oG0XliV\n8qkxbaVS8Eq9srxSz1RNSWswcjU0gdP3YjhzL5Zojf7J5wa+OXyX1a/Wpqzd03dDFBW812cWn64Z\nwsXA4xy+uoUuDQdluL8kSRy9/Zifz90HyWSkO3tbIQmWfNy+EpWcrajgaMmlkPT5B2kN/0f7T+A7\n8RsknQGnl+qjjYwm/sZtJEPG3haOzephX78GDvVrok9IJPCHNQiYasXb1a6ah2/S5OFI0Zl+l0kp\nCSzc/imvt/+A2l5NqOBWzewByenzS53TNG88sYnRONg450nWguRZ/c4HHAbgperPj+n0dDE5Hx5E\n3S04wfKB0up1TEXWr2Qj61dyKQrd4pIes+HIQgCGd5qcrR36nNKkartc5f3lhmwZ/0uWLGHChAk0\naNAAnU6HSqVi8ODBLFmypKDlyxV+koidWuTN6z5Yrv8DwJR0KIooHWzRPori4c4jPNx5JN11gfN/\nfXogCAgKEclgCnVQWFlkavin4tKmCc3+/JHzr04kfK8PB6t2ocGymbj37ZT/ChYADyLvcPfRTawt\nbM3lLGXSk7oqB3i3x/Pr+qsVIs287GnmZc+E1hKDNviS+CSnQWeUGPXXDQbVc2NIg7JYqUzvlKt9\nOUZ3m8rinVNZf2QBtbwa4+HydIcpMDKJZWcecP1hLDaJv2CB3hRqJFjTr/XndKvuYh777G5JSkQ0\nUSf+IcrnAiGb95i3BSKPnjUNEEXs6lbDoowLjy9cQ1QqqbtwKmV7pvfEe496NdffXabfk9ICrd60\niNEbdKw/sgAAG0t7yjl5cT/yDiqlmnE9Z2ZrV+Duo5vojan9PAQMRj3TNrzJJwMXvrBxSnEgNPoe\n9yNvY21hS13vZs8d5+FSGYAHkbcLSzQZGRmZ/zTrjywgITmWehWb57gSYnEkW8a/g4MD69evZ82a\nNURGRuLq6ooiC0O4qLGWdHx+cieROw6DIGD8rDt/i6YutWN7fkJNRWUij54j8uhZIg6eMl8nKBV4\nj3kN55YNcWxWn5gL17j+0Ryup8QyZOHUF97XsUldRJUSIyDp9Fz74Jtib/ynxs6lJvq2qNEFtTL7\n1XCKO/kZG5ibVbkoCHz6JKdBkiS8nSzxfZjIH1cesT8gipFNy9OlmjOiINCqVpPpHgEAACAASURB\nVHcu3znFCb/dLNk5jT7tfmThqTBS9EZTEy1Jj5PmZwTtRazUNkwd/BOP7sTSplV6/cK2H8Lv428x\n6vSoXZ1IfvAwU9kU1lY0+e177OvXRGmTt5yI3DCu10xW7puF0WikbZ1eJKbEcyP4HyLjHhIY5gdA\nWGA0K4VZ2fret54xLd57NX2Dfi8NZ8G2j7kV6suM30byXu9ZvFS9+P0W076fqV7/JlXbZ9kgxtP1\nifFfzD3/pTnmGGT9SjqyfiWX/NTtYqAPy/d8id6o5432E+nScFCGsNurd09z8sZe1EoLRnebWuCF\nXQrj2eUoMF2hUFC2bMZGUfnBvn37+PDDDzEYDIwePZopU6ZkGPPBBx+wd+9erK2tWbt2LY0aNcp0\nrvf+WEbkjQAUNtZ4//ghswPmkpJi8jD+uONzRnefikfPWtQZ1pOTW9aw0X8NCPBmrdHUfPVpwya3\nbm3o5LcH9cmTuGXzQaTdHTAmp6BP1BSJYZUTjJKRUzf2AtCmdu5DfswJo5JE3UVTKdtd3kGAjJ54\nv0cJrDgbgn9EEt/7BLPwRDAqhUij8rYo1K+hUF0gKNyf+bsWobE2dQFG0lFNXENU8kVsLOwY6z2G\n4C5T8EuJpeqP36BytCf61EWiTvxDzD/XzfdKfvAQ0coC5xYNcWnbDEGl4M6idYApfMe5Zea/ocLg\neYup8NhQPl39mrmplVb/4pK89yMCOR9wBJVCTd+X3sTR1pUvhqzk5/2zOeG3mx+2fcLgNuN4ueWo\nYluR67y/aSey+QsWKW4O5VEp1ETHPyIpJQFrC9vCEE9GRkam1LFi71ckJMcB8OvBuWw+uYzq5RtQ\n3aM+ErDr/AZzHtmrrcdS1tGzCKXNP7JV57+gMRgM1KhRg0OHDuHh4UGzZs34448/qFXraZfSPXv2\nsHTpUvbs2cO5c+eYOHEiZ8+ezTDX4cOHedj7PSKbOhLySgV8wy9jlDLGM6ciCCKSZArtyW2d9bSE\nHzjJ9Y/moIuNR9IbqDV7Et6jXsnTnAXNjeCLzPrfO7jau7P43Z1ZtpbOisO1e6GLfpoUa1PNGyuv\n8lh5uWNMTuHh7mMISgX1F3+BW7ei80ikrWpTb9FU3Lq1QZ+oQRMcStj2Q9xbtRlEgXo/Tse9d4cC\nkcEoSRwJfMz84/d49geo1AViF/8tAPF2k9Erq+CYtBwx5Ro2lvZMHbiEu50moY9LeOF9lPa2dPLd\nVSLyT9JyMdCHpbumo9EmYqW2Zsm7u7C1en7i9uIdUzl9cz/dGg1mZNenjgNJkth1fgO/H1+MhIRS\nocJKbVPsKgGFx4bywcq+WKis+Pn9Qy8sHzdl7VDuhQfw9bC1VCufeUK8jIyMjEzWDP+htTn8VHhS\nQiMzREHBhsmnM1RgK2zyq85/sahJef78eapWrUrFihVRqVQMGTKE7du3pxuzY8cORowYAUDz5s2J\niYnh0aNHmc636V0te9qGc/XRPwgCVCtfHyu1LVZqG1rW7E6LGl3xcq2CQlSaDX8wdbfV6bV50iV1\nt6Dhqm8ACFr5v0yTKYsTJ/x2A9C6ds9cG/5AukZPAIm37hF55Az3120lZNMeDAlJ6GPiuTJmOtro\n2GzNGX7gJIdr9+Jw7V6EHziZa9nS4vvhHHTRMeiiY7g88nOO1O3NoSqdOdXxTe4sWochSYMhIYkr\nY6Zz/7cdGHX6F0+aBQ93HeVQ1a4cqtaVR/tPAKZwoC7VnLGzeLpTZKkUmdLBmzn9e9CtydsISNjH\nfY9L5DjElGtYY8nAy1W4025iBsPfrnZVvN99jcbr59NgxSzULo6oXRypv3RGiTP8wbQrsHricepU\naIpGm8T/Tvz03LGhUUGcuXkAhaikX/MR6c4JgkDf5sP5eOAPgCm3IF4TY87dKC5ceNJVu1HlNtmq\nG52aDxJSzEN/ZGRkZIorYdHB6I2mwi7WFnZMfnkBi9/ZwXu9v6Zrw1cQhaf/PluprYvc8M9PioXx\nHxISgpeXl/nY09OTkJCQF4558OBBpvOlWENZR0+Gtp/AT+P28vWwNaz58DhrPvRhYr85fNh/HvNH\nbmb9pFOM6voZFkrTP7ZafTLTN47gfkRguvlOnsy50enWvQ3WFT3QBIfyaM/xHF9fWBw9fpSz/qbd\njrZ5CPkBsPQwhYSJVpY0WDGL1kc30Hjdt9T85kNEy6d5BMYULSfaDCVk0x5etPHkO3G22VC/9v6s\nHBvizz47SZIwap6WqJX0BrSRjxHUKqyrVEBQpflxG434TZ7HidZDePDHLoz6nN077noAN6b+wJUx\n09EnJKKPT+TKqGnEXLphHjO5nTcOlkocLJV83rEinas607C8HSM6vINgBASQFIAEXdcbUOy9gSFJ\ng0W5MoiWavwtjdRb8gWtj6yn1lcTcevWmnIDutDJbw+d/PYU6Q5LXhEEgbp2nVGICg5f2cLtsBuZ\njtt2djUSEu3r9sXV3j3TMU2qtsPG4mn/gdw0VCsIUt/Pc0+M/+Y1speX4OVaBTAl6hdXcvN3syQh\n61eykfUrueSHbpIk8evBuRiNBjrU68fqicdoWq09bo4etK3Ti1HdPmfyy99jZ+WInZUj43sXnsOo\nMJ5drpcxkiRx4sQJ2rXL+9Z5dmNwnzUUn3fdv7ujadDzFf49+pDQS5upV6+eOXki9Utt06YNClGJ\nVWI5xrz0LWUrO7B013QuX7jKu5cG8f7wKfRoMoTTp07j6+ub6fUvOq747hD+mjKLe/MW806fjgiC\nkKPrC+N437EdhIRH0uSlRni6Vs71fLUkSxL+vY2/lUSD5VMo16MLAFejwqBmeRqu+tqUPK2JQeXi\nQKX7MfhO/IY9K9ZQ8d3X6DrkFfN8kiRRR2HLg993cjUqFDCVW9XHJbCkWhvs69egy2uDEESRLdPn\nAjBk+be4dWuTQT5fX1/zsWQ08vvoyTxKjHpSvtWSx/1b49r+JTr2640giuxcuJy7P22kroUD5Qf3\n5Mi2nSQH3ULz0RwC5q7gWkwEokqZ4X7Vk0w7Cn4psTi3bETl8ETirvlzw5holh/ATxuLX4+hdB40\ngOpTx2K4f5uJFZ/Ke8LHh5h/fClz5CqqZvAw3FS60r2sFfV7DSLQWY19nWp07GtaqN1evpy75ezw\ngGLxPuX38cPgKKpatMJfc4LVh+bRveJoREE0n9+5byvb927Bxdua/i3eynK+8b1nMWPJRHT6FBxq\nOZOi03Dh3MUi1c/X15e4pBgCQq6iUlqgCRM5GXnyhdd7uJk8/6dPn6aiqmmxeV7ysXwsH8vHBX2c\nSl7mO/XvPnx8jmOltuH19z/IdLzmociIRl8VqX6+vr7ExpoiJYKDgxk9ejT5Qa5j/pOTk7G2tsZo\nNL548As4e/YsM2fOZN++fQDMnTsXURTTJf2OHTuWDh06MGTIEABq1qzJ8ePHMyQgHz58GMk+IVfx\nvMnaJNYfWcCRa9sAqFCmGtHxjxAEMVcxwoakZI41fRlddCzNd6zA6aX6OZapoJm/ZRIXA48zvNNk\nejV9PVdzSJLE2V5jiL18g2pTx1Llg+EvHB/61z5ufrnElCOgVCCqlCgs1Lh2aUXsP9dJCnq68yOo\nlAgKBSonB1LCwjOdU+XsQOcnScuZYdTpuf7RbEL/2o+gUtLgp5m493uxl1UyGAjbepDABatJuvvg\n6QlBwMLNBVGtQrRUk3TnQYbwLqWDHeUHdce6kgd3Fq1DkiScWzUi4uBpjClaRAs1Zbq0Ivr0ZRCg\n3MvdiPI5T+KtewCE1Fbi0z4JAXiz9mg6p0lG/y+hSUlk0q+DeJwQwTvdp9Opwcvmc6v2fc2Ra9to\nV7cP43s9vzFZKnqDjqnr3yQ44hb9W7zN0HY5a05WEOy/tJk1h76ladX25vCkFxEaFcSkXwfhal+O\npWN3FbCEMjIyMqWHhOQ4Jv8yiNikaN7tMYOO9fsXtUjZJr9i/pVZnVy3bt1zvetabd5i49PStGlT\nbt26RVBQEOXLl2fTpk388ccf6cb069ePpUuXMmTIEM6ePYujo+NzKw/lNpHPUm3NOz2+oHGVtqzc\n9zXBEbfM51buy165wYuBPqzYazJCxvb8kgojBnJ74RruLv+9QIz/1PsZJSNvd/mEVrV6mOP2n5Ul\n7fdiKm81k4TkWECgVc1uuZYhfP8JYi/fQO3qlK1a8IIg4PFqT8p0aU3ANz/x4LedGPUGjJoUwv7a\nD4BFuTJ4vNYLzyG9sa7oab5Wcz+MiCNniTxyhvD9T1fJuuhYbn65mErvvYGFm0u6+xmSkrnyznQi\nDp1GYW1FozVzcW3/UrZ0ExQKyr/SA/cBXThcoweGRFMFGiSJlEeRmV+jUlJv8XTK9myP4km4U8Ux\nr5nPJwWHcWvuCsK2HuTR7mPmz4N//RMwhU9VfHcIXd7oyygb62zJWZqxsrDhzY4fsXjnVP7wWUKz\n6h2xs3IkMi6M49d3IQgiA1qMzNZcSoWKMd2nMWPj2+w6v542tXuaQ2iKCnNjrxrZ/4Ne1skThagk\nMi6MZG0Slmr5PZGRkZHJDpt8fiI2KZoang1pX69vUYtTJGTp+VcoFDRu3BhLy4wJaEajkbNnz2LI\np2TWvXv3mkt9jho1is8//5yVK1cC8O677wLw/vvvs2/fPmxsbFizZg2NGzfOMM/hw4cz/TynxCRE\n8t6K3hiMeqLvafCuWY6fJxx+4XVjlnQmXmOqeGOltmHFG9s43nQgRq2Otif/wKZKhTzLptWncDvM\njxv3L7Ll9C8YnjQ2AlNGup21I/ZWjoRG3zOfUykt6FjPtLoVBIEj17ah06cQfU+DWyU7Nn58Lley\nSAYDpzoNJ8H/LrW++Qjv0TlvBHWoejdzAqugVtF4zTxcO7yUZVM1gIe7j3H9ozkYNClIOlMMt2ip\nxmtYfyq9PwxL9zIc238Aq2VbeXzuKione5r89gOOjWvnXFGeVnKSJKj1zYc4t2qEMUWLMVlLxLHz\n3P5hNcKTKkHZibWPueTHuX5jkfSm35CgEKm7cBrlXu6KqMpyXW7m5MnSW8sZnuonSRLfbBqLX/A/\ndGkwiNHdp7L64DwOXP6TVrW680HfOTma95cDczh05W9qeDbky6E/5ynRPS/sP7SXtZdnIAoiq94/\nhI2l3YsvesInqwdzP/I2s9/cQJVyuXunC5L/yrtZWpH1K9mUZv3yotutUF9mbHwbURSZN+J3vMpU\nzWfp8k5W+hWK579atWp8++23dOqUMTwiNewnv+jZsyc9e6bvmpZq9KeydOnSfLvfi3C0dWViv7ks\n2v4ZAJXK1nrBFSbSrqU02kRWnv2elq92JGrjfoJWbqLOd5/kSI5krYajvtvYfGI5BqMBN0cPHj2+\nj86Q2c6LgFEyEJsYRWxiVLozOn0KBy5vzvQeqjw09QrbepAE/7tYerrj9Wbuts7qL53B9Y9Mxlvd\nhVMp07lltq5z793BXIozztef2wvX8mjPce798ifBa7ciKET8UmKphRWW5d1o+r9F2FavmCsZ4Wkl\np8ywrVGJSu++lum55+HYuA4Nf52D74SvAai35Au5N8JzEASBt7tMYcraIRy+uoWGlVtz9JqpItjL\nLUfleL6h7SZw4dYx/B9c4ZjvDjrVH5DfImcL/5ArSJKRuhVb5MjwB1On3/uRtwmJulMsjX8ZGRmZ\n4oTBqOfXA3ORkOjdbFixNPwLiyw9/++88w4NGzZk/PjxGc7pdDq6du3KsWPHClK+HJNfnv9U7kcE\n8vn6YegNOj5/dQkNKrV67liDUc+Uta/zIPI2oqBAFEX0Bh0OFo40/V8C3mFWdPhnK2pXpwzX/nPr\nuLnLXA2P+ugMeh4+DuZxQkSm96pQpiq1vJpgobLk6LXtCILAuz1mUL9iC+I1McQlPebibR92nd+A\nJEm0rt0TrzJV4MnjDo4I5PS/+xAEkfG9Z9GsWoccfzdGrY4TbYeiuRdK3UXT8BzSO8dz5DdxfrdM\ni4BdR59+qBBpf+4vrDwzrwQjU3LYeHQRuy5sMB9X96jPrDfW5GquUzf2sWTXNGwtHfhh9N/YW2f8\nXULW4XN5Ze6fE7h693SGXIbs8PepVfx5aiX9mo/g9fYf5JtMMjIyMqWR3Rd+Y8PRH3C1L8f3I//E\nUl28G7BmRn55/otFk6/8JL+Nf4DtZ9fwh89SnG3dmD9y83M9dJtPLGfLmV9wtHFh3lt/kKxNYsXe\nr7j54DIAVfxEhtQbSb2PxwGmXYJ74QGc9T/E9rNrMm0uoVSoMBoNGJ/0I7BS27D43R3YWTnmq45p\nyawJVmYEr9vKjSnzsanmTeujGxCV2QtVKQwO1eiOPtbUle9FycAyJQdNSiIjf2xv/q3YWNrz6wdH\nX3BV5kiSxJw/38M36Bzt6vTOtJSbTq/lnaVd0GhNVZvyoxFgKonJ8byztAtGycjK9w48d/HxPM76\nH2LR9ik0qdKOTwYtzBeZZGRkZEobphzHL82dfD8ZuLBYNXnMCaWqyVdxx0lbmarl6hKdEM76Iwsy\nHeMbdI6tZ35FQOD9Pt/gaOOCu5MXM4auYninyahEFbfrGJlt+IW3FrZl4fYpfPTLQD5b97q5Tnkq\nSi18/spSFr+zg/UfnWLyywuwt3bC3tqJ9/t8k6+G/7OlpSB9E6xrE77OtBa/ISmZ2z+YPK7VPh1T\nrAx/gPpLvkDt4kiArUC9RdOKWpwCI7PnV5p4Vj8rC5t0ya0KMeu8kKwQBIFRXT9HpVDj47cbv3sX\nzOfuPrrJ2kPfMW5ZD7PhD+RLdbNULt72IeJuPLW9GufY8AfwdKkMwP2o2/kmU37yX3s3SxuyfiWb\n0qxfTnVbtmeG2fBXKlTF3vAvjGeXpcUWFBSESqXCw8NURTw+Pp5Zs2bh6+tL3bp1mT59Oo6OBeeB\nLi6IooJxvWby2bo3OH59Jy9V75Tu5YlJiGTp7i+QkBjU6h3qej+tJCMKIr2avk6DSi35+OdXkERI\n1iVx7kljLVuFLVXCbBEDIvi3sSnxs/UBJYZbW7Gf+zGio4ImVdvlm7fxRSSHRaBPeGrs6GPjOd31\nLbzeHED5gd1Q2pnq1Qev+ZuUR5HY169J2T4dC0W2nJAan68+eRK3Upr09F/l/T7fsGzPl4iCyLs9\nZuRpLncnL15uOYrNJ5cze/N4VEoLHKydCY99WmrWzcGDyPiHGI0GbCzt0epTUOchTyaV8/5PqvxU\nz50Xx93JC4WoICImlBSdBgtVydvClpGRkSkojEYDuy/8RmJyvPkzS5VcGQ1eEPbTrFkz5s2bZ95i\nGD58OJcuXeK9997j4MGDSJLE1q1bC03Y7FAQYT+p7L6wkQ1HF+Jo48L3I//E1soBo9HA7M3v4Rd8\ngToVmjJt8DLE53gjR37biiQhBQClUaTHUWecr8UhSgKCWokgiAgKBZJkxKhJQWFrTY3p4/EaPgBB\nLNhNGslgIHjtVgLmrsCQYCpnKVqoEVRK87HC2grHZnWJvfwv+vhEkCSa/PEDZTq2KFDZZGQKEp1e\ny4iFrc2hdQC2lg60qdOTDnX7UbFsDeKSHjNtw3AiYkNpV7cP43rOzHZzwsw4c/MgP+4wFRMY23Mm\nHXJZbm7yr68QEnWXuSN+o1LZmrmWR0ZGRqY0ERYdzPK9MwkIuQqASqHGUm2d73lbhU2BV/s5fvw4\nAQEBGI1Gjh8/jsFg4M8//2TOnDnUrl2bqlWrMnToUHx8fPKly29JoGeToZwPOIJ/yFXWHp7P+32+\nYevZ1fgFXzCH5DzP8Adoc9gSn1Ym47/1ARHXO/HYVKuI1/ABeLzaE5WjPWDyvt/4/HvC953gxmff\nE7rlAHW//yxPlWqyIu56AH4ff0vslX8BcOvRllqzJ2HlURZDcgqP9hzn/obtPD5zmajjT0MjBKUS\n1w7NC0QmGZnCQqU0/aOQlGIqN2ultmH5+H2olGrzGHtrJz5+eQFfbHwLn+u7qFS2Jj2bDM3V/ZK1\nGpbv+dJ8/PvxH3Nt/Hu4VCYk6i4hkXdk419GRuY/j1EycuDSZn4/vhitPgUnG1fe6fEFjarIEQBp\nea47+e7duwiCQFBQEEFBQWzfvh1ra2ucnZ0JCgoiJCQEQRC4e/duYcpbJKTGX5nCf75CrbTg5I29\n/HbsR/46tQoBgfd6f42TbZks5/F+YMmQFRYMWWGB9wNLmv29lDY+v1NxzGtmwx/AslwZGq2ZR8Nf\nZmPh5kLM+WucbPc6Byp14uHe4/miU/iBkxyu3ZOFns043W0ksVf+xbK8G43WzKXx2m+x8jA1UFNY\nWlB+YDeab/2JNid+R7R8Gu6gsLHKk/ezMCjNcY8g65dfvNf763R5NWkN/1S83aoztudMADYcWZgu\nRyA76A069l3axMSf+6PVm5wA0fc0eZLb06USAA+iit/fYfndLNnI+pVsSrN+mel2MdCH0Ys78eaC\nlqw9PB+tPoU2tXsyf+TmEmf4F8aze67x/9Zbb9GyZUvOnz+Ps7MzFy5cYNCgQYwYMYIRI0bQt29f\n7O3tGTFiRIELWZxwd/Kibe1eAOw8vx5JMtK/xds0qPTi2vT1Fk1F7eKI2sWRhr/MxqV14+caz4Ig\n4N6nI218fkO0MBkiRk0y18Z9men4nHJtwtfoomORtFowGvEeM5g2Pr9Rtmf7515jW60iDVd9jcrF\nEZWzA/WXfJEvssjIFDWpeTWr3j+U5ZZwq1rd6Nd8BEbJwKIdUwiPDX3h3EajAZ/ru/jol4GsPfQd\nsYlRuDtVwNrCFmtLuzzlLXg+6U4cEnUn13PIyMjIlHRW7P2KhORYDEY9AgKTBpiiM2ytHIpatGJJ\nljH/9+/fZ/Lkyfj5+dGkSRN+/PFHnJxMVSl++OEHoqKimD17dqEJmx0KMuY/lbRdfBWikvWTTqEQ\nC67azeHavdBFx5iPa8/7mApvDcz1fKFbDnBt/EzzsdLBji7++/MioozMfwaj0cC3f0/k6t0zVHSr\nwVdv/Jppsu2ZmwdZte9rUnQacz6Bp0tlXms3nqZVO+TLrllwxC0+XTMEd6cKLBpTvPKvZGRkZAqL\ntHZZXkpAF3cKpcOvl5cXmzdn3hV20qRJeb55acDawrZADX8w7Rhc/2gOhhQthoQk/p22EJuq3ri0\naZKjeYwpWm5+uZjgtVsAEC1UKGxsqLdoakGILSNTKhFFBRP6zmHa+jcJCvdn1OKOWCgt6VCvH0qF\nigeRd7gfeTtdxSBBEBnX80va1O6ZZV5QTinn5I0giDyKeZBvVYhkZGRkShrDOn7I8j0zAVMzRpms\nkev8Z4Nn46/G9vzSHB9cGC9ZatnKroGHqDT+DSSDgStjppF0L+TFFz9Bcz+Mc/3HEbx2C4JaRe1v\nP6Fr0DEsVj2/iVdpoDTHPYKsX1Fha2nPxwN/AEyx/Ikp8ez+5ze2n1vLxds+6Qx/03gH2tXtk8Hw\nz6t+KqUad0cvJMlIWHRwnubKb4rrs8svZP1KNrJ+JZfMdLO3MkWl1PJsTLNqHQpZovylyOv8y2RO\nYdbdf5bq08aSEHCXiEOnuTT8U1rsWmWuvf8sqZ16JZ0OyWjEkKjB0tOdRr/MxqFhrUKWXEamdOHl\nWgUrtY25CZhSoaJ/87fwcq2Cp2sVQqOD+OWAqVN2XvsRZIWnayXCHt8jJOoO3m7VCuw+MjIyMsWV\noHB/ACrKVc+yRZYx/yWRwoj5L2r08Ymc6TWGxFtBlOnWhsZr5iIoMoYSHKrRDX1sgvm4TJdW1Fsy\nA7WTfYaxMjIyOedioA8r980CTAZ+UdSP/p/PT2w7u5qBLUczuO24Qr+/jIyMTFHzw7ZPOB9whPG9\nvqJd3T5FLU6BkV8x/88N+1m6dKn5/wMDA/N8I5n8Q2lnQ+P136FytCPiwEkC5q0ynzPq9IRtO8jZ\nvu+mM/wV1pY0Xv+dbPjLyOQj2a0SVJAU53KfMjIyMoVB0KNUz3+NIpakZPBc43/q1KdJoKXdk/4i\nimPsnE0lTxr+MhtEkbtLNnCwcmeujp/J8WYDuTr2S2Iu+CJaWSJaWqBysqfBilmZdgkujrrlJ7J+\nJRtZvxdTXMt9ys+uZCPrV7Ipzfo9q1ticjzhsSGolBZ4PHGGlGSKNOa/cuXKTJ48mdq1a6PT6Vi9\nejWSJJnL06X+/8iRIwtcSJnMcWnTFIWlBYYkDYYkDWFbDgBgW70SFUa9QvlXuqO0sS5iKWVkZAqS\n8s7eCAg8fByM3qBDqVAVtUgyMjLZ4GKgDyv2fgWYCokU1e5hSSc13r+Ca9UCr75YWnhuzL+/vz/f\nffcd9+7d49ixY7Rt2zbTCY4eLV61VP8LMf9pSdsDQFCraPrbApzbNCn2nXdlZGTyj4mr+vMo5gHz\nR27G68lOgIyMTPFm5I/tSUoxhefaWzsVWSGRks7uCxvZcHQhnRsMZEz3aUUtToFS4HX+a9Sowa+/\n/gpAp06dOHLkSJ5vJpP/pPYAkIB6C6fi0rZpUYskIyNTyHi6VOZRzANCIu/Ixr+MTAng6t0zZsMf\nQKfXFqE0JZu7T+L9K8mVfrJNtur8HzlyBL1ej4+PD3/88Qc+Pj7o9fqClq3YUJxj51J7AHT225Or\nev3FWbf8QNavZCPrlz08XItf0q/87Eo2sn4Fx8VAH+Zv+QgAUTBV6kvWajgfkH9O1tL8/J7V7WmZ\nz9KR7FsYzy5bxv/NmzepVasWr7/+OosXL+b111+nZs2a/Pvvv3kWIDo6mq5du1K9enW6detGTExM\npuNGjhxJ2bJlqVevXp7vKSMjI1Oa8HSpDMCDyOKV9CsjI5Oe8wFH+GHbJ+gNOro1GszGj88yoMVI\nJIz8uONzLt8uvUZ7QZCi0xASdRdRUFDBtWpRi1NiyJbxP27cON555x3u37/PmTNnuH//PmPHjmX8\n+PF5FmDevHl07dqVgIAAOnfuzLx58zId9/bbb7Nv37483y83tGlTejvglmbdQNavpCPrlz08nhj/\nxanij/zsSjYlWb+LgT6MWdKZMUs6czHQJ9MxRaHfqRv7WLT9MwxGPb2bSvQqPQAAIABJREFUDePt\nLp8iCiKvtR1Pr6ZvYDDq+WHbJ/jeO5/lPMVVv8IirW7BEYFIkhEPl4qoVZZFKFX+URjPLlvG/5Ur\nV5g0aZI5iVQQBCZOnMjly5fzLMCOHTsYMWIEACNGjGDbtm2Zjmvbti1OTk55vp+MjIxMaSO1vF1o\n9D30Bl0RSyMjU7Qs2/Ml8ZoY4jUx5iZ8Rc0x3x0s3TUdo2Tg5ZajGNbhw3Q21ZsdP6Jrw1fQGbR8\nv+Uj/r2f0b4yGg34P7jCjzs+M+uXWi3ov8rT+v5yvH9OyJbxX758eY4dO5busxMnTuDh4ZFnAR49\nekTZsmUBKFu2LI8ePcrznPnNfyl2rrQh61eykfXLHn7BFxAEEYNRz5FrmTtQChv52ZVsSqp+jxMi\n0iXSpuiSMx1XWPpdDPThrYVtWLH3KyQkBrcZx2ttx2eoyCcIAm93nUKHev1I0SUz98/3GPljB8Ys\n6czmE8tZte9rxi3rwZe/j0KrTzFfF6+JZdOJZcQlPS4S/Z5HdnYnckta3e4+uglARbfSEe8PRVzn\nPy1z586lf//+9OnThwoVKnDv3j12797Nxo0bs3WTrl278vDhwwyfz549O92xIAj5UqJy/PjxVKhQ\nAQAHBwfq1atn3kZJ/VJzcuzr65un64vzsa+vb7GSR9ZP1k/WL+fH6y5/hSQZib6nYcm6uXRr9Gqx\n0E8+lo8L8/jg4f2sOzwfydGIIIhEBSUCGo5c3UqnBi8XiXzf/vUhNuVNdk18iBE341MP9bPjT586\nTW2bjmhrpXD63/08vG3Kgdyi+QWA6HsaHG1dada8KTeC/yHs9mOMRgNb+ZXdFzZSQdmYljW60bt7\nvyJ/Hsv2fMl9f5Mz9yfjF6yeeDzf5k/7/Z06dRrsTJV+ivr9Kwj9fH19iY2NBSA4OJjRo0eTHzy3\nzv+zBAQEsGnTJsLCwihfvjyDBw+mevXqeRagZs2aHDt2DHd3d8LCwujYsSM3b97MdGxQUBB9+/Y1\n/4OZGf+1Ov8yMjIyY5Z0Jl5jMhRUSgs2TDpdxBLJyBQuydokvtk0jsCw63i4VOLLoT9z+t/9rD08\nHwGBCX3n0KpWt0KVyWDU8+aClhglI5D9Wv56g463FrU1h/CJgoJBrcfQrFoHvFyrpnOS+odcZfvZ\nNVy6feLJWBGFqEQUFXRtOIj6lVpiZ+VI0CN/fj++GCi4hmKSJOEfcoWd5zdwMfB4unPjes2kfd2+\n+Xo/vUHH24vaoTNoWT3xGNYWdvk6f3GkwOv8P0v16tX54osv8nzDZ+nXrx/r1q1jypQprFu3jgED\nBuT7PWRkZGRKM2N7fsmyPV+SmByHKIjo9FpUSnVRiyUjUyho9Sl8v3UygWHXKeNQnmmDl2Fv7USP\nJkPQaBPZdGIZP+2ejqXaisZVMm9YWhAc992JUTLtQthZOvBujxnZuk6pUPFB3zms2PsVoqBgXK+Z\nzzXWa3g04NNBi7gXHsD2s2s5fXM/RoMWDLDrwkZ2XdiY4ZoFWyfToFJLyjiUp4xDeeI1sRy68jei\nIGZ5r2dJ26G4Y/0B3Aj+h8Cw6wDmBYiA6fks3zOT6PhwBrQYmW9NSEOigtAZtLg5evwnDP/8JFsx\n/wXJZ599xsGDB6levTpHjhzhs88+AyA0NJTevXubxw0dOpRWrVoREBCAl5cXa9asKTQZn92KKU2U\nZt1A1q+kI+uXPZpUbcevHxzF2606KTqN2QtYlMjPrmRTUvQzGPUs2TmV6/fO42DjwrTBy3C2czOf\nH9BiJH1fGoHBaGDhtk/xu3cBKHj9UnQa/jy1EoAJfb5h1YRDOfK2v1S9E6snHueXD45k6zpvt+p8\n0G8ONpb2gClESKlQUadCMyqUqYbAU4PbKBm5fOcUBy7/yW/HfmTHubUkpcSTkBzLou1TMuQPPI8V\ne78yJx7vOLeWwLDr2Fo6MLDlaJaN28uGSadZP+k0b3X+BAGBTSeW8euBuRiM+mx/D5mR+uyCwk1R\nIqWtuVdh/Pay7fkvKJydnTl0KOM2WPny5dm9e7f5+I8//ihMsWRkZGRKHO3q9GFD+A/4XN9F8xp5\n3xqWkSnOGCUjK/fO4sKtY9hY2DH11Z9wd/JKN0YQBF5vPwGNNoFDV/5m/pZJTHttWYHLtu/SJh4n\nRFCpbE1a1Oxa4PdLZXyvr1i5bxbJlko+6v+deeFwMdCHlftmIUkSA1uNxtXenYjYMMJjQzh0+W/0\nRlOIkc6gZdIvgxja/n061h+AKGTuI/a7d4HE5HjzsSCIvNX5E9rX7Yul2ird2B5NhuBkW4alu6Zz\n6OrfPE6I4IN+c7BQWT07bY4wV/pxK13Gf2GQ7Zj/koIc8y8jI/NfJSYxivHLeiIIsGzcPhxsnIta\nJBmZLEkbOvJsLHrac6O7TaW6R30SkuNI0MRx7e4Zdl3YgM6gRalQMWPIKqp71H/ufYySkWW7Z3Dy\nxl5AwMbClvG9ZxVI7HuCJpYPVvUjKSWBaYOXUa9i83y/R36SujAwGg0425UlOOIWAFXL1WVU18+o\n5F7LPDYk6i6/H1vMxdumCj6CIGCpsmZ871k0q9Yhy/vcfHCZ+VsmmcITRQXWatschRk9y8zfR3Pz\nwWWmvLKYRpVb52qOkkZ+xfzLxr+MjIxMKeK7vz/k0u0TDO80mV5NXy9qcWRksiRtsrpSoaKWZ2OS\ndRpSdBruR95GepIsmxXWFrasnnj8heP0Bh1vLWxr9nLbWzmxasKLE3Bzysaji9h1YQP1vJsXyi5D\nfiJJEmduHmTDkQU8TowEBFRKNWqlBdXK1+fa3TMYJQMWKisGtHibXk1fz5EHPyTqLh+vHmx+rlZq\nG3794CiiqMiRnEbJyKgfO6DRJrLivQM42rjk6PqSSn4Z/9mK+b9z5w5Dhw6lVq1aeHl5mf9LLadZ\n2ikpsY+5oTTrBrJ+JR1Zv5zTrm4fAHyu78r3uXOC/OxKNoWln06vNf+/3qDD9945boVeIzjiVgbD\n38HGBQ+XSlT3aIBSfBq1rFSosnUvpUKFlYUNYIqJT1svP7+IjHvI/kubABjafkK+z59dcvv8BEGg\nVa1uLBj9N72avgFI6PQp/L+9+46Oquj/OP7eTYc0QkgoASKRKiVAgJ+00EJVQBR4QJAaQKUJUqQI\noigKjwjBhyJNBKkqIEVKgNAUkCYdEiCFHkgh2dTd+f0RdyWUGNJu7mVe53COW7L7/bizc2d3Z+Ym\nJsdz6upBBIIWNd9gTuBG3nh1wHNP3SlT/CWKPrI4Nyk1keGLOvHrkRUkJMVl6zEOHjzI3dgbJKUm\nUqyou+YG/oVmzn/Pnj15+eWX+frrr3FwyN0cLUmSJCn/1PVpSlF7Z67fvUT43SuU96iodEmS9FSp\nackZA/c0sLW2p13dHlQrVxd7GwdsbewJvXmWtQf+h06nY3Dbj/Gr6G/5W/NUFSDbu+hAxtSieVsm\nA0kIIYg3xOBcpFieZdpwaCFpxlRerdKaCo9Ml1GbInaOvNNiFCFnNpOYkjG331pvzRd9VlG2xMu5\neux3209lwfZPSEtPwd62KNHxt1gVMof1hxZQxas2YbfOoddbZbkl6bU7FwDw9tTOyb0KUram/Tg7\nOxMTE4OV1fP9LKMEOe1HkqQX3ZKdX7Dr1AY61OtF7+YfKF2OJD3VpiPLWR0ShLdHZT7vs/KZi0vz\nmhCCz9e/z5nrR2jl+yYDW0/Ik8eNjA5j7LL/oNfp+O+An55YfKxGlvUAwsS77XI+P/9ZTMLE6auH\n+e3EGk5f+z3TbU4Ornw3LPipf7c6JIhNR5bzxqsD6N7kvTytqTAr0Gk/TZs25eTJk7l+MkmSJCn/\nmaf+HDy/Pcfb6h0P3U9gUEsCg1pyPHR/XpYn5RE1v0YJSXFs+iNjy+6ezYYX2MAfMqa29GnxIXqd\nFcGnfyH87uU8edw1+79FCBMta72piYE/ZGwjvGjobhYPy96Wo89Lr9NT26cxH3Wdx9cDfsLG2s5y\nW1JqIs/6fvr63YydfrS2zWdByda7rXz58rRt25ZBgwYxefJky7+PP87+T21qpuW5nVrOBjKf2sl8\nOfNyqeqUditPXOJ9/rr2R44e49E9vL/d+vx9vXzt8t+jr5F5V5y8kt/5Nv6xDENKAjXKN6Cm9//l\n63M9zfWLN2lTJ2Ph6fLdM585yMyui1EnOR4agp2NA10aDsyjKnOuMLTP51W6uDcjO87A0d4FyFgD\ncvjCjifud+DAAa7dydjj39tDe9N+CuK1y9bg32Aw8Nprr5GWlkZUVBRRUVFERkYSGRmZ3/VJkiRJ\nz0mn09HklYxv/0NyuPDXZDJa/js5NTHTwkypcDA9siA2OdWgYCXPJzr+lmVRbE8FF8W+1WgwTg6u\nXIg6wR+XdmV532f9yiKE4ND5HXy6ZjAAdXyaaG4BakGq+3JTFg/fw6A2kwBYtvsrYhPvZ7rPw6RY\n4g0xFLVzooRLaSXKVL1/XfBrNBrx8vJi4sSJ2NvbF0RNhU7jxo2VLiHfaDkbyHxqJ/PlXJNX2rPu\nwP84HhpCQnI8jn+f+TM7TMKEc9HiloV+JmFiy7EfeOPVAdl+DPna5b/mNTqy5dhKIOPkTPvPbaXp\nKx3y5LHzM9+6gwtIM6bSsGqbTHvIFyRzvu5N3mfxzums3PsNdXyaPHP3mv9tm0JicjwAX28cg6dr\nGcs5B0zinw/KZ8OP5n/x2VAY2mduNK/Zmd8v7eLM9SMs3TWDDzp9hU6XcZZizwoucCpjsa/5Oi0p\niNfuX7/5t7KyYv78+dja2uZ7MZIkSVLecHcuySvl65FmTOWPi1l/q/m4Pad/4daD6xQr6s7oN2YB\n8PPvS7gTG5UfpUo5ZPp7qkp5j0pAxkLvmw/CFaklu+sPIu5d4cDZrVjprQvFQs0WNTvh7VGZ+w/v\nsPnIiiduT0lLYt2B+ZaBP4DRlM7NB+HEG2IyDfwBTQ5GlZCxw9Nk7G2KcPTynky/zFzX8JSfgpKt\naT/vvPMO8+fPz+9aCi01zp3LLi1nA5lP7WS+3DEv/H2eqT8xCff4MWQuAH1ajaFexeY0qtqWtPQU\nlu/+Kttzo+Vrl//Cbp8DoEfTYTSs0oaUtCTmbv4oT6ZoPS3fowP8nSfXczx0P9v+/JGlu77k641j\nLOsP5m+b+szHXR0ShEAQUPstPF29cl1nTpnz6fVW9Gk5BoDNR7/nXtwtIGM6z7Erexm9pCs//74Y\nABsrWxxsi/KfpkOZ1X89C97fycrRfzCmy2ycixTDuUix59p2ND8VhvaZW+7OpejVfCQAS3d9Sbwh\nBoCQ/fsA7S72LTT7/B85coSgoCC++uorypYta/lkq9Pp2L9fXTsMSJIkvSjqV2zBUpsZXLn5Fzcf\nhFParfy//s2KPV9jSEmgdoXGNKiUsaVc7+YfcPLqQU5ePcSxK3upX6lFfpcu/QuTyWj5BrRCyapU\nKlOD0NtnuX73EqtC5tD37wFtXpq/bSoJyRknYlq6a8Yz75eQHMcvvy/htXq9sbH+Z9bAuYg/OXn1\nEA62RenyqvKLYs2qlq1NwyptOHxxB6v2fUP3Ju+zPHgmp68dBqBciYr0DxhHFa/aT/178444Ut5r\nWasLv1/cxbmIYyzd9SUjO83gVkwkVu7grdHBf0HI1j7/y5cvf/of63T06dMnr2vKFbnPvyRJ0j/m\nb5tKyNlfs7Uf9smrh/hyw3DsbOyZ1X8DJVxKWW7bcWIdy3Z/iZuTJ18P2IC9bZH8Ll3KQuS9UMYs\n604Jl9IEDf4VgLBb5/h4VT+MJiMfvvF1ppNiPep46H7L7kBZnUjpUTEJ93h/fnvLImOdTk+N8vUp\nWawsnq5eJCTFs/PkOlLSU0g3ZvzyULJYOfq1GkOtlxoihGDSyj6E3TpH18ZDeLNhYF78b8gz0fG3\nGbmoE+mPbI1bxM6Rbk3eI8D3Taz02fquVMoHd2NvMGZZd1LSkghsM5HvdkzH1tqO5SMPoNcX/vNP\n5aW82uc/W625b9++uX4iSZIkqeCZ9xvf+MdSKpSsRr2KzZ56v5S0JMu3uV0bDck08AcI8H2TkDOb\nuXrnAhsOLbL8HC8pI+z2eQB8SlazXOdT6hV6NB3Gyn3fsGD7J8zw/BF355KW203CxIWI43yzaRxp\nfw/Q/7dtCkuG783yuWIS7vHpmsGYhAm9zoqi9k5P/dDQvWnGh8uz4UdZuutLbj64zhfrh1GxdE0i\n7l0hJS2JInZOdPDrlSf/D/KSu3NJ9Hpr+Hvwb2Nly+yBv+BS1E3hyiQP1zL09B/Ost1fWvqo8h6V\nXriBf17K1pz/JUuWsHTp0qf+exFoYe7cs2g5G8h8aifz5d62P38EMuYwB/06gfsP7zz1fj8d/o57\ncTcp71GJdn49nrhdr7diQOsJ6NCx7c8fibh3Jcvnla9d/gq7lTHf36fkK5mub1/vbXwrNCIhOY4R\nizoRGNSSHSfW8mPIXIYueI1P1w6xDPwBEpPj+e34mifWcpjzZQz8h3DzQTjlSlRkwfs7+G5YcJa/\nFlQvX5+v+q3hbf8R2Nk4cOXmX6SkJQEZ05XsbZ++o05BetrrZ2fzz46GDnZFVT3wV7p95rWA2m/h\n5e6D0WTkQXgSRe2clC4p3xSaOf8//PBDphXst2/fJiwsjEaNGtG/f/98K06SJEnKO6npKQxb8Dr1\nK7WgXd3/UKlMLXQ6HeF3r7Dl6Ep06AhsM/GZUxx8SlUjoPZb7Dy5niU7v2BKz8VPnJnVPKXk7tV4\nHEr+N1/OCirB1dsXgIz5/o/S6/S81/4TBs8LwGhK52FSLMt2f2W5vYRLaXxKvsKZ8COkpqdkLOQO\nnsnZ8KMMaTcFRwcXy31jE6L/Hvhfp1yJikzqPh/nIsWyVZ+1lQ2vN3iHhtXaMGJRJ9KNaQDYPnIG\n18JmSLspLPxtGkChWbgrZdDr9MQk3LNcvnjjlILVqF+25vw/zdKlSzl//jyzZs3K65pyRc75lyRJ\n+sfx0P0s/G0aRmM6Xu4+XLl5xrI9oadrGeIMMaSlp2A0GWlTpzv9Wo3N8vESkx8ybOHrGFIeYm9T\nhKGvfUbZEj6E3jxL6K2z7Dy5DuPfJwjT6fQ0r9GJ6uXr80o5P1V/k1qYpBvT6PtNE4zGdJaM2EcR\nO8cn7tN/jj+GlIS/L+loWesNmrzSnkplamX6wHbkUjALf5uGISWB4k6eDO/4BZXL1CI2IZppawb/\nPfB/mUndF2R74P+446H7mb9tCjqdPttrDCTpcYFBLXmYFAuAk4Mr3w0LVriigpdXc/5zPPg3Go24\nu7sTExOT6yLykhz8S5IkPdv9h3fYdXIDwad/4mFSnOV6nU7HkuFPH0g+ru83TSxnlNWhQ5C9w4i7\ncyniDA+w1tvwXodPnrn+QMpa2K3zTPyhN6XdvPl64E9Pvc/x0P18u/VjhBAMafcxDSo/e8BwN/YG\nc3+dQOits+jQY2NtS7oxFZMw5XrgL0l5xfxFBmT8MvMifojMq8F/tub8m0ymTP8SEhJYtGgRxYrl\nvjN48OABAQEBVKpUidatWxMbG/vEfSIjI2nevDmvvPIK1atXZ+7cubl+3uehtblzj9JyNpD51E7m\ny3vFnTz5T9P3+XbINuxt/tmxx8G2aLYG/pCxGNJMIHBycKV2hcZ0bTyEtxoNwsnBleTb1vRq9gE9\nmg6lRvkG2FjbER1/i7T0FJJSE5i9cSxHL+/J9nkDChsl2+bVvxf7Vnhkse/j6r7clKUj9rFsZEiW\nA3/IWFA5tediXq//DgITqenJRF9PRK/Ta3bgL/sW9TFvqfqO71RND/wLzZx/a+sn71amTBm+++67\nXBcwY8YMAgICGDt2LF9++SUzZsxgxozM+wfb2Ngwe/ZsfH19SUhIoG7dugQEBFC1qjKnBZckSVI7\nWxt7hr0+nYW/Tfv72+Ep2f7bIe2msGD7JxhN6bzdbCQtanbOtC7srUaDOXjwII3rZ5ymvtP/9SM1\nPYUh37a2TEUxCSNfbxyDt0dlujYeQh2fJvLsqNlk2emn1LMH/8/L2sqGt5uNYPepn0hKTQSgqL2z\nJgf+kvSiy9a0n+vXr2e6XLRoUUqUKJEnBVSpUoWQkBA8PT25ffs2zZo14+LFi1n+TefOnRk2bNhT\nf/qQ034kSZIKJ/PP9kII6ldqwYnQ/cQkRgNQ0rVcxpQgK2s5L/xfjF3WnYh7oUx7exmVytTM08c+\nHrqfhdunge7FnVohSYVVgc75Hz58+FOn2owcOZJvvvkmVwUUK1bMsm5ACIGbm1uW6wiuX7+Ov78/\n586dw9HxyZ+o5eBfkiRJHVLTktl9+mc2/bGMOMMDy/Uv6mK+7EhJS6LvN03RoWPZyBDsbJTfNlOS\npIJRoHP+ly1b9tTrV6xYka0nCQgIoEaNGk/827x5c6b76XS6LH/2TUhI4K233mLOnDlPHfjnFy3O\nnTPTcjaQ+dRO5lOv7GSztbGnvV9P5gzanGkQ++g+9IWVUq/d9TuXEMJE2RI++Trw13LbBJlPzbSc\nDQrBnP8lS5YAkJ6eztKlSxFCWAbnYWFh2Z76s2vXrmfeZp7uU7JkSW7duoWHh8dT75eWlsabb75J\nr1696Ny5c5bP995771GuXDkAXFxcqFGjBo0bZ8w9Nf9PfZ7LZ86cydXfF+bLZ86cKVT1yHwyn8z3\nYl4e/vrnTJk3ktS0ZOo1eEXxegrr5T8u7QYyzuxbGOqRl+Xlgr5sVljqyc98Z86cIS4uY1e2iIgI\nBg4cSF7IctpPs2bN0Ol0HDhwgCZNmvzzRzodnp6ejBgxgv/7v//LVQFjx46lePHijBs3jhkzZhAb\nG/vEgl8hBH369KF48eLMnj07y8eT034kSZLUKSbhHu/+ry021nYsHhYsp7Q8xbwtkzh4fjsDW0+g\nle+bSpcjSVIByqtpP9ZZ3bhv3z4AJk6cyPTp03P9ZE8zfvx4unXrxpIlS/D29mbdunUA3Lx5k8DA\nQLZu3cqhQ4dYuXIlNWvWpHbt2gB88cUXtG3bNl9qkiRJkgpeMccS+JR6hbBb5zhz/Sh+Ff2VLqnQ\nCbv1904/WWzzKUmSlJVszfmfPn069+/fZ8WKFXz1VcZpwm/cuEFUVFSuC3Bzc2P37t1cvnyZnTt3\n4urqCkDp0qXZunUrkPGTiMlk4tSpU5w8eZKTJ08W6MD/8Z9itETL2UDmUzuZT71yms3v5YwB//HQ\nkLwsJ88p8dolJj/kVkw4Nla2lC3xcr4+l5bbJsh8aqblbFAw+bI1+A8JCaFy5cr8+OOPfPrppwBc\nuXKFd999N1+LkyRJkl4s5q0lT4QdwCRMCldTuFy7cwGAch4VsbayUbgaSZLUKltbffr6+jJr1ixa\ntWpl2ZozOTmZcuXKcffu3YKoM9vknH9JkiT1EkIwfFFH7sXd5NNey6lYuobSJRUam44sZ3VIEK1r\nd6N/wDily5EkqYAV6Faf4eHhtGrVKtN1NjY2GI3GXBcgSZIkSWY6nc7y7f+fhXzqT0GzzPfPwzP7\nSpL04snW4L9q1ar89ttvma4LDg6mRo0X4xsZLc8v03I2kPnUTuZTr9xkq2uZ978/r8rJc0q8dldv\nZwz+KxTAYl8tt02Q+dRMy9mgYPJluduP2ddff81rr71G+/btSU5OZtCgQfz6669s2rQpv+uTJEmS\nXjBVvWpTxM6RqOgwbsdEUrJYWaVLUly8IYbo+FvY2ThQxs1b6XIkSVKxbM35h4zdfVauXEl4eDjl\nypWjV69eeHl55Xd9z03O+ZckSVK/uZsncPjiDt5pMZr2fj2VLkdxJ8MO8uVPI6jqVYcpPb9TuhxJ\nkhRQoHP+AcqUKcO4ceP43//+x/jx47lx4wZdunTJdQGSJEmS9DjzvP/CvuVnQflnyk9VhSuRJEnt\nshz8x8fHM3bsWDp06MC0adMwmUwcPXqU5s2b06JFC0qWLFlQdSpKy/PLtJwNZD61k/nUK7fZalVo\niJXeiguRJ0lIjs+jqvLO8+Y7HrqfwKCWBAa1tKxlMJmMxBti2HFiHf3n+DNwbvNnrnMIu21e7PtK\n7grPJi23TZD51EzL2aAQzPl///33OXPmDK1bt2bDhg2cPHmSPXv2MGzYMNavX4+7u3u+FyhJkiS9\neBztnaniVYdzEcc4dfUQjau1U7qkXFmw/RMeJsUC8N9fRlPU3omEpHgEmWfezv11AstG7kev++e7\nOSGEZfBfEIt9JUnStizn/JcsWZLTp0/j6elJVFQU5cqVY9++fTRt2rQga3wucs6/JEmSNmz780dW\n7PkvDau0YXjHz596n+Oh+5m/fSpCmHiv/TTLdKHCpt83/iSlJjxxvaO9C4aUh5lOaFa7QiPebf8J\nzkWKARAdf5uhCzpQ1N6ZxcP2oNPpCqxuSZIKjwKZ85+YmIinpycAXl5eODo6FuqBvyRJkqQd5oH8\nqWuHSDemPfU+87dNISEpjsTkhwRtmViQ5WWbISUBa6uMH9ptre3p12osC9/fxaoPj7B4+B5Gv/Ff\nnIsUw8HWEXubIpy8eohxy3twLuJPIPN8fznwlyQpt7Ic/BuNRvbs2cOePXsIDg5GCGG5bP73ItDy\n/DItZwOZT+1kPvXKi2yerl6UdffBkJLAhaiTT9web4jBkPLPt+nJqQYuRJ7I9fNmx/PkWx0SxMOk\nWCqUrMaykSG0qdMdl6JuWOkzPhDUfbkpi4buZtnIEGYNWE9lL19iEu7x2ZohrD+4gCs3zwLgU7Jg\n5vuDttsmyHxqpuVsUAjm/Ht4eDBgwADL5eLFi2e6DHDt2rX8qUySJEl64dV92Z/I6DCOh4ZQo3x9\ny/WGlId8vu59TMKEXmeFlZU1aekp/PeXD/m013JKuZVTsOp/nIv4k12nNmClt2ZIu48tA/5ncXcu\nycf/WciGQ4vY+PtSfjr8z7ae2dyZW5IkKUvZ3udfLeScf0mSJO24cvMMk1f2pYRLaeYO2oxOpyMl\nLYnP1w/lUtQpPF29+KTnEpyLFGPWL6M5EXaAUsXK82mvZTg6uCi2n56kAAAgAElEQVRae3JqEmOX\nd+du7A26NhrMm40GPdffnw0/yvS171kWBTvau7B4+Ivxi7skSU8q8H3+JUmSJKmg+ZR6BZeixbkX\nd5PI6FDSjWl8vXEsl6JO4ebowcTu83F1dEevt2LYa9MpV6Iit2LCmb1p7DPXCRSUtQf+x93YG5Qr\nUZFO/9fvuf++evn6FLV3tlzW6+UhW5Kk3JM9STZoeX6ZlrOBzKd2Mp965VU2vU5PXZ8mABy7vJd5\nWyZx+tphnBxcmdj9f3i4lLbc18GuKGPf/AbXosU5F/Eni3d+8cypMk/bd/95/Fu+SzdO89vx1eh1\nVgxpNwVrK5vnfg6Ad9tPxblIMZyLFGNw249z9Bg5oeW2CTKfmmk5GxSCOf+SJEmSpDSXosUBWH9o\nIQAOtkWZ0HUeZYq/9MR93Z1LMqbLbD5ZHci+M5so7Vaejg36WG4XQnA37gZBWyaSnGoAYM7mjxjc\ndjJlS/hQ2s2b09d+Z8H2TwAY0m7Kc28fmpqewsLtnyAQdGzwTq7OymteDCxJkpRX5Jx/SZIkqVAL\nDGppOUEWwJQei6latnaWf3P08h6+3jgGAHsbBxpWbYsh5SGXok4Rkxj9zL/T66wAYdl33962CGO6\nzMbDpQzFnTw4efXQv34wWB0SxKYjyynt5s2Mvj9ia233vJElSZKekFdz/uU3/5IkSZJqFLFz/NeB\nP0D9Si2ws7EnJS2Z5LQk9vz1i+U2JwcXPF29iIy+il6np9ZLDTGa0oi8F8ad2KhMZ91NTjXw6ZrB\nAFjprTAJgfj7g8GczeN5s9EgnB2K4eTgys0H4fzy+2KSUhOBjA8HcuAvSVJho/jg/8GDB3Tv3p3w\n8HC8vb1Zt24drq6ume6TnJyMv78/KSkppKam0qlTJ7744osCq/HgwYM0bty4wJ6vIGk5G8h8aifz\nqVdeZhvSbgoLf5uGEIIh7aZk++9srTMG/wA2Vrb0azWWyl6+lHbzfubJslLSkgg+9TPrDy3EaDLi\nU6oaRpORe7E3Mv1i8CA8CbfyGd/yP/257ahUpuZzpCxctNw2QeZTMy1ng4LJp/iC3xkzZhAQEMDl\ny5dp2bIlM2bMeOI+9vb27N27l1OnTvHXX3+xd+/eAl3wcebMmQJ7roKm5Wwg86mdzKdeeZnNPO/9\nu2HBzzX/fki7KZbFsiM7fUmLWm9QpvhLWZ4l187Ggfb13mbZyP2sGHWIKT2+Y9rbS5n//g5WfHCI\nAQHjKWLnSNJ9QdNXXqNDvV40faUDtSs0+nvK0D+Po2Zabpsg86mZlrNBweRT/Jv/zZs3ExISAkCf\nPn1o1qzZUz8AFClSBIDU1FSMRiNubm4FVmNcXFyBPVdB03I2kPnUTuZTr8KQLa8Xy9ra2BNQuysB\ntbsyI2kG73UYn+n246H7WfjbNIAC3ZknPxSG1y8/yXzqpeVsUDD5FB/837lzB09PTwA8PT25c+fO\nU+9nMpmoU6cOYWFhvPvuu1SrVq0gy5QkSZKkLMmdeSRJUoMCGfwHBARw+/btJ66fPn16pss6ne6Z\nP8fq9XpOnTpFXFwcbdq0Yd++fTRr1iw/yn1CREREgTyPErScDWQ+tZP51EvL2UDmUzuZT720nA0K\nJp/iW31WqVKFffv2UbJkSW7dukXz5s25ePFiln/z6aef4uDgwIcffvjEbcHBwflVqiRJkiRJkiQp\nRhNbfXbs2JHvv/+ecePG8f3339O5c+cn7hMdHY21tTWurq4kJSWxa9cupkx5+o4PefE/RZIkSZIk\nSZK0SPFv/h88eEC3bt2IiIjItNXnzZs3CQwMZOvWrfz111/07dsXk8mEyWSid+/ejBkzRsmyJUmS\nJEmSJEl1FB/8S5IkSZJWCSGy3FpUkiSpoCm+z7+kDvIzoiQpw2QyKV2ClAty4K9eWj/uyb5FvXLb\nNuXgPw8kJiYqXUK+kwcwqbAxGAwcPHiQrVu3kpSUBGjrYG00GoGMnc5MJpOmsgHEx8fz888/s3bt\nWqVLyRc3btxg1KhRpKena+61A3ncUzPZt6hfbtum1dSpU6fmTSkvpvDwcPr160erVq2wt7dHr9fW\n56n79++zcOFCjh8/TtmyZXFyclK6pDyVkJDAgQMHuHTpEikpKZhMJhwdHZUuK09oORtA3759OX78\nOIsXL+bAgQP4+/trqn1OmjSJvXv3Ur16dRwdHdHpdBiNRs30MX369OHKlSt89913REVF4e/vj7W1\nNWlpaVhZWf37AxRyI0eOxN3dnZYtWyKEIDk5GRsbG03kk8c9dZN9i3rdu3ePpUuXUqJECYoVKwZk\n/ILzvB8G5Jz/XOrduzdlypRhxowZPHz4kMTERG7cuIGPjw+urq5Kl5dr3bt3x97enoiICGrWrMln\nn31Gamoq9vb2FC1aVOnycq1z5844Ojpy7do16tSpQ/HixWnQoAHNmzfH3t5e6fJyRcvZQkJC+PDD\nDzl27BgAH3zwAe7u7kycOBFQ/zzrffv20aVLF/r06UNoaCivv/46gYGBlkypqanY2toqXGXO7d27\nl48++og//vgDgA4dOmBjY0OxYsXo3LkznTp1UrjC3AkODmbChAkcOXIEgJkzZxIcHEypUqU0kU8e\n99RL9i3qfu99+OGH/Pjjj3Tu3Jnq1avTu3dvnJycMBgMFClSJNuPo/hWn2p27949bt++zbx58wAY\nMWIEd+7cwcPDAycnJ0aNGoW3t7eyRebCiRMnCA0N5fjx40DGNqq9evXCzc2NV155hcGDB6v6G5HL\nly8TFhbGmTNngIwB5e+//86uXbuws7OjRYsWCleYc1rOBhkHsN69e1su9+3bl169ejFkyBCKFy/O\nypUref3111U7EImIiGDIkCGMHDmS/fv3s3nzZoKDg+nXrx9t27Zl8eLFdOrUiTJlyihdao7s27eP\n9957D4AlS5Zw4sQJDh06xPbt25k4cSJlypTBz89P4Spzbs+ePRw7doydO3diMBgIDg5m5syZhISE\n8NFHH1G6dGnq1aundJk5Io976j7uyb5F3X3L6NGjiYqKom7duly4cIHp06fz8OFDqlatytChQ7P9\nOHLaTy4ULVqUY8eOER8fz8OHD9m/fz9r166lfPnyHDlyBDs7O6pXr650mTkWGhrKkSNHeOmll9i2\nbRtbtmxh69atODg4sG7dOkqXLk3FihWVLjPHUlJS+PXXXylRogSVK1fG29sbX19fbt68ycSJE2na\ntCklS5ZUuswc0XI2IQQVK1bE29sbNzc3dDodJUuWZOfOnTRo0IDjx4/zxRdfMHz4cKVLzbFatWpR\nr1493NzcqFixIr6+vqSlpbFt2zZmzpzJ7t27mTRpktJl5tirr75K3bp1AYiJiWHw4MFUqVKF+vXr\nEx0djcFgoE6dOgpXmXMtW7bk1VdfZdiwYcyfP59FixbRoEED6tevz507dzAYDJb8aiOPe+o+7j3a\nt1SqVIlatWrJvkUl0tPTcXR05Pz58xiNRgIDA7lw4QLffPMNZcuWpVSpUpQqVSpbjyUH/zlknmPl\n4uJCUFAQR48epX79+jRv3pwyZcoQGRnJ4cOH6dixo9Kl5lj58uW5d+8eixcvJjo6mu7du9OsWTOq\nVKnCjRs3OHv2LK1bt1a6zBxzcnKiSJEibNmyhdjYWDw8PChevDh+fn6WA7RaOwknJyecnZ3ZsmUL\nMTExmsqm0+mwtbXF09MTnU5nmccZExPDsWPHWL16NdOmTaNChQpKl5pjCQkJlm8XrayscHNzo3bt\n2lSuXJmvvvqKH374QdX5rK2tLX1ohQoV8PT0tNw2fvx4OnfujI+Pj4IV5pwQgoSEBKpVq8awYcNo\n1KgRzZs3t0yr+Oijj+jSpYsq88njnrqPewaDgaSkJJydnYGMBb+yb1EPvV6PXq+nQoUKLF++nAED\nBrBo0SIqVqxI1apV+euvv2jevHm2HksO/nNIp9Px8OFDXn75ZWrVqsX169dZuHAhMTExlC1blnHj\nxjFy5EhefvllpUvNFT8/P/r06YOHhwcLFizAzc2NEiVK8NFHHxEYGKjafMnJySQmJuLn50dcXBx/\n/fUXJ06c4Pz587i7uzN27Fi6d++u6m94ypcvz8OHDzl79iwnT57URLagoCDWrFnD7NmzSUlJoW7d\nuuj1essHgh49elCnTh3Gjx+vdKk5MnPmTH766SdmzJjBlStXqFevnmV9hpWVFWvWrCElJYWPP/5Y\n4Upz5ty5c6SmpuLs7GwZDD+6PuOzzz4jMTGRjz76SMkycywoKIi1a9cyZ84cEhISqF+/PhUqVMiU\nLyEhgQkTJihcac7I4556j3szZsxg7dq1fP7553h7e2fKIPsWdTAYDNjY2ODi4sL9+/dZtmwZBw4c\nYP/+/VSsWJF69eple1MPueA3B2bOnMmtW7c4cuQI/v7+jB07Fmtraw4dOsTmzZtJS0ujbt26DB48\nWOlSc+TcuXO4uLjg5eVluc5gMLBgwQJOnz5NVFQUtWvXZtasWQpWmXMzZszg+vXrHDt2jNmzZ9Ok\nSRMuXbrEvn37OHz4MPfv37e8rmpz7tw5XF1dLfM1hRAcPnyYs2fPcvToUW7fvq3abJcvX6Zr1658\n9tln6PV6Vq1axbRp0zIdxD7//HN69+5N2bJlFaw0Z8LCwggICGD16tXY2toydepUIiIiGDp0KAMG\nDADg7t276PV63N3dFa72+V24cIFGjRoxbNgwmjVrRq1atXBzcwMyvlGOjo7mt99+o2XLlqqcb/y0\n9vnJJ59YPmQnJCSwY8cOXn31VUqXLq1wtc9PHvfUe9y7cuUKXbt2ZdGiRVy+fJn79+/j4+NDUlIS\nXbt2BWTfUpgFBQVx7do1Tp8+TdeuXRkyZAhnz55l0qRJ9OzZk27duj33Y8rB/3N69ABtY2PD1KlT\nuXHjBiNGjOCdd94BMuZlWVurcy11Vm+iuLg44uLicHBwwMnJSZU7xjzaCV66dIl79+5RtWpVhBC0\nb98egKSkJOzs7FS37dnjr12NGjUsHbl5B4fExEQcHBxUlw2gX79+VK9endGjR5OWlsb48eOJjY1l\nyZIlADx48MDSVtVo1apVbNiwgV9++cVy3c6dOxk+fDgNGzYkKChI1TuNjBs3jgsXLlCvXj2uXLmC\nn58fjRs3plKlSjg6OhIdHa3KgYeZltunPO6p+7jXv39/qlatypgxY1izZg0DBw5k6NChrFu3jmrV\nqrFq1SpcXFyULjPHtNy3ZPWlV3x8PM7OzpbzNDzPDndy2s9z2r59Ow8ePGD06NGUKlWKHj164O3t\nzYQJEzh+/DgBAQHY2dmpdpvBWbNmUaRIEcqWLUtwcDDR0dFYW1vj6OiIi4sLSUlJeHp6WqZaqM2Y\nMWNo0aIF3bp148KFC3zwwQeUKFGCmTNnsmvXLl577TXLvsdq8/hrd//+faysrCxrG27cuEHx4sVV\nmc1gMHDnzh1atmyJp6cnVlZWVKpUidWrV9OrVy8OHz7MyJEjefvtt5UuNcd8fHw4dOgQer3e8m2x\nj48PgYGB7Nixgzp16lj2dVYbo9GIq6srvXr1okOHDhQtWpSQkBD+/PNPbGxsOHr0KH379mXo0KGy\nfRZC8rin3uOewWAgLS2N/v37Y2VlxaJFixgxYgTDhw9nxIgR7Nmzh7p166r2g6nW+5YPP/yQgIAA\n+vbty0svvcSRI0fYtWsXHTt2xN7enrt37+ZszCKk55KQkCAGDx4stm7dmun65ORkERgYKK5evapQ\nZbmXnp4ujhw5Im7duiWEEGLHjh1i0KBBIjAwUGzatEmsWLFCVK5cWZhMJoUrzZnExETx448/itTU\nVCGEEMOGDRPr16+33D5gwAARGhqqVHm5ovXXToiMjDExMZbLKSkpomPHjuLq1auia9euYvny5QpW\nlztGo1GYTCaxcuVKUb9+fTFlyhRx7949ER8fL4QQonbt2mLjxo0KV5k7JpNJGAwGy+Xk5GSxbNky\nERgYKNzc3MTChQsVrC73tNw+5XFP3X2nuXaTySTOnTsnhBAiLS1NCCGEv7//E6+r2mi1b0lMTBRB\nQUHir7/+slx39epV0aZNGyGEEIcPHxbt27fP0WPLwf9zkAdo9b6JzLTcCWr5tXv8wJueni6EEGLO\nnDnC2dlZtGvXTomy8sWFCxfEG2+8IZo0aSJGjRolunTpIlq1aqV0WXnK/J4TQojPPvtMVK9eXcFq\nck/L7VMe97TVdz5qzZo1omXLlgVYTf7TWt+SX18qyDn/OXTx4kUmTJhAdHQ09erV4/r168THx7Nr\n1y6lS8szj87hnD59OmvWrLGcNEqNRBZnfV27di3fffcdu3fvLuCq8ofWXjszc67k5GTs7e25efMm\n9evXZ+PGjao+cQtktM/U1FTs7OyAjLmep0+fpkSJElSoUIFy5copXGHuPf76mUwmFi1aRM2aNWnY\nsKHS5eWaltsnyOOemplzpaSkYGdnR1hYGKNGjWLcuHGafO9poW95fMxiNBqxsrJi7ty5TJ48mUaN\nGrFt27YcP7j0HEwmk0hOTrZcvnTpkli3bp3Yu3evCA8PV7CyvGP+5JyUlCSEyPjmZ/78+eLQoUNK\nlpVnzPnMr2NoaKjo2LGjJvJp+bUzT9cSQohmzZqJU6dOCSGEOHjwoFIl5YmnfTPXrFkzcf36dQWq\nyXvPymf+KfvRb+rU6Fn5tNI+hZDHPbV79D3WrFkzcebMGSGEEOfPn1eqpDyh9b7F7PG2eePGDVGm\nTBlx7NixHD+mHPw/p8cHIFo5QJs9nk9rb6LH82mlExRCe69dXFyciIyMFMHBwZmuX7lypaqnUZgZ\njcanXl69erVo27atEiXlqazyaf3100K+Rz0+eNTace/xfGrvOx8+fCgiIyPF3r17M12vlbb5Irz3\n8vtLBfXt91fAHj58yK1bt9i7dy8ANjY2QMa2fPb29pQvX17J8nItq3wODg7UqFEDQLVbuP1bPvNp\n6KtWrapYjTkVHx9PVFQUe/bsAbT32vXo0YNJkyYxefJkqlevzs8//wyAi4sLX3/9NZDxU69aLV26\nlEOHDvHw4UMg4+yNQgjS09MJCgoCMn7mVaus8s2dOxfQ7uun9nwJCQlERUWxb98+4J8+ZM2aNZo4\n7mWVTwt9Z2BgIB999BHTpk1j4MCBPHjwAKPRqIm2Cdp+75lMJuCfbTvNl81ts1atWgA0atQoV88j\nt/r8Fz179uTs2bP8/PPPTJo0ibJly1KtWjUiIiJ4++23cXd3x2g0qnLfdMg6X8+ePXF3dyc9PV3m\nK4S6dOnCkSNH2LBhA7Nnz6ZkyZJUrVqViIgIevTooepsO3bsYPv27WzZsoUBAwbg6urKl19+yfbt\n23n33XcpX748QgisrKyULjVHfvzxR/r164e9vT3R0dHY29tTrFgxrKysqFmzpmXbPTW+diDzqT1f\nnz592Lt3L1u2bOHAgQM0btwYW1tb/vrrLwYNGoSbm5uqj3tZ5QsMDMTNzU21fefatWsJCQlhxYoV\ndOjQgZCQEMqUKYO3t7cm2qbW33tLliwhKSmJYsWKWbbPFUJw+vTpvG2bufrdQOM2bdok/P39LZcH\nDBgg3NzcRPfu3cWDBw+EEFmvpC/sZD715vvtt9/E//3f/1kur1q1StSpU0d06tRJ3L17Vwih3mxC\nCBEcHCw6d+4sbt68memn92HDhokOHTqI2NhYBavLvenTp4uFCxeKzZs3iz59+ojhw4eLdevWWaZT\nrFixQuEKc0fmU2++NWvWiObNm4vY2FgRGRkpBg4cKA4cOKB0WXlG6/neeecdsWXLFsvluXPnitdf\nf91yedOmTUqUlWc+//xzzb73Vq1aJXQ6nXjvvffEokWLxNmzZzNN581L8pv/LBw7dgxra2sCAgIA\nsLe3p1y5cuj1eg4cOECbNm1UedIIM5lPvfkiIiI4f/48/v7+lp8CBw8ezOHDh1m+fDkdOnRQ5Zko\nzby8vDhx4gRhYWHUqVMHW1tbANq1a8eOHTsoVaoU3t7eyhaZCy+99BI1a9bE19cXf39/IiMjCQ4O\nJiYmhmXLlvHLL78wePBgpcvMMZlPvflmzpxJYGAgNWrUwNnZmfDwcH744Qd69OgBwObNm6lcubLC\nVeaclvMZjUacnZ3x8vLCw8MDgAoVKvDtt9/Sv39/Fi9ezLp16yxZ1UYIYfkFo3bt2pp7723ZsoVu\n3bpRu3ZtduzYwblz5zAYDDg6OuLq6soPP/xgmfaTa/nykUIjLl26JJo0aSJmzZol1q9fL/z8/MSO\nHTtEenq66NGjh+oXPcl86s2XmpoqRo8eLb788kuRkJCQ6bZ33nlH7Nu3T6HKcs/8Tce5c+fEa6+9\nJvz9/cWmTZvExYsXxbVr18RLL70kTpw4oXCVOWdenPb4orXw8HAxZswY4eDgII4fP65EaXlC5lNv\nvvT0dLFr1y7LRghCCHH37l3h6+srUlJSxIIFC0THjh0VrDB3tJ7PzHyeCfOvv+PHjxdr164VDRs2\nVHXf+SxaeO+ZTCYREREh7t27J4QQ4sGDB2LOnDmiZ8+eYtasWWLgwIGiTp06efZ86lzNUkAqVarE\nt99+y6xZs4iJiWHgwIG0bt0agPPnz5OWlqZwhbkj86kzX1paGjY2NvTv359x48axbds2Ro0aReXK\nlbGzs+PAgQOMHDlS6TJzxGAwUKRIEQCqVavGr7/+yvfff8+8efPw8vLizp07dO/endq1aytcac48\nms9kMqHX6zGZTOh0OsuvUu3bt6dOnToKV5ozMp+681lZWdGqVSvLQnMhBCVKlKBt27Zs3LiRFStW\nMG/ePIWrzDkt53u8bT66HsrPz4+uXbvywQcfqLbvXL58OZcuXcLNzQ0HBwd69+6Ni4sLAOXKlcPK\nykrV7z2dTkfZsmUtl4sVK8bw4cOJiIhg3rx5rFq1ioMHD+bZ88lpP0+xfPly1q5dy/Hjx0lLS2Ps\n2LEEBARYTtIyatQo7OzsGDRokMKV5ozMp958BoPBMp2nRIkS9OzZE51Ox5IlSzhz5gzr1q2jZcuW\n9OrVS+FKn9/+/fupUqUKqamptGjRwnK9r68vPXr0wNfXl/79+xMQEKDKxVyP5zNnMJ+4xWQy4ejo\nyJAhQyzTnNRE5lN3PoPBYNkxzJwJMgYlcXFxdO/ena5du9KnTx8ly8wxLed7vG2as6Wnp2NlZYWH\nhwfHjh1jwYIFlpMIqsn+/fuZOHEiLVq0wM7OjosXL7J06VL0ej3Vq1dHCEHRokVV+94zj1lOnjzJ\nyZMnqVy5suU47+Liwp49eyhevDgjRozIs+eUg//HPNrI7O3tOXr0KIsXLwagRo0axMfHk5SUxJgx\nY1TZyGQ+9ebT+uD4gw8+oGXLlpw5c4Zx48ZRsmRJatasCWTs3JCUlISbmxs6nU6VazWelc/8Wt2+\nfZuqVauqrl2ayXzqzfciDB61nO9ZbfPRb/979+5N0aJFFawy55YsWULt2rUZPXo01apVw8/PD1dX\nV4KDg3FwcMDHxwcvLy/VvvcU+WCTZxOINGLy5Mli+vTpQgghEhISRFRUlFizZo0YOHCg2LVrlxBC\nvSf+EELmE0K9+d544w0xbNgw0aZNG1G6dGmxcuXKTLffuHFDCKHOXX4SExPF/PnzLTsV/fzzz6J8\n+fLCz89PREZGij///FOMGDFC4Spz7t/yHT9+XAwfPlzhKnNO5lN3vn/rWxITEzOd4VdttJwvO33n\n0KFDFa4yd0JCQoS/v3+mtRoPHjwQ3377rfjPf/4j4uPjFawud7Ias+zcuVMIkT/HdDn4f0xWjax7\n9+4iLi5OwepyT+ZTZz6tD47NHl+8/NlnnwlXV1eh0+nEhg0bFKoq78h86qbFfFofPGo9n5kW2+aj\nPvvsM1G/fn3x5ZdfiqSkJMv1DRo0EOfOnVOwstxR6oONHPw/hVYbmZnMp15a7eAf3znl0b2NJ0+e\nLFq1alXQJeUpmU/mK+y02reYaTWf1tvmo/lCQkJEYGCg8PPzE1OmTBEjRowQTZo0UbC6vKHEmEXu\n9vMI8+4NEydOpEmTJqxcuZImTZrQoUMHYmNjsbW1pVq1akqXmWMyn3rzmbOZ52yad/yZOHEiKSkp\n/P7777z55psKV5lz5nnT5pypqanY2NiQmJhIeHi45ZTtaiXzyXyFldb7Fq3n03LbhH/yCSFo2rQp\nlSpVIjIyksWLF9O8eXPGjBmjcIU5p+iYJV8+UqiceX7VrVu3xNGjR8WgQYPE6tWrRVRUlMKV5Q2Z\nT73M34KYv8VKSEgQ77zzjjh//rySZeUJ897UQggxevRoyxqG27dvK1VSnpL51E3r+bTctwih7Xxa\nbZvm9XmPfvs/atSoTN+Oa4ESYxY5+H/Mo28iLTYymU+9tNbBx8bGiujoaHHp0iUhxD8d/bhx40Sv\nXr2EEOpcvGwm88l8aqG1vuVxWsun9bYZGRmZ6TUzT2V6NJ/aKf3B5oWf9hMXF0d6ejr379+nUqVK\nCCEAGD9+PHfv3rXstapWMp9682WV7c6dO5QuXRohBJ6engpXmjPvvvuuZfvO6dOnU7JkSSDj/AXm\n07M/frIaNZH5ZL7CSut9i9bzabltArz99tvExsYyYcIEunfvjo2NDSaTCU9PT4YMGQJkPleDmkRF\nRVGqVCmsrTOG30ajEb1eX+Bjlhd+8J+dN5FaGxnIfKDefFru4BcuXMjDhw9ZsWIFkydPZsGCBZZ8\nffv2pXjx4qp93UDmk/kKNy33LaDtfFpum0IIUlNTqV69Onfu3OH7779n8eLFfPvtt/zxxx+8++67\n2Nvbk56ebhk8q01h+WCjE+aPxC+ghQsXsmXLFsubyN3d3fIm6tq1q6rfRCDzqTmflrOlpaXRoEED\nFi1ahJ+fH++//z5nz56lfv36ALi7uzNu3DiFq8w5mU/mK8y03LeAtvNpvW2aXbhwgfnz5zN27Fi2\nbt3KzJkzuXnzJqGhoZQuXVrp8nLE/MFm1KhR3LlzB4PBQE0gw1IAAAjQSURBVFpamuWDTbdu3Qr0\ng436TgOaR9LS0li4cCFTpkyhWLFiCCHYu3cvYWFhhIWFWc4Kq8YOAmQ+NefTcjYAG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+ "text": [ + "" + ] + } + ], + "prompt_number": 37 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "figsize(11., 5)\n", + "returns = np.zeros((n_observations, 4))\n", + "\n", + "for i, (_stock, _returns) in enumerate(stock_returns.iteritems()):\n", + " returns[:, i] = _returns\n", + " plt.subplot(2, 2, i)\n", + " plt.hist(_returns, bins=20,\n", + " normed=True, histtype=\"stepfilled\",\n", + " color=colors[i], alpha=0.7)\n", + " plt.title(_stock + \" returns\")\n", + " plt.xlim(-0.15, 0.15)\n", + "\n", + "plt.tight_layout()\n", + "plt.suptitle(\"Histogram of daily returns\", size=14);" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "display_data", + "png": 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27Thw4AAAIDw8HH369JF9I0JOfefkmmtuwkmU/F2gvoJCgmO3IFg62tdxZLon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\nRBQwDiCIiIiIiChgHEAQEREREVHA/j/MPhkPaI5j+AAAAABJRU5ErkJggg==\n", + "text": [ + "" + ] + } + ], + "prompt_number": 38 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Below we perform the inference on the posterior mean return and posterior covariance matrix. " + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "obs = pm.MvNormal(\"observed returns\", mu, inv_cov_matrix, observed=True, value=returns)\n", + "\n", + "model = pm.Model([obs, mu, inv_cov_matrix])\n", + "mcmc = pm.MCMC()\n", + "\n", + "mcmc.sample(150000, 100000, 3)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + " \r", + "[****************100%******************] 150000 of 150000 complete" + ] + }, + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "\n" + ] + } + ], + "prompt_number": 39 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "figsize(12.5, 4)\n", + "\n", + "# examine the mean return first.\n", + "mu_samples = mcmc.trace(\"returns\")[:]\n", + "\n", + "for i in range(4):\n", + " plt.hist(mu_samples[:, i], alpha=0.8 - 0.05 * i, bins=30,\n", + " histtype=\"stepfilled\", normed=True,\n", + " label=\"%s\" % stock_returns.keys()[i])\n", + "\n", + "plt.vlines(mu_samples.mean(axis=0), 0, 500, linestyle=\"--\", linewidth=.5)\n", + "\n", + "plt.title(\"Posterior distribution of $\\mu$, daily stock returns\")\n", + "plt.legend();" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "display_data", + "png": 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GYPfu3YiLi8O5c+cwefJkFBUVYcWKFdDpdLY/Y86cORPPP/88rrvuOnFHQUREivjTn/4E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\naWqKLMuwXPY+YzE7nxVIAqDzc/1Mucni3kXvrth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+ "text": [ + "" + ] + } + ], + "prompt_number": 41 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "(Plots like these are what inspired the book's cover.)\n", + "\n", + "What can we say about the results above? Clearly TSLA has been a strong performer, and our analysis suggests that it has an almost 1% daily return! Similarly, most of the distribution of AAPL is negative, suggesting that it's *true daily return* is negative.\n", + "\n", + "\n", + "You may not have immediately noticed, but these variables are a whole order of magnitude *less* than our priors on them. For example, to put these one the same scale as the above prior distributions:" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "figsize(11.0, 3)\n", + "for i in range(4):\n", + " plt.subplot(2, 2, i + 1)\n", + " plt.hist(mu_samples[:, i], alpha=0.8 - 0.05 * i, bins=30,\n", + " histtype=\"stepfilled\", normed=True, color=colors[i],\n", + " label=\"%s\" % stock_returns.keys()[i])\n", + " plt.title(\"%s\" % stock_returns.keys()[i])\n", + " plt.xlim(-0.15, 0.15)\n", + "\n", + "plt.suptitle(\"Posterior distribution of daily stock returns\")\n", + "plt.tight_layout()" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "display_data", + "png": 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MGzcONzc3AgIC6N27NytWrDA5Z/Xq1fj5+dG/f39cXFyYMGGCcaPAypw/f5758+fj6+tL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\n5Gmrnair4ufnR7NmzXB2dsbV1ZWDBw+Sk5PDmDF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+ "text": [ + "" + ] + } + ], + "prompt_number": 43 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Why did this occur? Recall how I mentioned that finance has a very very low signal to noise ratio. This implies an environment where inference is much more difficult. One should be careful about over-interpreting these results: notice (in the first figure) that each distribution is positive at 0, implying that the stock may return nothing. Furthermore, the subjective priors influenced the results. From the fund managers point of view, this is good as it reflects his updated beliefs about the stocks, whereas from a neutral viewpoint this can be too subjective of a result. \n", + "\n", + "Below we show the posterior correlation matrix, and posterior standard deviations. An important caveat to know is that the Wishart distribution models the *inverse covariance matrix*, so we must invert it to get the covariance matrix. We also normalize the matrix to acquire the *correlation matrix*. Since we cannot plot hundreds of matrices effectively, we settle by summarizing the posterior distribution of correlation matrices by showing the *mean posterior correlation matrix* (defined on line 2)." + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "inv_cov_samples = mcmc.trace(\"inv_cov_matrix\")[:]\n", + "mean_covariance_matrix = np.linalg.inv(inv_cov_samples.mean(axis=0))\n", + "\n", + "\n", + "def cov2corr(A):\n", + " \"\"\"\n", + " covariance matrix to correlation matrix.\n", + " \"\"\"\n", + " d = np.sqrt(A.diagonal())\n", + " A = ((A.T / d).T) / d\n", + " #A[ np.diag_indices(A.shape[0]) ] = np.ones( A.shape[0] )\n", + " return A\n", + "\n", + "\n", + "plt.subplot(1, 2, 1)\n", + "plt.imshow(cov2corr(mean_covariance_matrix), interpolation=\"none\",\n", + " cmap=plt.cm.hot)\n", + "plt.xticks(np.arange(4), stock_returns.keys())\n", + "plt.yticks(np.arange(4), stock_returns.keys())\n", + "plt.colorbar(orientation=\"vertical\")\n", + "plt.title(\"(mean posterior) Correlation Matrix\")\n", + "\n", + "plt.subplot(1, 2, 2)\n", + "plt.bar(np.arange(4), np.sqrt(np.diag(mean_covariance_matrix)),\n", + " color=\"#348ABD\", alpha=0.7)\n", + "plt.xticks(np.arange(4) + 0.5, stock_returns.keys());\n", + "plt.title(\"(mean posterior) variances of daily stock returns\")\n", + "\n", + "plt.tight_layout();" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "display_data", + "png": 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6i3xJwpX9LSwN2Oov3fpsvpFuXSr3AFhKuL6JkyYhRMtTScR68OABhg59OBRK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\nVFZWYtOmTQ7nWiwWbN++HR999BG8vLzs9qlUKuzatQsHDhw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+ "text": [ + "" + ] + } + ], + "prompt_number": 47 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Looking at the above figures, we can say that it is likely that TSLA has an above-average volatility (looking at the return graph this is quite clear). The correlation matrix shows that there are no strong correlations present, but perhaps GOOG and AMZN express a higher correlation (about 0.30). \n", + "\n", + "With this Bayesian analysis of the stock market, we can throw it into a Mean-Variance optimizer (which I cannot stress enough to not use with frequentist point estimates) and find the minimum. This optimizer balances the tradeoff between a high return and high variance.\n", + "\n", + "$$ w_{opt} = \\min_{w} \\frac{1}{N}\\left( \\sum_{i=0}^N \\mu_i^T w - \\frac{\\lambda}{2}w^T\\Sigma_i w \\right)$$\n", + "\n", + "where $\\mu_i$ and $\\Sigma_i$ are the $i$th posterior estimate of the mean returns and the covariance matrix. This is another example of loss function optimization." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Protips for the Wishart distribution\n", + "\n", + "If you plan to be using the Wishart distribution, read on. Else, feel free to skip this. \n", + "\n", + "In the problem above, the Wishart distribution behaves pretty nicely. Unfortunately, this is rarely the case. The problem is that estimating an $NxN$ covariance matrix involves estimating $\\frac{1}{2}N(N-1)$ unknowns. This is a large number even for a modest $N$. Personally, I've tried performing a similar simulation as above with $N = 23$ stocks, and ended up giving considering that I was requesting my MCMC simulation to estimate at least $\\frac{1}{2}23*22 = 253$ additional unknowns (plus the other interesting unknowns in the problem). This is not easy for MCMC. Essentially, you are asking you MCMC to traverse a 250+ dimensional space. And the problem seemed so innocent initially! Below are some tips, in order of supremacy:\n", + "\n", + "1. Use conjugancy if it applies. See section below.\n", + "\n", + "2. Use a good starting value. What might be a good starting value? Why, the data's sample covariance matrix is! Note that this is not empirical Bayes: we are not touching the prior's parameters, we are modifying the starting value of the MCMC. Due to numerical instability, it is best to truncate the floats in the sample covariance matrix down a few degrees of precision (e.g. instability can cause unsymmetrical matrices, which can cause PyMC to cry.). \n", + "\n", + "3. Provide as much domain knowledge in the form of priors, if possible. I stress *if possible*. It is likely impossible to have an estimate about each $\\frac{1}{2}N(N-1)$ unknown. In this case, see number 4.\n", + "\n", + "4. Use empirical Bayes, i.e. use the sample covariance matrix as the prior's parameter.\n", + "\n", + "5. For problems where $N$ is very large, nothing is going to help. Instead, ask, do I really care about *every* correlation? Probably not. Furthermore ask yourself, do I really really care about correlations? Possibly not. In finance, we can set an informal hierarchy of what we might be interested in the most: first a good estimate of $\\mu$, the variances along the diagonal of the covariance matrix are secondly important, and finally the correlations are least important. So, it might be better to ignore the $\\frac{1}{2}(N-1)(N-2)$ correlations and instead focus on the more important unknowns.\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Conjugate Priors\n", + "\n", + "Recall that a $\\text{Beta}$ prior with $\\text{Binomial}$ data implies a $\\text{Beta}$ posterior. Graphically:\n", + "\n", + "$$ \\underbrace{\\text{Beta}}_{\\text{prior}} \\cdot \\overbrace{\\text{Binomial}}^{\\text{data}} = \\overbrace{\\text{Beta}}^{\\text{posterior} } $$ \n", + "\n", + "Notice the $\\text{Beta}$ on both sides of this equation (no, you cannot cancel them, this is not a *real* equation). This is a really useful property. It allows us to avoid using MCMC, since the posterior is known in closed form. Hence inference and analytics are easy to derive. This shortcut was the heart of the Bayesian Bandit algorithm above. Fortunately, there is an entire family of distributions that have similar behaviour. \n", + "\n", + "Suppose $X$ comes from, or is believed to come from, a well-known distribution, call it $f_{\\alpha}$, where $\\alpha$ are possibly unknown parameters of $f$. $f$ could be a Normal distribution, or Binomial distribution, etc. For particular distributions $f_{\\alpha}$, there may exist a prior distribution $p_{\\beta}$, such that:\n", + "\n", + "$$ \\overbrace{p_{\\beta}}^{\\text{prior}} \\cdot \\overbrace{f_{\\alpha}(X)}^{\\text{data}} = \\overbrace{p_{\\beta'}}^{\\text{posterior} } $$ \n", + "\n", + "where $\\beta'$ is a different set of parameters *but $p$ is the same distribution as the prior*. A prior $p$ that satisfies this relationship is called a *conjugate prior*. As I mentioned, they are useful computationally, as we can avoided approximate inference using MCMC and go directly to the posterior. This sounds great, right?\n", + "\n", + "Unfortunately, not quite. There are a few issues with conjugate priors.\n", + "\n", + "1. The conjugate prior is not objective. Hence it is only useful when a subjective prior is required. It is not guaranteed that the conjugate prior can accommodate the practitioner's subjective opinion.\n", + "\n", + "2. There typically exist conjugate priors for simple, one dimensional problems. For larger problems, involving more complicated structures, hope is lost to find a conjugate prior. For smaller models, Wikipedia has a nice [table of conjugate priors](http://en.wikipedia.org/wiki/Conjugate_prior#Table_of_conjugate_distributions).\n", + "\n", + "Really, conjugate priors are only useful for their mathematical convenience: it is simple to go from prior to posterior. I personally see conjugate priors as only a neat mathematical trick, and offer little insight into the problem at hand. " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Jefferys Priors\n", + "\n", + "Earlier, we talked about objective priors rarely being *objective*. Partly what we mean by this is that we want a prior that doesn't bias our posterior estimates. The flat prior seems like a reasonable choice as it assigns equal probability to all values. \n", + "\n", + "But the flat prior is not transformation invariant. What does this mean? Suppose we have a random variable $ \\bf X $ from Bernoulli($\\theta$). We define the prior on $p(\\theta) = 1$. " + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "figsize(12.5, 5)\n", + "\n", + "x = np.linspace(0.000, 1, 150)\n", + "y = np.linspace(1.0, 1.0, 150)\n", + "lines = plt.plot(x, y, color=\"#A60628\", lw=3)\n", + "plt.fill_between(x, 0, y, alpha=0.2, color=lines[0].get_color())\n", + "plt.autoscale(tight=True)\n", + "plt.ylim(0, 2);" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "display_data", + "png": 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ykhVSyAtZ5X1i5rjvhDc3N0d/f3/ceuutMTY2Fhs3boxFixbFtm3bIiJi06ZNsWPHjti6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\nRU5ErkJggg==\n", + "text": [ + "" + ] + } + ], + "prompt_number": 48 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now, let's transform $\\theta$ with the function $\\psi = log \\frac{\\theta}{1-\\theta}$. This is just a function to stretch $\\theta$ across the real line. Now how likely are different values of $\\psi$ under our transformation." + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "figsize(12.5, 5)\n", + "\n", + "psi = np.linspace(-10, 10, 150)\n", + "y = np.exp(psi) / (1 + np.exp(psi)) ** 2\n", + "lines = plt.plot(psi, y, color=\"#A60628\", lw=3)\n", + "plt.fill_between(psi, 0, y, alpha=0.2, color=lines[0].get_color())\n", + "plt.autoscale(tight=True)\n", + "plt.ylim(0, 1);" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "display_data", + "png": 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+ "text": [ + "" + ] + } + ], + "prompt_number": 49 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Oh no! Our function is no longer flat. It turns out flat priors do carry information in them after all. The point of Jeffreys Priors is to create priors that don't accidentally become informative when you transform the variables you placed them originally on.\n", + "\n", + "Jeffreys Priors are defined as:\n", + "\n", + "$$p_J(\\theta) \\propto \\mathbf{I}(\\theta)^\\frac{1}{2}$$\n", + "$$\\mathbf{I}(\\theta) = - \\mathbb{E}\\bigg[\\frac{d^2 \\text{ log } p(X|\\theta)}{d\\theta^2}\\bigg]$$\n", + "\n", + "$\\mathbf{I}$ being the *Fisher information*" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "##Effect of the prior as $N$ increases\n", + "\n", + "In the first chapter, I proposed that as the amount of observations, or data, that we posses, the less the prior matters. This is intuitive. After all, our prior is based on previous information, and eventually enough new information will shadow our previous information's value. The smothering of the prior by enough data is also helpful: if our prior is significantly wrong, then the self-correcting nature of the data will present to us a *less wrong*, and eventually *correct*, posterior. \n", + "\n", + "We can see this mathematically. First, recall Bayes Theorem from Chapter 1 that relates the prior to the posterior. The following is a sample from [What is the relationship between sample size and the influence of prior on posterior?](http://stats.stackexchange.com/questions/30387/what-is-the-relationship-between-sample-size-and-the-influence-of-prior-on-poste)[1] on CrossValidated.\n", + "\n", + ">The posterior distribution for a parameter $\\theta$, given a data set ${\\bf X}$ can be written as \n", + "\n", + "$$p(\\theta | {\\bf X}) \\propto \\underbrace{p({\\bf X} | \\theta)}_{{\\rm likelihood}} \\cdot \\overbrace{ p(\\theta) }^{ {\\rm prior} } $$\n", + "\n", + "\n", + "\n", + ">or, as is more commonly displayed on the log scale, \n", + "\n", + "$$ \\log( p(\\theta | {\\bf X}) ) = c + L(\\theta;{\\bf X}) + \\log(p(\\theta)) $$\n", + "\n", + ">The log-likelihood, $L(\\theta;{\\bf X}) = \\log \\left( p({\\bf X}|\\theta) \\right)$, **scales with the sample size**, since it is a function of the data, while the prior density does not. Therefore, as the sample size increases, the absolute value of $L(\\theta;{\\bf X})$ is getting larger while $\\log(p(\\theta))$ stays fixed (for a fixed value of $\\theta$), thus the sum $L(\\theta;{\\bf X}) + \\log(p(\\theta))$ becomes more heavily influenced by $L(\\theta;{\\bf X})$ as the sample size increases. \n", + "\n", + "There is an interesting consequence not immediately apparent. As the sample size increases, the chosen prior has less influence. Hence inference converges regardless of chosen prior, so long as the areas of non-zero probabilities are the same. \n", + "\n", + "Below we visualize this. We examine the convergence of two posteriors of a Binomial's parameter $\\theta$, one with a flat prior and the other with a biased prior towards 0. As the sample size increases, the posteriors, and hence the inference, converge." + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "figsize(12.5, 15)\n", + "\n", + "p = 0.6\n", + "beta1_params = np.array([1., 1.])\n", + "beta2_params = np.array([2, 10])\n", + "beta = stats.beta\n", + "\n", + "x = np.linspace(0.00, 1, 125)\n", + "data = pm.rbernoulli(p, size=500)\n", + "\n", + "plt.figure()\n", + "for i, N in enumerate([0, 4, 8, 32, 64, 128, 500]):\n", + " s = data[:N].sum()\n", + " plt.subplot(8, 1, i + 1)\n", + " params1 = beta1_params + np.array([s, N - s])\n", + " params2 = beta2_params + np.array([s, N - s])\n", + " y1, y2 = beta.pdf(x, *params1), beta.pdf(x, *params2)\n", + " plt.plot(x, y1, label=r\"flat prior\", lw=3)\n", + " plt.plot(x, y2, label=\"biased prior\", lw=3)\n", + " plt.fill_between(x, 0, y1, color=\"#348ABD\", alpha=0.15)\n", + " plt.fill_between(x, 0, y2, color=\"#A60628\", alpha=0.15)\n", + " plt.legend(title=\"N=%d\" % N)\n", + " plt.vlines(p, 0.0, 7.5, linestyles=\"--\", linewidth=1)\n", + " #plt.ylim( 0, 10)#" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "metadata": {}, + "output_type": "display_data", + "png": 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/LJvcZWsB8GkTSWi/JEL6JxLaL4nAHp1Ru+ldshBCCCGaB5fN852dnc2wYcM4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PGEXTgGdbAYwCX0HnaXTHGdg8JaO0V1dgprHRTV2imtb90AYa1KIslkoH+4gdRwo/cRbuz5M7AI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MtaqaqqMptmD7wFEqDhzFknf+N0bW0jKqjpZRdfRE/fIzGtC6u6H1cEfr4YbWxYjGaETjYkTr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\n6/26RqWdnD9/nsGDB9OzZ0/69evH3XffXSvwFkII0XqZLpdw8q0FWjn2d+O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+ "text": [ + "" + ] + } + ], + "prompt_number": 50 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Keep in mind, not all posteriors will \"forget\" the prior this quickly. This example was just to show that *eventually* the prior is forgotten. The \"forgetfulness\" of the prior as we become awash in more and more data is the reason why Bayesian and Frequentist inference eventually converge as well." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Bayesian perspective of Penalized Linear Regressions\n", + "\n", + "There is a very interesting relationship between a penalized least-squares regression and Bayesian priors. A penalized linear regression is a optimization problem of the form:\n", + "\n", + "$$ \\text{argmin}_{\\beta} \\;\\; (Y - X\\beta)^T(Y - X\\beta) + f(\\beta)$$\n", + "\n", + "for some function $f$ (typically a norm like $|| \\cdot ||_p^p$). \n", + "\n", + "We will first describe the probabilistic interpretation of least-squares linear regression. Denote our response variable $Y$, and features are contained in the data matrix $X$. The standard linear model is:\n", + "\n", + "\\begin{equation}\n", + "Y = X\\beta + \\epsilon\n", + "\\end{equation}\n", + "\n", + "where $\\epsilon \\sim \\text{Normal}( {\\bf 0}, \\sigma{\\bf I })$. Simply, the observed $Y$ is a linear function of $X$ (with coefficients $\\beta$) plus some noise term. Our unknown to be determined is $\\beta$. We use the following property of Normal random variables:\n", + "\n", + "$$ \\mu' + \\text{Normal}( \\mu, \\sigma ) \\sim \\text{Normal}( \\mu' + \\mu , \\sigma ) $$\n", + "\n", + "to rewrite the above linear model as:\n", + "\n", + "\\begin{align}\n", + "& Y = X\\beta + \\text{Normal}( {\\bf 0}, \\sigma{\\bf I }) \\\\\\\\\n", + "& Y = \\text{Normal}( X\\beta , \\sigma{\\bf I }) \\\\\\\\\n", + "\\end{align}\n", + "\n", + "In probabilistic notation, denote $f_Y(y \\; | \\; \\beta )$ the probability distribution of $Y$, and recalling the density function for a Normal random variable (see [here](http://en.wikipedia.org/wiki/Normal_distribution) ):\n", + "\n", + "$$ f_Y( Y \\; |\\; \\beta, X) = L(\\beta|\\; X,Y)= \\frac{1}{\\sqrt{ 2\\pi\\sigma} } \\exp \\left( \\frac{1}{2\\sigma^2} (Y - X\\beta)^T(Y - X\\beta) \\right) $$\n", + "\n", + "This is the likelihood function for $\\beta$. Taking the $\\log$:\n", + "\n", + "$$ \\ell(\\beta) = K - c(Y - X\\beta)^T(Y - X\\beta) $$\n", + "\n", + "where $K$ and $c>0$ are constants. Maximum likelihood techniques wish to maximize this for $\\beta$, \n", + "\n", + "$$\\hat{ \\beta } = \\text{argmax}_{\\beta} \\;\\; - (Y - X\\beta)^T(Y - X\\beta) $$\n", + "\n", + "Equivalently we can *minimize the negative* of the above:\n", + "\n", + "$$\\hat{ \\beta } = \\text{argmin}_{\\beta} \\;\\; (Y - X\\beta)^T(Y - X\\beta) $$\n", + "\n", + "This is the familiar least-squares linear regression equation. Therefore we showed that the solution to a linear least-squares is the same as the maximum likelihood assuming Normal noise. Next we extend this to show how we can arrive at penalized linear regression by a suitable choice of prior on $\\beta$. \n", + "\n", + "#### Penalized least-squares\n", + "\n", + "In the above, once we have the likelihood, we can include a prior distribution on $\\beta$ to derive to the equation for the posterior distribution:\n", + "\n", + "$$P( \\beta | Y, X ) = L(\\beta|\\;X,Y)p( \\beta )$$\n", + "\n", + "where $p(\\beta)$ is a prior on the elements of $\\beta$. What are some interesting priors? \n", + "\n", + "1\\. If we include *no explicit* prior term, we are actually including an uninformative prior, $P( \\beta ) \\propto 1$, think of it as uniform over all numbers. \n", + "\n", + "2\\. If we have reason to believe the elements of $\\beta$ are not too large, we can suppose that *a priori*:\n", + "\n", + "$$ \\beta \\sim \\text{Normal}({\\bf 0 }, \\lambda {\\bf I } ) $$\n", + "\n", + "The resulting posterior density function for $\\beta$ is *proportional to*:\n", + "\n", + "$$ \\exp \\left( \\frac{1}{2\\sigma^2} (Y - X\\beta)^T(Y - X\\beta) \\right) \\exp \\left( \\frac{1}{2\\lambda^2} \\beta^T\\beta \\right) $$\n", + "\n", + "and taking the $\\log$ of this, and combining and redefining constants, we arrive at:\n", + "\n", + "$$ \\ell(\\beta) \\propto K - (Y - X\\beta)^T(Y - X\\beta) - \\alpha \\beta^T\\beta $$\n", + "\n", + "we arrive at the function we wish to maximize (recall the point that maximizes the posterior distribution is the MAP, or *maximum a posterior*):\n", + "\n", + "$$\\hat{ \\beta } = \\text{argmax}_{\\beta} \\;\\; -(Y - X\\beta)^T(Y - X\\beta) - \\alpha \\;\\beta^T\\beta $$\n", + "\n", + "Equivalently, we can minimize the negative of the above, and rewriting $\\beta^T \\beta = ||\\beta||_2^2$:\n", + "\n", + "$$\\hat{ \\beta } = \\text{argmin}_{\\beta} \\;\\; (Y - X\\beta)^T(Y - X\\beta) + \\alpha \\;||\\beta||_2^2$$\n", + "\n", + "This above term is exactly Ridge Regression. Thus we can see that ridge regression corresponds to the MAP of a linear model with Normal errors and a Normal prior on $\\beta$.\n", + "\n", + "3\\. Similarly, if we assume a *Laplace* prior on $\\beta$, ie. \n", + "\n", + "$$ f_\\beta( \\beta) \\propto \\exp \\left(- \\lambda ||\\beta||_1 \\right)$$\n", + "\n", + "and following the same steps as above, we recover:\n", + "\n", + "$$\\hat{ \\beta } = \\text{argmin}_{\\beta} \\;\\; (Y - X\\beta)^T(Y - X\\beta) + \\alpha \\;||\\beta||_1$$\n", + "\n", + "which is LASSO regression. Some important notes about this equivalence. The sparsity that is a result of using a LASSO regularization is not a result of the prior assigning high probability to sparsity. Quite the opposite actually. It is the combination of the $|| \\cdot ||_1$ function and using the MAP that creates sparsity on $\\beta$: [purely a geometric argument](http://camdp.com/blogs/least-squares-regression-l1-penalty). The prior does contribute to an overall shrinking of the coefficients towards 0 though. An interesting discussion of this can be found in [2].\n", + "\n", + "For an example of Bayesian linear regression, see Chapter 4's example on financial losses." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "##### References\n", + "\n", + "1. Macro, . \"What is the relationship between sample size and the influence of prior on posterior?.\" 13 Jun 2013. StackOverflow, Online Posting to Cross-Validated. Web. 25 Apr. 2013.\n", + "\n", + "2. Starck, J.-L., , et al. \"Sparsity and the Bayesian Perspective.\" Astronomy & Astrophysics. (2013): n. page. Print.\n", + "\n", + "3. Kuleshov, Volodymyr, and Doina Precup. \"Algorithms for the multi-armed bandit problem.\" Journal of Machine Learning Research. (2000): 1-49. Print.\n", + "\n", + "4. Gelman, Andrew. \"Prior distributions for variance parameters in hierarchical models.\" Bayesian Analysis. 1.3 (2006): 515-533. Print.\n", + "\n", + "5. Gelman, Andrew, and Cosma R. Shalizi. \"Philosophy and the practice of Bayesian statistics.\" British Journal of Mathematical and Statistical Psychology. (2012): n. page. Web. 17 Apr. 2013.\n", + "\n", + "6. http://jmlr.csail.mit.edu/proceedings/papers/v22/kaufmann12/kaufmann12.pdf\n", + "\n", + "7. James, Neufeld. \"Reddit's \"best\" comment scoring algorithm as a multi-armed bandit task.\" Simple ML Hacks. Blogger, 09 Apr 2013. Web. 25 Apr. 2013.\n", + "\n", + "8. Oakley, J. E., Daneshkhah, A. and O\u2019Hagan, A. Nonparametric elicitation using the roulette method. Submitted to Bayesian Analysis.\n", + "\n", + "9. \"Eliciting priors from experts.\" 19 Jul 2010. StackOverflow, Online Posting to Cross-Validated. Web. 1 May. 2013. .\n", + "\n", + "10. Taleb, Nassim Nicholas (2007), The Black Swan: The Impact of the Highly Improbable, Random House, ISBN 978-1400063512" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from IPython.core.display import HTML\n", + "\n", + "\n", + "def css_styling():\n", + " styles = open(\"../styles/custom.css\", \"r\").read()\n", + " return HTML(styles)\n", + "css_styling()" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "html": [ + "\n", + "\n" + ], + "metadata": {}, + "output_type": "pyout", + "prompt_number": 1, + "text": [ + "" + ] + } + ], + "prompt_number": 1 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [], + "language": "python", + "metadata": {}, + "outputs": [] + } + ], + "metadata": {} + } + ] } \ No newline at end of file diff --git a/Chapter6_Priorities/README.md b/Chapter6_Priorities/README.md index 4c83950a..f3bb97ba 100644 --- a/Chapter6_Priorities/README.md +++ b/Chapter6_Priorities/README.md @@ -1,4 +1,4 @@ -Chapter 6: Getting our priorities straight -=========== - -### [Read it online here](http://nbviewer.ipython.org/urls/raw.github.com/CamDavidsonPilon/Probabilistic-Programming-and-Bayesian-Methods-for-Hackers/master/Chapter6_Priorities/Priors.ipynb) +Chapter 6: Getting our priorities straight +=========== + +### [Read it online here](http://nbviewer.ipython.org/urls/raw.github.com/CamDavidsonPilon/Probabilistic-Programming-and-Bayesian-Methods-for-Hackers/master/Chapter6_Priorities/Priors.ipynb) diff --git a/Chapter6_Priorities/d3bandits.js b/Chapter6_Priorities/d3bandits.js index 98af25ea..00795ee0 100644 --- a/Chapter6_Priorities/d3bandits.js +++ b/Chapter6_Priorities/d3bandits.js @@ -1,334 +1,334 @@ - var ARMS = [0,0,0,0,0,0]; - var _PROBS = [ rbeta(2,9), rbeta(5,9), rbeta(5,9) ]; - var BB_RUN = 0; - - d3.select( "#reveal-div" ) - .selectAll("p") - .data( _PROBS ) - .enter() - .append("p") - .text( function(d,i){ return "Arm " + (i + 1) + ": " +d.toFixed(4); } ) - - - function pdfbeta(x_array,a,b){ - //x is an array - _beta = Beta(a,b); - function _pdfbeta(x){ - return ( Math.pow(x,a-1)*Math.pow(1-x, b - 1) )/_beta - } - - return x_array.map( _pdfbeta ) - } - - function Beta(a,b){ - //stirlings approx - // use logs and exponentials to avoid underflow - // with logs is still giving me errors - - //var n = Math.pow(a, a - 0.5)*Math.pow(b, b-0.5) - - var log_n = Math.log(a)*(a - 0.5) + Math.log(b)*( b-0.5) - //var d = Math.pow( a + b, a+ b-0.5) - var log_d = Math.log( a + b)*(a+ b-0.5) - return Math.sqrt( 2*Math.PI)*Math.exp(log_n - log_d) - } - - - function rbeta(a,b){ - //from Simulation and MC, Wiley - - var p = a/b; - if (Math.min(a,b) <= 1){ - var lambda = Math.min(a,b) - }else{ - var lambda = Math.sqrt( (2*a*b - a - b)/(a+b-2) ) - } - - while (1){ - var R1 = Math.random(); - var R2 = Math.random(); - var y = Math.pow( ( 1./R1 - 1.), 1./lambda ); - if ( 4*R1*R2*R2 < (Math.pow(y, a - lambda)*Math.pow( (1.+ p)/(1 + p*y) , a + b ) )){ - return (p*y)/(1+ p*y) - } - } - } - - function rbeta_array( arm_counts){ - // to be used with ARMS with uniform prior. - samples = [] - for (var i=0; i < arm_counts.length/2; i++){ - samples.push( - rbeta(arm_counts[2*i + 1]+1, 1+arm_counts[2*i] - arm_counts[2*i+1] ) - ) - } - return samples - } - - function draw_arm( p ){ - if ( Math.random() < p){ return 1 } else { return 0 } - } - - - function update_arm( arm_number ){ - var result = draw_arm(_PROBS[arm_number] ); - ARMS[2*arm_number] += 1; - ARMS[2*arm_number+1] += result; - redraw(arm_number); - return - } - - - function bayesian_bandits(){ - //for (var i = 0; i < n_pulls; i++ ){ - //sample from Beta distributions - var samples = rbeta_array(ARMS); - var select = samples.indexOf( d3.max( samples) ); - update_arm( select ); - if (BB_RUN < 300){ - BB_RUN += 1; - window.setTimeout( bayesian_bandits, 100 ) - } - else{ - return - } - //} - } - - var x_array = []; - var _N = 100; - var max_data = 10 - for ( var i =0; i < _N; i++ ){ - x_array.push( .01*i ) - } - - var colors = ["#348ABD", "#A60628", "#7A68A6"]; - var fill_colors = [ "rgba(52, 128, 189,0.1)", "rgba(166, 6, 40, 0.1 )", "rgba( 122, 104, 166,0.1 )"]; - - var w = 600, - h = 150, - margin = 15, - y = d3.scale.linear().domain([0, max_data]).range([h - margin,0 + margin ]), - x = d3.scale.linear().domain([0,_N]).range([0 + margin, w - margin]) - - var vis = d3.select("#beta-graphs") - .append("svg:svg") - .attr("width", w ) - .attr("height", h ) - - var g = vis.append("svg:g") - - var line = d3.svg.line() - .x(function(d, i) { return x(i); }) - .y(y) - - - for ( var i =0; i < 3; i++){ - var _data = pdfbeta(x_array, 1 + ARMS[2*i+1],1+ARMS[2*i] - ARMS[2*i+1] ); - g.selectAll('path.line') - .data( [_data] ) - .enter() - .append("svg:path") - .attr("stroke", colors[i] ) - //.attr("fill", fill_colors[i] ) - //.attr("fill", fill_colors[i] ) - //.attr("stroke-width", 0 ) - .attr("d", line ) - .attr("id", "line-" + i ); - } - - - g.append("svg:line") - .attr("x1", x(0)) - .attr("y1", y(0)) - .attr("x2", x(w)) - .attr("y2", y(0)) - - g.append("svg:line") - .attr("x1", x(0)) - .attr("y1", y(0)) - .attr("x2", x(0)) - .attr("y2", y(max_data)) - - g.selectAll(".xLabel") - .data( d3.range(0,1.2,.2) ) - .enter().append("svg:text") - .attr("class", "xLabel") - .text(String) - .attr("x", function(d) { return x(100*d) }) - .attr("y", h) - .attr("text-anchor", "middle") - .attr("dy", 0.0 ) - /* - g.selectAll(".yLabel") - .data(y.ticks(4)) - .enter().append("svg:text") - .attr("class", "yLabel") - .text(String) - .attr("x", 0) - .attr("y", function(d) { return y(d) }) - .attr("text-anchor", "right") - .attr("dy", 4) - */ - g.selectAll(".xTicks") - .data(x.ticks(5)) - .enter().append("svg:line") - .attr("class", "xTicks") - .attr("x1", function(d) { return x(d); }) - .attr("y1", y(0)) - .attr("x2", function(d) { return x(d); }) - .attr("y2", y(-0.1)) - - vis.append("text") - .attr("x", (w / 2)) - .attr("y", 15 ) - .attr("text-anchor", "middle") - .style("font-size", "17px") - .text("Posterior Distributions"); - - /* - g.selectAll(".yTicks") - .data(y.ticks(4)) - .enter().append("svg:line") - .attr("class", "yTicks") - .attr("y1", function(d) { return -1 * y(d); }) - .attr("x1", x(-0.3)) - .attr("y2", function(d) { return -1 * y(d); }) - .attr("x2", x(0)) - */ - - - - - - - var data = ARMS; - var labellist = ["Arm 1", "", "Arm 2", "", "Arm 3", ""]; - - var w_bar = 600, - h_bar = 170, - labelpad = 50, - x_bar = d3.scale.linear().domain([0, 100]).range([0, w_bar]), - y_bar = d3.scale.ordinal().domain(d3.range(data.length)).rangeBands([0, h_bar], .2); - - var vis = d3.select("#paired-bar-chart") - .append("svg:svg") - .attr("width", w_bar + 40) - .attr("height", h_bar + 20) - .append("svg:g") - - var bars = vis.selectAll("g.bar") - .data(data) - .enter().append("svg:g") - .attr("class", "bar") - .attr("transform", function(d, i) { return "translate(" + labelpad + "," + y_bar(i) + ")"; }) - - - bars.append("svg:rect") - .attr("fill", function(d, i) { return (i%2)? colors[i]: fill_colors[i]; } ) //Alternate colors - .attr("width", function(d,i){ return x_bar(d)*0.5 }) - .attr("height", y_bar.rangeBand()); - - bars.append("svg:text") - .attr("x", 0) - .attr("y", 10 + y_bar.rangeBand() / 2) - .attr("dx", -6) - .attr("dy", ".50em") - .attr("text-anchor", "end") - .text(function(d, i) { return labellist[i]; }); - - var counts = bars.append("svg:text") - .attr("x", 0) - .attr("y", 10 + y_bar.rangeBand() / 2) - .attr("dx", -6) - .attr("dy", "-.40em") - .attr("text-anchor", "end") - .text(function(d, i) { return ""; }); - - - var rules = vis.selectAll("g.rule") - .data(x.ticks(10)) - .enter().append("svg:g") - .attr("class", "rule") - .attr("transform", function(d) { return "translate(" + x_bar(d) + ", 0)"; }); - - - rules.append("svg:line") - .attr("y1", 0) - .attr("y2", h_bar) - .attr("x1", labelpad) - .attr("x2", labelpad) - .attr("stroke", "white") - .attr("stroke-opacity", .3); - - - - function redraw(arm_number){ - - var _data = [] - for ( var i =0; i < 3; i++){ - _data.push( pdfbeta(x_array, 1 + ARMS[2*i+1],1+ARMS[2*i] - ARMS[2*i+1] ) ); - - } - //update what is max. - max_data = d3.max( [ - 10, - d3.max(_data[0]), - d3.max(_data[1]), - d3.max(_data[2]) ]) - - y = d3.scale.linear().domain([0, max_data]).range([h - margin,0 + margin ]) - line = d3.svg.line() - .x(function(d, i) { return x(i); }) - .y(y) - - for ( var i =0; i < 3; i++){ - g.select("#line-" + i) - .data( [_data[i]] ) - .attr("d", line ) - } - - - - - - - bars.data(ARMS) - .enter().append("svg:g") - .attr("class", "bar") - .attr("transform", function(d, i) { return "translate(" + labelpad + "," + y(i) + ")"; }); - - - bars.append("svg:rect") - .attr("fill", function(d, ix) {_ix = Math.floor(ix/2); return (ix%2)? fill_colors[_ix]: colors[_ix]; } ) //Alternate colors - .attr("width", function(d,i){ return x_bar(d)*0.5 }) - .attr("height", y_bar.rangeBand()); - - - counts - .attr("x", 0) - .attr("y", 10 + y_bar.rangeBand() / 2) - .attr("dx", function( d,i) { return !(i%2) ? 50 + 3.2*data[i] : 67 + 3.2*data[i] ;}) - .attr("dy", "-.40em") - .attr("text-anchor", "end") - .text(function(d, i) { return !(i%2) ? data[i] + " pulls" : data[i] + " rewards" ;}); - - //update scoreboard - var rewards = ARMS[1] + ARMS[3] + ARMS[5]; - var pulls = ARMS[0] + ARMS[2] + ARMS[4]; - document.getElementById("rewards").innerHTML = rewards ; - document.getElementById("pulls").innerHTML = pulls ; - document.getElementById("ratio").innerHTML = (rewards/pulls).toFixed(3) ; - - } - - - d3.select( "#reveal-div" ) - .selectAll("p") - .data( _PROBS ) - .enter() - .append("span") - .attr( "style", "margin-left:15; margin-right: 30px; margin-top:0" ) - .text( function(d,i){ return d.toFixed(4) ; } ) - //redraw() //to initialize + var ARMS = [0,0,0,0,0,0]; + var _PROBS = [ rbeta(2,9), rbeta(5,9), rbeta(5,9) ]; + var BB_RUN = 0; + + d3.select( "#reveal-div" ) + .selectAll("p") + .data( _PROBS ) + .enter() + .append("p") + .text( function(d,i){ return "Arm " + (i + 1) + ": " +d.toFixed(4); } ) + + + function pdfbeta(x_array,a,b){ + //x is an array + _beta = Beta(a,b); + function _pdfbeta(x){ + return ( Math.pow(x,a-1)*Math.pow(1-x, b - 1) )/_beta + } + + return x_array.map( _pdfbeta ) + } + + function Beta(a,b){ + //stirlings approx + // use logs and exponentials to avoid underflow + // with logs is still giving me errors + + //var n = Math.pow(a, a - 0.5)*Math.pow(b, b-0.5) + + var log_n = Math.log(a)*(a - 0.5) + Math.log(b)*( b-0.5) + //var d = Math.pow( a + b, a+ b-0.5) + var log_d = Math.log( a + b)*(a+ b-0.5) + return Math.sqrt( 2*Math.PI)*Math.exp(log_n - log_d) + } + + + function rbeta(a,b){ + //from Simulation and MC, Wiley + + var p = a/b; + if (Math.min(a,b) <= 1){ + var lambda = Math.min(a,b) + }else{ + var lambda = Math.sqrt( (2*a*b - a - b)/(a+b-2) ) + } + + while (1){ + var R1 = Math.random(); + var R2 = Math.random(); + var y = Math.pow( ( 1./R1 - 1.), 1./lambda ); + if ( 4*R1*R2*R2 < (Math.pow(y, a - lambda)*Math.pow( (1.+ p)/(1 + p*y) , a + b ) )){ + return (p*y)/(1+ p*y) + } + } + } + + function rbeta_array( arm_counts){ + // to be used with ARMS with uniform prior. + samples = [] + for (var i=0; i < arm_counts.length/2; i++){ + samples.push( + rbeta(arm_counts[2*i + 1]+1, 1+arm_counts[2*i] - arm_counts[2*i+1] ) + ) + } + return samples + } + + function draw_arm( p ){ + if ( Math.random() < p){ return 1 } else { return 0 } + } + + + function update_arm( arm_number ){ + var result = draw_arm(_PROBS[arm_number] ); + ARMS[2*arm_number] += 1; + ARMS[2*arm_number+1] += result; + redraw(arm_number); + return + } + + + function bayesian_bandits(){ + //for (var i = 0; i < n_pulls; i++ ){ + //sample from Beta distributions + var samples = rbeta_array(ARMS); + var select = samples.indexOf( d3.max( samples) ); + update_arm( select ); + if (BB_RUN < 300){ + BB_RUN += 1; + window.setTimeout( bayesian_bandits, 100 ) + } + else{ + return + } + //} + } + + var x_array = []; + var _N = 100; + var max_data = 10 + for ( var i =0; i < _N; i++ ){ + x_array.push( .01*i ) + } + + var colors = ["#348ABD", "#A60628", "#7A68A6"]; + var fill_colors = [ "rgba(52, 128, 189,0.1)", "rgba(166, 6, 40, 0.1 )", "rgba( 122, 104, 166,0.1 )"]; + + var w = 600, + h = 150, + margin = 15, + y = d3.scale.linear().domain([0, max_data]).range([h - margin,0 + margin ]), + x = d3.scale.linear().domain([0,_N]).range([0 + margin, w - margin]) + + var vis = d3.select("#beta-graphs") + .append("svg:svg") + .attr("width", w ) + .attr("height", h ) + + var g = vis.append("svg:g") + + var line = d3.svg.line() + .x(function(d, i) { return x(i); }) + .y(y) + + + for ( var i =0; i < 3; i++){ + var _data = pdfbeta(x_array, 1 + ARMS[2*i+1],1+ARMS[2*i] - ARMS[2*i+1] ); + g.selectAll('path.line') + .data( [_data] ) + .enter() + .append("svg:path") + .attr("stroke", colors[i] ) + //.attr("fill", fill_colors[i] ) + //.attr("fill", fill_colors[i] ) + //.attr("stroke-width", 0 ) + .attr("d", line ) + .attr("id", "line-" + i ); + } + + + g.append("svg:line") + .attr("x1", x(0)) + .attr("y1", y(0)) + .attr("x2", x(w)) + .attr("y2", y(0)) + + g.append("svg:line") + .attr("x1", x(0)) + .attr("y1", y(0)) + .attr("x2", x(0)) + .attr("y2", y(max_data)) + + g.selectAll(".xLabel") + .data( d3.range(0,1.2,.2) ) + .enter().append("svg:text") + .attr("class", "xLabel") + .text(String) + .attr("x", function(d) { return x(100*d) }) + .attr("y", h) + .attr("text-anchor", "middle") + .attr("dy", 0.0 ) + /* + g.selectAll(".yLabel") + .data(y.ticks(4)) + .enter().append("svg:text") + .attr("class", "yLabel") + .text(String) + .attr("x", 0) + .attr("y", function(d) { return y(d) }) + .attr("text-anchor", "right") + .attr("dy", 4) + */ + g.selectAll(".xTicks") + .data(x.ticks(5)) + .enter().append("svg:line") + .attr("class", "xTicks") + .attr("x1", function(d) { return x(d); }) + .attr("y1", y(0)) + .attr("x2", function(d) { return x(d); }) + .attr("y2", y(-0.1)) + + vis.append("text") + .attr("x", (w / 2)) + .attr("y", 15 ) + .attr("text-anchor", "middle") + .style("font-size", "17px") + .text("Posterior Distributions"); + + /* + g.selectAll(".yTicks") + .data(y.ticks(4)) + .enter().append("svg:line") + .attr("class", "yTicks") + .attr("y1", function(d) { return -1 * y(d); }) + .attr("x1", x(-0.3)) + .attr("y2", function(d) { return -1 * y(d); }) + .attr("x2", x(0)) + */ + + + + + + + var data = ARMS; + var labellist = ["Arm 1", "", "Arm 2", "", "Arm 3", ""]; + + var w_bar = 600, + h_bar = 170, + labelpad = 50, + x_bar = d3.scale.linear().domain([0, 100]).range([0, w_bar]), + y_bar = d3.scale.ordinal().domain(d3.range(data.length)).rangeBands([0, h_bar], .2); + + var vis = d3.select("#paired-bar-chart") + .append("svg:svg") + .attr("width", w_bar + 40) + .attr("height", h_bar + 20) + .append("svg:g") + + var bars = vis.selectAll("g.bar") + .data(data) + .enter().append("svg:g") + .attr("class", "bar") + .attr("transform", function(d, i) { return "translate(" + labelpad + "," + y_bar(i) + ")"; }) + + + bars.append("svg:rect") + .attr("fill", function(d, i) { return (i%2)? colors[i]: fill_colors[i]; } ) //Alternate colors + .attr("width", function(d,i){ return x_bar(d)*0.5 }) + .attr("height", y_bar.rangeBand()); + + bars.append("svg:text") + .attr("x", 0) + .attr("y", 10 + y_bar.rangeBand() / 2) + .attr("dx", -6) + .attr("dy", ".50em") + .attr("text-anchor", "end") + .text(function(d, i) { return labellist[i]; }); + + var counts = bars.append("svg:text") + .attr("x", 0) + .attr("y", 10 + y_bar.rangeBand() / 2) + .attr("dx", -6) + .attr("dy", "-.40em") + .attr("text-anchor", "end") + .text(function(d, i) { return ""; }); + + + var rules = vis.selectAll("g.rule") + .data(x.ticks(10)) + .enter().append("svg:g") + .attr("class", "rule") + .attr("transform", function(d) { return "translate(" + x_bar(d) + ", 0)"; }); + + + rules.append("svg:line") + .attr("y1", 0) + .attr("y2", h_bar) + .attr("x1", labelpad) + .attr("x2", labelpad) + .attr("stroke", "white") + .attr("stroke-opacity", .3); + + + + function redraw(arm_number){ + + var _data = [] + for ( var i =0; i < 3; i++){ + _data.push( pdfbeta(x_array, 1 + ARMS[2*i+1],1+ARMS[2*i] - ARMS[2*i+1] ) ); + + } + //update what is max. + max_data = d3.max( [ + 10, + d3.max(_data[0]), + d3.max(_data[1]), + d3.max(_data[2]) ]) + + y = d3.scale.linear().domain([0, max_data]).range([h - margin,0 + margin ]) + line = d3.svg.line() + .x(function(d, i) { return x(i); }) + .y(y) + + for ( var i =0; i < 3; i++){ + g.select("#line-" + i) + .data( [_data[i]] ) + .attr("d", line ) + } + + + + + + + bars.data(ARMS) + .enter().append("svg:g") + .attr("class", "bar") + .attr("transform", function(d, i) { return "translate(" + labelpad + "," + y(i) + ")"; }); + + + bars.append("svg:rect") + .attr("fill", function(d, ix) {_ix = Math.floor(ix/2); return (ix%2)? fill_colors[_ix]: colors[_ix]; } ) //Alternate colors + .attr("width", function(d,i){ return x_bar(d)*0.5 }) + .attr("height", y_bar.rangeBand()); + + + counts + .attr("x", 0) + .attr("y", 10 + y_bar.rangeBand() / 2) + .attr("dx", function( d,i) { return !(i%2) ? 50 + 3.2*data[i] : 67 + 3.2*data[i] ;}) + .attr("dy", "-.40em") + .attr("text-anchor", "end") + .text(function(d, i) { return !(i%2) ? data[i] + " pulls" : data[i] + " rewards" ;}); + + //update scoreboard + var rewards = ARMS[1] + ARMS[3] + ARMS[5]; + var pulls = ARMS[0] + ARMS[2] + ARMS[4]; + document.getElementById("rewards").innerHTML = rewards ; + document.getElementById("pulls").innerHTML = pulls ; + document.getElementById("ratio").innerHTML = (rewards/pulls).toFixed(3) ; + + } + + + d3.select( "#reveal-div" ) + .selectAll("p") + .data( _PROBS ) + .enter() + .append("span") + .attr( "style", "margin-left:15; margin-right: 30px; margin-top:0" ) + .text( function(d,i){ return d.toFixed(4) ; } ) + //redraw() //to initialize \ No newline at end of file diff --git a/Chapter6_Priorities/other_strats.py b/Chapter6_Priorities/other_strats.py index 430c08d7..73847b6f 100644 --- a/Chapter6_Priorities/other_strats.py +++ b/Chapter6_Priorities/other_strats.py @@ -1,125 +1,125 @@ -#other strats. -# TODO: UBC strat, epsilon-greedy - -import scipy.stats as stats -import numpy as np -from pymc import rbeta - -rand = np.random.rand -beta = stats.beta - - -class GeneralBanditStrat( object ): - - """ - Implements a online, learning strategy to solve - the Multi-Armed Bandit problem. - - parameters: - bandits: a Bandit class with .pull method - choice_function: accepts a self argument (which gives access to all the variables), and - returns and int between 0 and n-1 - methods: - sample_bandits(n): sample and train on n pulls. - - attributes: - N: the cumulative number of samples - choices: the historical choices as a (N,) array - bb_score: the historical score as a (N,) array - - """ - - def __init__(self, bandits, choice_function): - - self.bandits = bandits - n_bandits = len( self.bandits ) - self.wins = np.zeros( n_bandits ) - self.trials = np.zeros(n_bandits ) - self.N = 0 - self.choices = [] - self.score = [] - self.choice_function = choice_function - - def sample_bandits( self, n=1 ): - - score = np.zeros( n ) - choices = np.zeros( n ) - - for k in range(n): - #sample from the bandits's priors, and select the largest sample - choice = self.choice_function(self) - - #sample the chosen bandit - result = self.bandits.pull( choice ) - - #update priors and score - self.wins[ choice ] += result - self.trials[ choice ] += 1 - score[ k ] = result - self.N += 1 - choices[ k ] = choice - - self.score = np.r_[ self.score, score ] - self.choices = np.r_[ self.choices, choices ] - return - - -def bayesian_bandit_choice(self): - return np.argmax( rbeta( 1 + self.wins, 1 + self.trials - self.wins) ) - -def max_mean( self ): - """pick the bandit with the current best observed proportion of winning """ - return np.argmax( self.wins / ( self.trials +1 ) ) - -def lower_credible_choice( self ): - """pick the bandit with the best LOWER BOUND. See chapter 5""" - def lb(a,b): - return a/(a+b) - 1.65*np.sqrt( (a*b)/( (a+b)**2*(a+b+1) ) ) - a = self.wins + 1 - b = self.trials - self.wins + 1 - return np.argmax( lb(a,b) ) - -def upper_credible_choice( self ): - """pick the bandit with the best LOWER BOUND. See chapter 5""" - def lb(a,b): - return a/(a+b) + 1.65*np.sqrt( (a*b)/( (a+b)**2*(a+b+1) ) ) - a = self.wins + 1 - b = self.trials - self.wins + 1 - return np.argmax( lb(a,b) ) - -def random_choice( self): - return np.random.randint( 0, len( self.wins ) ) - - -def ucb_bayes( self ): - C = 0 - n = 10000 - alpha =1 - 1./( (self.N+1) ) - return np.argmax( beta.ppf( alpha, - 1 + self.wins, - 1 + self.trials - self.wins ) ) - - - - -class Bandits(object): - """ - This class represents N bandits machines. - - parameters: - p_array: a (n,) Numpy array of probabilities >0, <1. - - methods: - pull( i ): return the results, 0 or 1, of pulling - the ith bandit. - """ - def __init__(self, p_array): - self.p = p_array - self.optimal = np.argmax(p_array) - - def pull( self, i ): - #i is which arm to pull - return rand() < self.p[i] - - def __len__(self): - return len(self.p) +#other strats. +# TODO: UBC strat, epsilon-greedy + +import scipy.stats as stats +import numpy as np +from pymc import rbeta + +rand = np.random.rand +beta = stats.beta + + +class GeneralBanditStrat( object ): + + """ + Implements a online, learning strategy to solve + the Multi-Armed Bandit problem. + + parameters: + bandits: a Bandit class with .pull method + choice_function: accepts a self argument (which gives access to all the variables), and + returns and int between 0 and n-1 + methods: + sample_bandits(n): sample and train on n pulls. + + attributes: + N: the cumulative number of samples + choices: the historical choices as a (N,) array + bb_score: the historical score as a (N,) array + + """ + + def __init__(self, bandits, choice_function): + + self.bandits = bandits + n_bandits = len( self.bandits ) + self.wins = np.zeros( n_bandits ) + self.trials = np.zeros(n_bandits ) + self.N = 0 + self.choices = [] + self.score = [] + self.choice_function = choice_function + + def sample_bandits( self, n=1 ): + + score = np.zeros( n ) + choices = np.zeros( n ) + + for k in range(n): + #sample from the bandits's priors, and select the largest sample + choice = self.choice_function(self) + + #sample the chosen bandit + result = self.bandits.pull( choice ) + + #update priors and score + self.wins[ choice ] += result + self.trials[ choice ] += 1 + score[ k ] = result + self.N += 1 + choices[ k ] = choice + + self.score = np.r_[ self.score, score ] + self.choices = np.r_[ self.choices, choices ] + return + + +def bayesian_bandit_choice(self): + return np.argmax( rbeta( 1 + self.wins, 1 + self.trials - self.wins) ) + +def max_mean( self ): + """pick the bandit with the current best observed proportion of winning """ + return np.argmax( self.wins / ( self.trials +1 ) ) + +def lower_credible_choice( self ): + """pick the bandit with the best LOWER BOUND. See chapter 5""" + def lb(a,b): + return a/(a+b) - 1.65*np.sqrt( (a*b)/( (a+b)**2*(a+b+1) ) ) + a = self.wins + 1 + b = self.trials - self.wins + 1 + return np.argmax( lb(a,b) ) + +def upper_credible_choice( self ): + """pick the bandit with the best LOWER BOUND. See chapter 5""" + def lb(a,b): + return a/(a+b) + 1.65*np.sqrt( (a*b)/( (a+b)**2*(a+b+1) ) ) + a = self.wins + 1 + b = self.trials - self.wins + 1 + return np.argmax( lb(a,b) ) + +def random_choice( self): + return np.random.randint( 0, len( self.wins ) ) + + +def ucb_bayes( self ): + C = 0 + n = 10000 + alpha =1 - 1./( (self.N+1) ) + return np.argmax( beta.ppf( alpha, + 1 + self.wins, + 1 + self.trials - self.wins ) ) + + + + +class Bandits(object): + """ + This class represents N bandits machines. + + parameters: + p_array: a (n,) Numpy array of probabilities >0, <1. + + methods: + pull( i ): return the results, 0 or 1, of pulling + the ith bandit. + """ + def __init__(self, p_array): + self.p = p_array + self.optimal = np.argmax(p_array) + + def pull( self, i ): + #i is which arm to pull + return rand() < self.p[i] + + def __len__(self): + return len(self.p) diff --git a/Chapter6_Priorities/ystockquote.py b/Chapter6_Priorities/ystockquote.py index 22e7234f..e1377f8c 100644 --- a/Chapter6_Priorities/ystockquote.py +++ b/Chapter6_Priorities/ystockquote.py @@ -1,170 +1,170 @@ -# -# ystockquote : Python module - retrieve stock quote data from Yahoo Finance -# -# Copyright (c) 2007,2008,2013 Corey Goldberg (cgoldberg@gmail.com) -# -# license: GNU LGPL -# -# This library is free software; you can redistribute it and/or -# modify it under the terms of the GNU Lesser General Public -# License as published by the Free Software Foundation; either -# version 2.1 of the License, or (at your option) any later version. -# -# Requires: Python 2.7/3.2+ - - -__version__ = '0.2.2' - - -try: - # py3 - from urllib.request import Request, urlopen - from urllib.parse import urlencode -except ImportError: - # py2 - from urllib2 import Request, urlopen - from urllib import urlencode - - -def _request(symbol, stat): - url = 'http://finance.yahoo.com/d/quotes.csv?s=%s&f=%s' % (symbol, stat) - req = Request(url) - resp = urlopen(req) - return str(resp.read().decode('utf-8').strip()) - - -def get_all(symbol): - """ - Get all available quote data for the given ticker symbol. - - Returns a dictionary. - """ - values = _request(symbol, 'l1c1va2xj1b4j4dyekjm3m4rr5p5p6s7').split(',') - return dict( - price=values[0], - change=values[1], - volume=values[2], - avg_daily_volume=values[3], - stock_exchange=values[4], - market_cap=values[5], - book_value=values[6], - ebitda=values[7], - dividend_per_share=values[8], - dividend_yield=values[9], - earnings_per_share=values[10], - fifty_two_week_high=values[11], - fifty_two_week_low=values[12], - fifty_day_moving_avg=values[13], - two_hundred_day_moving_avg=values[14], - price_earnings_ratio=values[15], - price_earnings_growth_ratio=values[16], - price_sales_ratio=values[17], - price_book_ratio=values[18], - short_ratio=values[19], - ) - - -def get_price(symbol): - return _request(symbol, 'l1') - - -def get_change(symbol): - return _request(symbol, 'c1') - - -def get_volume(symbol): - return _request(symbol, 'v') - - -def get_avg_daily_volume(symbol): - return _request(symbol, 'a2') - - -def get_stock_exchange(symbol): - return _request(symbol, 'x') - - -def get_market_cap(symbol): - return _request(symbol, 'j1') - - -def get_book_value(symbol): - return _request(symbol, 'b4') - - -def get_ebitda(symbol): - return _request(symbol, 'j4') - - -def get_dividend_per_share(symbol): - return _request(symbol, 'd') - - -def get_dividend_yield(symbol): - return _request(symbol, 'y') - - -def get_earnings_per_share(symbol): - return _request(symbol, 'e') - - -def get_52_week_high(symbol): - return _request(symbol, 'k') - - -def get_52_week_low(symbol): - return _request(symbol, 'j') - - -def get_50day_moving_avg(symbol): - return _request(symbol, 'm3') - - -def get_200day_moving_avg(symbol): - return _request(symbol, 'm4') - - -def get_price_earnings_ratio(symbol): - return _request(symbol, 'r') - - -def get_price_earnings_growth_ratio(symbol): - return _request(symbol, 'r5') - - -def get_price_sales_ratio(symbol): - return _request(symbol, 'p5') - - -def get_price_book_ratio(symbol): - return _request(symbol, 'p6') - - -def get_short_ratio(symbol): - return _request(symbol, 's7') - - -def get_historical_prices(symbol, start_date, end_date): - """ - Get historical prices for the given ticker symbol. - Date format is 'YYYY-MM-DD' - - Returns a nested list (first item is list of column headers). - """ - params = urlencode({ - 's': symbol, - 'a': int(start_date[5:7]) - 1, - 'b': int(start_date[8:10]), - 'c': int(start_date[0:4]), - 'd': int(end_date[5:7]) - 1, - 'e': int(end_date[8:10]), - 'f': int(end_date[0:4]), - 'g': 'd', - 'ignore': '.csv', - }) - url = 'http://ichart.yahoo.com/table.csv?%s' % params - req = Request(url) - resp = urlopen(req) - content = str(resp.read().decode('utf-8').strip()) - days = content.splitlines() +# +# ystockquote : Python module - retrieve stock quote data from Yahoo Finance +# +# Copyright (c) 2007,2008,2013 Corey Goldberg (cgoldberg@gmail.com) +# +# license: GNU LGPL +# +# This library is free software; you can redistribute it and/or +# modify it under the terms of the GNU Lesser General Public +# License as published by the Free Software Foundation; either +# version 2.1 of the License, or (at your option) any later version. +# +# Requires: Python 2.7/3.2+ + + +__version__ = '0.2.2' + + +try: + # py3 + from urllib.request import Request, urlopen + from urllib.parse import urlencode +except ImportError: + # py2 + from urllib2 import Request, urlopen + from urllib import urlencode + + +def _request(symbol, stat): + url = 'http://finance.yahoo.com/d/quotes.csv?s=%s&f=%s' % (symbol, stat) + req = Request(url) + resp = urlopen(req) + return str(resp.read().decode('utf-8').strip()) + + +def get_all(symbol): + """ + Get all available quote data for the given ticker symbol. + + Returns a dictionary. + """ + values = _request(symbol, 'l1c1va2xj1b4j4dyekjm3m4rr5p5p6s7').split(',') + return dict( + price=values[0], + change=values[1], + volume=values[2], + avg_daily_volume=values[3], + stock_exchange=values[4], + market_cap=values[5], + book_value=values[6], + ebitda=values[7], + dividend_per_share=values[8], + dividend_yield=values[9], + earnings_per_share=values[10], + fifty_two_week_high=values[11], + fifty_two_week_low=values[12], + fifty_day_moving_avg=values[13], + two_hundred_day_moving_avg=values[14], + price_earnings_ratio=values[15], + price_earnings_growth_ratio=values[16], + price_sales_ratio=values[17], + price_book_ratio=values[18], + short_ratio=values[19], + ) + + +def get_price(symbol): + return _request(symbol, 'l1') + + +def get_change(symbol): + return _request(symbol, 'c1') + + +def get_volume(symbol): + return _request(symbol, 'v') + + +def get_avg_daily_volume(symbol): + return _request(symbol, 'a2') + + +def get_stock_exchange(symbol): + return _request(symbol, 'x') + + +def get_market_cap(symbol): + return _request(symbol, 'j1') + + +def get_book_value(symbol): + return _request(symbol, 'b4') + + +def get_ebitda(symbol): + return _request(symbol, 'j4') + + +def get_dividend_per_share(symbol): + return _request(symbol, 'd') + + +def get_dividend_yield(symbol): + return _request(symbol, 'y') + + +def get_earnings_per_share(symbol): + return _request(symbol, 'e') + + +def get_52_week_high(symbol): + return _request(symbol, 'k') + + +def get_52_week_low(symbol): + return _request(symbol, 'j') + + +def get_50day_moving_avg(symbol): + return _request(symbol, 'm3') + + +def get_200day_moving_avg(symbol): + return _request(symbol, 'm4') + + +def get_price_earnings_ratio(symbol): + return _request(symbol, 'r') + + +def get_price_earnings_growth_ratio(symbol): + return _request(symbol, 'r5') + + +def get_price_sales_ratio(symbol): + return _request(symbol, 'p5') + + +def get_price_book_ratio(symbol): + return _request(symbol, 'p6') + + +def get_short_ratio(symbol): + return _request(symbol, 's7') + + +def get_historical_prices(symbol, start_date, end_date): + """ + Get historical prices for the given ticker symbol. + Date format is 'YYYY-MM-DD' + + Returns a nested list (first item is list of column headers). + """ + params = urlencode({ + 's': symbol, + 'a': int(start_date[5:7]) - 1, + 'b': int(start_date[8:10]), + 'c': int(start_date[0:4]), + 'd': int(end_date[5:7]) - 1, + 'e': int(end_date[8:10]), + 'f': int(end_date[0:4]), + 'g': 'd', + 'ignore': '.csv', + }) + url = 'http://ichart.yahoo.com/table.csv?%s' % params + req = Request(url) + resp = urlopen(req) + content = str(resp.read().decode('utf-8').strip()) + days = content.splitlines() return [day.split(',') for day in days] \ No newline at end of file diff --git a/Chapter7_BayesianMachineLearning/DontOverfit.ipynb b/Chapter7_BayesianMachineLearning/DontOverfit.ipynb index 0d2f2b91..e6d411cc 100644 --- a/Chapter7_BayesianMachineLearning/DontOverfit.ipynb +++ b/Chapter7_BayesianMachineLearning/DontOverfit.ipynb @@ -1,577 +1,577 @@ -{ - "metadata": { - "name": "DontOverfit" - }, - "nbformat": 3, - "nbformat_minor": 0, - "worksheets": [ - { - "cells": [ - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Implementation of Salisman's Don't Overfit submission" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "From [Kaggle](http://www.kaggle.com/c/overfitting)\n", - ">In order to achieve this we have created a simulated data set with 200 variables and 20,000 cases. An \u2018equation\u2019 based on this data was created in order to generate a Target to be predicted. Given the all 20,000 cases, the problem is very easy to solve \u2013 but you only get given the Target value of 250 cases \u2013 the task is to build a model that gives the best predictions on the remaining 19,750 cases." - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "import gzip\n", - "import requests\n", - "import zipfile\n", - "\n", - "url = \"https://dl.dropbox.com/s/lnly9gw8pb1xhir/overfitting.zip/"\n", - "\n", - "\n", - "results = requests.get(url)" - ], - "language": "python", - "metadata": {}, - "outputs": [], - "prompt_number": 30 - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "import StringIO\n", - "z = zipfile.ZipFile(StringIO.StringIO(results.content))\n", - "# z.extractall()" - ], - "language": "python", - "metadata": {}, - "outputs": [], - "prompt_number": 31 - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "z.extractall()" - ], - "language": "python", - "metadata": {}, - "outputs": [], - "prompt_number": 32 - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "z.namelist()" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "output_type": "pyout", - "prompt_number": 38, - "text": [ - "['overfitting.csv']" - ] - } - ], - "prompt_number": 38 - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "d = z.open('overfitting.csv')\n", - "d.readline()" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "output_type": "pyout", - "prompt_number": 69, - "text": [ - "'case_id,train,Target_Practice,Target_Leaderboard,Target_Evaluate,var_1,var_2,var_3,var_4,var_5,var_6,var_7,var_8,var_9,var_10,var_11,var_12,var_13,var_14,var_15,var_16,var_17,var_18,var_19,var_20,var_21,var_22,var_23,var_24,var_25,var_26,var_27,var_28,var_29,var_30,var_31,var_32,var_33,var_34,var_35,var_36,var_37,var_38,var_39,var_40,var_41,var_42,var_43,var_44,var_45,var_46,var_47,var_48,var_49,var_50,var_51,var_52,var_53,var_54,var_55,var_56,var_57,var_58,var_59,var_60,var_61,var_62,var_63,var_64,var_65,var_66,var_67,var_68,var_69,var_70,var_71,var_72,var_73,var_74,var_75,var_76,var_77,var_78,var_79,var_80,var_81,var_82,var_83,var_84,var_85,var_86,var_87,var_88,var_89,var_90,var_91,var_92,var_93,var_94,var_95,var_96,var_97,var_98,var_99,var_100,var_101,var_102,var_103,var_104,var_105,var_106,var_107,var_108,var_109,var_110,var_111,var_112,var_113,var_114,var_115,var_116,var_117,var_118,var_119,var_120,var_121,var_122,var_123,var_124,var_125,var_126,var_127,var_128,var_129,var_130,var_131,var_132,var_133,var_134,var_135,var_136,var_137,var_138,var_139,var_140,var_141,var_142,var_143,var_144,var_145,var_146,var_147,var_148,var_149,var_150,var_151,var_152,var_153,var_154,var_155,var_156,var_157,var_158,var_159,var_160,var_161,var_162,var_163,var_164,var_165,var_166,var_167,var_168,var_169,var_170,var_171,var_172,var_173,var_174,var_175,var_176,var_177,var_178,var_179,var_180,var_181,var_182,var_183,var_184,var_185,var_186,var_187,var_188,var_189,var_190,var_191,var_192,var_193,var_194,var_195,var_196,var_197,var_198,var_199,var_200\\r\\n'" - ] - } - ], - "prompt_number": 69 - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "import numpy as np" - ], - "language": "python", - "metadata": {}, - "outputs": [], - "prompt_number": 70 - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "M = np.fromstring(d.read(), sep=\",\")" - ], - "language": "python", - "metadata": {}, - "outputs": [], - "prompt_number": 63 - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "len(d.read())" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "output_type": "pyout", - "prompt_number": 71, - "text": [ - "23919756" - ] - } - ], - "prompt_number": 71 - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "np.fromstring?" - ], - "language": "python", - "metadata": {}, - "outputs": [], - "prompt_number": 75 - }, - { - "cell_type": "code", - "collapsed": false, - "input": [], - "language": "python", - "metadata": {}, - "outputs": [] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "data = np.loadtxt(\"overfitting.csv\", delimiter=\",\", skiprows=1)" - ], - "language": "python", - "metadata": {}, - "outputs": [], - "prompt_number": 4 - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "print \"\"\"\n", - "There are also 5 other fields,\n", - "\n", - "case_id - 1 to 20,000, a unique identifier for each row\n", - "\n", - "train - 1/0, this is a flag for the first 250 rows which are the training dataset\n", - "\n", - "Target_Practice - we have provided all 20,000 Targets for this model, so you can develop your method completely off line.\n", - "\n", - "Target_Leaderboard - only 250 Targets are provided. You submit your predictions for the remaining 19,750 to the Kaggle leaderboard. \n", - "\n", - "Target_Evaluate - again only 250 Targets are provided. Those competitors who beat the 'benchmark' on the Leaderboard will be asked to make one further submission for the Evaluation model.\n", - "\n", - "\"\"\"\n", - "\n", - "data.shape" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "\n", - "There are also 5 other fields,\n", - "\n", - "case_id - 1 to 20,000, a unique identifier for each row\n", - "\n", - "train - 1/0, this is a flag for the first 250 rows which are the training dataset\n", - "\n", - "Target_Practice - we have provided all 20,000 Targets for this model, so you can develop your method completely off line.\n", - "\n", - "Target_Leaderboard - only 250 Targets are provided. You submit your predictions for the remaining 19,750 to the Kaggle leaderboard. \n", - "\n", - "Target_Evaluate - again only 250 Targets are provided. Those competitors who beat the 'benchmark' on the Leaderboard will be asked to make one further submission for the Evaluation model.\n", - "\n", - "\n" - ] - }, - { - "output_type": "pyout", - "prompt_number": 5, - "text": [ - "(20000L, 205L)" - ] - } - ], - "prompt_number": 5 - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "ix_training = data[:, 1] == 1\n", - "ix_testing = data[:, 1] == 0\n", - "\n", - "training_data = data[ix_training, 5:]\n", - "testing_data = data[ix_testing, 5:]\n", - "\n", - "training_labels = data[ix_training, 2]\n", - "testing_labels = data[ix_testing, 2]\n", - "\n", - "print \"training:\", training_data.shape, training_labels.shape\n", - "print \"testing: \", testing_data.shape, testing_labels.shape" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "training: (250L, 200L) (250L,)\n", - "testing: " - ] - }, - { - "output_type": "stream", - "stream": "stdout", - "text": [ - " (19750L, 200L) (19750L,)\n" - ] - } - ], - "prompt_number": 6 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Develop Tim's model\n", - "\n", - "He mentions that the X variables are from a Unifrom distribution. Let's investigate this:" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "figsize(12, 4)" - ], - "language": "python", - "metadata": {}, - "outputs": [], - "prompt_number": 7 - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "hist(training_data.flatten())\n", - "print training_data.shape[0] * training_data.shape[1]" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "50000\n" - ] - }, - { - "output_type": "display_data", - "png": 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LmJAL2InyDAAAAFhEeYbjMasGE3IBE3IBE3IBO1GeAQAAAIsoz3A8ZtVgQi5gQi5gQi5g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\nOB6zajAhFzAhFzA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- } - ], - "prompt_number": 8 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "looks pretty right" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "import pymc as pm\n", - "\n", - "to_include = pm.Bernoulli(\"to_include\", 0.5, size=200)" - ], - "language": "python", - "metadata": {}, - "outputs": [], - "prompt_number": 127 - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "coef = pm.Uniform(\"coefs\", 0, 1, size=200)" - ], - "language": "python", - "metadata": {}, - "outputs": [], - "prompt_number": 128 - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "@pm.deterministic\n", - "def Z(coef=coef, to_include=to_include, data=training_data):\n", - " ym = np.dot(to_include * training_data, coef)\n", - " return ym - ym.mean()" - ], - "language": "python", - "metadata": {}, - "outputs": [], - "prompt_number": 129 - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "@pm.deterministic\n", - "def T(z=Z):\n", - " return 0.45 * (np.sign(z) + 1.1)" - ], - "language": "python", - "metadata": {}, - "outputs": [], - "prompt_number": 130 - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "obs = pm.Bernoulli(\"obs\", T, value=training_labels, observed=True)\n", - "\n", - "model = pm.Model([to_include, coef, Z, T, obs])\n", - "map_ = pm.MAP(model)\n", - "map_.fit()" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "Warning: Stochastic to_include's value is neither numerical nor array with floating-point dtype. Recommend fitting method fmin (default).\n" - ] - } - ], - "prompt_number": 132 - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "mcmc = pm.MCMC(model)" - ], - "language": "python", - "metadata": {}, - "outputs": [], - "prompt_number": 133 - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "mcmc.sample(100000, 90000, 1)" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "output_type": "stream", - "stream": "stdout", - "text": [ - " \r", - "[****************100%******************] 100000 of 100000 complete" - ] - }, - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "\n" - ] - } - ], - "prompt_number": 176 - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "(np.round(T.value) == training_labels).mean()" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "output_type": "pyout", - "prompt_number": 177, - "text": [ - "0.73999999999999999" - ] - } - ], - "prompt_number": 177 - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "t_trace = mcmc.trace(\"T\")[:]\n", - "(np.round(t_trace[-500:-400, :]).mean(axis=0) == training_labels).mean()" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "output_type": "pyout", - "prompt_number": 178, - "text": [ - "0.72399999999999998" - ] - } - ], - "prompt_number": 178 - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "t_mean = np.round(t_trace).mean(axis=1)" - ], - "language": "python", - "metadata": {}, - "outputs": [], - "prompt_number": 179 - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "imshow(t_trace[-10000:, :], aspect=\"auto\")\n", - "colorbar()" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "output_type": "pyout", - "prompt_number": 180, - "text": [ - "" - ] - }, - { - "output_type": "display_data", - "png": 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KqVurtSa/PqkWjWpVfn12AF/vibdN1/Lbd6pNccXy269SQrmTiNz2LZpRboDa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\nKoM1J5YaGxtVXV2tubk5LS0taW5uTtu3b9f3v/99Pfjgg5KkBx98UC+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XaYIF79mRC/mc8GsJpMMv5dzIF68kVkSwTa8SMWQHKMbfxhn4npXPFeFVhNCa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7M/xQ5aBZLnFdHaGCuyQ8WBuOQvg3MmPy8WRp95WgvJ0afEWXuFE5fV2XBgogIDj2NAgsmp\nhfN4TkqEEifHNqc9Ql3H06lIQjZAJVsxqU9E+mrIwyCdfVQBECVb6BTZdUCJWDXRFlsbHQkNh3/U\nXg7v9a4xpyQFdJ5irOc3x+41dQ1VpIsVlTgrlOKL7vE/wNH2nBBtQX5bdp10/olHpqnvWnGMgHha\nG0lUa2nStZFSPMiZhGgb9Vxo2m9PFMlih/MohBbx5nsi13HEZb/T3xACk/bgjKgQEP2M8psq1Crr\nQFxSe63k2ie9BXpGTRWn90z8x2ZmJdAnrQb7znQ7uxxTvVMmgagl3oNeVD4dgU6UDVilXAy0N5eg\ncGHGsZsqhND9zAItkkfUOvcUqZY+Ohf8vHYkftaAh36KWtI9+Rsl12TiMpfby3qiuJnv4UrEJU3O\nhYllHpEV/c3y5kAUQiNW6JmpggX9rSieP5H1qifZa4Tvc0DDJIRQbLQoEGq17VevoK67hlKw1XCy\nVfNOQXXYgaoj46fecwvQqGoSOV8/3pAPaKKrGozgQPzhItzgMIUTR+4f/XsKXqgiP08p6OQ4ijql\nGg9hihX1/lPqMxJlT4hfTbkkZAJUUUElDmIFJ226bC0kLRZ4aE1vOnwvncRtLbEik+CIuOR31m3H\nrU2P8yf5b4FIXTnMFQi0yGGVASjIeKLr2D23boijrtMMJ1u74v5p2JtHCPFpZmaAFG4SXYeajurh\nN4Ov67XjB/qQaCRa+P7lbsbp6fE8hqgbPRyXlbB/6Ck2KAcpJUKGkkODsoeXk58zDrxMCPqQw9bI\n1oq92ViOS5wpfjcCQ9SECqxvAL21kYniSqhAZcadZ0qo4MPdcqp4FAYddBwoUUpoqWG4lKDz8FV2\nYAq2GetHtZ5IKtD96VFBriIprFnFjV2ZiY9RGhCLDgZhG6iSrR59SnpzGpCdKg5x0bYBPzkhy83M\nOqvhZ7PaBRCZiEOpvVzp4GUHP7ZHrunE5S8riA4Qq4hakVSgFSupEZexsHbPJlKDIZDIGFuE+PfS\nZLCSgz9iE+igzIxpDAqKfF0MTYiVQTu+mkVOluS4hCCc1jNN5jQzq9A0N08rlifZSa2NahK9IwCi\nZAdB+os1TpxP0YRsYTAJIUAJ2rm9TATfuPQp/o2Enqdn/c9DpXsgjC8Nm/JUM3GqvAM5tigcKUpQ\nq6LCF8sUJZx2UifinbVo0Ix4Z2QDZfGK2vQAq+9CqInEpap2h0QVT2k9K7QLJYHUFN7p+XDBgTgu\nN4uQAZ+lyM1N7wzfp/LPsO1ZPDPrh1vvyTxKjs2EBXRMNHm+SxX8NoFj0MMvVhBUNnXi6uqFF1Rb\nJC2o98czhbjfEQuaBv7h52njkNbl8Dqfu4Y5Jmvg72IcKNY5JQFVuJdyqB79NipQmbHvovwzaskd\ngLX1dL0QqlMJDSmtqdZaKh45El1l0apMQl0sfcF/3Vq6FH2daMoqh3jiMFWk+3wR6Cq2wqAZoU/J\ndSRf2yzebnUlJUW80ABfhSAmCroWrCdFC+TpcqZcSGq5phOX73VXR6hLbPcQ4tms5UgYsBrMQKKM\nn+f7Yu9TXQKHWajJufCFfajoK2VFzryqqBPvjkIhkcHGKXvq/mnKHp4hAk34/0qJuKaKI8enWEvg\n6NNgDtXtRImGgpoOCq3KHVC+MjkFCVKPH6kmB8ciqCeRoCdfeNVODCeLL4AD6pma6amOI7JWGHhC\nYikkGAk6+eI9K96bWPHwHpHTrNqu6T7VvaQkGUc0tkQjxz2b/soi/q0yR+9TdErA/St7SmiHNtyn\nHHTTCjuthTbzkqpqd/C7IhOdZma1bYyCIISC0icVWIO0zj0dJIrjMnbYjgqaiRbD06bbuPQZ/7EY\nngZPLZwq/ME14Eiqx/pASjzF8IYDwUxIONU+OUe0PEUHJ14p/PwV2seTuCHf1dMmSvvZg7ZSRULi\nuPToLY8Q95xqFScEuUdvKX5wEkJdj8vriwu/FOpStdB6hNYzmdoOJGDMnNzAZJ/APitOQioedB2+\n3hTEJ0rIb3NNNVd5BeK6d+h6okBTxSPywzydQgPgmVZCPvXnghIAvythwUf5M1Qob4tCRCx3P8XO\nZqKw77h91THrkWsycZk/sL4NRv8m58P1EFWWnZw5QUodK6rKthmt4orap3lhIfg58QuaMUiOUH2e\npHynwRvMKHGkuDTBmNZ3xDsIFVhPU0LBNT5Lh+D1CMHQ1TMjhAIldcvi/uvTwJcoOC6JW6YH7XMe\nhJRCXFYpQV/jwV2UbCrUgN5gYi0PiuXRZy4jG6kfqcpnxgglJeSYeIj8KdGkEvcU6JZq6QypsifU\noqISl+QwKNtQS9jeTXpbIcG6wpkKftdMOJmzmUIcl/Ruuk0eKEUB/aDKfkO5GrcG1SR25FcTXMo4\naEdcpwrnUKcEp23V1My1tTQY9NcdU4LIg+qb3hHWZ549U1XrGQJtWmcycQm0OCmlcV74Wg4hNOqN\nU+xTxia7aGiSGU86pSSkmUjEQnKk7EgOqU51FxIPfpsLcQnPX+0zTNA69qaHYoKQSIoDvUc8x+C3\nbRHvmc5RPiUlrvqd9TqvvwH7ikVixzBaRbFDfgiBBBWVkUQQb4J04UerhB7dvycJSO9fFRWqc9vC\nvyshL64C6sQWD5WovOUOSgS7WDmI45LPoYIP+fSpOwuoUC4LTojtgKIOFNzNGAywINDA5AdKKh2H\nXJOJy1zyieJmZgS4VHuIhsaoABCRQJvEr+WpgsaibRTWaWp3WCl2Vj7Ac4plQGLRoB+P5hFCPGJK\nKVGg50EbkKh2UGqr8UihHp9QogSVogQgxGVs0sLMbA44T4pdDpqp0lfbCoa89yH/AMi2q2Srp9KG\nzjwkOgrd9cmRJw4fNBt+tkxBu0BhUABEOqO2lZ381kp8pXMWnPm+4EKJrfSpYB4dMEdc6CmSEb2A\nR8vMXS8CsIROK63ZpgiAyNbS2ux+9hF+V2cGUP8imKfiUVu018f63wolTImWQpORpbGiOC5xoNIc\nF1VISmI/NR26ngS7G8boMp546OD6v1GRDJJjiseytiXc9k4sJma+djhK3Cj/IPa7PCgUev49EZiQ\nqKniJFJnRQY6rqBRZA7R1rTCFC8ehJRixVHtrbGCHJcqbiD/ZJb1CdmNlIhLtWaI41Lps9ghJDtF\n14OnGEvFi84Yxc09pel1xyR12M8DBxJQtYpToTblPKmUKFEc8mK8ByoiDuL79wzPjD5lU6g3VHcJ\nFRXUkE4azqOEOC7JQKvYlZK6qhBB3P3EMdlT4CoQz0wJ1WFbgEQZFTXkOyOaM/HbFiBGV/ynHrkm\nE5ehYNuT5PckAWkhdS9fjP8BIKoy4nGAeNotOBIiaqfEhfpdfRhpy+3QIgClyoDij6DEpfjNhDj0\ntPXQKepN9iJJbJFf0cxV0XbxtYGjXwPkhCLFXgFOqGYhfmgLkv+rZwz3siqCti1gMAsdTrYi4pIG\nSik0NnyunAxyjJgPSQ2zCDsfxevYMfYgLrFV2oFC4XbYdIUohQ6hfZu6DBb7bJQ9rc7Hdxc0qe22\nHo+ooASlB1GgnLzYdyCLWpRQqoigOdI/IZS2EoV2oSELKjm3fDlshz2Jc0RcygQt8Y/CRFkYvmFm\nVt8OiMtBPI2FnCoOQ1BmYD25SpoeVFvCAX0baXmdFIU6JyG0jyreUUJH0dIgnTUM4lOxhq/1PmEh\nykElQxzcskgI6G7VXh4rys7tBv5dJT2IXfj60ZdwDU3xUIatQlGpJHQgifIpacI5vRrlT1BcV/Dk\n5mCd0TAVMzVwUtCZQYzgoaZLSfGjBEFEDj3joseDNaNixBmi7QP/wEML5Xn+lFdInVCmGEVxqVIn\n2SLQWPRgPoaZ2TzQaChr1iKKly8T4nKc49LTOYGcbGLjUWWLEk2elgYVNHqUQqwURa84IRGrs1w1\nJeVHSRCFuFyAhJZ0vqB07SHS9gihfVT4UxItfMH/L5x8ctrVUqKhDY3L8ZUx4rdT6MUmoPf0fUa2\nQqmAARKXyo7hehJBKzozpMi761fNyRdfsxNHHzAzsxkk8k4YGDj2hQraKWj0CKJgHEZRDaYgJw/b\nTVT7GBVilG6Ctdm4JFqFU7YJwRpQiQYatuXhMqV2k9TE34SeIe49PVUcpqcXeW9EJ8/F/6cijSpE\nkE1Xg2Y8PK8kG0nonHrrZ3b84J1X/X9yOA4IJTXVJHjyQ2oCiUapSAqaOi6+ynSBASW0vUKJcAlG\noLZn4rj0FG/FOdjeSwMKHQjJEnQqmQkOasdQOc/gIuSNFtfHQnHCqeJKyNYqLmEazkO6XlLAw/0r\nlTkP62Z8CvNGOS7JByiqpDoVLxyDu9DVFT4lrc2BY8kQb/ZU9QY8h6aHF0R6JuVQqwYsKIUEpoEq\nqiOFvq/smB1CSUhPN4KK9xZXw9/XNxhs6kDpqsQlPWfsOkmcnFN0DSSrn4YBdoTgV2u5QQl6cX2i\nrOIcBeTorpLwuyYTlyGOS494EJdNCA7bS2G2ppR8D2ZpOS65ysLnkMFWLVdVgm6DwVKIy0WAGisp\ndMLvRiVNluB9Tl+/I/r6JOSUeERuY1CYnqVUFVymJFvmwpVugpqbcWupSk6QkqVWoNjksJnZkkBp\n7iF12eNzsH0KfvOkgi8Ui1cNSpWTQ4aBklCKwoB0Y+FGh/MjjDLpfOQD8gRmDqGEmqr0LoM+U3sT\nW+UVjUNCQVJwYTgIcWkAgint2IPfxXxE8QGDh3uOpHmB274LtXDirNzic3iiIzhzs1vxu0pAyt5d\n4U4FQtZVBM8zIZSWgX839VgObNOjxLFA0E9tC+vgFXEOJcjIB1JCreJVtc5p0IpAqZLzUKqG347H\nb66In+xJKsbyMsqBUrRmhN2gItkAikrqmZEPkHzSLyToXPQGlOwT75IKqCl5WSX9EzxPxSXc2kAL\n9rioKcT17fG8zfR147qpOmiMjmXiFP7WETFVys4TEoqdzcxKtV3Bz9UkdJICDABRU5g7AJQpANpM\nicfX4CJp/NAWj1C3pOcaSs+Tr6E8OkQ2WnyrOA23VfqkALBf4rgsOoqHyj+hhP82oFkzM+udC6/n\njiMZ4CmgbgOUrKLr8Mg1mbjMA5Q7y2tVbEpCSUPmaPsloWqaB3GpyJo3QsJ8xfclRGmSkVGZefpb\neXvYKCnhQrdArlTCrQg0TEVe34EQI8QpDRMxi28V9yCOPSLXMzjtu6BFR20/chgUqIqCA4LOq0qv\nR8gx9iTOKBk5yVV2/MF7R5+5CPtByI41LnGiowbvubPKyZlzgKwtOJLKSIlRcaCtFsNVW5eIPUNO\ns6eooYpHkkoiUgiFoYrztAYGW4j3zDGcydEKVBQ/ehckmz5qwDvbfz1fCCed8jonDiUSVcCgd0ac\n1WaMrOushAf0mTFKLCUSczCWaDl29/51x4TSbC2HkQbL53ifX3ff7uDnbRk0ApUQoFCUkNq4Gtog\nJBS0y3Mc6D2PUDuox2/1+GckxFdpZrYCensAg/hSorDMdIwQK0ilIxy0Qt3BjVsP+weetUkiZxrQ\nULU2203iZycACSHkzLi7QL1JKiCP++GHd20X37AmZB/VgDRKKOHwTuMYge5T+eHtpUvBz1WyNVaI\n+9SMu8VUIYJi9I5jeKaKEfn60K0m7EZsq7jHNihks6eNex4GuFobCm5ib9KT8bSKE3pR5SjQ1iua\nKQficmZPWFd4prd7+Pn3zQMFWmLU/Yaix8uXL9uf/umf2ttvv22FQsG+853v2B133GG/93u/Zx9+\n+KHt37/fvve979nWrRki4Jvf/Kb9y7/8i5VKJfvHf/xH+83f/E0zM3vllVfs61//ujWbTXvyySft\nH/7hH5LezKR4Kse0wWrbwtyPHsSlTLY6HGCq3LJjIqqGO8JVQ5XQIuVPDotqFScSWbXwqeVHOQxY\nBU/IcVkHJKJHlFFCYn6xNNuLYXemtiXeYaXkjIoxKlDRVJwr5GT1acqbmowHz1MlR/CXlRX5OyQ7\nASGjnHxsBRL3SdvWM82Q9oYy2M0uOHmw/pRgq3iPHSbSp8VKPBYMVb3DBihOuBm4UYWGjk12qE4G\nqrYrHUTBMXGZqgnZpAP6A+GYU1IbzxBOK3zcurzEX0Y2qBtPvUGiUHWehI6He49sfQv2eTxbqk5q\nI4Ldgeoj3dxy7Oc2FOLMDNtraf2VUk65cEjJ0T6opNuE1j5lnzehvZg6dfRJAKBwJGHVcB7Sz549\ni/ZZUQnNzAU/H8C7NDPrNdPpOlobym5NUQFbDAeiAjrFdQpxiVOA8QwWT1xJHJephWJk+sWKfshD\nY4B20IF4o84vj6wsCq57WDaUCFfxdg2miqtahyeuTSltADAocNEcUZY0N2lQMvAVUCJcrWXazqrg\nRTqQ9JyZWbEbfmYU16qhOeQeq6dPt/OFJC7/4i/+wp588kn793//d+t2u7aysmJ/+7d/a7/xG79h\nf/3Xf21/93d/Z0899ZQ99dRT9s4779i//du/2TvvvGOnT5+2X//1X7d3333XCoWC/dmf/Zl9+9vf\ntqNHj9qTTz5p3//+9+23fuu3rrhevpbHOS494qmC0gZLWZ1Ove1i0Q4DYUo7MG1aJkcilb/HL5fk\n944vJO4vrEwJxe+BVHu430g8Qxu64GQ2L3KrMLVJVWD4wKVmvLJS/hq1KtvN8F2qYkU8ggK6j5yd\nMG3djB1QStxMogdPPv+ynXj4sJn5hhnQ86TvUoMZqLVSGaVZSFB7hmCRkzcoc4HAcx1yGrFq6mjh\nVq2VJOrdeNDlJBRoNMXmJP2Mek7YU2prWRVcrjuAq0xJLIKZhk+Yicm5MMzDzKwLAzBQxD6jRLwc\nUAZSmbk6n9oV14dn6Rn0Mm7PTr3xEzt+6CujY0o20lRxJWRPtiRub6Ck6jYo0nL4y7q2WHUMtQNf\np020D0IkbzvsDUK7mcWjBAmFZCaKOiX2Kekc6u5RWUBPsjHld+GaEToYB+oIX5c42fotMVgThN6z\n8oHOAGetik/akSg5hbjstiB2FEXK6nR4b5TH7NnL5y/a4Z1XR12S71p1xFtlGPJhpgeehUTRDxWK\n8bYGBfRMSaxz4qk7KsMAACAASURBVDhtLMWj3aqO9vI9kJxzAaJkfAD0S6vK2oQF+TIFSpu6O1pi\nONbF5XCMqoonJKQ29byR8B4gJGLyae+wbol+ysysC++TWuXrW7grNmUnb2q56k5bWFiwp59+2r77\n3e9mJ5TLtmXLFvtv/+2/2cmTJ83M7I//+I/tiSeesKeeesr+8z//037/93/fKpWK7d+/326//XZ7\n4YUX7Oabb7alpSU7evSomZn90R/9kf3Hf/xHMHH5qxaJxMIKSDrnI3WDTizawtNVqCpAxO1BDouk\ncKIsv+DpIfSc2ndq2mpI1DNO2ab5RYsaNFIAiAAl9FS7EzkGHl2Zsk3LMwCk2ODWSkx4OypQZGQ1\nxyV9V/yajR2OZMZo8JSTVhWqzRXowYOmYNZ3L9GnrAtmfpVCRR3FGax4xIIiAmDP2qQkpByQFqk2\nZBKcEJcCVkUttB7BvakKjo6EO9HvkGPskfEkcKFUXndMrVXdhM/Ss/56AkFMbjaht1Y8lV2BKiOh\nteEJmlVCieyDbNODc3BwmuhUwAKFKCoQ6ntQCj9nqIO6hVr7PIU4FMUKBOtJFSlR1yScKu5pFVdd\nJLGxk17nsDY1Q31Q1r3n/mB0rHQTAihkFw10N3TZcvIzixvSasY20EM94kkcEcXHQDxnemYearqF\nSKoCM6aY+aLjUBWje1rFG9Rh1wYuXYWGhj2o3lgZeMuRMiwxqpCK/uo9Ey2DJ66uOMB6RLPjGhAn\n5KqR0Pvvv2+7du2yP/mTP7E33njDHnroIfv7v/97++yzz+y6664zM7PrrrvOPvvsMzMzO3PmjD38\n8MOj8/ft22enT5+2SqVi+/btG32+d+9eO336dPCa/2fjU9tezAzn6V7L9pbWqsnP/fBpMzN75LFj\nZmb2406Wfb+7MnPFcbfds5VPfmRmZjP77jUzs5VPfrSugvXy+YwbKT9+fTnj6npgS1YJem0hS0rc\nO1RKz/zsIzMze/zOm8zM7KXPLpiZ2ZHrdgSPP+hninl/cWp0/MzTT9vjx7Lf/8zT2f3kx69czDg/\nHtq+bd1xLu8Pv++W4fe9329YtdW3g7UM8vtWK6tuHazNWrFUtBfPnjczs6PX7zQzsxfPnrePnj5l\nx44fNzOzp0+dMjNbO/7xB2Zm9ugt2SS2Z98/Y2ZmNw4X5KvD3/Pg8Pe9evGSLf7iDZvbf5+ZmS19\n8KaZWXbc7dipt39uZmbH77nNzMxOvf1zuzh42r46fH8vDN9nfvzmSz80M7O7H3rEzMx+/MpzZrZm\nlHoLn5iZWWnLvtHxqWdfsBOPZAnxk8+9aGZmJx45agMzOzW8v+PD+8uPbxka3xfOfJ5d/4as8pC/\n30dvy77/2Z9n18u33VvDgQoHhxDrt5rLdvbNF+2OB7I1/+5rz5uZ2R0PPGy9Ts/eHP7/+4b/Pz++\ndahgXjh9Lrv+3oxv6/QgC4D2FurrjnM7/uKz2fM6+uix0fGZiz+xE0cOZff/0hvZ/Q+PPxyul5uH\n6yU/zttBn/vwrJmZPXJzxt/24qfD9bJnZ/D45PMvZ98/RAGefP5lO/NjsxsOZMdn3sn+fsOBw1Yr\nFey5Z4b79fHs9+bHefp+3Xoxs6efXr+/x/d7r92z15ey/Xn/XEZp8PrSoq1+8pZN3ZDt78aZbL9P\n3XCvFYpF++F7H5uZ2WO332hmNjp+cphQGF8vZmZvvJCtvwcfftzMzF59/pnR8WBg9szT2fp5/Fi2\nnp55+pTNLny07nmMP583G8P3PzW77vjEcD2f+tF7ZmZ2/N7bs/NfeGV4/pHsMRUKdvKFV+zEw0es\nNxjYx8P1cONwfXw8aNqz758evb/J9/leN2uHu2n4/j8avv+9g0y//XT497uGyPYXTmf74cEh7cer\nly+PjqvzNXv5XKbfDu/O9NvL5y5Ya/pdm7r+nuz5n307e/7D4x+99KyZmR04nO3nd17O9vNXF7K2\n2+c/+tTMzB6+ac/o+PSgecX6z49/3st+722l6dHxqWefx+f/0vD3Hhn+3vz4f+lnMN1cv43ru/ea\ny+v2t1m230uFgr36fL4+Hsuez/M/tPK5C/bQjqG+vjDU38PjxZ+/bmZmO+960MzMzv/0VTNbc5gm\nn/9Pu6s21S/Y3UNkz4+H7Yz5cW6PJu3THUO0xbPD/fXocL/9ope971tLU+uObxuOTXm7ndnLe6oz\no+PBR5/ZI0M+x+c+GK6n/ddbbzBAe5vL+P4zM3tu+HzH36+Z2f96f/Yenn7nF2ZmduzAraPjt3fP\n250PZvr0Z69m+vRqx3f8xn8xM7PXh/v3/q9m74f2331T2ft8d/j87xg+/3e7q3Z20F23v8yy/dZv\nd+35jzM/5+EbM98nP/7fhvc/qX9Pvpi9/+OPPWpmZqd++OzouFiuWvt8tv+rO7P93z7/nr26fDm4\n/7Lvey37/qMPrDs+MLz+s7/IfKpHb91rZmY/fHeo/+648Yrjcr1sr14afv+24fUuXbZe82Mrb99v\nZmbdix+YmY2OG6ez97vl1vvNzGzhF9n99fvZ8RXPP6Cvx4/fGPpbh2bXjvuv/9iO33+35XJq7Pil\nc5m/NrnfBtNZ0NA69zMzM6vtziaRvzbcv+PrOz/u9/rB+9/x3DNB+2Nm1l/K9sO4/zEuzU9/bGZm\n9T13j45Pvlqw4/cfGN7LO2Zmdvz+A1YtFoL779wrz9vtD3zVzMzee+0FM7PR8anXsvOP3TPcL29n\n++fX/ut/Wff34w8cGB1/PGgG1/Og179ivTz7i9P22cVLV/if+TH5J7k/GrJP/eVPrTSffX9vMbte\naX6v1ctFe2vIM3lwyB2ZHxeGCOJTb/40u5/77jKzNf98cj+XhoFR5+L7ZmZW2X7L6PjNl54drcd1\n67Pfv8L+58e5TPpPJ597Kfs9x7P1cOpUtj763cxBm/Rnlj54015fvDyaCv36Yqav75/fYoP+IPj/\nzcz6/cx+vj20l/cM7WfofY2OiyV7euhPHBv6E0//6D18/v1eH+3JQ8P7P/V6tp7z/XfqrXez4yEK\n+tQbP1l3POl/PPfhWdv+4mt24nB2fydfzu4vPz4zxBffYPV1x7lM/r73e2F/5qbilJWLhXX+p1nm\nj7Y/O2fTw/hvdRgP5seXf5Hpz0n/JZfJ9f/caua3jNvr/Ljf7Y78p6/uzeKJF05/brVnn0Z98qPh\n/r9vKmvNf7ORff9v1jN7+fLnF61ULY0Qa/l+C91/pzewn7yS2cOvPJTZx5+88rzNdlft3qF+ya+X\nH7809O9zHs2XP8/06221LOZ++p1sPx07cMvo+K3VJbtvevh7h8/jvuk5K5jZS89m/vKRRzP/+aVn\nn7Et734cXq9m1rkw3K87bll3nBfVQvFT/dUf2YkHs/d38tXsfZ548F6zYulK+/vSG/bJ52ft5vuy\n/f3hm9n+zo+XP87W4/wt2f9ffD87v7orW+/LH71lZmazNx0cHb/y+cV18a9ZFg9XamVb+nC4n28e\n7ufhcS6T+YD3h/7YLaX1x48N//+4vsiPe5c+svr1mX5vns30ff36A1YqFkbx8mT8/PAwcTepb3N7\nOXXDcP2fWb/+Q/HTp6tLQX93cKk3so/FuWz/j+zlvizemcy35PvhsWH+44dPrx2vtnt2drifrx/u\n57PvvGzP9D+yY3fvN7O1fMWxu/dbsVS8wl/Kj//r8H5eHK7Po8P1SfonPw7Zk/dee8H2H8rWzwdv\nZOtp/6GjViiWrHM+y3dUdmb5jvw4l/eG+uv2YfwSimfz40KpaC8O8xNHh/mJF898bud/9qrtvHMY\nT/wsiyfy45NvZdeb3G+945l/9PYwHrvnSOaP0v6r7LjFmt1eUJ+cFfFZHi+P5yfGpfVZZs9r12X2\n/JPh+fsKdftk0LR3Btl+37HSHL2zkFw1cdntdu3VV1+1f/7nf7YjR47YX/7lX9pTTz217v8UCgXk\nPvLIH0xdOXE0//o8IMvl3uosHheKhZHCyWX2poN2uHtydDwJwc8N5ORxXk3MN0wueYKSjnMFNX78\nyOPHRpXDPKGTH+cGMpf8+PuWGYhbJr7vluKUHaytta/kCUyzDIl1ePf20b/NzA7v3m43D5N4ZmsJ\ny1weuSkLyHIekfz4Fz/NAs17hwovb6m/tzZjMzcfHFWoZ27Onnd/MLBBt2PH7soSvHnrybG7brKz\njz4+qmjlCiQ/vu9IrrJt3XHh/8gc+PK29X3B5W032xOH7zUbBvhPHM4MmnVWrWBmJybuLz/+8P/6\n37PrD99XXtF85La964/3ZwmNl3qZgr9nmEDIn+c9lWnbNnQqzdYSNGYZwfTduQIcwrvz47yN+fCO\nreuOcwWQy+RxrhDGj287Wx4h+E48NLz/4fHNE+slP87bQR8fGqTR9w0TlHScJ4TGj//7GBIsTyiY\nZYiKh4bvN0dX5MeFoUGdv/XQuu+b3N+Tx7mCHz+eu3ntO8b/XayWRw5XLpPHecCSy6FhgJNXtseP\nO/3BKMGeIyK++tgx23XuTbMh6u+Jw0N9MzzOHYS86j86HlYnj33lpnXHeYI9r1uNH5cKBdtfmNAn\nhalRkGBm6/5tZldQbdxeXH9818TfJ4ngx4+rM1V79Jb13//oLdfbdHlNx07vXa9vjz766MTx8P1/\n8H9nv3eYMBz9/ltusGcKPxkdT67/PGE5fnziyCGzIc9l7rDmx3nCMpfJ40cnrv/oLTfYVP2D0fHB\nMQ6YYtHs8KPr9dPhRx+z8r+tfefhie+/7u6Hgsf5+rp96LCOH48P7rl7rDWxs9Kxe4fvqzNs58yP\n88JGXgDLJU9Y0nGeMBk/zpMiZmbHx/7dH5jdNRyYlxd98+McdT++/8zC7zf7gkw/HfvKzVccv77n\nIVtsZve350D2vBabHds2XbG7Dz+87vvy4xyh8eAjj6/7+xX2vLp2XC8W7ODE/R+szli5tYbgvXFs\n/XWbbTu8a9vo32Y2Os5ltP6GcuyJXzOztf08flwolqy2+651/7+2+y57sPyj0RkPbs1/78D6y5dH\n+qu/nDnk+fGFT7OERe6wjq4v9F+xVLzC/zm8c7sV2zeMWm+Lc9n7yo9r12UBTj5FPj/OCetz/ZhL\nSF+PS56wHD8+/viaznji8fX6Iw+YJo/zin6eMM/l1qG+yFs8x49L1VLQf9v61cdGk0MfHOr//DhP\nWOaSH7dXswCzOH/DFcfH71/7zXkC0yyziXnCPLePd5SnbebQ0RGq4pZhgJQfj7fNjx/n1CP53h0/\n/v7YGh5fz4VScZTQzuWxO260Dz+4PDqe9EfJP8lRjSH7VJjeNULjFKazAKzfbVunN7Cv5Pps+H6+\nMmGP8oRlLvdPrJf8uDf8/mKeoBs7zpOWZrbu38Xmgv3aA8Pvb2bvKz/+f4bP+/qhv5a/nyeOZAkJ\nG3ZZ5MfNH2QFx8ru7H00V9uj4/vnt65df+zfhWLhCv8nP879i9yfyo+PDe37yD+dOM4Tlrkcu/d2\ns3prDdlWz/Z7r90wK3O8k8t4AcFsDYCQoyjHj7srTTuyc6gfh5RTR3ZusxsfXfOxnnh0vb+VJwgm\nj3PUb/5+8+M9E+9j/Hip2bW5YUFlaehvz916v9XOfzJCw9WGCZ/8ePsw4M9lai477r/5/617Hrm/\nv3uQJfQuDZFyu23tuFAsjgpauTx843VWe/TYiB7r4aH/nh8/OLG/HpzaNrzeYN3f8+ObJvz58eNi\nwezAhH08cPhh2zY2UOrQxHAp8vc6q9l6eXj/niuO+5Xp0dTvPB7qdXpWKpo9/Ph6+/vw44/blp/8\n9xF6LH8++XF11/r1mh/3PsnivXuG/mrOVX5PcXqUtDSzdf+2dtNOHLpr9G8zsxOH7rIXLt8x+i93\nj8VnZmazN2b7N5+unR/n8ei2Ox5Y9/+33fGAPXjp/x0dj7+/UqloW4frL5fJ48l8wMGJ93GwvP44\nT1iOH1d33T7Sp/nz6nfb1usP7M4hgCa3F/kxXS9PWE4eD/pZAir3J3Kgy6O37rWPT691mB0Ziw8H\n/b4VZq5b9//z40IxK2BP+t/HJ+Lz8eNGu2dbb39g9G8zs623P2DH6xfW/v99d47+3Wv37NAwoZ5T\n1IyOh+/zoUfWx3ekf8wynyLkn+VFRDNb9+9CsWTV3Xeu+/9rx/8j+/8T8csDW7ficbFStocn4rmH\nb77e/vPAWgx+w4H18fik/5cf5+nDPGGZS3e4HruXPh1edO14tla2w4+u38+HH33cOuW1NXy7rV/P\nJ04cDx4X/+Pfzcxs6voD6/6+b8yf2Feoj46nZ3iopNkGEpf79u2zffv22ZEjGQLod3/3d+2b3/ym\n7dmzxz799FPbs2ePnT171nbvzhBje/futY8//nh0/ieffGL79u2zvXv32ieffLLu87171z/kSRnn\nuPRM2fPAzTvA70PweM9UcTW10vN9KUVNLiWh4SjF6TDBt5Lzq2G4uYQaQ59Ooc3k650V4M9wwP2J\nk021taj2iZDILgBHiwRxoslpfopNPiCzguS/Qfwl4j6RkwsI1lNPFSdRU62xjZ3aenrr7+Xkcy+O\nkqueFsZYocnhZmYr58JcRb2dqk0yfP/lWjwn2xS1KAmdVYH26tYlMWgFhF5ZURBWUluH1A3wt6Kg\ncSD9QGtGXZ9oNNT6K0PbsYdjkcTTuqJEDUgKSUlwXJIMxOCuEnATk85Qw3nonSlKlNo8nLPE+oze\ns09gQvmY33DyxddG6FIzbhWnNi3VjtxtQCuWQ832WvFcYdTCrFrBBtSO55kCC3uztRg/ZKUh/Caa\nNkttkmZ6QFOsUOxQgIFSZqK9nHi+Jb8dtRaKtl/k8hRt17AHSg7+V/QpxTrrka53cMCTqFZt4n7r\nChtUAR+V6BKUbvDw1qupwrm8/PnFDU0Wr5fD76xCQ06MW3gVxyU9G0+ncuoW0lhpQrxZEb4WiRrO\nQ/K5YxJ5dTY+rkaKFQdfJIniuCQ+abX8qVW8AJOrVXs96XNlNWP1pqIrwXMUBR/4bjQM14wHpLXg\nHNXe38UBZYJqEV5BSiofsw0kLvfs2WM33nij/exnP7M777zTfvCDH9g999xj99xzj333u9+1v/mb\nv7Hvfve79ju/8ztmZvbbv/3b9gd/8Af2V3/1V3b69Gl799137ejRo1YoFGx+ft5eeOEFO3r0qP3r\nv/6r/fmf/3nwmvnz6g3W/u0BdPZo2rAwfh1wZhsXFuN/gEM8/EKxoh4l8bQsnWEF14RkLw0gUbd4\nEYYjdZvxQ2MKLU5OlOvAVZSQe08FTbEcm1KI30pNjYQgvFIXBhue8wo4jCrPtgoE32qfk5JvLV8K\nfp5aaACKHA5DfCgwTGBy0FRhMBh9hpPARdBIjj5OtFUT62iapOB2If/PwwdDv7nQ44CBplpP7dYV\nvZBQzKZuxcM7RO9MTRVfBWJ+DsD5+rUt4UmDiuOyBXZzUAUbLJxcElWHxMFJwjGcjxwqp7hkiROu\n0I0PZkhnFByOMU2IV6ImTU7NhnXdHCRuLkZffa1NOPsx5XXHyMtISRu1ZkCfeXzNtuA5LpRvxL+F\nRA9ZwKtEn0E+gGc4z6zYSxTQyuFYsJ9oD6qk/hYagNHhBAAlO4njsuTwG4lH04w5Y5UOirWpit+R\n+AJ7YqCYHIa4CbIFBt2o51KbiuOGVcU7sptqadDwsvGCa7lWwgLsRkSBESjZ47E1JApA4En2ILgG\n3jNNgTbjHEHsujDjOFgJ6U3l01P+wpM47oi4mqQPBSe1z6Z3hpOAOPDUzBYbwGVZDScula9HsZuy\nW8S/qtZTSmkvMfCKpL4jPOyKbK1KznqAMkvAGZt6cNGGtOE//dM/2R/+4R9au9222267zb7zne9Y\nr9ezr33ta/btb3/b9u/fb9/73vfMzOzAgQP2ta99zQ4cOGDlctm+9a1vjdrIv/Wtb9nXv/51azQa\n9uSTT151MM94m6PHlyOAmKp0kiFpnAsnR2LJnc20Y+yZwhkv/ANq28LGt6uMHy1wGlgg7n+6Fj5H\nVj+K4WVcENWEWMSjElIKRL5vZtaKrM7J9e9QCmQYG5cZbUEJ4hYQeStDWqWgSZFSUxUcEuTS+MOa\nVcEEJYdmKoyqwuo0rL/+xDo/duLEiA+REloq2Y4JSkeix8PwvNoBxzihIVNTS8lprs7TdFgW2ufq\nqcxC0KwQSr0BTACEqe5met/ESg/285xAbpAzTSgcRI4ZJ3sJUWLmQ8klFVjPA7BNZo494BiMgSgo\nExO6pzipTIHer8qXf+Kr61s5MWiDBO0l0NlK1K1gcLZZ6w/uE6faCyH7WBKdEiRy0I7nnMiBLp5O\noUKbg/bNaHzCaedmRq/AU4hwDY3AKp2YKt6CbjWhT2JFJbsJcanuf/ky+I6wNpcF2ommqpccXUTj\nRZWHb9zNXzAmTUAQE3LNzOw2AgNcuhz83IyT57SeVadCEfSWJ64mMIBCqHUd9oHE0+FJekb69Mvh\n4oEvR0KJJlHUcLwbz2DJDnTSESBKdat2HfaJ0MC+wmI6UeuZ4h1KQpanuEhdA6dO5TVWaaBSwgFt\nZhtMXB46dMheeumlKz7/wQ9+EPz/3/jGN+wb3/jGFZ8/9NBD9tZbb0X+xEx8MHRquRJTeKkKn3Bq\nphJPq7iqwoakK5wPejbKkJTJy8IpeywUtMogrw8Krj4f/NxMtf7Db1aGhJKAIpqOTVDL9S8QMrEy\nd0O4YqOEFHldGRKo2lFy0IzXZrcRDkA8e3bW0Q5KiXMz4eSBgSnAWjZjp729yJU5rLRRm6JYl1Vo\n0eiucuIQJ4E7WhsxcSvajWjfVmfjE5dYgRQtj6TPVABGf6vOcnIiZeKyMh0uEim7Ob8tfE7hMujT\nadbN5Px4RLUPxVaUKzOcOKbEiSqeUZsOdoQIG0iFkOocr/PGhfC+7e3goloZ/CPam6pITDJwQB5J\nn1wUa4mmqqvABCdkL8djSykAkNcHtElhJr59kPazJ8hU6ofaEZtypCsgLsE/UIhL0qf9pqASIj+0\nHb4X1cVFoiYXU9AoqYwStmRjghzWnxnXVQil6hFPQlklLsvQEkJ+kGpVL0UmDbJzIA7xUD/AZZZE\nogOniouCV5M6GaGES10vZkyxQfGBEkpoUZusmaYRwHOQkiAecaxiRJKU06tLsJ9VgYTWrPpdPUDi\nlXvsaxD9xiBhe7tCXNJOn3ZMSOcENesT2oNKnxBKc9bxm6nrQBUcP1uNo5mhe1EAIrMNJi6/KBnn\nuPRkzElUQiO2VTs2aXg18VSaYqWkqinTYUXWgOqHEnLy1SAnapFpLX4eff1ik1vFiRLAI1X4zfOi\ntVMhWDdDqAoqW9gBcWkGXCSeAFScUp0N/zbiz1B7iYJj1Q5LP63Qim+3oOp8dYIT7+QPn7MTj2WE\n4hToqvskZB8ZnxokJ80Y1SRbRMDJ6bbiedRIyGE1Y/2cshVKCbWVKH63GwDZqN5zrBVSASAlAfrC\nBlcAKc8FIuFIwWUIUaJ+m6I+iI0ZGucYhUJoj06FE4eSry50DYEspnXeusy6iWygejfYxk5oZJXQ\nofU09p43ynFJz1I52cTnq+wW+TR9eP/ZHwHt4OBRo+yQB8FOwWlZIKtJ1HOmJIxCnROClAuBIjkC\nQVBRPDPyAwb1cIK4LHiOSdQ6o8cp/TN4zorHLPa7lG5AblRRjI0Vtc6ou0HtDQK3UEJPFRwRvYZn\nsH0aT/a9cPqcfXVvhrpUSYslSHQolCgVb1R7N1IWgeGu7WR+TvIdq9N8ffJP6MkohFoZ4iBC+ynx\n6GDlB5JQe7cHCejRDT0oHqn791Ad0OwMKmqp3A2pDYUe7EJcR9yPqthAP039ZuoKpa4XM/a3G453\nVofYRengOdAbqrDokWsycZkr574NRv/25Ac90G0MdBMmFFMmYT3iATp3N+knk/KVRoESagq9Bgab\nKtoqQU0tEipoUwF1tAAngoejQrYiwXXIMWiJZ+YJ2qgK3jNADrX5GtQqroTec1FwqZI3RevsCr7M\nUmX0GSIOEw4tId4zM0MlrIIZlQiOFVzPjgp0oR6PuKStoVZySj4chYaNXs3ihNYCDGFSLW/Uwov6\nlO+lAa3qSp9gK4xwTDuROsDjAyhT34pF6TkCI89vpvY9M05cpuyeGvTWgqlBv7PuGO8HlpOygYR2\n2JzeGt4bKgDFIpFnbSS0G6oQQr7bTuUDUbdOysJ+LZ7fq1uCrgOgRPEL0cKoziNYT47hPAVo7x5c\nYgAB2qeSh8cQOkLEYyYqEzUAhmLEjQzNmRQq7KoVSwCGcQT9oNsbHXs6NZQQEk4h9fG7wDz3VxnZ\n3G3GFTyVkJ6ZEnrGg5SmcygJqsTTKNNZDc/bUNQTeH3HUDmMXYQfjkAhNRyGkrqwz1R3DYlCUBdA\nb1GHpYfGQ0l7GTg+xW+uTIf3bYeemSi4etbmNMT1ruKZkGsycZnLbWOj43k6alqHgRzzXuOLJZ5W\nEqvkla4m1aM2OA4gEUioWFGJS2qvHRT4HFIKJB5DSghBMxHow/+Xl4f7V44MVVTbS2L6FySIqR22\nIbLdVOlWvxmHBsBj9hgSahEzY/h6wZE4wwmUE8/4+LFjV/0u2dbhmTQBUtsK5PON+MDAM1Ucq5bi\n+SPiTwQzsSh6cv7NfK3ifB0xBClWPalEAzyzioP6gdZ5acsO/K7SJUfQiJQE6dZ/tylsBgwgqRRF\nRZ0QlDTQStjTWOoTJYqPCLlMCYmprg8I2vGA4YmHj/L5Y0I6YLtC3MK+VbRnPmQjTXuGNlUP96Mj\nCUl2w9MNoiaN0jNTPmXKtme6TL/M3QXUwkmgg0pNPf/4wja16UmJRVwqE+zh0iQD3YuPnTxDSoli\nRPkHhNQnW6vQRkXHHqxvhVbdMR/kyHU7NEXAUIhewMM/Sx1BZqKA7uBrTCrwnum5mJl1wKZPwaAn\nJQoJR+Lhmq8AzY7Hp/TYM6RTEz61Z3YH6UcP6IBETXUnvekZuInXEHoOi8TCNjRhiDRRoFUExyXp\nRqVPqI2e19kiGgAAIABJREFU1hlOe7/KWr6mE5fjQvehNis9eOUwkMEkRe4xsGrdp+S49CTbiMxf\nthaSvnYoReQjcmTsFV8gGYaNOAgpJJb7S/4sbOFmwcSZQycTqqwGyUkzsxKcI5PqYPxqc9SKsjnT\nxj2cbDiZr8QqmfhYlJNJQsZHVdppaaSeGEdCOmjgqRonLKqoRCc5OZ6CmwoAUqqtYjm8BlWreB+K\nFITqknxIiOr7YknRSwoljkYwnbiSZmJhdFZgmITgsSO7lZSwXqyNWPus/EO6f494UG34XeJZ9prU\njptu/Xl8WuUf0vA8ye8WmQRKyftmJri3kl5lc4SejYyDFPUBCHYROfxTioPUOqMhNOUqJ1RiO39U\nsp1aO/WwLwB9JNzPMtnqiINiE2SFGtuTcp0ShAoJR4PwIDkyUNQfCbuVHDbQg2pTCcJYSak3lX/i\n6TDsRiY71ZolGgNPp8DSJtG8eewwCdKmq2Qz2EC1/xegEPClQFzmD2ac49JTgaTkiEoatagdFZID\nnkRj6omFlKDENj2xH2gAwYrkCSFUE3BRiKD99KUwCkUackpQCsRl41LCxAXcz+p5bpHYdWBn8HNk\nkVQtb72wspDnUCuWancAB3TP1nDQVhEKjoySGjJCiUsyvoqnh9bMquDRq8wSWTS/Z+TeQ4dtvZx6\n+hk7fuxxMzObd7Qdk6NNOggT2mZWgOdJnDtmbMg8HJcU6Kr2OSKG76+EK5NKmqBP2S3nCqTHJ1FI\nqGrSVt3wfSqurFhk42CJ+SKniHdKPLSamDhOknIS+QAGhBWBf9fMbGrbnvAfFuAawvmjdU5+i5nZ\nmU/DJPeUaDIz2zpHvJB4SrQMxhAlJ59/2U48fHjtOoQs7cWj+oqQtFD1XrI1s7tuwnPID1qEDgLZ\nDjobRkiotYHfpfgSI0U9Z0IIyVosJDs8/vZiExJ3TbYBscmZKgySyIQoTpQCIiRg/HRWTxKMJoH3\nRXJi5Vy6oRke0MUO0eFEUp+JC4G3RLc2mKkaJcUhO8Z8rRfPfG5Hb9h11evQEBrdDkuUBIqvL85w\nlua24d+KFUC1eYbzwNCWXsWBOBXXp2dWdfA4Esei0nPV6fgBqv8/e2/ybPl9lnm+Zz53zEmWLFvY\nptpURQVtOihbaQ2pTHcFBsIRvSQcbIAtayL4F2x2wJYANl4AER0BO3YdqdRgSbiohrLdBWU80JIt\nSzne6cynFzfz5snr7+fJ+3306ndvoX5Xec/J3/lN3+Ednvd5kALPKIZOdgHEJcV54DtR1KA8gYUS\nhUS49A8gqUcIXslzTecQ75nWwDVRbCFADBVDexsskvk0+HpK0OjCWp4Qm7IzmbgscVw6frEjDoLc\nNhCAO45UZsDkmOzQgSSAnOCVToZ6LxYnHCx+rRknR0id0jFCAqlAmzg2+Rz8nYP4I5MJCEAVdYSq\nduVPScBn7Thz0LMWEk7A7Wkrx0rv8WfZ7hx9Ru143n3C50JlcQnfqdZSmmZOYOIUfGTyOsnUvShF\ny1ojNccIjoGd8UzCXZmmlCE7mw6/GBQIxLupHU+6eGa0iQkkSu05aA0g9KyyTBSKZav7eav1yN+1\na102lRAFTV1I9ERErtozrbWJ53Da+pQ1gchX53DGAFJTEYK+oU6dpoySEEpkweGYO22rRcndFXFD\ndwBFUvFYkC9w5fPlYnmidY+Ug982WlszEZdqzCh0f5ap1l7a09W4oNjRQVwSGlb5lHNRDG3CHCSg\nwxlLquIKkERGiEuFRs5G8ZdMrZltEHxTYlNY8DKSwA71QJ8Q3MnP8kwmLh/YKselsyVylaGe4BhV\n5pLhk84ErzW9kdYPMKo2L0VCo9ZkMAVZMGodiMgVYSLE5fsiAPgl4At0zBGaofvcf4+FZmhkIq+F\nGMpjQAKpvDUle6eAdnJs36j0hqi00Qg8KQpileMSnRyRnKPlhDYyQlxHqDkj1ARhre1viUC/0hYH\nnATLFHOg5JhqFc9soVVOznrivkHjSbbJJa6nipMq02ods4M7AqUP+9Oowy3EtS1fyvlDXtK1+sBQ\nqZ1TYbFtlZbBVvbza1/8/Ina8GkNUoEJoRMcmyoEd7uMkJEcj/hbsNY6HJeJc9bJWUklckho1HZd\nRDBvtdq36H7G8IXDb6fMSYLUmuo8o4DWQfZm0mg4wbSiOCGjOSC7Doj7TwFFKK5cQUM///Of4B9Y\nPSZzzIifIq5rAmroMZOI0AKfui/4ZykJOJ/lodGVOfyjNDc9+qG8otLwnEIF/4/y+aFbMKK+Vdzh\nZpY0CpX+WXaBjtrr1TynPAkphLeTr5nivY9U4vIsGSIaBCcdmVa6NBJnldVeR5xnQ5AVk9CK40yT\nyUWBEH+gvhYR0QUFQscIcaneczVKVXgSKkFba5KLBJCtpNon+WfBmVH7OF0bb75isXR4l+Bz5ZjV\nIi6X4rqc3BQiK+HzyQ63vVOruGqRyBQHmoBjqtB7Dv9nbaCjKtDdylZ9ZSrRQnyyzvOnvU4lWhSy\nsWSUmMi2zELgYEuIrRm8U9VOo1EIJN61iIh9AyW2Syq4VmkZzFmbYT1VCTVKGqgkLJLMK/RsJc+t\n8hsWI0ieG4hLTnbX+0aaAz0vaGHeeoUcKX+ueBzpGLpNoqWK4P2BCt4RXrKNzEFQO6ADXGsn9bQw\nZGpukDiPSgLX+uH3ROKSaHZUPol8Wqe9v2cVL2ANEn4TFnDpRo2xlCmqpxCXuJ4bxVOneDElFgnF\nTS2omZowTBAKsS8HjU3vgGhE1DnId3USxxTvOjyOTrecTFzCenZuUM7fdHpcWCcQj1qDsSPho8px\n6XRiOGgbGshzgIfXJg0jdDDpLNiZTg5tvqp9iAqqtCmoWyS0jUN+rzb/Wudcved7QCOwKV4LteRa\ntWmjok0L5uCcQMJVBpSDBSOUKJhRrbW1LWxOyytVpiI4CJZJC3JMYFM4PjVefvnluHr1akR4SSiK\nJRy0j+K/JJvCHDy4BUR+wlBV3BDnUfdCgQ7dS18kFGk8W8iRhlrxpgeG2JHR8kRGjpmam/TO1DOr\nRSgoNHL0gGNSnGIKCfda4TZlvQ3eN4kz1hJOykRcrhQir7/+Zlx7/vHK4oSOUJx0mFAykrCOYIKz\nBlMi2hFTobnZNnj8tE9LhU3xg5DsoPmkigA4B402OdyDVHLEaZNsoPNKGiTBFEIrM9nkmIM4RB0E\nI67DGMFAwi1W4oM3f/x+XH66zIm/ah7ijhBSfP99ALH0iH94yDEF8Skr9Bx2BcKY1Qg1SEI5SuwG\n/ZgD7clE9jlFDRozC+E3oAhUhwFRtJ60YTypMUOvRvK/wufUYdiUaVXzSm7mdfZpaa+Tez1853Ty\nKjuTicsSx6VjTrvFQQNcNdm8S7X3qYKp2ZiURkU76KBuIqt5d+cARJDEYk0oNZVQmk8ezy1zUqOF\nRImpILcK/X8VTIE4jFpgSIRHVVqZ4xIWK5HobAFPiZob43twbU+XP5ZFBbgX1aaKsQQkLSIC9xES\nhjguzjxf+cypDmYiHskU5840cT29RxXAuzfxGKpAksiFMqsdEhKX6l3SHBhsi5J2A6bunwTakF5A\nINSwHVm13BHHJR9SbdmcuZlcknhtRpCj5jOt9Vayj4KZlTVr2WqdiMOZ/seGSJxPQFV8fHwRXr02\nCM5mgq5iuSgHWs56gu/ZQDWiQJ9RbFB+MyV1nftPTegN1vErmrdKPJAMeQzlHlB9mtSEBhYDxTn6\nII7TUv5RolF3w2zCPu10XFeMBdq5iIiYQ+zUVX44jOdVTYX5ZHb0tzP8lQ9IxRu1N9H6QL5eq8fJ\nqdlBuYCtOuJq25uVbgLtdZ1uvX84E/zwZPQ+1RrclBI4nt8oeFJSUelQ0PpIHW4K2EK+o+7IKJ9n\nQAU/o3ip8iqzg/L9nBPdr91J+Ro2ECWquGzLnyufdi9RO0TZmUxcPrBVjkvHMXaqJiSAgdw6hoeh\n4p8mOC6VtSDZdBuUxCK0Alut9UEd1lISE4u/UwUnm8E4k/xalZtcIggnIiIm98rJztm4vq2DWlRa\nAgnaBmd2KNSBxzgHoUXIoHFQHTqYoDU4NlEd99jfV1+6evRvqg6qcV47zAeCe5VQwsphoSq8kwSi\nfIJqb8fzGO1L2HLotMGI90KBhkKJ1yao1f8nXkR1zbTXkgO+FDyK84GRBKPqvLjo2tcmEZdgayJo\n6kIXASENFKrOoZjZctrhKJggJJx4/gvYApeDh2vQ1S/950c8P+c+yagQRgmQCF7rpvsKQf5k8VOn\nSN4FJfDWoL4jhcwR5yH0bgS30G2IsUHP2WkVx3MYooKUuFSxhjNmTzuhQaae8/heOQmRKR6p9i3y\nw9U1T8bEmUo0Dnxt073y/Xdk8erxz+bZpy499v9EML/cRQMhpnwq4prHhIZwqinZ01vLS8IrhBqd\nXwnI0jsj9Kgy8ukV6IL8Bgek4Kyb1MUyH3PBs7UFfqBoVcY1lUA/Ym2kn1LUD7XrqSz4wqtRHUG0\nBh2I/ZnyGlQ8Ge+x37IO4BrJC0oxEjxLWjMUjUrEGU9crhotyir7uzSQjfRSmF/vlFs6oj5Bq/47\nOVnKMcX8lNEqjkIvYoGlBJnD/ZgZGGWeR/o35BiI98zE/HnjWQUGtJBJGgEYG10I2hbzPG4lacIx\no/UJURjG6R2EDPKrCcQtXZuam5lCK7SZqSQozjMHiWa8HN3WUWfTg/qKPpnkqXEoASAAdFCFTQka\n1XY+NKFQHyGQWM5+JrhEp3D/3SEXLwi9QuM8m94A181WefxJ7kX4rZlSb28gOaSsPYT3mYnCSfZp\nT/uZrVPru2qHpeIB7IJOm6gyEjpRCQ3ahy0kJhT2VMsf7k8GZy2ZGppbgNLriGL4DDqvnHUrc944\n588UdJpP6gu7OGZVQovGrErQ0xiE+ax8MFI1l5y1VLwz1rlMcR7HnGQr0lwlJpsj6hGXDoBKrkyU\nN22Gscmk3oACPvyU4rjcgQSpRKmS6wpAJUq2k27IAzvTicvvzfePUJfWKzQqENlt3CXLpoLJ3LD6\nFy4UP990FnKDkJWqppL4dgzVQcGLOd0jx6zeAaVk65pwZBoJgsWwoFZxmQSDBDG1b42Xor0fNvm+\neGbUPkLEv/JdJipdtroM3a/1P4/f/Y0bL8dL91GXFEwpARrm6jKQ4oC4VMTLVHByCgT0W+r+50A9\ngSIXhjlBhjqE3o1Cr3ErDLVQCyQi0YVABVYZveeFEE4bXiyfZ5xM44IIBeKF3Rb8vxCcqZ2ZEoTk\nsKqWO9pPliIwuQ2O6ejee3jMHrRWdo2g/STz5vqrr8e1F58/+pvG0xwSLXvJaGgyxe9FSUVVDEYj\nUTeDQ4roahx1VrmfQKD9vkKOJAbnxDPcaqk2OUBCJYYH6qf2IRGaibhsjJOyIVVxpLEQL80Bt5DN\nIHE7VNcMscPqXv/WuzePUJfOkqF4/LrD8p7i8JkTQkt3t+SpitMaqFrFuyiOVI+SJc5qZSTOo3yt\nzUvb1efJNMffpdht2ePC6mCtPDaoW0ddlrPUERp3BPuJk7hWMSqNwYtAyRERMdwsjw06y/kneSwN\nYa9xEJfZdqYTl6vWUJK72pw2QWVWpS0RJehMPnSAwDFW+WSCQcvr6sIwFg6T0w6Fv9VUCYbMUhOE\nd6N+CyrnmJxS3DqEuOSzY4tKB7lFuNJLpji0Mt+zI8BBrYVOst0xCnTV3HRQkmQUtFht55Ccc0y2\nIyeOmQkUWyKaqQIr0Y4uOdp0ySKYQZBsMl8rvjZ4lg4KRTlyqrWoaIbSrDJyNagVLUJzIpUsm/qG\nlYvrEZfEc70wVMUdv2mUOWlPGdVo8f+q+89EFdFpFqLgRfsWJRqSx7nF5Wnsz2jkB4rfyo6FSqYS\n5GtUjFcCHJV7iiOopZKjhNJc/bzVbn1onX1IWWTElNjeacxla99wEkdIL3C6nZRO4rQpQ25qJepn\nxNu19ympjOBxqvlM90Pz2eG4zBRijIgIANFwiobPj0LJ4jkrcd1MO9OJy1WOS7Js8QlyJjOTA5Is\n2RjItcrmssoIAeWuMSAV2oNsMoMARKmKz6A62BG8S0gwnPeeJaS6sqIpwYP0nI3zy8QlJIKnxPFp\nEParjit6Z067CSVh90W7AU0BtWEjLyVSXzz69wtXrh59dh4qkJn0BsR9GhHRAY6/heDeo3aD8Z16\nXtA+oWDEXELEn4EocIxQIA7HZVNG70YRidO+Rc9ZIcQoQZntFNXG2ZkFwoh6R9dC1Rlq0zORUF2H\nNYhUxVUh9iTB6SraUhkJNgxFYEJ+k9praa/pr5/jg8AwB6t8QEpOGZy9meJQjmXmuRRCk4eZEO2A\na6Ol2UHuKV+fhE5qff0Ikx8e6HfUOMPkGvnnyUaxg7L1LUB1wXP+pOCZRgESQxxn1Z79+EOOS4dn\n2skBqniX/ABM9ouOnFan3MVA4pXKaGxmA0tQVdvYa2l/Ukk7WjeaymciB7eIg5TvWHsesuy6Cf1c\nE125ETwHFcflcl7OBdAaoMTJKHZR3bfku38kVMVLgZszJ50W6veAqyvTEmnfLFOuz+ReGe6uNj+i\nsKEWWgpyIliFt7fGvFsUtCw7HBg67VC1piZ4B0j2yfZUxcoIWsg60DoSEfiiqdKqNpLRvfdrLisi\n2MmjVuWOaseHe9H8HZA4Xa9v3aCEmuT43AYicRGAYqswtZCLhN4QEpfEXxLBaFzHWBxHJMEAhZEp\nmKCqybSeOciNjkA81v6ccr5mozI37ATEFyJEezMJdwlVcRQnMiIwFYDVOqCSXw7mgLpirOgjKb2B\nWhDPme5fJTpGUNih4pUjzuNw4rXB1yCxxQgWu5K86fjOxLuB5+kUKIjiouuI0yQWadXUnI2gEKJ8\nSkG/Uvz/4v6pGLlcF0J0MAaoeDKbOFx1/ACoVVxa5fogQRJGUpvolzLRwGrO3N2HxJVKaMLvEV+n\n2rcdnyITSckIqfpz9DYYKEJtv8Rx2RIFOiehgfEeADhkosdIalIc0l0TVDJgtZoaTZnydZxnRsJd\nqitytAeJYFhPJJ+10bNLCffTBhYoDnhFm1X8LZGjoLOowioJG0qqP8POZOLygdOwynHpmKMqTsjC\nxkRbThkGTvfpBNpOiwBNSoUCQdVCpWqd6DDQNSuUKqmDos6RGH4L2PydypBM9sHzdMDIlNDQoiGw\nYZEyYEckp+Fe9OYHJgLt6uTIsf++ynFJc7MDybkInreUoJUcWkgvwPOcEhpKBIiM3M/OcIDHkAM2\n3atHgyMKx9gbrPU00ZTztSD1ePF7qnJbMiUaQ4/GaRVXTnbmO6A9aCYeGiW70AcQ88yZmzSee0Kc\nJ721qWTzh2vD9de+GddeeO6xhyBnsnjH1Cquii2ZAiiOMEO7Dwgxi+IHimdWUae+5c6xVFSNwb2I\nyRljLWnK169eZ0Ikm4Qj6ohj4PmNTgXiMlTiPPRzNAfUOKdrVq+ZzrOaHFvluFSGwhiPPfJnTRXD\nKXHplEFobJIATER9slMlepDiRlhmstlCw1KRUNxnZrcIdysareIO/20qjYgoUlYeky1CR/PMEa+k\nfbMPHTTKZHs9PDVKXP6bUhV/sDm0o/XY7LajKq6cb8eZrDV1BiehVpuglSpr1D4lTkGLP1Us1Dsj\n52Oyc4svwDCqqNKm6CTBlThPbWWkJxyJWsUuZbORQG/WIi7FM6PgeEPx6MFCPoax0eqUhaaUUWtz\nhOBY7HIShoyqtsfb62eL5dFnlJxw2sdoDva2uFBE6EXmGI1Yh6BhslufuCR35d4PfozHDIHInJJz\n8vzEEyOcbJoDaj1FZKdA4WRuW4QGd9ZARHUJlDiR/O+KuUnJpmlicmBmJLvV2Yn+xBG7o5b8xQEL\nBlxEYYI8hMqHxc2WYcML5XWbii0RnKDsQGvt4TF1xeC5GLPTvXIBNxOf4+wnKpghSgS1BhKC2Qka\naU9v9Xk+URxA5x8IRd1M7keFkiXflXlZ+TzYLSVQZXibiYkGZZskNKPEeeBzKpJvqzZJY60jP2gV\ncdfutU+EwNuE/3NHFeNhrnfX2KejNR39Y0EZ1mrXA5MQcQmt2irRgxzsYswswA/rDesRl0glJcbS\n3u2d4udOvOfQhVASctZhX6N9Djpv5qJVGeYadZE4Hbay4LYs32eXuoiS1zny9xWCeP8nt4ufj2Fx\nnik0MnyuntkOABg+EojLB/bZ7sNFzUFbdIwqAzpGhGgwNit1hApO8ZjEoJWUU2+rChgt8hCcqlfZ\nh0SH5APDXnV+/4PtMkrLcdrJNoX6V61NlcPqoBdRaEL1Sue11xOCVsXFtGFO9+8WP1/OuYW7ZdwL\ntopPmK+RFnl0/o5tvlevXl05BlAAAiVL56dlS1Vme+vl4FwjLvMQ7KTCq9CbmOwFZUJlhLbpiM3/\nANZNElqK8NbzJvJD/XWuztaibdrnGEHSg7ExXShxIgNdXulT7L1bdgojIlpE2G600HLbvUAOkQLk\nDnPWDg2SfVJhnSVmzlfX5i8994UT7Tv0bNQeSGJv6p0xQkisQbAGYpug5MSDdcNBXDbURWSprVbO\nTescgkqIDJWT9ZnKn6rkSKKoXaoJPxSpXBKDVrU3zuHaaM2KqEe9Oq3iamk8yRy8/PEnHvt/lCnK\nKjKiDItgH/H2uJ4qoN3LUxWn4p1KXE4BqLEQvg5Zbyh0GBJNdR/WmuMHUyFGonSJG1bRXFH3KxRV\nVIGiBVkXBVTrwP5Aoyk7cdnfKN/nBgB4IiJGN8uxMHEmK25mBl3wMRcEB3CmncnEZenBOLQCbWPB\nnsI7IbSXYyoJe9qOCbXwUdIggisjhA5QHJc0WRzFrhhz0EbP2YHUE0pUOaa16B2FuMzkuNS8R+U5\nQNw6apwTSk8FwKltiiQ0pLhd6AuHk40SDYo/BNYgxUtZKwDRFknQHnFcirlJQXgmVYO6ZjKnQOFU\ndMksNDSgxJU5SVBKtPQ32ZknpxE5LlWyu6E9sJbGYXogindUoBC/1xUt2cVziHWe9rPOgOfmqFLs\nLCJXAEKcBL/igk/5PofCB8RWLDE3qbthAsWziIhW+5PFzwm9dVtybFLiMm/OOAhBp1OpKZEDLB5O\nhRBdpUCYRqNTIYLHmaUqTmdPDKgdsa/MsalsF3jrZbyFYqz1QTuZw1vu+CeU7HbmpqLfoYIPLRuq\ntZs6r3qQtFFGvgbxjEfktvfOJvVzg+JqtQZnXnPubylqtPJeq4pH6G/DedS2RT+luiLn8/L7pFA8\nu1Wc7JIARFHHHPLfinwH8VUq3vDauAbjw8f8zplMXD6wVY5L2i/UYM1MdBASsmsUWdQ7cdTUak0+\nFVLNNIJ2RDsZRLnzxCpTRC7agJKKyjEdnK8LWiXikhwD8cq64JhM90VCFXkhKZjknyJBHTU3CHFp\nOeaQbCS0lzIHuUF2fMF+5caNuPLSSxGhW5LJqpWTBV8m0RuoDZtaeJXaMBm2t0NCNYLnuXKyMAnn\nBACViFdlCt3vdCTUmhIHQpJvpDbiMUOP+bTBRhaRv/iuCVVnhcYm1G9XCOE1YivP5fprb8S1F754\n9DcFdO1+eQ1WBWcqHg26BoeU8k/gPWeq/WYK7WS39y8g4e74lMgz7BRCoBB7eJ66ua5EDsiaWLNt\nM3wqTjQ4aOBEig/hN80qxVhlUQOuWcZ7J/A33/rJzUeUxZswBaAh380RYiQ/wAEKUQFfUVbR+Z0i\ntZO4oqesxn8XKGYcU8KaZJRUlyKh1JUkQB+11ERqyUCfUiU7G6K4IOsqoVwwEtWibjGHRkN3i9UX\nwx0704nLD2qZ5NeEdqGK2Vk2+VQMJ5sGf6YzLQ0dUFbBJUXRTFO8NKnPhjZMmdQHdUwD1UVJVSkA\nAsGMSk44HHu1ZvnLYvPNjAFpPXOUk1mhO3fOUnCWeZ654KvsAu0QJe4jcpGVtaru8rdES3oTMbBe\nzxKLhBaqpfwAFIK7V9uOqsYsrAGpr8VphxX7TCbFTDdzoVvlvVrMH/0bzBKnSbzmptAWmetmZvE2\nGz1J1Atk6vkjZ6khDDHCxHEz6FH1/on7D/+/2ue6gJBqbJzXIx4pQaXuE+l/HAow4xja01cLTu1u\nR4tmPu4czQxNtNpxGcE8kspQUEmJiTSEOCRzVuAm5qDTeaiSU7g+ijWYCg6Z96+m7GxcLkbSEpz9\nXjqQuFQIYqJLwP8v9hOn84lQmtl2JhOXDxbaz7TXH7voWsgV8XCH8B0RuTumfLKmHCA0ahM0lNmc\nFs4+LJjZiMu2QA9l2XSPW/ucZ4NGG6aYGyTA0Ve8nBCcU9JA8c4RkbV0TOGr3vq54ufKyV9W3kuE\nSKoaARBtGMef2QtXrhx9NoNWKBWAUoIM1dxUEhDGjEbPUWBg8C4ZBRJWW87jP3aev3MeNTcVqqDW\niMtUoWRJnXB+F0TQxvVCNwp1juNM7Fu1iC/lAyDqGtqNDr8qPwMMgIHbybVMRdMPy649f/mRv+nZ\nIHJGzU0SJzJukfhKI6K6tU0rdH/4xeBOctdPG9Za1XJGXSRYcBN7ELXJLQXistaIj02ZWpuc9Zye\nmRVQT8pFf5Wc6G8AJxzQTymjea7iwR3wjzJNoY0mu2V/f0s44nSfq50vz3364ye6thGMQbXO03qi\n1hlClmKruuLLBJqhzPiM6B0iBGex4p+FMTDZv1d3YcGIS0Wl5NCm0TXXKrRHuElN2LcF6KM/gPUZ\n3pkUvITTqD2IEu4NUUOj3d3nvALR8+HcFIhzQmlKIT763KH6E3YmE5clcwYL8peIRWkE39GmrPjl\nzqrJFhVYFG6Jdgtqk6EFTnFcUjVBOuxE3i9g8E5Fj4x4tNTmm4psAydTGZ2f1NYjoprLcZ8IY4MV\ndZWh2jIktVsdVvlrQbJROTk4bdRzoRYFpd5eabVVNtdI6EO9y314nrSeKiMnY3KPixpEyaBa4smI\nRkDN5YOD+veMnGzCYVCoglrD9nqxZm5fAIXsWyTOVJ8cUTy/DuKyFiU2n9QjLhWNBCktOhyDKAwh\nxublJyZdAAAgAElEQVQavIPhNotBTEE1siG6QvQpFoBcUvePYm8NJWdp/DnoRacQQ0UqJzktk5DY\nkSF+sDI4XYjknFM8qjWnVVz+HqoNG1Q28Gws6gvBs5tNMVBrW8Sjp5JQRsKZzOniQmSpEBwko9uU\nnU+wPs5G9TEF2UzQTw02yz663AMT204poaLmM+1Bc0DoKVMq9WRrW3lULo4fRvOcuugimB+d4rAI\nBkQtDUEhsl2JXizPwR75eg5VgBjnFKMoxCWBSygJqdbGDSjsqvXkYEbnyUWjnsnE5YN5scpx2VSh\nv4lkuqOA2pRRdVTtIxRQI6pM9DB3iHzfqNoqJFymejiZcmRqEycSaJGYtHASqg7HJVY6xThz+K1q\nzWoTNsR5TmqvvnIjXrxyyHFJCCEVtFIsgUlgkQR1hFYoCM9EDqkW5iZMBZNLWOscfjdVhc/cUuYQ\ntHQFYX61EJ6TaLESOgLVVPlzJEqgTK1n1eqgBrJ42aqnkXAsMzfUmj8MTK5/86249tyzjz3GQVyS\naqfsiAGEyuDcx/igSlOBAa3BznpKx2RSLClzEopOboxa3lTQTNc2hPGU/cyoEOMkLi20C+zpDnry\nLNu80t9V+7bjh5wkefzmT94/kbJ4LS1QBCcIVecN6TDQmFXdZUglZAT8luBiIhLMiUOcLh7ygxpa\ntq3CKhZ9jdipZSjR01mUOA/Z3NDocIwosBQavw3PxqFTd7i+lwBK+0ggLh/Mi8Xy4b+9fEKeY0TI\nnf337lSfQxP257UW4jlUC/Glp4qfK2U6SvZQ9l/ZBJCd1FYXEbHslZW0Wjvv4zFE/pyZ0Fx/onxd\nEdoxKJlqk3SsA4nT4Xm+ZlLO3Yd3pkbyYKNcaVW8GpwEg/MbxNOyrYRoWgyHhRINx6kSuu3W0WeD\n7TIvo0JcUgBG81lxKU33y4kWVU07B+0epH6njK65u14fTKn2JTLk8jXWDEvpUwRGE3AmMUEt9gws\nOAnE4c9dKr9PEk5qAVVERMQ6BEa3BXqVnHkS1YvgNi0yyTNmtJ0ONi+Wv/hp+eOWaBWnQGf/3Zt4\nzKfXwckV53FaYmuttZiu/Hv+6N/ggc+BemAuOkXG98qIivMGCkYGrfA8KQlyz0nQ95mzl4wSCkRJ\n4hqNJ+m3wvOkmNlBO2GnTvC1rcMaTEhkZSpmHwNyxUHWon8kYg1CYimEFu5PDYlc9GHeSgGKSl7M\nTbE2oHikcIRJPXvVP+reHZ7IX0Lf1fA1VOKMCj5k0z2O3Wjflp1flUZUERFCHEjQZdDYcBKXe4S4\nFXzmTM3F56Ero/XEiYMHolNjOf9x9e/t7wLq14iFW/DMSNU9goWLOrnM5WgU1+0a+zN1KylVcYod\nVbL3bmInobIzmbh8YP+u83CxbqoJgTamzlozIjxOpam2cu3gw86JtmfipWwNykGrahWnidRb38Zj\nMHEkWqhrnXPZuQC3M9nldo/ayrk6/3JWv5BlJmhpI+0phBiMc0dp04KhA9pCKSPSK2sZ52+Dk3+8\ntfX5F186+mx8rzyeia/UMTUuJ/fKreLKqO3S4clxqtNkKtlL10YO61xMzhk4oFY7qJhPmeg5pPgQ\n56egES25dcRZN2qTxxJZC8mZ7pyDtupAR/x/CkBmouWQXqdq+erCuuUoypKt7udXX7j8gfANCh3i\nCXBA+5RAFNAxDsclnsPgP6XEpfNclH9I42lDrduV64PyAbCLwkD7DKwx4+x1UDwS+xbzORuFVUdV\nHBeUZgR9CImk1rOIunmj/HCVbPog9sVnnjz6t1obKHFZX9LwxixR6ajf6sK64RSD6ZhN4kqMiL5R\n9CbrQLyrDDkBxTrjIC4zBXSRL1PM8y50H6r5pJLH5d8SnZzwoIkaMEK0ihP/LlD/HF4bfiXOX17r\nJ0pQB8AlZG2BqqTxpFDn6zCfJQe4YWc6cblqDoeXFcyQMMKWwcUBpq4qW9W3ZM4ZZKWRqpbgzKtW\n8Y+fKy/+U0F83JqVEzqLA0ZVEeKSTPmrtGFnCjpJhS/pmJUNkzOGw0KLlZoaA9jIFLKUEg0KjYsG\ngYFqFcdXIAQ4ak2NM3KMZ6KizeeBVrhLZaGjiIjlzbvV5yFnWimBk9F4Ushu4opSCR1yzBzcCLWi\nOckJlexdS+RYo/tXgRnx7pDztdjbwd/aP1c+j3LYyJnP3E8dVfFFl/eAQWUxdCkcYzLyWyJYaGKy\nz/N8Piu3RNOjcQoUIXhBiWJlsHWh+DkhmiK8RAO1iqughRLOhFyol3gIC4VCQavDP6yMaH7uGaIZ\ntD+qVjRPII1+C/5/Ms20s57R+0QuXVW4AQS5EvNAvjYHDWysGyTOQ/cfEbF3t25XHwr6pwmIcarQ\nNZPmhjqftpSqOryz7lC8M/i59V75i/Ed3utRgMUwil3uik4NpGQwtq3Jzu3qY2gPUHza4936biGK\naxwEN5lKXFKeRGVPMoUAaQ9QHKO0btCYUcVL3LdEwEeAFIUg5/MD4pRQrcEK4Wo/RXBJMur+TCcu\n/2W+f4S6dAAlDifWfmUi8rQJqdOtUgEzImKNNl8iBRe/RQGws8CqVmES5yHnT90/jbNMp4SSo9nW\nW693MglVd74nhG5gUVzr8jMjAQAcG6rSbyiBI+JSJS5pwwK0y/FnucpxSe0zKtlM39AGM9lhp4jO\no1pLKeHu0EigAqPgi6XEWV+0XlHQRPeiZjkNMwchqRIttcuDJOw3xJ6U0mHJliMeZ8yZq6rDHz5f\n3mSP5zmpYypUZ29YuT8ojkv4riuSoyOiFxAO+BRUKGn8KWQ/Bc2rlCTXX3/zZ5TFS0aJQ1VYRn43\nA+MpUf+VvotaG6jg4iS1+RxOK5roroDP1dygQIfWBvX8segrWsURPEj/34ikVJFUCZFVnyeZX+ys\n2nmgvlBWK1ykAA9IP+XoA6zswW+881588ROHBSMNoIBitGqVNtSmZ+CH0vYkKVbgNJYIFflnKnEL\na+0CqBqUqQQ5mRI1I6O1UYnKZa4AmQlFqWmQWXQmihGx1+JzxsK+QVdi2IZI9tNcI3CZumain5LI\nVmN/duxMJy5XrW8kCB3FOELOOoE2mQqynAU71cBhGjqtYETwLX6KWg4VpJ1I1gnqHVGPuHSMNvgI\njfgqmSbYNlqVid9qLBIQtWVIRzFO/NwaiSnA2HCeizLaR5cH9TB4dBgLf38YVNAsdMTveHyzjAVS\n1bQxqlbWO3kbTpseiVlkUiU4BN9ShKqe9yjTaK+zWvKNtiJMqjfAr6hMvecWJEG0OE/e+0TuR4Fs\ndtBr1NpHT8ZBTrVW3n9ruXzkbzIKGiW9guC/rDUHUUAtV4p8P9M/zFwDPVRjPcelY/g4BcUOcmlS\nDjR5acqk/nBsaXD2Isdj4r04z0WtZwpdXjIluElUPuqSCdzwyNycL47+Vn7DCPZHUhSO4OKR4jJF\nZKlRvJoAN6zjUznmFDxpTxnv3Kr+LSreqGfGaHTHPzYEhQy/xQHxUGGH4joHCag4LsloP8kuEKFP\nJ/wD4pPdn5WfWX+dFerJ1VDPmdagjxTicpXj0knyUzWrI/h4qNCCaCPHMZdJqNMNzsgDO21gqVIV\nJ7SLQtxlJgFoIVGVqdr3LFXdhZNRaxLZCt+RY6RUO5EUnc/O3HuA+HOei0KO0LzVqtp15z9+iiv3\n0Zb/sxrPjfp1zuGJIXPOTxs2tsgF5/qzA9PMbYOcH4XEqqVyUeq09JyVw0am3k2v0tGX3RXwok85\n/yD3GVrrFHJk2fANHUdbYsHHmM/UEq04uGlPUUXSTKcdRf0SBeLawj8mk4VVA22BXKLGHkymUKp0\nniWUETun7SAbJoVAwXdTir6UbCJRR8dU0OzQidWOTfXMCMHtxHurnz/71KUTxQuIqjLWbAdxSTPQ\nWZudTkY6jzMuzrKdVQS1WoMRKKM4JilGNOI6Oo3iaySrFYnNNuUHEyAEBXTVetZQl7NjZzJxWRoY\nit+KjJIjSmmUXDZKXDoiJ2fbx6nnNUAzJjITbIvAwOAYzGzxH0J7s1oUahG8UhnRqECR2m9HESJD\ncL41gPufMn8GVVrVMCOEjLWRw704VTsVNFJFldYTlZyjqqXka4TP6V5UIaYHRObLW4L3Cu5ncq++\nrQKRiAeCFJs4Fo12aMdmYq8hozGgknBOdZSMWu9Hd5hL9VNPlFvvnedMy6bT8qWs9s0o3ikqno0k\ncqLu/EuDy1ch9AhtsBD79nC9vNZmgmGXLV5PU1GCfdgDHH6z3Ty0jQpMaN/OFEBxivEqABxsXix+\nflGgcMinQa42EcwSb7aaT6ioSh1ByfEaBZqNARsMkj/cn4zfsgSiYG1S1huWEUeUhCSREWUqcTi8\nkLdvkr0jCo7/C4knigQ1xdVYcBT+GXVeqb2WjEAXym/owh4wE2h8Fm+sBzDQMFcIRYqFZQsvXde4\nvAZa3NSGqWumsUFFb+LsjuCC688JeglKRGYm55wcgRLCnO6UBVTpmruGdglQ2UZExAB+z6FRUHYm\nE5cP7Pvzg/j5zpp9vKwogtEhJPLgmBr2KjhtxOABnBMD/C5wfy2360VjpolQ4+W8/vyZjqHj5JAp\nPiTHKOE+3edkY22krSrtdD8k5hLBzqSVuDTEeTKDk95GeV3bO7ZZvP7KjXj+Puoys32GlhlC20UI\nfjVRUcf11EE8w28pQaGD98qE6cs5r2cUNNHrlwqQMJ4dbqOFcKYTaYc0JxXYGiQ7qdLuCIqpVnGn\n5asWiZLN/VftABu8d1RsiIiYISVBfYLU4YVEW7nP66+9Edde+OJjD6GgtS/EebAYLTnpDPQkHLNu\nCFMwx2VeosNJGim3lQJAp4vECag5EWwo6mLtMtc/IzdUFSJoDli+cwe6WARSfrAN/OgGnziZ5H81\nqifkO44N/4T8fad4uOqfv/WTm/Hsxy9FhL7/O8AzfUmch2Lk2YjjAGqJ78LkGN0ScmNPlo+ZQju6\nModGYw5jpicAHLQ+OhyHVPBR3Mz9deZnr7XMbj0Vh1EingRgIkTHInTYKc5kSl7fUwlquB+kDEtG\nXBKAYEdwrVNcTy3cPeGD0PNU6xnF7x+pVvFVayqf5wT0taYcY0elPNVggKnLouqUcnLIyMmUySng\n47GcLMMQISSqZoPzW+Xfci7AWDAzOVvJlgPmz6AARIkQ0TjrDKC4IURjCAUwFhsZrtddh5kf5tmx\ndX++fPgZFTWcYA757YTQzey98hqo2iSJMJx4kpR1IHO5mPJvIU+MUYhyWq4oMPDEeTgwczigyWiv\nU8HcFgjNYCucSFxS8SAbcVm71SrO4gD1cCI4t8xI9ipz+J3aler1qiMFkz2riY7l8pG/KThFnmOD\nrmWNiM5D8Iv1RYEd1qAmeLaV0VpvcZgZreIq0Kw11dpKPkWrw/4htgOSEGPlvIjQ+zZ91RjiEtSG\nWjI5Ae+gk+drqqDZSd33wA+msUn0EhG8P6itiRI6q3v9fLY4EQKR0E6Odfr1QkdUv1brCc0n2clY\nGe9IzmAH3ASLndwDKk0Vj2oRrxH1NFvK6LdU4q4LBdShUtWuHM+yEAanUZ0ClGwbJ2snkDkxei3o\nYAqdjxGcoFX7duYapOxMJy5X0ZYOv5VjtFw6qtZkaq10Ws+rz6++hN2HFOsieCF1WtsoaFXVLGrT\naw3qE6dkyjGnqa+czNm4XLWkI2SruBHQ0rVljnMFwqFxLjkuaWyMaWyUk8MRYaEAkPtMkvwTRAMQ\nQscG2rWrV4/+nalST5u8GrPkgLZ7YoPF89Sv51N4llQEiOAkXEc4BXRtlgAFVCCdfJYkbM8EvEFC\nQ+0BVGnFhJJIdpNlq4rX2mBbjHMQ51EubrV4oFG1xtZiYWoPQML8TPdsZW2+9vwXTrRWU/FEBc1U\nCHKSzZloC+XrZiau6D0rARIyxRdLAaAKGhvhRcx8Z8nCYRY1E5jVkULrtqJsaoBLUBX8JiBAIX+v\n8r2p9WQ2BgCHoj+C31ulsXjumY+d6Npof9QJLThG+EfoB8K24SThnFZxp1PEMRQ0MvZnZ55TC7Uy\n8h07xtpA71PFAZSgl6rilXNT/W96zrJ4Bu/z1EUiRXLw4E4d6tehslJGxQuaG7SePw6IcKYTl6tm\nqX8hDNvhy2xmsGaip6zzb5STAPfUhk2VVsMxtBYFFOcx0B6GOW3civel1lpG1YystyGQqJVzYC5S\n5DNwTBRZMyFUZqOyqner/bS4ujzTJP/AyUXBnBiXNGZVoqEW1aLWRnLYFOKScr1WOyJ8PgFel8Pz\nlJ/N4AKjgWtNtShlUjyoVmVCtjrm7I8HlSgtyctKKF1jb1AJ8tohKAsHkLgE4FK6IWeuUBVfM+Yg\nEuZn5izEQ2PEpdN1UJ+gJ5uN9qqPIY5Ny4z770CBYqqQxXR68R0FtFIYoVLVWnFoIcfljAvrqCqO\ndcjcpB3FO047rJNQadF4Er+FCtmGQjmeo4EClTKF4HZovvrbZZSe0xGyD3vwOQmUgSKtSAJSt5oT\nItMxmRyL9FwieN4qoAiZswc5nTeZHIszo72dEtcK9Y77tjiPg2Ino0em4iMshpIPlNwO3RnWd4UO\naW5i130uQpL22v+f47LC1CZDhuI8mUg0YU0gLuUZEpNgrXWBeAOj4FQljlsQNDbFJepscqol9zRN\n8ejVmnrERIqtbFFZHXIcCVJIzzZsOTzmR71y40ZceSlfWbxWNChCIHEEsJraux3EJfnfCh0w3Ss7\nZk5yjoNT4fwkJhSlcFai0RhQra1zSg6QcnEy+XsTAa3cM4zgvLbt2uG41ImO8jMbbjPCh1qLUhGX\nK2Pp+mtvxrUXLov/fGgOqowKQWoPSFUIp6SBokQgWgxxXfRr5NNm0xXRM5NFNUDZYqeGw+NooL6p\nQKTFE5sBPTBdAiQaWg71CT/nTOoDB1jgdOXVJkeI3zEiortWjp3U2niSsfHmT96Pyx9/4rH/j1XF\nH3voz5jaNyhB7SThkBam74gK5sWu1MKuLHNvUGtwZndJ6n4m0dj1fNK4phpxHT0yRZezqBT9zU5c\nOpaZP3La63vkUyQD/85m9qRgmXGJWpQ3YSPLTDQ1xXFJwaET5KljaIFxWsXXYVNUXBzUKq4sE3FJ\nHEqTXcG9R5wj8P+lU+A47bCQyHYfErQhNUGR0OmDk6eqidVBS/JiSQIUasPCYQbXdpysutN++Fkm\n95iDtkLnQzgSO4D4UgEAGUosCFRZqgox8YImCzOQKcRlE1Qq6vyTWV0ivCMI5htihakO6CRCDhKX\nzr1QwVXxy5EpddrzUG1XtCyKzL1k2Umw2vnsINS87h4lmkL8r6fLf0rPxkHDK6VRFucxEh3G+xwQ\n2kc8MxplTRU2MxH0NP6kr0dggCn79DRuWpUJAGVqaBLqX/lnMziGgnOVnHWofE5C2dRqtU8EnCG1\nYam2TIl4Q9WcYkTFDZ1Z2HXiIJoDLWMP6K3ldfEom0Dx0FEV7ybycsrEJWkaNIMHw06+kSo4JYvt\nZJlC9xMvJq2bQ8HZ6zQRnIP1sWPonSg704nLVbRlA/QpEeE5U7XWwClsW47KbZeqOk4TCR12h99N\nOJmIuFSCQoZCbK31N0WyFZwJJ83iKMNxZcZoH4QHrfYk4ndT8w8T5LDBqBb6FinqivMjx2Vipe14\nXPTClatHn5HTLKvjlQ6YEiHrAl/e8l3e4DP5YOhOhpe2+fw75RbOJsSpIgQvqxhn9J0KjDKFLrrQ\noqKCdgqaKOCa7pTpHSL4/tfE/Tv79nY12kYE4MRxKVBN1KaDwVRiN0QEB+cKvYgImdTK8sPncu3F\n5/J+95hlcgY7iE9KhKsiRLsHqK5EwYBsNDTdjSMO5SAux+TrGErs2HaeXG3BdsSGVMWpSN3qcQDq\nKEGTOR1RlJzodPn+p/vlfYgCfXVdC4Ni4SR2+enHoy0jIrbAP5wo0RIjsO5tlNcgWoHUM0OhGWdt\nJhE0cY/TUfmq1+Aelc2Ndti7iRyDHgd7+Zq1qB4Uo0USFBP04tpquTxV8YyW56ES54HP2ddNbhUH\nsFxf7AFUcKCx0TFiRynEB7v9R6pVfNWaYjapdaYcJ0+tL5kOEC0+Mjm0c6f4uRqsc0LbQJZd3f8d\n4H60MvaiYpLZKk6DsyeqGbXIEaW27RgtcG3DYdiH9vKB2BTmcP8k8hHBGxkFjQpRQeT/avOfkEKy\ngSwmJ0txfCKHVCKqUK1nLeA9Ug4LbfKOqjgtWzv/+m71b80FosBBHOF5UsU0+Lr2k0m2a40CbUJ2\nTwUvKa0nyqh4ohzwVKAstYoroDxxcNOzVErsMG8X4h6Jy3EKnMERXDwiNLplkARWZvGLEdpK8QxD\ncNIdMtqG3pvyD8ioVdwpXmbuG2tq34DPqbvp8CDoSEn0gxQ3NZ0FW+GMwkkmh5syGhtL8NsjIlqQ\nuFTPDH1qRwgR5qBy22t5lpXReRSV0vyU9+AhJGjnikqWnrPoYqF10+EGJp9G8exSkaapVl3mmq8/\nv+T5BVMgnlrLFOeZ7t/FY5CzVez1a9CV5xitz6eNuHQKUQdCCXxwvuyHjIiyqSti9ESEXfbcPJOJ\nywebxirHJbajJqMXaSFxyJLJVEXdqYBlEoO3huUWPpXQ7YjBX2v0bFRypDUvL+SKw6i27VY9Y3JX\nVGuh4uUrnkONGSOpawUtFEwYc5MqnapNb18s2NUG96KSJk24pcdvf5Xjcnih/j0z9UD5czUuJ4DG\nJBRQBAcTHaNHZCMx05SpQCmVRitb0SJMxfHEfbB2bYrIDRoJ2XlnP89hj/CCBrJlB5Bw4pJR6Cbx\nugaXLuJ3t0EFd7JzG4+hfbD3IbXEXH/9zbj2/Ak4LkkARiBnKNGg6EqoSCYRBZWUJYrjEi2Rg90p\n3CjEN32zq9D4hPiDa2uqrY/eTWrLazCqRgW6qTxilGwUAShyYBuJS8cIcajWU5rPThIOO2JU4hBQ\nVav0N2/++P0j1KUqrNM1S5ov2Gt70F0TUV88UJ1n1HUguxvAaA1QYABiGUPB2eBn1pQ4D5mzbVjc\nwIaqOq5Ngubt4KDO31P+3OmWFNgUzRR1uLX2RewABQdaA9TS3IKSo4pPdkm4KXl/PpOJy5LldiLx\nj52DhdQJ5sjUUuU4jbUbiVorW4PyZFGceMQH4gxWh6cGK3CDPP4OZVNIAlL1IyKit153bdSiFBER\n3bM5jdVQpuBQJQ6HgFDAcabGH/F1irUBFcI3uFUZQQjjchLweOJ+sVwefUYOg0IPktG7Ua3iiOoi\nwQhhB7frUaoUNK5dOofH7PyoHo1ZayqY7CKRvXMeoxXIoEToDsp7nUpOkHJnGxLEam0czSDZnZwc\nq+2u2HtXKEcTcmDJfsOoEnW8NJSrld2DxJFKwo0rgwmrs2F57N8rf1d3KqjEJYxZ2mcieK+RreIo\nglMfTpHSaKvPCqT0BjITXVKddVzmTCVfO9vIp1DUC+Tv0tDoV3K/uqa5VLFMmXd+gezFxF1ickaN\nM0pQqS42ms9UPGuL9tXeej1CjPi5V+fmcrk40Vx1+FcpcUL7dgT7IR43cF4hgGJE0k2I4MSNyhFQ\n51NrVp8EJKS66hRhYU/x/KkQ4vCCGsUjFIITicvJCHwNmAsqcUlnUTsQjUDydbNRhQSWm1T6YBFc\nWB5QsSlwyMjYgVDfHylxng+iKK5MZbn3wJlfAx41R21crclW6zltJLQoKkcCBtjFbXaMKThvr23w\necCoVVgT/8JkAYc5ol6h2rG9H5fb7iMitn7uqeLnuMCqTQkQl5KvERyTOW0WERiArYMzNxGPmJBo\nVLGJiGjBxMGg0eC4nAnnDx3jLlen6R1MoFX2+Ht+6aWrR/8mZ0aJQJFRAKCQiB2oACrE5fYQkGiG\nY0qBrkqC3f3+j4ufr5/fqj4/IovVQE+0kUj2PpHZ92wIOo0ocWnsZ4S6vyRaa7lLMZP7s95dUsnW\n2mSH4jEkP2T8/i0+PwpQ1IsMUJz1QduRT4K2jIjoDcu+htrnNz9eXs80LU7ZD1GCRtQRQTzbaszg\n8zQCg0wFUhU0UkD3CTWfIKClZLMKGjMFdcZEi2QUVbJ5MVFV3OA/XZLY2P49PIbejXN+p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xGxExhIpaptCLMlSBBedXGc3ngzuM6mqfuwTf1KEWIhjxrAxRionJyaZMradYhVd0EfCV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\nnB2qlbAlZ+DSE2yj71mV5kJbP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ad97Ro0fnfXz37t2xe/fuix6//vrr4/HHH190uBqONQF9VkMVBPqphvoH9FcNNRBg1lB3\nFQcAAAAAGMagSyBeFldGxP0D12u6cVmyAyyT61ICy1OyA0Cv7I092RGYU7IDACQq2QEAmtF04xIA\nyNd1IE6zDwAAWCmXZAfoUrMDAKSq2QEAktTsAACJanYAgGY03bgEAAAAAPqp6cZlyQ4AkKpkBwBI\nUrIDACQq2QEAmuEal9AQN3QCAAAAmNV047KGY030y6CbXGho9lUNVRDopxrqH9BfNdRAGL2um0r6\nm7tdTZ8qDgAAAAD0U9MjLkt2gIY4MgB9VLIDACQp2QEAEpXsAADNaLpxCQAAQH91DdLoGtwBQFsG\n1ewr47K4v2O9pk8Vr9kBAFLV7AAASWp2AIBENTsAQDOablwCAAAAAP3U9KniJTsAQKqSHYAV4JQ3\nWIySHQAgUckOANCMphuXAAAAAKuJG+jC6DTduKzhWBMslZFba0ENVRDopxrqH6w9mjmLVUMNBJjV\ndOMSAAAAAFjdBh28uiyujOi4r3jTN+cp2QEAUpXsAABJSnYAgEQlOwBAM5puXAIAAAAA/dR047Jm\nBwBIVbMDACSp2QEAEtXsAADNcI1LAIAecfM2AGC16/o+40Zga0vTIy5LdgCAVCU7AECSkh0AIFHJ\nDgDQDCMuoSGODAEAAADMarpxWcOxJlYvQ9dZvhqqINBPNdQ/WHt8P16sGmogwKymG5cA9Itr7wEA\nAPAy17gEaFbJDgCQpGQHAEhUsgMANMOIS2BVMBJveF4zAAAAVrOmR1zW7AAAqWp2AIAkNTsAQKKa\nHQCgGUZcAqwCLli/dhgJCwDAauG7K9mablyW7AAAqUp2AIAkJTsA0Ih+Nk1KdgCAZjR9qjgAAAAA\n0E9Nj7is4VgT0Gc1VEFa0M/RLuSqof4B/VVDDQSY1XTjEuBlg67xqKHCatN1vVLvZwAAgHOaPlW8\nZAcASFWyAwAkKdkBABKV7AAAzWi6cQkAAAAA9FPTp4rXcKwJ6LMaqiDQTzXUv3a4XAuMWw01EGBW\n041LAAAglwYlAGtB17XmaVfTp4qX7AAAqUp2AIAkJTsAQKKSHQCgGU03LgEAAACAfmq6cVmzAwCk\nqtkBAJLU7AAAiWp2AIBmuMYlAKxBg65J59o+AADAatH0iMuSHQAgVckOAJCkZAcASFSyAwA0o+nG\nJQAAAADQT003Lmt2AIBUNTsAQJKaHQAgUc0OANCMphuXAAAAAEA/NX1znpIdACBVyQ4AkKRkBwBI\nVOb+q+umeoNuxAewlhhxCQAAAAA0p+kRlzUcbwf6rIYqCOMzaFSLES0Zaqh/QH/VUAMBZhlxCQAA\nAAA0p+kRlyU7AECqkh2AFWD0HixGyQ4AkKhkBwBohhGXAAAAAEBzmm5c1uwAAKlqdgCAJDU7AECi\nmh0AoBlNnyoOAAAALF7XZWkG3YgOoFVNj7gs2QEAUpXsAABJSnYAgEQlOwBAM5puXAIAAAAA/dR0\n47JmBwBIVbMDACSp2QEAEtXsAADNaLpxCQAAAAD0U9M35ynZAQBSlewAEBHdF/LvugEALF3JDgCQ\nqGQHAGiGEZcAAAAAQHOablzW7AAAqWp2AIAkNTsAQKKaHQCgGU2fKg4AMC5OewcAgLY0PeKyZAcA\nSFWyAwAkKdkBABKV7AAAzTDicgUNGrnRdZMDAAAAAKDxEZc1OwBAqpodACBJzQ4AkKhmBwBohhGX\nAAAAAKwazmTtj6YblyU7AECqkh1g7AZ9AXHTFOibkh0AlsXvLZanZAcAaEbTjUsAAGB4GmcAwFrQ\ndOOyhmNNLzMMGvqohioI9FMN9a8dRsPDuNVQAwFmNd24BKBf/BHcJj8XGB1NQGClGfQCtGjQd50r\n47K4v2O9phuXJTsArGJdX1j8cbRalOwAAElKdgCAiMj6Tl1WaLsAq0/TjUsA+sVIJIDVw0FShmUk\nIADDarpxWcOxJqDPaqiCQD/VUP+A/qqhBgJrzaCDV5fFlREdJ4s33bgEAPIZVQUAAGS4JDtAl5Id\nACBVyQ4AkKRkBwBIVLIDADTDiEsAAGAgI6uH55rNADAaTTcuazjWBPRZDVUQ6Kca6h/QXzXUQKAF\nLdxUrenGJQAAMDwj/gCAtcA1LgGaVbIDACQp2QEAEpXsAADNaLpxCQAAAAD0U9ONy5odACBVzQ4A\nkKRmBwBIVLMDADSj6cYlAAAAANBPi2pcvvTSS3HdddfFu9/97oiI+NnPfhbbtm2LN73pTXHLLbfE\nM888M7fsvn374qqrroqrr746vv3tb889/uijj8Y111wTV111VXz84x9fVLgyxBMBWHtKdgCAJCU7\nAECikh0AoBmLuqv4vffeG1u2bIlnn302IiKmp6dj27Ztcffdd8c999wT09PTMT09HcePH49Dhw7F\n8ePHY2ZmJm6++eY4ceJETExMxF133RUHDhyIrVu3xvbt2+PIkSNx6623ruiTAwCAlrirNwDA4i04\n4vLUqVPxzW9+Mz784Q/H2bNnIyLioYceil27dkVExK5du+KBBx6IiIgHH3wwbr/99li/fn2UUmLz\n5s1x7NixePrpp+PZZ5+NrVu3RkTEHXfcMbdOl7rUZwWwJtTsAABJanYAgEQ1OwBAMxYccfnXf/3X\n8fd///fx85//fO6xM2fOxMaNGyMiYuPGjXHmzJmIiHjqqafixhtvnFtuamoqZmZmYv369TE1NTX3\n+OTkZMzMzAzc5wMRcUVEPBMRpyNi03lz66//LUuerktYe1z7XyjBsHsbRd5RT9cG0pxz/hLDLr/c\nBKPZWh24RPfeR5dgXNPzz61DLr+aPi+nz5sedu3s/KPeeov1dGn7X9r0sGuPp/4M3uKwy7deT7Pr\n2bDPf9y/UUe//8XVv0EJFtr6sJ/nYfc/rs9/1/5rx9az69moPs/Dr1FWZHstvp5d+x80fc75Sywt\nzeAEw26v1fffUvN17/3lR04vuHzX/uui0yx/Ovv93OLnfylbW+r+R729lX7+S30+udN14BLDbm98\n7/+l7u3i6YOxa+ASu2Jvx94vXv6VUzUifvTr6dc+91zccNG653Q2Lv/pn/4pNmzYENddd108/PDD\n8y4zMTERExMTXZsZ2m2dc8uyp0vn3O7pld7/QusPu7dR5B31dOmcO97pYV/fUScYzdbKwCUWWj//\nJzDc9Pxzy8Alht1b9vO7ePrGzrkLTWfnH/XWW6yny9n/Sr+e2T+fYZdv4/1WFlxiVNOj3v+Fc7M/\n7+Ouf6N4/5XOucNvb5TTS9l/6ZibXc/GXe8y6lPpmDuO17Nr/wtNj6a+zp+g61IJey74A/jc4wcH\nrjO7vaUlHDQ97Nor8/4rA+cvZv+lc+5op7Pfzy1+/pezduvPZ7n5Rv16DTt9cIEaNP/65aJHlrr/\ncb//h9/bfNODEyy0ftfy5RXTl73qVRet+Uqdjct//ud/joceeii++c1vxgsvvBA///nP4wMf+EBs\n3LgxTp8+HZs2bYqnn346NmzYEBGzIylPnjw5t/6pU6diamoqJicn49SpU+c9Pjk52RkMAAAAAOiv\nzmtc/t3f/V2cPHkynnzyybj//vvjj//4j+O+++6LHTt2xMGDs0e+Dh48GLfdNjtGcseOHXH//ffH\niy++GE8++WScOHEitm7dGps2bYrLL788jh07FmfPno377rtvbp0udfnPD2AVq9kBAJLU7AAAiWp2\nAIBmLOqu4i97+ZTwz3zmM7Fz5844cOBAlFLi8OHDERGxZcuW2LlzZ2zZsiXWrVsX+/fvn1tn//79\nceedd8bzzz8f27dvd0dxmMeg02dePnUGAAAAYBxa6EUsunH59re/Pd7+9rdHRMRrXvOaOHr06LzL\n7d69O3bv3n3R49dff308/vjjQ4UrQy0NsNaU7AAASUp2AIBEJTsAQDOGGnEJAAAAAKx9i7mp2krr\nvMZltpodACBVzQ4AkKRmBwBIVLMDADSj6cYlAAAAANBPTTcuS3YAgFQlOwBAkpIdACBRyQ4A0AzX\nuAQA1pwWrscDAAAsT9ONyxqONQF9VkMVBPqphvoH9FeN5dRAB++AtaTpU8UBAAAAgH5qesRlyQ4A\nkKpkBwBIUrIDACQq2QEARm7QaPAr47K4v2O9phuXsFZ1nb4B0Bo1CwAAyND0qeI1OwBAqpodACBJ\nzQ4AkKhmBwBoRtONSwAAAACgn5puXJbsAACpSnYAgCQlOwBAopIdAKAZTTcuAQAAAIB+avrmPDUc\nawL6rIYqCPRTDfWvfXti78B5buoFy1FDDQSY1XTjEgAAGJ7GIQCcr+uAG+1q+lTxkh0AIFXJDgCQ\npGQHAEhUsgMANKPpxiUAAAAA0E9Nnypew7EmoM9qqIJrj2vCwWLUUP+A/qqhBgLMarpxCQAAAACM\nXwvXBW26cVmyAwCkKtkBAJKU7ADACmjhD+DVoWQHAGiGa1wCAAAAAM1punFZswMApKrZAQCS1OwA\nAIlqdgCAZjR9qjisVYNOk3FjDgAAAIBZTY+4LNkBAFKV7AAASUp2AIBEJTsAQDOablwCAAAAAP3U\n9KniNRxrAvqshioI9FMN9Q/orxpqILDWDLpk3mVxZUTcP3A9Iy4BAAAAgOY03bgs2QEAUpXsAABJ\nSnYAgEQlOwBAM5puXAIAAAAA/dR047JmBwBIVbMDACSp2QEAEtXsAADNaLpxCQAAAAD0U9ONy5Id\nACBVyQ4AkKRkBwBIVLIDADSj6cYlAAAAANBPTTcua3YAgFQ1OwBAkpodACBRzQ4A0Ix12QEAoE/2\nxp7sCEAP7Im98z6uBgHkUYNheE2PuCzZAQBSlewAAElKdgCARCU7AEAzmm5cAgAAAAD91HTjsmYH\nAEhVswMAJKnZAQAS1ewAAM1wjUsAeqXr2kKDrgkHAKxtg74f+G4A9FkLfzs13bgs2QEAUpXsAABJ\nSnaAVc8NIGA1K9kBAJrR9KniAAAAAEA/NT3isoZjTUCf1VAFWSqntrG61VD/gP6qoQYCzGq6cQks\nnVPEAAAAgNWs6cZlyQ4AkKpkBwBIUrIDACQq2QFgWQyiYZSablxm8AEDAAAAgHxNNy5rONYES9V1\nfTsN+tWihioI9FMN9Q/orxpqIMAsdxUHAAAAAJrTdOOyZAcASFWyAwAkKdkBABKV7AAAzWi6cQkA\nAAAA9JNrXAI0q4YqCPRTDfUP1p6u66x3XZ+9f2qogQCzmm5cAgAAAADj18JBpaYblyU7AIxZC0WB\nlpTsANArg2pw1wghVkrJDgCQqGQHAGhG041LAAAAgNXEQU/WihYu8dH0zXlqdgCAVDU7AECSmh0A\nIFHNDgDQDCMuAWiGo9MAo+HSBwDAWtB047JkBwBIVbIDACQp2QHoIc1e2lGyAwA0o+nGJQAAwDho\nUAJAe5puXNZwrAnosxqqINBPNdS/9mn0wUqpoQYCzGq6cck5LdzJCQAAAADGpenGZckOAJCqZAcA\nSFKyA7AIXQfPjcaE5SjZAQCacUl2AAAAAACACzXduKzZAQBS1ewAAElqdgCARDU7AEAzmj5VHAAA\n1pJBp1c7tRqYj9oA9F3TjcuSHQAgVckOAJCkZAcASFSyA8Ca5KbHq1PTjUsAAGB4RmkBAGtB043L\nGo41AX1WYzlVsO+nI342Pjfv45+Lz445CTC8Gr4FAv1VQw0EmNV04xIAlmoizmZHAAAAYBmavqt4\nyQ4AkKpkBwBIUrIDACQq2QEAmmHEJQAAACvOzS8AGFbTIy5rdgCAVDU7AECSmh0AIFHNDgDQjKYb\nlwAAAABAPzXduCzZAQBSlewAAElKdgCARCU7AEAzXOMSAADWmEHXEtwbe8acBABg6ZoecVmzAwCk\nqtkBAJLU7AAAiWp2AIBmGHEJwJpkVBEAAMDq1nTjsmQHAEhVlrW2xh2wepXsAACJSnYAgGY03bgE\ngHHS7AXWinHUMzUTAFhpTTcuazjWRL8M+gNg0AX2Wetq9K0KupkEmbzPWlKjb/UP4JwaaiDArKZv\nzgMAAAAA9FPTIy5LdgCAVCU7AECSkh1gxRjZCyysZAcAaMaiGpfPPPNMfPjDH44f//jHMTExEV/7\n2tfiqquuive+973x05/+NEopcfjw4bjiiisiImLfvn3x1a9+NS699NL4whe+ELfccktERDz66KNx\n5513xguETp9tAAAbaklEQVQvvBDbt2+Pe++9d+WeGQAA9NRauvTGaswMQHtcgm11WlTj8uMf/3hs\n3749/vEf/zF++ctfxi9+8Yv427/929i2bVvcfffdcc8998T09HRMT0/H8ePH49ChQ3H8+PGYmZmJ\nm2++OU6cOBETExNx1113xYEDB2Lr1q2xffv2OHLkSNx6660D91vDsSagz2qogmtP1xcmf5zDy2qo\nf0B/1VAD16a1dFAJxmXBxuV///d/x/e+9704ePDg7Arr1sWrX/3qeOihh+K73/1uRETs2rUr3vGO\nd8T09HQ8+OCDcfvtt8f69eujlBKbN2+OY8eOxRvf+MZ49tlnY+vWrRERcccdd8QDDzzQ2bgEABgX\nf0wAAEBbFmxcPvnkk/Ha1742PvjBD8a///u/x/XXXx+f//zn48yZM7Fx48aIiNi4cWOcOXMmIiKe\neuqpuPHGG+fWn5qaipmZmVi/fn1MTU3NPT45ORkzMzPz7vOBiLji1/99OiI2nTe3/vrfsuTp2jF3\nFNsf9/5Hvb2Vnq4NpDnn/CWGXX65CS6cO+zyde7/599f99a6lmhzev65dcjlV9Pn5eXHyhLXXul8\n3dOj3nqL9W9p+++aO3iLy0+7vOlR/fzPGVXC+eeO+v2ZXc9G/fyzX/9R1b9BCRbe+sVL1Fjqsx9m\njaVNL2X/tWPrLdbTV1rp/XfvfTT7qx1zs38/DZo+5/wllpZmcIKlbS/v9Rz1/gfNPefCR4bb/qh/\n/y00nf1+bvHzP879j3p72dNtpRl9PRvf+3+pe5tvenCC7r13L18j4ke/nn7tc8/FDRete86Cjctf\n/vKX8cMf/jC+9KUvxdve9rb4xCc+EdPT0+ctMzExERMTEwttatFu65xblj1dOuaOYvvj3v+ot7fS\n06Vz7ninL3xk2OWXOz3s9uefWwYusVCa/J/AcNPzzy0Dlxh2b9nPr2t60IivV44Qu3Dt7Pyj3nqL\n9W85+59/7uAtLpxmZadH/fNvs54ufXsrXc9G/fyzX/+Vfj8Nu/xCn+elbG+U00vZf+mY22I97Zrb\nwus57HTpmJv9+2mh6dH8/hmcYGnbGzzd4udvnNsb9f6Hnc5+P6+11z97e9nTbaUZfT0b9/t/+L3N\nNz04wULrdy1fXjF92ateddGar7Rg43JqaiqmpqbibW97W0RE/Nmf/Vns27cvNm3aFKdPn45NmzbF\n008/HRs2bIiI2ZGUJ0+enFv/1KlTMTU1FZOTk3Hq1KnzHp+cnOzcd435njhAX9RQBYF+qqH+ARF9\nvVxHDTUQWGsG1fMr47K4v2O9BRuXmzZtite//vXxxBNPxJve9KY4evRovOUtb4m3vOUtcfDgwfj0\npz8dBw8ejNtumx0nuWPHjnj/+98fn/zkJ2NmZiZOnDgRW7dujYmJibj88svj2LFjsXXr1rjvvvvi\nYx/72JKeLADQbTGjdAEAAFq2qLuKf/GLX4y/+Iu/iBdffDH+z//5P/G1r30tXnrppdi5c2ccOHAg\nSilx+PDhiIjYsmVL7Ny5M7Zs2RLr1q2L/fv3z51Gvn///rjzzjvj+eefj+3bty94Y56yvOcGsMqV\n7ACsgHGNHNGgZHUr2QF6p5+j2hi3rveZ31uvVLIDADRjUY3La6+9Nv71X//1osePHj067/K7d++O\n3bt3X/T49ddfH48//viC+/PFCQAAAAD6bVGNyzw1HG0C+qvGcmrgoJELDg4B7avhOyDQXzXUQIBZ\nl2QHAAAAAAC4UOONy5IdACBRyQ4AkKRkBwBIVLIDADSj8VPFAQAAAIBxa+HGaU02Ll9+YWqcO9bk\nmmxA/9RwxB3opxrqH9BfNdRAgFlNNi4B6CcHqQAAAHhZ09e4LNkBAFKV7AAASUp2AIBEJTsAQDOM\nuATomUHXKTHaEQAAgJY03bis4VgT0Gc1VEGgn2qof0ALcg7s1lADAWY1fao4AAAAANBPTTcuS3YA\ngFQlOwBAkpIdACBRyQ4A0IymG5cAAAAAQD813bis2QEAUtXsAABJanYAgEQ1OwBAM5puXAIAAAAA\n/dR047JkBwBIVbIDACQp2QEAEpXsAADNWJcdAAAAaNee2Dvv43tjz5iTAAB90/SIy5odACBVzQ4A\nkKRmBwBIVLMDADSj6cYlAAAAANBPTZ8qXrIDLNOg02oAFqdkBwBIUrIDACQqy1rb36HAWtJ04xIA\nAAD6qqsJ6TqzMJyuz4yGf7uaPlW8ZgcASFWzAwAkqdkBABLV7AAAzWi6cQkAAAAA9FPTjcuSHQAg\nVckOAJCkZAcASFSyAwA0o+nGJQAAAADQT03fnKeGY01An9VYiSroQu5A+2r4Fgj0Vw01EGBW041L\nAAAA6CsHnIG+a7pxWbIDAKQq2QFYg7r+ANoTe8eYBLqU7AAAiUp2AIBmNN24pB1df8w6CggAAADA\nqDXduKzhWBPQZzVUwVlGAkLf1FD/gP6q8XINNIAE6Dt3FQcAAAAAmtN047JkBwBIVbIDACQp2QEA\nEpXsAADNaPpUcQAAAOgrp4MDfdf0iMuaHQAgVc0OAJCkZgcASFSzAwA0o+nGJQAAAADQT003Lkt2\nAIBUJTsAQJKSHQAgUckOANCMphuXAAAAAEA/Nd24rNkBAFLV7AAASWp2AIBENTsAQDPcVRwAAGCE\n3AkaAEaj6cZlyQ4AkKpkBwBIUrID8AqacDBuJTsAQDOaPlUcAAAAAOinphuXNTsAQKqaHQAgSc0O\nAJCoZgcAaEbTjUsAAAAAoJ9c4xKgWSU7wNjtib3ZEYAmlOwAAIlKdgCAZhhxCQAAAAA0p+nGZc0O\nAJCqZgcASFKzAwAkqtkBAJrRdOMSAAAAAOinphuXJTsAQKqSHQAgSckOAJCoZAcAaEbTjUsAAAAA\noJ+avqt4DceagD6roQrC+OyNPdkRmFND/QP6q4YaCDDLiEsAAAAAoDlNNy5LdgCAVCU7AECSkh0A\nIFHJDgDQjKZPFQeAPtkTe7MjAACwQlyWBobXdOOyhmNNsFR+Ka4FNVRBoJ9qqH9Af9VQAwFmNX2q\nOAAAAADQT003Lkt2AIBUJTsAQJKSHQAgUckOANCMphuXAAAAAEA/Nd24rNkBAFLV7AAASWp2AIBE\nNTsAQDOablwCAAAAAP3UdOOyZAcASFWyAwAkKdkBABKV7AAAzViXHQAAAAAAFmtv7Bk4b0/sHWMS\nVlrTIy5rdgCAVDU7AECSmh0AIFHNDgDQDCMuAQAAAEZk0Ii/rlGCwPyablyW7AAAqUp2AIAkJTsA\nsAKcvrlYJTsAQDOablwCMHqOAAMAALAauMYlQLNqdgCAJDU7AECimh0AoBlGXMIa1XUqjpF1AAAA\nQOuaHnFZsgMApCrZAQCSlOwAAIlKdgCAZjTduAQAAAAA+qnpxmXNDgCQqmYHAEhSswMAJKrZAQCa\n4RqXAAAx+NrArgsMAAA5mh5xWbIDAKQq2QEAkpTsAACJSnYAgGY03bgEAAAAAPqp6VPFazjWBPRZ\nDVUQxscp4S2pof4B/VVDDVzdfKeA0THiEgAAAABoTtONy5IdACBVyQ4AkKRkBwBIVLIDADSj6cYl\nAAAAANBPTTcua3YAgFQ1OwB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Wb/3WeY8NqnkPPvhg3H777bF+/foopcTmzZvnDvAArEbz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\nwMsxXAIAAAAAL8dwCQAAAAC8nD9FAWBsJd2iIQAAAABJRU5ErkJggg==\n" - } - ], - "prompt_number": 184 - }, - { - "cell_type": "code", - "collapsed": false, - "input": [], - "language": "python", - "metadata": {}, - "outputs": [] - } - ], - "metadata": {} - } - ] +{ + "metadata": { + "name": "DontOverfit" + }, + "nbformat": 3, + "nbformat_minor": 0, + "worksheets": [ + { + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Implementation of Salisman's Don't Overfit submission" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "From [Kaggle](http://www.kaggle.com/c/overfitting)\n", + ">In order to achieve this we have created a simulated data set with 200 variables and 20,000 cases. An \u2018equation\u2019 based on this data was created in order to generate a Target to be predicted. Given the all 20,000 cases, the problem is very easy to solve \u2013 but you only get given the Target value of 250 cases \u2013 the task is to build a model that gives the best predictions on the remaining 19,750 cases." + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import gzip\n", + "import requests\n", + "import zipfile\n", + "\n", + "url = \"https://dl.dropbox.com/s/lnly9gw8pb1xhir/overfitting.zip/"\n", + "\n", + "\n", + "results = requests.get(url)" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 30 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import StringIO\n", + "z = zipfile.ZipFile(StringIO.StringIO(results.content))\n", + "# z.extractall()" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 31 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "z.extractall()" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 32 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "z.namelist()" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "pyout", + "prompt_number": 38, + "text": [ + "['overfitting.csv']" + ] + } + ], + "prompt_number": 38 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "d = z.open('overfitting.csv')\n", + "d.readline()" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "pyout", + "prompt_number": 69, + "text": [ + "'case_id,train,Target_Practice,Target_Leaderboard,Target_Evaluate,var_1,var_2,var_3,var_4,var_5,var_6,var_7,var_8,var_9,var_10,var_11,var_12,var_13,var_14,var_15,var_16,var_17,var_18,var_19,var_20,var_21,var_22,var_23,var_24,var_25,var_26,var_27,var_28,var_29,var_30,var_31,var_32,var_33,var_34,var_35,var_36,var_37,var_38,var_39,var_40,var_41,var_42,var_43,var_44,var_45,var_46,var_47,var_48,var_49,var_50,var_51,var_52,var_53,var_54,var_55,var_56,var_57,var_58,var_59,var_60,var_61,var_62,var_63,var_64,var_65,var_66,var_67,var_68,var_69,var_70,var_71,var_72,var_73,var_74,var_75,var_76,var_77,var_78,var_79,var_80,var_81,var_82,var_83,var_84,var_85,var_86,var_87,var_88,var_89,var_90,var_91,var_92,var_93,var_94,var_95,var_96,var_97,var_98,var_99,var_100,var_101,var_102,var_103,var_104,var_105,var_106,var_107,var_108,var_109,var_110,var_111,var_112,var_113,var_114,var_115,var_116,var_117,var_118,var_119,var_120,var_121,var_122,var_123,var_124,var_125,var_126,var_127,var_128,var_129,var_130,var_131,var_132,var_133,var_134,var_135,var_136,var_137,var_138,var_139,var_140,var_141,var_142,var_143,var_144,var_145,var_146,var_147,var_148,var_149,var_150,var_151,var_152,var_153,var_154,var_155,var_156,var_157,var_158,var_159,var_160,var_161,var_162,var_163,var_164,var_165,var_166,var_167,var_168,var_169,var_170,var_171,var_172,var_173,var_174,var_175,var_176,var_177,var_178,var_179,var_180,var_181,var_182,var_183,var_184,var_185,var_186,var_187,var_188,var_189,var_190,var_191,var_192,var_193,var_194,var_195,var_196,var_197,var_198,var_199,var_200\\r\\n'" + ] + } + ], + "prompt_number": 69 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import numpy as np" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 70 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "M = np.fromstring(d.read(), sep=\",\")" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 63 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "len(d.read())" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "pyout", + "prompt_number": 71, + "text": [ + "23919756" + ] + } + ], + "prompt_number": 71 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "np.fromstring?" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 75 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [], + "language": "python", + "metadata": {}, + "outputs": [] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "data = np.loadtxt(\"overfitting.csv\", delimiter=\",\", skiprows=1)" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 4 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "print \"\"\"\n", + "There are also 5 other fields,\n", + "\n", + "case_id - 1 to 20,000, a unique identifier for each row\n", + "\n", + "train - 1/0, this is a flag for the first 250 rows which are the training dataset\n", + "\n", + "Target_Practice - we have provided all 20,000 Targets for this model, so you can develop your method completely off line.\n", + "\n", + "Target_Leaderboard - only 250 Targets are provided. You submit your predictions for the remaining 19,750 to the Kaggle leaderboard. \n", + "\n", + "Target_Evaluate - again only 250 Targets are provided. Those competitors who beat the 'benchmark' on the Leaderboard will be asked to make one further submission for the Evaluation model.\n", + "\n", + "\"\"\"\n", + "\n", + "data.shape" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "\n", + "There are also 5 other fields,\n", + "\n", + "case_id - 1 to 20,000, a unique identifier for each row\n", + "\n", + "train - 1/0, this is a flag for the first 250 rows which are the training dataset\n", + "\n", + "Target_Practice - we have provided all 20,000 Targets for this model, so you can develop your method completely off line.\n", + "\n", + "Target_Leaderboard - only 250 Targets are provided. You submit your predictions for the remaining 19,750 to the Kaggle leaderboard. \n", + "\n", + "Target_Evaluate - again only 250 Targets are provided. Those competitors who beat the 'benchmark' on the Leaderboard will be asked to make one further submission for the Evaluation model.\n", + "\n", + "\n" + ] + }, + { + "output_type": "pyout", + "prompt_number": 5, + "text": [ + "(20000L, 205L)" + ] + } + ], + "prompt_number": 5 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "ix_training = data[:, 1] == 1\n", + "ix_testing = data[:, 1] == 0\n", + "\n", + "training_data = data[ix_training, 5:]\n", + "testing_data = data[ix_testing, 5:]\n", + "\n", + "training_labels = data[ix_training, 2]\n", + "testing_labels = data[ix_testing, 2]\n", + "\n", + "print \"training:\", training_data.shape, training_labels.shape\n", + "print \"testing: \", testing_data.shape, testing_labels.shape" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "training: (250L, 200L) (250L,)\n", + "testing: " + ] + }, + { + "output_type": "stream", + "stream": "stdout", + "text": [ + " (19750L, 200L) (19750L,)\n" + ] + } + ], + "prompt_number": 6 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Develop Tim's model\n", + "\n", + "He mentions that the X variables are from a Unifrom distribution. Let's investigate this:" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "figsize(12, 4)" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 7 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "hist(training_data.flatten())\n", + "print training_data.shape[0] * training_data.shape[1]" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "50000\n" + ] + }, + { + "output_type": "display_data", + "png": 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LmJAL2InyDAAAAFhEeYbjMasGE3IBE3IBE3IBO1GeAQAAAIsoz3A8ZtVgQi5gQi5gQi5g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\nwKL/D71Max2EVz3vAAAAAElFTkSuQmCC\n" + } + ], + "prompt_number": 8 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "looks pretty right" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import pymc as pm\n", + "\n", + "to_include = pm.Bernoulli(\"to_include\", 0.5, size=200)" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 127 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "coef = pm.Uniform(\"coefs\", 0, 1, size=200)" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 128 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "@pm.deterministic\n", + "def Z(coef=coef, to_include=to_include, data=training_data):\n", + " ym = np.dot(to_include * training_data, coef)\n", + " return ym - ym.mean()" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 129 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "@pm.deterministic\n", + "def T(z=Z):\n", + " return 0.45 * (np.sign(z) + 1.1)" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 130 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "obs = pm.Bernoulli(\"obs\", T, value=training_labels, observed=True)\n", + "\n", + "model = pm.Model([to_include, coef, Z, T, obs])\n", + "map_ = pm.MAP(model)\n", + "map_.fit()" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Warning: Stochastic to_include's value is neither numerical nor array with floating-point dtype. Recommend fitting method fmin (default).\n" + ] + } + ], + "prompt_number": 132 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "mcmc = pm.MCMC(model)" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 133 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "mcmc.sample(100000, 90000, 1)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + " \r", + "[****************100%******************] 100000 of 100000 complete" + ] + }, + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "\n" + ] + } + ], + "prompt_number": 176 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "(np.round(T.value) == training_labels).mean()" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "pyout", + "prompt_number": 177, + "text": [ + "0.73999999999999999" + ] + } + ], + "prompt_number": 177 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "t_trace = mcmc.trace(\"T\")[:]\n", + "(np.round(t_trace[-500:-400, :]).mean(axis=0) == training_labels).mean()" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "pyout", + "prompt_number": 178, + "text": [ + "0.72399999999999998" + ] + } + ], + "prompt_number": 178 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "t_mean = np.round(t_trace).mean(axis=1)" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 179 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "imshow(t_trace[-10000:, :], aspect=\"auto\")\n", + "colorbar()" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "pyout", + "prompt_number": 180, + "text": [ + "" + ] + }, + { + "output_type": "display_data", + "png": 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KqVurtSa/PqkWjWpVfn12AF/vibdN1/Lbd6pNccXy269SQrmTiNz2LZpRboDa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\nKoM1J5YaGxtVXV2tubk5LS0taW5uTtu3b9f3v/99Pfjgg5KkBx98UC+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XaYIF79mRC/mc8GsJpMMv5dzIF68kVkSwTa8SMWQHKMbfxhn4npXPFeFVhNCa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7M/xQ5aBZLnFdHaGCuyQ8WBuOQvg3MmPy8WRp95WgvJ0afEWXuFE5fV2XBgogIDj2NAgsmp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xGxExhIpaptCLMlSBBedXGc3ngzuM6mqfuwTf1KEWIhjxrAxRionJyaZMradYhVd0EfCV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\nnB2qlbAlZ+DSE2yj71mV5kJbP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ad97Ro0fnfXz37t2xe/fuix6//vrr4/HHH190uBqONQF9VkMVBPqphvoH9FcNNRBg1lB3\nFQcAAAAAGMagSyBeFldGxP0D12u6cVmyAyyT61ICy1OyA0Cv7I092RGYU7IDACQq2QEAmtF04xIA\nyNd1IE6zDwAAWCmXZAfoUrMDAKSq2QEAktTsAACJanYAgGY03bgEAAAAAPqp6cZlyQ4AkKpkBwBI\nUrIDACQq2QEAmuEal9AQN3QCAAAAmNV047KGY030y6CbXGho9lUNVRDopxrqH9BfNdRAGL2um0r6\nm7tdTZ8qDgAAAAD0U9MjLkt2gIY4MgB9VLIDACQp2QEAEpXsAADNaLpxCQAAQH91DdLoGtwBQFsG\n1ewr47K4v2O9pk8Vr9kBAFLV7AAASWp2AIBENTsAQDOablwCAAAAAP3U9KniJTsAQKqSHYAV4JQ3\nWIySHQAgUckOANCMphuXAAAAAKuJG+jC6DTduKzhWBMslZFba0ENVRDopxrqH6w9mjmLVUMNBJjV\ndOMSAAAAAFjdBh28uiyujOi4r3jTN+cp2QEAUpXsAABJSnYAgEQlOwBAM5puXAIAAAAA/dR047Jm\nBwBIVbMDACSp2QEAEtXsAADNcI1LAIAecfM2AGC16/o+40Zga0vTIy5LdgCAVCU7AECSkh0AIFHJ\nDgDQDCMuoSGODAEAAADMarpxWcOxJlYvQ9dZvhqqINBPNdQ/WHt8P16sGmogwKymG5cA9Itr7wEA\nAPAy17gEaFbJDgCQpGQHAEhUsgMANMOIS2BVMBJveF4zAAAAVrOmR1zW7AAAqWp2AIAkNTsAQKKa\nHQCgGUZcAqwCLli/dhgJCwDAauG7K9mablyW7AAAqUp2AIAkJTsA0Ih+Nk1KdgCAZjR9qjgAAAAA\n0E9Nj7is4VgT0Gc1VEFa0M/RLuSqof4B/VVDDQSY1XTjEuBlg67xqKHCatN1vVLvZwAAgHOaPlW8\nZAcASFWyAwAkKdkBABKV7AAAzWi6cQkAAAAA9FPTp4rXcKwJ6LMaqiDQTzXUv3a4XAuMWw01EGBW\n041LAAAglwYlAGtB17XmaVfTp4qX7AAAqUp2AIAkJTsAQKKSHQCgGU03LgEAAACAfmq6cVmzAwCk\nqtkBAJLU7AAAiWp2AIBmuMYlAKxBg65J59o+AADAatH0iMuSHQAgVckOAJCkZAcASFSyAwA0o+nG\nJQAAAADQT003Lmt2AIBUNTsAQJKaHQAgUc0OANCMphuXAAAAAEA/NX1znpIdACBVyQ4AkKRkBwBI\nVOb+q+umeoNuxAewlhhxCQAAAAA0p+kRlzUcbwf6rIYqCOMzaFSLES0Zaqh/QH/VUAMBZhlxCQAA\nAAA0p+kRlyU7AECqkh2AFWD0HixGyQ4AkKhkBwBohhGXAAAAAEBzmm5c1uwAAKlqdgCAJDU7AECi\nmh0AoBlNnyoOAAAALF7XZWkG3YgOoFVNj7gs2QEAUpXsAABJSnYAgEQlOwBAM5puXAIAAAAA/dR0\n47JmBwBIVbMDACSp2QEAEtXsAADNaLpxCQAAAAD0U9M35ynZAQBSlewAEBHdF/LvugEALF3JDgCQ\nqGQHAGiGEZcAAAAAQHOablzW7AAAqWp2AIAkNTsAQKKaHQCgGU2fKg4AMC5OewcAgLY0PeKyZAcA\nSFWyAwAkKdkBABKV7AAAzTDicgUNGrnRdZMDAAAAAKDxEZc1OwBAqpodACBJzQ4AkKhmBwBohhGX\nAAAAAKwazmTtj6YblyU7AECqkh1g7AZ9AXHTFOibkh0AlsXvLZanZAcAaEbTjUsAAGB4GmcAwFrQ\ndOOyhmNNLzMMGvqohioI9FMN9a8dRsPDuNVQAwFmNd24BKBf/BHcJj8XGB1NQGClGfQCtGjQd50r\n47K4v2O9phuXJTsArGJdX1j8cbRalOwAAElKdgCAiMj6Tl1WaLsAq0/TjUsA+sVIJIDVw0FShmUk\nIADDarpxWcOxJqDPaqiCQD/VUP+A/qqhBgJrzaCDV5fFlREdJ4s33bgEAPIZVQUAAGS4JDtAl5Id\nACBVyQ4AkKRkBwBIVLIDADTDiEsAAGAgI6uH55rNADAaTTcuazjWBPRZDVUQ6Kca6h/QXzXUQKAF\nLdxUrenGJQAAMDwj/gCAtcA1LgGaVbIDACQp2QEAEpXsAADNaLpxCQAAAAD0U9ONy5odACBVzQ4A\nkKRmBwBIVLMDADSj6cYlAAAAANBPi2pcvvTSS3HdddfFu9/97oiI+NnPfhbbtm2LN73pTXHLLbfE\nM888M7fsvn374qqrroqrr746vv3tb889/uijj8Y111wTV111VXz84x9fVLgyxBMBWHtKdgCAJCU7\nAECikh0AoBmLuqv4vffeG1u2bIlnn302IiKmp6dj27Ztcffdd8c999wT09PTMT09HcePH49Dhw7F\n8ePHY2ZmJm6++eY4ceJETExMxF133RUHDhyIrVu3xvbt2+PIkSNx6623ruiTAwCAlrirNwDA4i04\n4vLUqVPxzW9+Mz784Q/H2bNnIyLioYceil27dkVExK5du+KBBx6IiIgHH3wwbr/99li/fn2UUmLz\n5s1x7NixePrpp+PZZ5+NrVu3RkTEHXfcMbdOl7rUZwWwJtTsAABJanYAgEQ1OwBAMxYccfnXf/3X\n8fd///fx85//fO6xM2fOxMaNGyMiYuPGjXHmzJmIiHjqqafixhtvnFtuamoqZmZmYv369TE1NTX3\n+OTkZMzMzAzc5wMRcUVEPBMRpyNi03lz66//LUuerktYe1z7XyjBsHsbRd5RT9cG0pxz/hLDLr/c\nBKPZWh24RPfeR5dgXNPzz61DLr+aPi+nz5sedu3s/KPeeov1dGn7X9r0sGuPp/4M3uKwy7deT7Pr\n2bDPf9y/UUe//8XVv0EJFtr6sJ/nYfc/rs9/1/5rx9az69moPs/Dr1FWZHstvp5d+x80fc75Sywt\nzeAEw26v1fffUvN17/3lR04vuHzX/uui0yx/Ovv93OLnfylbW+r+R729lX7+S30+udN14BLDbm98\n7/+l7u3i6YOxa+ASu2Jvx94vXv6VUzUifvTr6dc+91zccNG653Q2Lv/pn/4pNmzYENddd108/PDD\n8y4zMTERExMTXZsZ2m2dc8uyp0vn3O7pld7/QusPu7dR5B31dOmcO97pYV/fUScYzdbKwCUWWj//\nJzDc9Pxzy8Alht1b9vO7ePrGzrkLTWfnH/XWW6yny9n/Sr+e2T+fYZdv4/1WFlxiVNOj3v+Fc7M/\n7+Ouf6N4/5XOucNvb5TTS9l/6ZibXc/GXe8y6lPpmDuO17Nr/wtNj6a+zp+g61IJey74A/jc4wcH\nrjO7vaUlHDQ97Nor8/4rA+cvZv+lc+5op7Pfzy1+/pezduvPZ7n5Rv16DTt9cIEaNP/65aJHlrr/\ncb//h9/bfNODEyy0ftfy5RXTl73qVRet+Uqdjct//ud/joceeii++c1vxgsvvBA///nP4wMf+EBs\n3LgxTp8+HZs2bYqnn346NmzYEBGzIylPnjw5t/6pU6diamoqJicn49SpU+c9Pjk52RkMAAAAAOiv\nzmtc/t3f/V2cPHkynnzyybj//vvjj//4j+O+++6LHTt2xMGDs0e+Dh48GLfdNjtGcseOHXH//ffH\niy++GE8++WScOHEitm7dGps2bYrLL788jh07FmfPno377rtvbp0udfnPD2AVq9kBAJLU7AAAiWp2\nAIBmLOqu4i97+ZTwz3zmM7Fz5844cOBAlFLi8OHDERGxZcuW2LlzZ2zZsiXWrVsX+/fvn1tn//79\nceedd8bzzz8f27dvd0dxmMeg02dePnUGAAAAYBxa6EUsunH59re/Pd7+9rdHRMRrXvOaOHr06LzL\n7d69O3bv3n3R49dff308/vjjQ4UrQy0NsNaU7AAASUp2AIBEJTsAQDOGGnEJAAAAAKx9i7mp2krr\nvMZltpodACBVzQ4AkKRmBwBIVLMDADSj6cYlAAAAANBPTTcuS3YAgFQlOwBAkpIdACBRyQ4A0AzX\nuAQA1pwWrscDAAAsT9ONyxqONQF9VkMVBPqphvoH9FeN5dRAB++AtaTpU8UBAAAAgH5qesRlyQ4A\nkKpkBwBIUrIDACQq2QEARm7QaPAr47K4v2O9phuXsFZ1nb4B0Bo1CwAAyND0qeI1OwBAqpodACBJ\nzQ4AkKhmBwBoRtONSwAAAACgn5puXJbsAACpSnYAgCQlOwBAopIdAKAZTTcuAQAAAIB+avrmPDUc\nawL6rIYqCPRTDfWvfXti78B5buoFy1FDDQSY1XTjEgAAGJ7GIQCcr+uAG+1q+lTxkh0AIFXJDgCQ\npGQHAEhUsgMANKPpxiUAAAAA0E9Nnypew7EmoM9qqIJrj2vCwWLUUP+A/qqhBgLMarpxCQAAAACM\nXwvXBW26cVmyAwCkKtkBAJKU7ADACmjhD+DVoWQHAGiGa1wCAAAAAM1punFZswMApKrZAQCS1OwA\nAIlqdgCAZjR9qjisVYNOk3FjDgAAAIBZTY+4LNkBAFKV7AAASUp2AIBEJTsAQDOablwCAAAAAP3U\n9KniNRxrAvqshioI9FMN9Q/orxpqILDWDLpk3mVxZUTcP3A9Iy4BAAAAgOY03bgs2QEAUpXsAABJ\nSnYAgEQlOwBAM5puXAIAAAAA/dR047JmBwBIVbMDACSp2QEAEtXsAADNaLpxCQAAAAD0U9ONy5Id\nACBVyQ4AkKRkBwBIVLIDADSj6cYlAAAAANBPTTcua3YAgFQ1OwBAkpodACBRzQ4A0Ix12QEAoE/2\nxp7sCEAP7Im98z6uBgHkUYNheE2PuCzZAQBSlewAAElKdgCARCU7AEAzmm5cAgAAAAD91HTjsmYH\nAEhVswMAJKnZAQAS1ewAAM1wjUsAeqXr2kKDrgkHAKxtg74f+G4A9FkLfzs13bgs2QEAUpXsAABJ\nSnaAVc8NIGA1K9kBAJrR9KniAAAAAEA/NT3isoZjTUCf1VAFWSqntrG61VD/gP6qoQYCzGq6cQks\nnVPEAAAAgNWs6cZlyQ4AkKpkBwBIUrIDACQq2QFgWQyiYZSablxm8AEDAAAAgHxNNy5rONYES9V1\nfTsN+tWihioI9FMN9Q/orxpqIMAsdxUHAAAAAJrTdOOyZAcASFWyAwAkKdkBABKV7AAAzWi6cQkA\nAAAA9JNrXAI0q4YqCPRTDfUP1p6u66x3XZ+9f2qogQCzmm5cAgAAAADj18JBpaYblyU7AIxZC0WB\nlpTsANArg2pw1wghVkrJDgCQqGQHAGhG041LAAAAgNXEQU/WihYu8dH0zXlqdgCAVDU7AECSmh0A\nIFHNDgDQDCMuAWiGo9MAo+HSBwDAWtB047JkBwBIVbIDACQp2QHoIc1e2lGyAwA0o+nGJQAAwDho\nUAJAe5puXNZwrAnosxqqINBPNdS/9mn0wUqpoQYCzGq6cck5LdzJCQAAAADGpenGZckOAJCqZAcA\nSFKyA7AIXQfPjcaE5SjZAQCacUl2AAAAAACACzXduKzZAQBS1ewAAElqdgCARDU7AEAzmj5VHAAA\n1pJBp1c7tRqYj9oA9F3TjcuSHQAgVckOAJCkZAcASFSyA8Ca5KbHq1PTjUsAAGB4RmkBAGtB043L\nGo41AX1WYzlVsO+nI342Pjfv45+Lz445CTC8Gr4FAv1VQw0EmNV04xIAlmoizmZHAAAAYBmavqt4\nyQ4AkKpkBwBIUrIDACQq2QEAmmHEJQAAACvOzS8AGFbTIy5rdgCAVDU7AECSmh0AIFHNDgDQjKYb\nlwAAAABAPzXduCzZAQBSlewAAElKdgCARCU7AEAzXOMSAADWmEHXEtwbe8acBABg6ZoecVmzAwCk\nqtkBAJLU7AAAiWp2AIBmGHEJwJpkVBEAAMDq1nTjsmQHAEhVlrW2xh2wepXsAACJSnYAgGY03bgE\ngHHS7AXWinHUMzUTAFhpTTcuazjWRL8M+gNg0AX2Wetq9K0KupkEmbzPWlKjb/UP4JwaaiDArKZv\nzgMAAAAA9FPTIy5LdgCAVCU7AECSkh1gxRjZCyysZAcAaMaiGpfPPPNMfPjDH44f//jHMTExEV/7\n2tfiqquuive+973x05/+NEopcfjw4bjiiisiImLfvn3x1a9+NS699NL4whe+ELfccktERDz66KNx\n5513xguETp9tAAAbaklEQVQvvBDbt2+Pe++9d+WeGQAA9NRauvTGaswMQHtcgm11WlTj8uMf/3hs\n3749/vEf/zF++ctfxi9+8Yv427/929i2bVvcfffdcc8998T09HRMT0/H8ePH49ChQ3H8+PGYmZmJ\nm2++OU6cOBETExNx1113xYEDB2Lr1q2xffv2OHLkSNx6660D91vDsSagz2qogmtP1xcmf5zDy2qo\nf0B/1VAD16a1dFAJxmXBxuV///d/x/e+9704ePDg7Arr1sWrX/3qeOihh+K73/1uRETs2rUr3vGO\nd8T09HQ8+OCDcfvtt8f69eujlBKbN2+OY8eOxRvf+MZ49tlnY+vWrRERcccdd8QDDzzQ2bgEABgX\nf0wAAEBbFmxcPvnkk/Ha1742PvjBD8a///u/x/XXXx+f//zn48yZM7Fx48aIiNi4cWOcOXMmIiKe\neuqpuPHGG+fWn5qaipmZmVi/fn1MTU3NPT45ORkzMzPz7vOBiLji1/99OiI2nTe3/vrfsuTp2jF3\nFNsf9/5Hvb2Vnq4NpDnn/CWGXX65CS6cO+zyde7/599f99a6lmhzev65dcjlV9Pn5eXHyhLXXul8\n3dOj3nqL9W9p+++aO3iLy0+7vOlR/fzPGVXC+eeO+v2ZXc9G/fyzX/9R1b9BCRbe+sVL1Fjqsx9m\njaVNL2X/tWPrLdbTV1rp/XfvfTT7qx1zs38/DZo+5/wllpZmcIKlbS/v9Rz1/gfNPefCR4bb/qh/\n/y00nf1+bvHzP879j3p72dNtpRl9PRvf+3+pe5tvenCC7r13L18j4ke/nn7tc8/FDRete86Cjctf\n/vKX8cMf/jC+9KUvxdve9rb4xCc+EdPT0+ctMzExERMTEwttatFu65xblj1dOuaOYvvj3v+ot7fS\n06Vz7ninL3xk2OWXOz3s9uefWwYusVCa/J/AcNPzzy0Dlxh2b9nPr2t60IivV44Qu3Dt7Pyj3nqL\n9W85+59/7uAtLpxmZadH/fNvs54ufXsrXc9G/fyzX/+Vfj8Nu/xCn+elbG+U00vZf+mY22I97Zrb\nwus57HTpmJv9+2mh6dH8/hmcYGnbGzzd4udvnNsb9f6Hnc5+P6+11z97e9nTbaUZfT0b9/t/+L3N\nNz04wULrdy1fXjF92ateddGar7Rg43JqaiqmpqbibW97W0RE/Nmf/Vns27cvNm3aFKdPn45NmzbF\n008/HRs2bIiI2ZGUJ0+enFv/1KlTMTU1FZOTk3Hq1KnzHp+cnOzcd435njhAX9RQBYF+qqH+ARF9\nvVxHDTUQWGsG1fMr47K4v2O9BRuXmzZtite//vXxxBNPxJve9KY4evRovOUtb4m3vOUtcfDgwfj0\npz8dBw8ejNtumx0nuWPHjnj/+98fn/zkJ2NmZiZOnDgRW7dujYmJibj88svj2LFjsXXr1rjvvvvi\nYx/72JKeLADQbTGjdAEAAFq2qLuKf/GLX4y/+Iu/iBdffDH+z//5P/G1r30tXnrppdi5c2ccOHAg\nSilx+PDhiIjYsmVL7Ny5M7Zs2RLr1q2L/fv3z51Gvn///rjzzjvj+eefj+3bty94Y56yvOcGsMqV\n7ACsgHGNHNGgZHUr2QF6p5+j2hi3rveZ31uvVLIDADRjUY3La6+9Nv71X//1osePHj067/K7d++O\n3bt3X/T49ddfH48//viC+/PFCQAAAAD6bVGNyzw1HG0C+qvGcmrgoJELDg4B7avhOyDQXzXUQIBZ\nl2QHAAAAAAC4UOONy5IdACBRyQ4AkKRkBwBIVLIDADSj8VPFAQAAAIBxa+HGaU02Ll9+YWqcO9bk\nmmxA/9RwxB3opxrqH9BfNdRAgFlNNi4B6CcHqQAAAHhZ09e4LNkBAFKV7AAASUp2AIBEJTsAQDOM\nuATomUHXKTHaEQAAgJY03bis4VgT0Gc1VEGgn2qof0ALcg7s1lADAWY1fao4AAAAANBPTTcuS3YA\ngFQlOwBAkpIdACBRyQ4A0IymG5cAAAAAQD813bis2QEAUtXsAABJanYAgEQ1OwBAM5puXAIAAAAA\n/dR047JkBwBIVbIDACQp2QEAEpXsAADNWJcdAAAAaNee2Dvv43tjz5iTAAB90/SIy5odACBVzQ4A\nkKRmBwBIVLMDADSj6cYlAAAAANBPTZ8qXrIDLNOg02oAFqdkBwBIUrIDACQqy1rb36HAWtJ04xIA\nAAD6qqsJ6TqzMJyuz4yGf7uaPlW8ZgcASFWzAwAkqdkBABLV7AAAzWi6cQkAAAAA9FPTjcuSHQAg\nVckOAJCkZAcASFSyAwA0o+nGJQAAAADQT03fnKeGY01An9VYiSroQu5A+2r4Fgj0Vw01EGBW041L\nAAAA6CsHnIG+a7pxWbIDAKQq2QFYg7r+ANoTe8eYBLqU7AAAiUp2AIBmNN24pB1df8w6CggAAADA\nqDXduKzhWBPQZzVUwVlGAkLf1FD/gP6q8XINNIAE6Dt3FQcAAAAAmtN047JkBwBIVbIDACQp2QEA\nEpXsAADNaPpUcQAAAOgrp4MDfdf0iMuaHQAgVc0OAJCkZgcASFSzAwA0o+nGJQAAAADQT003Lkt2\nAIBUJTsAQJKSHQAgUckOANCMphuXAAAAAEA/Nd24rNkBAFLV7AAASWp2AIBENTsAQDPcVRwAAGCE\n3AkaAEaj6cZlyQ4AkKpkBwBIUrID8AqacDBuJTsAQDOaPlUcAAAAAOinphuXNTsAQKqaHQAgSc0O\nAJCoZgcAaEbTjUsAAAAAoJ9c4xKgWSU7wNjtib3ZEYAmlOwAAIlKdgCAZhhxCQAAAAA0p+nGZc0O\nAJCqZgcASFKzAwAkqtkBAJrRdOMSAAAAAOinphuXJTsAQKqSHQAgSckOAJCoZAcAaEbTjUsAAAAA\noJ+avqt4DceagD6roQrC+OyNPdkRmFND/QP6q4YaCDDLiEsAAAAAoDlNNy5LdgCAVCU7AECSkh0A\nIFHJDgDQjKZPFQeAPtkTe7MjAACwQlyWBobXdOOyhmNNsFR+Ka4FNVRBoJ9qqH9Af9VQAwFmNX2q\nOAAAAADQT003Lkt2AIBUJTsAQJKSHQAgUckOANCMphuXAAAAAEA/Nd24rNkBAFLV7AAASWp2AIBE\nNTsAQDOablwCAAAAAP3UdOOyZAcASFWyAwAkKdkBABKV7AAAzViXHQAAAAAAFmtv7Bk4b0/sHWMS\nVlrTIy5rdgCAVDU7AECSmh0AIFHNDgDQDCMuAQAAAEZk0Ii/rlGCwPyablyW7AAAqUp2AIAkJTsA\nsAKcvrlYJTsAQDOablwCMHqOAAMAALAauMYlQLNqdgCAJDU7AECimh0AoBlGXMIa1XUqjpF1AAAA\nQOuaHnFZsgMApCrZAQCSlOwAAIlKdgCAZjTduAQAAAAA+qnpxmXNDgCQqmYHAEhSswMAJKrZAQCa\n4RqXAAAx+NrArgsMAAA5mh5xWbIDAKQq2QEAkpTsAACJSnYAgGY03bgEAAAAAPqp6VPFazjWBPRZ\nDVUQxscp4S2pof4B/VVDDVzdfKeA0THiEgAAAABoTtONy5IdACBVyQ4AkKRkBwBIVLIDADSj6cYl\nAAAAANBPTTcua3YAgFQ1OwB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Wb/3WeY8NqnkPPvhg3H777bF+/foopcTmzZvnDvAArEbz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\nwMsxXAIAAAAAL8dwCQAAAAC8nD9FAWBsJd2iIQAAAABJRU5ErkJggg==\n" + } + ], + "prompt_number": 184 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [], + "language": "python", + "metadata": {}, + "outputs": [] + } + ], + "metadata": {} + } + ] } \ No newline at end of file diff --git a/Chapter7_BayesianMachineLearning/MachineLearning.ipynb b/Chapter7_BayesianMachineLearning/MachineLearning.ipynb index dad13cfc..f29f0374 100644 --- a/Chapter7_BayesianMachineLearning/MachineLearning.ipynb +++ b/Chapter7_BayesianMachineLearning/MachineLearning.ipynb @@ -1,164 +1,164 @@ -{ - "metadata": { - "name": "MachineLearning" - }, - "nbformat": 3, - "nbformat_minor": 0, - "worksheets": [ - { - "cells": [ - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "List of topics to cover:\n", - "\n", - "- Bayesian solution to overfitting\n", - " - Salisman's solution to the Don't Overfit\n", - "- Predictive distributions; \"how do I evaluate testing data?\"\n", - "- model fitting, BIC + visualization tools\n", - "- Gaussian Processes\n", - "\n", - "\n", - "Would be nice/cool to cover:\n", - "\n", - "- classification models (using the books text)\n", - "- Bayesian networks?" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [], - "language": "python", - "metadata": {}, - "outputs": [], - "prompt_number": 6 - }, - { - "cell_type": "code", - "collapsed": false, - "input": [], - "language": "python", - "metadata": {}, - "outputs": [], - "prompt_number": 6 - }, - { - "cell_type": "code", - "collapsed": false, - "input": [], - "language": "python", - "metadata": {}, - "outputs": [], - "prompt_number": 6 - }, - { - "cell_type": "code", - "collapsed": false, - "input": [], - "language": "python", - "metadata": {}, - "outputs": [], - "prompt_number": 6 - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "from IPython.core.display import HTML\n", - "\n", - "\n", - "def css_styling():\n", - " styles = open(\"../styles/custom.css\", \"r\").read()\n", - " return HTML(styles)\n", - "css_styling()" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "html": [ - "\n", - "" - ], - "output_type": "pyout", - "prompt_number": 10, - "text": [ - "" - ] - } - ], - "prompt_number": 10 - }, - { - "cell_type": "code", - "collapsed": false, - "input": [], - "language": "python", - "metadata": {}, - "outputs": [] - } - ], - "metadata": {} - } - ] +{ + "metadata": { + "name": "MachineLearning" + }, + "nbformat": 3, + "nbformat_minor": 0, + "worksheets": [ + { + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "List of topics to cover:\n", + "\n", + "- Bayesian solution to overfitting\n", + " - Salisman's solution to the Don't Overfit\n", + "- Predictive distributions; \"how do I evaluate testing data?\"\n", + "- model fitting, BIC + visualization tools\n", + "- Gaussian Processes\n", + "\n", + "\n", + "Would be nice/cool to cover:\n", + "\n", + "- classification models (using the books text)\n", + "- Bayesian networks?" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 6 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 6 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 6 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 6 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from IPython.core.display import HTML\n", + "\n", + "\n", + "def css_styling():\n", + " styles = open(\"../styles/custom.css\", \"r\").read()\n", + " return HTML(styles)\n", + "css_styling()" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "html": [ + "\n", + "" + ], + "output_type": "pyout", + "prompt_number": 10, + "text": [ + "" + ] + } + ], + "prompt_number": 10 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [], + "language": "python", + "metadata": {}, + "outputs": [] + } + ], + "metadata": {} + } + ] } \ No newline at end of file diff --git a/Chapter7_BayesianMachineLearning/auc.py b/Chapter7_BayesianMachineLearning/auc.py index 0f2e68f0..223e918b 100644 --- a/Chapter7_BayesianMachineLearning/auc.py +++ b/Chapter7_BayesianMachineLearning/auc.py @@ -1,61 +1,61 @@ -#contributed by Ben Hammer, 2013 - - -def tied_rank(x): - """ - Computes the tied rank of elements in x. - - This function computes the tied rank of elements in x. - - Parameters - ---------- - x : list of numbers, numpy array - - Returns - ------- - score : list of numbers - The tied rank f each element in x - - """ - sorted_x = sorted(zip(x,range(len(x)))) - r = [0 for k in x] - cur_val = sorted_x[0][0] - last_rank = 0 - for i in range(len(sorted_x)): - if cur_val != sorted_x[i][0]: - cur_val = sorted_x[i][0] - for j in range(last_rank, i): - r[sorted_x[j][1]] = float(last_rank+1+i)/2.0 - last_rank = i - if i==len(sorted_x)-1: - for j in range(last_rank, i+1): - r[sorted_x[j][1]] = float(last_rank+i+2)/2.0 - return r - -def auc(actual, posterior): - """ - Computes the area under the receiver-operater characteristic (AUC) - - This function computes the AUC error metric for binary classification. - - Parameters - ---------- - actual : list of binary numbers, numpy array - The ground truth value - posterior : same type as actual - Defines a ranking on the binary numbers, from most likely to - be positive to least likely to be positive. - - Returns - ------- - score : double - The mean squared error between actual and posterior - - """ - r = tied_rank(posterior) - num_positive = len([0 for x in actual if x==1]) - num_negative = len(actual)-num_positive - sum_positive = sum([r[i] for i in range(len(r)) if actual[i]==1]) - auc = ((sum_positive - num_positive*(num_positive+1)/2.0) / - (num_negative*num_positive)) +#contributed by Ben Hammer, 2013 + + +def tied_rank(x): + """ + Computes the tied rank of elements in x. + + This function computes the tied rank of elements in x. + + Parameters + ---------- + x : list of numbers, numpy array + + Returns + ------- + score : list of numbers + The tied rank f each element in x + + """ + sorted_x = sorted(zip(x,range(len(x)))) + r = [0 for k in x] + cur_val = sorted_x[0][0] + last_rank = 0 + for i in range(len(sorted_x)): + if cur_val != sorted_x[i][0]: + cur_val = sorted_x[i][0] + for j in range(last_rank, i): + r[sorted_x[j][1]] = float(last_rank+1+i)/2.0 + last_rank = i + if i==len(sorted_x)-1: + for j in range(last_rank, i+1): + r[sorted_x[j][1]] = float(last_rank+i+2)/2.0 + return r + +def auc(actual, posterior): + """ + Computes the area under the receiver-operater characteristic (AUC) + + This function computes the AUC error metric for binary classification. + + Parameters + ---------- + actual : list of binary numbers, numpy array + The ground truth value + posterior : same type as actual + Defines a ranking on the binary numbers, from most likely to + be positive to least likely to be positive. + + Returns + ------- + score : double + The mean squared error between actual and posterior + + """ + r = tied_rank(posterior) + num_positive = len([0 for x in actual if x==1]) + num_negative = len(actual)-num_positive + sum_positive = sum([r[i] for i in range(len(r)) if actual[i]==1]) + auc = ((sum_positive - num_positive*(num_positive+1)/2.0) / + (num_negative*num_positive)) return auc \ No newline at end of file diff --git a/ExamplesFromChapters/Chapter1/SMS_behaviour.py b/ExamplesFromChapters/Chapter1/SMS_behaviour.py index 489571c0..686bf34c 100644 --- a/ExamplesFromChapters/Chapter1/SMS_behaviour.py +++ b/ExamplesFromChapters/Chapter1/SMS_behaviour.py @@ -1,28 +1,28 @@ -import pymc as pm -import numpy as np - -count_data = np.loadtxt("../../Chapter1_Introduction/data/txtdata.csv") -n_count_data = len(count_data) - -alpha = 1.0 / count_data.mean() # recall count_data is - # the variable that holds our txt counts - -lambda_1 = pm.Exponential("lambda_1", alpha) -lambda_2 = pm.Exponential("lambda_2", alpha) - -tau = pm.DiscreteUniform("tau", lower=0, upper=n_count_data) - - -@pm.deterministic -def lambda_(tau=tau, lambda_1=lambda_1, lambda_2=lambda_2): - out = np.zeros(n_count_data) - out[:tau] = lambda_1 # lambda before tau is lambda1 - out[tau:] = lambda_2 # lambda after tau is lambda2 - return out - -observation = pm.Poisson("obs", lambda_, value=count_data, observed=True) -model = pm.Model([observation, lambda_1, lambda_2, tau]) - - -mcmc = pm.MCMC(model) -mcmc.sample(100000, 50000, 1) +import pymc as pm +import numpy as np + +count_data = np.loadtxt("../../Chapter1_Introduction/data/txtdata.csv") +n_count_data = len(count_data) + +alpha = 1.0 / count_data.mean() # recall count_data is + # the variable that holds our txt counts + +lambda_1 = pm.Exponential("lambda_1", alpha) +lambda_2 = pm.Exponential("lambda_2", alpha) + +tau = pm.DiscreteUniform("tau", lower=0, upper=n_count_data) + + +@pm.deterministic +def lambda_(tau=tau, lambda_1=lambda_1, lambda_2=lambda_2): + out = np.zeros(n_count_data) + out[:tau] = lambda_1 # lambda before tau is lambda1 + out[tau:] = lambda_2 # lambda after tau is lambda2 + return out + +observation = pm.Poisson("obs", lambda_, value=count_data, observed=True) +model = pm.Model([observation, lambda_1, lambda_2, tau]) + + +mcmc = pm.MCMC(model) +mcmc.sample(100000, 50000, 1) diff --git a/ExamplesFromChapters/Chapter2/ABtesting.py b/ExamplesFromChapters/Chapter2/ABtesting.py index bccef2e7..afcca8f7 100644 --- a/ExamplesFromChapters/Chapter2/ABtesting.py +++ b/ExamplesFromChapters/Chapter2/ABtesting.py @@ -1,39 +1,39 @@ -""" -This is an example of using Bayesian A/B testing - -""" - -import pymc as pm - -# these two quantities are unknown to us. -true_p_A = 0.05 -true_p_B = 0.04 - -# notice the unequal sample sizes -- no problem in Bayesian analysis. -N_A = 1500 -N_B = 1000 - -# generate data -observations_A = pm.rbernoulli(true_p_A, N_A) -observations_B = pm.rbernoulli(true_p_B, N_B) - - -# set up the pymc model. Again assume Uniform priors for p_A and p_B -p_A = pm.Uniform("p_A", 0, 1) -p_B = pm.Uniform("p_B", 0, 1) - - -# define the deterministic delta function. This is our unknown of interest. - -@pm.deterministic -def delta(p_A=p_A, p_B=p_B): - return p_A - p_B - - -# set of observations, in this case we have two observation datasets. -obs_A = pm.Bernoulli("obs_A", p_A, value=observations_A, observed=True) -obs_B = pm.Bernoulli("obs_B", p_B, value=observations_B, observed=True) - -# to be explained in chapter 3. -mcmc = pm.MCMC([p_A, p_B, delta, obs_A, obs_B]) -mcmc.sample(20000, 1000) +""" +This is an example of using Bayesian A/B testing + +""" + +import pymc as pm + +# these two quantities are unknown to us. +true_p_A = 0.05 +true_p_B = 0.04 + +# notice the unequal sample sizes -- no problem in Bayesian analysis. +N_A = 1500 +N_B = 1000 + +# generate data +observations_A = pm.rbernoulli(true_p_A, N_A) +observations_B = pm.rbernoulli(true_p_B, N_B) + + +# set up the pymc model. Again assume Uniform priors for p_A and p_B +p_A = pm.Uniform("p_A", 0, 1) +p_B = pm.Uniform("p_B", 0, 1) + + +# define the deterministic delta function. This is our unknown of interest. + +@pm.deterministic +def delta(p_A=p_A, p_B=p_B): + return p_A - p_B + + +# set of observations, in this case we have two observation datasets. +obs_A = pm.Bernoulli("obs_A", p_A, value=observations_A, observed=True) +obs_B = pm.Bernoulli("obs_B", p_B, value=observations_B, observed=True) + +# to be explained in chapter 3. +mcmc = pm.MCMC([p_A, p_B, delta, obs_A, obs_B]) +mcmc.sample(20000, 1000) diff --git a/ExamplesFromChapters/Chapter2/FreqOfCheaters.py b/ExamplesFromChapters/Chapter2/FreqOfCheaters.py index 9c2a0a10..4ba58be9 100644 --- a/ExamplesFromChapters/Chapter2/FreqOfCheaters.py +++ b/ExamplesFromChapters/Chapter2/FreqOfCheaters.py @@ -1,17 +1,17 @@ -import pymc as pm - -p = pm.Uniform("freq_cheating", 0, 1) - - -@pm.deterministic -def p_skewed(p=p): - return 0.5 * p + 0.25 - -yes_responses = pm.Binomial( - "number_cheaters", 100, p_skewed, value=35, observed=True) - -model = pm.Model([yes_responses, p_skewed, p]) - -# To Be Explained in Chapter 3! -mcmc = pm.MCMC(model) -mcmc.sample(50000, 25000) +import pymc as pm + +p = pm.Uniform("freq_cheating", 0, 1) + + +@pm.deterministic +def p_skewed(p=p): + return 0.5 * p + 0.25 + +yes_responses = pm.Binomial( + "number_cheaters", 100, p_skewed, value=35, observed=True) + +model = pm.Model([yes_responses, p_skewed, p]) + +# To Be Explained in Chapter 3! +mcmc = pm.MCMC(model) +mcmc.sample(50000, 25000) diff --git a/ExamplesFromChapters/Chapter2/ORingFailure.py b/ExamplesFromChapters/Chapter2/ORingFailure.py index f216e526..e7eb0f8c 100644 --- a/ExamplesFromChapters/Chapter2/ORingFailure.py +++ b/ExamplesFromChapters/Chapter2/ORingFailure.py @@ -1,32 +1,32 @@ -import numpy as np -import pymc as pm - - -challenger_data = np.genfromtxt( - "../../Chapter2_MorePyMC/data/challenger_data.csv", - skip_header=1, usecols=[1, 2], missing_values="NA", delimiter=",") -# drop the NA values -challenger_data = challenger_data[~np.isnan(challenger_data[:, 1])] - - -temperature = challenger_data[:, 0] -D = challenger_data[:, 1] # defect or not? - -beta = pm.Normal("beta", 0, 0.001, value=0) -alpha = pm.Normal("alpha", 0, 0.001, value=0) - - -@pm.deterministic -def p(temp=temperature, alpha=alpha, beta=beta): - return 1.0 / (1. + np.exp(beta * temperature + alpha)) - - -observed = pm.Bernoulli("bernoulli_obs", p, value=D, observed=True) - -model = pm.Model([observed, beta, alpha]) - -# mysterious code to be explained in Chapter 3 -map_ = pm.MAP(model) -map_.fit() -mcmc = pm.MCMC(model) -mcmc.sample(260000, 220000, 2) +import numpy as np +import pymc as pm + + +challenger_data = np.genfromtxt( + "../../Chapter2_MorePyMC/data/challenger_data.csv", + skip_header=1, usecols=[1, 2], missing_values="NA", delimiter=",") +# drop the NA values +challenger_data = challenger_data[~np.isnan(challenger_data[:, 1])] + + +temperature = challenger_data[:, 0] +D = challenger_data[:, 1] # defect or not? + +beta = pm.Normal("beta", 0, 0.001, value=0) +alpha = pm.Normal("alpha", 0, 0.001, value=0) + + +@pm.deterministic +def p(temp=temperature, alpha=alpha, beta=beta): + return 1.0 / (1. + np.exp(beta * temperature + alpha)) + + +observed = pm.Bernoulli("bernoulli_obs", p, value=D, observed=True) + +model = pm.Model([observed, beta, alpha]) + +# mysterious code to be explained in Chapter 3 +map_ = pm.MAP(model) +map_.fit() +mcmc = pm.MCMC(model) +mcmc.sample(260000, 220000, 2) diff --git a/ExamplesFromChapters/Chapter3/ClusteringWithGaussians.py b/ExamplesFromChapters/Chapter3/ClusteringWithGaussians.py index 4cfac7db..e1a3d5b4 100644 --- a/ExamplesFromChapters/Chapter3/ClusteringWithGaussians.py +++ b/ExamplesFromChapters/Chapter3/ClusteringWithGaussians.py @@ -1,41 +1,41 @@ -import numpy as np -import pymc as pm - - -data = np.loadtxt("../../Chapter3_MCMC/data/mixture_data.csv", delimiter=",") - - -p = pm.Uniform("p", 0, 1) - -assignment = pm.Categorical("assignment", [p, 1 - p], size=data.shape[0]) - -taus = 1.0 / pm.Uniform("stds", 0, 100, size=2) ** 2 # notice the size! -centers = pm.Normal("centers", [150, 150], [0.001, 0.001], size=2) - -""" -The below deterministic functions map a assingment, in this case 0 or 1, -to a set of parameters, located in the (1,2) arrays `taus` and `centers.` -""" - - -@pm.deterministic -def center_i(assignment=assignment, centers=centers): - return centers[assignment] - - -@pm.deterministic -def tau_i(assignment=assignment, taus=taus): - return taus[assignment] - -# and to combine it with the observations: -observations = pm.Normal("obs", center_i, tau_i, - value=data, observed=True) - -# below we create a model class -model = pm.Model([p, assignment, taus, centers]) - - -map_ = pm.MAP(model) -map_.fit() -mcmc = pm.MCMC(model) -mcmc.sample(100000, 50000) +import numpy as np +import pymc as pm + + +data = np.loadtxt("../../Chapter3_MCMC/data/mixture_data.csv", delimiter=",") + + +p = pm.Uniform("p", 0, 1) + +assignment = pm.Categorical("assignment", [p, 1 - p], size=data.shape[0]) + +taus = 1.0 / pm.Uniform("stds", 0, 100, size=2) ** 2 # notice the size! +centers = pm.Normal("centers", [150, 150], [0.001, 0.001], size=2) + +""" +The below deterministic functions map a assingment, in this case 0 or 1, +to a set of parameters, located in the (1,2) arrays `taus` and `centers.` +""" + + +@pm.deterministic +def center_i(assignment=assignment, centers=centers): + return centers[assignment] + + +@pm.deterministic +def tau_i(assignment=assignment, taus=taus): + return taus[assignment] + +# and to combine it with the observations: +observations = pm.Normal("obs", center_i, tau_i, + value=data, observed=True) + +# below we create a model class +model = pm.Model([p, assignment, taus, centers]) + + +map_ = pm.MAP(model) +map_.fit() +mcmc = pm.MCMC(model) +mcmc.sample(100000, 50000) diff --git a/ExamplesFromChapters/README.md b/ExamplesFromChapters/README.md index bde59920..167ea12e 100644 --- a/ExamplesFromChapters/README.md +++ b/ExamplesFromChapters/README.md @@ -1,5 +1,5 @@ -## Read Me - - -Included is all PyMC examples and models *out of context*, this is for users to easily view the entire Python program. - +## Read Me + + +Included is all PyMC examples and models *out of context*, this is for users to easily view the entire Python program. + diff --git a/LICENSE.txt b/LICENSE.txt index 08a0c072..9b99b029 100644 --- a/LICENSE.txt +++ b/LICENSE.txt @@ -1,22 +1,22 @@ -Copyright (c) 2013 Cameron Davidson-Pilon - -Permission is hereby granted, free of charge, to any person -obtaining a copy of this software and associated documentation -files (the "Software"), to deal in the Software without -restriction, including without limitation the rights to use, -copy, modify, merge, publish, distribute, sublicense, and/or sell -copies of the Software, and to permit persons to whom the -Software is furnished to do so, subject to the following -conditions: - -The above copyright notice and this permission notice shall be -included in all copies or substantial portions of the Software. - -THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, -EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES -OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND -NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT -HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, -WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING -FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR -OTHER DEALINGS IN THE SOFTWARE. +Copyright (c) 2013 Cameron Davidson-Pilon + +Permission is hereby granted, free of charge, to any person +obtaining a copy of this software and associated documentation +files (the "Software"), to deal in the Software without +restriction, including without limitation the rights to use, +copy, modify, merge, publish, distribute, sublicense, and/or sell +copies of the Software, and to permit persons to whom the +Software is furnished to do so, subject to the following +conditions: + +The above copyright notice and this permission notice shall be +included in all copies or substantial portions of the Software. + +THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, +EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES +OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND +NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT +HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, +WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING +FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR +OTHER DEALINGS IN THE SOFTWARE. diff --git a/Prologue/Prologue.ipynb b/Prologue/Prologue.ipynb index 0f6284b5..8f981dda 100644 --- a/Prologue/Prologue.ipynb +++ b/Prologue/Prologue.ipynb @@ -1,285 +1,285 @@ -{ - "metadata": { - "name": "Prologue" - }, - "nbformat": 3, - "nbformat_minor": 0, - "worksheets": [ - { - "cells": [ - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Probabilistic Programming and \n", - "=====\n", - "\n", - "Bayesian Methods for Hackers \n", - "=======" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "###Probabilistic Programming & Bayesian Methods for Hackers \n", - "#### *Using Python and PyMC*\n", - "\n", - "\n", - "\n", - "\n", - "The Bayesian method is the natural approach to inference, yet it is hidden from readers behind chapters of slow, mathematical analysis. The typical text on Bayesian inference involves two to three chapters on probability theory, then enters what Bayesian inference is. Unfortunately, due to mathematical intractability of most Bayesian models, the reader is only shown simple, artificial examples. This can leave the user with a *so-what* feeling about Bayesian inference. In fact, this was the author's own prior opinion.\n", - "\n", - "\n", - "
\n", - "\n", - "After some recent success of Bayesian methods in machine-learning competitions, I decided to investigate the subject again. Even with my mathematical background, it took me three straight-days of reading examples and trying to put the pieces together to understand the methods. There was simply not enough literature bridging theory to practice. The problem with my misunderstanding was the disconnect between Bayesian mathematics and probabilistic programming. That being said, I suffered then so the reader would not have to now. This book attempts to bridge the gap.\n", - "\n", - "If Bayesian inference is the destination, then mathematical analysis is a particular path to towards it. On the other hand, computing power is cheap enough that we can afford to take an alternate route via probabilistic programming. The latter path is much more useful, as it denies the necessity of mathematical intervention at each step, that is, we remove often-intractable mathematical analysis as a prerequisite to Bayesian inference. Simply put, this latter computational path proceeds via small intermediate jumps from beginning to end, where as the first path proceeds by enormous leaps, often landing far away from our target. Furthermore, without a strong mathematical background, the analysis required by the first path cannot even take place.\n", - "\n", - "*Bayesian Methods for Hackers* is designed as a introduction to Bayesian inference from a computational/understanding-first, and mathematics-second, point of view. Of course as an introductory book, we can only leave it at that: an introductory book. For the mathematically trained, they may cure the curiosity this text generates with other texts designed with mathematical analysis in mind. For the enthusiast with less mathematical-background, or one who is not interested in the mathematics but simply the practice of Bayesian methods, this text should be sufficient and entertaining.\n", - "\n", - "\n", - "The choice of PyMC as the probabilistic programming language is two-fold. As of this writing, there is currently no central resource for examples and explanations in the PyMC universe. The official documentation assumes prior knowledge of Bayesian inference and probabilistic programming. We hope this book encourages users at every level to look at PyMC. Secondly, with recent core developments and popularity of the scientific stack in Python, PyMC is likely to become a core component soon enough.\n", - "\n", - "PyMC does have dependencies to run, namely NumPy and (optionally) SciPy. To not limit the user, the examples in this book will rely only on PyMC, NumPy, SciPy and Matplotlib only.\n", - "\n", - "\n", - "Contents\n", - "------\n", - "\n", - "(The below chapters are rendered via the *nbviewer* at\n", - "[nbviewer.ipython.org/](http://nbviewer.ipython.org/), and is read-only and rendered in real-time.\n", - "Interactive notebooks + examples can be downloaded by cloning! )\n", - "\n", - "\n", - "* [**Prologue:**](http://nbviewer.ipython.org/urls/raw.github.com/CamDavidsonPilon/Probabilistic-Programming-and-Bayesian-Methods-for-Hackers/master/Prologue/Prologue.ipynb) Why we do it.\n", - "\n", - "* [**Chapter 1: Introduction to Bayesian Methods**](http://nbviewer.ipython.org/urls/raw.github.com/CamDavidsonPilon/Probabilistic-Programming-and-Bayesian-Methods-for-Hackers/master/Chapter1_Introduction/Chapter1_Introduction.ipynb)\n", - " Introduction to the philosophy and practice of Bayesian methods and answering the question \"What is probabilistic programming?\" Examples include:\n", - " - Inferring human behaviour changes from text message rates.\n", - " \n", - "* [**Chapter 2: A little more on PyMC**](http://nbviewer.ipython.org/urls/raw.github.com/CamDavidsonPilon/Probabilistic-Programming-and-Bayesian-Methods-for-Hackers/master/Chapter2_MorePyMC/MorePyMC.ipynb)\n", - " We explore modeling Bayesian problems using Python's PyMC library through examples. How do we create Bayesian models? Examples include:\n", - " - Detecting the frequency of cheating students, while avoiding liars.\n", - " - Calculating probabilities of the Challenger space-shuttle disaster.\n", - " \n", - "* [**Chapter 3: Opening the Black Box of MCMC**](http://nbviewer.ipython.org/urls/raw.github.com/CamDavidsonPilon/Probabilistic-Programming-and-Bayesian-Methods-for-Hackers/master/Chapter3_MCMC/IntroMCMC.ipynb)\n", - " We discuss how MCMC operates and diagnostic tools. Examples include:\n", - " - Bayesian clustering with mixture models\n", - " \n", - "* [**Chapter 4: The Greatest Theorem Never Told**](http://nbviewer.ipython.org/urls/raw.github.com/CamDavidsonPilon/Probabilistic-Programming-and-Bayesian-Methods-for-Hackers/master/Chapter4_TheGreatestTheoremNeverTold/LawOfLargeNumbers.ipynb)\n", - " We explore an incredibly useful, and dangerous, theorem: The Law of Large Numbers. Examples include:\n", - " - Exploring a Kaggle dataset and the pitfalls of naive analysis\n", - " - How to sort Reddit comments from best to worst (not as easy as you think)\n", - " \n", - "* [**Chapter 5: Would you rather loss an arm or a leg?**](http://nbviewer.ipython.org/urls/raw.github.com/CamDavidsonPilon/Probabilistic-Programming-and-Bayesian-Methods-for-Hackers/master/Chapter5_LossFunctions/LossFunctions.ipynb)\n", - " The introduction of Loss functions and their (awesome) use in Bayesian methods. Examples include:\n", - " - Solving the Price is Right's Showdown\n", - " - Optimizing financial predictions\n", - " - Winning solution to the Kaggle Dark World's competition.\n", - " \n", - "* [**Chapter 6: Getting our *prior*-ities straight**](http://nbviewer.ipython.org/urls/raw.github.com/CamDavidsonPilon/Probabilistic-Programming-and-Bayesian-Methods-for-Hackers/master/Chapter6_Priorities/Priors.ipynb)\n", - " Probably the most important chapter. We draw on expert opinions to answer questions. Examples include:\n", - " - Multi-Armed Bandits and the Bayesian Bandit solution.\n", - " - what is the relationship between data sample size and prior?\n", - " - estimating financial unknowns using expert priors.\n", - " \n", - " We explore useful tips to be objective in analysis, and common pitfalls of priors. \n", - " \n", - "* **Chapter X1: Bayesian Markov Models**\n", - " \n", - "* **Chapter X2: Bayesian methods in Machine Learning** \n", - " We explore how to resolve the overfitting problem plus popular ML methods. Also included are probablistic explainations of Ridge Regression and LASSO Regression.\n", - " - Bayesian spam filtering plus *how to defeat Bayesian spam filtering*\n", - " - Tim Saliman's winning solution to Kaggle's *Don't Overfit* problem \n", - " \n", - "* **Chapter X3: More PyMC Hackery**\n", - " We explore the gritty details of PyMC. Examples include:\n", - " - Analysis on real-time GitHub repo stars and forks.\n", - "\n", - "* **Chapter X4: Troubleshooting and debugging**\n", - "\n", - " \n", - "**More questions about PyMC?**\n", - "Please post your modeling, convergence, or any other PyMC question on [cross-validated](http://stats.stackexchange.com/), the statistics stack-exchange.\n", - " \n", - " \n", - "Using the book\n", - "-------\n", - "\n", - "The book can be read in three different ways, starting from most recommended to least recommended: \n", - "\n", - "1. The most recommended option is to clone the repository to download the .ipynb files to your local machine. If you have IPython installed, you can view the \n", - "chapters in your browser *plus* edit and run the code provided (and try some practice questions). This is the preferred option to read\n", - "this book, though it comes with some dependencies. \n", - " - IPython 0.13 is a requirement to view the ipynb files. It can be downloaded [here](http://ipython.org/)\n", - " - For Linux users, you should not have a problem installing Numpy, Scipy, Matplotlib and PyMC. For Windows users, check out [pre-compiled versions](http://www.lfd.uci.edu/~gohlke/pythonlibs/) if you have difficulty. \n", - " - In the styles/ directory are a number of files (.matplotlirc) that used to make things pretty. These are not only designed for the book, but they offer many improvements over the default settings of matplotlib and the IPython notebook.\n", - " - while technically not required, it may help to run the IPython notebook with `--pylab inline` if you encounter runtime errors.\n", - "2. The second, preferred, option is to use the nbviewer.ipython.org site, which display IPython notebooks in the browser ([example](http://nbviewer.ipython.org/urls/raw.github.com/CamDavidsonPilon/Probabilistic-Programming-and-Bayesian-Methods-for-Hackers/master/Chapter1_Introduction/Chapter1_Introduction.ipynb)).\n", - "The contents are updated synchronously as commits are made to the book. You can use the Contents section above to link to the chapters.\n", - " \n", - "3. **PDF versions are coming.** PDFs are the least-prefered method to read the book, as pdf's are static and non-interactive. If PDFs are desired, they can be created dynamically using Chrome's builtin print-to-pdf feature.\n", - " \n", - "\n", - "Installation and configuration\n", - "------\n", - "If you would like to run the IPython notebooks locally, (option 1. above), you'll need to install the following:\n", - "\n", - "- IPython 0.13 is a requirement to view the ipynb files. It can be downloaded [here](http://ipython.org/ipython-doc/dev/install/index.html)\n", - "- For Linux users, you should not have a problem installing Numpy, Scipy and PyMC. For Windows users, check out [pre-compiled versions](http://www.lfd.uci.edu/~gohlke/pythonlibs/) if you have difficulty. \n", - " - also recommended, for data-mining exercises, are [PRAW](https://github.com/praw-dev/praw) and [requests](https://github.com/kennethreitz/requests). \n", - "- In the styles/ directory are a number of files that are customized for the notebook. \n", - "These are not only designed for the book, but they offer many improvements over the \n", - "default settings of matplotlib and the IPython notebook. The in notebook style has not been finalized yet.\n", - "\n", - "\n", - "Contributions and Thanks\n", - "-----\n", - "\n", - "\n", - "Thanks to all our contributing authors, including (in chronological order):\n", - "\n", - "- [Cameron Davidson-Pilon](http://www.camdp.com)\n", - "- [Stef Gibson](http://stefgibson.com)\n", - "- [Vincent Ohprecio](http://bigsnarf.wordpress.com/)\n", - "- [Lars Buitinck](https://github.com/larsman)\n", - "- [Paul Magwene](http://github.com/pmagwene) \n", - "- [Matthias Bussonnier](https://github.com/Carreau)\n", - "- [Jens Rantil](https://github.com/JensRantil)\n", - "- [y-p](https://github.com/y-p)\n", - "- [Ethan Brown](http://www.etano.net/)\n", - "- [Jonathan Whitmore](http://jonathanwhitmore.com/)\n", - "- [Mattia Rigotti](https://github.com/matrig)\n", - "- [Colby Lemon](https://github.com/colibius)\n", - "- [Gustav W Delius](https://github.com/gustavdelius)\n", - "- [Matthew Conlen](http://www.mathisonian.com/) \n", - "- [Jim Radford](https://github.com/radford)\n", - "- [Vannessa Sabino](http://baniverso.com/)\n", - "- [Thomas Bratt](https://github.com/thomasbratt)\n", - "- [Nisan Haramati](https://github.com/nisanharamati)\n", - "- [Thomas Bratt](https://github.com/thomasbratt)\n", - "- [Robert Grant](https://github.com/bgrant)\n", - "- [Yaroslav Halchenko](https://github.com/yarikoptic)\n", - "- [Alex Garel](https://github.com/alexgarel)\n", - "\n", - "\n", - "We would like to thank the Python community for building an amazing architecture. We would like to thank the \n", - "statistics community for building an amazing architecture. \n", - "\n", - "Similarly, the book is only possible because of the [PyMC](http://github.com/pymc-devs/pymc) library. A big thanks to the core devs of PyMC: Chris Fonnesbeck, Anand Patil, David Huard and John Salvatier.\n", - "\n", - "One final thanks. This book was generated by IPython Notebook, a wonderful tool for developing in Python. We thank the IPython \n", - "community for developing the Notebook interface. All IPython notebook files are available for download on the GitHub repository. \n", - "\n", - "\n", - "\n", - "####Contact\n", - "Contact the main author, Cam Davidson-Pilon at cam.davidson.pilon@gmail.com or [@cmrndp](https://twitter.com/cmrn_dp)\n", - "\n", - "\n", - "![Imgur](http://i.imgur.com/Zb79QZb.png)\n" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "from IPython.core.display import HTML\n", - "\n", - "\n", - "def css_styling():\n", - " styles = open(\"../styles/custom.css\", \"r\").read()\n", - " return HTML(styles)\n", - "css_styling()" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "html": [ - "\n", - "" - ], - "output_type": "pyout", - "prompt_number": 1, - "text": [ - "" - ] - } - ], - "prompt_number": 1 - }, - { - "cell_type": "code", - "collapsed": false, - "input": [], - "language": "python", - "metadata": {}, - "outputs": [] - } - ], - "metadata": {} - } - ] +{ + "metadata": { + "name": "Prologue" + }, + "nbformat": 3, + "nbformat_minor": 0, + "worksheets": [ + { + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Probabilistic Programming and \n", + "=====\n", + "\n", + "Bayesian Methods for Hackers \n", + "=======" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "###Probabilistic Programming & Bayesian Methods for Hackers \n", + "#### *Using Python and PyMC*\n", + "\n", + "\n", + "\n", + "\n", + "The Bayesian method is the natural approach to inference, yet it is hidden from readers behind chapters of slow, mathematical analysis. The typical text on Bayesian inference involves two to three chapters on probability theory, then enters what Bayesian inference is. Unfortunately, due to mathematical intractability of most Bayesian models, the reader is only shown simple, artificial examples. This can leave the user with a *so-what* feeling about Bayesian inference. In fact, this was the author's own prior opinion.\n", + "\n", + "\n", + "
\n", + "\n", + "After some recent success of Bayesian methods in machine-learning competitions, I decided to investigate the subject again. Even with my mathematical background, it took me three straight-days of reading examples and trying to put the pieces together to understand the methods. There was simply not enough literature bridging theory to practice. The problem with my misunderstanding was the disconnect between Bayesian mathematics and probabilistic programming. That being said, I suffered then so the reader would not have to now. This book attempts to bridge the gap.\n", + "\n", + "If Bayesian inference is the destination, then mathematical analysis is a particular path to towards it. On the other hand, computing power is cheap enough that we can afford to take an alternate route via probabilistic programming. The latter path is much more useful, as it denies the necessity of mathematical intervention at each step, that is, we remove often-intractable mathematical analysis as a prerequisite to Bayesian inference. Simply put, this latter computational path proceeds via small intermediate jumps from beginning to end, where as the first path proceeds by enormous leaps, often landing far away from our target. Furthermore, without a strong mathematical background, the analysis required by the first path cannot even take place.\n", + "\n", + "*Bayesian Methods for Hackers* is designed as a introduction to Bayesian inference from a computational/understanding-first, and mathematics-second, point of view. Of course as an introductory book, we can only leave it at that: an introductory book. For the mathematically trained, they may cure the curiosity this text generates with other texts designed with mathematical analysis in mind. For the enthusiast with less mathematical-background, or one who is not interested in the mathematics but simply the practice of Bayesian methods, this text should be sufficient and entertaining.\n", + "\n", + "\n", + "The choice of PyMC as the probabilistic programming language is two-fold. As of this writing, there is currently no central resource for examples and explanations in the PyMC universe. The official documentation assumes prior knowledge of Bayesian inference and probabilistic programming. We hope this book encourages users at every level to look at PyMC. Secondly, with recent core developments and popularity of the scientific stack in Python, PyMC is likely to become a core component soon enough.\n", + "\n", + "PyMC does have dependencies to run, namely NumPy and (optionally) SciPy. To not limit the user, the examples in this book will rely only on PyMC, NumPy, SciPy and Matplotlib only.\n", + "\n", + "\n", + "Contents\n", + "------\n", + "\n", + "(The below chapters are rendered via the *nbviewer* at\n", + "[nbviewer.ipython.org/](http://nbviewer.ipython.org/), and is read-only and rendered in real-time.\n", + "Interactive notebooks + examples can be downloaded by cloning! )\n", + "\n", + "\n", + "* [**Prologue:**](http://nbviewer.ipython.org/urls/raw.github.com/CamDavidsonPilon/Probabilistic-Programming-and-Bayesian-Methods-for-Hackers/master/Prologue/Prologue.ipynb) Why we do it.\n", + "\n", + "* [**Chapter 1: Introduction to Bayesian Methods**](http://nbviewer.ipython.org/urls/raw.github.com/CamDavidsonPilon/Probabilistic-Programming-and-Bayesian-Methods-for-Hackers/master/Chapter1_Introduction/Chapter1_Introduction.ipynb)\n", + " Introduction to the philosophy and practice of Bayesian methods and answering the question \"What is probabilistic programming?\" Examples include:\n", + " - Inferring human behaviour changes from text message rates.\n", + " \n", + "* [**Chapter 2: A little more on PyMC**](http://nbviewer.ipython.org/urls/raw.github.com/CamDavidsonPilon/Probabilistic-Programming-and-Bayesian-Methods-for-Hackers/master/Chapter2_MorePyMC/MorePyMC.ipynb)\n", + " We explore modeling Bayesian problems using Python's PyMC library through examples. How do we create Bayesian models? Examples include:\n", + " - Detecting the frequency of cheating students, while avoiding liars.\n", + " - Calculating probabilities of the Challenger space-shuttle disaster.\n", + " \n", + "* [**Chapter 3: Opening the Black Box of MCMC**](http://nbviewer.ipython.org/urls/raw.github.com/CamDavidsonPilon/Probabilistic-Programming-and-Bayesian-Methods-for-Hackers/master/Chapter3_MCMC/IntroMCMC.ipynb)\n", + " We discuss how MCMC operates and diagnostic tools. Examples include:\n", + " - Bayesian clustering with mixture models\n", + " \n", + "* [**Chapter 4: The Greatest Theorem Never Told**](http://nbviewer.ipython.org/urls/raw.github.com/CamDavidsonPilon/Probabilistic-Programming-and-Bayesian-Methods-for-Hackers/master/Chapter4_TheGreatestTheoremNeverTold/LawOfLargeNumbers.ipynb)\n", + " We explore an incredibly useful, and dangerous, theorem: The Law of Large Numbers. Examples include:\n", + " - Exploring a Kaggle dataset and the pitfalls of naive analysis\n", + " - How to sort Reddit comments from best to worst (not as easy as you think)\n", + " \n", + "* [**Chapter 5: Would you rather loss an arm or a leg?**](http://nbviewer.ipython.org/urls/raw.github.com/CamDavidsonPilon/Probabilistic-Programming-and-Bayesian-Methods-for-Hackers/master/Chapter5_LossFunctions/LossFunctions.ipynb)\n", + " The introduction of Loss functions and their (awesome) use in Bayesian methods. Examples include:\n", + " - Solving the Price is Right's Showdown\n", + " - Optimizing financial predictions\n", + " - Winning solution to the Kaggle Dark World's competition.\n", + " \n", + "* [**Chapter 6: Getting our *prior*-ities straight**](http://nbviewer.ipython.org/urls/raw.github.com/CamDavidsonPilon/Probabilistic-Programming-and-Bayesian-Methods-for-Hackers/master/Chapter6_Priorities/Priors.ipynb)\n", + " Probably the most important chapter. We draw on expert opinions to answer questions. Examples include:\n", + " - Multi-Armed Bandits and the Bayesian Bandit solution.\n", + " - what is the relationship between data sample size and prior?\n", + " - estimating financial unknowns using expert priors.\n", + " \n", + " We explore useful tips to be objective in analysis, and common pitfalls of priors. \n", + " \n", + "* **Chapter X1: Bayesian Markov Models**\n", + " \n", + "* **Chapter X2: Bayesian methods in Machine Learning** \n", + " We explore how to resolve the overfitting problem plus popular ML methods. Also included are probablistic explainations of Ridge Regression and LASSO Regression.\n", + " - Bayesian spam filtering plus *how to defeat Bayesian spam filtering*\n", + " - Tim Saliman's winning solution to Kaggle's *Don't Overfit* problem \n", + " \n", + "* **Chapter X3: More PyMC Hackery**\n", + " We explore the gritty details of PyMC. Examples include:\n", + " - Analysis on real-time GitHub repo stars and forks.\n", + "\n", + "* **Chapter X4: Troubleshooting and debugging**\n", + "\n", + " \n", + "**More questions about PyMC?**\n", + "Please post your modeling, convergence, or any other PyMC question on [cross-validated](http://stats.stackexchange.com/), the statistics stack-exchange.\n", + " \n", + " \n", + "Using the book\n", + "-------\n", + "\n", + "The book can be read in three different ways, starting from most recommended to least recommended: \n", + "\n", + "1. The most recommended option is to clone the repository to download the .ipynb files to your local machine. If you have IPython installed, you can view the \n", + "chapters in your browser *plus* edit and run the code provided (and try some practice questions). This is the preferred option to read\n", + "this book, though it comes with some dependencies. \n", + " - IPython 0.13 is a requirement to view the ipynb files. It can be downloaded [here](http://ipython.org/)\n", + " - For Linux users, you should not have a problem installing Numpy, Scipy, Matplotlib and PyMC. For Windows users, check out [pre-compiled versions](http://www.lfd.uci.edu/~gohlke/pythonlibs/) if you have difficulty. \n", + " - In the styles/ directory are a number of files (.matplotlirc) that used to make things pretty. These are not only designed for the book, but they offer many improvements over the default settings of matplotlib and the IPython notebook.\n", + " - while technically not required, it may help to run the IPython notebook with `--pylab inline` if you encounter runtime errors.\n", + "2. The second, preferred, option is to use the nbviewer.ipython.org site, which display IPython notebooks in the browser ([example](http://nbviewer.ipython.org/urls/raw.github.com/CamDavidsonPilon/Probabilistic-Programming-and-Bayesian-Methods-for-Hackers/master/Chapter1_Introduction/Chapter1_Introduction.ipynb)).\n", + "The contents are updated synchronously as commits are made to the book. You can use the Contents section above to link to the chapters.\n", + " \n", + "3. **PDF versions are coming.** PDFs are the least-prefered method to read the book, as pdf's are static and non-interactive. If PDFs are desired, they can be created dynamically using Chrome's builtin print-to-pdf feature.\n", + " \n", + "\n", + "Installation and configuration\n", + "------\n", + "If you would like to run the IPython notebooks locally, (option 1. above), you'll need to install the following:\n", + "\n", + "- IPython 0.13 is a requirement to view the ipynb files. It can be downloaded [here](http://ipython.org/ipython-doc/dev/install/index.html)\n", + "- For Linux users, you should not have a problem installing Numpy, Scipy and PyMC. For Windows users, check out [pre-compiled versions](http://www.lfd.uci.edu/~gohlke/pythonlibs/) if you have difficulty. \n", + " - also recommended, for data-mining exercises, are [PRAW](https://github.com/praw-dev/praw) and [requests](https://github.com/kennethreitz/requests). \n", + "- In the styles/ directory are a number of files that are customized for the notebook. \n", + "These are not only designed for the book, but they offer many improvements over the \n", + "default settings of matplotlib and the IPython notebook. The in notebook style has not been finalized yet.\n", + "\n", + "\n", + "Contributions and Thanks\n", + "-----\n", + "\n", + "\n", + "Thanks to all our contributing authors, including (in chronological order):\n", + "\n", + "- [Cameron Davidson-Pilon](http://www.camdp.com)\n", + "- [Stef Gibson](http://stefgibson.com)\n", + "- [Vincent Ohprecio](http://bigsnarf.wordpress.com/)\n", + "- [Lars Buitinck](https://github.com/larsman)\n", + "- [Paul Magwene](http://github.com/pmagwene) \n", + "- [Matthias Bussonnier](https://github.com/Carreau)\n", + "- [Jens Rantil](https://github.com/JensRantil)\n", + "- [y-p](https://github.com/y-p)\n", + "- [Ethan Brown](http://www.etano.net/)\n", + "- [Jonathan Whitmore](http://jonathanwhitmore.com/)\n", + "- [Mattia Rigotti](https://github.com/matrig)\n", + "- [Colby Lemon](https://github.com/colibius)\n", + "- [Gustav W Delius](https://github.com/gustavdelius)\n", + "- [Matthew Conlen](http://www.mathisonian.com/) \n", + "- [Jim Radford](https://github.com/radford)\n", + "- [Vannessa Sabino](http://baniverso.com/)\n", + "- [Thomas Bratt](https://github.com/thomasbratt)\n", + "- [Nisan Haramati](https://github.com/nisanharamati)\n", + "- [Thomas Bratt](https://github.com/thomasbratt)\n", + "- [Robert Grant](https://github.com/bgrant)\n", + "- [Yaroslav Halchenko](https://github.com/yarikoptic)\n", + "- [Alex Garel](https://github.com/alexgarel)\n", + "\n", + "\n", + "We would like to thank the Python community for building an amazing architecture. We would like to thank the \n", + "statistics community for building an amazing architecture. \n", + "\n", + "Similarly, the book is only possible because of the [PyMC](http://github.com/pymc-devs/pymc) library. A big thanks to the core devs of PyMC: Chris Fonnesbeck, Anand Patil, David Huard and John Salvatier.\n", + "\n", + "One final thanks. This book was generated by IPython Notebook, a wonderful tool for developing in Python. We thank the IPython \n", + "community for developing the Notebook interface. All IPython notebook files are available for download on the GitHub repository. \n", + "\n", + "\n", + "\n", + "####Contact\n", + "Contact the main author, Cam Davidson-Pilon at cam.davidson.pilon@gmail.com or [@cmrndp](https://twitter.com/cmrn_dp)\n", + "\n", + "\n", + "![Imgur](http://i.imgur.com/Zb79QZb.png)\n" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from IPython.core.display import HTML\n", + "\n", + "\n", + "def css_styling():\n", + " styles = open(\"../styles/custom.css\", \"r\").read()\n", + " return HTML(styles)\n", + "css_styling()" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "html": [ + "\n", + "" + ], + "output_type": "pyout", + "prompt_number": 1, + "text": [ + "" + ] + } + ], + "prompt_number": 1 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [], + "language": "python", + "metadata": {}, + "outputs": [] + } + ], + "metadata": {} + } + ] } \ No newline at end of file diff --git a/README.md b/README.md index 438244f9..7c618755 100644 --- a/README.md +++ b/README.md @@ -1,194 +1,194 @@ -#[Bayesian Methods for Hackers](http://camdavidsonpilon.github.io/Probabilistic-Programming-and-Bayesian-Methods-for-Hackers/) -#### *Using Python and PyMC* - - - - -The Bayesian method is the natural approach to inference, yet it is hidden from readers behind chapters of slow, mathematical analysis. The typical text on Bayesian inference involves two to three chapters on probability theory, then enters what Bayesian inference is. Unfortunately, due to mathematical intractability of most Bayesian models, the reader is only shown simple, artificial examples. This can leave the user with a *so-what* feeling about Bayesian inference. In fact, this was the author's own prior opinion. - - -
- -After some recent success of Bayesian methods in machine-learning competitions, I decided to investigate the subject again. Even with my mathematical background, it took me three straight-days of reading examples and trying to put the pieces together to understand the methods. There was simply not enough literature bridging theory to practice. The problem with my misunderstanding was the disconnect between Bayesian mathematics and probabilistic programming. That being said, I suffered then so the reader would not have to now. This book attempts to bridge the gap. - -If Bayesian inference is the destination, then mathematical analysis is a particular path to towards it. On the other hand, computing power is cheap enough that we can afford to take an alternate route via probabilistic programming. The latter path is much more useful, as it denies the necessity of mathematical intervention at each step, that is, we remove often-intractable mathematical analysis as a prerequisite to Bayesian inference. Simply put, this latter computational path proceeds via small intermediate jumps from beginning to end, where as the first path proceeds by enormous leaps, often landing far away from our target. Furthermore, without a strong mathematical background, the analysis required by the first path cannot even take place. - -*Bayesian Methods for Hackers* is designed as a introduction to Bayesian inference from a computational/understanding-first, and mathematics-second, point of view. Of course as an introductory book, we can only leave it at that: an introductory book. For the mathematically trained, they may cure the curiosity this text generates with other texts designed with mathematical analysis in mind. For the enthusiast with less mathematical-background, or one who is not interested in the mathematics but simply the practice of Bayesian methods, this text should be sufficient and entertaining. - -The choice of PyMC as the probabilistic programming language is two-fold. As of this writing, there is currently no central resource for examples and explanations in the PyMC universe. The official documentation assumes prior knowledge of Bayesian inference and probabilistic programming. We hope this book encourages users at every level to look at PyMC. Secondly, with recent core developments and popularity of the scientific stack in Python, PyMC is likely to become a core component soon enough. - -PyMC does have dependencies to run, namely NumPy and (optionally) SciPy. To not limit the user, the examples in this book will rely only on PyMC, NumPy, SciPy and Matplotlib only. - - - - -Contents ------- - -See the project homepage [here](http://camdavidsonpilon.github.io/Probabilistic-Programming-and-Bayesian-Methods-for-Hackers/) for examples, too. - - -The below chapters are rendered via the *nbviewer* at -[nbviewer.ipython.org/](http://nbviewer.ipython.org/), and is read-only and rendered in real-time. -Interactive notebooks + examples can be downloaded by cloning! - - -* [**Prologue:**](http://nbviewer.ipython.org/urls/raw.github.com/CamDavidsonPilon/Probabilistic-Programming-and-Bayesian-Methods-for-Hackers/master/Prologue/Prologue.ipynb) Why we do it. - -* [**Chapter 1: Introduction to Bayesian Methods**](http://nbviewer.ipython.org/urls/raw.github.com/CamDavidsonPilon/Probabilistic-Programming-and-Bayesian-Methods-for-Hackers/master/Chapter1_Introduction/Chapter1_Introduction.ipynb) - Introduction to the philosophy and practice of Bayesian methods and answering the question, "What is probabilistic programming?" Examples include: - - Inferring human behaviour changes from text message rates - -* [**Chapter 2: A little more on PyMC**](http://nbviewer.ipython.org/urls/raw.github.com/CamDavidsonPilon/Probabilistic-Programming-and-Bayesian-Methods-for-Hackers/master/Chapter2_MorePyMC/MorePyMC.ipynb) - We explore modeling Bayesian problems using Python's PyMC library through examples. How do we create Bayesian models? Examples include: - - Detecting the frequency of cheating students, while avoiding liars - - Calculating probabilities of the Challenger space-shuttle disaster - -* [**Chapter 3: Opening the Black Box of MCMC**](http://nbviewer.ipython.org/urls/raw.github.com/CamDavidsonPilon/Probabilistic-Programming-and-Bayesian-Methods-for-Hackers/master/Chapter3_MCMC/IntroMCMC.ipynb) - We discuss how MCMC operates and diagnostic tools. Examples include: - - Bayesian clustering with mixture models - -* [**Chapter 4: The Greatest Theorem Never Told**](http://nbviewer.ipython.org/urls/raw.github.com/CamDavidsonPilon/Probabilistic-Programming-and-Bayesian-Methods-for-Hackers/master/Chapter4_TheGreatestTheoremNeverTold/LawOfLargeNumbers.ipynb) - We explore an incredibly useful, and dangerous, theorem: The Law of Large Numbers. Examples include: - - Exploring a Kaggle dataset and the pitfalls of naive analysis - - How to sort Reddit comments from best to worst (not as easy as you think) - -* [**Chapter 5: Would you rather lose an arm or a leg?**](http://nbviewer.ipython.org/urls/raw.github.com/CamDavidsonPilon/Probabilistic-Programming-and-Bayesian-Methods-for-Hackers/master/Chapter5_LossFunctions/LossFunctions.ipynb) - The introduction of loss functions and their (awesome) use in Bayesian methods. Examples include: - - Solving the *Price is Right*'s Showdown - - Optimizing financial predictions - - Winning solution to the Kaggle Dark World's competition - -* [**Chapter 6: Getting our *prior*-ities straight**](http://nbviewer.ipython.org/urls/raw.github.com/CamDavidsonPilon/Probabilistic-Programming-and-Bayesian-Methods-for-Hackers/master/Chapter6_Priorities/Priors.ipynb) - Probably the most important chapter. We draw on expert opinions to answer questions. Examples include: - - Multi-Armed Bandits and the Bayesian Bandit solution. - - What is the relationship between data sample size and prior? - - Estimating financial unknowns using expert priors - - We explore useful tips to be objective in analysis as well as common pitfalls of priors. - -* **Chapter X1: Bayesian methods in Machine Learning and Model Validation** - We explore how to resolve the overfitting problem plus popular ML methods. Also included are probablistic explainations of ridge regression and LASSO regression. - - Tim Saliman's winning solution to Kaggle's *Don't Overfit* problem - -* **Chapter X2: More PyMC Hackery** - We explore the gritty details of PyMC. Examples include: - - Analysis on real-time GitHub repo stars and forks. - - - -**More questions about PyMC?** -Please post your modeling, convergence, or any other PyMC question on [cross-validated](http://stats.stackexchange.com/), the statistics stack-exchange. - - -Using the book -------- - -The book can be read in three different ways, starting from most recommended to least recommended: - -1. The most recommended option is to clone the repository to download the .ipynb files to your local machine. If you have IPython installed, you can view the -chapters in your browser *plus* edit and run the code provided (and try some practice questions). This is the preferred option to read -this book, though it comes with some dependencies. - - IPython v0.13 (or greater) is a requirement to view the ipynb files. It can be downloaded [here](http://ipython.org/). IPython notebooks can be run by `(your-virtualenv) ~/path/to/the/book/Chapter1_Introduction $ ipython notebook` - - For Linux users, you should not have a problem installing NumPy, SciPy, Matplotlib and PyMC. For Windows users, check out [pre-compiled versions](http://www.lfd.uci.edu/~gohlke/pythonlibs/) if you have difficulty. - - In the styles/ directory are a number of files (.matplotlirc) that used to make things pretty. These are not only designed for the book, but they offer many improvements over the default settings of matplotlib. -2. The second, preferred, option is to use the nbviewer.ipython.org site, which display IPython notebooks in the browser ([example](http://nbviewer.ipython.org/urls/raw.github.com/CamDavidsonPilon/Probabilistic-Programming-and-Bayesian-Methods-for-Hackers/master/Chapter1_Introduction/Chapter1_Introduction.ipynb)). -The contents are updated synchronously as commits are made to the book. You can use the Contents section above to link to the chapters. - -3. PDFs are the least-prefered method to read the book, as pdf's are static and non-interactive. If PDFs are desired, they can be created dynamically using the [nbconvert](https://github.com/ipython/nbconvert) utility. - - -Installation and configuration ------- - - -If you would like to run the IPython notebooks locally, (option 1. above), you'll need to install the following: - -- IPython 0.13+ is a requirement to view the ipynb files. It can be downloaded [here](http://ipython.org/ipython-doc/dev/install/index.html) -- Necessary packages are PyMC 2.2, NumPy, SciPy and Matplotlib. - - For Linux/OSX users, you should not have a problem installing the above, [*except for Matplotlib on OSX*](http://www.penandpants.com/2012/02/24/install-python/). - - For Windows users, check out [pre-compiled versions](http://www.lfd.uci.edu/~gohlke/pythonlibs/) if you have difficulty. - - also recommended, for data-mining exercises, are [PRAW](https://github.com/praw-dev/praw) and [requests](https://github.com/kennethreitz/requests). -- New to Python or IPython, and help with the namespaces? Check out [this answer](http://stackoverflow.com/questions/12987624/confusion-between-numpy-scipy-matplotlib-and-pylab). - -- In the styles/ directory are a number of files that are customized for the notebook. -These are not only designed for the book, but they offer many improvements over the -default settings of matplotlib and the IPython notebook. The in notebook style has not been finalized yet. - - - -Development ------- - -This book has an unusual development design. The content is open-sourced, meaning anyone can be an author. -Authors submit content or revisions using the GitHub interface. - -### How to contribute - -####What to contribute? - -- The current chapter list is not finalized. If you see something that is missing (MCMC, MAP, Bayesian networks, good prior choices, Potential classes etc.), -feel free to start there. -- Cleaning up Python code and making code more PyMC-esque -- Giving better explanations -- Spelling/grammar mistakes -- Suggestions -- Contributing to the IPython notebook styles - - -####Commiting - -- All commits are welcome, even if they are minor ;) -- If you are unfamiliar with Github, you can email me contributions to the email below. - -Reviews ------- -*these are satirical, but real* - -"No, but it looks good" - [John D. Cook](https://twitter.com/JohnDCook/status/359672133695184896) - -"I ... read this book ... I like it!" - [Andrew Gelman](http://www.andrewgelman.com/2013/07/21/bayes-related) - -"This book is a godsend, and a direct refutation to that 'hmph! you don't know maths, piss off!' school of thought... -The publishing model is so unusual. Not only is it open source but it relies on pull requests from anyone in order to progress the book. This is ingenious and heartening" - [excited Reddit user](http://www.reddit.com/r/Python/comments/1alnal/probabilistic_programming_and_bayesian_methods/) - - - -Contributions and Thanks ------ - - -Thanks to all our contributing authors, including (in chronological order): - -Authors | | | | ---- | --- | --- | --- -[Cameron Davidson-Pilon](http://www.camdp.com) | [Stef Gibson](http://stefgibson.com) | [Vincent Ohprecio](http://bigsnarf.wordpress.com/) |[Lars Buitinck](https://github.com/larsman) -[Paul Magwene](http://github.com/pmagwene) | [Matthias Bussonnier](https://github.com/Carreau) | [Jens Rantil](https://github.com/JensRantil) | [y-p](https://github.com/y-p) -[Ethan Brown](http://www.etano.net/) | [Jonathan Whitmore](http://jonathanwhitmore.com/) | [Mattia Rigotti](https://github.com/matrig) | [Colby Lemon](https://github.com/colibius) -[Gustav W Delius](https://github.com/gustavdelius) | [Matthew Conlen](http://www.mathisonian.com/) | [Jim Radford](https://github.com/radford) | [Vannessa Sabino](http://baniverso.com/) -[Thomas Bratt](https://github.com/thomasbratt) | [Nisan Haramati](https://github.com/nisanharamati) | [Robert Grant](https://github.com/bgrant) | [Matthew Wampler-Doty](https://github.com/xcthulhu) -[Yaroslav Halchenko](https://github.com/yarikoptic) | [Alex Garel](https://github.com/alexgarel) | [Oleksandr Lysenko](https://twitter.com/sash_ko) | [liori](https://github.com/liori) -[ducky427](https://github.com/ducky427) | [Pablo de Oliveira Castro](https://github.com/pablooliveira) | [sergeyfogelson](https://github.com/sergeyfogelson) | [Mattia Rigotti](http://neurotheory.columbia.edu/~mrigotti/) -[Matt Bauman](https://github.com/mbauman) | [Andrew Duberstein](http://www.andrewduberstein.com/) | [Carsten Brandt](http://cebe.cc/) | [Bob Jansen](http://web2docx.com) - [ugurthemaster](https://github.com/ugurthemaster) | [William Scott](https://github.com/williamscott) | [Min RK](http://twitter.com/minrk) | [Bulwersator](https://github.com/Bulwersator) - [elpres](https://github.com/elpres) | [Augusto Hack](https://github.com/hackaugusto) | [Michael Feldmann](https://github.com/michaf) | [Youki](https://github.com/Youki) - [Jens Rantil](http://jensrantil.github.io) | [Kyle Meyer](http://kyleam.com) | [Eric Martin](http://ericmart.in) | [Inconditus](https://github.com/Inconditus) - [Kleptine](https://github.com/Kleptine) | [Stuart Layton](https://github.com/slayton) | [Antonino Ingargiola](https://github.com/tritemio) | [vsl9](https://github.com/vsl9) - [Tom Christie](https://github.com/tom-christie) | [bclow](https://github.com/bclow) | [Simon Potter](http://sjp.co.nz/) | [Garth Snyder](https://github.com/GarthSnyder) - [Daniel Beauchamp](http://twitter.com/pushmatrix) | [Philipp Singer](http://www.philippsinger.info) | [gbenmartin](https://github.com/gbenmartin) | - -We would like to thank the Python community for building an amazing architecture. We would like to thank the -statistics community for building an amazing architecture. - -Similarly, the book is only possible because of the [PyMC](http://github.com/pymc-devs/pymc) library. A big thanks to the core devs of PyMC: Chris Fonnesbeck, Anand Patil, David Huard and John Salvatier. - -One final thanks. This book was generated by IPython Notebook, a wonderful tool for developing in Python. We thank the IPython -community for developing the Notebook interface. All IPython notebook files are available for download on the GitHub repository. - - - -####Contact -Contact the main author, Cam Davidson-Pilon at cam.davidson.pilon@gmail.com or [@cmrndp](https://twitter.com/cmrn_dp) - - -![Imgur](http://i.imgur.com/Zb79QZb.png) +#[Bayesian Methods for Hackers](http://camdavidsonpilon.github.io/Probabilistic-Programming-and-Bayesian-Methods-for-Hackers/) +#### *Using Python and PyMC* + + + + +The Bayesian method is the natural approach to inference, yet it is hidden from readers behind chapters of slow, mathematical analysis. The typical text on Bayesian inference involves two to three chapters on probability theory, then enters what Bayesian inference is. Unfortunately, due to mathematical intractability of most Bayesian models, the reader is only shown simple, artificial examples. This can leave the user with a *so-what* feeling about Bayesian inference. In fact, this was the author's own prior opinion. + + +
+ +After some recent success of Bayesian methods in machine-learning competitions, I decided to investigate the subject again. Even with my mathematical background, it took me three straight-days of reading examples and trying to put the pieces together to understand the methods. There was simply not enough literature bridging theory to practice. The problem with my misunderstanding was the disconnect between Bayesian mathematics and probabilistic programming. That being said, I suffered then so the reader would not have to now. This book attempts to bridge the gap. + +If Bayesian inference is the destination, then mathematical analysis is a particular path to towards it. On the other hand, computing power is cheap enough that we can afford to take an alternate route via probabilistic programming. The latter path is much more useful, as it denies the necessity of mathematical intervention at each step, that is, we remove often-intractable mathematical analysis as a prerequisite to Bayesian inference. Simply put, this latter computational path proceeds via small intermediate jumps from beginning to end, where as the first path proceeds by enormous leaps, often landing far away from our target. Furthermore, without a strong mathematical background, the analysis required by the first path cannot even take place. + +*Bayesian Methods for Hackers* is designed as a introduction to Bayesian inference from a computational/understanding-first, and mathematics-second, point of view. Of course as an introductory book, we can only leave it at that: an introductory book. For the mathematically trained, they may cure the curiosity this text generates with other texts designed with mathematical analysis in mind. For the enthusiast with less mathematical-background, or one who is not interested in the mathematics but simply the practice of Bayesian methods, this text should be sufficient and entertaining. + +The choice of PyMC as the probabilistic programming language is two-fold. As of this writing, there is currently no central resource for examples and explanations in the PyMC universe. The official documentation assumes prior knowledge of Bayesian inference and probabilistic programming. We hope this book encourages users at every level to look at PyMC. Secondly, with recent core developments and popularity of the scientific stack in Python, PyMC is likely to become a core component soon enough. + +PyMC does have dependencies to run, namely NumPy and (optionally) SciPy. To not limit the user, the examples in this book will rely only on PyMC, NumPy, SciPy and Matplotlib only. + + + + +Contents +------ + +See the project homepage [here](http://camdavidsonpilon.github.io/Probabilistic-Programming-and-Bayesian-Methods-for-Hackers/) for examples, too. + + +The below chapters are rendered via the *nbviewer* at +[nbviewer.ipython.org/](http://nbviewer.ipython.org/), and is read-only and rendered in real-time. +Interactive notebooks + examples can be downloaded by cloning! + + +* [**Prologue:**](http://nbviewer.ipython.org/urls/raw.github.com/CamDavidsonPilon/Probabilistic-Programming-and-Bayesian-Methods-for-Hackers/master/Prologue/Prologue.ipynb) Why we do it. + +* [**Chapter 1: Introduction to Bayesian Methods**](http://nbviewer.ipython.org/urls/raw.github.com/CamDavidsonPilon/Probabilistic-Programming-and-Bayesian-Methods-for-Hackers/master/Chapter1_Introduction/Chapter1_Introduction.ipynb) + Introduction to the philosophy and practice of Bayesian methods and answering the question, "What is probabilistic programming?" Examples include: + - Inferring human behaviour changes from text message rates + +* [**Chapter 2: A little more on PyMC**](http://nbviewer.ipython.org/urls/raw.github.com/CamDavidsonPilon/Probabilistic-Programming-and-Bayesian-Methods-for-Hackers/master/Chapter2_MorePyMC/MorePyMC.ipynb) + We explore modeling Bayesian problems using Python's PyMC library through examples. How do we create Bayesian models? Examples include: + - Detecting the frequency of cheating students, while avoiding liars + - Calculating probabilities of the Challenger space-shuttle disaster + +* [**Chapter 3: Opening the Black Box of MCMC**](http://nbviewer.ipython.org/urls/raw.github.com/CamDavidsonPilon/Probabilistic-Programming-and-Bayesian-Methods-for-Hackers/master/Chapter3_MCMC/IntroMCMC.ipynb) + We discuss how MCMC operates and diagnostic tools. Examples include: + - Bayesian clustering with mixture models + +* [**Chapter 4: The Greatest Theorem Never Told**](http://nbviewer.ipython.org/urls/raw.github.com/CamDavidsonPilon/Probabilistic-Programming-and-Bayesian-Methods-for-Hackers/master/Chapter4_TheGreatestTheoremNeverTold/LawOfLargeNumbers.ipynb) + We explore an incredibly useful, and dangerous, theorem: The Law of Large Numbers. Examples include: + - Exploring a Kaggle dataset and the pitfalls of naive analysis + - How to sort Reddit comments from best to worst (not as easy as you think) + +* [**Chapter 5: Would you rather lose an arm or a leg?**](http://nbviewer.ipython.org/urls/raw.github.com/CamDavidsonPilon/Probabilistic-Programming-and-Bayesian-Methods-for-Hackers/master/Chapter5_LossFunctions/LossFunctions.ipynb) + The introduction of loss functions and their (awesome) use in Bayesian methods. Examples include: + - Solving the *Price is Right*'s Showdown + - Optimizing financial predictions + - Winning solution to the Kaggle Dark World's competition + +* [**Chapter 6: Getting our *prior*-ities straight**](http://nbviewer.ipython.org/urls/raw.github.com/CamDavidsonPilon/Probabilistic-Programming-and-Bayesian-Methods-for-Hackers/master/Chapter6_Priorities/Priors.ipynb) + Probably the most important chapter. We draw on expert opinions to answer questions. Examples include: + - Multi-Armed Bandits and the Bayesian Bandit solution. + - What is the relationship between data sample size and prior? + - Estimating financial unknowns using expert priors + + We explore useful tips to be objective in analysis as well as common pitfalls of priors. + +* **Chapter X1: Bayesian methods in Machine Learning and Model Validation** + We explore how to resolve the overfitting problem plus popular ML methods. Also included are probablistic explainations of ridge regression and LASSO regression. + - Tim Saliman's winning solution to Kaggle's *Don't Overfit* problem + +* **Chapter X2: More PyMC Hackery** + We explore the gritty details of PyMC. Examples include: + - Analysis on real-time GitHub repo stars and forks. + + + +**More questions about PyMC?** +Please post your modeling, convergence, or any other PyMC question on [cross-validated](http://stats.stackexchange.com/), the statistics stack-exchange. + + +Using the book +------- + +The book can be read in three different ways, starting from most recommended to least recommended: + +1. The most recommended option is to clone the repository to download the .ipynb files to your local machine. If you have IPython installed, you can view the +chapters in your browser *plus* edit and run the code provided (and try some practice questions). This is the preferred option to read +this book, though it comes with some dependencies. + - IPython v0.13 (or greater) is a requirement to view the ipynb files. It can be downloaded [here](http://ipython.org/). IPython notebooks can be run by `(your-virtualenv) ~/path/to/the/book/Chapter1_Introduction $ ipython notebook` + - For Linux users, you should not have a problem installing NumPy, SciPy, Matplotlib and PyMC. For Windows users, check out [pre-compiled versions](http://www.lfd.uci.edu/~gohlke/pythonlibs/) if you have difficulty. + - In the styles/ directory are a number of files (.matplotlirc) that used to make things pretty. These are not only designed for the book, but they offer many improvements over the default settings of matplotlib. +2. The second, preferred, option is to use the nbviewer.ipython.org site, which display IPython notebooks in the browser ([example](http://nbviewer.ipython.org/urls/raw.github.com/CamDavidsonPilon/Probabilistic-Programming-and-Bayesian-Methods-for-Hackers/master/Chapter1_Introduction/Chapter1_Introduction.ipynb)). +The contents are updated synchronously as commits are made to the book. You can use the Contents section above to link to the chapters. + +3. PDFs are the least-prefered method to read the book, as pdf's are static and non-interactive. If PDFs are desired, they can be created dynamically using the [nbconvert](https://github.com/ipython/nbconvert) utility. + + +Installation and configuration +------ + + +If you would like to run the IPython notebooks locally, (option 1. above), you'll need to install the following: + +- IPython 0.13+ is a requirement to view the ipynb files. It can be downloaded [here](http://ipython.org/ipython-doc/dev/install/index.html) +- Necessary packages are PyMC 2.2, NumPy, SciPy and Matplotlib. + - For Linux/OSX users, you should not have a problem installing the above, [*except for Matplotlib on OSX*](http://www.penandpants.com/2012/02/24/install-python/). + - For Windows users, check out [pre-compiled versions](http://www.lfd.uci.edu/~gohlke/pythonlibs/) if you have difficulty. + - also recommended, for data-mining exercises, are [PRAW](https://github.com/praw-dev/praw) and [requests](https://github.com/kennethreitz/requests). +- New to Python or IPython, and help with the namespaces? Check out [this answer](http://stackoverflow.com/questions/12987624/confusion-between-numpy-scipy-matplotlib-and-pylab). + +- In the styles/ directory are a number of files that are customized for the notebook. +These are not only designed for the book, but they offer many improvements over the +default settings of matplotlib and the IPython notebook. The in notebook style has not been finalized yet. + + + +Development +------ + +This book has an unusual development design. The content is open-sourced, meaning anyone can be an author. +Authors submit content or revisions using the GitHub interface. + +### How to contribute + +####What to contribute? + +- The current chapter list is not finalized. If you see something that is missing (MCMC, MAP, Bayesian networks, good prior choices, Potential classes etc.), +feel free to start there. +- Cleaning up Python code and making code more PyMC-esque +- Giving better explanations +- Spelling/grammar mistakes +- Suggestions +- Contributing to the IPython notebook styles + + +####Commiting + +- All commits are welcome, even if they are minor ;) +- If you are unfamiliar with Github, you can email me contributions to the email below. + +Reviews +------ +*these are satirical, but real* + +"No, but it looks good" - [John D. Cook](https://twitter.com/JohnDCook/status/359672133695184896) + +"I ... read this book ... I like it!" - [Andrew Gelman](http://www.andrewgelman.com/2013/07/21/bayes-related) + +"This book is a godsend, and a direct refutation to that 'hmph! you don't know maths, piss off!' school of thought... +The publishing model is so unusual. Not only is it open source but it relies on pull requests from anyone in order to progress the book. This is ingenious and heartening" - [excited Reddit user](http://www.reddit.com/r/Python/comments/1alnal/probabilistic_programming_and_bayesian_methods/) + + + +Contributions and Thanks +----- + + +Thanks to all our contributing authors, including (in chronological order): + +Authors | | | | +--- | --- | --- | --- +[Cameron Davidson-Pilon](http://www.camdp.com) | [Stef Gibson](http://stefgibson.com) | [Vincent Ohprecio](http://bigsnarf.wordpress.com/) |[Lars Buitinck](https://github.com/larsman) +[Paul Magwene](http://github.com/pmagwene) | [Matthias Bussonnier](https://github.com/Carreau) | [Jens Rantil](https://github.com/JensRantil) | [y-p](https://github.com/y-p) +[Ethan Brown](http://www.etano.net/) | [Jonathan Whitmore](http://jonathanwhitmore.com/) | [Mattia Rigotti](https://github.com/matrig) | [Colby Lemon](https://github.com/colibius) +[Gustav W Delius](https://github.com/gustavdelius) | [Matthew Conlen](http://www.mathisonian.com/) | [Jim Radford](https://github.com/radford) | [Vannessa Sabino](http://baniverso.com/) +[Thomas Bratt](https://github.com/thomasbratt) | [Nisan Haramati](https://github.com/nisanharamati) | [Robert Grant](https://github.com/bgrant) | [Matthew Wampler-Doty](https://github.com/xcthulhu) +[Yaroslav Halchenko](https://github.com/yarikoptic) | [Alex Garel](https://github.com/alexgarel) | [Oleksandr Lysenko](https://twitter.com/sash_ko) | [liori](https://github.com/liori) +[ducky427](https://github.com/ducky427) | [Pablo de Oliveira Castro](https://github.com/pablooliveira) | [sergeyfogelson](https://github.com/sergeyfogelson) | [Mattia Rigotti](http://neurotheory.columbia.edu/~mrigotti/) +[Matt Bauman](https://github.com/mbauman) | [Andrew Duberstein](http://www.andrewduberstein.com/) | [Carsten Brandt](http://cebe.cc/) | [Bob Jansen](http://web2docx.com) + [ugurthemaster](https://github.com/ugurthemaster) | [William Scott](https://github.com/williamscott) | [Min RK](http://twitter.com/minrk) | [Bulwersator](https://github.com/Bulwersator) + [elpres](https://github.com/elpres) | [Augusto Hack](https://github.com/hackaugusto) | [Michael Feldmann](https://github.com/michaf) | [Youki](https://github.com/Youki) + [Jens Rantil](http://jensrantil.github.io) | [Kyle Meyer](http://kyleam.com) | [Eric Martin](http://ericmart.in) | [Inconditus](https://github.com/Inconditus) + [Kleptine](https://github.com/Kleptine) | [Stuart Layton](https://github.com/slayton) | [Antonino Ingargiola](https://github.com/tritemio) | [vsl9](https://github.com/vsl9) + [Tom Christie](https://github.com/tom-christie) | [bclow](https://github.com/bclow) | [Simon Potter](http://sjp.co.nz/) | [Garth Snyder](https://github.com/GarthSnyder) + [Daniel Beauchamp](http://twitter.com/pushmatrix) | [Philipp Singer](http://www.philippsinger.info) | [gbenmartin](https://github.com/gbenmartin) | + +We would like to thank the Python community for building an amazing architecture. We would like to thank the +statistics community for building an amazing architecture. + +Similarly, the book is only possible because of the [PyMC](http://github.com/pymc-devs/pymc) library. A big thanks to the core devs of PyMC: Chris Fonnesbeck, Anand Patil, David Huard and John Salvatier. + +One final thanks. This book was generated by IPython Notebook, a wonderful tool for developing in Python. We thank the IPython +community for developing the Notebook interface. All IPython notebook files are available for download on the GitHub repository. + + + +####Contact +Contact the main author, Cam Davidson-Pilon at cam.davidson.pilon@gmail.com or [@cmrndp](https://twitter.com/cmrn_dp) + + +![Imgur](http://i.imgur.com/Zb79QZb.png) diff --git a/book_layout.txt b/book_layout.txt index 8d806783..da82e9cf 100644 --- a/book_layout.txt +++ b/book_layout.txt @@ -1,59 +1,59 @@ -# Bayesian Methods for Hackers Layout - -\section{ Preamble} - - -\chapter1{ Introduction } - - -\chapter2{More PyMC / Modeling in PyMC} - #flexible about what this section is. Basically it's more intro to the - syntax of PyMC, with examples + distributions. - -\chapter3{ Intro to MCMC and Diagnogstics } - - -\chapter4{ The greatest theorem never told } - #This is about the law of large numbers and how a bayesian uses it for estimates. - - - -\chapter5{ Would you rather lose an arm or a leg? } - #Introduction to loss functions and point estimation. - - - ->>>>>>>>> -Below is subject to change - -\chapter6{What should my prior look like?} - \subsection{Noninformative priors...} - \subsection{Noninformative priors do not exist} - \subsection{Good choices of priors } - -\chapter7{ Bayesian Networks } - #I do not know too much about this. - - -\chapter8{ Gaussian Processes } - # pymc.gp - - -\chapter9{ Large Scale systems } - #how can we scale PyMC to larger systems/datasets? - -\chapter10{More hacking with PyMC} - #some examples from PyMC. - # Potential class? - - - - -\section{Appendix} - \subsection{A} - #Chart of distributions and their support - \subsection{B} - #Appendix on MCMC - \section{C} - #Proofs +# Bayesian Methods for Hackers Layout + +\section{ Preamble} + + +\chapter1{ Introduction } + + +\chapter2{More PyMC / Modeling in PyMC} + #flexible about what this section is. Basically it's more intro to the + syntax of PyMC, with examples + distributions. + +\chapter3{ Intro to MCMC and Diagnogstics } + + +\chapter4{ The greatest theorem never told } + #This is about the law of large numbers and how a bayesian uses it for estimates. + + + +\chapter5{ Would you rather lose an arm or a leg? } + #Introduction to loss functions and point estimation. + + + +>>>>>>>>> +Below is subject to change + +\chapter6{What should my prior look like?} + \subsection{Noninformative priors...} + \subsection{Noninformative priors do not exist} + \subsection{Good choices of priors } + +\chapter7{ Bayesian Networks } + #I do not know too much about this. + + +\chapter8{ Gaussian Processes } + # pymc.gp + + +\chapter9{ Large Scale systems } + #how can we scale PyMC to larger systems/datasets? + +\chapter10{More hacking with PyMC} + #some examples from PyMC. + # Potential class? + + + + +\section{Appendix} + \subsection{A} + #Chart of distributions and their support + \subsection{B} + #Appendix on MCMC + \section{C} + #Proofs \ No newline at end of file diff --git a/requirements.txt b/requirements.txt index 3bad851d..50d60397 100644 --- a/requirements.txt +++ b/requirements.txt @@ -1,9 +1,9 @@ -ipython>=0.13.2 -matplotlib>=1.2.1 -numpy>=1.7.1 -pymc>=2.2 -pyzmq>=13.1.0 -scipy>=0.12.0 -tornado>=3.0.2 -wsgiref>=0.1.2 -praw>=2.0.0 +ipython>=0.13.2 +matplotlib>=1.2.1 +numpy>=1.7.1 +pymc>=2.2 +pyzmq>=13.1.0 +scipy>=0.12.0 +tornado>=3.0.2 +wsgiref>=0.1.2 +praw>=2.0.0 diff --git a/sandbox/ABCtests.ipynb b/sandbox/ABCtests.ipynb index 0c302a7b..a411db7e 100644 --- a/sandbox/ABCtests.ipynb +++ b/sandbox/ABCtests.ipynb @@ -1,259 +1,259 @@ -{ - "metadata": { - "name": "ABCtests" - }, - "nbformat": 3, - "nbformat_minor": 0, - "worksheets": [ - { - "cells": [ - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## ABC" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "import pymc as pm" - ], - "language": "python", - "metadata": {}, - "outputs": [], - "prompt_number": 1 - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "obs = np.array([0, 0, 1])\n", - "\n", - "uni = pm.Uniform(\"prop\", 0, 1)\n", - "fake_obs = pm.Bernoulli(\"fake_obs\", uni, size=3)\n", - "\n", - "\n", - "@pm.deterministic\n", - "def accept(uni=uni, fake_obs=fake_obs, obs=obs):\n", - " if np.array_equal(fake_obs, obs):\n", - " return uni\n", - " else:\n", - " return None" - ], - "language": "python", - "metadata": {}, - "outputs": [], - "prompt_number": 132 - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "mcmc = pm.MCMC([uni, fake_obs, accept])" - ], - "language": "python", - "metadata": {}, - "outputs": [], - "prompt_number": 133 - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "mcmc.sample(10000)" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "output_type": "stream", - "stream": "stdout", - "text": [ - " \r", - "[****************100%******************] 10000 of 10000 complete" - ] - }, - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "\n" - ] - } - ], - "prompt_number": 134 - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "samples = mcmc.trace('accept')[:]" - ], - "language": "python", - "metadata": {}, - "outputs": [], - "prompt_number": 135 - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "hist(samples[samples > 0])" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "output_type": "pyout", - "prompt_number": 136, - "text": [ - "(array([ 47., 118., 158., 125., 141., 95., 74., 48., 33., 10.]),\n", - " array([ 0.01977077, 0.11150485, 0.20323893, 0.29497301, 0.38670709,\n", - " 0.47844116, 0.57017524, 0.66190932, 0.7536434 , 0.84537748,\n", - " 0.93711155]),\n", - " )" - ] - }, - { - "output_type": "display_data", - "png": 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"nbformat": 3, + "nbformat_minor": 0, + "worksheets": [ + { + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## ABC" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import pymc as pm" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 1 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "obs = np.array([0, 0, 1])\n", + "\n", + "uni = pm.Uniform(\"prop\", 0, 1)\n", + "fake_obs = pm.Bernoulli(\"fake_obs\", uni, size=3)\n", + "\n", + "\n", + "@pm.deterministic\n", + "def accept(uni=uni, fake_obs=fake_obs, obs=obs):\n", + " if np.array_equal(fake_obs, obs):\n", + " return uni\n", + " else:\n", + " return None" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 132 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "mcmc = pm.MCMC([uni, fake_obs, accept])" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 133 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "mcmc.sample(10000)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + " \r", + "[****************100%******************] 10000 of 10000 complete" + ] + }, + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "\n" + ] + } + ], + "prompt_number": 134 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "samples = mcmc.trace('accept')[:]" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 135 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "hist(samples[samples > 0])" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "pyout", + "prompt_number": 136, + "text": [ + "(array([ 47., 118., 158., 125., 141., 95., 74., 48., 33., 10.]),\n", + " array([ 0.01977077, 0.11150485, 0.20323893, 0.29497301, 0.38670709,\n", + " 0.47844116, 0.57017524, 0.66190932, 0.7536434 , 0.84537748,\n", + " 0.93711155]),\n", + " )" + ] + }, + { + "output_type": "display_data", + "png": 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a/sandbox/Chapter10_/More hacking with PyMC.ipynb b/sandbox/Chapter10_/More hacking with PyMC.ipynb index d0377f34..2533f02a 100644 --- a/sandbox/Chapter10_/More hacking with PyMC.ipynb +++ b/sandbox/Chapter10_/More hacking with PyMC.ipynb @@ -1,908 +1,908 @@ -{ - "metadata": { - "name": "More hacking with PyMC" - }, - "nbformat": 3, - "nbformat_minor": 0, - "worksheets": [ - { - "cells": [ - { - "cell_type": "code", - "collapsed": false, - "input": [ - "figsize(12.5, 4)\n", - "import scipy.stats as stats;" - ], - "language": "python", - "metadata": {}, - "outputs": [], - "prompt_number": 2 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "# Chapter 11 \n", - "___________\n", - "## More Hacking with PyMC\n", - "\n", - "This chapter introduces useful or advanced techniques with PyMC including building your own stochastic variables, user-defined steps etc." - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "\n", - "##### Example: Real-time Github Popularity Measures\n", - "\n", - "\n", - "Most of you are likely familar with the git-repository website Github. An observed phenomenon on Github is the *scale-ness* of the popularity of repositories. Here, for lack of a better measure, we use the numbers of *stars* and *forks* to measure popularity. This is not a bad measure, but it can ignore page-views, downloads and tends to overemphasize older repositories. Since we will be studying *all* repositories and not a single one, the absense of these measures is not as relevant. \n", - "\n", - "Contained in this folder is a Python script for scrapping data from Github on the popularity of repos. The script requires the `Requests` and `BeautifulSoup` libraries, but if you don't have that installed, provided in the `./data` folder is the same data from a previous date (Feburary 18, 2013 at last pull). The data is the fraction of repositories with stars equal to or greater than $2^k,\\; k = 0,...,15$ and the fraction of repositories with forks equal to or than $2^k,\\; k = 0,...,15$.\n", - " " - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "run github_datapull.py;" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "Scrapping data from Github. Sorry Github...\n", - "The data is contained in variables `foo_to_explore` and `repo_with_foo`\n", - "\n", - "stars first...\n", - "number of repos with greater than or equal to 0 stars: 2738541" - ] - }, - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "\n", - "number of repos with greater than or equal to 1 stars: 1704779" - ] - }, - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "\n", - "number of repos with greater than or equal to 2 stars: 493529" - ] - }, - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "\n", - "number of repos with greater than or equal to 4 stars: 212099" - ] - }, - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "\n", - "number of repos with greater than or equal to 8 stars: 106973" - ] - }, - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "\n", - "number of repos with greater than or equal to 16 stars: 58101" - ] - }, - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "\n", - "number of repos with greater than or equal to 32 stars: 31877" - ] - }, - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "\n", - "number of repos with greater than or equal to 64 stars: 17370" - ] - }, - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "\n", - "number of repos with greater than or equal to 128 stars: 9239" - ] - }, - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "\n", - "number of repos with greater than or equal to 256 stars: 4578" - ] - }, - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "\n", - "number of repos with greater than or equal to 512 stars: 2150" - ] - }, - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "\n", - "number of repos with greater than or equal to 1024 stars: 872" - ] - }, - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "\n", - "number of repos with greater than or equal to 2048 stars: 286" - ] - }, - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "\n", - "number of repos with greater than or equal to 4096 stars: 84" - ] - }, - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "\n", - "number of repos with greater than or equal to 8192 stars: 22" - ] - }, - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "\n", - "number of repos with greater than or equal to 16384 stars: 5" - ] - }, - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "\n", - "number of repos with greater than or equal to 32768 stars: 1" - ] - }, - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "\n", - "\n", - "forks second...\n", - "number of repos with greater than or equal to 0 forks: 2738548" - ] - }, - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "\n", - "number of repos with greater than or equal to 1 forks: 334539" - ] - }, - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "\n", - "number of repos with greater than or equal to 2 forks: 159206" - ] - }, - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "\n", - "number of repos with greater than or equal to 4 forks: 74836" - ] - }, - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "\n", - "number of repos with greater than or equal to 8 forks: 36532" - ] - }, - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "\n", - "number of repos with greater than or equal to 16 forks: 17948" - ] - }, - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "\n", - "number of repos with greater than or equal to 32 forks: 8394" - ] - }, - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "\n", - "number of repos with greater than or equal to 64 forks: 3841" - ] - }, - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "\n", - "number of repos with greater than or equal to 128 forks: 1580" - ] - }, - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "\n", - "number of repos with greater than or equal to 256 forks: 605" - ] - }, - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "\n", - "number of repos with greater than or equal to 512 forks: 222" - ] - }, - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "\n", - "number of repos with greater than or equal to 1024 forks: 69" - ] - }, - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "\n", - "number of repos with greater than or equal to 2048 forks: 17" - ] - }, - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "\n", - "number of repos with greater than or equal to 4096 forks: 4" - ] - }, - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "\n", - "number of repos with greater than or equal to 8192 forks: 2" - ] - }, - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "\n", - "number of repos with greater than or equal to 16384 forks: 0" - ] - }, - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "\n", - "number of repos with greater than or equal to 32768 forks: 0" - ] - }, - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "\n" - ] - } - ], - "prompt_number": 1 - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "plt.plot((stars_to_explore), repo_with_stars, label=\"stars\")\n", - "plt.plot((forks_to_explore), repo_with_forks, label=\"forks\")\n", - "plt.legend(loc=\"lower right\")\n", - "plt.title(\"Popularity of Repos (as measured by stars and forks)\")\n", - "plt.xlabel(\"$K$\")\n", - "plt.ylabel(\"number of repos with stars/forks $K$\")\n", - "plt.xlim(-200, 35000);" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "output_type": "pyout", - "prompt_number": 3, - "text": [ - "(-200, 35000)" - ] - }, - { - "output_type": "display_data", - "png": 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Kzz//fK0BlQ87MBMA3njjDezevRvXr1/HqlWr8OKLL2p0l7mf+/2C9TC/gALV42ecnZ3R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\nRERERGbzX8VMdv/FLvLEAAAAAElFTkSuQmCC\n" - } - ], - "prompt_number": 3 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Clearly, we need to adjust the scale of this plot as most of the action is hidden. The number of repos falls very quickly. We will put it on a log-log plot." - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "plt.plot(log2(stars_to_explore + 1), log2(repo_with_stars + 1), 'o-', label=\"stars\")\n", - "plt.plot(log2(forks_to_explore + 1), log2(repo_with_forks + 1), 'o-', label=\"forks\",)\n", - "plt.legend(loc=\"upper right\")\n", - "plt.title(\"Log-Log plot of Popularity of Repos (as measured by stars and forks)\")\n", - "plt.xlabel(\"$\\log{K}$\")\n", - "plt.ylabel(\"$\\log$(number of repos with stars/forks < K )\");" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "output_type": "pyout", - "prompt_number": 4, - "text": [ - "" - ] - }, - { - "output_type": "display_data", - "png": 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Tg3379mHu3Lkqj9d8EwkJCdiwYQPu3buHhw8fYvXq1fD3969y5gagYT9Vkagu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- } - ], - "prompt_number": 4 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Both characteristics look like a straight line plotted on a log-log plot. What does this mean? Denote the fraction of repos with greater than or equal to $k$ stars (or forks) $P(k)$. So in the above plot, $\\log{P(k)}$ on the y-axis and $\\log{k}$ is on the x-axis. The above linear relationship can be written as:\n", - "\n", - "$$ \\log_2{P(k)} = \\beta\\log_2{k} + \\alpha$$\n", - "\n", - "rearranging by taking both sides to the power of 2:\n", - "\n", - "$$ P(k) = 2^\\alpha k^{\\beta} = C k^{\\beta}, \\;\\; C = 2^{\\alpha}$$\n", - "\n", - "This relationship is very interesting. It is called a *power-law*, and occurs very freqently in social datasets. Why does it occur so frequently in social datasets? It has much to do with a \"winner-take-all\" or \"winner-take-most\" effect. Winners in a power-law enviroment are components that seem take a disproportiante amount of the popularity, and keep winning. In term of popularity of repos, *winning repos* are repos that are very good quailty (intially are winners), and are shared/talked about often (keep winning). \n", - "\n", - "\n", - "The above plot is also telling us that the majority of repos have very few stars and forks, only a handful have hundreds, and an incredibly small number have thousands. This is not-so obvious after browsing Github's website, where you see some repos with 36000+ stars, but fail to see the millions that do not have any stars (as they are not popular, they won't be common on your tour of the site.)\n", - "\n", - "Distributions like this are also said to have *fat-tails*, i.e. the probability does not drop quickly as we extend into the tail of the dataset, but most of the probability is still centered near zero. \n", - "\n", - "\n", - "The heaviness of the tail and strength of \"winner-take-all\" effect are both influenced by the $\\beta$ parameter. The small the $\\beta$, the more pronounced these effects. Below is a list of distributions that follow a power-law and an approximate $\\beta$ exponent [1]. Recall though that *we never observe these numbers*, we must infer them from the data.\n", - "\n", - "\n", - "
PhenomenonAssumed Exponent
Frequency of word use-1.2
Number of hits on website-1.4
US book sales-1.5
Intensity of wars-0.8
New worth of Americans-1.1
Github Stars??
\n", - "\n", - "\n", - "\n", - "### The estimation problem\n", - "\n", - "It is very easy to *overestimate* the true paramter $\\beta$. This is because the tail events (the events of 500+ stars) are very rare. For example, suppose in our Github dataset we only observe 100 samples. With very high probability (about 30%), all of these samples will have less than 31 stars. This is because\n", - "approximately 99% ( Number of all repos - Number of repos with greater than 31 stars)/(Number of all repos) of all repos have less than 31 stars. Thus, we would have no samples in our dataset from the *tail* of the distribution. If I then told you that there existed a repo with 36000+ stars, you would call me crazy, as it would be about 1000 times larger than your observed most popular repo. You would assign a very large $\\beta$ exponent to your dataset (recall large $\\beta$ means thinner tails). Similarly, with the same 30% probability we would not see repos more popular than 64 stars if we had a sample of 1000. Taking this to its logical conclusion, how confident should we be that there might not exist a theoretical repo that can attain 72000+ stars, or 150000+ stars, one which would push an estimated $\\beta$ down even more. \n", - "\n", - "\n", - "### Yule-Simon distribution\n", - "\n", - "The \n", - "\n", - "\n", - "\n", - "\n", - "\n" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "from scipy.special import beta\n", - "import pymc as pm\n", - "\n", - "\n", - "param = pm.Exponential(\"param\", 1)\n", - "\n", - "\n", - "@pm.stochastic(dtype=int, observed=True)\n", - "def yule_simon(value=repo_with_stars, rho=param):\n", - " \"\"\"test\"\"\"\n", - "\n", - " def logp(value, rho):\n", - " return np.log(rho) + np.log(beta(value, rho + 1))\n", - "\n", - " def random(rho):\n", - " W = stats.expon.rvs(scale=1. / rho)\n", - " return stats.geom.rvs(np.exp(-W))\n", - "\n", - "\n", - "model = pm.Model([param, yule_simon])\n", - "mcmc = pm.MCMC(model)\n", - "\n", - "mcmc.sample(10000, 8000);" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "ename": "TypeError", - "evalue": "yule_simon: computed log-probability [-20.51503062 -19.93158602 -18.31405136 -17.21386783 -16.32349938\n -15.53050299 -14.75010755 -13.96101721 -13.13877723 -12.2264853\n -11.23694781 -10.06769225 -8.63087616 -7.0237458 -5.33941252\n -3.44559118 -1.4738842 ] cannot be cast to float", - "output_type": "pyerr", - "traceback": [ - "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m\n\u001b[1;31mTypeError\u001b[0m Traceback (most recent call last)", - "\u001b[1;32m\u001b[0m in \u001b[0;36m\u001b[1;34m()\u001b[0m\n\u001b[0;32m 8\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 9\u001b[0m \u001b[1;33m@\u001b[0m\u001b[0mmc\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mstochastic\u001b[0m\u001b[1;33m(\u001b[0m \u001b[0mdtype\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mint\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mobserved\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mTrue\u001b[0m \u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m---> 10\u001b[1;33m \u001b[1;32mdef\u001b[0m \u001b[0myule_simon\u001b[0m\u001b[1;33m(\u001b[0m \u001b[0mvalue\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mrepo_with_stars\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mrho\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mparam\u001b[0m \u001b[1;33m)\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m 11\u001b[0m \u001b[1;34m\"\"\"test\"\"\"\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 12\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n", - "\u001b[1;32mc:\\Python27\\lib\\site-packages\\pymc\\InstantiationDecorators.pyc\u001b[0m in \u001b[0;36minstantiate_p\u001b[1;34m(__func__)\u001b[0m\n\u001b[0;32m 147\u001b[0m \u001b[1;32mdef\u001b[0m \u001b[0minstantiate_p\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0m__func__\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 148\u001b[0m \u001b[0mvalue\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mparents\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0m_extract\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0m__func__\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mkwds\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mkeys\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;34m'Stochastic'\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m--> 149\u001b[1;33m \u001b[1;32mreturn\u001b[0m \u001b[0m__class__\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mvalue\u001b[0m\u001b[1;33m=\u001b[0m\u001b[0mvalue\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mparents\u001b[0m\u001b[1;33m=\u001b[0m\u001b[0mparents\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;33m**\u001b[0m\u001b[0mkwds\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m 150\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 151\u001b[0m \u001b[0mkeys\u001b[0m \u001b[1;33m=\u001b[0m \u001b[1;33m[\u001b[0m\u001b[1;34m'logp'\u001b[0m\u001b[1;33m,\u001b[0m\u001b[1;34m'random'\u001b[0m\u001b[1;33m,\u001b[0m\u001b[1;34m'rseed'\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n", - "\u001b[1;32mc:\\Python27\\lib\\site-packages\\pymc\\PyMCObjects.pyc\u001b[0m in \u001b[0;36m__init__\u001b[1;34m(self, logp, doc, name, parents, random, trace, value, dtype, rseed, observed, cache_depth, plot, verbose, isdata, check_logp, logp_partial_gradients)\u001b[0m\n\u001b[0;32m 714\u001b[0m \u001b[1;32mif\u001b[0m \u001b[0mcheck_logp\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 715\u001b[0m \u001b[1;31m# Check initial value\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m--> 716\u001b[1;33m \u001b[1;32mif\u001b[0m \u001b[1;32mnot\u001b[0m \u001b[0misinstance\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mlogp\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mfloat\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m 717\u001b[0m \u001b[1;32mraise\u001b[0m \u001b[0mValueError\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;34m\"Stochastic \"\u001b[0m \u001b[1;33m+\u001b[0m \u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0m__name__\u001b[0m \u001b[1;33m+\u001b[0m \u001b[1;34m\"'s initial log-probability is %s, should be a float.\"\u001b[0m \u001b[1;33m%\u001b[0m\u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mlogp\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0m__repr__\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 718\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n", - "\u001b[1;32mc:\\Python27\\lib\\site-packages\\pymc\\PyMCObjects.pyc\u001b[0m in \u001b[0;36mget_logp\u001b[1;34m(self)\u001b[0m\n\u001b[0;32m 833\u001b[0m \u001b[0mlogp\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mfloat\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mlogp\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 834\u001b[0m \u001b[1;32mexcept\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m--> 835\u001b[1;33m \u001b[1;32mraise\u001b[0m \u001b[0mTypeError\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0m__name__\u001b[0m \u001b[1;33m+\u001b[0m \u001b[1;34m': computed log-probability '\u001b[0m \u001b[1;33m+\u001b[0m \u001b[0mstr\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mlogp\u001b[0m\u001b[1;33m)\u001b[0m \u001b[1;33m+\u001b[0m \u001b[1;34m' cannot be cast to float'\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m 836\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 837\u001b[0m \u001b[1;32mif\u001b[0m \u001b[0mlogp\u001b[0m \u001b[1;33m!=\u001b[0m \u001b[0mlogp\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n", - "\u001b[1;31mTypeError\u001b[0m: yule_simon: computed log-probability [-20.51503062 -19.93158602 -18.31405136 -17.21386783 -16.32349938\n -15.53050299 -14.75010755 -13.96101721 -13.13877723 -12.2264853\n -11.23694781 -10.06769225 -8.63087616 -7.0237458 -5.33941252\n -3.44559118 -1.4738842 ] cannot be cast to float" - ] - } - ], - "prompt_number": 83 - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "def logp(value, rho):\n", - " return np.log(rho) + np.log(beta(value, rho + 1))\n", - "\n", - "beta(repo_with_stars, 1.3);" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "output_type": "pyout", - "prompt_number": 84, - "text": [ - "array([ 3.96781274e-09, 7.12048348e-09, 3.60230434e-08,\n", - " 1.08508004e-07, 2.64859823e-07, 5.86390404e-07,\n", - " 1.28195491e-06, 2.82711390e-06, 6.44529816e-06,\n", - " 1.60819963e-05, 4.33570545e-05, 1.39960612e-04,\n", - " 5.90762159e-04, 2.95765600e-03, 1.59980669e-02,\n", - " 1.06728840e-01, 7.69230769e-01])" - ] - } - ], - "prompt_number": 84 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### Exercises:\n", - "1. Distributions like the Normal distribution have very skinny tails. Compare the PDFs of the Normal versus a power-law distribution." - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "x = np.linspace(1, 50, 200)\n", - "plt.plot(x, exp(-(x - 1) ** 2), label=\"Normal distribution\")\n", - "plt.plot(x, x ** (-2), label=r\"Power law, $\\beta = -2$\")\n", - "plt.plot(x, x ** (-1), label=r\"Power law, $\\beta = -1$\")\n", - "plt.legend();" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "output_type": "pyout", - "prompt_number": 20, - "text": [ - "" - ] - }, - { - "output_type": "display_data", - "png": 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oImJiYrztJHFxcWRkZDB27FjvaK7JZGL58uXs2LGD0aNHk5WVxaOPPkp1dbXf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\nEvg4W1VBVawJ3fZeRUSivV1UKErcHQ7PIsJRhES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- } - ], - "prompt_number": 20 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### References\n", - "1. Taleb, Nassim. The Black Swan. 1st edition. New York: Random House, 2007. Print." - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "from IPython.core.display import HTML\n", - "\n", - "\n", - "def css_styling():\n", - " styles = open(\"../styles/custom.css\", \"r\").read()\n", - " return HTML(styles)\n", - "css_styling();" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "html": [ - "\n", - "" - ], - "output_type": "pyout", - "prompt_number": 1, - "text": [ - "" - ] - } - ], - "prompt_number": 1 - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "import pymc as pm\n", - "\n", - "beta = pm.Uniform(\"beta\", -100, 100)\n", - "\n", - "\n", - "@pm.observed\n", - "def survival(value=y_, beta=beta):\n", - " return np.sum([value[i - 1] * np.log((i + 0.) ** beta - (i + 1.) ** beta) for i in range(1, 99)]);" - ], - "language": "python", - "metadata": {}, - "outputs": [], - "prompt_number": 167 - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "model = pm.Model([survival, beta])\n", - "#map_ = pm.MAP( model )\n", - "# map_.fit()\n", - "\n", - "mcmc = pm.MCMC(model)\n", - "mcmc.sample(50000, 40000);" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "output_type": "stream", - "stream": "stdout", - "text": [ - " \r", - "[****************100%******************] 50000 of 50000 complete" - ] - }, - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "\n" - ] - } - ], - "prompt_number": 168 - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "from pymc.Matplot import plot as mcplot\n", - "mcplot(mcmc);" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "Plotting beta\n" - ] - }, - { - "output_type": "display_data", - "png": 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AE++CeL8pbY8fP15v5/cLicCfDl6De0MB/jyaL7P/xt0WJNUNQtLN+7hxJQOhHg4mMR76\n3L5hMwQdXSLs/iUFAe1+SvuL29SdD7AHABRmX8TZFhfW8jQVZaO42R54YYje9dfn86XvbQA4d+4c\nysrKAABvvvkmKBQKhfIEnkhF0JdQKERNjaJnYNOmTZKVQRs3bkRWVhYOHTqk0O/SpUsYO3Ys/vjj\nD4SHh+Odd96Bo6MjNmzYAGdnZzx48EDS18XFBXV1st6ftLQ0jBw5klG2yC+vAAAm+zpj3SRv9Zpy\nmF+u3sUXF3q8SClLQmX2pRbWYevp25Jt+f1c5MuLlfgh9y4A3egrftYWhQ3G/FB2SXHFx4zxcsSG\nSB81vSnSZGVlYfLkycYWQyeo+g0zJYxRrkwc66TJNJqpllVbf/wWsiqf5KG7tLbn+R31UZpC3zUT\nvSD0G2Aw2dTRmzHV5h5qi6nee3n09ful0rOWmpqq8uC9e/ciKSkJaWmKDyQACAQCCAQChIeHA+gp\npyJeLu7m5oaamhq4u7ujuroagwYN0kZ+YtDng6YqsXh1Y5vM9sXyBvSzsUKQm73W1zP1Pxq2edZN\nXQ9N4JIuFPOAxjqRD72HhkPrmLXk5GRs3boViYmJsLW1Zezj7u4OT09PFBQUAOj5yhw6dCgAYMaM\nGfj6668BAF9//TVmzZqllRzaLLirbmzDfy5U4H5rh1bXND3Yl4H5x2/FeOfXAj3Kwl3o2k4KVyHF\n0CdFTpIgZUxJkVNfaG2srVixAs3NzRAKhQgNDcWyZcsAAFVVVZg+fbqk386dO7FgwQKEhIQgNzdX\nkqxx/fr1SE1Nhb+/P06ePIn169f3UhX2rE26hZ+v3sPmU6Van6OutQOXKxtZpw7R54OmylTTh4HB\nlT8arugBcEsXCoVCocii9QKDwsJCxnYPDw+ZQuchISHIzMxU6Ofi4qKQgdtQ3GluBwDkVDfjTMkD\nPDfEWeNz/Cu1GDfvtWJD5NMY4+WkaxE1gvT6yu1d3ejoEuFyRSNGezmhjxXN1UyhGBIas2a+0Jg1\nMiD+rdhbz9GHaaVaHXfzXisAIP9OC6v+XMqDpUtdvrpUhZe/ysGfDlzDhydLsStDB+k2pKxXkUiE\nqsY2Rg+oud+TRx1dOJJ/TyfhADQBMEVTaI4u8qH30HAQb6wZG1PwapmACFqzP7snZUtzexcA4EyJ\nbpMcH8y9i0U/5OOrS9WM+8sePEJbZ7dOr0kKuzOr8dkfFVh9lNlLzpb/u1CJmXtzOBQDan6Q4rEg\nRU6SIGVMSZFTXxBvrBn7g17aUCqpe4i45FsoYchar9eYNQNbjGx1EYlE+L8Llfit4L6eJVLOd1d6\nUs8cyFHM4+foE4Ilh65jReJNQ4ulc7R5vnKre1INVEqtGH7Y0YXLFY3o6mb/h3Xo6l20dYmQfNN4\n95lCoVC4DFHG2s5z5fjgRInMlJbIhNborT9+C5cqmvDe8VsGva4xPWtnih/gw7QSRu/UrfsPcejq\nXXx8pkxv179+twVpt+qULvRQNTbnb/dUvyh98Ejj67a2dxmslJS+YPIn/iu1GO8lFzEat1wgNjYW\nbm5uCA4OlmnfuXMnAgMDMWzYMKxbt07SHh8fDz8/PwQEBCAlJUXSfvnyZQQHB8PPzw+rVq0ymPz6\ngtYGNV9obVAyIMpY+/V6LdJL61H/qFMv52941KnRCk9A1qv14GGPXHUPFeXT64NmYGtNWpcPT5bi\nTEk9km7UKvR7pGJ6saapDddqmnsty6ojBdjy+21cv9sqaZMeDlVOx6Lci1pdUyQSYdY3ufjLzzck\n3il90vioE4W1rSr7aPV8MTzm2VU99yS95IHiTranFYlMNoZt8eLFSE5Olmk7deoUjhw5gtzcXFy9\nehWrV68GAOTn5+PgwYPIz89HcnIyli1bJvltePvtt7F7924UFhaisLBQ4ZwU9dB4J/Kh99BwEGWs\n6Zs/H7qO944XIV3HcVP6RmXqDg1emmdL6lFer7mXCQBaOxQNM6bpYDELD+bjbwyxUprIK01j2xMD\nWdpAUzY2d5ratb7PWVVPDLTMCv0bawsPXsPywzdx8x67xSxsyCxvxG0197pbJEJBbatGU6IA8P9+\nK0Lsj/kaH2cIJkyYAGdn2dXfX3zxBd577z1YW1sDAFxdXQEAiYmJiImJgbW1Nby9veHr64uMjAxU\nV1ejqakJERERAICFCxdqXNvY1CAlHogUOUmClDElRU59oZPaoEZFB++DP27XY6SHg8QzllPdjOee\nVp7OY+e5csn/2Tq15B+0C7cbkFXVhLdG85FeUo/92TXYEOkDNwcb1nJ3dYtgacHTiWPtWk0zNqSV\nAFBfoontH81nf1T0Wi62KBsDJiMSAD48WQIHnxEybV3dIuy9VIVRno4IGeyAqsY25FYrev/utzwJ\npNfWuNQEsQ5Xa1rwjCtz5QlNf8j+329Fanrw8P2VGnyTVYOXAwdi5ThP1ue+9NiArWlqA9+JOWG2\nKVFYWIgzZ84gLi4Otra2+Pe//41Ro0ahqqoKY8aMkfQTCASorKyEtbU1BAKBpJ3P56OyUvkqZlX1\njU2lPivd7m19254ydE1F2ZBGvC3+rWkqysa1ftUQ+k0zKfnptvbbeXl5aGzsCakpKyvTW21j8o01\nHfC/qSWYO/xJuavObhHikm9htKcTZg51lenb8KgTv15/MuWXmH8PC0LdYaGhxfQ/qcUAgGFu9tj0\nODnvrouV+OfkIayOL6t/hCU/Xcf8EW5wd+gj0+7VX/MXpDIvy7nSehTUtmJR2GBWCxkOPo51mhfi\nxrhfJBLJBLTrCk3XWFQ2KMqQdqsOB3Pv4mDuXaQsCcWiH/Jl9jOtdmzrFEEkEul8kUdXtwgfnb4N\nH5e+kjZl8ZndIhEsdHx9Hg9IzO95zo9er9XIWJM6i05l0hednZ148OABLly4gMzMTMydOxfFxcU6\nO//nn3+udJ+8kW2sbXEOK0NenylHl7rj5dtMZfyOPo5Tlv8AZNoeGuZldHmlt6VDKDQ9PisrS6Zd\nn/Iy5VkzhW1lY6JriJgGLXvwCD9fvcu4T1d+DXHhbwA4XfwAlyqa8Pl5Rc+Q/NROU1sXzpQ8QAXD\ny18aZTFFTW1dkv+nl9Qj+eZ9takkzpXWY8lP1wEA32fLBoJv0yKYv6tbhE/PljPue/9ECfZn30Ge\nVHyZMl1EIhF2Z1Zhd2aVUo/Tr9drEfvjdaWyaH8/ewyDts5uSToQVTS3dyl8Bde2qE49cfS6Ylxe\nYv49bDpZyl5Mlpwrrcepogf4MrNK0sY0pPuyqhH1VQ4SU07pXAZbDZMTy99zVfZj46NOk0mZIhAI\nEB0dDQAIDw+HhYUFamtrwefzUV7+5O+ioqICAoEAfD4fFRUVMu18Pt/gcpMOjXciH3oPDQcRxtqm\nU6X4zwUdJEtlSYecQaZuqquk7hG6dDQdti29DF9fZs4JJub9EyUy29Ivxfy7msc1lT5Qv6pRnAdN\nGTVNssaqsnCln6/eYy2XJog9m2dLtY831NY5dVpF7NuFskatzvmQwZBhGtJ9WTXo6BbhdPGTBQEF\n91rxz5QiBe/htZpmfHCiBHUs8qEV3X8oqfSha6oa2zD3uzws+em6SSxEmDVrFk6ePAkAKCgoQHt7\nOwYOHIgZM2bgwIEDaG9vR0lJCQoLCxEREQF3d3c4OjoiIyMDIpEI+/bt07q2salASjwQKXKSBClj\nSoqc+oIIY01VigR9/NRLv7NTCu5j7ndXcV2FEcTjqRdEkwctu0qzoPXeTjbJT+GpCgz//I9ynHjo\noWDA/lZQJ+Ml1PYlrO27W6yBJsfLT1GwXVyhLnC+Vc6wPXztHuof6iBhrIrLPjVslOT/K4/cREZZ\nIzadlDXq/3a0EOml9dhxjtmLqoq45Fs4U6x6haj8c3SvhdnYq2xoQ7eop+xbp4EXIcTExODZZ59F\nQUEBPD098dVXXyE2NhbFxcUIDg5GTEwMvvnmGwBAUFAQ5s6di6CgILz00ktISEiQ6JiQkIAlS5bA\nz88Pvr6+mDp1qkH1oFAo5gX5MWtyv/WlDx6in40lBtqzD9RXxb8fTyvuyazC1ul+OjmnDAyWli5e\nX13dImRVNqGlXf1Uk3y83YWyBozz7i/TJl7GII5jeuWbXLw+0l2mT42UJ6a9y8Aek8c69OaqJ26x\nS1fxiZIpYzHyXtaE8xW4cbcF65/31lKyHlTpJr1PbP/cV2Ig/nG7QeNrX6powqWKJqSoWHgjb8Cv\nOXYLKUtCUVr3ECmFdXgtxA2OtlZGzYy4f/9+xvZ9+/YxtsfFxSEuLk6hPSwsDHl5eTqVzZjQ2qDm\nC60NSgZEGmsZUlNL1Y+n3xKv3cOd5nb8lNcTe6ZuRaMqmDxVOY9XBWr7opF+0KS9LEzX0tS71Nfa\nUqEtMf8e66ljCzkpmALppYPbm4qyAZ8R2JVRJd9Jwivf5LK6tq5g412sbGjDv8/cxsKRgwH06CHv\nXdMXJ4seYNlYAT45W4bpAQMxSuCo0/OX5l0CxnvJtBlihlHeQGPyOm46VYrSB4/QLRLhL2MEkP8r\nqmvtwJH8e3jpmYEarYamkA2NdSIfeg8NBxHToPJsS38SRH/rfs8U6efnKySGWq/RMHhJ02lI6bgy\nXbxPmVaiXihj7z2xkHsKrjBMwz5UkgJDGjbVJNSNlSbjoWnajI/P3Ma1Oy1YZ+AKE2L2ZdXgXGkD\n4pLVpc1QYsSrOqCXD9In6dpVmfi/jCcfBPuz7yB6n6KRLq4QcfNeT2Jf+dv234uV+D77Dj47r/n0\nLEU3kOKxIEVOkiBlTEmRU18QaayxoaapDTe0CLYH9JNwQPpBk86MJh/f1MOTtxmbFXPyCw4ARW+Z\nKuQztZ0rbZBZ/QkAey9V4/bjhQjKvFH68uTcvNeCN3/Kx6WKRlytacbDjp4x0zTcqUVurA3lVRPT\nJJW4VytUDbBgmEbd5TmuZV1P6QUjHd0ilUa9OL2IvFziadkMLRdjUCgUCtfhrLG28GA+Vh4pwF2p\nOKr7rR141KF6VaMhkHbcMRkc4pfZ91dqELU3B1cqn3i6VC10kEbeW6aM3Oom/E+Koqen4J5seaM7\nze1qU2LowlZj8pYlnK9AeX0b4pKL8O7RQpmkxBqdu7fCsb2Oni6k6rT5d1skRiyb/tpS+uAhyusf\n4eMzt2X+tthgwRBXaCrpO8wdWhvUfKG1QclAa2NtzZo1CAwMREhICKKjo9HQwDztVl9fjzlz5iAw\nMBBBQUHIyMjQ6PjelqypamxDdlUTyh48Qsz3V/Hqd1d7dT5lb0BVUnZ1i3A6PV2yLe3HYjpO3Lb3\ncQqPdcdvoatbhK5uEVYdKVAr4g85d1gnSV197BbKleSIk0/HcbKoJwBfPj+ZRG4Wt0qb9Bh3mmSN\nAvFCAOkVp+L/qZoald8jrYf8NZRxm0WaE33x1aVqXLvDXE+1qShbUjlAjD6qK3yYVorVxwrxW0Ed\nPkxT9Oiqgicx1p7IdaKwTua56eiixpu5QHN0kQ+9h4ZDa2MtMjIS165dQ05ODvz9/REfH8/Yb9Wq\nVZg2bRquX7+O3NxcBAQEaHT8N1mqc46p44/bDVibdAtLDvUkYmXzJa+pQaEue/2iH/LxfmqJxLiQ\n6c7yhbpg/1Us2M/O0Pwyswr3epkja1dGJf4fi9gqadjErGmDsvFlutq/VSUFViHenw5eYyXL0kM3\nWPVjgkmN/DstqNagosPffn1ST/Vypey04QdpJTIF3xvbunRusDW3d0rKst24p7q4vDziqXlpkdrk\nVg3LJ3mmGAZS4oFIkZMkSBlTUuTUF1oba0KhEBaP59pGjx4tk9FbTENDA9LT0xEbGwsAsLKygpOT\nE+vjAeDXfMWs8Zqgac4yQHXM2iEllRRUcae5HVZewVLxaU+uwPQqLX3wCNfkYsbqHnai7iH7mCf5\nl6CmiAClHjelsV4sLqmN7aCslJem53rYaZiYNbZi3W1uxzu/FmD1McWC9mzYmFYq+b9Yl1NFsulH\nTpfUo6mtEysSb2p1DXnqWrWPu7Ow6Jnal46x7OqWNfHF5cooFAqF8gSdxKzt2bMH06ZNU2gvKSmB\nq6srFi9ejJEjR2Lp0qVobVX8Gld2vC4Qr0TTFb1ZcSp+KUkbH8oMjv9lWDSgCfeVJCTVJ6p8lt0i\nEW7Vtqp+HveuAAAgAElEQVSt9KDRalAND7zbrIPEtCxg683a+UdP7N29x2WuurpFrKYBPzhRgtb2\nLsbEw/J2bXpxPY7k10pWYhoa6bHggSeZ2hcjr68pVDQwR2jMmvlCY9bIQGWeNaFQiJqaGoX2TZs2\nISoqCgCwceNG2NjYYP78+Qr9Ojs7kZWVhc8++wzh4eF45513sHnzZmzYsEHSR9XxAHDj+82wcOop\nsm5paw87D1+JF+FJzFGozLb8fk237QPDGPefPXsWTUWFCv15oVOV9m/v7AbggKaibJw/1wg7G0v0\n9R4u6V9gWQ7AU+H4hkedvdKnrUuktr8yfdRti9vk9/98/CSaiu4zHn8o7y627U9Se/42SwsAIRL5\nAMCC58zY/4+zZ9FUVKS1PnfSf2J8nrTZ/jCtBL4PiyHo3wfDwkYz9r+ddwlNVU1w8BmBioZHOHHq\njGR/V7cIs+O/R2NbF35+L0bl9dIxAgGD7FBXmI2Orm6Ze1EEZwBPSfqXt/SDz3MTWOmj7fOganv3\nL3cB9Pz9Vl+/jKa7LTL7b/Fc0FD8AHW3stFW9/i3JnQtKNyHxjqRD72HhkOlsZaamqry4L179yIp\nKQlpaWmM+wUCAQQCAcLDwwEAc+bMwebNm1kfDwCBC9bLlDGSRvyjL/56l5/W0nZb2fnGjx8Phxv2\nCv3FsUjy/S09g7E5tViyPebZcbCxssD/phRL+vuEuOOPrBqdys92W5k+6rblX8piHH1HwKHrvkJ/\noKeAO5vzSxcPHz9+PC6UNeDOjWKF/uuSbmF6YDAcfBwA9DjWNNVH2lBj01/V9pmSepyBC1JeDpUk\nPZbv/2BAABz69uxrae+S2d/S3oVWtyBYoaeeKI+n+nr3Wztg6z0ctnL7fYcPQlbuXck239sJfR6P\nqb6eB1XbGSJbAD3ebcHQMFQ4NMrs9wlxQ47FXdgO6THQH0e1gWJYSIkHIkVOkiBlTEmRU19oXcEg\nOTkZW7duxenTp2Fra8vYx93dHZ6enigoKIC/vz9OnDiBoUOHsj7eWLSySACrjqs1zdiT+STDv4PP\nCIgAHLl2D1lScXTGmvU5VVSH531ctDpWWayXLqawHsktAPmflGLGfleqmhiT92qCvmLWzpUyr2xu\nlUqtIT/bKT1229LLYKlmkUtpnez0vqrcd5ZGTNAjnUeQaYUynfWkUCgU9Wj9M75ixQo0NzdDKBQi\nNDQUy5YtAwBUVVVh+vTpkn47d+7EggULEBISgtzcXEmdPWXHa4Oxf+9b27tlVuEBwLtHC1ErV7ZJ\nJBJJylaJYVMZQB/En7qNo9d7t3hDHlVZVszlpfyP34qwXUkeOOnxeefXAqX7AEDd+pAsJYYqs42n\njzTPmsO0GlYE2b9fM3lMTA4as2a+0Jg1MtDas1ZYyLyCzcPDA8eOHZNsh4SEIDMzk/Xx2mBsQ0DZ\nClHpjPk9U4fDFF5Y2qwu1RU7tEwuq6ympj7yerFFm0vrozboxXLlWfhVpY3prVdSoovcAyYSGddU\nk1ars5c5EyncgsY7kQ+9h4bD5CsYKItXk+Z/TzBPlZka50obtEoKSwqqXsV3NMz7pmky5I9O30Z5\nvW5X/hqSk7ceqO/Egpv3FCtcsH3mGh71shwWA9J30cHGUmG/fOoOinEgJR6IFDlJgpQxJUVOfaG1\nZ81Q9LHkqc0ZRkJNQQefEdj5R7nG9SxNEX3XBi2rf4QlP12HYx/Fl7syGh51auwpNHRtUFX01sMq\n1iW7Snaa/eqdZowSOLA6x46z+i2kbsmQMO+nvLuwUpZIj0KhUCgACPCs9Ta5qynBBUNNFbrS7+fH\nhksjC6+qNPLxgCShr2ejqa1LbYUNMUV1+s3F9ntxPWM7nR41PjRmzXyhMWtkYPKeNa6gj/goY6Hv\nmDVD+VlM6Z70duxU6cJ2PBseaWYcs0E66S0t2k6RhsY7kQ+9h4bD5D1rFHLQ1av42I376jtxDH36\nlpJusFv1266HIuqaekcpxoGUeCBS5CQJUsaUFDn1BTXWNKCsFwHspuLB0QXKY9bIms4ypXvS25lA\nVboU3n/I6hwdHAo5oFAoFC5BjTUNyKo0/YUMxuT8beZksBT1kGboUrgFjVkzX2jMGhnQmDUNKKxl\n56FgwpTio3qLMl1Ic8youif/vVhpUFl6WzWDS88XxTyg8U7kQ++h4aDGmgakFtYZWwSKgfgx13jJ\niikUQ0NKPBApcqoit7oZTrbsX70Cpz7wcNRfSUZSxpQUOfUFNdYMBJe8HlzRhSt6ANzShULhMr8V\n1OG3AvYf/p+87AcPRz0KRCECGrNGoVAoZg6NWTNfaMwaGVDPmoHgUkwRV3Thih4At3ShmAc03ol8\n6D00HNSzRqFQKGYOKfFApMhJEqSMKSly6gtqrBkILnk9uKILV/QAuKULhUKhUGShxhqFQqGYOTRm\nzXyhMWtkQI01A9FUlG1sEXQGV3Thih4At3TRJ7GxsXBzc0NwcLDCvo8//hgWFhaoq3uyUi8+Ph5+\nfn4ICAhASkqKpP3y5csIDg6Gn58fVq1aZRDZucbKlStpzBPh0HtoOKixRqFQzIbFixcjOTlZob28\nvBypqal46qmnJG35+fk4ePAg8vPzkZycjGXLlkkqTbz99tvYvXs3CgsLUVhYyHhOkiAlHogUOUmC\nlDElRU59obWxtmbNGgQGBiIkJATR0dFoaGAuNVRfX485c+YgMDAQQUFBuHDhgsx+pq9ZLsKlmCKu\n6MIVPQBu6aJPJkyYAGdnZ4X2d999Fx999JFMW2JiImJiYmBtbQ1vb2/4+voiIyMD1dXVaGpqQkRE\nBABg4cKFOHz4sEHkp1Ao5onWqTsiIyOxZcsWWFhYYP369YiPj8fmzZsV+q1atQrTpk3DTz/9hM7O\nTrS0tEj2MX3NUigUiiFJTEyEQCDA8OHDZdqrqqowZswYybZAIEBlZSWsra0hEAgk7Xw+H5WVysuT\nLV++HF5eXgAAR0dHBAcHS7wE4jgcY2+L2wx5/R07dqC0tBTR0dGsj//iiy9MdPzcASiGI4i3xR9T\n2mxfuViLoTOEepM/Ly8Pb7/9tlbHv/vuuwCAbdu26U0+8bb8s6rv62kyfo2NPXXDy8rK8Oabb0If\n8EQ6qCD9yy+/4NChQ/j2229l2hsaGhAaGori4mLG41599VX885//xMyZM3H58mW4uLjI7E9LS8P6\nLF5vxTMJuJQHiyu6cEUPgFu6bB4pwuTJk/V2/tLSUkRFRSEvLw+tra14/vnnkZqaCkdHRwwZMgSX\nLl3CgAEDsGLFCowZMwYLFiwAACxZsgQvvfQSvL29sX79eqSmpgIA0tPT8dFHH+HXX39VuFZaWhpG\njhypN110xdmzZ4mYZjJVOdcfv4WsyibJ9qW1Pc/vqI/Sen3uT172w1D3fr0+jzJMdUzlIUXOrKws\nvfx+6SQp7p49exATE6PQXlJSAldXVyxevBg5OTkICwvD9u3bYWdnp/RrVuEcB7egj0vPV4ulrT3s\nPHx79ZVCt3u/LcZU5NF2u7XqlknJY67bANBUnIO2upqejZFrYSiKiopQWlqKkJAQAEBFRQXCwsKQ\nkZEBPp+P8vJySd+KigoIBALw+XxUVFTItPP5fIPJrA9IeAkC5MhJEqSMKSly6guVnjWhUIiamhqF\n9k2bNiEqKgoAsHHjRmRlZeHQoUMK/S5duoSxY8fijz/+QHh4ON555x04Ojrivffew6RJkxi/ZqXh\nkmeNQqGww5CeNXmGDBki8fLn5+dj/vz5uHjxIiorKzFlyhTcunULPB4Po0ePxo4dOxAREYHp06dj\n5cqVmDp1qsL5SPGsUXoHyZ41im7Rl2dN5QKD1NRU5OXlKfwTG2p79+5FUlISvvvuO8bjBQIBBAIB\nwsPDAQBz5sxBVlaWzNfskCFDJF+zd+/e1bF6FAqF8oSYmBg8++yzKCgogKenJ7766iuZ/Tzek4/D\noKAgzJ07F0FBQXjppZeQkJAg2Z+QkIAlS5bAz88Pvr6+jIYaSdA8a+YLzbNGBlpPgyYnJ2Pr1q04\nffo0bG1tGfu4u7vD09MTBQUF8Pf3x4kTJzB06FAMGzYMd+7ckfST/prlKlyKKeKKLlzRA+CWLvpk\n//79KvfLx9fGxcUhLi5OoV9YWBijZ47CHpqfi3zoPTQcWhtrK1asQHt7O4TCnlUqY8eORUJCAqqq\nqrB06VIcO3YMALBz504sWLAA7e3t8PHxUfiSBWS/ZikUCoViWEiJBzKUnGUPHqKmuZ1VXysLHu40\nsetritB7TwZaG2uFhYWM7R4eHhJDDQBCQkKQmZmp8lzKVotyCS55PbiiC1f0ALilC4VibG7df4jN\nv982thgUigRawYBCoVDMHBqzZr7QmDUy0EnqDop6uBRTxBVduKIHwC1dKOYBjXciH3oPDQf1rFEo\nFIqZQ0o8EClykgQpY0qKnPqCGmsGgkteD67owhU9AG7pQqFQKBRZqLFGoVAoZg6NWTNfaMwaGdCY\nNQPBpZgirujCFT0AbulCMQ9ovBP50HtoOKhnjUKhUMwcUuKBSJGTJEgZU1Lk1BfUWDMQXPJ6cEUX\nrugBcEsXCoVCochCjTUKhaI3Fo50N7YIFBbQmDXzhcaskYHZxawNsLPG/dYOg1+XSzFFXNGFK3oA\npqsLLSVHUQaNdyIfeg8Nh9l51izou4NCMRjPuNoZWwQKC0iJByJFTpIgZUxJkVNfmJ2xZqwPfVP0\nemgLV3Thih6A6eoySuBobBEoFAqFeMzOWKNQKBSKLDRmzXyhMWtkQI01PfDT68EKbU1F2UaQRBG/\ngX17fQ5T0UVT+lrLPu760sMYU+2k3hOK+bJy5Uoa80Q49B4aDrMz1oR+A/R+DUdb01234aRj2Tyd\n+uj0fPpkuHs/g1ynW6Sb89DwSoqhICUeiBQ5SYKUMSVFTn1hdsba66HGSSVgqjFF2iCty5qJT0n+\nP97bSXfX6GOps3OJkbehTP2eqIqv/NeUITLbYl1c7KzwavAgWFtqb+pNe0b/HzQUCoVCYY/Wxtqa\nNWsQGBiIkJAQREdHo6GhgbFffX095syZg8DAQAQFBeHChQuSfTt37kRgYCCGDRuGdevWaSuKRlia\n+XJQXWtvITWe/5z8xIDwHdC76VZD3qVNU30Mch3P/n0wxNlWo2PClQToKzNm+1pZYuloPnxctB9/\nY/6N9MLGpPQCGrNmvtCYNTLQ2liLjIzEtWvXkJOTA39/f8THxzP2W7VqFaZNm4br168jNzcXgYGB\nAIBTp07hyJEjyM3NxdWrV7F69Wql1xrv7YS/PivQVlS9EzhIfXoC+Zii6GGu6GNleMfmn0YO7vU5\npHXplprzk86p1dtVt7qermVCrIcu7INIPxe1fcZ4OcF3oGapLF70Zz6vvJdQ/vnqzUysMVOjmfvH\nlDlB453Ih95Dw6G1tSAUCmFh0XP46NGjUVFRodCnoaEB6enpiI2NBQBYWVnByalnquyLL77Ae++9\nB2trawCAq6ur8mv5DcCMIOX7e8tQN3u9nVsZfxkjwEA7a6X7ezONpYqAQbrTdeLT/XUWnyXPUxp6\noIyNvY3yadvJvs4AgBf9B2BphIdG550wpD+jwSbS07gbG5pE1ziQEg9EipwkQcqYkiKnvtCJa2fP\nnj2YNm2aQntJSQlcXV2xePFijBw5EkuXLkVraysAoLCwEGfOnMGYMWMwadIkXLp0ifHcJQe34Pv/\nfIotW7bAqyRVxoPQVJSNtb5NMtvy++W3pV2p4v3iaTDxdoSnI+vzyW/Pdr7DuN/BZ4Rke7RXz/lr\nC64oPV8Y30Gr62ujv6bb4vgon4fFuJJ5XrL/7NmzOpdX2+3oYa4y2wPsrFGZf1nBA9VUlC3xQvXm\neiKpbZvHhrZ4e+3Ep3DkjeEou3oJVy9nsD5/Y1E2zp07J5kKld//nE2FwvN1r+BKr8eP18vjpbfZ\nPG9NRdmoSv0aJQe3oPTgFlAoFApFFpVzTUKhEDU1NQrtmzZtQlRUFABg48aNsLGxwfz58xX6dXZ2\nIisrC5999hnCw8PxzjvvYPPmzdiwYQM6Ozvx4MEDXLhwAZmZmZg7dy6Ki4sVzjFk3josiHwaY7yc\ncL+1AzHfX5Xse3bceEyZ5IePbvW8oOQDxpm2x48PBW7I9ufJ9e/32EvC5nzy23OmDlPbX+xRs/YK\nhkN7F2N/HnhaXV/dNpP+2p5v5Oix8B3QF4UnSuA30A7jQ93hcMNer/Kz3X7apa/MtgUP8AgMQ6VD\no0J/sZdKk/P7DuiLW5C+X0/2Bw6yR05185Pni8eDrbXlky9DluO/ecksjH/aGWeKHyjsF4mA4LAx\nONNeIXP8QMee1bkNjzqNOv7ibbbPm/j/T/W3BfAQFMNy9uxZg3suxLFOmkyjGUNOrtObMdXmHmqL\nud97lcZaamqqyoP37t2LpKQkpKWlMe4XCAQQCAQIDw8HAMyePRtbtmyR7IuOjgYAhIeHw8LCAvfv\n38eAAYor0fQ9McJmRsmlrxXqHnYq3W9twUNHtwiOtszTYdIeKfH1PPv3wfW7rRpKaxiGD+6Hf7zg\njbnfXVXYJ62LBY+H/xU+rdCnt7NZPAMsMehNPU3HPrJ/OtLT1rqYyYt7wRvPPe2sdL8IIpnriHUR\ne/UseyWE8mPD+A64XNmkdL80A5RM868a74ntZ8tl2kZ7OeLG3Va8PtIdqC9hLyqFWGisE/nQe2g4\ntJ4GTU5OxtatW5GYmAhbW+b4Ind3d3h6eqKgoAAAkJaWhqFDhwIAZs2ahZMnTwIACgoK0N7ezmio\nAYBrPxvGdrYrDtUF8svH/2jznvtl4XAcXjgc1pYshvTx9QxhkGiLwLEP+vdVHlPHJSy0+SuQu3V9\nrS2ldrG/r2ulUp9IM3FIf5XHiQBMYjDm3nve+/F+3QW1Pe/z5DrTAgayOubZp5zw7WtDFdp/fD0Y\n0xnO8UGkD35YMAyDHcnJ28clSPFYkCInSZAypqTIqS+0NtZWrFiB5uZmCIVChIaGYtmyZQCAqqoq\nTJ8+XdJv586dWLBgAUJCQpCbm4u4uDgAQGxsLIqLixEcHIyYmBh88803jNfZPScQTytJQ7B4lOzK\nxr+N92Tspy6om9VrTc3718bKAnYqgsxlprBYXM7KhFfFOfiMQF9rC3j3VzTShX4ucLGzQqiHg0x7\nb1N5bJ3uq1F/NoHq4nsyYvATWd8IY7daVv7sL2mQm8zVvscIfsbVDlOUrCKVlp/xeRHJJl928BmB\nT6L8MOTx30pXN/M12SA/dNKbbB9La0ueZGVnyOAnyYhVrfLl8Uz584VCoVCMh9bGWmFhIW7fvo0r\nV67gypUrSEhIAAB4eHjg2LFjkn4hISHIzMxETk4Ofv75Z8lqUGtra+zbtw95eXm4fPkyJk2axHgd\nTymDQP6H3NZa1jjS1UqyKb6KL1B7a90laZW8fFWI66BkOlWXrJvE7NUBgIkqpuAA4Oc/DYcNg8dy\nzcSnsD9mGGyl9s0MGoiV45gNaaVIjQ3fsQ9CpAwqcdUEPxUGIPPQMpvJ0ukivFmuQpV+1P400h0u\nUlN+6p7CNROfwtMufbHiWdkx6f/YkHnGVX16j0Fy3ubYUYMx1O2JUeQvd46pWia6fdHfRUZXbf7E\nlOWKE7NK6tmgxppxoHnWzBeaZ40MiKpgoM4jpexFommagzCpl8uc4EGY9LSz1i87MRG8Mil5dDdF\n9e4EL8n/P3zxaTzt0ruUF88+5YS9c4MQyndQ2qepKFtlPiwejyf3guchYJA9jiwKkTHiVLFARaWJ\nWUNdcWD+MGyf+Qzj/lXjPVkZFUz1ND0ZvIVMqDy9mmuP8HDAf6IDFAyq0V6O2BUdgH9P91N67K7Z\nAfjwxacV5CzIviizPS/ETbUQSvj4ZT+Zv5fZwwbJ7Ffl+5K+Z2x9ZEsjPHr9t0UhE5qji3zoPTQc\nRBlr+sLO2kKpR2XqMwMQ94K3TCyaQIt6mPp6IUnHE4ULHPHZrAB88coz4DPE/uyY4S+zzfQ6tbbg\nwUPHcUPilz8bQ23CkP44HjtCZupb3rQNHtwPLnbWSqeKpwcMRJBcPjmRCHDoozgFN294jzHy7WtD\n8cnLfvBiaazpywfk7dJXZYylt3NfRHiqL+vVX8ukwsHu/SA94t4sKyFsmuojM4UsHTOn6tNkJN9B\nxvDXd5q12NhYuLm5ITg4WNKmqhpLfHw8/Pz8EBAQgJSUFEn75cuXERwcDD8/P6xatUq/QhsAUuKB\nSJGTJEgZU1Lk1BdEGWva/o6r98jx8Jmcl+ZfU4ZgaYSH1Mv7yVm2veyncgoRAP493Vcm6a30gyae\nwtLFe0laNx6PBysLHnwG2DG+9OxYTOVqEuul8jxqeyhH/PIWxzcNkfcWsnBMDnbsg2/mBcm0/Xk0\nH+ECB8Q/zqvn4DMCwx4Xdx/UzwZDlRR6H+ulaBzpw6joZ6N91Qa/EREy2/LTpJog/wywUVXbGEsL\nhYHUr7W2ePFiJCcny7Qpq8aSn5+PgwcPIj8/H8nJyVi2bJnEK/72229j9+7dKCwsRGFhocI5KRQK\nRZcQZaxpgnjxwdzhg9T0fIzcO2Kcd3+8Opx5Kql/X2tMZohrk2b4YAd89DgoXlwPcscMf0QPc2U8\n7/vCpxm9YerQaEqV4T3oIxf3pat1DbKVElTL+OuiEMb2T6P88GrwILwz3kumna2h5O4gO54udtbY\nONUXYQJHvDWaj9GejjJT3sqI9HdRKFKvS5Pig8in8exTTlgQqt3UpTKYVouyIViJ0QoAd5rbWZ1D\nehpUPHbSCw0k/eQXM+jZszZhwgQ4O8uOi7JqLImJiYiJiYG1tTW8vb3h6+uLjIwMVFdXo6mpCRER\nPQbywoULcfjwYf0KrmdozJr5QmPWyED/BRiNxGshbpj0tDPcHWyQmH9PB2fU/C0icLLFgfnD4Ghr\nJUnop6zc09innDD2KSdEfnmFcX+ohwOuVCnmt+pt+Jv88fIFwiP9XJBSWCfT1hPrFaryvCOkVoMq\nE/GbeUGwsuDJTvtJdeY72WLpaL7CcdLTZnEveOP7KzVwtbdBZkWjQl9lMswOHgS3hgJYWagv4u43\n0A5jvJxwr6UdCw/m9zSqeBw0fVJGezlhNIP3TgybW1xw5SIwYoaGV2ZmnLcTYkcNRjCDcdWlRX0x\nvpMtDv0pmLEkl4WJLSnYs2cPYmJiAPSsbB8zZoxkn0AgQGVlJaytrSEQPKlVzOfzUVlZaXBZSYfG\nOpEPvYeGg7PGGo/H0yhnU++SiCrHRUX9T03oJ/Wimxk0EIn5tQA0K9jNZoWkfKH3vz/nhVXjPTH9\nqxwNriR3BalLSF9N3vPFFumps0lPO2PS087Yea5cxRHa4WpvjU+i/CVTitLyqnpaTL28ZYCrHV7w\ndUHCecV6vkDP+L42QmqxgJRCk32d8X8ZmhsmTPGCANC/r2y7Wz8b1Gt8dt2gqhpLb1i+fDm8vHq8\nw46OjggODpaERYi9BXSb3ba4Td/Xg3tPCIV0OTdNtsVoe7z09pWLtRg6Q6hffR9j7Puranv8+PEm\nJY94Oy8vD42NPY6CsrIyvPnmm9AHRBlr0i9Bpuk6Ze9INt4nSwsevnjlGYYYGt3AFByp7kovPTMA\nx2/eV+gsnV+L7epKZcg7ShzlAtN5PJ5Mdn5LHnA4bkGvrtlbNJmqdbK1QsOjTnj2VzQM1QWs9rW2\nVBr7ZWoZweRj1lSx43F8pjJjTRXqEiWP8XLEhbJGPPuU6kUQX70ahJb2LoXnjcn7ZgiYqrHw+XyU\nlz/5CKioqIBAIACfz5dMlYrb+XxFD7CYzz//XOk++WeQbpvG9slbPbMJplCyLTTiyepwUxkfuv1k\nW74tKysL+oComDVpw4QpF5UNm+oBKvAZYCdJKmp0RMDysQL8a8oQJL4xXMY0kDY+LS14OLxwOI4o\nifuShik+SNNJLX9XO7g5aBa8LrMIQsPrMcFkUCuzsbe97IeowIFYN9Fb4+swnVIc4xc4SHkuNFMx\n43T13THycRoXt8eG6yIViYPfneCFDZFPY4KaCgx8pz4KqUuMhbJqLDNmzMCBAwfQ3t6OkpISFBYW\nIiIiAu7u7nB0dERGRgZEIhH27duHWbNmGVGD3kNj1kwXCwse7re2s/7X3tmt/qRS0Jg1MiDKsyZd\n0odp2nKUwAEv+rvAd4BpvASk0aYIrY2VBcZ597z0pLV9wdcZ316pwbjHgduqKieoQ9OYN98Bdqx1\nsbO2QGtHN4a6PYnT602Inau9Ne61dGg0tezZ3xYrlCTkVacHk7HzjxeG4HJlIyL9XNAlApJu1CIq\nsKd80rKxfHx5sQqx4XxkVtxgLaM6BtmrN44Lsi8CobqJWZPnBR9n9O9rBb/Hf1fzQ92x93I1Y9/+\nfa0xRkX8nbGJiYnB6dOnUVtbC09PT7z//vuIj49He3s7hMKeqaaxY8ciISEBQUFBmDt3LoKCgmBl\nZYWEhATJlHBCQgIWLVqEhw8fYtq0aZg6daox1SISGu/EjvXHb7F2RNjbWPZkIrDSfjW4JtB7aDiI\nMtaksZCaC9s+wx+tHV3o18cKf39OMaWGvIHw0TRfrE26pWcJdYyU4SBwskXiG8N7PQUKyObD+sdk\nb7X9rS15gPJ69jLsfjUIN+62YKyaKTG2fD1vKLq7RYxpImYPG4Sj12sxV8kKXm1gckzxnfqA7+QK\noCcJ7PwRbpIX+KyhgzAjyFXnU+lBbvb423hPvXl9//6cFz4+U6Z0P4/HQxhf9apZHeZ51iv79+9X\naIuNjVXaPy4uTlIiT5qwsDDk5eXpVDZjQkoOK1Lk1CUPO7rxsIOdt0ybBUCkjCkpcuoLYo016ddh\noJIVlmLkXyQjPBzw4+vBePXbPNYJYJ8b0h97L1Wpnd5RBmPMWi/e6X21KH+lmNGKJzM2zw1Rn+rB\nyoLH+o9mgJ21xDPIFlUFyK0seEoD1gY79sGxxSNUVlaQR50ebO6PfE4yeUNt2VjlsUya8JKaAuqa\nxNI/gUQAACAASURBVKyJ2T9/GGpb2jFAR4tgKBQKhaIfiIpZk6a3qzedbK3w85+C8eWcQFb9Xeys\ncXBBsEx5J0Oir4B2th9ir4W4oY8lDzOCXPUihy7QxFBjgy5qzaoLyNcn6qQfYGeNZ1ztMdDeBh++\n6IOEWczlu5h4azQfk321y+NGMT1ozJr5QmPWyIA4z5q3sy1KHzxCuKf6ZKZilAUy91OSTkAZqsoA\nqYM5Poq9MaCbmTWmk7Cz1mLDPbBo1GBY8Hhaxd+ZImpj1gwoS29pKsoGQmXjpgbYszcUIzT4ewJ6\n8tQBQNqtBxodR6GIofFO5EPvoeEgzlj793Q/XLvTotHLJdi9Hza/5MO6SLehWDxqMN49WiiptiCN\nvAmlC8PB3kbO2OT1JNutaryvMmu9GF3EYr0W4oavL1djTjDLyhJGxNTzpQHAV68G4vrdVvSpaVbY\nN3+EO5rauiD0c0E2Q0JlCkUMKR9fpMhJEqSMKSly6gvijDVHWyutAtZHqgmQ1jdMD9ow9344tjhE\npki8MqRznWnKZ7OeQWt7F+OU3Bthg+Fip758ljS9+aOZP8INE7z7Q8CQ98zQqI1ZI8C3xneyBd/J\nFvCboLDP3sZSMm1PjTUKhUIhF2Jj1rgCG0MNABaFeeBpl75YO1F1AXkm/AfayZR/mjCkP6wteBjF\nd0D/vtb408jBrBda9BYejwcvZ1ulXjpTWlRIgmfNVFC1MIRi+tCYNfOFxqyRAXGeNVLpbZzXAHtr\n/Cc6QCey/HPyEHR1i7QOyNdnzJoh7SMuxayp04WU1BoU84HGO5EPvYeGQ2tjbc2aNTh69ChsbGzg\n4+ODr776Ck5OitOT9fX1WLJkCa5duwYej4c9e/ZgzJgxuHjxIv7617+io6NDknAyPDy8V8pQ2KPr\nlZO6wpSmHqlnjT2mdN8omkNKPJC2cj5o7UBzexfr/g2PWCaT5ABcv/dcQWtjLTIyElu2bIGFhQXW\nr1+P+Ph4bN68WaHfqlWrMG3aNPz000/o7OxES0sLAGDt2rX44IMP8OKLL+L48eNYu3YtTp06pb0m\nRqQfiwoCXHrQ9KqLAd/56vOs6UAYA3m0uPR8USi65k5zO1YeKTC2GBSK1mgdsyYUCmFh0XP46NGj\nZQobi2loaEB6erokQ7iVlZXE+zZ48GA0NDQA6PG+qSqEbKp8NM0XIz0csHKccXKvcRG+gWLnVCGu\nkODtbFqrhykUfUFj1swXGrNGBjqJWduzZw9iYmIU2ktKSuDq6orFixcjJycHYWFh2L59O+zs7LB5\n82aMHz8eq1evRnd3N86fP8947uXLl8PLq8cYcnR0RHBwsMSLIL55xtpuLs7By46Am4Ov2v7SD5qq\n8zcVFcLBZ0Sv5QscZI/rWRlw7msNIFSn+svrpIvx/OKVZ7D7lxR4tzQB8NCpvMq2v/jiC8bn6T+v\njMKJW3XwarmFs2fLtD5/U1E2rjrWYJLPS3rXh83z1VSU/biH7p4H8fPK4/XueTp37hzKynpKXr35\n5pugcB8a70Q+9B4aDp5IpDz0WCgUoqamRqF906ZNiIqKAgBs3LgRWVlZOHTokEK/S5cuYezYsfjj\njz8QHh6Od955B46OjtiwYQOmTJmC5cuX45VXXsGPP/6IXbt2ITU1Veb4tLQ0jBw5src6mgRsg/Ln\nf38Vta0d+MsYPqKHaZ+LrKW9C0ev1+J5H2cM6qfbor7mkhS3N0R+eQUAEPe8Nyb56D/Tvzpdvrlc\njW+v9PwtpywJ1dl1xXp+NM1XZsVxb8jKysLkyZN1ci5jw6XfMJK5cbfFoNOgl9b2PL+jPkoz2DWB\nnpCcXbMDMNDeMIXcKYro6/dLpWdN3niSZ+/evUhKSkJaGvMDKRAIIBAIJAsHZs+ejS1btgAALl68\niBMnTgAA5syZgyVLlmgsPEmwNQr+Z8oQnCutx3Q1tSDVYW9jiXkhuitqLg0XDDWAO3oA3NKFQqFQ\nKLJoHbOWnJyMrVu3IjExEba2zLE97u7u8PT0REFBzxdNWloahg4dCgDw9fXF6dOnAQAnT56Ev7+/\ntqJwioBB9ngzgt+r0lYU4zNhSH/Y21hihIf6yhAUirGhMWvmC41ZIwOtY9ZWrFiB9vZ2CIVCAMDY\nsWORkJCAqqoqLF26FMeOHQMA7Ny5EwsWLEB7e7skxQcA7Nq1C8uXL0dbWxv69u2LXbt26UAd04Ur\nU4cAd3TRpx7/eMEbbV0i2BrI6ObKPaGYDzTeiXzoPTQcWhtrhYWFjO0eHh4SQw0AQkJCkJmZqdBv\n1KhRyMjI0PbyFIpJw+PxYGtFc49RyIAUQ58UOUmClDElRU59QefaDASXHjSu6MIVPQDj6SL2HNI0\nJxQKhaI/qLFGoVC05ocFw7B//jD072ttbFEovYDGrJkvNGaNDKixZiC49KBxRReu6AEYTxdba0sM\nsKOGGkVzVq5cSWOeCIfeQ8NBjTUKxQwYbAKVISimCykhAaTISRKkjCkpcuoLnVQwoKiHSw8aV3Th\nih6Ael1e8HFGXWsHQvm6SVxLoVAoFMNBPWsUihlgacHDvBA3+A+0M7YoFBOExqyZLzRmjQyosWYg\nuPSgcUUXrugBcEsXinlA453Ih95Dw0GNNQqFQjFzSAkJIEVOkiBlTEmRU19QY81AcOlB44ouXNED\n4JYuFAqFQpGFGmsUCoVi5tCYNfOFxqyRATXWDASXHjSu6MIVPQBu6UIxD2i8E/nQe2g4qLFGoVAo\nZg4p0+ikyEkSpIwpKXLqC2qsGQguPWhc0YUregDc0kWfxMbGws3NDcHBwZK2uro6CIVC+Pv7IzIy\nEvX19ZJ98fHx8PPzQ0BAAFJSUiTtly9fRnBwMPz8/LBq1SqD6kChUMwPaqxRKBSzYfHixUhOTpZp\n27x5M4RCIQoKCjB58mRs3rwZAJCfn4+DBw8iPz8fycnJWLZsGUQiEQDg7bffxu7du1FYWIjCwkKF\nc5IGjVkzX2jMGhlQY81AcOlB44ouXNED4JYu+mTChAlwdnaWaTty5AjeeOMNAMAbb7yBw4cPAwAS\nExMRExMDa2treHt7w9fXFxkZGaiurkZTUxMiIiIAAAsXLpQcQ2EPjXciH3oPDQc11gxEXl6esUXQ\nGVzRhSt6ANzSxdDcuXMHbm5uAAA3NzfcuXMHAFBVVQWBQCDpJxAIUFlZqdDO5/NRWVlpWKF1DCnT\n6KTISRKkjCkpcuoLrWuDrlmzBkePHoWNjQ18fHzw1VdfwcnJSabPzZs38dprr0m2i4uL8cEHH2Dl\nypWoq6vDvHnzcPv2bXh7e+OHH35A//79tdfExGlsbDS2CDqDK7pwRQ+AW7oYEx6PBx6Pp9NzLl++\nHF5eXgAAR0dHBAcHS148Yo8o3dbv9kD/UABAU1E2AMDBZ4Ret8UY6nri7fpb2cg4X4fpUybpdPzo\ntvLtvLw8ye9vWVkZ3nzzTegDnkgchKEhqampmDx5MiwsLLB+/XoAkMR6MNHd3Q0+n4+LFy/C09MT\na9euxcCBA7F27Vps2bIFDx48UDg+LS0NI0eO1EY8k2PLli1Yt26dscXQCVzRhSt6ANzSJSsrC5Mn\nT9bb+UtLSxEVFSXxRgYEBOD333+Hu7s7qqur8fzzz+PGjRuS3yPx79vUqVPx/vvv46mnnsLzzz+P\n69evAwD279+P06dP4z//+Y/CtUj5DTt79qzBPRfiWCdNptG0lfPG3RasPFKg8XHacmltz/M76qM0\ng10TAPrZWGLX7AAMtLdhfUxv7r0291BbjPGMaoO+fr+0ngYVCoWwsOg5fPTo0aioqFDZ/8SJE/Dx\n8YGnpycA5XEiXKWsrMzYIugMrujCFT0AbuliaGbMmIGvv/4aAPD1119j1qxZkvYDBw6gvb0dJSUl\nKCwsREREBNzd3eHo6IiMjAyIRCLs27dPcgyFPTTeiXzoPTQcWnvWpImKikJMTAzmz5+vtE9sbCxG\njRqFZcuWAQCcnZ3x4MEDAIBIJIKLi4tkW0xammG/SigUimmgyZfpwoULERMTg5deeklt35iYGJw+\nfRq1tbVwc3PDhg0bMHPmTMydOxdlZWUKIRmbNm3Cnj17YGVlhe3bt+PFF18E0JO6Y9GiRXj48CGm\nTZumdEUcKZ41rkM9axRDoS/PmkpjTSgUoqamRqF906ZNiIqKAgBs3LgRWVlZOHTokNKLtLe3g8/n\nIz8/H66urgBkjTUAcHFxQV1dndaKUCgU86StrQ0HDx7EsWPH8Oyzz2LJkiWwt7c3tlgAqLFmKlBj\njWIojDINmpqairy8PIV/YkNt7969SEpKwnfffafyIsePH0dYWJjEUAN6Vl2JDcHq6moMGjSot7pQ\nKBQz5P79+yguLoaTkxPc3NwQGxtrbJGIg+ZZM19onjUy0Ho1aHJyMrZu3YrTp0/D1tZWZd/9+/cj\nJiZGpk0cJ7Ju3TqZOBEKhULRhI8//hjLli2Dj48PAEjiYimmDY11Ih96Dw2H1gsMVqxYgebmZgiF\nQoSGhkpi0aqqqjB9+nRJv5aWFpw4cQLR0dEyx69fvx6pqanw9/fHyZMnJSuuKBQKRRMmTZokMdSO\nHTuGcePGGVki8iBhlR1AjpwkQcqYkiKnvtDaWCssLMTt27dx5coVXLlyBQkJCQAADw8PHDt2TNLP\n3t4etbW1cHBwkDnexcUFJ06cQEFBAVJSUhRyrCUnJyMgIAB+fn7YsmWLtmLqjfLycjz//PMYOnQo\nhg0bJnEFk1xnsKurC6GhoZJpblJ1qa+vx5w5cxAYGIigoCBkZGQQq0t8fDyGDh2K4OBgzJ8/H21t\nbUToou8anG1tbZg3bx78/Pzw5z//Gbdv3wYApKen6103CoVCMTQmWcGgq6sLf/3rX5GcnIz8/Hzs\n379fktPIVLC2tsYnn3yCa9eu4cKFC/j8889x/fp1ousMbt++HUFBQZKkoKTqsmrVKkybNg3Xr19H\nbm4uAgICiNSltLQU//3vf5GVlYW8vDx0dXXhwIEDROii7xqcu3fvxoABA1BYWAh/f38sWrQIJ0+e\nlFQfoGgGjVkzX2jMGhmYpLF28eJF+Pr6wtvbG9bW1njttdeQmJhobLFkcHd3x4gRPVmj+/Xrh8DA\nQFRWVhJbZ7CiogJJSUlYsmSJ5EVJoi4NDQ1IT0+XBJlbWVnBycmJSF0cHR1hbW2N1tZWdHZ2orW1\nFR4eHkToou8anNLn+vnnn5GZmYkbN27g008/1ateFN1Bc3SRD72HhsMkjbXKykqZIGFxTT5TpbS0\nFFeuXMHo0aOJrTP4t7/9DVu3bpUkOgbIrJlYUlICV1dXLF68GCNHjsTSpUvR0tJCpC4uLi74+9//\nDi8vL3h4eKB///4QCoVE6gLo9nmS/o2oqqpCnz59UFZWhu3btxtKHU5BSjwQKXKSBCljSoqc+sIk\njTVd1+bTJ83NzZg9eza2b9+uEJenjzqD+uDo0aMYNGgQQkNDoSztHim6dHZ2IisrC8uWLUNWVhbs\n7e0VypiRoktRURE+/fRTlJaWoqqqCs3Nzfj2229l+pCiizy6lHvbtm2ws7PDK6+8gnnz5unknBQK\nhWJKmKSxxufzUV5eLtkuLy+X+cI2FTo6/n979x5WVZU/fvwNgtdU1BIUMBJQwAviIFpNZZlyMdEx\nNc3USSzHUqMsdZz5zs96JkWbmpk0/ZqaOfkVLZtEC8mgLKXwEl1INFEhLiKmiKigh8v+/eFwRhQU\ngX3OXuzP63l6cp+zzj6fvdc6m3XW+py1y3j00UeZNGmSdemR2taPu/aYcnNz8fDwwN3dvdqtunJz\nc3F3d7fhUcDXX3/Ntm3buOuuu5gwYQKff/45kyZNUvJYPDw88PDwYMCAAQCMGTOG1NRU3NzclDuW\nAwcOcM8999CpUyecnJwYPXo033zzjZLHAo3z2ai6Dri7u1tvsRUQEMClS5cYOHAgPXv2tNXhNCmS\ns2ZekrOmBkN21oKDg8nIyCArKwuLxcLmzZuJjIy0d1jVaJpGVFQUAQEBREdHWx9X8T6DixYtIicn\nh8zMTDZt2sRDDz3Ee++9p+SxuLm54enpyZEjV1YrT0xMpFevXowYMUK5Y/Hz8yMlJYXS0lI0TSMx\nMZGAgAAlj6UqvobGPXLkyOv2FRsbS/PmzRk7dixjx461+XGJ+pF8J/VJHdpOvRfF1ZOTkxPLly8n\nNDSUiooKoqKi8Pf3t3dY1SQnJ7Nhwwb69u1LUFAQcGX5gfnz5zNu3DjWrl1rvc8gXPn2P27cOAIC\nAnBycmLFihXWaaAVK1ZUu89gWFiY3Y4L/jsNreqxLFu2jIkTJ2KxWPD29mbdunVUVFQodyyBgYFM\nnjyZ4OBgHB0d6d+/P08//TTnz583/LFcfQ9OT09PXnnllUZtT1FRUUyaNAlfX19cXFxYsWIFI0eO\nrDYSJ+pOlXwgVeJUiSrnVJU49dIoN3IXQgh7eeqpp2jevDlvvfUWzzzzjHXNRyOQe4Mag9wbVNiK\nXe4NKoQQRnfbbbdZf2XaqlUrO0ejJslZMy/JWVODIadBhRCirm6//XZ2797NnDlzqi09I4xNcp3U\nJ3VoO9JZE0Io7U9/+hOHDx+msrKSgIAAe4ejJFXygVSJUyWqnFNV4tSLdNaEEEqbMGECAKWlpQB2\nuQOIEELoSeYMhBBKi42NJTY2lo8++oj777/f3uEoSXLWzEty1tQgI2tCCKUdPHgQBwcHysrKOHjw\noL3DEXUk+U7qkzq0HemsCSGUtmXLFgBatGghfzzqSZV8IFXiVIkq51SVOPUinTUhhNKCg4Ot/87N\nzSU3N5fhw4fbMSIhhGhckrMmhFDamjVrOHToEIcPH2bNmjWcPn3a3iEpR3LWzEty1tQgI2tCCKX5\n+fnx4osvAvDrr78yZcoUO0ck6kKmrNUndWg70lkTQigvKioKBwcH650MxK1RJR9IlThVoso5VSVO\nvUhnTQihtFdffZXc3FxcXFxo0aKFvcMRQohGJzlrQgilRUdH8/LLL9OuXTtmzZpl73CUJDlr5iU5\na2qQkTUhhNIcHR258847AXBxcbFzNKKuJN9JfVKHtiMja0IIpbVo0YL09HSWLVvG2bNn7R2OklTJ\nB1IlTpWock5ViVMvMrImhFCWpmmMGTOG06dPo2kazzzzjL1DEkKIRicja0IIZTk4OPDFF18QHh5O\nREQEzZo1s3dISpKcNfOSnDU1GHpkLSkpyd4hCCHsYMiQIXUqFxcXR1xcHJ9++ikdO3YE4IMPPqjX\ney5evJgNGzbg6OhInz59WLduHRcvXuSxxx7jl19+wcvLi/fff9+aF7d48WLeeecdmjVrxptvvsmw\nYcPq9b5mJflO6pM6tB1Dd9YA+vfvb+8Q7GbJkiXMmzfP3mHYhRy7OY8dIDU1tc5lExISSE5OZsaM\nGaxcubLe75mVlcXq1as5dOgQLVq04LHHHmPTpk0cPHiQoUOHMnfuXJYsWUJMTAwxMTGkp6ezefNm\n0tPTycvL4+GHH+bIkSM4Oqo5WaFKPpAqcapElXOqSpx6UfPKIoQQQHZ2Np988gnZ2dnEx8cTHx9f\nr/20a9cOZ2dnSkpKKC8vp6SkhK5du7Jt2zbrHRGmTJnC1q1bgSsjehMmTMDZ2RkvLy98fHzYt29f\nox2XEEJczfAja2aWnZ1t7xDsRo5d1MXYsWM5ffo048aN49dff633fjp27MicOXPo1q0brVq1IjQ0\nlKFDh1JQUGC9K4KrqysFBQUAnDhxgkGDBllf7+HhQV5eXo37fvbZZ+nWrRtwpVPYp08f6yhBVR6O\nvberHrPl+7/55ptkZWUxevToOr9+5cqV9Tp/t/cIAuD8se8BaOvdT9ftKrZ6v6rtoqPfs/ebQoY/\nPLjO5yctLY0ZM2bc0vms2n7hhRcAeOONN+r1+lvZvrat6v1+t3L+iouLgSvX7qioKPTgoGmapsue\nG0FSUpKpp0FXrlxp/RCZjRy7OY8drkyD1jVnrbEcO3aMESNGsHv3btq3b8/YsWN59NFHmTVrVrXl\nQDp27EhhYSGzZs1i0KBBTJw4EYBp06YRERHB6NGjq+1XlWvYnj17lJhmqm+ch09dZPa2IzpEVLMD\nc6+03+Clts27vq15M95+1I/b2zSv82uaet3bml7XL5kGNTAz/8GWYxe2dODAAe655x46deqEk5MT\no0eP5ptvvsHNzY2TJ08CkJ+fT+fOnQFwd3cnJyfH+vrc3Fzc3d3tEntjUOGPIKgTp0pUOaeqxKkX\n6awJIUzPz8+PlJQUSktL0TSNxMREAgICGDFiBOvXrwdg/fr1jBo1CoDIyEg2bdqExWIhMzOTjIwM\nQkJC7HkIQogmTDprBmbmdWXk2IUtBQYGMnnyZIKDg+nbty8ATz/9NPPnz+ezzz6jR48efP7558yf\nPx+AgIAAxo0bR0BAAOHh4axYsQIHBwd7HkKDyDpr5iXrrKlBfmAghBDA3LlzmTt3brXHOnbsSGJi\nYo3lFyxYwIIFC2wRWpPUkDW6LBWVnL9cXufyjgp3pI1M1lmzHd06a1OnTuWTTz6hc+fOpKWl1Vhm\n9uzZ7Nixg9atW/Puu+8SFBSkVzhKMvMcvRy7ELajSpurivPC5Qrm7zhGUWndOmxlFZV6hqU01ere\nrHSbBn3yySdJSEio9fn4+HiOHj1KRkYGb7/9dr2Tqjdu3MiaNWvqVDY2NpaysrJ6vY8QQgjjKL5U\nzrk6/ldSJp01oTbdOmv33XcfHTp0qPX5qxebHDhwIEVFRdY1jG7FreSJxMbGYrFYbvk96quysvoF\n4lZXSTHzHL0cuxC2Izlr5iU5a2qwW85aXl4enp6e1m0PDw9yc3OtC1BWudmCkkeOHOHo0aN89tln\nnDhxghdffJGRI0eyceNGVq5cSWVlJTExMbRs2ZLvvvuOsLAwJkyYQEBAAH/5y1+4fPkyjz/+OM89\n91y1Be+WL1/OBx98QElJCa+99hqDBw/m/fffZ8WKFbRr145+/foxbNgwtm7dSlpaGs2aNeOxxx7D\n29ubP//5z9xzzz0cOnSIrl27AnD69GkeeeQR7rrrrjovuFc1fWykBQBl2zYLlBopHlscb3JysnUx\nYL0WlRTGIvlO6pM6tB1dF8XNyspixIgRNeasjRgxgvnz53PvvfcC8PDDD7N06dJqC0jWZUHJjRs3\n8uWXX7Jq1SqSkpJITExk7ty5PP3003zwwQdcvHiRCRMmsG3bNuvP7Vu3bk1paSmtWrWisrKSYcOG\n8cknn9CiRQvrfque//XXX5k6dSrbt29n8uTJvPjii/Tt2xdN0zh16hRRUVF8/PHH5OTkEB0dzYcf\nfkhQUBAfffQRXl5eLFmyBE3TrL8iE3UzZcoULBYL7777brV6EU2fPRbF1Ysqi+KqprCkjBkfHeZs\nHXPWbM1ei+I2b+bAq6He1PWPepvmzfC9vbWuMZmNXtcvu42sNdaikg4ODgQGBgIQFBTEqlWryMzM\n5PDhw0RGRgJw5syZ6173/fff89prr1FWVkZ2djanT5+u9v6bN29my5YtODo6curUKeDKLWaqftbv\n4OBATk4OvXv3BsDT05Nz584B4OLigpeXl3Vf8sOJW/fZZ59x6dKl66aShRBC1MxSofFS/NE6lw/v\n2Ynn7+umY0SisdhtnbXIyEj+9a9/AZCSkoKLi8t1U6B1oWkaP/74IwDfffcd3t7eeHl50atXL7Zt\n28a2bdv48ssvAXB2dqa8/Mo3sWXLlvHGG28QFxdHly5drssnW716Ndu3b2fNmjXWDoO7u7v1vTRN\no1u3bqSlpaFpGtnZ2bi4uADg6Fj9tNZ3/SUzz9GbuZNm5noX9iE5a+YlOWtq0G1kbcKECXz55Zec\nPn0aT09PXn75ZesvMadPn05ERATx8fH4+PjQpk0b1q1bV6/3cXBwwGKxMHbsWEpKSli9ejUdO3Zk\n9OjRPPLIIzRr1oyAgAAWL15MWFgYU6dOJTIykhEjRvDEE08QEBBA27Ztr9vvoEGDCAsLIzg4mNtu\nuw2AhQsXEh0djaZp9OvXj1deeYWIiAhCQ0NxdHRk6dKltcYohBDivyTfSX1Sh7YjN3IXhtS1a1cu\nXbpEXl4erVq1snc4woYkZ03cjOSsNQ6ZBm18ciN3IYQQQggTks6agZl5jl5y1oSwHclZMy/JWVOD\n3BtUCCGEzUm+k/qkDm1HRtYMzMz3Qrv2F7VmYuZ6F/ahSptTJU6VqHJOVYlTL+b9iyiEEEIIoQDp\nrBmYmefoJWdNCNuRnDXzkpw1NUjOmhBCCJuTfCf1SR3ajoysGZiZ5+glZ00I21GlzakSp0pUOaeq\nxKkX8/5FFEIIIYRQgHTWDMzMc/SSsyaE7UjOmnlJzpoaJGdNCCGEzUm+k/qkDm1HRtYMzMxz9JKz\nJoTtqNLmVIlTJaqcU1Xi1It5/yIKIYQQQihAOmsGZuY5eslZE8J2JGfNvCRnTQ2SsyaEEMLmJN9J\nfVKHtiMjawZm5jl6yVkTwnZUaXOqxKkSVc6pKnHqRbe/iAkJCfj5+eHr68uSJUuue/706dOEhYXR\nr18/evfuzbvvvqtXKEIIIYQQytKls1ZRUcHMmTNJSEggPT2d2NhYDh06VK3M8uXLCQoK4vvvv2fX\nrl3MmTOH8vJyPcJRlpnn6CVnTQjbkZw185KcNTXokrO2b98+fHx88PLyAmD8+PHExcXh7+9vLdOl\nSxd+/PFHAIqLi+nUqRNOTpJCJ4QQZiD5TuqTOrQdXUbW8vLy8PT0tG57eHiQl5dXrcxTTz3FwYMH\n6dq1K4GBgfzzn//UIxSlmXmOXnLWhK0VFRUxZswY/P39CQgIYO/evRQWFjJ06FB69OjBsGHDKCoq\nspZfvHgxvr6++Pn5sXPnTjtG3nCqtDlV4lSJKudUlTj1ostQloODw03LLFq0iH79+rFr1y6OHTvG\n0KFD+eGHH2jbtm21cs8++yzdunUDoF27dvTp08daaVXDorLdNLcBvv76a4YMGWKIeGRbn22AMwhp\nSgAAIABJREFU5ORksrOzAYiKisIennvuOSIiItiyZQvl5eVcvHiRV199laFDhzJ37lyWLFlCTEwM\nMTExpKens3nzZtLT08nLy+Phhx/myJEjpv6SIYTQj4OmaVpj7zQlJYWFCxeSkJAAXPkG6ujoyLx5\n86xlIiIi+NOf/sS9994LwJAhQ1iyZAnBwcHWMklJSfTv37+xw1PGnj17TPttws3NDYvFQl5eHq1a\ntbJ3ODZl5noHSE1NtXbQbeXcuXMEBQVx/Pjxao/7+fnx5Zdf4urqysmTJxk8eDCHDx++7poWFhbG\nwoULGTRoULXXq3INs0ebq8p1upWptKo4C0vKmPHRYc6WGjPP+cDcK+03eGmSnSO5sfCenRjgkF3v\nuq9PHdaXKtdFva5fuoysBQcHk5GRQVZWFl27dmXz5s3ExsZWK+Pn50diYiL33nsvBQUF/Pzzz3Tv\n3l2PcIQQ4oYyMzO54447ePLJJ/nhhx/4zW9+wz/+8Q8KCgpwdXUFwNXVlYKCAgBOnDhRrWNWU6pH\nFRVmB6rY8v1nz57Nnj17qv0Rvtnr09LSAAjoPxCA88e+B6Ctdz9DbVcxSjy1bWelHaClQ0G96/Pa\nLyJGac+23E5LS6O4uBiA7Oxs3WYGdBlZA9ixYwfR0dFUVFQQFRXFH//4R1atWgXA9OnTOX36NE8+\n+STZ2dlUVlbyxz/+kccff7zaPlT5VioaX9euXbl06ZIpR9bMzh4jawcOHODuu+/m66+/ZsCAAURH\nR9O2bVuWL1/O2bNnreU6duxIYWEhs2bNYtCgQUycOBGAadOmERERwejRo6vtV65h+pCRtcYR3rMT\nz9/Xzd5hNClKjawBhIeHEx4eXu2x6dOnW/99++23s337dr3eXggh6szDwwMPDw8GDBgAwJgxY1i8\neDFubm6cPHkSNzc38vPz6dy5MwDu7u7k5ORYX5+bm4u7u7tdYhdCNH2SDWtgZl5XRtZZE7bk5uaG\np6cnR44cASAxMZFevXoxYsQI1q9fD8D69esZNWoUAJGRkWzatAmLxUJmZiYZGRmEhITYLf6GknXW\nzEvWWVODLGwmhBDAsmXLmDhxIhaLBW9vb9atW0dFRQXjxo1j7dq1eHl58f777wMQEBDAuHHjCAgI\nwMnJiRUrVtTpV/Div2SNLvVJHdqOdNYMTIVfvujFzEsgmLne7SkwMJD9+/df93hiYmKN5RcsWMCC\nBQv0DssmVGlzqsSpElXOqSpx6sW8fxGFIZWXl1NcXEzV716Ki4spKyuzc1RCCCGE/UhnzcDMOEd/\n4MABvLy8uHz5MgD+/v4kJRn7F1WNzYz1LuxLctbMS3LW1CDToEIIIWxO8p3UJ3VoOzKyZmBmnqM3\nc7K2metd2IcqbU6VOFWiyjlVJU69SGdNCCGEEMLApLNmYGaeo9fpxhpKMHO9C/uQnDXzkpw1NUjO\nmhBCCJuTfCf1SR3ajoysGZiZ5+glZ00I21GlzakSp0pUOaeqxKkX6awJIYQQQhiYdNYMzMxz9JKz\nJoTtSM6aeUnOmhokZ00IIYTNSb6T+qQObUdG1gzMzHP0krMmhO2o0uZUiVMlqpxTVeLUi3TWhBBC\nCCEMTDprBmbmOXrJWRPCdiRnzbwkZ00NuuWsJSQkEB0dTUVFBdOmTWPevHnXldm1axfPP/88ZWVl\n3H777ezatUuvcIQQQhiI5DupT+rQdnTprFVUVDBz5kwSExNxd3dnwIABREZG4u/vby1TVFTEs88+\ny6effoqHhwenT5/WIxSlmXmO3sHBwbSja2aud2EfqrQ5VeJUiSrnVJU49aLLNOi+ffvw8fHBy8sL\nZ2dnxo8fT1xcXLUyGzdu5NFHH8XDwwOA22+/XY9QhBBCCCGUpsvIWl5eHp6entZtDw8P9u7dW61M\nRkYGZWVlPPjgg5w/f57nnnuOSZMmXbevZ599lm7dugHQrl07+vTpY+1hV81hN9XtlStXmup49+zZ\nQ3p6OlBzzpoR4rPFdtVjRonHFsebnJxMdnY2AFFRUQjb2rNnj81HLqpynW5lKs0ecTZ1DTmn9anD\n+jJ73TtoOsw1ffjhhyQkJLB69WoANmzYwN69e1m2bJm1zMyZM0lNTSUpKYmSkhLuvvtuPvnkE3x9\nfa1lkpKS6N+/f2OHpwwzNs6UlBQiIiKqPbZx40bCwsLsFJHtmbHer5aamsqQIUPsHUajUOUapkqb\nq4qzsKSMGR8d5mxpub1DqtGBuVfab/DSJDtHcmPhPTsxwCFbqbo3Or2uX7qMrLm7u5OTk2PdzsnJ\nsU53VvH09OT222+nVatWtGrVivvvv58ffvihWmfN7FRomHqRnDUhbMcIbS6rsJTS8soblunUI4hD\npy7SzMGByzcpK+rGCHVfF6rEqRddOmvBwcFkZGSQlZVF165d2bx5M7GxsdXKjBw5kpkzZ1JRUcHl\ny5fZu3cvL7zwgh7hCCGEMLiEI2f490+/2jsMIQxJlx8YODk5sXz5ckJDQwkICOCxxx7D39+fVatW\nsWrVKgD8/PwICwujb9++DBw4kKeeeoqAgAA9wlGWmdeVMeuoGpi73oV9qLLO2vlj3+sUjXnJOmtq\n0G2dtfDwcMLDw6s9Nn369GrbL774Ii+++KJeIQghhDAoWaNLfVKHtiN3MDAwM8/Ry71BhbAdVdpc\nW+9+9g6hyVGl7lWJUy/SWRNCCCGEMDDprBmYmefoJWdNCNuRnDXzkpw1NeiWsybErfrb3/7G3/72\nt+se//3vf8+0adP461//aoeohBB6kHwn9Ukd2o6MrBmY2eboy8vLsVgsQPWcNYvFQnm5MRe/1IPZ\n6l3YnyptTnLWGp8qda9KnHqRzpoQQvxHRUUFQUFBjBgxAoDCwkKGDh1Kjx49GDZsGEVFRdayixcv\nxtfXFz8/P3bu3GmvkIUQJiCdNQMz8xy95KwJe/jnP/9JQECAdWQ3JiaGoUOHcuTIEYYMGUJMTAwA\n6enpbN68mfT0dBISEnjmmWeorFR3RX3JWTMvyVlTg3TWhBACyM3NJT4+nmnTplm/LGzbto0pU6YA\nMGXKFLZu3QpAXFwcEyZMwNnZGS8vL3x8fNi3b5/dYlfR7NmzJedJcVKHtiM/MDAwM8/Ry71Bha09\n//zzvPbaaxQXF1sfKygowNXVFQBXV1cKCgoAOHHiBIMGDbKW8/DwIC8vr8b9Pvvss3Tr1g2Adu3a\n0adPH2sdV40WyPaV7aqRs6rctGu3qx6r7XmjbF8dqxHiqW07K+0AA/p2tsZr7/q/0fZvf/tbQ8VT\ntZ2Wlma9ZmRnZxMVFYUeHDQD/0VMSkqif//+9g5D2EhMTAxLly4Fru+sPf3009YpKNG0paamMmTI\nEJu+58cff8yOHTt466232LVrF6+//jrbt2+nQ4cOnD171lquY8eOFBYWMmvWLAYNGsTEiRMBmDZt\nGhEREYwePbrafuUaVnf/m5LbZO4NemDulfYbvDTJzpHcWJe2zRndu/PNC/5HYJfb8OrYSseI1KfX\n9UtG1gxsz549ph1lMfB3CN2Zud7t5euvv2bbtm3Ex8dz6dIliouLmTRpEq6urpw8eRI3Nzfy8/Pp\n3PnKHzZ3d3dycnKsr8/NzcXd3d1e4TeYPdpcVa7TrUyjXT2qJhou/7yFmA0f1/mc/r+H76rWWatP\nHdaX2a+LkrMmhDC9RYsWkZOTQ2ZmJps2beKhhx7ivffeIzIykvXr1wOwfv16Ro0aBUBkZCSbNm3C\nYrGQmZlJRkYGISEh9jwE5Ui+k/qkDm1HRtYMzMzfIiRnTdhT1a9B58+fz7hx41i7di1eXl68//77\nAAQEBDBu3DgCAgJwcnJixYoVSt/PVpU2J6NqjU+Vc6pKG9WLdNaEEOIqDzzwAA888ABwJUctMTGx\nxnILFixgwYIFtgxNCGFSMg1qYGZeV8aso2pg7noX9iHrrJlXQ86prLNmOzKyJoQQwuYk10l9Uoe2\no9vIWkJCAn5+fvj6+rJkyZJay+3fvx8nJyf+/e9/6xWKssw8R69y/k9DmbnehX2o0uZUya9SiSrn\nVJU2qhddOmsVFRXMnDmThIQE0tPTiY2N5dChQzWWmzdvHmFhYaae9hJCCCGEqI0unbV9+/bh4+OD\nl5cXzs7OjB8/nri4uOvKLVu2jDFjxnDHHXfoEYbyzDxHb+bOu5nrXdiH5KyZl+SsqUGXnLW8vDw8\nPT2t2x4eHuzdu/e6MnFxcXz++efs37+/1mkvM9+qJS0tzVDx6L2dnZ3Njdg7Plttm/F4k5OTrfWv\n1+1ahLFIvpP6pA5tR5fbTX344YckJCSwevVqADZs2MDevXtZtmyZtczYsWN58cUXGThwIL///e8Z\nMWIEjz76aLX9yK1azEVuNyXAPreb0otcw+pObjdlfP/v4bu418vF3mEYmlK3m7r2Viw5OTl4eHhU\nK/Ptt98yfvx4AE6fPs2OHTtwdnYmMjJSj5CEwU2YMIHdu3fX+vx7773Hjz/+SHx8vA2jEkIIIexP\nl5y14OBgMjIyyMrKwmKxsHnz5us6YcePHyczM5PMzEzGjBnDypUrpaN2DTPN0Z89e5aSkhLr9rUD\nvqWlpRQWFto6LLswU70LY5CcNfOSnDU16DKy5uTkxPLlywkNDaWiooKoqCj8/f1ZtWoVANOnT9fj\nbYUQQihC8p3UJ3VoO7otihseHk54eHi1x2rrpK1bt06vMJRm5nVl5N6gQtiOKm1OlTXBVKLKOVWl\njepFbjclhBBCCGFg0lkzMDPP0Zt1VA3MXe/CPiRnzbwkZ00Ncm9QIYQQNif5TuqTOrQdGVkzMDPP\n0cu9QYWwHVXanCr5VSpR5Zyq0kb1Ip01IYQQQggDk86agZl5jl5y1oSwHclZMy/JWVOD5KwJIYSw\nOcl3Up/Uoe3IyJqBmXmOXnLWhLAdVdqcKvlVKlHlnKrSRvUinTVhV+Xl5WzdupWzZ8/etOyFCxfY\nunUrpaWlNohMCCGEMAbprBmYGeboLRYLU6dO5dixY9Ueryln7dSpU0ydOrVOHTuVmaHehbFIzpp5\nSc6aGiRnTQghhM1JvpP6pA5tRzprBmbmOXq5N6gQtqNKm1Mlv0olt3JOTxRfJr3gYp3Lu97mTKc2\nzesT1nVUaaN6kc6aEEIIIW5q9b4Tt1T+f0f70amNTsGYjOSsGZiZ5+jNOqoG5q53YR+Ss2ZeDTmn\nj5Ts5pGS3Y0YTe3Mfl2UkTUhhBA2J/lO6vu49X32DsE0ZGTNwMw8Ry/rrAlhO6q0OclZa3yqnFNV\n2qhedOusJSQk4Ofnh6+vL0uWLLnu+f/7v/8jMDCQvn37cu+99/Ljjz/qFYoQQggbO1tSRsH5y3X6\n7/RFC5fKKu0dshCGpcs0aEVFBTNnziQxMRF3d3cGDBhAZGQk/v7+1jLdu3fnq6++on379iQkJPD0\n00+TkpKiRzjK2rNnT5P+NlFUVMShQ4dqfO5GOWs//fQTLVq0oFOnTnqFZldNvd6NKCcnh8mTJ3Pq\n1CkcHBx4+umnmT17NoWFhTz22GP88ssveHl58f777+Pi4gLA4sWLeeedd2jWrBlvvvkmw4YNs/NR\n1J8ebe7nX0tYmHi81ucjLl7JdYpvc2UqrbIOaarnj32vzEiQKhpyTqvy1WwxHWr266IuI2v79u3D\nx8cHLy8vnJ2dGT9+PHFxcdXK3H333bRv3x6AgQMHkpubq0cowsC+/vprhg8ffsuvGz9+PJ9++qkO\nEQmzcnZ25u9//zsHDx4kJSWFt956i0OHDhETE8PQoUM5cuQIQ4YMISYmBoD09HQ2b95Meno6CQkJ\nPPPMM1RWysjQtSq12v/7uPV9fNz6Puu2UE9VHQr96dJZy8vLw9PT07rt4eFBXl5ereXXrl1LRESE\nHqEozczfIiRnTdiSm5sb/fpdGV247bbb8Pf3Jy8vj23btjFlyhQApkyZwtatWwGIi4tjwoQJODs7\n4+XlhY+PD/v27bNb/A2lSpuTUbXGp8o5VaWN6kWXadBb+UP7xRdf8M4775CcnFzj888++yzdunUD\noF27dvTp08daaVU/5ZVtNbdrmwKtzbVTo/aOX7YbZxsgOTmZ7OxsAKKiorCnrKw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- } - ], - "prompt_number": 150 - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "y = [(a >= i).sum() for i in range(1, 100)];" - ], - "language": "python", - "metadata": {}, - "outputs": [], - "prompt_number": 165 - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "y_ = -np.diff(y)\n", - "print y_\n", - "\n", - "print y;" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "[41264 5572 1638 646 313 181 101 70 48 47 22 14\n", - " 14 14 7 11 4 6 4 0 1 0 2 0\n", - " 0 1 2 1 3 0 2 2 1 0 1 1\n", - " 2 1 0 1 0 0 0 0 0 0 0 0\n", - " 1 1 0 0 0 0 0 0 0 0 0 0\n", - " 0 0 0 0 0 0 0 0 0 0 0 0\n", - " 0 0 0 0 0 0 0 0 0 0 0 0\n", - " 0 0 0 0 0 0 0 0 0 0 0 0\n", - " 0 0]\n", - "[50000, 8736, 3164, 1526, 880, 567, 386, 285, 215, 167, 120, 98, 84, 70, 56, 49, 38, 34, 28, 24, 24, 23, 23, 21, 21, 21, 20, 18, 17, 14, 14, 12, 10, 9, 9, 8, 7, 5, 4, 4, 3, 3, 3, 3, 3, 3, 3, 3, 3, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]\n" - ] - } - ], - "prompt_number": 166 - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "b = -2.3;" - ], - "language": "python", - "metadata": {}, - "outputs": [], - "prompt_number": 112 - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "np.sum([y_[i - 1] * np.log((i + 0.) ** b - (i + 1.) ** b) for i in range(1, 7)]) + y[-1] * np.log(7);" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "output_type": "pyout", - "prompt_number": 113, - "text": [ - "-13526.483069774908" - ] - } - ], - "prompt_number": 113 - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "y_;" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "output_type": "pyout", - "prompt_number": 114, - "text": [ - "array([48930, 940, 103, 19, 7, 1])" - ] - } - ], - "prompt_number": 114 - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "np.append(y_, y[-1]);" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "output_type": "pyout", - "prompt_number": 116, - "text": [ - "array([48930, 940, 103, 19, 7, 1, 0])" - ] - } - ], - "prompt_number": 116 - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "mc.Uninformative?" - ], - "language": "python", - "metadata": {}, - "outputs": [], - "prompt_number": 129 - } - ], - "metadata": {} - } - ] +{ + "metadata": { + "name": "More hacking with PyMC" + }, + "nbformat": 3, + "nbformat_minor": 0, + "worksheets": [ + { + "cells": [ + { + "cell_type": "code", + "collapsed": false, + "input": [ + "figsize(12.5, 4)\n", + "import scipy.stats as stats;" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 2 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Chapter 11 \n", + "___________\n", + "## More Hacking with PyMC\n", + "\n", + "This chapter introduces useful or advanced techniques with PyMC including building your own stochastic variables, user-defined steps etc." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "##### Example: Real-time Github Popularity Measures\n", + "\n", + "\n", + "Most of you are likely familar with the git-repository website Github. An observed phenomenon on Github is the *scale-ness* of the popularity of repositories. Here, for lack of a better measure, we use the numbers of *stars* and *forks* to measure popularity. This is not a bad measure, but it can ignore page-views, downloads and tends to overemphasize older repositories. Since we will be studying *all* repositories and not a single one, the absense of these measures is not as relevant. \n", + "\n", + "Contained in this folder is a Python script for scrapping data from Github on the popularity of repos. The script requires the `Requests` and `BeautifulSoup` libraries, but if you don't have that installed, provided in the `./data` folder is the same data from a previous date (Feburary 18, 2013 at last pull). The data is the fraction of repositories with stars equal to or greater than $2^k,\\; k = 0,...,15$ and the fraction of repositories with forks equal to or than $2^k,\\; k = 0,...,15$.\n", + " " + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "run github_datapull.py;" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Scrapping data from Github. Sorry Github...\n", + "The data is contained in variables `foo_to_explore` and `repo_with_foo`\n", + "\n", + "stars first...\n", + "number of repos with greater than or equal to 0 stars: 2738541" + ] + }, + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "\n", + "number of repos with greater than or equal to 1 stars: 1704779" + ] + }, + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "\n", + "number of repos with greater than or equal to 2 stars: 493529" + ] + }, + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "\n", + "number of repos with greater than or equal to 4 stars: 212099" + ] + }, + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "\n", + "number of repos with greater than or equal to 8 stars: 106973" + ] + }, + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "\n", + "number of repos with greater than or equal to 16 stars: 58101" + ] + }, + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "\n", + "number of repos with greater than or equal to 32 stars: 31877" + ] + }, + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "\n", + "number of repos with greater than or equal to 64 stars: 17370" + ] + }, + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "\n", + "number of repos with greater than or equal to 128 stars: 9239" + ] + }, + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "\n", + "number of repos with greater than or equal to 256 stars: 4578" + ] + }, + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "\n", + "number of repos with greater than or equal to 512 stars: 2150" + ] + }, + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "\n", + "number of repos with greater than or equal to 1024 stars: 872" + ] + }, + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "\n", + "number of repos with greater than or equal to 2048 stars: 286" + ] + }, + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "\n", + "number of repos with greater than or equal to 4096 stars: 84" + ] + }, + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "\n", + "number of repos with greater than or equal to 8192 stars: 22" + ] + }, + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "\n", + "number of repos with greater than or equal to 16384 stars: 5" + ] + }, + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "\n", + "number of repos with greater than or equal to 32768 stars: 1" + ] + }, + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "\n", + "\n", + "forks second...\n", + "number of repos with greater than or equal to 0 forks: 2738548" + ] + }, + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "\n", + "number of repos with greater than or equal to 1 forks: 334539" + ] + }, + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "\n", + "number of repos with greater than or equal to 2 forks: 159206" + ] + }, + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "\n", + "number of repos with greater than or equal to 4 forks: 74836" + ] + }, + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "\n", + "number of repos with greater than or equal to 8 forks: 36532" + ] + }, + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "\n", + "number of repos with greater than or equal to 16 forks: 17948" + ] + }, + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "\n", + "number of repos with greater than or equal to 32 forks: 8394" + ] + }, + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "\n", + "number of repos with greater than or equal to 64 forks: 3841" + ] + }, + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "\n", + "number of repos with greater than or equal to 128 forks: 1580" + ] + }, + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "\n", + "number of repos with greater than or equal to 256 forks: 605" + ] + }, + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "\n", + "number of repos with greater than or equal to 512 forks: 222" + ] + }, + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "\n", + "number of repos with greater than or equal to 1024 forks: 69" + ] + }, + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "\n", + "number of repos with greater than or equal to 2048 forks: 17" + ] + }, + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "\n", + "number of repos with greater than or equal to 4096 forks: 4" + ] + }, + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "\n", + "number of repos with greater than or equal to 8192 forks: 2" + ] + }, + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "\n", + "number of repos with greater than or equal to 16384 forks: 0" + ] + }, + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "\n", + "number of repos with greater than or equal to 32768 forks: 0" + ] + }, + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "\n" + ] + } + ], + "prompt_number": 1 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "plt.plot((stars_to_explore), repo_with_stars, label=\"stars\")\n", + "plt.plot((forks_to_explore), repo_with_forks, label=\"forks\")\n", + "plt.legend(loc=\"lower right\")\n", + "plt.title(\"Popularity of Repos (as measured by stars and forks)\")\n", + "plt.xlabel(\"$K$\")\n", + "plt.ylabel(\"number of repos with stars/forks $K$\")\n", + "plt.xlim(-200, 35000);" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "pyout", + "prompt_number": 3, + "text": [ + "(-200, 35000)" + ] + }, + { + "output_type": "display_data", + "png": 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Kzz//fK0BlQ87MBMA3njjDezevRvXr1/HqlWr8OKLL2p0l7mf+/2C9TC/gALV42ecnZ3R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\nRERERGbzX8VMdv/FLvLEAAAAAElFTkSuQmCC\n" + } + ], + "prompt_number": 3 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Clearly, we need to adjust the scale of this plot as most of the action is hidden. The number of repos falls very quickly. We will put it on a log-log plot." + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "plt.plot(log2(stars_to_explore + 1), log2(repo_with_stars + 1), 'o-', label=\"stars\")\n", + "plt.plot(log2(forks_to_explore + 1), log2(repo_with_forks + 1), 'o-', label=\"forks\",)\n", + "plt.legend(loc=\"upper right\")\n", + "plt.title(\"Log-Log plot of Popularity of Repos (as measured by stars and forks)\")\n", + "plt.xlabel(\"$\\log{K}$\")\n", + "plt.ylabel(\"$\\log$(number of repos with stars/forks < K )\");" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "pyout", + "prompt_number": 4, + "text": [ + "" + ] + }, + { + "output_type": "display_data", + "png": 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Tg3379mHu3Lkqj9d8EwkJCdiwYQPu3buHhw8fYvXq1fD3969y5gagYT9Vkagu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+ } + ], + "prompt_number": 4 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Both characteristics look like a straight line plotted on a log-log plot. What does this mean? Denote the fraction of repos with greater than or equal to $k$ stars (or forks) $P(k)$. So in the above plot, $\\log{P(k)}$ on the y-axis and $\\log{k}$ is on the x-axis. The above linear relationship can be written as:\n", + "\n", + "$$ \\log_2{P(k)} = \\beta\\log_2{k} + \\alpha$$\n", + "\n", + "rearranging by taking both sides to the power of 2:\n", + "\n", + "$$ P(k) = 2^\\alpha k^{\\beta} = C k^{\\beta}, \\;\\; C = 2^{\\alpha}$$\n", + "\n", + "This relationship is very interesting. It is called a *power-law*, and occurs very freqently in social datasets. Why does it occur so frequently in social datasets? It has much to do with a \"winner-take-all\" or \"winner-take-most\" effect. Winners in a power-law enviroment are components that seem take a disproportiante amount of the popularity, and keep winning. In term of popularity of repos, *winning repos* are repos that are very good quailty (intially are winners), and are shared/talked about often (keep winning). \n", + "\n", + "\n", + "The above plot is also telling us that the majority of repos have very few stars and forks, only a handful have hundreds, and an incredibly small number have thousands. This is not-so obvious after browsing Github's website, where you see some repos with 36000+ stars, but fail to see the millions that do not have any stars (as they are not popular, they won't be common on your tour of the site.)\n", + "\n", + "Distributions like this are also said to have *fat-tails*, i.e. the probability does not drop quickly as we extend into the tail of the dataset, but most of the probability is still centered near zero. \n", + "\n", + "\n", + "The heaviness of the tail and strength of \"winner-take-all\" effect are both influenced by the $\\beta$ parameter. The small the $\\beta$, the more pronounced these effects. Below is a list of distributions that follow a power-law and an approximate $\\beta$ exponent [1]. Recall though that *we never observe these numbers*, we must infer them from the data.\n", + "\n", + "\n", + "
PhenomenonAssumed Exponent
Frequency of word use-1.2
Number of hits on website-1.4
US book sales-1.5
Intensity of wars-0.8
New worth of Americans-1.1
Github Stars??
\n", + "\n", + "\n", + "\n", + "### The estimation problem\n", + "\n", + "It is very easy to *overestimate* the true paramter $\\beta$. This is because the tail events (the events of 500+ stars) are very rare. For example, suppose in our Github dataset we only observe 100 samples. With very high probability (about 30%), all of these samples will have less than 31 stars. This is because\n", + "approximately 99% ( Number of all repos - Number of repos with greater than 31 stars)/(Number of all repos) of all repos have less than 31 stars. Thus, we would have no samples in our dataset from the *tail* of the distribution. If I then told you that there existed a repo with 36000+ stars, you would call me crazy, as it would be about 1000 times larger than your observed most popular repo. You would assign a very large $\\beta$ exponent to your dataset (recall large $\\beta$ means thinner tails). Similarly, with the same 30% probability we would not see repos more popular than 64 stars if we had a sample of 1000. Taking this to its logical conclusion, how confident should we be that there might not exist a theoretical repo that can attain 72000+ stars, or 150000+ stars, one which would push an estimated $\\beta$ down even more. \n", + "\n", + "\n", + "### Yule-Simon distribution\n", + "\n", + "The \n", + "\n", + "\n", + "\n", + "\n", + "\n" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from scipy.special import beta\n", + "import pymc as pm\n", + "\n", + "\n", + "param = pm.Exponential(\"param\", 1)\n", + "\n", + "\n", + "@pm.stochastic(dtype=int, observed=True)\n", + "def yule_simon(value=repo_with_stars, rho=param):\n", + " \"\"\"test\"\"\"\n", + "\n", + " def logp(value, rho):\n", + " return np.log(rho) + np.log(beta(value, rho + 1))\n", + "\n", + " def random(rho):\n", + " W = stats.expon.rvs(scale=1. / rho)\n", + " return stats.geom.rvs(np.exp(-W))\n", + "\n", + "\n", + "model = pm.Model([param, yule_simon])\n", + "mcmc = pm.MCMC(model)\n", + "\n", + "mcmc.sample(10000, 8000);" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "ename": "TypeError", + "evalue": "yule_simon: computed log-probability [-20.51503062 -19.93158602 -18.31405136 -17.21386783 -16.32349938\n -15.53050299 -14.75010755 -13.96101721 -13.13877723 -12.2264853\n -11.23694781 -10.06769225 -8.63087616 -7.0237458 -5.33941252\n -3.44559118 -1.4738842 ] cannot be cast to float", + "output_type": "pyerr", + "traceback": [ + "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m\n\u001b[1;31mTypeError\u001b[0m Traceback (most recent call last)", + "\u001b[1;32m\u001b[0m in \u001b[0;36m\u001b[1;34m()\u001b[0m\n\u001b[0;32m 8\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 9\u001b[0m \u001b[1;33m@\u001b[0m\u001b[0mmc\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mstochastic\u001b[0m\u001b[1;33m(\u001b[0m \u001b[0mdtype\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mint\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mobserved\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mTrue\u001b[0m \u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m---> 10\u001b[1;33m \u001b[1;32mdef\u001b[0m \u001b[0myule_simon\u001b[0m\u001b[1;33m(\u001b[0m \u001b[0mvalue\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mrepo_with_stars\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mrho\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mparam\u001b[0m \u001b[1;33m)\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m 11\u001b[0m \u001b[1;34m\"\"\"test\"\"\"\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 12\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n", + "\u001b[1;32mc:\\Python27\\lib\\site-packages\\pymc\\InstantiationDecorators.pyc\u001b[0m in \u001b[0;36minstantiate_p\u001b[1;34m(__func__)\u001b[0m\n\u001b[0;32m 147\u001b[0m \u001b[1;32mdef\u001b[0m \u001b[0minstantiate_p\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0m__func__\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 148\u001b[0m \u001b[0mvalue\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mparents\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0m_extract\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0m__func__\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mkwds\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mkeys\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;34m'Stochastic'\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m--> 149\u001b[1;33m \u001b[1;32mreturn\u001b[0m \u001b[0m__class__\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mvalue\u001b[0m\u001b[1;33m=\u001b[0m\u001b[0mvalue\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mparents\u001b[0m\u001b[1;33m=\u001b[0m\u001b[0mparents\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;33m**\u001b[0m\u001b[0mkwds\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m 150\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 151\u001b[0m \u001b[0mkeys\u001b[0m \u001b[1;33m=\u001b[0m \u001b[1;33m[\u001b[0m\u001b[1;34m'logp'\u001b[0m\u001b[1;33m,\u001b[0m\u001b[1;34m'random'\u001b[0m\u001b[1;33m,\u001b[0m\u001b[1;34m'rseed'\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n", + "\u001b[1;32mc:\\Python27\\lib\\site-packages\\pymc\\PyMCObjects.pyc\u001b[0m in \u001b[0;36m__init__\u001b[1;34m(self, logp, doc, name, parents, random, trace, value, dtype, rseed, observed, cache_depth, plot, verbose, isdata, check_logp, logp_partial_gradients)\u001b[0m\n\u001b[0;32m 714\u001b[0m \u001b[1;32mif\u001b[0m \u001b[0mcheck_logp\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 715\u001b[0m \u001b[1;31m# Check initial value\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m--> 716\u001b[1;33m \u001b[1;32mif\u001b[0m \u001b[1;32mnot\u001b[0m \u001b[0misinstance\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mlogp\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mfloat\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m 717\u001b[0m \u001b[1;32mraise\u001b[0m \u001b[0mValueError\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;34m\"Stochastic \"\u001b[0m \u001b[1;33m+\u001b[0m \u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0m__name__\u001b[0m \u001b[1;33m+\u001b[0m \u001b[1;34m\"'s initial log-probability is %s, should be a float.\"\u001b[0m \u001b[1;33m%\u001b[0m\u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mlogp\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0m__repr__\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 718\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n", + "\u001b[1;32mc:\\Python27\\lib\\site-packages\\pymc\\PyMCObjects.pyc\u001b[0m in \u001b[0;36mget_logp\u001b[1;34m(self)\u001b[0m\n\u001b[0;32m 833\u001b[0m \u001b[0mlogp\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mfloat\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mlogp\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 834\u001b[0m \u001b[1;32mexcept\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m--> 835\u001b[1;33m \u001b[1;32mraise\u001b[0m \u001b[0mTypeError\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0m__name__\u001b[0m \u001b[1;33m+\u001b[0m \u001b[1;34m': computed log-probability '\u001b[0m \u001b[1;33m+\u001b[0m \u001b[0mstr\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mlogp\u001b[0m\u001b[1;33m)\u001b[0m \u001b[1;33m+\u001b[0m \u001b[1;34m' cannot be cast to float'\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m 836\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 837\u001b[0m \u001b[1;32mif\u001b[0m \u001b[0mlogp\u001b[0m \u001b[1;33m!=\u001b[0m \u001b[0mlogp\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n", + "\u001b[1;31mTypeError\u001b[0m: yule_simon: computed log-probability [-20.51503062 -19.93158602 -18.31405136 -17.21386783 -16.32349938\n -15.53050299 -14.75010755 -13.96101721 -13.13877723 -12.2264853\n -11.23694781 -10.06769225 -8.63087616 -7.0237458 -5.33941252\n -3.44559118 -1.4738842 ] cannot be cast to float" + ] + } + ], + "prompt_number": 83 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "def logp(value, rho):\n", + " return np.log(rho) + np.log(beta(value, rho + 1))\n", + "\n", + "beta(repo_with_stars, 1.3);" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "pyout", + "prompt_number": 84, + "text": [ + "array([ 3.96781274e-09, 7.12048348e-09, 3.60230434e-08,\n", + " 1.08508004e-07, 2.64859823e-07, 5.86390404e-07,\n", + " 1.28195491e-06, 2.82711390e-06, 6.44529816e-06,\n", + " 1.60819963e-05, 4.33570545e-05, 1.39960612e-04,\n", + " 5.90762159e-04, 2.95765600e-03, 1.59980669e-02,\n", + " 1.06728840e-01, 7.69230769e-01])" + ] + } + ], + "prompt_number": 84 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Exercises:\n", + "1. Distributions like the Normal distribution have very skinny tails. Compare the PDFs of the Normal versus a power-law distribution." + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "x = np.linspace(1, 50, 200)\n", + "plt.plot(x, exp(-(x - 1) ** 2), label=\"Normal distribution\")\n", + "plt.plot(x, x ** (-2), label=r\"Power law, $\\beta = -2$\")\n", + "plt.plot(x, x ** (-1), label=r\"Power law, $\\beta = -1$\")\n", + "plt.legend();" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "pyout", + "prompt_number": 20, + "text": [ + "" + ] + }, + { + "output_type": "display_data", + "png": 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oImJiYrztJHFxcWRkZDB27FjvaK7JZGL58uXs2LGD0aNHk5WVxaOPPkp1dbXf\n8WRnZzNv3jymTJlCdnY2u3fv5sorr2x1ji8xARw9epSxY8ee8Yw9e/YwceJEVqxYwTvvvMPLL7/M\nq6++SmxsrN/x+uOll15i2bJl5ObmsmDBAqqqqgL6PH8Z7i748WDdunWMHj36nK8vfuvvfPXAvzJg\nxiQscx9gzcodDBkxgEU1bqwmg3fvzwnqXzOIiIhI5yguLiYpKam7w5AWGhsbufbaa8nNzcVsNrc6\n9tZbb3HLLbd0U2Sdp728y8vLY9KkSX7fL2RHwOuqGgi3mLC73NTbO57jUkREREQCIywsjA0bNpxR\nfENw92F3pxApwFv0gDcV4FUVNuI0F3iPk5ub290hSAhRvoivlCsi3aPlNIdySogU4KdGwGPjPAV4\ndVXLAlxTEYqIiIhIaAiRAvzUCLjFaiYqJgy3y03vpl9raCaUnkOzFIg/lC/iK+WKiASTECnAPSPg\njro6AOLiPQV5jLtpMR4V4CIiIiISIkKkAD81Ag4Q28tTkEe7mlfDVAHeU6hPU/yhfBFfKVd6jmCe\n21l6rs7OuxApwE/1gAPemVDC7J7e7yqbesBFREQuBOHh4ZSWlqoQly5TV1fX5gwv5yMkVsI0R4QD\n4LI14nY6iW1qQbE0OAATlWpB6THUpyn+UL6Ir5QrPUdiYiI1NTUUFxcDmuZOAsvtdmM2m+nXr1+n\n3jckCnDDZMIcFYmzrh5nvc3bgoLNDpZwtaCIiIhcQGJiYoiJienuMETOWUi0oEDrPvD4pgLcUdMI\nQLVaUHoM9WmKP5Qv4ivlivhD+SKBFkIF+Kk+8IS+0QDUV9ZjuN1UagRcREREREJECBXgp0bAw8It\nxMZH4HK6ibQ7NQ1hD6I+TfGH8kV8pVwRfyhfJNBCqABvngvcMxNKYj9P71e03aECXERERERCRggV\n4K3nAk/s52lDibM7aXC6sTlc3RabdB713Yk/lC/iK+WK+EP5IoEWQgV467nAm0fAe7m0GqaIiIiI\nhI6QKcCtcZ4Rb0dlDQAJfZtaUBo9hXe1XsTsEdR3J/5QvoivlCviD+WLBFroFOAJvQBoLK8ETrWg\nhNns4HZrNUwRERERCQkhU4CHJcQDYC+tACAyKoyomDBMLjcRDpemIuwh1Hcn/lC+iK+UK+IP5YsE\nWggV4E0j4GWV3n2aCUVEREREQk3IFODWphHwxrIK777mAjymUQV4T6G+O/GH8kV8pVwRfyhfJNBC\npgAPS+wfb7bpAAAgAElEQVQNgL3lCHjTipjRdidVDeoBFxEREZHgd9YCfM2aNWRnZ5OVlcWCBQva\nPOeTTz5h1KhRXHrppVx33XWdHSNwqge8sbTcu8/bgqIR8B5DfXfiD+WL+Eq5Iv5QvkigWTo66HQ6\nefjhh1m7di3JyclcfvnlzJgxg6FDh3rPqaioYN68efztb38jJSWFkydPBiRQa2JzC8qpEfCEphHw\nGLuDKps9IM8VEREREelMHY6Ab9q0iczMTAYNGoTVamXmzJmsXr261TmvvfYa3/nOd0hJSQGgT58+\nAQnU2isOAHt5FW6np90kOjYca7gFq8tNbXVjQJ4rXUt9d+IP5Yv4Srki/lC+SKB1OAJeVFREamqq\ndzslJYWNGze2Omffvn3Y7Xauv/56qqur+ed//mfuueeeM+41b9480tLSAIiLi2P48OHeBG/+Vc/Z\ntq29YrFXVPPp3/6OJS6GCRMmEN8niq2bv6DIfRS+e4lf99O2trWtbW1rW9va1ra2fd3esWMHVVVV\nABQUFDB79mzOheF2u93tHVy5ciVr1qzhpZdeAmDp0qVs3LiR559/3nvOww8/TF5eHuvWraOuro5x\n48bx3nvvkZWV5T1n3bp1jB49+pwCbOmzq2ZSd6CACf9YTkxWOgDv/mU7e7Yd5UC/OBY/Ov68nyHd\nKzc315voImejfBFfKVfEH8oX8VVeXh6TJk3y+7oOW1CSk5MpLCz0bhcWFnpbTZqlpqZyww03EBkZ\nSWJiItdccw1fffWV34H4oq0XMfsPiAXAarNjd7oC8lwRERERkc7SYQE+ZswY9u3bR35+Po2Njbzx\nxhvMmDGj1Tk333wzubm5OJ1O6urq2LhxI8OGDQtIsM2L8djbWoyn0aGpCHsAjTiIP5Qv4ivlivhD\n+SKBZunwoMXCokWLmDJlCk6nk9mzZzN06FCWLFkCwNy5c8nOzmbq1KmMGDECk8nEnDlzAlaAd7gY\nj91Jlc1BYpQ1IM8WEREREekMHRbgANOmTWPatGmt9s2dO7fV9pNPPsmTTz7ZuZG1oa3l6OPiI3CZ\nDMKdLkorbWQkRAY8Dgkc9d2JP5Qv4ivlivhD+SKBFjIrYQKEJTa1oJSeGgE3TAbu6DAAjhVXd0tc\nIiIiIiK+CrEC/MwWFABLrygASo9WdXlM0rk04iD+UL6Ir5Qr4g/liwRaSBXg1jZaUAAim1bErDqm\nEXARERERCW4hVYA3T0PYsgUFoFd/z1SEDaW1XR6TdK7mSe9FfKF8EV8pV8QfyhcJtJAqwNsbAU/o\nF43dZOC2OaiutHVHaCIiIiIiPgmpArz5JczG00fAI6xUhnumHyw+UnHGdRI61Hcn/lC+iK+UK+IP\n5YsEWkgV4JbYaAyLGWdtHU5bg3d/bIT5VAFeWNne5SIiIiIi3S6kCnDDME6thll+asaT+AiLtwAv\nUQEe0tR3J/5QvoivlCviD+WLBFpIFeDQ9mqYceEWKiOaW1AqcTld3RKbiIiIiMjZhFwB7l0Ns0Uf\neHSYGYfZRJ3FjMPu5OTxmu4KT86T+u7EH8oX8ZVyRfyhfJFAC70CvHk1zBYj4GaTQWy4+sBFRERE\nJPiFXAFu9a6G2brIjoto0YZSqJlQQpX67sQfyhfxlXJF/KF8kUALuQLc+xJmWwV4uAXw9IGLiIiI\niASjECzAm0bAT5sLPC7cTFW4FcNkUHq8hgabozvCk/Okvjvxh/JFfKVcEX8oXyTQQq4At7bxEiZ4\npiJ0GwYRCVHghhKNgouIiIhIEAq5Aty7GmbZ6SPgnvYTc+8oQCtihir13Yk/lC/iK+WK+EP5IoEW\negV4Oz3gsRGeAtwZHwHAkUPlXRuYiIiIiIgPQq4Ab2shHoD4cDMA9bFNBXh+GQ67s2uDk/Omvjvx\nh/JFfKVcEX8oXyTQQq4Ab7kQj9vt9u6PaxoBr3Yb9EuKxWF3cSRfo+AiIiIiElxCrgA3R4ZjjorE\nbXfgrKnz7m8uwCsbHAzK6gNA/r6T3RKjnDv13Yk/lC/iK+WK+EP5IoEWcgU4QFjimW0ocU0tKNU2\nFeAiIiIiErxCsgD3TkXY4kXM+KYR8KoGJ8npvbGGmTl5rIbqSlu3xCjnRn134g/li/hKuSL+UL5I\noIVkAd68GI+9xVzgsU3TEFY3ODDMBqmDEwA4vF+j4CIiIiISPEKyAG9rMR6zySA6zIzLDTUNTjKa\n2lAOqQ0lpKjvTvyhfBFfKVfEH8oXCbSQLMBPLcbTei7w+AhPH3hVixcxD+8rxeVyIyIiIiISDEKz\nAG9uQTltLvDmNpQqm5NeiVHE947EVm/nWJGWpQ8V6rsTfyhfxFfKFfGH8kUCLUQL8PZGwJsLcAeG\nYWg2FBEREREJOiFZgHtXwyxtvdBO81SEVQ0OAAYNUQEeatR3J/5QvoivlCviD+WLBFpIFuBhib0B\naDx5WgHunYrQU4CnDU7AMBkcLaykvq6xa4MUEREREWlDSBbgkSn9Aag/UtJqf1xTD3ilzQlAeISV\ntMEJuF1u9u863rVByjlR3534Q/kivlKuiD+ULxJoIVmAhyf1xTCbaSg5ibO+wbu/eQS82ubw7sse\nkQTA7q+KuzZIEREREZE2hGQBbrJYiEgZALQeBY9rmoawsuFUAZ51SX9MZoPCg6XUVjcgwU19d+IP\n5Yv4Srki/lC+SKCFZAEOEJXmGdmuLzjq3RfXYhrCZhGRVjKy+uB2w94drVtWRERERES6WsgW4JFp\nAwGoa1GAt5yGsKXsHE+xvme72lCCnfruxB/KF/GVckX8oXyRQAvdAjzdU4C3OQLe0LoAvyi7Hxar\niaMFFVSW13ddkCIiIiIipwnZAvxUC8qpUe3Y5qXobQ7c7lPLz4eFW7hoaD8A9u7QKHgwU9+d+EP5\nIr5Srog/lC8SaGctwNesWUN2djZZWVksWLCg3fM2b96MxWJh1apVnRpgeyLTkwGoO1zk3RdmNhFp\nNeF0Q53d1er85tlQ9mxXH7iIiIiIdJ8OC3Cn08nDDz/MmjVr2LVrF8uXL2f37t1tnjd//nymTp3a\nauQ5kKJSzxwBh5YvYrZuQ8nI6kNYuIXjR6soO1HbJTGK/9R3J/5QvoivlCviD+WLBFqHBfimTZvI\nzMxk0KBBWK1WZs6cyerVq8847/nnn+f222+nb9++AQv0dNbEXpijInFU1WCvqPLu905FeFoBbrGa\nybrEs4DPrm1FiIiIiIh0B0tHB4uKikhNTfVup6SksHHjxjPOWb16NR999BGbN2/GMIw27zVv3jzS\n0tIAiIuLY/jw4d6fMJt7rfzdjkwfSM3uA3y0+l2iL0pjwoQJxIVbqD7wJbm5J8i+7YZW51962TB2\n5hWx+s2/4Qw/xrXXXn1ez9d252+37LsLhni0Hdzbyhdt+7rdvC9Y4tF2cG837wuWeLQdPNs7duyg\nqsoz8FtQUMDs2bM5F4a7g56RlStXsmbNGl566SUAli5dysaNG3n++ee959xxxx08+eSTjB07lvvu\nu4/p06fzne98p9V91q1bx+jRo88pwI7k3Tuf43/7ByNf+jUDpl8PwH99nM9HB8r58bXpTM5KaHW+\n2+3m/57/nJMlNdz03REMHTmw02OS85Obm+tNdJGzUb6Ir5Qr4g/li/gqLy+PSZMm+X2dpaODycnJ\nFBYWercLCwtJSUlpdc7WrVuZOXMmACdPnuSDDz7AarUyY8YMv4PxV2Qbi/HEtjMVIYBhGIy6Mp2/\nv7WTbV8UqAAPQvoLT/yhfBFfKVfEH8oXCbQOe8DHjBnDvn37yM/Pp7GxkTfeeOOMwvrgwYMcOnSI\nQ4cOcfvtt7N48eIuKb4BotLbWozn1FSEbRk2MonwCAtHCyo4VlQZ+CBFRERERFrosAC3WCwsWrSI\nKVOmMGzYMO68806GDh3KkiVLWLJkSVfF2K7m1TBbLcbTvBpmg7PNa6xhFi69zDOKv+2LggBHKP5q\n2X8ncjbKF/GVckX8oXyRQOuwBQVg2rRpTJs2rdW+uXPntnnun/70p86JykfNLSh1LaYibF6OvqLe\n3u51I8emsvXzfPZ8Vcy10y4mMiossIGKiIiIiDQJ2ZUwocUIeGExbpdn4Z3ekVYAyurbbkEB6N0n\nmowhfXA4XOzYoikJg4n67sQfyhfxlXJF/KF8kUAL6QLcEhVJWJ/euBvtNJScBCAxyjMCXlbX/gg4\nwKgrPVMifvlFAU6nq8NzRUREREQ6S0gX4ABRzUvSN/WBJ0Q1jYDX2TtclTNjSF8S+kZTVVHPzjyN\nggcL9d2JP5Qv4ivlivhD+SKBFvIFuHcqwsOeAjzSaibCYqLR6abO3v7ItmEyGD8xE4AvPj6A06FR\ncBEREREJvB5QgJ/qA2/WPApeepY2lCHDB5DYL4aqChtfaxQ8KKjvTvyhfBFfKVfEH8oXCbSQL8Db\nmgvc1z5wk8lg/MSLAM8ouEOj4CIiIiISYCFfgJ/eggKQ0DQTSnkHUxE2G3LpAPr0j6G60saOLUcC\nE6T4TH134g/li/hKuSL+UL5IoPWAAvzMEfDe3hcx25+KsJlhMhg/ydMLvvGTAzjsbS/gIyIiIiLS\nGUK+AI8Y2A/DbKah5CROWwPQeiYUX2QN60/fpFhqqhrI23A4YLHK2anvTvyhfBFfKVfEH8oXCbSQ\nL8BNFgsRyf3B7aa+sASAhMimHnAfWlDAMwp+zZSLAdjw0QGqK22BCVZERERELnghX4ADRGelA1Cz\n+wDQcgT87C0ozTKG9CFrWH/sjU4+/WBv5wcpPlHfnfhD+SK+Uq6IP5QvEmg9ogCPH+EZva7cvgfw\nvwWl2XU3ZWOxmNizvZiCA6WdG6SIiIiICD2kAI8bkQ1A1XbPyLW/LSjN4ntHMva6wQCse2e3lqjv\nBuq7E38oX8RXyhXxh/JFAq1HFODxOc0F+B7cbjdxERbMBlQ3OGn0s4i+/OoMeiVEUXq8hm16IVNE\nREREOlmPKMDDk/oS1qc39opq6guLMRkGvZvnAvejDxzAYjUz8duegj737/spO1nb6fFK+9R3J/5Q\nvoivlCviD+WLBFqPKMANwyCueRT8y9P6wP1sQwEYnN2PoSOTcNidvL9iOy61ooiIiIhIJ+kRBTi0\n9SKmb8vRt2fS9GHExkdQcqSSLz452DlBylmp7078oXwRXylXxB/KFwm0HlOAn/ki5rnNhNIsItLK\ntNuHA7Dh4wMUF1Z0QpQiIiIicqHrQQW4ZwS8+UXMUy0o/vWAt5R2USJjJgzC7XLz/ortNDac+73E\nN+q7E38oX8RXyhXxh/JFAq3HFOARA/u1ehGzuQAvP8cR8GYTvpVFn/4xlJfW8bdVX+N2uzsjXBER\nERG5QPWYAvz0FzF7N80FXnoOL2G2ZLGamX7XSMLCzezdUcLmzw6dd6zSPvXdiT+UL+Ir5Yr4Q/ki\ngdZjCnBo/SJm4jmuhtmWxL4x3PjdHAA++/AbDn1z4rzvKSIiIiIXph5VgLd8EfPUcvSd07edObQf\n4ydlghveff0ryks1P3ggqO9O/KF8EV8pV8QfyhcJtB5WgJ96ETM+wgxAeb0dVyf1bY+7/iIyh/aj\nweZg1Z+3UlfT0Cn3FREREZELR48qwCMG9iMs0fMipvPoMWLDzbjcUGXrnFFww2Qw7Y4R9BsYR3lp\nHSv/vJWGTrq3eKjvTvyhfBFfKVfEH8oXCbQeVYAbhkHcyFMvYja3oZR2UhsKQHiEhe/cexm9EqI4\ndrSKt5bm4bA7O+3+IiIiItKz9agCHE57EbNpMZ7y85wJ5XTRseHc/v0xRMeGU3iwjPfe2I5Ty9V3\nCvXdiT+UL+Ir5Yr4Q/kigdbzCvDRlwBQ9nkevc9zOfqO9EqI4vb7xhAeYWHfrmO8u/wrHA4V4SIi\nIiLSsR5XgCdcNRpTeBiVX+6mT2MdEJgCHKBvUiy333+qCF+9NA+72lHOi/ruxB/KF/GVckX8oXyR\nQOtxBbglKpKE8aPA7SZx59fA+S1HfzZJqb248wdXEBll5dA3J3nzla1asl5ERERE2tXjCnCAvpPG\nARC1JQ8I3Ah4s34D47hzzhVEx4ZTcKCMN17eRE2VLaDP7KnUdyf+UL6Ir5Qr4g/liwRajyzA+0wa\nD4B7Ux6G0xnwAhygT/9YZs65gviESI4VVbFs8RecKK4O+HNFREREJLT0yAI8OiOFqIvScFfXkHQk\nn7JOngWlPb37RPO9B8cxMK0X1ZU2lr/4BQf3atl6f6jvTvyhfBFfKVfEH8oXCbQeWYDDqTaUwXu/\n7rTl6H0RFR3Gd2dfTvaIJBobnKx6ZSsbPtqP29U5q3GKiIiISGjruQX4ZE8byuBvdmJzuKht7LrZ\nSSxWMzd9dwTjJ2UC8Pna/ax6ZSv1dY1dFkOoUt+d+EP5Ir5Srog/lC8SaGctwNesWUN2djZZWVks\nWLDgjOPLli0jJyeHESNGcNVVV7F9+/aABOqvhLE5mKMi6VNSRExlOSXVDV36fMNkMH5SJt+5d4x3\nhpRXnl/PkfyyLo1DRERERIJLhwW40+nk4YcfZs2aNezatYvly5eze/fuVucMHjyYzz77jO3bt/Pz\nn/+cH/7whwEN2Fem8DASrxkDQMY3Oymq7NoCvFnGkD7c8/B4klI9feGvv7SJTz/Yq0V72qG+O/GH\n8kV8pVwRfyhfJNA6LMA3bdpEZmYmgwYNwmq1MnPmTFavXt3qnHHjxhEfHw/A2LFjOXLkSOCi9VNz\nG0rGNzspquqeAhwgrlckM+dcwZXXDcYANv/jEEtfWM/xo1XdFpOIiIiIdA9LRweLiopITU31bqek\npLBx48Z2z//DH/7AjTfe2OaxefPmkZaWBkBcXBzDhw/3/oTZ3GvV2dtjJnpexKz7ZgvffPIJs0bO\nDOjzzrp9wwQGZ/dj0X+/xuGjNkpP1DLmqkG4I0uwWMxdH08QbrfsuwuGeLQd3NvKF237ut28L1ji\n0XZwbzfvC5Z4tB082zt27KCqyjOAWlBQwOzZszkXhtvtbnd6jpUrV7JmzRpeeuklAJYuXcrGjRt5\n/vnnzzj3448/Zt68eXz++ef07t271bF169YxevTocwrwfK2bfD/2r/ey4/tz+NF/3t8tMZzO3ujg\nHx/uI2/DYXB7RsgnzxjK4Ox+3R1at8vNzfUmusjZKF/EV8oV8YfyRXyVl5fHpEmT/L6uwxaU5ORk\nCgsLvduFhYWkpKSccd727duZM2cOb7/99hnFd3dL+t7NAPRft66bIznFGmZh4reH8r0Hx9EvKZaq\ninpWvZLHyv/bSumJmu4Or1vpLzzxh/JFfKVcEX8oXyTQOizAx4wZw759+8jPz6exsZE33niDGTNm\ntDqnoKCA2267jaVLl5KZmRnQYM9F5ndvoCEikn6HD3Lsy73dHU4rSSnx3P3QOK678WLCws0c2nuC\nPz/3Oeve2aUpC0VERER6qA4LcIvFwqJFi5gyZQrDhg3jzjvvZOjQoSxZsoQlS5YA8O///u+Ul5fz\n4IMPMmrUKK644oouCdxXYdFRFI719IIf+NOqbo7mTCaziTETMpj9+DWMuDwF3G62bSjgpd98yvp1\n+2mwObo7xC7Vsv9O5GyUL+Ir5Yr4Q/kigWY52wnTpk1j2rRprfbNnTvX+/3ll1/m5Zdf7vzIOlHt\nlG/Bpx9R9c5aHL9+BEtMdHeHdIbo2HBuuPVSRl2Zzqdr9pK/7yTr1+0nb/1hrrgmg5FXphEWftb/\nXCIiIiIS5My//OUvfxnohxw6dIikpKRAP6Zdu+1WqtfnEXfyOJGpA4nPye62WM4mOjacYaMGkjo4\ngcqyOspO1nL4QClfbSrEbnfSd0AsVqu5u8MMmOaZckR8oXwRXylXxB/KF/FVcXExgwcP9vu6HrsU\nfUvJceFsv+JqAApfeZMOJn4JGqkZCdw55wq+c98YktN7Y6u3s+GjA7z4zKesfXsXpccv7Jc1RURE\nRELVhVGAx4ezb9hIGmNiqNrxDVVf7unukHxiGAYZQ/owa+5YZv7wCjKG9MHe6OTLLwr407O5rPjD\nJvbtPIbL2XNW1VTfnfhD+SK+Uq6IP5QvEmgXRFNxclw4TquVPZeNY8Snf+fAc39m9J8XdHdYfkkZ\nlEDKfQmcLKlm2xcF7PryKAUHyig4UEZsfAQ5Y1MZMSaFqJjw7g5VRERERDrQ4UI8naU7F+IBcLnd\n3PznrzBXVPLQ8/+Oq66esasX03tsTrfFdL4abHZ25h1l24bDlJfWAWA2GwzO7sewUQPJGNIXi+WC\n+AWHiIiISLc414V4LogRcJNhMDAunEPOOOLvvYPyxa+w999fYOy7SzAMo7vDOyfhEVZGj09n1JVp\nHD5QyrYNhzmw9wT7dh5j385jRERauXj4AIaNGsjAtF4h++cUERER6WkumCHS5HhPa0btrd8mrG8C\nFVu/5th7n3RvUJ3AMBkMyurDrf90GXN/fB3XTruYvkmx2OrtfLWpkOVLNvLyf39G7t/3cfxoVdC/\ngKq+O/GH8kV8pVwRfyhfJNAuiBFw8PSBAxx1mLnmydnsmv8bvvn1YvpNuRqTtWf8a4iNj+DyqzO4\n/OoMTpRUs+vLo+z+8iiV5fV88fEBvvj4AHG9Iskc1o+sYf1JTu+FyXzB/AwmIiIiEhQuiB5wgDV7\nS/ndPwqYlNmbH12VwufX303t/gKGPv0E6fd/p1tjCySXy82RQ2Xs2V7MgT0nqK1u8B6LiLRy0dB+\nZA7tR9pFCYRHWLsxUhEREZHQoh7wsxjYNAJeVNmAyWphyFMPse3+n7D/mZfoP+0aIgb07eYIA8Nk\nMki7KJG0ixJxu9wUH6lk/65j7Nt1jPKTdezMK2JnXhGGyWBgajyDsvowKKsP/ZPjMZnUNy4iIiLS\n2S6Y/oPmFpSiKs8IcL+pV9Nn4pXYy6vY8f/+A7er58yl3R7DZDAwrRfXTL2Y2Y9fw/2PTeDqG7JI\nTu8NQNHhCj5fu59li7/ghV+t4+3XtvHVpkJKj9d0We+4+u7EH8oX8ZVyRfyhfJFAu2BGwBOiLERY\nTFQ3OKmyOYiLsDD82af4/Pp/ovQfW8hfvJyMed/r7jC7VGLfGBKvi2HsdRfRYLNTeLCM/P2l5O87\nSUVpHd98fYxvvj4GQGSU1TMXeUZvUgb1pm9SnEbIRURERM7BBdMDDvDAqj0cLKtn4YwhZPeLBuDE\n2vVsvftJDIuZK999kfiRQ7s5yuBQUVZH/r6TFB4q48ih8la94wBh4RYGpsWTlNKLpNR4BqT2Iio6\nrJuiFREREel66gH3QXJ8OAfL6imqavAW4H0njydt9h0U/OEvfPXQLxn/4R+xxER3c6Tdr1dCFCPH\npjFybBput5uKsjqOHCrnSH45Rw6VUVleT/6+UvL3lba6Jik1nqTUXvRPjqPvgFjCwi+oFBMRERE5\nqwuqOkppmgu8oMLWav/FP3+Iss+3UrPnINtmP8VlrzyDKVyjuc0Mw6B3YjS9E6MZPiYFgOpKG0cL\nKigurKC4sJJjRyupKKujoqyO3V8VN10IvROi6Dswjn5JsfRL8nxGx4a3uzBQbm4uEyZM6Ko/moQ4\n5Yv4Srki/lC+SKBdUAX4xX2jAPi6pLbVfnNEOKP++DQbZzxA6aeb2P7//oOcxb/EMJu7I8yQEBsf\nwcXDB3Dx8AEAOJ0uSo/VUHykkuLCCo4freLk8RrKS+soL63jmx0l3msjo8OaCvJY+g6II6FfNIl9\no7GGXVDpKCIiIheoC6oHvMrm4I6lO7CYDFb90wjCLa0ngana8Q2bbpuHo7qW1H+6hWELfqQl3M+D\n0+Gi9EQNJ4qrOV5czfHiKk4UV2Ort7d5flyvCBL6xpDYL7rp0/M9Mkq/jRAREZHgox5wH8RFWBic\nGMmB0np2H69l5MDY1seHD2H0/z3DllmPUfjKW1hiohny84dUhJ8js8XU1HYSxyVN+9xuN9WVNk9B\nfrSKk8eqKT1RS/nJWqoqbFRV2Mjfd7LVfSKjw0jsG02vxCh6J0bRKyGKXomef7R4kIiIiISaC6oA\nB8hJiuFAaT1fFdecUYADJIwfxcgX/4Nt3/8ph/5nGbaSEwz//U/VE95JDMMgrlckcb0iyRzaz7vf\n5XRRUV7P3//2EYNSLqH0eA1lx2soPVFLfW0jR2obOZJffsb9IqOs9EqMpldiJL0To4lPiCS+dxRx\nvSKIiQ3HZL5gprq/IKlPU3ylXBF/KF8k0C64AnxEUgyrvj7B9uJqIKnNc/pNuZrR/7eAL+f+guJV\nH2IrOsaoP/0XYQnxXRvsBcRkNpHQJ5rk9N6MnTDYu795xLzsRK3nJc/Spn+aXvisr7NTX+d5GfR0\nhskgNi7cW/DH9opo+n7qU33nIiIi0tUuqB5wgOoGB7e/6ukDX/lPI4iwtD9CWrVzH1vvfpKG4hNE\nZaQw8sVfETd8SBdGKx1xu93UVjdQ3rIoL62jqqKeqgrbGXOXtyUyykpsr0ji4iOIifeMmsfEhRMd\nG0FMnOd7RKRVbUgiIiJyBvWA+yg23MJFiZHsL61nTxt94C3FXZLFuPdfZus9T1L99T423PgDMn/0\nAwbP+55mSAkChmEQExdBTFwEqRkJZxx3OFxUV9ZTXWHzFuUtP6sr6ptG0O0cP1rV7nPMFtOpwjzu\nVJEeExtBdGwYUTHhREWHERllVcuLiIiInNUFV4CDpw1lfwd94C1FJPXlyreXsPfXiyn4w1/Y95//\ny4m16xn+7FNED07toogvHJ3Zd2exmLzzl7fF7XJTV9voKcorbdRWNVBTZaOmuoGaqgZqm7432BxU\nltdTWV7f8QMNiIy0EhXtKcojY8Kavrf8DPduh0dYNLJ+ntSnKb5Srog/lC8SaBdkAZ6TFHvWPvCW\nzFERDPv1Y/T71nh2PPprKjZtJ/fa75H+gzu46NH7sMZ3XMRLcDJMBtGx4UTHhpPUwc9S9kZHi6K8\ngZpqGzVVDdRUN1Bb3UBdbSN1NY3U1zV6R9RLT9S2f8MmJrPhGTlvGj2PiAojMtJKRJSViEgrkVFh\nRIv/Y7IAABGnSURBVERZPcciPZ/hkVbMGmUXEREJaRdcDzj41wd+usbyKvb+2/MUvfE+uN1YE3uR\n+eRsUmZ9G3NEeACjlmDncrmx1XmK8braRm9h7vlsOG27kcYGxzk9Jyzc0qow93z3jKh7/rG2/oy0\nEB5uITzSisVi0qi7iIhIJznXHvALsgAHeOjNPewvreeZGzPP2obSlsqv9rDnX5+j/IuvAAjv34dB\nP7yT1HtvwRLTdsuDSEsOu9NbqNvq7NjqPaPntno7tjrPvvp6u+dYnZ36ukZs9XbO5/9Yk9nwFuYR\nERbCIqxNnxYiIq2ezwjPZ3iEhbAwM2HhFqzhp76HhZnV6y4iIoJewvSbP33gbYnPyeaKN/+HY+99\nwoHf/YnqXfvZ+x8vcGDhK6TMuomU791MTFZ6ACLv2S6kvjuL1eydItFXbpebhgZHU5HeXLB7ivUG\nm4MGm+fTZnPQaLNjq3fQaHNgs9lptDlwOFzU1zZSX9t4nrGbsIZZCAtvLspbfA+3YG0u1ts4fuqY\nxXsfs9k4p5H5Cylf5PwoV8QfyhcJtAu2APe3D7wthmEw4NvX0/+m6zi5bgMHn3+V8o1fkf+/r5P/\nv6/T+8ocUmZ9m35Tr1GfuHQKw2R42k4irXDmxC9n5bA7PYV6g4OG+uai/VThfvr3xgYH9gYHjQ1O\nGhtPfTrsLhz2RurP3uru85/L2lSMe4pyM1arGWuYGUvTp7XFp6Xpc/+e4/SOKvJut3edxarWGxER\nCR4XbAtKdYOD7y7dgRt4+fahpMRHdMp9K7ftpnDZaopX/R1nnWfWDMNqoc+1VzBgxiT6ThpHWGKv\nTnmWSHdwu9047E5PMd7gKdIbG51NxXpzoe7w6bjD7sRud+JyBvivIcMzK47F4inGLRYzZqsJq8WE\nxWrG3PTZfMxiMZ36bjVhtpixWlue2/I8c6tzvfssJrXqiIj0cOoBPwe//0cBH+wtZVJmb+ZfN6hT\n7+2oqaX4rbUUv7WWsvXbwOXyHDAM4kcNo+/EK0m85nLic7K1zL1c8JxOF/bGpoK80VOUt73twt7o\naNrn+e7Z1/41drsTp8PVLX8uw2Q0Ff4mzBYTZnPTZ9P389tveH4YOO2c5u9t7TeZzq3VR0RE2qYC\n/ByUVDdw/4pduIGXvjOU1F6dMwp+uoYTZRx77xOOvf8pZV98ibvR7j1mhFmJz8mm9+Uj6HXFcHqP\nGU5Yn94BiSMUqO9O/OFrvrhcbpwOT9HudLhw2D3FvMPhxNG83fTpdLiw20999x47/bqme9ntThwO\nJ06764x7Bf5vVz8ZtCrMTSYDs9mEyez5bPnd++k9x4TZbLTz6TnfZGp9rPX9mo6ZPD88NJ/b4b1N\nnus744cG/d0i/lC+iK/0EuY5GBAbzpQhiby/t5Rl20r4yfWDAvKc8L4JpN13G2n33Yajto6yz/M4\n8dEGyjd8Rc3eg1Rs3kHF5h3wP57zoy5KI37ExcQMvYjYoRfx/9s735i4yjWB/845M0CnUEALA0Kv\nVJubgtELWbTrbqqxtelGN9Smidr1IlEajYlp6iZut8l+2HUT28Q1pokm6/rBVj/4535RtJSrrrSb\naoCblqak5d6il7ZA6R+KFCh/hjnn7IdzZubMmTNTOuWvPL+EvOd93ud5z/MOD8PznHPmnZy195JV\nGpQrV4KQJqqqoGb48M/hzSbTNDF0k3DYQNetZF0PG4Qdx7MrN6PyiA+mYUaLicVEXHKvWgm6qirx\nPxFZREdVo8eKqtD1cxeDPdlWQWHLNE1Fse01TUFR3XPY8ySZ19MXzWHj7rv8V5SYf1YfeZ8XhCXC\nkr4CDnB5JMQLfziDYZr8z7ZyfjNLV8GTMTU0zNDx0/zyp1MMtXUw1H4aY3wyQc+Xs5zstfeQU34v\ngdWrCJSVECgrYdndd+ELTH8XDUEQli7WnQBHwq4bGLqJbhgYYbvVDXTdjG8NEyNst17jkXl0I3oO\nwzDj5RF9wyoODMPqx425W8OY/c8HLDAUhWhSHknQ45N0V19VUBMSeWcfq7BQiLex7eJsNJet49g9\nd6RgUDXV9llFUUn0xWMdVt8qNhQlIrNsifrlGI+8Jk7dSN8ej/iLFDHCHCNXwNMkmJPB5t/ewaE/\nW1fB9zxWNqfn9+etoGDjwxRsfBgAYyrMyOkuRs78xEjnz4x0/sxo518JXfsldqXcRWbhnSyzE/Ks\nuwrJKiqw2uJCsooL8N+ZJ29IgiDYdwI0/Gjz7cq0MU0Tw5n428eGYWIaplUUGCamXUiYhomuW2OR\nJN/SMzBte92IjMfmsvQMW2aPRfpOme6WOfqe4y6Zqx9Zn2mYmCaYJui6CUus8JhJIgm5ZwLvLEQ8\nEvg4W1VBVawJ3fZeRUSivV1UKErcHQ7PIsJRhES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+ } + ], + "prompt_number": 20 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### References\n", + "1. Taleb, Nassim. The Black Swan. 1st edition. New York: Random House, 2007. Print." + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from IPython.core.display import HTML\n", + "\n", + "\n", + "def css_styling():\n", + " styles = open(\"../styles/custom.css\", \"r\").read()\n", + " return HTML(styles)\n", + "css_styling();" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "html": [ + "\n", + "" + ], + "output_type": "pyout", + "prompt_number": 1, + "text": [ + "" + ] + } + ], + "prompt_number": 1 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import pymc as pm\n", + "\n", + "beta = pm.Uniform(\"beta\", -100, 100)\n", + "\n", + "\n", + "@pm.observed\n", + "def survival(value=y_, beta=beta):\n", + " return np.sum([value[i - 1] * np.log((i + 0.) ** beta - (i + 1.) ** beta) for i in range(1, 99)]);" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 167 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "model = pm.Model([survival, beta])\n", + "#map_ = pm.MAP( model )\n", + "# map_.fit()\n", + "\n", + "mcmc = pm.MCMC(model)\n", + "mcmc.sample(50000, 40000);" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + " \r", + "[****************100%******************] 50000 of 50000 complete" + ] + }, + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "\n" + ] + } + ], + "prompt_number": 168 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from pymc.Matplot import plot as mcplot\n", + "mcplot(mcmc);" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Plotting beta\n" + ] + }, + { + "output_type": "display_data", + "png": 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AE++CeL8pbY8fP15v5/cLicCfDl6De0MB/jyaL7P/xt0WJNUNQtLN+7hxJQOhHg4mMR76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+ } + ], + "prompt_number": 150 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "y = [(a >= i).sum() for i in range(1, 100)];" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 165 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "y_ = -np.diff(y)\n", + "print y_\n", + "\n", + "print y;" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "[41264 5572 1638 646 313 181 101 70 48 47 22 14\n", + " 14 14 7 11 4 6 4 0 1 0 2 0\n", + " 0 1 2 1 3 0 2 2 1 0 1 1\n", + " 2 1 0 1 0 0 0 0 0 0 0 0\n", + " 1 1 0 0 0 0 0 0 0 0 0 0\n", + " 0 0 0 0 0 0 0 0 0 0 0 0\n", + " 0 0 0 0 0 0 0 0 0 0 0 0\n", + " 0 0 0 0 0 0 0 0 0 0 0 0\n", + " 0 0]\n", + "[50000, 8736, 3164, 1526, 880, 567, 386, 285, 215, 167, 120, 98, 84, 70, 56, 49, 38, 34, 28, 24, 24, 23, 23, 21, 21, 21, 20, 18, 17, 14, 14, 12, 10, 9, 9, 8, 7, 5, 4, 4, 3, 3, 3, 3, 3, 3, 3, 3, 3, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]\n" + ] + } + ], + "prompt_number": 166 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "b = -2.3;" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 112 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "np.sum([y_[i - 1] * np.log((i + 0.) ** b - (i + 1.) ** b) for i in range(1, 7)]) + y[-1] * np.log(7);" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "pyout", + "prompt_number": 113, + "text": [ + "-13526.483069774908" + ] + } + ], + "prompt_number": 113 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "y_;" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "pyout", + "prompt_number": 114, + "text": [ + "array([48930, 940, 103, 19, 7, 1])" + ] + } + ], + "prompt_number": 114 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "np.append(y_, y[-1]);" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "pyout", + "prompt_number": 116, + "text": [ + "array([48930, 940, 103, 19, 7, 1, 0])" + ] + } + ], + "prompt_number": 116 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "mc.Uninformative?" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 129 + } + ], + "metadata": {} + } + ] } \ No newline at end of file diff --git a/sandbox/Chapter10_/data/gh_forks.csv b/sandbox/Chapter10_/data/gh_forks.csv index afd0d589..123ae490 100644 --- a/sandbox/Chapter10_/data/gh_forks.csv +++ b/sandbox/Chapter10_/data/gh_forks.csv @@ -1,34 +1,34 @@ -0.000000000000000000e+00 -1.000000000000000000e+00 -2.000000000000000000e+00 -4.000000000000000000e+00 -8.000000000000000000e+00 -1.600000000000000000e+01 -3.200000000000000000e+01 -6.400000000000000000e+01 -1.280000000000000000e+02 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- stars_to_explore = ( 2**np.arange( -1, 16 ) ).astype("int") - forks_to_explore = ( 2**np.arange( -1, 16 ) ).astype("int") - repo_with_stars = np.ones_like( stars_to_explore ) - repo_with_forks = np.ones_like( forks_to_explore ) - - URL = "https://github.com/search" - print "Scrapping data from Github. Sorry Github..." - print "The data is contained in variables `foo_to_explore` and `repo_with_foo`" - print - print "stars first..." - payload = {"q":""} - for i, _star in enumerate(stars_to_explore): - payload["q"] = "stars:>=%d"%_star - r = get( URL, params = payload ) - soup = BeautifulSoup( r.text ) - try: - h3 = soup.find( class_="sort-bar").find( "h3" ).text #hopefully the github search results page plays nicely. - value = int( h3.split(" ")[2].replace(",", "" ) ) - except AttributeError as e: - #there might be less than 10 repos, so I'll count the number of display results - value = len( soup.findAll(class_= "mega-icon-public-repo" ) ) - - repo_with_stars[i] = value - print "number of repos with greater than or equal to %d stars: %d"%(_star, value ) - - #repo_with_stars = repo_with_stars.astype("float")/repo_with_stars[0] - - - print - print "forks second..." - payload = {"q":""} - for i, _fork in enumerate(stars_to_explore): - payload["q"] = "forks:>=%d"%_fork - r = get( URL, params = payload ) - soup = BeautifulSoup( r.text ) - try: - h3 = soup.find( class_="sort-bar").find( "h3" ).text #hopefully the github search results page plays nicely. - value = int( h3.split(" ")[2].replace(",", "" ) ) - except AttributeError as e: - #there might be less than 10 repos, so I'll count the number of display results - value = len( soup.findAll(class_= "mega-icon-public-repo" ) ) - - repo_with_forks[i] = value - print "number of repos with greater than or equal to %d forks: %d"%(_fork, value ) - - #repo_with_forks = repo_with_forks.astype("float")/repo_with_forks[0] - - np.savetxt( "data/gh_forks.csv", np.concatenate( [forks_to_explore, repo_with_forks], axis=1) ) - np.savetxt( "data/gh_stars.csv", np.concatenate( [stars_to_explore, repo_with_stars], axis=1) ) - -except ImportError as e: - print e - print "requests / BeautifulSoup not found. Using data pulled on Feburary 11, 2013" - _data = np.genfromtxt( "data/gh_forks.csv", delimiter = "," ) #cehck this. - forks_to_explore = _data[:,0] - repo_with_forks = _data[:,1] - - _data = np.genfromtxt( "data/gh_stars.csv", delimiter = "," ) #cehck this. - stars_to_explore = _data[:,0] - repo_with_stars = _data[:,1] - - + +try: + import numpy as np + from requests import get + from bs4 import BeautifulSoup + + + + + stars_to_explore = ( 2**np.arange( -1, 16 ) ).astype("int") + forks_to_explore = ( 2**np.arange( -1, 16 ) ).astype("int") + repo_with_stars = np.ones_like( stars_to_explore ) + repo_with_forks = np.ones_like( forks_to_explore ) + + URL = "https://github.com/search" + print "Scrapping data from Github. Sorry Github..." + print "The data is contained in variables `foo_to_explore` and `repo_with_foo`" + print + print "stars first..." + payload = {"q":""} + for i, _star in enumerate(stars_to_explore): + payload["q"] = "stars:>=%d"%_star + r = get( URL, params = payload ) + soup = BeautifulSoup( r.text ) + try: + h3 = soup.find( class_="sort-bar").find( "h3" ).text #hopefully the github search results page plays nicely. + value = int( h3.split(" ")[2].replace(",", "" ) ) + except AttributeError as e: + #there might be less than 10 repos, so I'll count the number of display results + value = len( soup.findAll(class_= "mega-icon-public-repo" ) ) + + repo_with_stars[i] = value + print "number of repos with greater than or equal to %d stars: %d"%(_star, value ) + + #repo_with_stars = repo_with_stars.astype("float")/repo_with_stars[0] + + + print + print "forks second..." + payload = {"q":""} + for i, _fork in enumerate(stars_to_explore): + payload["q"] = "forks:>=%d"%_fork + r = get( URL, params = payload ) + soup = BeautifulSoup( r.text ) + try: + h3 = soup.find( class_="sort-bar").find( "h3" ).text #hopefully the github search results page plays nicely. + value = int( h3.split(" ")[2].replace(",", "" ) ) + except AttributeError as e: + #there might be less than 10 repos, so I'll count the number of display results + value = len( soup.findAll(class_= "mega-icon-public-repo" ) ) + + repo_with_forks[i] = value + print "number of repos with greater than or equal to %d forks: %d"%(_fork, value ) + + #repo_with_forks = repo_with_forks.astype("float")/repo_with_forks[0] + + np.savetxt( "data/gh_forks.csv", np.concatenate( [forks_to_explore, repo_with_forks], axis=1) ) + np.savetxt( "data/gh_stars.csv", np.concatenate( [stars_to_explore, repo_with_stars], axis=1) ) + +except ImportError as e: + print e + print "requests / BeautifulSoup not found. Using data pulled on Feburary 11, 2013" + _data = np.genfromtxt( "data/gh_forks.csv", delimiter = "," ) #cehck this. + forks_to_explore = _data[:,0] + repo_with_forks = _data[:,1] + + _data = np.genfromtxt( "data/gh_stars.csv", delimiter = "," ) #cehck this. + stars_to_explore = _data[:,0] + repo_with_stars = _data[:,1] + + \ No newline at end of file diff --git a/sandbox/CommitDataForChapter1.ipynb b/sandbox/CommitDataForChapter1.ipynb index 74030b76..3a0b3232 100644 --- a/sandbox/CommitDataForChapter1.ipynb +++ b/sandbox/CommitDataForChapter1.ipynb @@ -1,261 +1,261 @@ -{ - "metadata": { - "name": "CommitDataForChapter1" - }, - "nbformat": 3, - "nbformat_minor": 0, - "worksheets": [ - { - "cells": [ - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "To replace the data in chapter 1 with this real time data." - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "from requests import get\n", - "response = get('https://api.github.com/repos/CamDavidsonPilon/Probabilistic-Programming-and-Bayesian-Methods-for-Hackers/stats/commit_activity').json()\n", - "weekly_totals = np.array(map(lambda x: x['total'], response))\n", - "weekly_totals = weekly_totals[np.where(weekly_totals)[0]] # gives me 52 weeks, but project started < 1 year ago so it backwards fills with 0s" - ], - "language": "python", - "metadata": {}, - "outputs": [], - "prompt_number": 6 - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "count_data = weekly_totals\n", - "n_count_data = len(weekly_totals)\n", - "\n", - "plt.bar(range(n_count_data), weekly_totals);\n", - "print weekly_totals\n", - "print n_count_data" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "[13 16 7 26 5 46 25 6 4 28 19 22 13 28 7 10 8 15 13 6 36 5 4 8 8\n", - " 3 2 11 20 9 1]\n", - "31\n" - ] - }, - { - "output_type": "display_data", - "png": 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PLHaSOdyNLO5GFnn0ravSvbAwqunpS1b8/rm5IzU1Nb7zAADA2TAvGQg7ySzy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\nPvOZz1SV+7EaXioL92N1fPe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- } - ], - "prompt_number": 27 - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "import pymc as pm\n", - "\n", - "\n", - "alpha = 1.0 / count_data.mean() # Recall count_data is the\n", - " # variable that holds our txt counts\n", - "\n", - "lambda_1 = pm.Exponential(\"lambda_1\", alpha)\n", - "lambda_2 = pm.Exponential(\"lambda_2\", alpha)\n", - "\n", - "tau = pm.DiscreteUniform(\"tau\", lower=0, upper=n_count_data)" - ], - "language": "python", - "metadata": {}, - "outputs": [], - "prompt_number": 12 - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "@pm.deterministic\n", - "def lambda_(tau=tau, lambda_1=lambda_1, lambda_2=lambda_2):\n", - " out = np.zeros(n_count_data)\n", - " out[:tau] = lambda_1 # lambda before tau is lambda1\n", - " out[tau:] = lambda_2 # lambda after tau is lambda2\n", - " return out" - ], - "language": "python", - "metadata": {}, - "outputs": [], - "prompt_number": 13 - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "observation = pm.Poisson(\"obs\", lambda_, value=count_data, observed=True)\n", - "\n", - "model = pm.Model([observation, lambda_1, lambda_2, tau])" - ], - "language": "python", - "metadata": {}, - "outputs": [], - "prompt_number": 14 - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "# Mysterious code to be explained in Chapter 3.\n", - "mcmc = pm.MCMC(model)\n", - "mcmc.sample(40000, 10000, 1)" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "output_type": "stream", - "stream": "stdout", - "text": [ - " \r", - "[****************100%******************] 40000 of 40000 complete" - ] - }, - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "\n" - ] - } - ], - "prompt_number": 15 - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "lambda_1_samples = mcmc.trace('lambda_1')[:]\n", - "lambda_2_samples = mcmc.trace('lambda_2')[:]\n", - "tau_samples = mcmc.trace('tau')[:]" - ], - "language": "python", - "metadata": {}, - "outputs": [], - "prompt_number": 16 - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "figsize(12.5, 10)\n", - "# histogram of the samples:\n", - "\n", - "ax = plt.subplot(311)\n", - "ax.set_autoscaley_on(False)\n", - "\n", - "plt.hist(lambda_1_samples, histtype='stepfilled', bins=30, alpha=0.85,\n", - " label=\"posterior of $\\lambda_1$\", color=\"#A60628\", normed=True)\n", - "plt.legend(loc=\"upper left\")\n", - "plt.title(r\"Posterior distributions of the variables \\\n", - " $\\lambda_1,\\;\\lambda_2,\\;\\tau$\")\n", - "\n", - "plt.xlabel(\"$\\lambda_1$ value\")\n", - "\n", - "ax = plt.subplot(312)\n", - "ax.set_autoscaley_on(False)\n", - "\n", - "plt.hist(lambda_2_samples, histtype='stepfilled', bins=30, alpha=0.85,\n", - " label=\"posterior of $\\lambda_2$\", color=\"#7A68A6\", normed=True)\n", - "plt.legend(loc=\"upper left\")\n", - "\n", - "plt.xlabel(\"$\\lambda_2$ value\")\n", - "\n", - "plt.subplot(313)\n", - "\n", - "\n", - "#w = 1.0 / tau_samples.shape[0] * np.ones_like(tau_samples)\n", - "plt.hist(tau_samples, bins=n_count_data, alpha=1,\n", - " label=r\"posterior of $\\tau$\",\n", - " color=\"#467821\", rwidth=2.)\n", - "plt.xticks(np.arange(n_count_data))\n", - "\n", - "plt.legend(loc=\"upper left\")\n", - "plt.ylim([0, .75])\n", - "plt.xlabel(\"$\\tau$ (in days)\")\n", - "plt.ylabel(\"probability\")" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "output_type": "pyout", - "prompt_number": 29, - "text": [ - "" - ] - }, - { - "output_type": "display_data", - "png": 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CqLs09XRDpw/rbvz0MT4Zhpl93qyB192Vi/nKw2zlYbbyMFt5mK1psehG3r6N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- } - ], - "prompt_number": 29 - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "n_count_data" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "output_type": "pyout", - "prompt_number": 21, - "text": [ - "31" - ] - } - ], - "prompt_number": 21 - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "lambda_2_samples" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "output_type": "pyout", - "prompt_number": 28, - "text": [ - "array([ 7.7774429 , 7.7774429 , 7.7774429 , ..., 8.21626815,\n", - " 8.21626815, 8.80155957])" - ] - } - ], - "prompt_number": 28 - }, - { - "cell_type": "code", - "collapsed": false, - "input": [], - "language": "python", - "metadata": {}, - "outputs": [] - } - ], - "metadata": {} - } - ] +{ + "metadata": { + "name": "CommitDataForChapter1" + }, + "nbformat": 3, + "nbformat_minor": 0, + "worksheets": [ + { + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "To replace the data in chapter 1 with this real time data." + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from requests import get\n", + "response = get('https://api.github.com/repos/CamDavidsonPilon/Probabilistic-Programming-and-Bayesian-Methods-for-Hackers/stats/commit_activity').json()\n", + "weekly_totals = np.array(map(lambda x: x['total'], response))\n", + "weekly_totals = weekly_totals[np.where(weekly_totals)[0]] # gives me 52 weeks, but project started < 1 year ago so it backwards fills with 0s" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 6 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "count_data = weekly_totals\n", + "n_count_data = len(weekly_totals)\n", + "\n", + "plt.bar(range(n_count_data), weekly_totals);\n", + "print weekly_totals\n", + "print n_count_data" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "[13 16 7 26 5 46 25 6 4 28 19 22 13 28 7 10 8 15 13 6 36 5 4 8 8\n", + " 3 2 11 20 9 1]\n", + "31\n" + ] + }, + { + "output_type": "display_data", + "png": 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wk8xil5dFHjk8q7K4G1nk0TelGwAAGlO6B8JOMotdXhZ55PCsyuJuZJFH35RuAABoTOke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\nPvOZz1SV+7EaXioL92N1fPe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+ } + ], + "prompt_number": 27 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import pymc as pm\n", + "\n", + "\n", + "alpha = 1.0 / count_data.mean() # Recall count_data is the\n", + " # variable that holds our txt counts\n", + "\n", + "lambda_1 = pm.Exponential(\"lambda_1\", alpha)\n", + "lambda_2 = pm.Exponential(\"lambda_2\", alpha)\n", + "\n", + "tau = pm.DiscreteUniform(\"tau\", lower=0, upper=n_count_data)" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 12 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "@pm.deterministic\n", + "def lambda_(tau=tau, lambda_1=lambda_1, lambda_2=lambda_2):\n", + " out = np.zeros(n_count_data)\n", + " out[:tau] = lambda_1 # lambda before tau is lambda1\n", + " out[tau:] = lambda_2 # lambda after tau is lambda2\n", + " return out" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 13 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "observation = pm.Poisson(\"obs\", lambda_, value=count_data, observed=True)\n", + "\n", + "model = pm.Model([observation, lambda_1, lambda_2, tau])" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 14 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# Mysterious code to be explained in Chapter 3.\n", + "mcmc = pm.MCMC(model)\n", + "mcmc.sample(40000, 10000, 1)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + " \r", + "[****************100%******************] 40000 of 40000 complete" + ] + }, + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "\n" + ] + } + ], + "prompt_number": 15 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "lambda_1_samples = mcmc.trace('lambda_1')[:]\n", + "lambda_2_samples = mcmc.trace('lambda_2')[:]\n", + "tau_samples = mcmc.trace('tau')[:]" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 16 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "figsize(12.5, 10)\n", + "# histogram of the samples:\n", + "\n", + "ax = plt.subplot(311)\n", + "ax.set_autoscaley_on(False)\n", + "\n", + "plt.hist(lambda_1_samples, histtype='stepfilled', bins=30, alpha=0.85,\n", + " label=\"posterior of $\\lambda_1$\", color=\"#A60628\", normed=True)\n", + "plt.legend(loc=\"upper left\")\n", + "plt.title(r\"Posterior distributions of the variables \\\n", + " $\\lambda_1,\\;\\lambda_2,\\;\\tau$\")\n", + "\n", + "plt.xlabel(\"$\\lambda_1$ value\")\n", + "\n", + "ax = plt.subplot(312)\n", + "ax.set_autoscaley_on(False)\n", + "\n", + "plt.hist(lambda_2_samples, histtype='stepfilled', bins=30, alpha=0.85,\n", + " label=\"posterior of $\\lambda_2$\", color=\"#7A68A6\", normed=True)\n", + "plt.legend(loc=\"upper left\")\n", + "\n", + "plt.xlabel(\"$\\lambda_2$ value\")\n", + "\n", + "plt.subplot(313)\n", + "\n", + "\n", + "#w = 1.0 / tau_samples.shape[0] * np.ones_like(tau_samples)\n", + "plt.hist(tau_samples, bins=n_count_data, alpha=1,\n", + " label=r\"posterior of $\\tau$\",\n", + " color=\"#467821\", rwidth=2.)\n", + "plt.xticks(np.arange(n_count_data))\n", + "\n", + "plt.legend(loc=\"upper left\")\n", + "plt.ylim([0, .75])\n", + "plt.xlabel(\"$\\tau$ (in days)\")\n", + "plt.ylabel(\"probability\")" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "pyout", + "prompt_number": 29, + "text": [ + "" + ] + }, + { + "output_type": "display_data", + "png": 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CqLs09XRDpw/rbvz0MT4Zhpl93qyB192Vi/nKw2zlYbbyMFt5mK1psehG3r6N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+ } + ], + "prompt_number": 29 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "n_count_data" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "pyout", + "prompt_number": 21, + "text": [ + "31" + ] + } + ], + "prompt_number": 21 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "lambda_2_samples" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "pyout", + "prompt_number": 28, + "text": [ + "array([ 7.7774429 , 7.7774429 , 7.7774429 , ..., 8.21626815,\n", + " 8.21626815, 8.80155957])" + ] + } + ], + "prompt_number": 28 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [], + "language": "python", + "metadata": {}, + "outputs": [] + } + ], + "metadata": {} + } + ] } \ No newline at end of file diff --git a/sandbox/GithubUsers.ipynb b/sandbox/GithubUsers.ipynb index 795fb2ea..445f8429 100644 --- a/sandbox/GithubUsers.ipynb +++ b/sandbox/GithubUsers.ipynb @@ -1,244 +1,244 @@ -{ - "metadata": { - "name": "GithubUsers" - }, - "nbformat": 3, - "nbformat_minor": 0, - "worksheets": [ - { - "cells": [ - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "##### Example: Number of Github users\n", - "\n", - "\n", - "This is a fun example. Suppose we wish to predict how many sign-ups there are on Github.com. Officially, Github does not release an up-to-date count, and at last offical annoucment (January 2013) the count was 3 million. What if we wish to measure it today? We *could* [extrapolate future numbers from previous annoucements](http://redmonk.com/dberkholz/2013/01/21/github-will-hit-5-million-users-within-a-year/), but this uses little data and we could potentially be off by hundreds of thousands, and you are essentially just curve fitting complicated models. \n", - "\n", - "Instead, what we are going to use is `user id` numbers from real-time feeds on Github. The script `github_events.py` will pull the most recent 300 events from the [Github Public Timeline feed](https://github.com/timeline) (we'll be accessing data using their API). From this, we pull out the `user ids` associated with each event. We run the script below and display some output:" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "%run github_events.py\n", - "\n", - "\n", - "print \"Some User ids from the latest events (push, star, fork etc.) on Github.\"\n", - "print ids[:10]\n", - "print\n", - "print \"Number of unique ids found: \", ids.shape[0]\n", - "print \"Largest user id: \", ids.max()" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "ename": "KeyError", - "evalue": "'id'", - "output_type": "pyerr", - "traceback": [ - "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m\n\u001b[1;31mKeyError\u001b[0m Traceback (most recent call last)", - "\u001b[1;32mc:\\Python27\\lib\\site-packages\\IPython\\utils\\py3compat.pyc\u001b[0m in \u001b[0;36mexecfile\u001b[1;34m(fname, glob, loc)\u001b[0m\n\u001b[0;32m 169\u001b[0m \u001b[1;32melse\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 170\u001b[0m \u001b[0mfilename\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mfname\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m--> 171\u001b[1;33m \u001b[1;32mexec\u001b[0m \u001b[0mcompile\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mscripttext\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mfilename\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;34m'exec'\u001b[0m\u001b[1;33m)\u001b[0m \u001b[1;32min\u001b[0m \u001b[0mglob\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mloc\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m 172\u001b[0m \u001b[1;32melse\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 173\u001b[0m \u001b[1;32mdef\u001b[0m \u001b[0mexecfile\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mfname\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;33m*\u001b[0m\u001b[0mwhere\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n", - "\u001b[1;32mC:\\Users\\Cameron\\Dropbox\\My Work\\Probabilistic-Programming-and-Bayesian-Methods-for-Hackers\\Chapter2_MorePyMC\\github_events.py\u001b[0m in \u001b[0;36m\u001b[1;34m()\u001b[0m\n\u001b[0;32m 22\u001b[0m \u001b[0mdata\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mloads\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mr\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mtext\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 23\u001b[0m \u001b[1;32mfor\u001b[0m \u001b[0mevent\u001b[0m \u001b[1;32min\u001b[0m \u001b[0mdata\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m---> 24\u001b[1;33m \u001b[0mids\u001b[0m\u001b[1;33m[\u001b[0m\u001b[0mk\u001b[0m\u001b[1;33m]\u001b[0m \u001b[1;33m=\u001b[0m \u001b[1;33m(\u001b[0m \u001b[0mevent\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;34m\"actor\"\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;34m\"id\"\u001b[0m\u001b[1;33m]\u001b[0m \u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m 25\u001b[0m \u001b[0mk\u001b[0m\u001b[1;33m+=\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 26\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n", - "\u001b[1;31mKeyError\u001b[0m: 'id'" - ] - }, - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "Some User ids from the latest events (push, star, fork etc.) on Github.\n", - "[1524995 1978503 1926860 1524995 3707208 374604 37715 770655 502701\n", - " 4349707]" - ] - }, - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "\n", - "\n" - ] - }, - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "Number of unique ids found: 300\n", - "Largest user id: " - ] - }, - { - "output_type": "stream", - "stream": "stdout", - "text": [ - " 2085773151\n" - ] - } - ], - "prompt_number": 1 - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "figsize(12.5, 3)\n", - "plt.hist(ids, bins=45, alpha=0.9)\n", - "plt.title(\"Histogram of %d Github User ids\" % ids.shape[0]);\n", - "plt.xlabel(\"User id\")\n", - "plt.ylabel(\"Frequency\");" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "ename": "NameError", - "evalue": "name 'figsize' is not defined", - "output_type": "pyerr", - "traceback": [ - "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m\n\u001b[1;31mNameError\u001b[0m Traceback (most recent call last)", - "\u001b[1;32m\u001b[0m in \u001b[0;36m\u001b[1;34m()\u001b[0m\n\u001b[1;32m----> 1\u001b[1;33m \u001b[0mfigsize\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;36m12.5\u001b[0m\u001b[1;33m,\u001b[0m\u001b[1;36m3\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m 2\u001b[0m \u001b[0mplt\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mhist\u001b[0m\u001b[1;33m(\u001b[0m \u001b[0mids\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mbins\u001b[0m \u001b[1;33m=\u001b[0m \u001b[1;36m45\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0malpha\u001b[0m \u001b[1;33m=\u001b[0m \u001b[1;36m0.9\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 3\u001b[0m \u001b[0mplt\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mtitle\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;34m\"Histogram of %d Github User ids\"\u001b[0m\u001b[1;33m%\u001b[0m\u001b[0mids\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mshape\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;36m0\u001b[0m\u001b[1;33m]\u001b[0m \u001b[1;33m)\u001b[0m\u001b[1;33m;\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 4\u001b[0m \u001b[0mplt\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mxlabel\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;34m\"User id\"\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 5\u001b[0m \u001b[0mplt\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mylabel\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;34m\"Frequency\"\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m;\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n", - "\u001b[1;31mNameError\u001b[0m: name 'figsize' is not defined" - ] - } - ], - "prompt_number": 2 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "There are some users with multiple events, but we are only interested in unique `user ids`, hence why we have less than 300 ids. Above I printed the largest `user id`. Why is this important? If Github assigns `user ids` serially, which is a fair assumption, then we **know** that there are certainly more users than that number. Remember, we are only looking at less than 300 individuals out of a much larger population, so it is unlikely that we would have sampled the most recent sign-up. \n", - "\n", - "At best, we can only estimate the total number of sign-ups. Let's get more familar with this problem. Consider a fictional website that we wish to estimate the number of users:\n", - "\n", - "1. Suppose we sampled only two individuals in a similar manner to above: the ids are 3 and 10 respectively. Would it be likely that the website has millions of users? Not very. Alternatively, it is more likely the website has less than 100 users. \n", - "\n", - "2. On the other hand, if the ids were 3 and 34 989, we might be more willing to guess there could possibly thousands, or millions of user sign-ups. We are not very confident in an estimate, due to a lack of data.\n", - "\n", - "3. If we sample thousands of users, and the maximum `user id` is still 34 989, then is seems likely that the total number of sign ups is near 35 000. Hence our inference should be more confident.\n", - "\n", - "\n", - "We make the following assumption:\n", - "\n", - "**Assumption:** Every user is equally likely to perform an event. Clearly, looking at the above histogram, this assumption is violated. The participation on Github is skewed towards early adopters, likely as these early-adopting individuals have a) more invested in Github, and b) saw the value earlier in Github, therefore are more interested in it. The distribution is also skewed towards new sign ups, who likely signed up just to push a project. \n", - "\n", - "To create a Bayesian model of this is easy. Based on the above assumption, all `user_ids` sampled are from a `DiscreteUniform` model, with lower bound 1 and an unknown upperbound. We don't have a strong belief about what the upper-bound might be, but we do know it will be larger than `ids.max()`. \n", - "\n", - "Working with such large numbers can cause numerical problem, hence we will scale everything by a million. Thus, instead of a `DiscreteUniform`, we will used a `Uniform`:" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "FACTOR = 1000000.\n", - "\n", - "import pymc as pm\n", - "\n", - "upper_bound = pm.Uniform(\"n_sign_ups\", ids.max() / FACTOR, (ids.max()) / FACTOR + 1)\n", - "obs = pm.Uniform(\"obs\", 0, upper_bound, value=ids / FACTOR, observed=True)\n", - "\n", - "# code to be examplained in Chp. 3.\n", - "mcmc = pm.MCMC([upper_bound, obs])\n", - "mcmc.sample(100000, 45000)" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "ename": "ZeroProbability", - "evalue": "Stochastic obs's value is outside its support,\n or it forbids its parents' current values.", - "output_type": "pyerr", - "traceback": [ - "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m\n\u001b[1;31mZeroProbability\u001b[0m Traceback (most recent call last)", - "\u001b[1;32m\u001b[0m in \u001b[0;36m\u001b[1;34m()\u001b[0m\n\u001b[0;32m 4\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 5\u001b[0m \u001b[0mupper_bound\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mmc\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mUniform\u001b[0m\u001b[1;33m(\u001b[0m \u001b[1;34m\"n_sign_ups\"\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mids\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mmax\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m/\u001b[0m\u001b[0mFACTOR\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;33m(\u001b[0m\u001b[0mids\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mmax\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m/\u001b[0m\u001b[0mFACTOR\u001b[0m \u001b[1;33m+\u001b[0m \u001b[1;36m1\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m----> 6\u001b[1;33m \u001b[0mobs\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mmc\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mUniform\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;34m\"obs\"\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;36m0\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mupper_bound\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mvalue\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mids\u001b[0m\u001b[1;33m/\u001b[0m\u001b[0mFACTOR\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mobserved\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mTrue\u001b[0m \u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m 7\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 8\u001b[0m \u001b[1;31m#code to be examplained in Chp. 3.\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n", - "\u001b[1;32mc:\\Python27\\lib\\site-packages\\pymc\\distributions.pyc\u001b[0m in \u001b[0;36m__init__\u001b[1;34m(self, *args, **kwds)\u001b[0m\n\u001b[0;32m 268\u001b[0m \u001b[0mrandom\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mdebug_wrapper\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mrandom\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 269\u001b[0m \u001b[1;32melse\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m--> 270\u001b[1;33m \u001b[0mStochastic\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0m__init__\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mself\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mlogp\u001b[0m\u001b[1;33m=\u001b[0m\u001b[0mlogp\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mrandom\u001b[0m\u001b[1;33m=\u001b[0m\u001b[0mrandom\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mlogp_partial_gradients\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mlogp_partial_gradients\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mdtype\u001b[0m\u001b[1;33m=\u001b[0m\u001b[0mdtype\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;33m**\u001b[0m\u001b[0marg_dict_out\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m 271\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 272\u001b[0m \u001b[0mnew_class\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0m__name__\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mname\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n", - "\u001b[1;32mc:\\Python27\\lib\\site-packages\\pymc\\PyMCObjects.pyc\u001b[0m in \u001b[0;36m__init__\u001b[1;34m(self, logp, doc, name, parents, random, trace, value, dtype, rseed, observed, cache_depth, plot, verbose, isdata, check_logp, logp_partial_gradients)\u001b[0m\n\u001b[0;32m 714\u001b[0m \u001b[1;32mif\u001b[0m \u001b[0mcheck_logp\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 715\u001b[0m \u001b[1;31m# Check initial value\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m--> 716\u001b[1;33m \u001b[1;32mif\u001b[0m \u001b[1;32mnot\u001b[0m \u001b[0misinstance\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mlogp\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mfloat\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m 717\u001b[0m \u001b[1;32mraise\u001b[0m \u001b[0mValueError\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;34m\"Stochastic \"\u001b[0m \u001b[1;33m+\u001b[0m \u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0m__name__\u001b[0m \u001b[1;33m+\u001b[0m \u001b[1;34m\"'s initial log-probability is %s, should be a float.\"\u001b[0m \u001b[1;33m%\u001b[0m\u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mlogp\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0m__repr__\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 718\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n", - "\u001b[1;32mc:\\Python27\\lib\\site-packages\\pymc\\PyMCObjects.pyc\u001b[0m in \u001b[0;36mget_logp\u001b[1;34m(self)\u001b[0m\n\u001b[0;32m 846\u001b[0m \u001b[1;32mraise\u001b[0m \u001b[0mZeroProbability\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0merrmsg\u001b[0m \u001b[1;33m+\u001b[0m \u001b[1;34m\"\\nValue: %s\\nParents' values:%s\"\u001b[0m \u001b[1;33m%\u001b[0m \u001b[1;33m(\u001b[0m\u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0m_value\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0m_parents\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mvalue\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 847\u001b[0m \u001b[1;32melse\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m--> 848\u001b[1;33m \u001b[1;32mraise\u001b[0m \u001b[0mZeroProbability\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0merrmsg\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m 849\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 850\u001b[0m \u001b[1;32mreturn\u001b[0m \u001b[0mlogp\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n", - "\u001b[1;31mZeroProbability\u001b[0m: Stochastic obs's value is outside its support,\n or it forbids its parents' current values." - ] - } - ], - "prompt_number": 3 - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "from scipy.stats.mstats import mquantiles\n", - "\n", - "samples = mcmc.trace(\"n_sign_ups\")[:]\n", - "\n", - "hist(samples, bins=100,\n", - " label=\"Uniform prior\",\n", - " normed=True, alpha=0.8,\n", - " histtype=\"stepfilled\", color=\"#7A68A6\");\n", - "\n", - "quantiles_mean = np.append(mquantiles(samples, [0.05, 0.5, 0.95]), samples.mean())\n", - "print \"Quantiles: \", quantiles_mean[:3]\n", - "print \"Mean: \", quantiles_mean[-1]\n", - "plt.vlines(quantiles_mean, 0, 33,\n", - " linewidth=2, linestyles=[\"--\", \"--\", \"--\", \"-\"],\n", - " )\n", - "plt.title(\"Posterior distribution of total number of Github users\")\n", - "plt.xlabel(\"number of users (in millions)\")\n", - "plt.legend()\n", - "plt.xlim(ids.max() / FACTOR - 0.01, ids.max() / FACTOR + 0.12);" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "ename": "NameError", - "evalue": "name 'mcmc' is not defined", - "output_type": "pyerr", - "traceback": [ - "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m\n\u001b[1;31mNameError\u001b[0m Traceback (most recent call last)", - "\u001b[1;32m\u001b[0m in \u001b[0;36m\u001b[1;34m()\u001b[0m\n\u001b[0;32m 1\u001b[0m \u001b[1;32mfrom\u001b[0m \u001b[0mscipy\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mstats\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mmstats\u001b[0m \u001b[1;32mimport\u001b[0m \u001b[0mmquantiles\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 2\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m----> 3\u001b[1;33m \u001b[0msamples\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mmcmc\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mtrace\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;34m\"n_sign_ups\"\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m 4\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 5\u001b[0m hist(samples, bins = 100, \n", - "\u001b[1;31mNameError\u001b[0m: name 'mcmc' is not defined" - ] - } - ], - "prompt_number": 4 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Above we have plotted the posterior distribution. Note that there is no posterior probability assigned to the number of users being less than `ids.max()`. That is good, as it would be an impossible situation. \n", - "\n", - "The three dashed vertical bars, from left to right, are the 5%, 50% and 95% quantitle lines. That is, 5% of the probability is before the first line, 50% before the second and 95% before the third. The 50% quantitle is also know as the *median* and is a better measure of centrality than the mean for heavily skewed distributions like this one. The solid line is the posterior distribution's mean.\n", - "\n", - "So what can we say? Using the data above, there is a 95% chance that there are less than 4.4 million users, and is probably around 4.36 million users. I was wondering how accurate this figure was. At the time of this writing, it seems a bit high considering only five months prior the number was at 3 million:\n", - "\n", - "\n", - "

Last night @github crossed the 3M user mark #turntup

— Rick Bradley (@rickbradley) January 15, 2013
\n", - "\n", - "\n", - "\n", - "I thought perhaps the `user_id` parameter was being used liberally to users/bots/changed names etc, so I contacted Github Support about it:\n", - "\n", - "

@cmrn_dp User IDs are assigned to new users/organizations, whether they\u2019re controlled by humans, groups, or bots.

— GitHub Support (@GitHubHelp) May 6, 2013
\n", - "\n", - "\n", - "\n", - "So we may be overestimating by including organizations, which perhaps should not be counted as users. TODO: estimate the number of organizations. Any takers?" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [], - "language": "python", - "metadata": {}, - "outputs": [] - } - ], - "metadata": {} - } - ] +{ + "metadata": { + "name": "GithubUsers" + }, + "nbformat": 3, + "nbformat_minor": 0, + "worksheets": [ + { + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "##### Example: Number of Github users\n", + "\n", + "\n", + "This is a fun example. Suppose we wish to predict how many sign-ups there are on Github.com. Officially, Github does not release an up-to-date count, and at last offical annoucment (January 2013) the count was 3 million. What if we wish to measure it today? We *could* [extrapolate future numbers from previous annoucements](http://redmonk.com/dberkholz/2013/01/21/github-will-hit-5-million-users-within-a-year/), but this uses little data and we could potentially be off by hundreds of thousands, and you are essentially just curve fitting complicated models. \n", + "\n", + "Instead, what we are going to use is `user id` numbers from real-time feeds on Github. The script `github_events.py` will pull the most recent 300 events from the [Github Public Timeline feed](https://github.com/timeline) (we'll be accessing data using their API). From this, we pull out the `user ids` associated with each event. We run the script below and display some output:" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "%run github_events.py\n", + "\n", + "\n", + "print \"Some User ids from the latest events (push, star, fork etc.) on Github.\"\n", + "print ids[:10]\n", + "print\n", + "print \"Number of unique ids found: \", ids.shape[0]\n", + "print \"Largest user id: \", ids.max()" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "ename": "KeyError", + "evalue": "'id'", + "output_type": "pyerr", + "traceback": [ + "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m\n\u001b[1;31mKeyError\u001b[0m Traceback (most recent call last)", + "\u001b[1;32mc:\\Python27\\lib\\site-packages\\IPython\\utils\\py3compat.pyc\u001b[0m in \u001b[0;36mexecfile\u001b[1;34m(fname, glob, loc)\u001b[0m\n\u001b[0;32m 169\u001b[0m \u001b[1;32melse\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 170\u001b[0m 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Work\\Probabilistic-Programming-and-Bayesian-Methods-for-Hackers\\Chapter2_MorePyMC\\github_events.py\u001b[0m in \u001b[0;36m\u001b[1;34m()\u001b[0m\n\u001b[0;32m 22\u001b[0m \u001b[0mdata\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mloads\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mr\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mtext\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 23\u001b[0m \u001b[1;32mfor\u001b[0m \u001b[0mevent\u001b[0m \u001b[1;32min\u001b[0m \u001b[0mdata\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m---> 24\u001b[1;33m \u001b[0mids\u001b[0m\u001b[1;33m[\u001b[0m\u001b[0mk\u001b[0m\u001b[1;33m]\u001b[0m \u001b[1;33m=\u001b[0m \u001b[1;33m(\u001b[0m \u001b[0mevent\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;34m\"actor\"\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;34m\"id\"\u001b[0m\u001b[1;33m]\u001b[0m \u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m 25\u001b[0m \u001b[0mk\u001b[0m\u001b[1;33m+=\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 26\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n", + "\u001b[1;31mKeyError\u001b[0m: 'id'" + ] + }, + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Some User ids from the latest events (push, star, fork etc.) on Github.\n", + "[1524995 1978503 1926860 1524995 3707208 374604 37715 770655 502701\n", + " 4349707]" + ] + }, + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "\n", + "\n" + ] + }, + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Number of unique ids found: 300\n", + "Largest user id: " + ] + }, + { + "output_type": "stream", + "stream": "stdout", + "text": [ + " 2085773151\n" + ] + } + ], + "prompt_number": 1 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "figsize(12.5, 3)\n", + "plt.hist(ids, bins=45, alpha=0.9)\n", + "plt.title(\"Histogram of %d Github User ids\" % ids.shape[0]);\n", + "plt.xlabel(\"User id\")\n", + "plt.ylabel(\"Frequency\");" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "ename": "NameError", + "evalue": "name 'figsize' is not defined", + "output_type": "pyerr", + "traceback": [ + "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m\n\u001b[1;31mNameError\u001b[0m Traceback (most recent call last)", + "\u001b[1;32m\u001b[0m in \u001b[0;36m\u001b[1;34m()\u001b[0m\n\u001b[1;32m----> 1\u001b[1;33m \u001b[0mfigsize\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;36m12.5\u001b[0m\u001b[1;33m,\u001b[0m\u001b[1;36m3\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m 2\u001b[0m \u001b[0mplt\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mhist\u001b[0m\u001b[1;33m(\u001b[0m \u001b[0mids\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mbins\u001b[0m \u001b[1;33m=\u001b[0m \u001b[1;36m45\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0malpha\u001b[0m \u001b[1;33m=\u001b[0m \u001b[1;36m0.9\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 3\u001b[0m \u001b[0mplt\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mtitle\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;34m\"Histogram of %d Github User ids\"\u001b[0m\u001b[1;33m%\u001b[0m\u001b[0mids\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mshape\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;36m0\u001b[0m\u001b[1;33m]\u001b[0m \u001b[1;33m)\u001b[0m\u001b[1;33m;\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 4\u001b[0m \u001b[0mplt\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mxlabel\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;34m\"User id\"\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 5\u001b[0m \u001b[0mplt\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mylabel\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;34m\"Frequency\"\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m;\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n", + "\u001b[1;31mNameError\u001b[0m: name 'figsize' is not defined" + ] + } + ], + "prompt_number": 2 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "There are some users with multiple events, but we are only interested in unique `user ids`, hence why we have less than 300 ids. Above I printed the largest `user id`. Why is this important? If Github assigns `user ids` serially, which is a fair assumption, then we **know** that there are certainly more users than that number. Remember, we are only looking at less than 300 individuals out of a much larger population, so it is unlikely that we would have sampled the most recent sign-up. \n", + "\n", + "At best, we can only estimate the total number of sign-ups. Let's get more familar with this problem. Consider a fictional website that we wish to estimate the number of users:\n", + "\n", + "1. Suppose we sampled only two individuals in a similar manner to above: the ids are 3 and 10 respectively. Would it be likely that the website has millions of users? Not very. Alternatively, it is more likely the website has less than 100 users. \n", + "\n", + "2. On the other hand, if the ids were 3 and 34 989, we might be more willing to guess there could possibly thousands, or millions of user sign-ups. We are not very confident in an estimate, due to a lack of data.\n", + "\n", + "3. If we sample thousands of users, and the maximum `user id` is still 34 989, then is seems likely that the total number of sign ups is near 35 000. Hence our inference should be more confident.\n", + "\n", + "\n", + "We make the following assumption:\n", + "\n", + "**Assumption:** Every user is equally likely to perform an event. Clearly, looking at the above histogram, this assumption is violated. The participation on Github is skewed towards early adopters, likely as these early-adopting individuals have a) more invested in Github, and b) saw the value earlier in Github, therefore are more interested in it. The distribution is also skewed towards new sign ups, who likely signed up just to push a project. \n", + "\n", + "To create a Bayesian model of this is easy. Based on the above assumption, all `user_ids` sampled are from a `DiscreteUniform` model, with lower bound 1 and an unknown upperbound. We don't have a strong belief about what the upper-bound might be, but we do know it will be larger than `ids.max()`. \n", + "\n", + "Working with such large numbers can cause numerical problem, hence we will scale everything by a million. Thus, instead of a `DiscreteUniform`, we will used a `Uniform`:" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "FACTOR = 1000000.\n", + "\n", + "import pymc as pm\n", + "\n", + "upper_bound = pm.Uniform(\"n_sign_ups\", ids.max() / FACTOR, (ids.max()) / FACTOR + 1)\n", + "obs = pm.Uniform(\"obs\", 0, upper_bound, value=ids / FACTOR, observed=True)\n", + "\n", + "# code to be examplained in Chp. 3.\n", + "mcmc = pm.MCMC([upper_bound, obs])\n", + "mcmc.sample(100000, 45000)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "ename": "ZeroProbability", + "evalue": "Stochastic obs's value is outside its support,\n or it forbids its parents' current values.", + "output_type": "pyerr", + "traceback": [ + "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m\n\u001b[1;31mZeroProbability\u001b[0m Traceback (most recent call last)", + "\u001b[1;32m\u001b[0m in \u001b[0;36m\u001b[1;34m()\u001b[0m\n\u001b[0;32m 4\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 5\u001b[0m \u001b[0mupper_bound\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mmc\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mUniform\u001b[0m\u001b[1;33m(\u001b[0m \u001b[1;34m\"n_sign_ups\"\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mids\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mmax\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m/\u001b[0m\u001b[0mFACTOR\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;33m(\u001b[0m\u001b[0mids\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mmax\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m/\u001b[0m\u001b[0mFACTOR\u001b[0m \u001b[1;33m+\u001b[0m \u001b[1;36m1\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m----> 6\u001b[1;33m \u001b[0mobs\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mmc\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mUniform\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;34m\"obs\"\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;36m0\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mupper_bound\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mvalue\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mids\u001b[0m\u001b[1;33m/\u001b[0m\u001b[0mFACTOR\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mobserved\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mTrue\u001b[0m \u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m 7\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 8\u001b[0m \u001b[1;31m#code to be examplained in Chp. 3.\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n", + "\u001b[1;32mc:\\Python27\\lib\\site-packages\\pymc\\distributions.pyc\u001b[0m in \u001b[0;36m__init__\u001b[1;34m(self, *args, **kwds)\u001b[0m\n\u001b[0;32m 268\u001b[0m \u001b[0mrandom\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mdebug_wrapper\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mrandom\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 269\u001b[0m \u001b[1;32melse\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m--> 270\u001b[1;33m \u001b[0mStochastic\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0m__init__\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mself\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mlogp\u001b[0m\u001b[1;33m=\u001b[0m\u001b[0mlogp\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mrandom\u001b[0m\u001b[1;33m=\u001b[0m\u001b[0mrandom\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mlogp_partial_gradients\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mlogp_partial_gradients\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mdtype\u001b[0m\u001b[1;33m=\u001b[0m\u001b[0mdtype\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;33m**\u001b[0m\u001b[0marg_dict_out\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m 271\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 272\u001b[0m \u001b[0mnew_class\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0m__name__\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mname\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n", + "\u001b[1;32mc:\\Python27\\lib\\site-packages\\pymc\\PyMCObjects.pyc\u001b[0m in \u001b[0;36m__init__\u001b[1;34m(self, logp, doc, name, parents, random, trace, value, dtype, rseed, observed, cache_depth, plot, verbose, isdata, check_logp, logp_partial_gradients)\u001b[0m\n\u001b[0;32m 714\u001b[0m \u001b[1;32mif\u001b[0m \u001b[0mcheck_logp\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 715\u001b[0m \u001b[1;31m# Check initial value\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m--> 716\u001b[1;33m \u001b[1;32mif\u001b[0m \u001b[1;32mnot\u001b[0m \u001b[0misinstance\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mlogp\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mfloat\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m 717\u001b[0m \u001b[1;32mraise\u001b[0m \u001b[0mValueError\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;34m\"Stochastic \"\u001b[0m \u001b[1;33m+\u001b[0m \u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0m__name__\u001b[0m \u001b[1;33m+\u001b[0m \u001b[1;34m\"'s initial log-probability is %s, should be a float.\"\u001b[0m \u001b[1;33m%\u001b[0m\u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mlogp\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0m__repr__\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 718\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n", + "\u001b[1;32mc:\\Python27\\lib\\site-packages\\pymc\\PyMCObjects.pyc\u001b[0m in \u001b[0;36mget_logp\u001b[1;34m(self)\u001b[0m\n\u001b[0;32m 846\u001b[0m \u001b[1;32mraise\u001b[0m \u001b[0mZeroProbability\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0merrmsg\u001b[0m \u001b[1;33m+\u001b[0m \u001b[1;34m\"\\nValue: %s\\nParents' values:%s\"\u001b[0m \u001b[1;33m%\u001b[0m \u001b[1;33m(\u001b[0m\u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0m_value\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0m_parents\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mvalue\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 847\u001b[0m \u001b[1;32melse\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m--> 848\u001b[1;33m \u001b[1;32mraise\u001b[0m \u001b[0mZeroProbability\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0merrmsg\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m 849\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 850\u001b[0m \u001b[1;32mreturn\u001b[0m \u001b[0mlogp\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n", + "\u001b[1;31mZeroProbability\u001b[0m: Stochastic obs's value is outside its support,\n or it forbids its parents' current values." + ] + } + ], + "prompt_number": 3 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from scipy.stats.mstats import mquantiles\n", + "\n", + "samples = mcmc.trace(\"n_sign_ups\")[:]\n", + "\n", + "hist(samples, bins=100,\n", + " label=\"Uniform prior\",\n", + " normed=True, alpha=0.8,\n", + " histtype=\"stepfilled\", color=\"#7A68A6\");\n", + "\n", + "quantiles_mean = np.append(mquantiles(samples, [0.05, 0.5, 0.95]), samples.mean())\n", + "print \"Quantiles: \", quantiles_mean[:3]\n", + "print \"Mean: \", quantiles_mean[-1]\n", + "plt.vlines(quantiles_mean, 0, 33,\n", + " linewidth=2, linestyles=[\"--\", \"--\", \"--\", \"-\"],\n", + " )\n", + "plt.title(\"Posterior distribution of total number of Github users\")\n", + "plt.xlabel(\"number of users (in millions)\")\n", + "plt.legend()\n", + "plt.xlim(ids.max() / FACTOR - 0.01, ids.max() / FACTOR + 0.12);" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "ename": "NameError", + "evalue": "name 'mcmc' is not defined", + "output_type": "pyerr", + "traceback": [ + "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m\n\u001b[1;31mNameError\u001b[0m Traceback (most recent call last)", + "\u001b[1;32m\u001b[0m in \u001b[0;36m\u001b[1;34m()\u001b[0m\n\u001b[0;32m 1\u001b[0m \u001b[1;32mfrom\u001b[0m \u001b[0mscipy\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mstats\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mmstats\u001b[0m \u001b[1;32mimport\u001b[0m \u001b[0mmquantiles\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 2\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m----> 3\u001b[1;33m \u001b[0msamples\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mmcmc\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mtrace\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;34m\"n_sign_ups\"\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m 4\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 5\u001b[0m hist(samples, bins = 100, \n", + "\u001b[1;31mNameError\u001b[0m: name 'mcmc' is not defined" + ] + } + ], + "prompt_number": 4 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Above we have plotted the posterior distribution. Note that there is no posterior probability assigned to the number of users being less than `ids.max()`. That is good, as it would be an impossible situation. \n", + "\n", + "The three dashed vertical bars, from left to right, are the 5%, 50% and 95% quantitle lines. That is, 5% of the probability is before the first line, 50% before the second and 95% before the third. The 50% quantitle is also know as the *median* and is a better measure of centrality than the mean for heavily skewed distributions like this one. The solid line is the posterior distribution's mean.\n", + "\n", + "So what can we say? Using the data above, there is a 95% chance that there are less than 4.4 million users, and is probably around 4.36 million users. I was wondering how accurate this figure was. At the time of this writing, it seems a bit high considering only five months prior the number was at 3 million:\n", + "\n", + "\n", + "

Last night @github crossed the 3M user mark #turntup

— Rick Bradley (@rickbradley) January 15, 2013
\n", + "\n", + "\n", + "\n", + "I thought perhaps the `user_id` parameter was being used liberally to users/bots/changed names etc, so I contacted Github Support about it:\n", + "\n", + "

@cmrn_dp User IDs are assigned to new users/organizations, whether they\u2019re controlled by humans, groups, or bots.

— GitHub Support (@GitHubHelp) May 6, 2013
\n", + "\n", + "\n", + "\n", + "So we may be overestimating by including organizations, which perhaps should not be counted as users. TODO: estimate the number of organizations. Any takers?" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [], + "language": "python", + "metadata": {}, + "outputs": [] + } + ], + "metadata": {} + } + ] } \ No newline at end of file diff --git a/sandbox/SpaceShuttleBayesFactor.ipynb b/sandbox/SpaceShuttleBayesFactor.ipynb index a26ccc13..4f3cf172 100644 --- a/sandbox/SpaceShuttleBayesFactor.ipynb +++ b/sandbox/SpaceShuttleBayesFactor.ipynb @@ -1,332 +1,332 @@ -{ - "metadata": { - "name": "SpaceShuttleBayesFactor" - }, - "nbformat": 3, - "nbformat_minor": 0, - "worksheets": [ - { - "cells": [ - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "###Bayes Factor for Log Regression/" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "#####Is there really a relationship between failure and temperature?\n", - "\n", - "An critism of our above analysis is that *assumed* that the relationship followed a logistic model, this we implictly assumed that the probabilities change over temperature. Let's look at the data again. (Top figure)\n", - "\n", - "Could it be that infact this particular sequence of defects occured by chance? After all, I can produce similar plots. (Bottom figure) This might explain the large overlap in temperatures." - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "figsize(12.5, 6)\n", - "subplot(211)\n", - "plt.scatter(challenger_data[:, 0], challenger_data[:, 1], s=75,\n", - " color=\"k\", alpha=0.5)\n", - "plt.yticks([0, 1])\n", - "plt.ylabel(\"Damage Incident?\")\n", - "plt.title(\"(Real) Defects of the Space Shuttle O-Rings vs temperature\")\n", - "\n", - "subplot(212)\n", - "n = challenger_data.shape[0]\n", - "plt.scatter(challenger_data[:, 0], stats.bernoulli.rvs(0.6, size=n),\n", - " s=75, color=\"k\", alpha=0.5)\n", - "plt.yticks([0, 1])\n", - "plt.ylabel(\"Damage Incident?\")\n", - "plt.xlabel(\"Outside temperature (Farhenhit)\")\n", - "plt.title(\"(Artificial) Defects of the Space Shuttle O-Rings vs \\\n", - "temperature\")" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "ename": "NameError", - "evalue": "name 'figsize' is not defined", - "output_type": "pyerr", - "traceback": [ - "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m\n\u001b[1;31mNameError\u001b[0m Traceback (most recent call last)", - "\u001b[1;32m\u001b[0m in \u001b[0;36m\u001b[1;34m()\u001b[0m\n\u001b[1;32m----> 1\u001b[1;33m \u001b[0mfigsize\u001b[0m\u001b[1;33m(\u001b[0m \u001b[1;36m12.5\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;36m6\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m 2\u001b[0m \u001b[0msubplot\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;36m211\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 3\u001b[0m plt.scatter( challenger_data[:,0], challenger_data[:,1], s = 75, \\\n\u001b[0;32m 4\u001b[0m color=\"k\", alpha = 0.5) \n\u001b[0;32m 5\u001b[0m \u001b[0mplt\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0myticks\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;36m0\u001b[0m\u001b[1;33m,\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n", - "\u001b[1;31mNameError\u001b[0m: name 'figsize' is not defined" - ] - } - ], - "prompt_number": 1 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "#### Introducing the Bayes factor \n", - "\n", - "The *Bayes factor* is a measure comparing two models. In our example, on the one hand we believe that temperature plays an important role in the probability of O-ring failures. On the other hand, we believe that there is no significant connection, and the pattern appears by coincidence. We can compare these model using the ratio of the *probabilities of observing the data, given the model*:\n", - "\n", - "$$ \\frac{ P( \\text{observations} | \\text{Model}_1 ) }{ P( \\text{observations} | \\text{Model}_2 ) }$$\n", - "\n", - "\n", - "Calculating this is not at all obvious. For simplicity, let's select a set of parameters from the posterior distribution (which is tantamount to selecting a particular model)." - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "alpha_hat = alpha_samples[0, 0] # select the first alpha sample\n", - "beta_hat = beta_samples[0, 0] # select the first beta sample\n", - "\n", - "p_hat = logistic(temperature, beta_hat, alpha_hat)\n", - "print \"estimates of probability at observed temperature, defects: \"\n", - "print np.array(zip(p_hat, temperature, D))[:3, :]\n", - "print \"...\"" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "ename": "NameError", - "evalue": "name 'alpha_samples' is not defined", - "output_type": "pyerr", - "traceback": [ - "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m\n\u001b[1;31mNameError\u001b[0m Traceback (most recent call last)", - "\u001b[1;32m\u001b[0m in \u001b[0;36m\u001b[1;34m()\u001b[0m\n\u001b[1;32m----> 1\u001b[1;33m \u001b[0malpha_hat\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0malpha_samples\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;36m0\u001b[0m\u001b[1;33m,\u001b[0m\u001b[1;36m0\u001b[0m\u001b[1;33m]\u001b[0m \u001b[1;31m#select the first alpha sample\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m 2\u001b[0m \u001b[0mbeta_hat\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mbeta_samples\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;36m0\u001b[0m\u001b[1;33m,\u001b[0m\u001b[1;36m0\u001b[0m\u001b[1;33m]\u001b[0m \u001b[1;31m#select the first beta sample\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 3\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 4\u001b[0m \u001b[0mp_hat\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mlogistic\u001b[0m\u001b[1;33m(\u001b[0m \u001b[0mtemperature\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mbeta_hat\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0malpha_hat\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 5\u001b[0m \u001b[1;32mprint\u001b[0m \u001b[1;34m\"estimates of probability at observed temperature, defects: \"\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n", - "\u001b[1;31mNameError\u001b[0m: name 'alpha_samples' is not defined" - ] - } - ], - "prompt_number": 2 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "To calculate the numerator in the Bayes factor, we start by **assuming a model**, in our case assume `alpha_hat`, `beta_hat` are true, and calculate the probability of the defects we observe, equal to the product of:\n", - "\n", - "$$ P(\\; \\text{Ber}(\\; p(t_i \\; | \\; \\hat{\\beta}, \\hat{\\alpha} )\\; ) = D_i \\; ),\\;\\; i=1..N $$\n", - "\n", - "For example, using the output above, the first computation, $i=0$, would look like \n", - "\n", - "\\begin{align}\n", - "& p = p(t_1 \\; | \\; \\hat{\\beta}, \\hat{\\alpha} ) = 0.667 \\\\\\\\\n", - "& d = D_0 = 0 \\\\\\\\\n", - "& \\Rightarrow \\; P( \\; \\text{Ber}(p) = d ) = ?? \n", - "\\end{align}\n", - "\n", - "The probability of this ocurring is $(1-0.667) = 0.333\\; $ (Recall the definition of a Bernoulli random variable $\\text{Ber}(p)$: it is equal to $1$ with probability $p$ and equal to 0 with probability $1-p$). As each observation is independent, we multiply all the observations together. A clever way to do this for a specific $i$ is, recalling the $D_i$ can only be 1 or 0:\n", - "\n", - "$$\\left( p(t_1 \\; | \\; \\hat{\\beta}, \\hat{\\alpha} )\\right)^{D_i} \\left( 1 - p(t_1 \\; | \\; \\hat{\\beta}, \\hat{\\alpha} ) \\right)^{(1-D_i)}$$\n", - "\n", - "\n", - "(it is possible that the quantity can overflow, so it is recommended to take the $\\log$ of the above::\n", - "\n", - "$$ D_i\\log( p(t_1 \\; | \\; \\hat{\\beta}, \\hat{\\alpha} ) ) + (1-D_i)\\log( 1- p(t_1 \\; | \\; \\hat{\\beta}, \\hat{\\alpha} ) ) $$\n", - "\n", - "and sum the terms instead of multiplying. Be sure to use this transform for both models you are comparing.)" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "print p_hat\n", - "_product = p_hat ** (D) * (1 - p_hat) ** (1 - D)\n", - "prob_given_model_1 = _product.prod()\n", - "print \"probability of observations, model 1: %.10f\" % prob_given_model_1" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "ename": "NameError", - "evalue": "name 'p_hat' is not defined", - "output_type": "pyerr", - "traceback": [ - "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m\n\u001b[1;31mNameError\u001b[0m Traceback (most recent call last)", - "\u001b[1;32m\u001b[0m in \u001b[0;36m\u001b[1;34m()\u001b[0m\n\u001b[1;32m----> 1\u001b[1;33m \u001b[1;32mprint\u001b[0m \u001b[0mp_hat\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m 2\u001b[0m \u001b[0m_product\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mp_hat\u001b[0m\u001b[1;33m**\u001b[0m\u001b[1;33m(\u001b[0m \u001b[0mD\u001b[0m \u001b[1;33m)\u001b[0m\u001b[1;33m*\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m-\u001b[0m\u001b[0mp_hat\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m**\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m-\u001b[0m\u001b[0mD\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 3\u001b[0m \u001b[0mprob_given_model_1\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0m_product\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mprod\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 4\u001b[0m \u001b[1;32mprint\u001b[0m \u001b[1;34m\"probability of observations, model 1: %.10f\"\u001b[0m\u001b[1;33m%\u001b[0m\u001b[0mprob_given_model_1\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n", - "\u001b[1;31mNameError\u001b[0m: name 'p_hat' is not defined" - ] - } - ], - "prompt_number": 3 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "The second model we are comparing against is that $\\beta=0$, i.e. there is no relationship between probabilites and temperature. We perform the same calculations as above. Notice that `beta=0` here in the below PyMC code:" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "beta = 0\n", - "alpha = pm.Normal(\"alpha\", 0, 0.001, value=0)\n", - "\n", - "\n", - "@pm.deterministic\n", - "def p(temp=temperature, alpha=alpha, beta=beta):\n", - " return 1.0 / (1. + np.exp(beta * temperature + alpha))\n", - "\n", - "\n", - "observed = pm.Bernoulli(\"bernoulli_obs\", p,\n", - " value=D, observed=True)\n", - "\n", - "model = pm.Model({\"observed\": observed, \"beta\": beta, \"alpha\": alpha})\n", - "\n", - "# mysterious code to be explained in Chapter 3\n", - "map_ = pm.MAP(model)\n", - "map_.fit()\n", - "mcmc = pm.MCMC(model)\n", - "mcmc.sample(260000, 220000, 3)\n", - "######\n", - "\n", - "alpha_samples_model_2 = mcmc.trace(\"alpha\")[:, None]\n", - "alpha_hat = alpha_samples_model_2[0] # use the first 'model'\n", - "beta_hat = 0\n", - "\n", - "p_hat = logistic(temperature, beta_hat, alpha_hat)\n", - "print \"estimates of probability at observed temperature, defects: \"\n", - "print np.array(zip(p_hat, temperature, D))[:3, :]\n", - "print\n", - "print \"Notice the probability is constant for all temperatures?\"" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "ename": "NameError", - "evalue": "name 'mc' is not defined", - "output_type": "pyerr", - "traceback": [ - "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m\n\u001b[1;31mNameError\u001b[0m Traceback (most recent call last)", - "\u001b[1;32m\u001b[0m in \u001b[0;36m\u001b[1;34m()\u001b[0m\n\u001b[0;32m 1\u001b[0m \u001b[0mbeta\u001b[0m \u001b[1;33m=\u001b[0m \u001b[1;36m0\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m----> 2\u001b[1;33m \u001b[0malpha\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mmc\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mNormal\u001b[0m\u001b[1;33m(\u001b[0m \u001b[1;34m\"alpha\"\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;36m0\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;36m0.001\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mvalue\u001b[0m \u001b[1;33m=\u001b[0m \u001b[1;36m0\u001b[0m \u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m 3\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 4\u001b[0m \u001b[1;33m@\u001b[0m\u001b[0mmc\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mdeterministic\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 5\u001b[0m \u001b[1;32mdef\u001b[0m \u001b[0mp\u001b[0m\u001b[1;33m(\u001b[0m \u001b[0mtemp\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mtemperature\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0malpha\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0malpha\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mbeta\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mbeta\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n", - "\u001b[1;31mNameError\u001b[0m: name 'mc' is not defined" - ] - } - ], - "prompt_number": 4 - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "# compute the probability of observations given the model_2\n", - "\n", - "_product = p_hat ** (D) * (1 - p_hat) ** (1 - D)\n", - "prob_given_model_2 = _product.prod()\n", - "print \"probability of observations, model 2: %.10f\" % prob_given_model_2" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "ename": "NameError", - "evalue": "name 'p_hat' is not defined", - "output_type": "pyerr", - "traceback": [ - "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m\n\u001b[1;31mNameError\u001b[0m Traceback (most recent call last)", - "\u001b[1;32m\u001b[0m in \u001b[0;36m\u001b[1;34m()\u001b[0m\n\u001b[0;32m 1\u001b[0m \u001b[1;31m#compute the probability of observations given the model_2\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 2\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m----> 3\u001b[1;33m \u001b[0m_product\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mp_hat\u001b[0m\u001b[1;33m**\u001b[0m\u001b[1;33m(\u001b[0m \u001b[0mD\u001b[0m \u001b[1;33m)\u001b[0m\u001b[1;33m*\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m-\u001b[0m\u001b[0mp_hat\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m**\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m-\u001b[0m\u001b[0mD\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m 4\u001b[0m \u001b[0mprob_given_model_2\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0m_product\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mprod\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 5\u001b[0m \u001b[1;32mprint\u001b[0m \u001b[1;34m\"probability of observations, model 2: %.10f\"\u001b[0m\u001b[1;33m%\u001b[0m\u001b[0mprob_given_model_2\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n", - "\u001b[1;31mNameError\u001b[0m: name 'p_hat' is not defined" - ] - } - ], - "prompt_number": 5 - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "print \"Bayes factor = %.3f\" % (prob_given_model_1 / prob_given_model_2)" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "ename": "NameError", - "evalue": "name 'prob_given_model_1' is not defined", - "output_type": "pyerr", - "traceback": [ - "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m\n\u001b[1;31mNameError\u001b[0m Traceback (most recent call last)", - "\u001b[1;32m\u001b[0m in \u001b[0;36m\u001b[1;34m()\u001b[0m\n\u001b[1;32m----> 1\u001b[1;33m \u001b[1;32mprint\u001b[0m \u001b[1;34m\"Bayes factor = %.3f\"\u001b[0m\u001b[1;33m%\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mprob_given_model_1\u001b[0m\u001b[1;33m/\u001b[0m\u001b[0mprob_given_model_2\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m", - "\u001b[1;31mNameError\u001b[0m: name 'prob_given_model_1' is not defined" - ] - } - ], - "prompt_number": 7 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Is this good? Below is a chart that can be used to compare the computed Bayes factors to a degree of confidence in M1. \n", - "\n", - "
Bayes factorSupporting M1
<1:1 Negative (supports M2)
1:1 to 3:1 Barely worth mentioning
3:1 to 10:1 Substantial
10:1 to 30:1 Strong
30:1 to 100:1 Very strong
> 100:1 Decisive
\n", - "\n", - "We are not done yet. If you recall, we selected only one model, but recall we actually have a distribution of possible models (sequential pairs of ($\\beta, \\alpha$) from the posterior distributions). So to be correct we need to average over samples from the posterior:" - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "p = logistic(temperature[None, :], beta_samples, alpha_samples)\n", - "_product = p ** (D) * (1 - p) ** (1 - D)\n", - "prob_given_model_1 = _product.prod(axis=1).mean()\n", - "print \"expected prob. of obs., given model 1: %.10f\" % prob_given_model_1\n", - "\n", - "\n", - "p_model_2 = logistic(temperature[:, None],\n", - " np.zeros_like(temperature), alpha_samples_model_2)\n", - "\n", - "_product = p_model_2 ** (D) * (1 - p_model_2) ** (1 - D)\n", - "prob_given_model_2 = _product.prod(axis=1).mean()\n", - "print \"expected prob. of obs., given model 2: %.10f\" % prob_given_model_2\n", - "print\n", - "print \"Bayes factor: %.3f\" % (prob_given_model_1 / prob_given_model_2)" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "ename": "NameError", - "evalue": "name 'logistic' is not defined", - "output_type": "pyerr", - "traceback": [ - "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m\n\u001b[1;31mNameError\u001b[0m Traceback (most recent call last)", - "\u001b[1;32m\u001b[0m in \u001b[0;36m\u001b[1;34m()\u001b[0m\n\u001b[1;32m----> 1\u001b[1;33m \u001b[0mp\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mlogistic\u001b[0m\u001b[1;33m(\u001b[0m \u001b[0mtemperature\u001b[0m\u001b[1;33m[\u001b[0m\u001b[0mNone\u001b[0m\u001b[1;33m,\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mbeta_samples\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0malpha_samples\u001b[0m \u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m 2\u001b[0m \u001b[0m_product\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mp\u001b[0m\u001b[1;33m**\u001b[0m\u001b[1;33m(\u001b[0m \u001b[0mD\u001b[0m \u001b[1;33m)\u001b[0m\u001b[1;33m*\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m-\u001b[0m\u001b[0mp\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m**\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m-\u001b[0m\u001b[0mD\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 3\u001b[0m \u001b[0mprob_given_model_1\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0m_product\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mprod\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0maxis\u001b[0m\u001b[1;33m=\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mmean\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 4\u001b[0m \u001b[1;32mprint\u001b[0m \u001b[1;34m\"expected prob. of obs., given model 1: %.10f\"\u001b[0m\u001b[1;33m%\u001b[0m\u001b[0mprob_given_model_1\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 5\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n", - "\u001b[1;31mNameError\u001b[0m: name 'logistic' is not defined" - ] - } - ], - "prompt_number": 9 - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "It looks we have a pretty good model, and temperature *is* significant. Look at you, you're a rocket scientist now." - ] - }, - { - "cell_type": "code", - "collapsed": false, - "input": [], - "language": "python", - "metadata": {}, - "outputs": [] - } - ], - "metadata": {} - } - ] +{ + "metadata": { + "name": "SpaceShuttleBayesFactor" + }, + "nbformat": 3, + "nbformat_minor": 0, + "worksheets": [ + { + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "###Bayes Factor for Log Regression/" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "#####Is there really a relationship between failure and temperature?\n", + "\n", + "An critism of our above analysis is that *assumed* that the relationship followed a logistic model, this we implictly assumed that the probabilities change over temperature. Let's look at the data again. (Top figure)\n", + "\n", + "Could it be that infact this particular sequence of defects occured by chance? After all, I can produce similar plots. (Bottom figure) This might explain the large overlap in temperatures." + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "figsize(12.5, 6)\n", + "subplot(211)\n", + "plt.scatter(challenger_data[:, 0], challenger_data[:, 1], s=75,\n", + " color=\"k\", alpha=0.5)\n", + "plt.yticks([0, 1])\n", + "plt.ylabel(\"Damage Incident?\")\n", + "plt.title(\"(Real) Defects of the Space Shuttle O-Rings vs temperature\")\n", + "\n", + "subplot(212)\n", + "n = challenger_data.shape[0]\n", + "plt.scatter(challenger_data[:, 0], stats.bernoulli.rvs(0.6, size=n),\n", + " s=75, color=\"k\", alpha=0.5)\n", + "plt.yticks([0, 1])\n", + "plt.ylabel(\"Damage Incident?\")\n", + "plt.xlabel(\"Outside temperature (Farhenhit)\")\n", + "plt.title(\"(Artificial) Defects of the Space Shuttle O-Rings vs \\\n", + "temperature\")" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "ename": "NameError", + "evalue": "name 'figsize' is not defined", + "output_type": "pyerr", + "traceback": [ + "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m\n\u001b[1;31mNameError\u001b[0m Traceback (most recent call last)", + "\u001b[1;32m\u001b[0m in \u001b[0;36m\u001b[1;34m()\u001b[0m\n\u001b[1;32m----> 1\u001b[1;33m \u001b[0mfigsize\u001b[0m\u001b[1;33m(\u001b[0m \u001b[1;36m12.5\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;36m6\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m 2\u001b[0m \u001b[0msubplot\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;36m211\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 3\u001b[0m plt.scatter( challenger_data[:,0], challenger_data[:,1], s = 75, \\\n\u001b[0;32m 4\u001b[0m color=\"k\", alpha = 0.5) \n\u001b[0;32m 5\u001b[0m \u001b[0mplt\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0myticks\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;36m0\u001b[0m\u001b[1;33m,\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n", + "\u001b[1;31mNameError\u001b[0m: name 'figsize' is not defined" + ] + } + ], + "prompt_number": 1 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "#### Introducing the Bayes factor \n", + "\n", + "The *Bayes factor* is a measure comparing two models. In our example, on the one hand we believe that temperature plays an important role in the probability of O-ring failures. On the other hand, we believe that there is no significant connection, and the pattern appears by coincidence. We can compare these model using the ratio of the *probabilities of observing the data, given the model*:\n", + "\n", + "$$ \\frac{ P( \\text{observations} | \\text{Model}_1 ) }{ P( \\text{observations} | \\text{Model}_2 ) }$$\n", + "\n", + "\n", + "Calculating this is not at all obvious. For simplicity, let's select a set of parameters from the posterior distribution (which is tantamount to selecting a particular model)." + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "alpha_hat = alpha_samples[0, 0] # select the first alpha sample\n", + "beta_hat = beta_samples[0, 0] # select the first beta sample\n", + "\n", + "p_hat = logistic(temperature, beta_hat, alpha_hat)\n", + "print \"estimates of probability at observed temperature, defects: \"\n", + "print np.array(zip(p_hat, temperature, D))[:3, :]\n", + "print \"...\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "ename": "NameError", + "evalue": "name 'alpha_samples' is not defined", + "output_type": "pyerr", + "traceback": [ + "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m\n\u001b[1;31mNameError\u001b[0m Traceback (most recent call last)", + "\u001b[1;32m\u001b[0m in \u001b[0;36m\u001b[1;34m()\u001b[0m\n\u001b[1;32m----> 1\u001b[1;33m \u001b[0malpha_hat\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0malpha_samples\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;36m0\u001b[0m\u001b[1;33m,\u001b[0m\u001b[1;36m0\u001b[0m\u001b[1;33m]\u001b[0m \u001b[1;31m#select the first alpha sample\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m 2\u001b[0m \u001b[0mbeta_hat\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mbeta_samples\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;36m0\u001b[0m\u001b[1;33m,\u001b[0m\u001b[1;36m0\u001b[0m\u001b[1;33m]\u001b[0m \u001b[1;31m#select the first beta sample\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 3\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 4\u001b[0m \u001b[0mp_hat\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mlogistic\u001b[0m\u001b[1;33m(\u001b[0m \u001b[0mtemperature\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mbeta_hat\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0malpha_hat\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 5\u001b[0m \u001b[1;32mprint\u001b[0m \u001b[1;34m\"estimates of probability at observed temperature, defects: \"\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n", + "\u001b[1;31mNameError\u001b[0m: name 'alpha_samples' is not defined" + ] + } + ], + "prompt_number": 2 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "To calculate the numerator in the Bayes factor, we start by **assuming a model**, in our case assume `alpha_hat`, `beta_hat` are true, and calculate the probability of the defects we observe, equal to the product of:\n", + "\n", + "$$ P(\\; \\text{Ber}(\\; p(t_i \\; | \\; \\hat{\\beta}, \\hat{\\alpha} )\\; ) = D_i \\; ),\\;\\; i=1..N $$\n", + "\n", + "For example, using the output above, the first computation, $i=0$, would look like \n", + "\n", + "\\begin{align}\n", + "& p = p(t_1 \\; | \\; \\hat{\\beta}, \\hat{\\alpha} ) = 0.667 \\\\\\\\\n", + "& d = D_0 = 0 \\\\\\\\\n", + "& \\Rightarrow \\; P( \\; \\text{Ber}(p) = d ) = ?? \n", + "\\end{align}\n", + "\n", + "The probability of this ocurring is $(1-0.667) = 0.333\\; $ (Recall the definition of a Bernoulli random variable $\\text{Ber}(p)$: it is equal to $1$ with probability $p$ and equal to 0 with probability $1-p$). As each observation is independent, we multiply all the observations together. A clever way to do this for a specific $i$ is, recalling the $D_i$ can only be 1 or 0:\n", + "\n", + "$$\\left( p(t_1 \\; | \\; \\hat{\\beta}, \\hat{\\alpha} )\\right)^{D_i} \\left( 1 - p(t_1 \\; | \\; \\hat{\\beta}, \\hat{\\alpha} ) \\right)^{(1-D_i)}$$\n", + "\n", + "\n", + "(it is possible that the quantity can overflow, so it is recommended to take the $\\log$ of the above::\n", + "\n", + "$$ D_i\\log( p(t_1 \\; | \\; \\hat{\\beta}, \\hat{\\alpha} ) ) + (1-D_i)\\log( 1- p(t_1 \\; | \\; \\hat{\\beta}, \\hat{\\alpha} ) ) $$\n", + "\n", + "and sum the terms instead of multiplying. Be sure to use this transform for both models you are comparing.)" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "print p_hat\n", + "_product = p_hat ** (D) * (1 - p_hat) ** (1 - D)\n", + "prob_given_model_1 = _product.prod()\n", + "print \"probability of observations, model 1: %.10f\" % prob_given_model_1" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "ename": "NameError", + "evalue": "name 'p_hat' is not defined", + "output_type": "pyerr", + "traceback": [ + "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m\n\u001b[1;31mNameError\u001b[0m Traceback (most recent call last)", + "\u001b[1;32m\u001b[0m in \u001b[0;36m\u001b[1;34m()\u001b[0m\n\u001b[1;32m----> 1\u001b[1;33m \u001b[1;32mprint\u001b[0m \u001b[0mp_hat\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m 2\u001b[0m \u001b[0m_product\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mp_hat\u001b[0m\u001b[1;33m**\u001b[0m\u001b[1;33m(\u001b[0m \u001b[0mD\u001b[0m \u001b[1;33m)\u001b[0m\u001b[1;33m*\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m-\u001b[0m\u001b[0mp_hat\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m**\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m-\u001b[0m\u001b[0mD\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 3\u001b[0m \u001b[0mprob_given_model_1\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0m_product\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mprod\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 4\u001b[0m \u001b[1;32mprint\u001b[0m \u001b[1;34m\"probability of observations, model 1: %.10f\"\u001b[0m\u001b[1;33m%\u001b[0m\u001b[0mprob_given_model_1\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n", + "\u001b[1;31mNameError\u001b[0m: name 'p_hat' is not defined" + ] + } + ], + "prompt_number": 3 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The second model we are comparing against is that $\\beta=0$, i.e. there is no relationship between probabilites and temperature. We perform the same calculations as above. Notice that `beta=0` here in the below PyMC code:" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "beta = 0\n", + "alpha = pm.Normal(\"alpha\", 0, 0.001, value=0)\n", + "\n", + "\n", + "@pm.deterministic\n", + "def p(temp=temperature, alpha=alpha, beta=beta):\n", + " return 1.0 / (1. + np.exp(beta * temperature + alpha))\n", + "\n", + "\n", + "observed = pm.Bernoulli(\"bernoulli_obs\", p,\n", + " value=D, observed=True)\n", + "\n", + "model = pm.Model({\"observed\": observed, \"beta\": beta, \"alpha\": alpha})\n", + "\n", + "# mysterious code to be explained in Chapter 3\n", + "map_ = pm.MAP(model)\n", + "map_.fit()\n", + "mcmc = pm.MCMC(model)\n", + "mcmc.sample(260000, 220000, 3)\n", + "######\n", + "\n", + "alpha_samples_model_2 = mcmc.trace(\"alpha\")[:, None]\n", + "alpha_hat = alpha_samples_model_2[0] # use the first 'model'\n", + "beta_hat = 0\n", + "\n", + "p_hat = logistic(temperature, beta_hat, alpha_hat)\n", + "print \"estimates of probability at observed temperature, defects: \"\n", + "print np.array(zip(p_hat, temperature, D))[:3, :]\n", + "print\n", + "print \"Notice the probability is constant for all temperatures?\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "ename": "NameError", + "evalue": "name 'mc' is not defined", + "output_type": "pyerr", + "traceback": [ + "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m\n\u001b[1;31mNameError\u001b[0m Traceback (most recent call last)", + "\u001b[1;32m\u001b[0m in \u001b[0;36m\u001b[1;34m()\u001b[0m\n\u001b[0;32m 1\u001b[0m \u001b[0mbeta\u001b[0m \u001b[1;33m=\u001b[0m \u001b[1;36m0\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m----> 2\u001b[1;33m \u001b[0malpha\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mmc\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mNormal\u001b[0m\u001b[1;33m(\u001b[0m \u001b[1;34m\"alpha\"\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;36m0\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;36m0.001\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mvalue\u001b[0m \u001b[1;33m=\u001b[0m \u001b[1;36m0\u001b[0m \u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m 3\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 4\u001b[0m \u001b[1;33m@\u001b[0m\u001b[0mmc\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mdeterministic\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 5\u001b[0m \u001b[1;32mdef\u001b[0m \u001b[0mp\u001b[0m\u001b[1;33m(\u001b[0m \u001b[0mtemp\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mtemperature\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0malpha\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0malpha\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mbeta\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mbeta\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n", + "\u001b[1;31mNameError\u001b[0m: name 'mc' is not defined" + ] + } + ], + "prompt_number": 4 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# compute the probability of observations given the model_2\n", + "\n", + "_product = p_hat ** (D) * (1 - p_hat) ** (1 - D)\n", + "prob_given_model_2 = _product.prod()\n", + "print \"probability of observations, model 2: %.10f\" % prob_given_model_2" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "ename": "NameError", + "evalue": "name 'p_hat' is not defined", + "output_type": "pyerr", + "traceback": [ + "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m\n\u001b[1;31mNameError\u001b[0m Traceback (most recent call last)", + "\u001b[1;32m\u001b[0m in \u001b[0;36m\u001b[1;34m()\u001b[0m\n\u001b[0;32m 1\u001b[0m \u001b[1;31m#compute the probability of observations given the model_2\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 2\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m----> 3\u001b[1;33m \u001b[0m_product\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mp_hat\u001b[0m\u001b[1;33m**\u001b[0m\u001b[1;33m(\u001b[0m \u001b[0mD\u001b[0m \u001b[1;33m)\u001b[0m\u001b[1;33m*\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m-\u001b[0m\u001b[0mp_hat\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m**\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m-\u001b[0m\u001b[0mD\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m 4\u001b[0m \u001b[0mprob_given_model_2\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0m_product\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mprod\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 5\u001b[0m \u001b[1;32mprint\u001b[0m \u001b[1;34m\"probability of observations, model 2: %.10f\"\u001b[0m\u001b[1;33m%\u001b[0m\u001b[0mprob_given_model_2\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n", + "\u001b[1;31mNameError\u001b[0m: name 'p_hat' is not defined" + ] + } + ], + "prompt_number": 5 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "print \"Bayes factor = %.3f\" % (prob_given_model_1 / prob_given_model_2)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "ename": "NameError", + "evalue": "name 'prob_given_model_1' is not defined", + "output_type": "pyerr", + "traceback": [ + "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m\n\u001b[1;31mNameError\u001b[0m Traceback (most recent call last)", + "\u001b[1;32m\u001b[0m in \u001b[0;36m\u001b[1;34m()\u001b[0m\n\u001b[1;32m----> 1\u001b[1;33m \u001b[1;32mprint\u001b[0m \u001b[1;34m\"Bayes factor = %.3f\"\u001b[0m\u001b[1;33m%\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mprob_given_model_1\u001b[0m\u001b[1;33m/\u001b[0m\u001b[0mprob_given_model_2\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m", + "\u001b[1;31mNameError\u001b[0m: name 'prob_given_model_1' is not defined" + ] + } + ], + "prompt_number": 7 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Is this good? Below is a chart that can be used to compare the computed Bayes factors to a degree of confidence in M1. \n", + "\n", + "
Bayes factorSupporting M1
<1:1 Negative (supports M2)
1:1 to 3:1 Barely worth mentioning
3:1 to 10:1 Substantial
10:1 to 30:1 Strong
30:1 to 100:1 Very strong
> 100:1 Decisive
\n", + "\n", + "We are not done yet. If you recall, we selected only one model, but recall we actually have a distribution of possible models (sequential pairs of ($\\beta, \\alpha$) from the posterior distributions). So to be correct we need to average over samples from the posterior:" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "p = logistic(temperature[None, :], beta_samples, alpha_samples)\n", + "_product = p ** (D) * (1 - p) ** (1 - D)\n", + "prob_given_model_1 = _product.prod(axis=1).mean()\n", + "print \"expected prob. of obs., given model 1: %.10f\" % prob_given_model_1\n", + "\n", + "\n", + "p_model_2 = logistic(temperature[:, None],\n", + " np.zeros_like(temperature), alpha_samples_model_2)\n", + "\n", + "_product = p_model_2 ** (D) * (1 - p_model_2) ** (1 - D)\n", + "prob_given_model_2 = _product.prod(axis=1).mean()\n", + "print \"expected prob. of obs., given model 2: %.10f\" % prob_given_model_2\n", + "print\n", + "print \"Bayes factor: %.3f\" % (prob_given_model_1 / prob_given_model_2)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "ename": "NameError", + "evalue": "name 'logistic' is not defined", + "output_type": "pyerr", + "traceback": [ + "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m\n\u001b[1;31mNameError\u001b[0m Traceback (most recent call last)", + "\u001b[1;32m\u001b[0m in \u001b[0;36m\u001b[1;34m()\u001b[0m\n\u001b[1;32m----> 1\u001b[1;33m \u001b[0mp\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mlogistic\u001b[0m\u001b[1;33m(\u001b[0m \u001b[0mtemperature\u001b[0m\u001b[1;33m[\u001b[0m\u001b[0mNone\u001b[0m\u001b[1;33m,\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mbeta_samples\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0malpha_samples\u001b[0m \u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m 2\u001b[0m \u001b[0m_product\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mp\u001b[0m\u001b[1;33m**\u001b[0m\u001b[1;33m(\u001b[0m \u001b[0mD\u001b[0m \u001b[1;33m)\u001b[0m\u001b[1;33m*\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m-\u001b[0m\u001b[0mp\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m**\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m-\u001b[0m\u001b[0mD\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 3\u001b[0m \u001b[0mprob_given_model_1\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0m_product\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mprod\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0maxis\u001b[0m\u001b[1;33m=\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mmean\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 4\u001b[0m \u001b[1;32mprint\u001b[0m \u001b[1;34m\"expected prob. of obs., given model 1: %.10f\"\u001b[0m\u001b[1;33m%\u001b[0m\u001b[0mprob_given_model_1\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 5\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n", + "\u001b[1;31mNameError\u001b[0m: name 'logistic' is not defined" + ] + } + ], + "prompt_number": 9 + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "It looks we have a pretty good model, and temperature *is* significant. Look at you, you're a rocket scientist now." + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [], + "language": "python", + "metadata": {}, + "outputs": [] + } + ], + "metadata": {} + } + ] } \ No newline at end of file diff --git a/sandbox/Sum of Gaussian Distributions + noise.ipynb b/sandbox/Sum of Gaussian Distributions + noise.ipynb index 4e672231..096dc069 100644 --- a/sandbox/Sum of Gaussian Distributions + noise.ipynb +++ b/sandbox/Sum of Gaussian Distributions + noise.ipynb @@ -1,272 +1,272 @@ -{ - "metadata": { - "name": "Sum of Gaussian Distributions + noise" - }, - "nbformat": 3, - "nbformat_minor": 0, - "worksheets": [ - { - "cells": [ - { - "cell_type": "code", - "collapsed": false, - "input": [ - "import pymc as pm\n", - "import numpy as np\n", - "import pylab as pl\n", - "\n", - "\n", - "def GaussFunc(x, amplitude, centroid, sigma):\n", - " return amplitude * np.exp(-0.5 * ((x - centroid) / sigma) ** 2)\n", - "\n", - "wavelength = np.arange(5000, 5050, 0.02)\n", - "\n", - "# Profile 1\n", - "centroid_one = 5025.0\n", - "sigma_one = 2.2\n", - "height_one = 0.8\n", - "profile1 = GaussFunc(wavelength, height_one, centroid_one, sigma_one, )\n", - "\n", - "# Profile 2\n", - "centroid_two = 5027.0\n", - "sigma_two = 1.2\n", - "height_two = 0.5\n", - "profile2 = GaussFunc(wavelength, height_two, centroid_two, sigma_two, )\n", - "\n", - "# Measured values\n", - "noise = np.random.normal(0.0, 0.02, len(wavelength))\n", - "combined = profile1 + profile2 + noise\n", - "\n", - "# If you want to plot what this looks like\n", - "pl.plot(wavelength, combined, label=\"Measured\")\n", - "pl.plot(wavelength, profile1, color='red', linestyle='dashed', label=\"1\")\n", - "pl.plot(wavelength, profile2, color='green', linestyle='dashed', label=\"2\")\n", - "pl.title(\"Feature One and Two\")\n", - "pl.legend()" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "output_type": "pyout", - "prompt_number": 1, - "text": [ - "" - ] - }, - { - "output_type": "display_data", - "png": 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D8HRS8Odhmt6AUqVudB1Fu9AhdGE+xAowgeA2Hz68jHeqLiGfPLlOmcqnn0Zy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\n+VkSgJ8A99JCKuRbUUi66c81D5mSyvac83emvUq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- } - ], - "prompt_number": 1 - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "# Unknowns\n", - "\n", - "est_centroid_one = pm.Uniform(\"est_centroid_one\", 5000, 5050)\n", - "est_centroid_two = pm.Uniform(\"est_centroid_two\", 5000, 5050)\n", - "\n", - "est_sigma_one = pm.Uniform(\"est_sigma_one\", 0, 5)\n", - "est_sigma_two = pm.Uniform(\"est_sigma_two\", 0, 5)\n", - "\n", - "est_height_one = pm.Uniform(\"est_height_one\", 0, 5)\n", - "est_height_two = pm.Uniform(\"est_height_two\", 0, 5)\n", - "\n", - "std_deviation = 1. / mc.Uniform(\"std\", 0, 1) ** 2\n", - "\n", - "# Set up the inference\n", - "\n", - "\n", - "@pm.deterministic(trace=False)\n", - "def est_profile_1(x=wavelength, centroid=est_centroid_one, sigma=est_sigma_one, height=est_height_one):\n", - " return GaussFunc(x, height, centroid, sigma)\n", - "\n", - "\n", - "@pm.deterministic(trace=False)\n", - "def est_profile_2(x=wavelength, centroid=est_centroid_two, sigma=est_sigma_two, height=est_height_two):\n", - " return GaussFunc(x, height, centroid, sigma)\n", - "\n", - "\n", - "@pm.deterministic(trace=False)\n", - "def mean(profile_1=est_profile_1, profile_2=est_profile_2):\n", - " return profile_1 + profile_2\n", - "\n", - "\n", - "observations = pm.Normal(\"obs\", mean, std_deviation, value=combined, observed=True)" - ], - "language": "python", - "metadata": {}, - "outputs": [], - "prompt_number": 5 - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "model = pm.Model([est_centroid_one,\n", - " est_centroid_two,\n", - " est_height_one,\n", - " est_height_two,\n", - " est_sigma_one,\n", - " est_sigma_two,\n", - " std_deviation])\n", - "\n", - "map_ = pm.MAP(model)\n", - "map_.fit()" - ], - "language": "python", - "metadata": {}, - "outputs": [], - "prompt_number": 17 - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "mcmc = pm.MCMC(model)\n", - "mcmc.sample(70000, 60000)" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "output_type": "stream", - "stream": "stdout", - "text": [ - " \r", - "[****************100%******************] 70000 of 70000 complete" - ] - }, - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "\n" - ] - } - ], - "prompt_number": 18 - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "mcplot(mcmc)" - ], - "language": "python", - "metadata": {}, - "outputs": [ - { - "output_type": "stream", - "stream": "stdout", - "text": [ - "Plotting est_height_one\n", - "Plotting" - ] - }, - { - "output_type": "stream", - "stream": "stdout", - "text": [ - " est_sigma_two\n", - "Plotting" - ] - }, - { - "output_type": "stream", - "stream": "stdout", - "text": [ - " est_height_two\n", - "Plotting" - ] - }, - { - "output_type": "stream", - "stream": "stdout", - "text": [ - " est_centroid_two\n", - "Plotting" - ] - }, - { - "output_type": "stream", - "stream": "stdout", - "text": [ - " est_centroid_one\n", - "Plotting" - ] - }, - { - "output_type": "stream", - "stream": "stdout", - "text": [ - " est_sigma_one\n", - "Plotting" - ] - }, - { - "output_type": "stream", - "stream": "stdout", - "text": [ - " std\n" - ] - }, - { - "output_type": "display_data", - "png": 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ERISFhRlVFiFztbBSpayWobm8Un6vlZSUaGlJIGhH2/NLo72+oKAA3t4tAbeK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lFjzElnPF+HCSJwb1tqGvXy6qwXu/5imVrc27ilmTo/Hb7WqlNhV9WzTUBQuH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\nyeNXrlzh22+/ZdasWQC4ubmZdLy0pnK/Sy3QSl20Ug/QVl3sLSIigk2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7WIQchukY0guq8JyXneqGBuSLUw9x/mElvnzeF7KPekntnCok97z4sFKp89Xd\nks9okoNkJnxJahpb8XLCTfj1sMLnk30Y28hm2iS814TrHTMa1flqcDm/HEEEV/Q0XLET4I6tdHaW\n1DThbqnqxNf6fAflyvXUFkY97Cj5zKB72DhaKUvuQM+TGvoZkzZ9QqiZjrKY800wpZ90eghZsbki\nxyvzcQ32/12C3NKO7deLdZuBXBtfgvMPRW9VZ+6XK42yqPpySzrQpXXKk3+O7tNdbp2imY50jnlT\nqxBVja1SZZDYgsZ5viQCsLKTPJhCd/+ekUSsBAKBoDFG7XxVN3ZEQejKDE3xVz9f1qqkbDwsl3eU\nmpVEByz4JnKfXq9iWBIAckrr8N6xHPxwqVjK8Th48ykq6rnx8DM14akVZZFFnaCLOhEacdNdCrR9\nxoLksOOs4J7U33XNrXK6Q0XQ3b9ahvsS2AEb9ElE82UYjM1OY9F8GbXztfVcR13KuQNd5LYrSz+h\njOUH78itq7x3XWF7FxszuQcYk9xXKw9lQ1H6pf9KnJu26cyX9VpRNT5L7ZgsYMLjdapcjSLHjW74\n14QHRAc6Sa0T5V+jOS5EotP46yUa26ZPNL0nNyRm7Xa37Ij0XsyvQvTuvxkdg+5aX3jYNcs1ETTH\nWGryEQyLsfQjo3a+zkkICoNduslt13QYRl0JzLuje8kNcymaNckUdXRT+mTt8Xs4/aAjdcevmU+Q\nX6E4RYaqO9AmEzMUOwKS4nExLW1CeNnLC/xpjysUdgktk5utOfW3puWF6F4Adlw27oihscEVPQ1X\n7AS4Yyuxk50YtfOljFfCXDrtAEmiLIu6l72F3LAjnfOgHrpzHJh8CSrqm/HB8XvIK9NdzUZAPvK1\naH8WWtuEtJHDljYhTGUcasWaL3ndHZvRNLt9sURqDU2dzYbmNiw/cFtufW0TGXokEAgETeiSztfK\nYR54JcwVTXosqSIZgQA6/+CvbdKe46gJL/18E1eLqvEazRCsOqi6CrLRmkfVTdh8+iFqm+RnNY7t\n251xNFPYBSJfNTLOkTopPiRJynqKB+Xy0cvapla0CYXECeMAbND9EM2XYTA2O4nmi4MM8bCBi40Z\npgaIdEGyDpEilg5xU9lGkbZITIhrN6wZ5QX/HlaMPlMViopJawNVXwJFjmOZitmIdDS1SDuRF/Mr\n8WFyLp60nx+dv/BnbrlcSaFRve0R5m4LU5npk4ruS5sQyGWY2oMNaPIDKjvUrcVAL8WnqQ8Q83Mm\ndb8IBEU3nzecAAAgAElEQVQYi1aHYFiMpR8ZtfM1rq8o9cDScJHz9GlkX+x6KVAtrdfJpaF4KcRZ\n4XbnbmbwsFPsxK0cJirDwuPxMMnPEQE9rRl/Nlu5TDNk+qy2GS8n3FT7WG8cviu1/Mkf93G5sIrK\nSaUoOFUkk6n+n+N7A2Cu4xMC+CA5Vz1jOYbstUu8of3JBWl5lWhqFeLYHfn6mgT2wBU9DVfsBLhj\nK7GTnRi18yXW/9i3JzTl8aQzl8tGBna8GIBtM/qp/Rk9rc0obZGDlXTy1NtPauXaawtdRRtUfQno\nhuvyKxoUzsyUpDdNxntJxIcWz5CkSxECKBbqM9V8cUnvBWj2wyQbNZQdhtQmmk5e0QWLFy+Gs7Mz\ngoODqXXvvvsuAgICEBISgpkzZ6KysmMyzoYNG+Dr6wt/f3+cPHmSWn/16lUEBwfD19cXb775pl7P\ngUAgGDdG7XyJ9UJMSsUM9bKFp72F3LCVGEU5wXydLBEjERkzkXELZB/x2nxGbT79UHsHUwO6S8Q0\nE7KLDbOh3ksFVfgw+R4aGORD04R1yfdUtqlubMEvf5egnCM51WSRnSmqjBlBPfDr/GCM95FPVKvw\n+BLenYBFzteiRYuQnJwstW7SpEm4desWbty4AT8/P2zYsAEAkJWVhcTERGRlZSE5ORmvv/469VK2\nYsUK7NixAzk5OcjJyZE7Jpdgg+6HaL4Mg7HZ2WU0X8nJyfD394evry82btwot720tBSTJ0/GwIED\n0b9/f+zatYvxvrom9V45AOlkqwpR8Zx6a4QX7fp/DPeEo5WA0hbxeKLUEmIGukqnuNCmOPlprW4i\nX6q+BHTOLFPny4SmxylKgXC5sBqvH8pWecyxfTscBhcbM6ltijRfOaXK9V5Pa5swf98tbL9UjI9P\n3ldpg67RTPPFvK2HnTlsLfiYH+rK3Ka8jpQi2ozodpaRI0eie3dpJ3LixIkwae98Q4cORWFhIQAg\nKSkJc+fOhUAggLe3N3x8fJCeno5Hjx6huroa4eHhAIAFCxbg0KFD+j0RI8NYtDoEw2Is/UhpbcfW\n1lasWrUKKSkpcHd3x5AhQxAdHY2AgACqzbZt2xAaGooNGzagtLQU/fr1w/z588Hj8VTuq0sks3ef\nflCBF/r3lGsz2MOW+rt7e6khV5mHtypsLfioknDuTHg89HGwpJbH+zhItTfnay/YaKhcX7SRL6b7\n0qyrb26DtZmpWjZIDnFK3keBlgrA/l/KA6oKQfZT1TXQ2EBrmxAFFQ3o1d0CPB5Prbxe4lqh6uQd\nlpywoK3rrg927tyJuXPnAgCKi4vx3HPPUds8PDxQVFQEgUAADw8Par27uzuKiopoj7dy5Up4eYle\nzmxtbREcHEwNE4udZrLMbFm8ji32KFseMWKEQa6PJEz3l20PiPqr+OVULM+QXS65k4Hz3Z9gzKiR\nOj8/Q1xPJsuZmZmoqhLpnPPz87FkyRJoA6XO16VLl+Dj4wNvb28AwJw5c5CUlCTlQLm6uuLvv0WZ\nsquqquDo6Ag+n48LFy6o3FeXHLndIQBW9FxwsBLg/yb1wcm7z7CkfUajlZkppvo7KqzTSIcJj0d1\n1oaWNlibdTzB+DIf3ksmCejwXnboYS1AUhZ7BMuq9EVMhnEVUUFT+HrloWx8Pc1XY93QBImhMoFM\naE1Z/jVlsM3hYqL5WvJrFoqrmrBkiBtiQpypyFc3M1PGei+ehHssWwxelr9yy6m/+XQhTRby2Wef\nwczMDPPmzdPaMb/99luF22TvG1kmy51ZlkXT411Nywcg//sou+zsH4bhEb5as5+Ly7LrMjIyoA2U\n/mIWFRXB09OTWha/FUqybNky3Lp1C25ubggJCcHWrVsZ76tLHkgk/5R9IEvynJcdPp7QB3YWHX6o\nuk6AZPPKhha42Jhj+VB3rB3TS85RmeQnrR2zt+BjfhjzoR42UNkg7UB9dTafUdb/CG87WieguKoR\nezIe47uLmvUPnsQ1NuNzJwKjbcSRUHH2efE9YTIkKI6SSXZXVWlRpAvXs38Cw65du/D777/j559/\npta5u7ujoKCjVFdhYSE8PDzg7u5ODU2K17u7u+vVXm3CBt0P0XwZBmOz01g0X0ojXzwGEY7PP/8c\nAwcOxKlTp5Cbm4uJEyfixo0bjA3QVci+rrmNCqEKvEaptf9E/zAcvV0Kv8YHSEurpbb3b3mACw8r\npUK0aWm18BsYLqMtCsWs4J5IS0tD2mO6ELA1tX9Bqx0EQ6dTy4DiEDDdsqR92gq5itcp2i5wDZKy\n5zgGoreDpUp7H2VdReajGtrtR26Xqtx/lVcFNvyVJ7cdCKXsa2xpA2BDba8rvgfnkS9qfH0llw0Z\nApe9N3TtZe29dPEcqnMfwil4iMrz69nNDGlpaahqaAEgGoJ8ePMKqnPLGV0foRL7AeDcuXPIzxe9\nbWsrbK8OycnJ2Lx5M06fPg0Li47oc3R0NObNm4d33nkHRUVFyMnJQXh4OHg8HmxtbZGeno7w8HDs\n2bPHKHQmhoRcP4I2MJZ+xBMqeWW9ePEiPvnkE2qWz4YNG2BiYoK1a9dSbaZMmYIPP/wQERERAIDx\n48dj48aNaGlpUblvamoqwsLCtH5SQqEQkTs6nKGR3vb4aEJvtY5R29QKK4GJlAPa2ibE9ktFOHjz\nKbXu5NJQVDW0IHL9HuqhdHJpqNJjT/rhGvX3rP49sTTcDVE7lSdpVYSqz9IESc0FHaful+PzP/Ok\n1r0Q1AO/3XpKv0M7Cwe5YvfVRxrbdXJpKGJ+zkS5xNDlK2EueEUmcih5fatzr2s89Cj72YZE1T0B\npM/75NJQ5Fc0YOmvt+HczUxpUt73x/TCuHZtYlldM+bEi/K1zRvozLjw+KrhHogO7MGobUZGBsaP\nH8+orSbMnTsXp0+fRmlpKZydnbF+/Xps2LABTU1NcHAQneewYcMQGxsLQPQCuXPnTvD5fGzduhWR\nkZEARKkmXn31VdTX12PKlCm0b9u6+g0jEOgQ99+ysrJOHWdrWj4jaU2/Hlb48nlfmKkjBjVytPX7\npTTyNXjwYOTk5CAvLw9ubm5ITExEQkKCVBt/f3+kpKQgIiICJSUlyM7ORp8+fWBra6tyX10hOwRm\nIVC/49AJwE1NpMX0YmzMTTV+wJuasGumGMBE8yW/js7xsjU3RZVEDcYXgnog/tpjNHcix1azTDIx\nuvvhYWeOwkpRElbJ+/L6MHfEXpAf2nxnpBccrPj45wnDz2pUBBPNlyzi9yplw+iBztaU4wVI31t1\nyi+xKW0a3e/M4sWLFbZft24d1q1bJ7d+0KBByMzM1KptBAKBAKjQfPH5fGzbtg2RkZEIDAxETEwM\nAgICEBcXh7i4OACiH64rV64gJCQEEyZMwKZNm+Dg4KBwX30gO8vL3kKpj6kW42RmLwLMhme1wZg+\n3als/Ybkd4aTET6f7CO1bM43gb1l5+6FrGaMLlmqbMUBazNT7IkJwnQFkRkPO3P4OWmn7BObEH8N\nlDlf5jJvtJIaxawnisX2NJ+mjmkEPcMG3Q/RfBkGY7OzS2i+ACAqKgpRUVFS65YvX0797eTkhCNH\njjDeVx/IZlpXVv5HXfgmPIS52SCjuFpqvXh4K1DN8kHqzByMCXFGRpF8aR9to2qIK6OoWuE2MfMG\nOsNPRrBtasLrdEoCBys+yuo6hh0d21OESCI5wcKpPBufLIqGs5opRCTp72z4klBMhh1lEaenVRZY\nla0gINkdPewskPmYmQPGAb09wcAYi1aHYFiMpR8Z5UBus0wFYdkZhp2Fbvi7u6XICRjsYaNyf8ln\noTojjjwe82SmhkbsAPeTccA6+5Buk0l4b0kzpBzgLPpMgSkPrw/zUBnV4kH5sNmzumYUVTaoa6pO\nufOkFkeyniqdZSikZjAq7jSRMt8NyZeBMX2YZ7snvhe70WTY2hBwxU6AO7YSO9mJ9sbjWISkVsXO\ngq91TdXI3t1xubAaNuYdurCvV8zEqfvltMlcZZF8UIltUyWKBkSeMo9xOlPN0caXQPzgb2iR9pam\n+jvhh/ZUCJogO6RMl0ZkRlBPmJuaYLCHLVxtVUc9hVCe/PZRdRMW/XIbSQsHwFKgXjJYbTFixAi0\ntgmp/iIuSO5pb4GBbtIOv9hpEn8NZLt/QE8r3H4iymMW0ctOaptkU3USApPIF4FAIDDHKCNfklGM\nIB0MGU3yc8A/x3nj+5kdGja/HlZ4bai72pnaxbUL98wJUj2jjibydSTraXt6AHZBPYxlHsrTg5jN\niFN4XJllurxefBMepgX2YOR4iWFy3ySHO/XNjUfViNp5HYezpCc2lNbK150URwPFjmpZfbNUQXOx\nFm+Ylx0sZJxJyevbLBtmVIKiAugEdsAG3Q/RfBkGY7Ozy2i+uIhkdERRoezOYMLjYZTMkIwmmhwA\naJIVqCmBB6C6UVpw/s35QpzNq8CmKb70O0kgFArxwfFcZBRXo4+DJf4305+2nbJzkUxeq4yKdodQ\n9uw6W15JdgaelYpIFJP7wnQSQFOrbop8M+GTHw8DPQOx7XwhvCSqJJy4+wwTfB2kJh6I+/+5vEoA\nIqdRctKJtZmpQkffQuL+SJYPUgWJfBFUYSxaHYJhMZZ+ZPSRrx7d5AXZbKKPg3S5oQVhLgrb2pjz\ncSDzidz668U1jD7ralE1NVHgflk9s4LjMmy/xCwL/bD2WoH5FfJaKTeaiFTyEuWpOoa0a+lktVm2\nnZzJKjDlwcPOQnVDKC4Arg8k3yHe+/0e9bfYGa2RuJcPy0XX/JaS0kCKMDXh4bcFA3B44QCpmpli\nFI3gE9+L3XBFT8MVOwHu2ErsZCecdL4elNXj/eP3cF9BFEbyGdmZOoTqoGnHkY2lzA9zReLL/RE/\nN4ha99YIT/zfxD5wsBLIaajUoaxOeohKUR4nZedypVD5TMevp/lhy1QfRHjbKWyzYXJfzJLRxpnw\nePhqmi8WDnKVir4AwOLBrvhoQh8AwNoxvaj1DlaqHS/Zc/F1ks4L5snQ8QIME91Jz6/Em4ezIXQP\npt1uYy66BpJBOXFeu0l+kmlRmH8PrM1M5YYjxchGksM9RQ4aiXwRCAQCczjpfH2QfA8ZRdVYKxEB\nkEQyQsGy/KVyBNCkpuhuKYCTtRk1RPeclx2e66XYmWFKZxw3pjhY8THA1YaaYUc3G9HV1hzLn3NH\nzACRA7Z5qkiDFOTcDS+HusjNkIzyd6IcsghvexxfPBCbp/pg67R+atsnOzyrjq7JEHx08j5uP6lD\nrYLC2GL7JYcdxS8c3dp1bMN72Sl8UVFGG41zbsID1o31ppbFOcSI78Vu2KD7IZovw2BsdhLNlwEp\nbxc+yxZ4FiP5zBjhba8PkzTWfNFlaBfzzXQ/VDW0wkEil5WDJR9l9ZoJv7NkhqGEEOnAGlrapGbx\naXoudLwS5oLv04sR0FM+3cOScHcsCVderDh+bpBU0XNANDQW4qo6pQcgfy6ywvoPxngzOg5gWAdD\nUZmk++26rFaJFw7xn+LIpqa6RzsaLZyrrTn8Je4l9bkk9EVQgbFodQiGxVj6ESedLx5P+W+9eOYV\nD4C/mklP9Umv7sqHvLy7yztmnvYWKKtnpvGS5c/ccqnltjZgfcoDnH9Yid0vBao1O1ARPbtJJzOd\nFtADAhMTWv2QIiRvrZO15slRFTGytz3OPqgAACnxuirY6F6IXzQkI1/i/k+lmjARRazULQEkzl0n\nyarhHnCxMccQDxu0CYFe9hZIz69i5bUhdMAVPQ1X7AS4Yyuxk51wcthR0Xt8Q0sbfr72GE/a82Vp\nM7O9KtTpOG9EeAIQPcjU5dXBrqobMWR9yn2cfyiaEffdxUIqN1dnvgSyGjtzvgmmB/WAuxr3QiwY\n1wZ05/JMQvtmos64tAE9DEW1Q8XDupL6vevFNfjkj/tUVMqUx4NAw/F32dJEgc7dAACfTfbBhigf\nKu8Ym2o7EggEAtvhpvOlYBjl8z8fYPfVR3j/eC4A/Ynt1eX5ACccXzyQ8dCZJHRJRTXlztM66u+L\n+VW4XNhRuqhNKMT7v9/Dt+cLtfZ5TFE0nKwtJIdflfkkvWSiYrosgH7mfjkWJN5CnpraLLGDJVvj\n8vzDSjS1a/xMTXjqOZkSSOonPxznLeeMsfMbRpCFDbofovkyDMZmp7FovrjpfClYfzFfuu6hPn0v\ndTu4pg9yFxszmHWyPqIirrbPZExLS0NeeQMyiquRJJPUk2uoui/KHHT5BK66C+98+mceHlc34etz\nBbTbq3Ov065vbQMq6ptRSFP+SJxDzoSn+YuI5PD+aCXlhpSVOSIQAJFWx1j0OgTDYSz9iJPOlyLv\nq6dMTi9dR1AMga0FH7tfCsK0ACetH1vy8Uk30w0A3Gy1r8HiCr/8LZ9jTRs0NHfMZFSU/kMRz+qa\nMS/hFjb89VBum3gmpCmPp/GsX1XWiJ064nqxG67oabhiJ8AdW4md7ISTzpei50j/dj2KmHINZwVq\ngj47jqO1AAKZ6Ne/Ux4oTJqaeKMES37JUnlccfBixIgRcvnHOuDWQBPdfaGbeQkA/5vpjzdHeHas\nkPEoZCcsaIOS6iZE7/5b4XaH9hmHspovSWdKdshRTFp7hnsTEx7+NaE3bMxN8a8JvTtpsTTigBoJ\nfBEIBAJzuOl80QyhHL9TqpOHI1txl5mZeDavAkdvl9K23XG5GAWVjSqPWVYvkYRVwcOUzvXq3u4g\nKHJq2Iai4FIfB0tM9e+IKOojA1haXoXUsqwTo8inYRIgE2vbyuqaMcDVBr/OD0aEhqlXVEXOiO/F\nbtig+yGaL8NgbHYai+aLm6kmaNZ9lSavlZGNDukSbebGYgJdGgDZDPbq0r+9CHlaWhp69Ouo/dcm\nFOKnq48Q7NqNml3naWdOOXQBPa2xLNydlaWc6O6LqihNd0s+yutb4OdkpVZ9Q02Q7aN3S+to2ynK\n88UE8YxWRRNVlLF4iBt2Xi7GkiFutNvFRySaL4IqjEGnQzA8xtKPuOl8MXyGzAzqoVtDDAidY3n0\ndilmBPVUK62DJN0lkrlKPks3nXooiipeL6HWvT/WGysPZVPLmn4mHV72FrQ1IbWFKkdha7QfUu+V\nY0ZQD9Q3t+HU/Y6IamNLW6eLg0siO3tQF5/RGeaEOGOijwMcrekda00cOoL+4Yqehit2AtyxldjJ\nTlT+wicnJ8Pf3x++vr7YuHGj3PYtW7YgNDQUoaGhCA4OBp/PR0WFaChl69atCA4ORv/+/bF161at\nGc3Gn3t9dxw+jfPVKgQW/ZKFczJDWUx52p4fTfZcJIdzxYJ7gSkP743uBVcbMyxTkaVeXZTVhVQX\nuvuiqhi3i405Xg51gbWZKYbL2KIoMqUpdE7W+8fly2bJRr1G99ZP5QYACh0voOO7SPJ8EQgEAnOU\nOl+tra1YtWoVkpOTkZWVhYSEBNy+fVuqzZo1a3Dt2jVcu3YNGzZswJgxY2Bvb4+bN2/ihx9+wOXL\nl3Hjxg0cPXoUubm5WjG6rpmhGseI38rpIiZi1qc80OiY2y8VUzUEKxTMFG1uT19gJTDFBF8H7I4J\n0mrUC9C9c/2P9iS3LzCIjA5yl87F9qyTQ7uy2NOU8LklkYdM0bW4Vqy8wLkk430Up4joLOKv2L4b\nJQqF/wTDwwbdD9F8GQZjs9NYNF9Kna9Lly7Bx8cH3t7eEAgEmDNnDpKSkhS2j4+Px9y5cwEAt2/f\nxtChQ2FhYQFTU1OMHj0aBw8eVGlQXVMrzj6owCv7bmFvxiPaNt1k6vOl5JQpPJa+0HcHr25Qfm7K\nUhasGeWlcFtRVSPS0tJw6BZ9fi9x7ih96uk6A919cbM1x4klA7FimOoKAzbm0s7R53/macs0AKIS\nT3Q0t7ZvaL/Msnm+6hkWSR/XtztWj+qlqXkqkXwR+vnaY519DoH7GEt+JoJhMZZ+pHT8paioCJ6e\nHVPvPTw8kJ6eTtu2rq4OJ06cQGxsLAAgODgY//znP1FWVgYLCwscO3YM4eHhcvutXLkSXl4iZ8DW\n1hZnqrvjmUM/AMC3vyTDu86XGjpKS0vDk+om1DSJ3uSrc6/j+wNP8Gt5T2oZ6BiiuZ2RjjThQ6n9\nARjFcqi7jdz5Si7fKqlFFfXAtqa2D3Dthom+A7HlTD7t/hkXy+Bhb47mViHt9ur2ZYEJT2fnx7Ps\nS31eWlptp46XmZlJu53HY26/5PUTEaq1873zpBaAfP9tahUi/UIaKnIeAO795bYLhfL9XXbZ+kkW\nRvj3At/EW2v2yi63Sti///dU9K33prl+wLlz55Cfnw8AWLJkCQj6hSt6Gq7YCXDHVmInO+EJlaiP\nDxw4gOTkZGzfvh0AsHfvXqSnp+Obb76Ra5uYmIj4+HipyNjOnTsRGxsLa2trBAUFwdzcHF999RW1\nPTU1FWFhYVLHmfTDNanlk0tDpZbfOXIXNyWGZUx5Iq0THfvm9YeDFftm4GmDNqEQk3fQZz0HgG3T\n+8Gvhyj1g+Q1fXOEJ6b6O8ldZzH/jfaDf09rvJGULVV+SJaji0JgZqobUfhPVx9hb3sURfb+GwJF\nfXLfjRLUNLZgaSc0bxfzK/Hxyfty6w+8Egwbcz5eTriJp7XyQ51R/RxxPPuZ0mN7d7fA97MCNLaN\nCVcKq7AuWSQncLQSIGFef5X7ZGRkYPz48Tq1S1/Q/YYRCLrCwcEBAFBWRj/aw5Stafk4dkf57wcA\n9OthhS+f99XZbz0X0dbvl9Ir6u7ujoKCjhQOBQUF8PCgH6rZt28fNeQoZvHixbhy5QpOnz4Ne3t7\n9OvXr9MGN8sMpylyvAAYreMFaF4uxlTFfuLLWdIuvleELr+MbJfqid9Xdl4uxv6/n6CqE5UU2hS8\n+4i7Od21GOJhg9cZDJnqA0nztK2HI2gPNuh+iObLMBibnV1C8zV48GDk5OQgLy8PTU1NSExMRHR0\ntFy7yspKnDlzBtOnT5da/+SJqBxLfn4+fvvtN8ybN0/hZyl6CMnS2VxWuoJtHVzR9RQL9RUJ9tuE\nQqSlpem1OoAsY/uKhpWHeXV+1qMu7kuTjMcv+0KgDoq6/Y9XiqW2S2q+Fg52Y5SKooGhLqwzSDqH\nsuW9CARJjEWrQzAsxtKPlP6C8/l8bNu2DZGRkQgMDERMTAwCAgIQFxeHuLg4qt2hQ4cQGRkJS0tL\nqf1ffPFFBAUFITo6GrGxsbC1taX9nL9yyxC14zquFFbRbpeEbgiGjsEeNqobcZwfXlR/SEkcsDq0\nYADtdjZMWPOws8ChBQPwyUTtlsLRFtkyw7GdSTCq6Hr/3j4kIN7u49RRPUCgZKbrZ5F9qb/L9fCi\nIhmBFZiQoQm2whU9DVfsBLhjK7GTnahMshoVFYWoqCipdcuXL5daXrhwIRYuXCi375kzZxgZIS4K\nvPGUfHFgTdF0WE5TDNFxXGwUF7kWP7RlZz3y2geKzBREToRCISIiIoA7ivVk+sBKZkarpmjjvjhZ\nCVAq4chkFFVJRRY747CqiviKh/I2LpuBV/eL6nNaCRRfmyGetgh1s8G14mqM6qO7FBN0FFU1oqGl\nDRYsSRBLIBAIbIVVv5LK0iOoiyptkzGgTHclbFdvicXQYmzMlTs1bUKguEq53qurIRthjL9egvd+\n70iE2pl+q8z3khxitxSYYHqgE57zsoVzu9Md6edAu997Y3phyRA3LB5MXxJIm9TKpHPRZ3oXAnPY\nIIsgmi/DYGx2Govmy+DlhfZd78gNxFT3xQRlSUh1gb5rO6pCfCllk3FKTkJwtBLIiaSrG1uRcyMN\nAP2DnWto475YmZli75wgzN93i3Z7a6eGHRXv+2dux4ym9PPnsHL8GKntq0f1grutOXZekc6H52gl\nQEyIs8Y2qUOOTMZ/kmiVoAhj0Ol0NZpa2lDV0ML4e+1io92E23QYSz8yuPMl+eCoa26DCU/5MI6N\nuSmqGxW/XYe4dsPfj2owxd9Rm2ZyDkXXUDI5ajdzUznna9fVYkRaye5F6NlN8RBvpyJfSrZVSiTS\nVVRDcc5AF/B4POy4XKyxDZ1Bdnhfmy9QBO3BphdDZXDFToA7tnbGzgflDZiXQP/SKUuYuw2+iPLR\n+LO4cj21hcGdL1lUPcdszflKna/Vo7xgJTBVWb9P27Ct4+SU1mGAaze59ZJDlXSDlgUVjRg4Zhgg\nUTSby+jjvihLd6KKpvYZiWP6dJcq4A1IOzLDhkcoPIYh3R1bC+lhbG1KBwgEAnNyn9WhlMGENFMT\nHh6U1evBIoIyWOd8KeNifiWKqhqVtrE0gOPFRg7efIJZwT3l1lsKOlwuRdGUZwxnlBJEdGaoTZww\nOOtJjdw2J4khYmWj6GP7dMfOy8V6LbatiMbOeKIEncEGWYRYp6Ns2IgNdjKFbbam5VXg52slcuur\nc69TVS/YDNPryaQfcQFWCe7pKKrscLaY1NWzM5DjZShR48JBrrTrFY3+WEvMIlT0QN9+8ITSz2RS\nkJot6OO+dCbaI54Z6EwzrCl52IsXzis8hrONGY68GoJ147w1tkNThveSdvj+38E7ereBwA2MJT8T\nwbAYSz9ivfP18R8ds/XIO7U8Eb3sQFfjurSuGen5lXLrJTU61grSOdx+Uku7XsxrQzUvp2OMNGsY\n7WlubcNfuaKhxiBn+SFiyeStqqaPmPNNFEYydUnPbmY4vFA+Z9z14mp8dCKXZL1nCWyK0CiDK3YC\n3LGVC1EvgDvXU1uw3vkqqBBFvk7dL0ejiozdvbpb6MMkWgzVcbwdLLF/fjDtto9kaga+NlQ69cA7\nI70Q6GyNzyf3lVov+WV1pCnRZKrnmaSdQR/3Zc2xHGw7X6C6oQy/3XqKmvbUDHSX9Ne/O4YQhkco\n1nwZGguavGPv/X4P6QVV+D69yAAWEQgEArthvfMFAPXNrSqHHH+cHYD/veCvH4NYho05s6HWF4Ol\n0w+42prj62l+GOxBX3kAAL6f1TWvKR0TfRWn3zicVYonKuphyvKwvIH6my5qVaVkYglXuCGT6oRg\nGMvmvkYAACAASURBVNiQ64nk+TIMkqXJ2ExXy/PFCedr99VHKttYm5kaNCLDlS8iEyS/rEwdO7ai\nzfuiqnuV14uG2K4WVeHzP/PkEpDKInm4e8/qFLYDgPPnzjExkRU0SUSo7S1JvUeCCGPR6hAMi7H0\nI044XwdvPlXZxhB6F0LXQragtixiidYHx3Nx6n45EiQSCNNR2cC8eLkZnbCPpVRInNf9snqk5JTh\n52vKr4U2Wbx4MZydnREc3DEcX1ZWhokTJ8LPzw+TJk1CRUUFtW3Dhg3w9fWFv78/Tp48Sa2/evUq\ngoOD4evrizfffFNv9usCruhpuGInwB1bieaLnXDC+WKCoR9Nhu44C8JcMN6nu1R6Ak3hypeVCdq8\nL6r62OqjOfjkjw6d3ZVC5UNuj6o7hikbmpXrGUeOHKnSPrYgG4HedPohdl99JDVzWZcsWrQIycnJ\nUuu++OILTJw4EXfv3sX48ePxxRdfAACysrKQmJiIrKwsJCcn4/XXX6cKpa9YsQI7duxATk4OcnJy\n5I5JIBAImsIa5+u7Tuq1OKQB1wnzw1yxdow3mRGqQ1QNa7e0CXH+YccM0/tl9bQOR0V9Mz5NfYD8\nig7Nl5e94SaLaBtFWe4bVEyY0RYjR45E9+7SRcUPHz6MhQsXAgAWLlyIQ4cOAQCSkpIwd+5cCAQC\neHt7w8fHB+np6Xj06BGqq6sRHh4OAFiwYAG1DxdhgyyCaL4MA9F8sRNWOF/hnrbo62jZqWMYetiR\nLV9EoRbcL/GXdWm47gsz6xpt3hcHDaKK/0jKxuNqaQfs4M2nOPOgQmqdsiLpAHv6FxPiLrJvhmNJ\nSQmcnUUTTpydnVFSIppJWlxcDA8PD6qdh4cHioqK5Na7u7ujqIh958UljEWrQzAsxtKPWKGmzn6q\nXGzMhK4e+aLQYuhLnABUkq58nYf3skPiDfkM0sqoaWrF/6U8QKxEZJcu95XAlIf9L/dHqxCYG3+z\n07bqm172FnjYHsmTdSzZBo/H0+rL2sqVK+Hl5QUAsLW1RXBwMDXcLXaayTKzZfE6ttijbHnEiBEG\nuT6SyG4XvziLpSOyUS9F27W1zLXryWQ5MzMTVVVVAID8/HwsWbIE2oAnFBquEm5qairez+BBYMrD\nsUUDMemHa9Q2525mKFFj6v7hV0NonYWuRszPmSivpxdyn1waqnA/yWsv5u0Rnojyd8Llgip8eEKU\n7NaUBxxfovg4xszj6kYsSMzSaF/Ja//lmYc4cbdMavvyoe5UOSi6e6Hs3rGBZb/eppwvRXz3gj/6\nOloiIyMD48eP16k9eXl5mDZtGjIzMwEA/v7+OHXqFFxcXPDo0SOMHTsWd+7cobRf77//PgBg8uTJ\nWL9+PXr16oWxY8fi9u3bAICEhAScPn0a//vf/6Q+JzU1FWFhYTo9FwJBjIODKN1NWVmZ3LbdV4tp\nywvpi84W1uYK2vr9UumtJCcnw9/fH76+vti4caPc9i1btiA0NBShoaEIDg4Gn8+nZhJt2LABQUFB\nCA4Oxrx589DYSC+4fSVMukSOj6MluluqF5Tj0GQwnaLNusZ27fdgiKctAnpaAQD6u8hnYu8q8LQ0\nrcOUJuoyuZ+jVo5tKCb6Kc6Bxgaio6Oxe/duAMDu3bsxY8YMav2+ffvQ1NSEBw8eICcnB+Hh4XBx\ncYGtrS3S09MhFAqxZ88eah8uwoZha6L5MgxE88VOlDpfra2tWLVqFZKTk5GVlYWEhATqTVDMmjVr\ncO3aNVy7dg0bNmzAmDFjYG9vj7y8PGzfvh0ZGRnIzMxEa2sr9u3bJ/cZ/3neF7P6S9cKFEL90TMT\novkCoF76AkWIv6ySMdGPJ/TBgjAXfGiA+oGdgS33RRITmrFbRaWexLDxPCR5kaaIuyy1TZ3vm0yY\nO3cuhg8fjuzsbHh6euLHH3/E+++/jz/++AN+fn74888/qUhXYGAgXnrpJQQGBiIqKgqxsbHUkGRs\nbCyWLl0KX19f+Pj4YPLkyXqx31gxFq0OwbAYSz9SGl66dOkSfHx84O3tDQCYM2cOkpKSEBAQQNs+\nPj4ec+fOBSDSPggEAtTV1cHU1BR1dXVwd5evCUgXSREKASuakiVinKwEcLU1R38XayRcF4VZu7IW\nSRtM8OmOlHvlCrc7WgkwP4y+iDdBPYwxSsvk5efk3TIMcLXRuS0JCQm061NSUmjXr1u3DuvWrZNb\nP2jQIGrYkusYOhUOU7hiJ8AdW7mSOogr11NbKHW+ioqK4OnpSS17eHggPT2dtm1dXR1OnDiB2NhY\nAKKx6dWrV8PLywuWlpaIjIzEhAkT5PaTFKuWZFXBys0H5j2HY0m4GxZ+mQhAXtw3fdpErBzugf/b\ndRjVuc9g03cgeDxelxNf0i0PNXmG9DYvqevFRAz57uheCG7Nw45LxUB7+8wrFyEs7MYq8aMmy2I6\ne7zLF8+jOveBxmLUU2fO4l5pHeASKLV98YxJMvZaS20fGD4MI0aEsuZ6KlpWJvatvn8DF8/UYuV+\nM60JVgkEAoGrKBXcHzhwAMnJydi+fTsAYO/evUhPT8c333wj1zYxMRHx8fFISkoCAOTm5mLatGk4\ne/Ys7OzsMHv2bLz44ot4+eWXqX1kxaqXCqqw60oxPhjrDU97C+zJeIQ9GfKZsaP6OeLtkV6Iv/YY\nu9pLD7FdkKwvhEIh8isasOzAHbltTK7RrivFiG+PJv5rQm9EeNtr3UauUl7fjJifNZuJuDHKB2uP\n36PdNrmfI94Z6UUtywruN0b5INRd9xGjzkI3UUCSTyP7ItzTVi+Ce33BFcG95AxCQyHW6SgbMmKD\nnUwxhK2aCO6rc6/rJfrVWcE90+vJpB/pEr0I7t3d3VFQUEAtFxQUSOW+kWTfvn3UkCMAXLlyBcOH\nD4ejoyP4fD5mzpyJ8+fPKzUm3NMWsS/4w7M94aSioYyS9szgbEooyhZNDo/HQ6/umudMmxfqQkUs\nfJ2stGWWwdDmfbGz0DwziyLHC1A9ZN7fxZo1/YspdHn7FCVfJXQNjEWrQzAsxtKPlDpfgwcPRk5O\nDvLy8tDU1ITExERER0fLtausrMSZM2cwffp0ap2/vz8uXryI+vp6CIVCpKSkIDAwUC3j7jyppV1f\n016wuKZReeFigvqYmZrg08i+2DsnCD27mRnaHFZB5yMtHyqvY1SXZpmakbNlxOsCFQlY2UYvewts\nm95Pbj1xvgwHV6JJXLET4I6tRPPFTpT+qvP5fGzbtg2RkZEIDAxETEwMAgICEBcXh7i4OKrdoUOH\nEBkZCUvLjrfdkJAQLFiwAIMHD8aAAQMAAK+99ppaxt14VEP9/eqgDrF3S3s+hcIq5XmF9AnbO86q\n4fQRSzrGjxllNI6Xru7LnpggfPW8L2YF90SIa+fSb/yRIz2EsDTcDa420tef7f1LEnc7c9pSTG36\nqS5EIBAIrEflK3VUVBSys7Nx7949fPDBBwCA5cuXY/ny5VSbhQsXIj4+Xm7f9957D7du3UJmZiZ2\n794NgUC98ixNrR2/1vNCXai/LQUisxcPdoOLjRnWcSz9gSGIDuyhuhFBJeZ8E5jzTeBsY4ag9pm6\n2o7n8Hg8Tju/iiY+ksiX4WDDsDXJ82UYSJ4vdsLq8QzZ3+rNU30Q7GKNNaNE4uTeDpb4KSYIY/p0\np9lbv3Dli8gEci708Hg8HHwlGAdfCZZaTzdnxayT+ST8e1pLLXPhnozwtgMAjOpNP0njWnE1qrSQ\nh47ATYxFq0MwLMbSj9jtfMksh7ja4Mvn/eBuZ2EQewgEgamJnAarlSag4+PIfLKC7BAjAMzgYKTy\nrRFe+PekPhjVW/Qy9GlkX8QM6NCvHbvzDC/uNY68WVyDK8PWXLET4I6tRPPFTlhRWFsRAlOenBiZ\nrRhTxyHnoh5tNDWdhGoMRtIlGna0FmBOiDOV+Z4L98TWgo+hXnbUcrinLcI9bXH0zjPUNpHJMQQC\ngSCG1ZEvY0h1YCj+N9Of+tvd1tyAlhBU8fow+skQi4e4ISbEWc/WaB/ieBkeNgxbE82XYSCaL3bC\naufrnZFe6OtoiU8j+xjaFJWw7YvYx6Fj5ulAN/Vm47HtXDqDPs6FLsblasPM4X0jwlNlXUeA2/fE\n0444/wTj0eoQDIux9CNWDzt62Vvguxf8VTckKKWFZliMoBs2RvngVkkNZg9wRm1zK9Lzq5S2n+rv\nqCfLDMfsAc74z9l8Q5vRpeHCsDXAHTsB7thKNF/shNWRLy7B5o6jru/F5nNRF32fS6i7DeaHucKc\nb4J/T+qLBWEuStvzGBSkBrh9T5hE9ggEAqErQZyvLgCJfOkWZemrJvkZf2RLFT2s1cvvR9A+bBi2\nJpovw0A0X+yEOF9ags1fREcr9R5+bD4XddHHuYxoz2sV7GItt01V3UamcPme+Pe0hq+T5vVGCcaB\nsWh1CIbFWPoRqzVfhM7x70l98FduOeYYwYw5NjM7uCf6Olgi0JnO+dKS98VxZgT1xObTDw1tRpeF\nK8PWXLET4I6tRPPFTojzpSXY2HGGetlJ5V1iChvPRVP0cS6mJjwM8bRVuE0REd7M7w3X7wmfxNgJ\nBAKBgjhfBIIO4Stxvt4d1UuPlhgWvgnxvgxJWlqawR14sU5H2ZARG+xkij5szX5ai2tF1XLr911/\nLG/PgwraY1TnXudE9Ivp9WTSj7gAcb60BJd+NFRBzkV7CJQ4X1ZqzAI09Hl0Fisz4nx1dbj+sDQE\nWSW12Hnlkdx6unVdBWPpR+QXkUDQIcqGHbsSIa42hjahS8MVx50rdgLcsZULUS+AO9dTWxDnS0sY\nU8ch56I9tOV8Gfo8Oouy4VcCgUDoahDni0DQE5F+DoY2gdBFYUOqEpLnyzCQPF/shGi+tATXNTmS\nkHPRLjteDEBdcyv8nKxw4m6ZRsdgw3kQCJ3BWLQ6BMNiLP1IZeQrOTkZ/v7+8PX1xcaNG+W2b9my\nBaGhoQgNDUVwcDD4fD4qKiqQnZ1NrQ8NDYWdnZ1ReKsEgrp42lugXw/pHGA25qTkDkF/cMVx54qd\nAHdsJZovdqI08tXa2opVq1YhJSUF7u7uGDJkCKKjoxEQEEC1WbNmDdasWQMAOHr0KL7++mvY29vD\n3t4e165dAwC0tbXB3d0dL7zwgg5PxbAYU8ch56J7fByt1GrP1vNQh57dBHhS02xoMwgEAsHgKI18\nXbp0CT4+PvD29oZAIMCcOXOQlJSksH18fDzmzp0rtz4lJQV9+/aFp6dn5y0mEDiKZBHtrig/3zTF\nFzGk2oJBYIM+iWi+DAPRfLETpZGvoqIiKYfJw8MD6enptG3r6upw4sQJxMbGym3bt28f5s2bR7vf\nypUr4eXlBQCwtbVFcHAw9ZYvvhlcWJbsOGywpzPLsudkaHs6s5yZmYkVK1awxp7q3BzY9B2IV8Jc\nukz/AoBz584hPz8fABC6ZAkIXQ9j0eoQDIux9COeUCgUKtp44MABJCcnY/v27QCAvXv3Ij09Hd98\n841c28TERMTHx8tFxpqamuDu7o6srCz06NFDaltqairCwsK0cR4Gx5gE0eRcdMcXf+WhqbUNH0/o\no9Z+bDuPzpCRkYHx48cb2gytYEy/YQT28dvNJ/juYhG1fOU90fdm8KZUQ5mkkDB3G3wR5WNoM3SO\ntn6/lEa+3N3dUVBQQC0XFBTAw8ODtu2+fftohxyPHz+OQYMGyTlexoaxPBgBci665P2x3hrtx7bz\nIBAIBILmKNV8DR48GDk5OcjLy0NTUxMSExMRHR0t166yshJnzpzB9OnT5bYlJCTQOmUEAoFA0A9s\n0CcRzZdhIJovdqLU+eLz+di2bRsiIyMRGBiImJgYBAQEIC4uDnFxcVS7Q4cOITIyEpaWllL719bW\nIiUlBTNnztSN9SyCK19EJpBzYR/Gch6Erssbb7xhNHodguEwln6kMslqVFQUoqKipNYtX75cannh\nwoVYuHCh3L7W1tYoLS3tpIkEAoFA6AxcGbbmip0Ad2wleb7YCSkvpCWMqeOQc2EfxnIeBAKBQCDO\nF4FAIBg9bBi2Jpovw0A0X+yEOF9agitfRCaQc2EfxnIehK6LsWh1CIbFWPoRcb7+f3t3HxdVnf//\n/wEOZZaokIIyGCYQjCJCeFmuFqJiSV5lkiklml+vSrcrq1u3z9buJrZb6aa2brlpV0LbhWAqGWgp\nlpDiBQkiKigXSiIiGCpX5/cHPya5UEcY5swZXvfbzdvNc+bMOc83c5h58z6veR8hhLBxWrlsrZWc\noJ2sUvNlnaTzZSa2dOJIW6yPrbRDCCGEdL6EEMLmWcNla6n5UofUfFkn6XyZiVZ+EU0hbbE+ttIO\n0XbZSq2OUJetnEfS+RJCtAlLly6lT58++Pn58fjjj3PlyhWKi4sJCQnB29ubUaNGUVJSUm97Ly8v\nfHx82LZtm4rJW04rl621khO0k1VqvqyTdL7MxJZOHGmL9bGVdqglJyeHDz74gNTUVNLS0qiuriY6\nOpqoqChCQkI4evQowcHBREVFAZCenk5MTAzp6enEx8czb948ampqVG6FEMJWSOdLCGHzHB0dcXBw\noLy8nKqqKsrLy+nRowdxcXHGu3NERESwceNGAGJjYwkPD8fBwQEPDw88PT1JSUlRswktYg2XraXm\nSx1S82Wdbnh7IWGapKQkmxmdkLZYH1tph1qcnJx47rnn6NmzJ7fddhujR48mJCSEwsJCXFxcAHBx\ncaGwsBCAgoICBg8ebHy+Xq8nPz+/yX3Pnz+fnj17ArWdPD8/P+NrVfeBovZyHTXzPPPMMyQlJdU7\nlxtun5aWZhU/L2tZPrI/hbLjZ6956bCuY1X3eFPL5QXHrvu4OZct8fMJDAy06OuRlpZGaWkpAKdO\nnSIyMhJzsFMURTHLnpohMTGRwMBAtQ5vVrb04ShtsT620g6A1NRUgoODLXrM48ePM27cOHbt2kWn\nTp149NFHmTRpEgsXLuT8+fPG7ZycnCguLmbhwoUMHjyYadOmATBr1izGjh3LxIkT6+3Xlt7DhPX5\n5tffeH/PH53+vS/W/t4EvZWoVqRrCnTrSFSop9oxWp253r/ksqOZ2MoHI0hbrJGttEMte/fuZejQ\noTg7O6PT6Zg4cSI///wzrq6unDlzBoDTp0/TrVs3ANzc3MjNzTU+Py8vDzc3N1WyCyFsj3S+hBA2\nz8fHhz179nDp0iUURSEhIQGDwcC4ceNYv349AOvXr2f8+PEAhIWFER0dTUVFBdnZ2WRlZTFw4EA1\nm9Ai1lCfJDVf6pCaL+skNV9mYkuXhaQt1sdW2qEWf39/ZsyYQVBQEPb29gQGBvL0009TVlbGlClT\nWLt2LR4eHnzxxRcAGAwGpkyZgsFgQKfTsXr1auzs7FRuhbbZwtxMQn22ch7JyJeZ1BWK2gJpi/Wx\nlXao6cUXX+Tw4cOkpaWxfv16HBwccHJyIiEhgaNHj7Jt2zY6d+5s3P6VV17h2LFjHDlyhNGjR6uY\nvOW00nHXSk7QTlaZ58s63bDzFR8fj4+PD15eXixbtqzR4//85z8JCAggICAAPz8/dDqdcaLCkpIS\nJk+ejK+vLwaDgT179pi/BVai7tsQtkDaYn1spR1CCCFu0Pmqrq5mwYIFxMfHk56ezoYNG8jIyKi3\nzfPPP8/+/fvZv38/S5cuZcSIEca/Hp999lnGjh1LRkYGhw4dwtfXt/VaIoQQoknWUJ8kNV/qkJov\n63Tdmq+UlBQ8PT3x8PAAYOrUqcTGxl6zE/X5558THh4OwIULF9i1a5exmFWn09GpUyczRrcup06d\nUjuC2UhbrI+ttEO0XbZSqyPUZSvn0XU7X/n5+bi7uxuX9Xo9ycnJTW5bXl7Od999x+rVqwHIzs6m\na9euPPXUUxw8eJB7772XFStW0KFDh3rPS01NbWkbrEJkZKS0xQrZSltspR3NNWPGDMLDwwkNDVU7\niiZppZ5GKzlBO1ml5ss6XbfzdTPf7tm0aRP333+/8ZJjVVUVqamprFy5kgEDBrBo0SKioqJ44403\njM+x9ESLQght+uCDD4iJieGxxx5j6NChzJo1i9tvv13tWEII0SzXrflqONFgbm4uer2+yW2jo6ON\nlxyhdpRMr9czYMAAACZPntym/3IXQjTfuXPnOHHiBJ06dcLFxYWZM2eqHUlTrKE+SWq+1CE1X9bp\nuiNfQUFBZGVlkZOTQ48ePYiJiWHDhg2Ntrtw4QI7d+7k888/N65zdXXF3d2do0eP4u3tTUJCAn36\n9DF/C4QQNu/tt99m3rx59O7dG6BeOYTQBlup1RHqspXz6LqdL51Ox8qVKxk9ejTV1dVERkbi6+vL\nmjVrAJgzZw4AGzduZPTo0dx22231nv/ee+8xbdo0Kioq6N27Nx999FErNUMIYctGjBhh7Hht3ryZ\nhx56SOVE2qKVehqt5ATtZJWaL+t0w3m+QkNDyczM5NixY7z88stAbaerruMFEBERUW/Uq46/vz+/\n/PILBw8e5Ouvv673bccbzR9mDXJzc3nggQfo06cPffv2NQ51FhcXExISgre3N6NGjTLOawawdOlS\nvLy88PHxYdu2bcb1+/btw8/PDy8vL5599lmLtwVqpw4JCAhg3LhxgHbb0XD+uOTkZM22ZenSpfTp\n0wc/Pz8ef/xxrly5oom2zJw5ExcXF/z8/IzrzJn7ypUrPPbYY3h5eTF48GA2bdpkfGzXrl2t3Doh\nhGhdqsxwb8r8YdbAwcGBd999l8OHD7Nnzx5WrVpFRkYGUVFRhISEcPToUYKDg4mKigIgPT2dmJgY\n0tPTiY+PZ968eSiKAsDcuXNZu3YtWVlZZGVlER8fb/H2rFixAoPBYPwihVbb0XD+OB8fH022JScn\nhw8++IDU1FTS0tKorq4mOjpaE2156qmnGh3DnLnXrl2Ls7MzWVlZLF68mO+//57ExES2b99OYWFh\nq7bNFllDfZLUfKlDar6skyqdr6vnD3NwcDDOH2ZtXF1d6d+/dsj2jjvuwNfXl/z8fOLi4oiIiABq\nR/02btwIQGxsLOHh4Tg4OODh4YGnpyfJycmcPn2asrIy4415Z8yYYXyOpeTl5bFlyxZmzZpl/ODT\nYjvq5o+rK7iumz9Oi21xdHTEwcGB8vJyqqqqKC8vp0ePHppoy7Bhw+jSpUu9debMffW+Jk2aRGlp\nKUePHuXIkSMsX768VdsmWsczzzxjM/U6Qj22ch6p0vlqav6w/Px8NaKYLCcnh/379zNo0CAKCwtx\ncXEBwMXFxfiXeEFBQb1vg9a1q+F6Nzc3i7d38eLF/OMf/8De/o+XXIvtuHr+uMDAQGbPns3vv/+u\nybY4OTnx3HPP0bNnT3r06EHnzp0JCQnRZFvAvOfT1e8ROp2ODh06cPr0ac6ePcuKFSss1SSboZV6\nGq3kBO1klZov66RK5+tm5g+zBhcvXmTSpEmsWLGCjh071nvMzs7O6tvz7bff0q1bNwICAoyjXg1p\noR3wx/xx8+bNIzU1ldtvv914eauOVtpy/Phxli9fTk5ODgUFBVy8eJFPP/203jZaaUtD5s594cIF\nRo8ezdSpU3nsscfMtl8hhFCDKp2vm5k/TG2VlZVMmjSJ6dOnM378eKD2r/ozZ84AcPr0abp16wY0\nbldeXh56vR43Nzfy8vLqrXdzc7NYG3766Sfi4uLo1asX4eHhbN++nenTp2uuHXDt+eNcXV0115a9\ne/cydOhQnJ2d0el0TJw4kZ9//lmTbQHz/F7UvQ+4ubkZb6lUVVVFTU0N9913H/fccw/33HOPpZpk\nM6yhPklqvtQhNV/WSZXO19Xzh1VUVBATE0NYWJgaUa5LURQiIyMxGAwsWrTIuD4sLMx4z8r169cb\nO2VhYWFER0dTUVFBdnY2WVlZDBw4EFdXVxwdHUlOTkZRFD755BPjcyzhzTffJDc3l+zsbKKjo3nw\nwQf55JNPNNcOqD9/HGCcP27cuHGaa4uPjw979uzh0qVLKIpCQkICBoNBk22py9fS3I888kijfX35\n5Zc4Ojoybtw4Hn30UR599FGLt020nK3U6gh12cp5dN15vlrtoNeYP8za7N69m08//ZR+/foREBAA\n1H5lfsmSJUyZMoW1a9fi4eHBF198AYDBYGDKlCkYDAZ0Oh2rV682XnpZvXo1Tz75JJcuXWLs2LGM\nGTNGtXbVZdJqO5qaP666ulpzbfH392fGjBkEBQVhb29PYGAgTz/9NGVlZVbflvDwcH788UeKiopw\nd3fnjTfeMOv5FBkZyfTp0/Hy8sLZ2Znvv/+e8vJyBgwYUG+0TJhGK/U01pTzyG+/893Rc9fZoif7\nkmpHZyf7dcOtU3vLBLtJUvNlneyUaxUBCSGElZg9eza33HILq1atYt68eaxevVrtSAAkJiYSGBio\ndgzRCnbnlPB6QrZJ2344yZeeXczf+frm1994f88fX57Z+2Lt/ZCD3ko0+7FaKtCtI1GhnmrHaHWp\nqalmuS+1KpcdhRDiZtxxxx3Gb1I2vJOGuDFrqE+ytZovrdRSaSVnW6v5UuWyoxBC3Iw777yTXbt2\n8dxzz9WbLkVohy3U6Qj12cp5JJ0vIYTVe/XVVzly5Ag1NTUYDAa142iOVupptJITtFNLpZWcWnrt\nzUE6X0IIqxceHg7ApUuXACx+NwIhhDAn6XwJIazehg0bgNrpX959912V02hPUlKS6iMLdXU617ts\n1Jycp0uvcP5SpUnb3nn7LXS745ab2v+1lB0/oIlRJa3kNPW1N+U80gLpfAkhrN7hw4exs7OjsrKS\nw4cPqx1HNENrfVgWXqzgxS3HTNr2X2HeZut8CXVovdNVRzpfQgir9+WXXwJw66232sybryWpPepl\nKq3kBO3UUmklp5Zee3OQzpcQwuoFBQUZ/5+Xl0deXh4PPfSQiomEEKL55DvbQgir9+GHH5KRkcGR\nI0f48MMPKSoqUjuSpljD/Fkyz5c6tJJT5vkSQggr4+Pjw/PPPw/A2bNniYiIUDmRuFlyuViYAO/w\nxgAAIABJREFUg62cR9L5EkJoQmRkJHZ2dsaZ7oXptFJPo5WcoJ1aKq3k1NJrbw7S+RJCWL2///3v\n5OXl0blzZ2699Va14wghRItIzZcQwuotWrSI119/HUdHRxYuXKh2HM2xhloqqflSh1ZySs2XEEJY\nGXt7e+666y4AOnfurHIa0Ry2UqvTlHb2dly4VGXStrc52HOLTsY9mstWziPpfAkhrN6tt95Keno6\n7733HufPn1c7juZopZ5GKzmhfi3Vc98exaGdaR2qt8Z60t3RcpfOpebLOknnSwhh1RRFYfLkyRQV\nFaEoCvPmzVM7khD1FJs46iVEHRn7FEJYNTs7O3bs2EFoaChjx46lXbt2akfSHGuopZKaL3VoJafU\nfFlQYmKimocXQqgkODjY5G1jY2OJjY3lu+++w8nJCYD//e9/rRVNtBJbqdUR6rKV80j1y46BgYFq\nR1DNsmXLeOmll9SOoYq23HZo2+1PTU29qe3j4+PZvXs3c+fO5f3332+lVLZNK/U0WskJ2qml0kpO\nLb325iCXHYUQVu3UqVNs3ryZU6dOsWXLFrZs2aJ2JCGEaBHpfKno1KlTakdQTVtuO0j7b8ajjz5K\nUVERU6ZM4ezZs5w9e1btSJpjDbVUUvOlDq3klJovYTF9+/ZVO4Jq2nLbQdp/M5588km1IwgzsJVa\nHaEuWzmPZORLRXPnzlU7gmracttB2q+WkpISJk+ejK+vLwaDgeTkZIqLiwkJCcHb25tRo0ZRUlJi\n3H7p0qV4eXnh4+PDtm3bVEzeMlqpp9FKTtBOLZVWcmrptTcH6XwJIdqMZ599lrFjx5KRkcGhQ4fw\n8fEhKiqKkJAQjh49SnBwMFFRUQCkp6cTExNDeno68fHxzJs3j5qaGpVbIISwBdL5UpGW6hvMrS23\nHaT9arhw4QK7du1i5syZAOh0Ojp16kRcXBwREREAREREsHHjRqB2iovw8HAcHBzw8PDA09OTlJQU\n1fK3hDWcb1LzpQ6t5JSaLyGEsEHZ2dl07dqVp556ioMHD3LvvfeyfPlyCgsLcXFxAcDFxYXCwkIA\nCgoKGDx4sPH5er2e/Pz8RvudP38+PXv2BMDR0RE/Pz/jJZS6DxS1l+uomeeZZ54hKSmJpKSka26f\nlpZ20/vPLr4E3An80dGou9TWcDk15WeKOrc3ef832l9zllP2lPDIqAdMOv6R/SmUHT97zUuHphyv\nvOCYWfNfb9kS51NgYKBFz9+0tDRKS0uB2i9KRUZGYg52iqIozXnizJkz2bx5M926dTP+wjT0zDPP\nsHXrVjp06MC6desICAio93hiYmKbnudLiLYoNTX1piZZNZe9e/cyZMgQfvrpJwYMGMCiRYvo2LEj\nK1eurHe/SCcnJ4qLi1m4cCGDBw9m2rRpAMyaNYuxY8cyceJE47byHtY6jp8r5+tffzNp24LSKxwu\nLDdp24h7XXFzbG/Stqn5pcQfLTZp25uxforB5Hs7fvPrb7y/548O/94Xa39vgt6yvgnKA906EhXq\nqXaMVmeu969mj3w99dRTLFy4kBkzZjT5+JYtWzh27BhZWVkkJyczd+5c9uzZ0+ygN7JhwwYmT56M\ng4NDo8eSkpLYtm0bb7zxxg33s2LFCiZMmGD8S7ah4ODgRjPz7969G1dXV3r37t3kcz7++ONr/pyE\nEJah1+vR6/UMGDAAgMmTJ7N06VJcXV05c+YMrq6unD59mm7dugHg5uZGbm6u8fl5eXm4ubmpkr2t\nuVxVw/dZ5r+B+vp9Z8y+TyGao9k1X8OGDaNLly7XfPzqOopBgwZRUlJiHM5vDRs2bKCioqLJx+zs\n7Ezez7PPPnvNjte1JCUlcfz48Ws+vn79+ms+z9KuHuhUs3hYS7UdraGtt18Nrq6uuLu7c/ToUQAS\nEhLo06cP48aNM/6Orl+/nvHjxwMQFhZGdHQ0FRUVZGdnk5WVxcCBA1XL3xLWcL5JzZc6tJJTar7M\nJD8/H3d3d+OyXq8nLy/PWFtR50b1EhUVFcTExFBYWMjly5f585//jJeXF//v//0/Ll++jF6vZ9Gi\nRaSlpTFmzBgGDx7MP/7xD+PzobbzlZGRwUMPPcSZM2f47LPP8PHxYcWKFXz55ZfcfvvtPP3003Tr\n1o3ly5fzt7/9DU9PT8aPH8/vv//OgAEDKC8vZ+rUqZSWlvLSSy+xf/9+4xv3559/zqZNm/jPf/7D\nokWL6uWvGwF85JFHePDBB9m8eTPbtm1j7ty5nDt3DoC33nqLuLg43nzzTeLi4nB0dGTJkiXccsst\nQO31Z0VRePDBB6murqZr166sW7eOgwcPkpCQwE8//UT79u0ZPXo0Xl5erFu3jrKyMuzt7Vm8eDE6\nnY5Vq1ZRWlrKgAED+OGHHxg6dCgZGRk899xzqtejyLJtL0Pt6HDdxLLmqplojvfee49p06ZRUVFB\n7969+eijj6iurmbKlCmsXbsWDw8PvvjiCwAMBgNTpkzBYDCg0+lYvXr1Tf0hJ+qzlfmZhLps5Txq\nds0XQE5ODuPGjWuy5mvcuHEsWbKE++67D4CRI0fy1ltv1auPMKVe4oMPPqBDhw5MmzaNjRs3kp+f\nT6dOnaioqGDmzJkoioKdnZ3xr9QOHTo02kdSUhJvv/0233zzDYmJiezYsYO//e1vhIaGsmnTJuzs\n7Hj44YfZvHkzzzzzDAsWLCAzM5Nff/2VV199lY8//phffvmF9957j8DAQDZt2kT37t0ZNmwYu3fv\nZtmyZQQGBhISEtJkG66+VDlhwgS++uorZs+eDcBf//pX/va3v7Fy5UpGjBhBQkICV65cYfz48Y0u\nb166dInbbruN999/nzvuuIPQ0FCmTZvG5s2b0el0KIrCqlWr6NixIxEREfzzn//E3d0dvV7P0qVL\n+fbbbwEICAjgm2++wcPD47o/+9a0aNEiCgsLeeedd+jevbtqOYTlqVXz1Rqk5qt1HC68yOJNWWrH\naBVS86Vt5nr/arWpJsxVL5GZmclHH31EWFgYa9asobi4mPHjx3Py5EnmzJlj/Cv1euzs7Iwzivfo\n0YMLFy5QVFTE8ePHmThxIhMmTKC0tJSioiLjc3JycujXrx8A/fr1M16u69y5M25ubtjb29O+/R+F\nm6b2Yf38/NiyZQs9e/akXbt27Nq1iyFDhlBUVIRer+eWW26hY8eO6HS6epcFL168yLPPPsu4ceP4\n7LPPOH36NCdPnqR///7odDpjO7Ozs41fbAgICODEiRMA9O//x7dlOnfurErH6+TJk6xbt4677rqL\n6OhovvvuOwYNGsQLL7zAL7/8YvE8QgghhBparfMVFhbGxx9/DMCePXvo3Llzo0uOpvD29ubpp58m\nLi6OrVu38vLLL6PT6Xj99ddZs2YNK1asQFEUHBwcqKqquuZ+rr5coCgKzs7OeHl58dVXXxEXF8eP\nP/5oLLQF6NWrl3FE7+qRvaYuOzg4OFBdXW3SsYcMGcI777zD0KFD6dixI2vWrGHIkCE4OzuTm5vL\nlStXKC0tpbKyEnv7P16eHTt24OHhwaZNm3j88cdRFIVevXpx8OBBY7tramq4++672bdvH1DbQ6/7\nEsDV+7r6/5aQlJTE008/zfjx4/nzn/9MWVmZ8ed18eJF1q5dy9SpUwkODuaHH34wfq3XlmmptkVo\nnzWcb1LzpQ6t5JSaLxOFh4fz448/UlRUhLu7O6+//jqVlZUAzJkzh7Fjx7JlyxY8PT25/fbb+eij\nj5p1nIiICBYvXsznn38O1NaI/f7773zwwQdA7SU9Ozs7xowZw8yZM3nkkUeYPn16o/3UdYDs7OyM\n/5577jkmTpyIvb09d955J2vXrjVu/9BDD/HNN98wYcIE7rrrria/RVm3z2HDhvH666+TlJTE3//+\n90bbeXp68uSTTzJ//nwGDRrE4cOHGTRoEKdOnTL+jKD2UtzDDz+MnZ0dr776ar19BAUF8e6773Lo\n0CG6deuGXq/HycmJ6dOnExoaSocOHfjzn//M9OnTmTNnDl9//TXdunVj8eLFJCcn1+sAWqJuJSsr\ni+3bt/Ppp5+SlZV1zS9D1Dl//jwXLlxg4sSJeHp6Mnz4cCZMmMDQoUNbPasQovXZSq2OUJetnEct\nqvlqKWuvl6iqqkKn07F+/XpKS0tZuHCh2pGsmqIorF27lpiYGLKzsykurp0jp127do1GBnU6XaOR\nSnt7+3qXWm+77TYcHR1ZtGgRY8eOrfcFDqFdUvMlbkRqvmpJzZf1UX2eL2tVVwB/tY0bNzbrUtu0\nadP4/fffad++fb1RsWspLS3liSeeqLfur3/9K/7+/jd9bK3IyMhg27ZtJCUlNfqCQEtdvnyZS5cu\n8fLLL/Pyyy9jMBgYNGgQjz/+OH5+fsZvgwohhBBaYnOdr/vuu4+4uDiz7CsmJuamtnd0dLypY199\nmw2tOH/+PGlpaWzfvp2vvvqK8+fPU15u2uzSV2vOgGt6errxCxju7u4MGjSI4cOH88ADD9CjR4+b\n3p+atPjaC+2yhvOtrk7nepeNrCGnqcqOH7jmbX+siaVyFpRe4eeTJVSbMH2kUwcdBpc76q0z9bU3\n5TzSApvrfAnzunTpEgUFBXz77bd88803FBQU1PtWaLt27VTJlZubS25uLl9++SXt27fnrrvuYuzY\nsQwfPpz+/fvj6OioSi4hRNO0/mEpru9MWQX/9322SduO9OzSqPNlKls5j6TzpSJr/AuvoqKC8+fP\n89VXX7Fjxw5OnDhBdnbtL1RTdVrNZc6i/8rKSjIzM8nMzOTdd9+lS5cuuLm58dhjj/GnP/0JDw8P\nOnbsaLbjmYM1vvbCdmnlfNNKTkATo16gnZxaeu3NQTpfbVxNTQ2//vor27Zt4+DBg2RkZHDixIlG\nxe9acv78eUpKSnjttdeA2tvKdO/enSFDhjBhwgQ8PT3p1KmTyimFEEK0VdL5UpGl6xtqamooKSlh\n586dJCcnk5GRQVpaGufPn8fOzq5ZdVjNZcljnTlzht9++439+/ezevVqOnXqhF6vx9PTk9GjR3P/\n/fdz55131ps0t7VpqbZFaJ81nG9S86UOreSUmi9hU/bs2cOOHTs4cuQIhw8f5sSJE01O/dCWXLhw\ngQsXLpCZmUlsbCxQe0eGHj160KdPH8aPH09AQIDVXaoUQsu0/mEprIOtnEfS+VKRuf/C+/XXX/nx\nxx85fPgwmZmZ7N+/32o7WtZ2g+L8/Hzy8/NJTU1l3bp1QO3kuG5ubgQEBDBhwgSz1o5p5a97YRu0\ncr5pJSdop5ZKKzm19Nqbg3S+NKayspKysjKSkpJISkri5MmT5ObmkpOTw5UrVyx6Oc/WHTt2jGPH\njvHjjz+yfPlybr31Vrp164azszMGg4Hg4GD69u2LXq/ntttuUzuuEEIIjZDOl4pudI27srKSCxcu\n8PPPP7Nt2zaOHTtGQUGB8YblDYvirW006Xq02Em8cuUKubm5FBQUcODAAeMtr5ycnHB2diYgIIAR\nI0YQEBDAXXfddd0aMi3Vtgjts4bzTWq+ainUzol1I3bAxSstv2ohNV/WSTpfVqKyspLz58+TmprK\n5s2bOXLkCIWFheTl5QHmneZBmFdxcTGlpaVkZWXxxRdfANCpUyecnJy47777GDx4MP3796d3797c\neqtptxURwtZo/cPSXJ78Il3tCJpmK+eRdL5UUlpaSseOHXnttdfYt28fBQUFnDp1Cmj6Xoi2Rkuj\ndM1x4cIFysrKyM7O5tNPPwVqO2TdunXjoYceIigoiPz8fNzc3FROKtoCrYwmaSUnaKeWSis5tfTa\nm4N0vizg0qVLnD17lsTERHbs2EF2djYnT57k4sWLakcTFlT3Lcvly5cDtTcO79SpE76+vowePZqA\ngAC8vb1lDjIhhLBx0vkys5qaGi5evEhKSgqxsbEcOXKEvLw8CgsLgbYxqmUKLdZ8mdulS5eoqKjg\nzJkz7NixA6i9P2iXLl0YMmQIwcHB3Hvvvbi7u6t2GydhG6yhlkpqvtShlZxS8yVMVlpaSm5uLmlp\naSQmJnLixAmKioqMBfFSpyVuVmlpKeXl5URHRxMdHQ38UT82cOBA/P39MRgM+Pr60rVrV5XTCmE6\nrX9YCutgK+eRdL5MlJ+fz+HDhzl06BA//PADubm5XLhwgdLSUqDxNw/F9dl6zZc51Z1n2dnZxMTE\nANC+fXtuvfVWAgMDueeee/Dx8WHgwIH4+PionFZYI62MJmklJ2inlkorObX02ptDsztf8fHxLFq0\niOrqambNmsVLL71U7/GioiKeeOIJzpw5Q1VVFc8//zxPPvlkS/NaRE5ODvv37+fw4cPs3LmTEydO\nUFZWRmVlpdrRhABqb4B++fJlduzYYbxk6eDggJ2dHf3798dgMODt7c2QIUPw9/dXOa0QQoirNavz\nVV1dzYIFC0hISMDNzY0BAwYQFhaGr6+vcZuVK1cSEBDA0qVLKSoq4p577uGJJ55Ap7Oewbb8/HwO\nHjxIZmYmx48f5+DBg2RnZ3Pp0qV6NUlSp2V+UvNlfoqiUFlZSUpKCikpKUDtuasoCj4+Pnh4eODm\n5oa/vz/Dhw/H2dnZovezFOqxhloqqflSh1ZySs2XCVJSUvD09MTDwwOAqVOnEhsbW6/z1b17dw4d\nOgTU1rE4Ozur0vEqKyvj1KlT7Nq1i4MHD/Lbb79RWFhIfn4+ZWVljS4V1n1YCWErampqSE9PJz29\n/vxCjo6OODs707FjR3r16sXgwYPx8fHhnnvuwdXVVaW0wlZp/cNSWAdbOY+a1RvKz8/H3d3duKzX\n60lOTq63zezZs3nwwQfp0aMHZWVlxsknW8tvv/1GVlYWmZmZ/PLLLxw5coRz587x22+/UVFRAWh7\nRnhbIz979ZWWllJaWkq7du04dOiQ8SbjOp2ODh064O7ujp+fH7169cLb25uAgAB69uypcmrRHFoZ\nTdJKTtBOLZVWcmrptTeHZnW+TPngfPPNN+nfvz8//PADx48fJyQkhIMHDza6MfH8+fONb+iOjo74\n+fkZX4SkpCSg9kWpqalh586dZGdnU1NTQ15eHvv37yc3N5eioiIuX75cryarqW8aNhzRamqEy5yj\nXpbev7SnZcezxP4tfbzm7L+qqory8nIOHz7M4cOHjevt7e3R6XR4e3vTo0cPqqqq6NmzJ48//ji9\nevXi8OHD2NvbN/r9Bdi9e7dxEuHIyMibziSEELakWZ0vNzc343QKALm5uej1+nrb/PTTT7z66qsA\n9O7dm169epGZmUlQUFC97VatWmX8f01NDWfOnGHnzp2cPHmSffv2cfz4cZYsWcK5c+eMc2U1ZGpN\nlp2dXb0Po4bLdevMpal9mXv/Wm1PU50CLbfnWvu/UedHS+2B2kL/X3/9lV9//dW4bt26dQB06dKF\n22+/HVdXV/z9/bnrrrvQ6/UYDAZeeOEF7OzssLOzIzU11ayZxI1ZQy2V1HypQys5pebLBEFBQWRl\nZZGTk0OPHj2IiYlhw4YN9bbx8fEhISGB++67j8LCQjIzM7n77rsb7WvixImcPXuW/Px8Ll26xJUr\n9W84KsXuQmjD+fPnKS0tJS8vj7179xrX141COzs706VLF/7973+rmFKoResflsI62Mp51KzOl06n\nY+XKlYwePZrq6moiIyPx9fVlzZo1AMyZM4dXXnmFp556Cn9/f2pqanjrrbdwcnJqtK8ffvih3n5F\n2yA1X23PuXPnOHfunNox2iStjCZpJSdop5ZKKzm19NqbQ7N7O6GhoYSGhtZbN2fOHOP/77zzTjZt\n2tT8ZEIIIWzGxStVlFeaNhG1HfLHmbBtMtQkVCHTeQhhOdZQS/XfNasB+N5x+DW3uXDsAJ08+1NT\nY/3vD1qppdJKTqn5EkIIIcxsTPgsFsRmQtW1R78qq2u4cp3HhdB6p6uOvdoBRNskNV9CWI7ao16m\n0sIITR2tZNVKTq2co+YinS8hhBBCCAuSzpdQhdR8CWE5V094q5b4DR/ycPmu625TdvyAhdK0nFay\naiWnqefov/71L2Pdl5ZJzZcQQohWZ6z5EqIFpOZLiBaQmi8hLEcr9TRaqU8C7WTVSk6tnKPmIp0v\nIYQQQggLks6XUIXUfAlhOVLzZX5ayaqVnFLzJYQQQpiZ1HwJc5CaLyFaQGq+hBqqq6sJCAhg3Lhx\nABQXFxMSEoK3tzejRo2ipKTEuO3SpUvx8vLCx8eHbdu2qRXZLLRST6OV+iTQTlat5NTKOWou0vkS\nQrQZK1aswGAwGDv/UVFRhISEcPToUYKDg4mKigIgPT2dmJgY0tPTiY+PZ968edTUyMzrQgjzkM6X\nUIXUfAlLy8vLY8uWLcyaNct4/sXFxREREQFAREQEGzduBCA2Npbw8HAcHBzw8PDA09OTlJQU1bK3\nlNR8mZ9Wsmolp9R8CSGEDVq8eDH/+Mc/KC0tNa4rLCzExcUFABcXFwoLCwEoKChg8ODBxu30ej35\n+flN7nf+/Pn07NkTAEdHR/z8/IyXUOo+UNRerqNmnjHhs4h4Jwb440bPdR2DuuXygmP1lhs+3taX\nGzLl+eUFx6wmv7Ej6PkA0LzzKTAw0KLnb1pamvE949SpU0RGRmIOdoqKQxCJiYmMHDnSuKzT6aiq\nqqq3Tbt27aiurr7ufprapql92dvb17t0YGdn12gEpql9mZKh4b611p6Gz5X2mL89LdmXLbUnISGB\n4ODg6+7H3L799lu2bt3KqlWr+OGHH3j77bfZtGkTXbp04fz588btnJycKC4uZuHChQwePJhp06YB\nMGvWLMaOHcvEiRPr7TcxMZHAwECLtkWrjp4tl4L7Ftr7Yu3vTdBbiSonaZmRnl14cYSH2jGaJTU1\n1SzvXzLyJYSweT/99BNxcXFs2bKFy5cvU1payvTp03FxceHMmTO4urpy+vRpunXrBoCbmxu5ubnG\n5+fl5eHm5qZWfCGEjZGaL6EKqfkSlvTmm2+Sm5tLdnY20dHRPPjgg3zyySeEhYWxfv16ANavX8/4\n8eMBCAsLIzo6moqKCrKzs8nKymLgwIFqNqFFpObL/LSSVSs521rNV7M7X/Hx8fj4+ODl5cWyZcua\n3OaHH34gICCAvn37MmLEiOYeSgghzKru245Llizh+++/x9vbm+3bt7NkyRIADAYDU6ZMwWAwEBoa\nyurVq2V6lBYaEz6LbzsMUzuG0LhnnnnGJub6atZlx+rqahYsWEBCQgJubm4MGDCAsLAwfH19jduU\nlJQwf/58vvvuO/R6PUVFRWYLLbRPPsiEWoYPH87w4cOB2hqvhISEJrd75ZVXeOWVVywZrdVoZQ4l\nrcxJBdrJqpWcWjlHzaVZI18pKSl4enri4eGBg4MDU6dOJTY2tt42n3/+OZMmTUKv1wNw5513tjyt\nEEIIIYTGNavzlZ+fj7u7u3G5qa9hZ2VlUVxczAMPPEBQUBCffPLJDffb1DepzFkb1HBfTe27NY/X\n2vvXUntM2ZeW2mPq/i19PGtoj9T3qU9qvsxPK1m1krOt1Xw167KjKZeMKisrSU1NJTExkfLycoYM\nGcLgwYPx8vK65nOa+iq7OS9PNfy6flNTGZj7eKasa8n+pT0tO54p61qy/xt1PNpCe+QSswC5t6Mw\nD1uo94Jmdr4afg07NzfXeHmxjru7O3feeSe33XYbt912G3/60584ePDgdTtfou2QD2QhLEcr9TRa\nqU8C7WTVSk6tnKPm0qzLjkFBQWRlZZGTk0NFRQUxMTGEhYXV2+aRRx4hKSmJ6upqysvLSU5OxmAw\nmCW0EEIIIYRWNavzpdPpWLlyJaNHj8ZgMPDYY4/h6+vLmjVrWLNmDQA+Pj6MGTOGfv36MWjQIGbP\nni2dL2EkdUBCWI7UfJmfVrJqJafUfJkoNDSU0NDQeuvmzJlTb/n555/n+eefb+4hhBBC2Aip+RLm\nYCs1XzLDvVCF1HwJYTlaqafRSn0SaCerVnJq5Rw1F+l8CSGEEEJYkNxYW6hCar6EsJykpCTVRxbi\nN3zIw3DdWwyVHT+gmZEarWS1xpzpv/3O90fPcfWnQHpqMobAQY227dm5PT7dbjcu19V7af3yo3S+\nhBBCtDqp+RJ1Ckor+MfOU/XWlR0vpOPFU422nezXrV7nS+udrjpy2VGoQmq+hLActUe9TGVtIzTX\no5WsktM6SedLCCGEEMKCpPMlVCE1X0JYjszzZX5ayWprOdv8PF9CCCGEqaTmS5iD1HwJ0QJS8yWE\n5UjNl/lpJavktE7S+RJCCCGEsCDpfAlVSM2XEJYjNV/mp5WstpZTar6EEEIIE0nNlzAHqfkSogWk\n5ksIy5GaL/PTSlbJaZ2k8yWEEEIIYUHS+RKqkJovISxHar7MTytZbS2n1HwJIYQQJpKaL2EObb7m\nKz4+Hh8fH7y8vFi2bNk1t/vll1/Q6XR8/fXXzT2UsEFS8yWE5UjNl/lpJavktE7N6nxVV1ezYMEC\n4uPjSU9PZ8OGDWRkZDS53UsvvcSYMWPkMpMQQgghBM3sfKWkpODp6YmHhwcODg5MnTqV2NjYRtu9\n9957TJ48ma5du7Y4qLAt0hkXwnKk5sv8tJLV1nK26Zqv/Px83N3djct6vZ7k5ORG28TGxrJ9+3Z+\n+eUXky4z1dTUNFpnzg/phvtqat+tebzW3r+0p2XHs8T+LX08a2iPdLQFSM2XMI82XfNlSkdq0aJF\nREVFYWdnh6IoJr0B29s3jmPO2qCG+2pq3615vNbev5baY8q+tNQeU/dv6eNZQ3ukvk99UvNlflrJ\nKjmtU7NGvtzc3MjNzTUu5+bmotfr622zb98+pk6dCkBRURFbt27FwcGBsLCwFsQVQgghhNC2Zo18\nBQUFkZWVRU5ODhUVFcTExDTqVJ04cYLs7Gyys7OZPHky77//vnS8hJFcihLCcqTmy/y0ktXWcrbp\nmi+dTsfKlSsZPXo01dXVREZG4uvry5o1awCYM2eOWUMKIYTQNqn5EuZgKzVfzZ5kNTTMhqj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DBmHy5MmIiIjQvEUSKCtsZ2slua+psfjHxawn2NRKQSBj+mTM8fv4/HKO+LE7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z/3hw84Gu8Fmu9dngPEIWDH5IZXI8aZTB1cWRV3nB8lSJYIjTlDxVVU+XZbl8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\nwrlz5xAREYGkpCR88803AIAmTZrg/v376Ny5MxiGgZ2dHdtjV/N8NY+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xiG9jwY3BMAxK\nS0s1ngxR2x+dlpWVCXqhZSFfe2I8qKZK+KimyrBo+I9opLCwEPb29jA1NeXk/B4eHli3bh3Gjh3L\nyfkJIfWjmipxoZoq9VBPFYf4NhZsSMZe8GvM154Ih9jvU7HXGwHiz5Fv9yg1qkijnTlzRmkCRK4s\nX74cK1as4DoMQgghBAA1qjjFt7FgdRUVFeH69etaHUMXE/lnZmYiMzNT6+NwQajXnhgXqqkSPqqp\nMiyqqSKNsnLlSuzatYvrMFgnTpzAqFGj8Mcff3AdCiGkBqqpEheqqVIPNao4xLex4IaUlZUhIyMD\nWVlZWh9LVzVVhYWFuHHjBsrKytCkSROYmAij81Vo154YJ7Hfp2KvNwJU51j8XIGMwjKN1mNs38IM\n1q2a6SI0neDbPUqNKqK2Pn36ICcnh+swaikoKIClpSUuXrwIR0dHrsMhhBBeKyqT4+OjqRq9dolv\nN141qvhGGH/WixTfxoLrUlBQgMWLF7PrpumCLmqqXrR27VrExcXp/Lj6IJRrT4wb1VQJn65yHFZy\nAcNKLujkWLrEt89S6qkiDSoqKsLq1ashlfL7dtm5cyecnZ3h5eXFdSiEGD2qqRKXo80HAAD6cRwH\n32ncUyWTyeDo6AgHB4d6f9Z++fJlSKVSHDhwQNNTiRbfxoJV2bt3L7sIrS7pa56q77//XhAFlUK4\n9oSI/T411poqMeHbPapRo0qhUGD27NmQyWRISUlBWFgYbt68qXK/hQsXYsiQIXoZ7iH6dfz4cRw7\ndgy5ublch6K2R48e4fLly1i/fj3XoRBCCDEyGjWq4uPjYW9vD1tbW5iZmWHcuHEIDw+vtd+aNWsw\natQodOjQQetAxYhvY8Ev2rVrF44cOaKXY+uzkX379m0sWrRIb8fXBb5fe0IAqqkSA6qpMiyNimRy\nc3NhY2PDbltbW9cqEM7NzUV4eDjOnDmDy5cv1zncM2vWLHTp0gUAYG5uDhcXF7Y7r/rNEut2cnIy\nr+Kpue3n58fGV01VQ0iXjaMXj6XN+SoqKtC7d2/MmTMHkyZNAsCv99eYtgEgJiaGnYojKCgIRPyo\npkpcqKZKPRJGg2/F/fv3QyaTYePGjQCqCoTj4uKwZs0adp/Ro0dj/vz58PLywuTJkzF8+HCMHDlS\n6TiRkZHo1auXlikQXSorK8ODBw/Qv39/lJaWKj0nlUohl8uVHjM1NYVCoaj3mKr2UXUsExMTVFZW\nstsSiaRWI0rVsVQ9Vv3aTZs24a233kKbNm3qjZEYTkJCAry9vbkOQyfoM6xh+cXPMWXfTY3mROKr\nKwuq7l/PlZEcR2J4S3y7obeNOddhcKahzy+Nhv+srKyQnZ3NbmdnZ8Pa2lppn6tXr2LcuHGws7PD\n/v37ERISgsOHD2tyOmJAycnJ6NWrF54/F8dfl9OmTcOvv/7KdRiEEEKMgEaNKk9PT6SmpiIjIwPl\n5eXYs2cPAgIClPa5d+8e0tPTkZ6ejlGjRmHdunW19jF2fBsLTkpKwrFjxwxyLkP+cCEpKQlHjx41\n2PnUwbdrT4gqVFMlfFRTZVga1VRJpVKEhobC19cXCoUCQUFBcHJyYn9xFRwcrNMgiWGcOnWK9x+C\nmjh16hSKioowbNgwrkMhxGhQTZW4UE2VejSezdHPzw9+fn5Kj9XVmNq6daumpxE1Ps2vMXfuXJw6\ndcpg59PXPFV1SUlJwRtvvAGZTIaXXnrJoOdWhU/XnpC6iP0+FfscToD4c+TbPUrL1BAAQFpaGvLz\n87kOQ29KS0uRnJysVAhPCCGE6BI1qjjEh7Hg8vJyWFlZIT4+3qDn5WoyWAcHB8hkMk7OXRMfrj0h\nDaGaKuGjmirD4vdibkSvcnNzERkZidLSUoMPx3GlrKwMZ8+eRbt27dC7d2+uwyFEtKimSlyopko9\n1FPFIS7HgjMzM3Hw4EHMmzePk/Nz2YjbuHEjQkNDcf36dc5i4FsdACGqiP0+FXu9ESD+HPl2j1JP\nlRHKzc3FqlWrsGvXLq5D4cyRI0dw/fp1HDp0CFZWVpBK6X8FQggh2qGeKg4Zeiy4rKwMx48fh7+/\nP+cNKj4ssJ2bmwsPDw/s3r0bOTk5Bj033+oACFGFaqqEj2qqDIv+PDcS+fn5iI+PR2BgIExNTbkO\nh1fmzp2LuXPnYty4cXB0dOQ6HEJEgWqqxIVqqtRDPVUcMtRY8OnTp/Hll18iMDDQIOdTB98K43/+\n+WcEBwdj06ZNBjkf3+oACFFF7Pep2OuNAPHnyLd7lBpVIqVQKPD48WN4enpiwoQJOHDgANch8V5y\ncjK++OILvPLKK4iLi0NZWRnXIRFCCBEQalRxSJ9jwXfu3IGdnR0yMzNRUVGht/Noig81VaowDIPi\n4mL4+flh48aNejsP3+oACFGFaqqEj2qqDItqqkRo69atWLx4MddhCN7y5ctx5coVbNu2jetQCBEc\nqqkSF6qpUg/1VHFI12PBly5dwoQJE7B8+XI8efJEp8fWNb7VVKlSWlqKyMhI9OrVCxcvXkRRUZHO\njs23OgBCVBH7fSr2eiNA/Dny7R6lniqBq6ysRHZ2Nvbt24cVK1ZAoVBwHZKolJSUICMjA8OGDcP4\n8eMxevRoDBw4ECYm9PcIIYQQZdSo4lB0dHSjWtmXL19GVFQUUlJSEBkZiYqKCigUCsjlcgDC6P2p\nxteaqvqEhYUhLCwMUqkUDMOgRYsW8PDwgJ2dHd566y0MHz5c7WM19toTwgVt7tPqeqqxU4J1GZJO\nFaclib4nR1c5/lNP1U3rY+kS3z5LqVHFc5WVlXj69CkGDx6Mu3fvorKykn3OxMREaZsYBsMwUCgU\nePLkCc6dO4dz585h586dMDExwalTp9C9e3c0bdqU6zAJ4RTVVIkL1VSph8YwOKRO6zo3Nxe2tra4\nd++eqBpQQupVU1d5eTneeOMNtWar59NfVoTURez3qdh7qQDx58i3e1TjRpVMJoOjoyMcHBywYsWK\nWs///vvvcHNzg6urK/r378/p4rVCVFBQgPXr12PQoEFch0IaafHixQgKCkJ2djbXoRBCCDEgjRpV\nCoUCs2fPhkwmQ0pKCsLCwnDz5k2lfbp27Yrz58/j+vXr+PrrrzFjxgydBCwmL86v8eTJE0RFRSE4\nOBi+vr74/PPP8fDhQ46i0y8h1lSp68mTJzh48CB69+6NGTNmYO/evcjMzFTah29zqxCiCs1TJXw0\nT5VhaVRTFR8fD3t7e9ja2gIAxo0bh/DwcDg5ObH79Ov3z8irl5eXwResFZrw8HD8+uuviIuLg6mp\nKf2KTwTkcjn++OMP/PHHH7C3t8fQoUPx7bffch0WIQZBNVXiQjVV6tGopyo3Nxc2NjbstrW1NXJz\nc+vcf/PmzfD399fkVKL2r3/9CzExMfDx8UFQUBDi4uK4DslgxFhTVZ+7d+9izZo16NixI86fP48e\nPXpwHRIhDeJbvYquib3eCBB/jny7RzXqqWrMF+LZs2exZcsWxMTEqHx+1qxZ6NKlCwDA3NwcLi4u\n7JtU3a0nxu3CwkLs2rULX3/9dV1vXYNeHEJTNaSmy2E2Qx9fbPlUVlaisrIS7777Lr7++mtYWVnB\n0tKSF/ejPrcBICYmBllZWQCAoKCg+t42QggRLAmjwbdIbGwsFi1aBJlMBgBYtmwZTExMsHDhQqX9\nrl+/jhEjRkAmk8He3r7WcapnqzY2t2/fxtGjR7FkyRKVz6sa/pNKpex8VNVenFJBIpHU+iJXdSxV\nj734WlXTNaiKQZ2hSnVjEHI+6lyfF/n7+yMkJASvv/56vecTm4SEBHh7e3Mdhk6I/TNMV/NUTdl3\nE/JK/tVRajqH05UFVfev58pIXYekc7qep6rfe5PR28Zc6+PpiqHnqWro80ujnipPT0+kpqYiIyMD\nlpaW2LNnD8LCwpT2ycrKwogRI7Bz506VDSpjo1AokJGRgS1btuD8+fO4ceMG1yERjkVERCA2Nhbe\n3t4ICQmBnZ0dzM3582FFiDaopkpcqKZKPRo1qqRSKUJDQ+Hr6wuFQoGgoCA4OTlh/fr1AIDg4GB8\n9913KCwsxMyZMwEAZmZmiI+P113kAvDs2TNcunQJMTExuHPnDo4fP05F6P/P2Gqq6vL48WPs27cP\n+/btQ79+/dClSxf069cPI0aMQPPmzWk5HMIpvtWr6JrY640A8efIt3tU4xnV/fz84Ofnp/RYcPA/\nyxFs2rQJmzZt0jwygfrrr79w/fp17Nu3DydOnOD9wsaEPy5duoRLly5h//79mDdvHoYNG4aBAwfi\njTfegIODA9fhEUIIaQAtU6Mjcrkcq1atwsGDB3H37l0AVT16RDUxz1OlK0ePHsXRo0fRtm1buLu7\nY/fu3TA1NaVePmIwtPaf8NHaf4ZF3/paqqiowJMnT+Du7o5nz55xHQ4RoUePHuHs2bPo2LEjwsLC\n8K9//QstWrTgOixC6kU1VeJCNVXqoUaVhk6fPo0jR47g8uXLuHXrFtW+NBL1tmhm/PjxsLGxQdeu\nXTF69GiMGTOGekSJ3vCpB0AfxN5LBYg/R77do/Rp3AiZmZnsVAgVFRVUcE44kZ2djdzcXJw7dw6f\nfvopxowZg5EjR/Luw4UQQowNNarqkJubi9jYWBw/fhyZmZkoKipCenp6vfMOEfVRTZVulJaWYtu2\nbdi+fTtatWqFrl27ws7ODi4uLhgwYAA8PDy4DpEIGNVUCR/VVBkWNapeEBsbi4MHDyI+Ph7Xrl0D\noN6EkIRwiWEYPH36FAkJCUhISMD+/fthaWkJFxcXzJw5Ex4eHnj55Ze5DpMYEaqpEheqqVKP0Teq\nysrKkJaWhosXL2LLli3IzMxEWVkZ12GJHtVU6V9eXh7y8/Nx4sQJdOvWDd7e3vDz84OhEH5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HWEwPN7w9NhAA8z2N7NYRH00Ooa3beq4U312mJ3wdHtAJHZzsMTbEAxHeHQW3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B1DiC1vzYUbakHS7IER9UAsuRkk+T8JlzPqQkiz1wSWXOnKF/u9ZUmiGLkKls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- } - ], - "prompt_number": 19 - }, - { - "cell_type": "code", - "collapsed": false, - "input": [ - "mcplot?" - ], - "language": "python", - "metadata": {}, - "outputs": [], - "prompt_number": 20 - }, - { - "cell_type": "code", - "collapsed": false, - "input": [], - "language": "python", - "metadata": {}, - "outputs": [] - } - ], - "metadata": {} - } - ] +{ + "metadata": { + "name": "Sum of Gaussian Distributions + noise" + }, + "nbformat": 3, + "nbformat_minor": 0, + "worksheets": [ + { + "cells": [ + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import pymc as pm\n", + "import numpy as np\n", + "import pylab as pl\n", + "\n", + "\n", + "def GaussFunc(x, amplitude, centroid, sigma):\n", + " return amplitude * np.exp(-0.5 * ((x - centroid) / sigma) ** 2)\n", + "\n", + "wavelength = np.arange(5000, 5050, 0.02)\n", + "\n", + "# Profile 1\n", + "centroid_one = 5025.0\n", + "sigma_one = 2.2\n", + "height_one = 0.8\n", + "profile1 = GaussFunc(wavelength, height_one, centroid_one, sigma_one, )\n", + "\n", + "# Profile 2\n", + "centroid_two = 5027.0\n", + "sigma_two = 1.2\n", + "height_two = 0.5\n", + "profile2 = GaussFunc(wavelength, height_two, centroid_two, sigma_two, )\n", + "\n", + "# Measured values\n", + "noise = np.random.normal(0.0, 0.02, len(wavelength))\n", + "combined = profile1 + profile2 + noise\n", + "\n", + "# If you want to plot what this looks like\n", + "pl.plot(wavelength, combined, label=\"Measured\")\n", + "pl.plot(wavelength, profile1, color='red', linestyle='dashed', label=\"1\")\n", + "pl.plot(wavelength, profile2, color='green', linestyle='dashed', label=\"2\")\n", + "pl.title(\"Feature One and Two\")\n", + "pl.legend()" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "pyout", + "prompt_number": 1, + "text": [ + "" + ] + }, + { + "output_type": "display_data", + "png": 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D8HRS8Odhmt6AUqVudB1Fu9AhdGE+xAowgeA2Hz68jHeqLiGfPLlOmcqnn0Zy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\n+VkSgJ8A99JCKuRbUUi66c81D5mSyvac83emvUq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+ } + ], + "prompt_number": 1 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "# Unknowns\n", + "\n", + "est_centroid_one = pm.Uniform(\"est_centroid_one\", 5000, 5050)\n", + "est_centroid_two = pm.Uniform(\"est_centroid_two\", 5000, 5050)\n", + "\n", + "est_sigma_one = pm.Uniform(\"est_sigma_one\", 0, 5)\n", + "est_sigma_two = pm.Uniform(\"est_sigma_two\", 0, 5)\n", + "\n", + "est_height_one = pm.Uniform(\"est_height_one\", 0, 5)\n", + "est_height_two = pm.Uniform(\"est_height_two\", 0, 5)\n", + "\n", + "std_deviation = 1. / mc.Uniform(\"std\", 0, 1) ** 2\n", + "\n", + "# Set up the inference\n", + "\n", + "\n", + "@pm.deterministic(trace=False)\n", + "def est_profile_1(x=wavelength, centroid=est_centroid_one, sigma=est_sigma_one, height=est_height_one):\n", + " return GaussFunc(x, height, centroid, sigma)\n", + "\n", + "\n", + "@pm.deterministic(trace=False)\n", + "def est_profile_2(x=wavelength, centroid=est_centroid_two, sigma=est_sigma_two, height=est_height_two):\n", + " return GaussFunc(x, height, centroid, sigma)\n", + "\n", + "\n", + "@pm.deterministic(trace=False)\n", + "def mean(profile_1=est_profile_1, profile_2=est_profile_2):\n", + " return profile_1 + profile_2\n", + "\n", + "\n", + "observations = pm.Normal(\"obs\", mean, std_deviation, value=combined, observed=True)" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 5 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "model = pm.Model([est_centroid_one,\n", + " est_centroid_two,\n", + " est_height_one,\n", + " est_height_two,\n", + " est_sigma_one,\n", + " est_sigma_two,\n", + " std_deviation])\n", + "\n", + "map_ = pm.MAP(model)\n", + "map_.fit()" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 17 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "mcmc = pm.MCMC(model)\n", + "mcmc.sample(70000, 60000)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + " \r", + "[****************100%******************] 70000 of 70000 complete" + ] + }, + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "\n" + ] + } + ], + "prompt_number": 18 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "mcplot(mcmc)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Plotting est_height_one\n", + "Plotting" + ] + }, + { + "output_type": "stream", + "stream": "stdout", + "text": [ + " est_sigma_two\n", + "Plotting" + ] + }, + { + "output_type": "stream", + "stream": "stdout", + "text": [ + " est_height_two\n", + "Plotting" + ] + }, + { + "output_type": "stream", + "stream": "stdout", + "text": [ + " est_centroid_two\n", + "Plotting" + ] + }, + { + "output_type": "stream", + "stream": "stdout", + "text": [ + " est_centroid_one\n", + "Plotting" + ] + }, + { + "output_type": "stream", + "stream": "stdout", + "text": [ + " est_sigma_one\n", + "Plotting" + ] + }, + { + "output_type": "stream", + "stream": "stdout", + "text": [ + " std\n" + ] + }, + { + "output_type": "display_data", + "png": 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ERISFhRlVFiFztbBSpayWobm8Un6vlZSUaGlJIGhH2/NLo72+oKAA3t4tAbeK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lFjzElnPF+HCSJwb1tqGvXy6qwXu/5imVrc27ilmTo/Hb7WqlNhV9WzTUBQuH\n9gUg93tV/PAx3HtYGZ0GqPBhE17YsBd2XiE6zVvd41asP1WAKYN7Y/TAHgCAlUk5uPlA2X3K/43p\nj8mDeonSZz7S0tIwfvx4vdR99uxZ2NraYtGiRcjMzAQgfzetW7cOR44cgVQqRXl5OZycnJCVlYUF\nCxbg8uXLKCkpwYQJE5CbmwuJRIKwsDBs3rwZYWFhmDZtGlasWIEpU6aotdeRd5guGNp0g7Qnfnsz\nZ84EAFRVVanlP2psQfyhHJ00X/7OtpxtmvqcGrI9sd5fGjVfLS0tmDNnDhYuXMgpeGVkZGDJkiVI\nSkpSE7wAwMHBAdOnT8fvv4tnAP3p6bt483Aupu64ip+zyunrsT/cxF9/vYPcCvmHhe1DWl4vX9hc\nIWbSS2vx4fF8NcELUPZcz6yZoihlL+4c/f74RAHO5j/Ed2llrPnl9c2cghcA5FU2cuZ1Fh1w5q81\na37LR0VDCz45VSCovJRnq7aMEUh65+VSLP7xJr5Lu9fRLopOWwcneN+1+7hcXIuPTsgPjNQ3t6kJ\nXkyaWmXYlVaGu9XGt9Y0MXr0aLV30FdffYV3330XUqn8x46Tk9xZ8qFDhzB//nxIpVJ4eHjA29sb\nFy9eRFlZGWpraxEWFgYAWLRoEQ4ePGjYgXBg6vY0pL2u36aptycWvDZfFEUhLi4Ofn5+WLVqFWuZ\nwsJCzJ49G7t374a3tzd9vaKiAhYWFujRowcaGxtx/PhxfPDBB6J1/HR+u9uHL88V41k/JxQwPhZn\n8h/Cp7cNq6uJ47lVeGN0f1Q1tKpngl/AYX4GmYLdnnInFNwqYi1HX6Mo2t6pgOPD9kVqEet1BR39\nEAtB28X8sFFcG67sB/VIzqnE4rB+sLViX6JCzLXsvEJ4Q+ZYW7QLZvufeL3fe/Ue/jisr3Yd1jMy\nioKdV4jO9zeoGO9+n84uYCpmak/6Pey/dh+70u7prKE0JnJzc3HmzBmsXr0a1tbW+OyzzzB8+HCU\nlpZi5MiRdDk3NzeUlJRAKpXCzc2Nvu7q6oqSkhLO+uPj49G/f38AgL29PQIDA+m/IcWWCEmTNDOt\nQDX/wrlUVN4qAvoFAABtFqD4++dKAz5GNT5TSmdmZqKmRu4NobCwEHFxcRADXuErNTUVu3fvRlBQ\nEEJD5S/hdevWobBQrhFatmwZ1q5di+rqaixfvhyA/ITkpUuXUFpaipdffhkymQwymQwvvfSS3rYa\nFDxsbBcnBuJPAAAgAElEQVSmZE+EFK5P778uFKOumdvYnoumFhlt+M6s+06VsjDFJhtcLma4s+AQ\nHi4WqvvFYlLK0NYYD+Ju061IugVArrWKH+WmoTQ/zAMV9c1t6G5pTqd/vlmB1yLdO1S/IRBw6JYX\n5tMpqG7EhcJHvOULq9UDnx+4/gBn7jzE3yd7cgrExkprayuqq6tx4cIFXL58Gc8//zzu3LkjWv1b\ntmzhzFP9IdPRtOo1sevXpb0vvvgCaWlpWLFihUmOT+z2+PJHjopEr/L2bUfVH12a0mztMwU+fY+P\nqz2FvZequwl9tSdmWvVaWloaxID3LRoVFQWZjP/Nn5iYiMTERLXrQUFBonVSJ558cVRdTSg4lFUB\nj57sR3P5mLs7E/OC+mBJmKvS9dq8q8p/CAzpqk1GobGlDaU17YJTdrnmcEVsGMIaSds9dH2dGqxo\nEC5osvWgNu8q6txG0+mGFmXhq6sgoyj19aXl/Qq+TC3SaNPGlv2vC3LNz8m8asz0445xaoy4ublh\n9uzZAIARI0bAzMwMFRUVcHV1RVFRu6a5uLgYbm5ucHV1VTq1XVxcDFdXV7V6CXKI/yaCJsgaUcek\nPNyrfjRO3K7ijcnIJTJokiUUgZnv1XELBxTkriooisJrh3Iwe1cmsh903L+VMTpHaNOT8MXnCZ8C\ncLW0Fjfu83v9Zwbx7kKeJZTo6FZz4cN2TdbDplbOWVUIZXxRIRpbZCivb0Z6SW2H+mRIYmJicPLk\nSQDArVu30NzcjN69e2PmzJnYt28fmpubkZ+fj9zcXISFhcHFxQX29va4ePEiKIrCrl27OO1dDY2p\n29OQ9rp+m6benlh0rf0DDTC/GbkVDbSQxEkHP8YfHmvfulDVSuz8vQw7fy+D1FxCe8q/Wqr8wWpq\nlcHKXGJ0p+u0Xcy6bItRFKVx3GcLHqJNRimdZlXQ1NKGt4/cBsB9ctLOK8QkgkW3UerrSxuY81z0\n8DGnxrfhyTY8l7ZYwR/23gAA/PPZQfBz7q5zv/TB/Pnzcfr0aVRWVsLd3R1r165FbGwsYmNjERgY\nCEtLS3z33XcAAD8/Pzz//PPw8/ODhYUFtm7dSs/V1q1b8fLLL6OxsRHTpk1jPelIIBAIumJSmi+m\n+FUu4KhuR2SvVhklyFkoM0SRqgJj5jfX8Onpu3SaT0tHY4Tqm5qmVrRoKYG1CNTmXCxit09qbBXW\nHjO2JNfpViaGPLkpFCH95sNcRZji0mxtOS/fahMqrypOFBsTe/fuRWlpKR4/foyioiK88sorkEql\n2LVrFzIzM3HlyhUldzerV6/G7du3kZ2djcmTJ9PXhw0bhszMTNy+fVtv/ol0wRh8NqlC/HwZb3ud\n0Sbx8yUMkxK+mN8YMwEjY27HMBHyqZv17TWlNNNZJRcPVTyKA6B9UN0qb8Dyn3IEtAzcq32stbAD\nACn5D/Hm4VyNpxOFLOZbjA/vD5kPsDo5j6e0OnyRBZiUsMWGRPuBCgVs8yHkmXQF2p7YfOmKqrcN\nTRpH5kliPiij3AQnGBoSt4+gCbJG1DEZ4auwuknpF7vqr31tEOI64XGbuB+ePx8SJnjdfNCARfuz\nEPvDTXx8Ih+Z9/htnpisPZGPjLI6fHuF3ceYNuSrnO68Via8HwAw//vryCjTbDf070ul9L+TGP7c\nmKJWRlktijiENCZGqDQUhIYzLxpR3UbsyB89cwqNUUto6pi6PQ1pr+u3aertiYXJ2Hy9ejAbG6a2\n+xnTZLfCx6+31D0Pa6IjNjnacP6Jm4D7dc24X9eM0/kPtfbF1MSxZfefjPtw7CbFBAGLuVWEL29S\nVgWyHjTA3soc04b0BgDc53GloYijCShv5755+Dak5urPW/WZsPW45FETDlwvZ8kxHvj8fHHZxAFA\nQVUjNqUUolhFMBXLxrCrCrMEAoHQ2ZiM5qu5jVIyVrG16nouBQwF20ezor4ZiZdK8Q+GDRofWfc7\nfnLzYVMrdlwuxT9T2o/7//1kPmvZ2xrsi1oEaCLZXGK8dfg2fr5ZofHezoTrNOmL32di6o6ruFLM\n7hvuoxP5uPmgQW2LtyOyV8kj9q16gmEwBvsdVYjNl/G21xltEpsvYfAKX0VFRYiOjoa/vz8CAgJY\nJ2/Pnj0IDg5GUFAQIiMjkZGRIfhesWG6FbBk0YTok860L6p9rG5Lpi2PW9s/8EIW8/Fc7bWDqjSz\naOBKa9i3Dx+x2MtpQvWZUFCeq+6W5mqHJkYNcNC6HX0jk7GvL0WEhnc57O1qOOzq7LT8YfKA4VLF\n2dayvV9E9UUAsechaIasEXV4hS+pVIpNmzbhxo0buHDhArZs2YKbN28qlfH09MSZM2eQkZGB999/\nH0uXLhV8r9jw+ScyZio5Tk0mzBwk6P6X9t1AnRYCGJvmozNcMrB9utm6UVjdxLqtqC3/ulCCObsy\necsYo2sKXf2ocTm/1TYwO/MwA3M7n8hehsfU7WlIe12/TVNvTyx4hS8XFxeEhMhtTWxtbeHr64vS\n0lKlMhEREXBwkGsLwsPDac/QQu7VJ4b+MHTE5mv+99dZrw92shF0f0OLTC28kbYwBdfOXMxs9kgf\nncjnDZDNheozYbqdANiFE02yV1JWOf55ttCgWh9KRz9fXJovvjGy2fIxL33DOKxBZC8CgUDQDcFf\ntIKCAqSnpyM8PJyzzPbt2zFt2jSd7hUbU/gwaKOE0Wa8XU1jcfdhEx1PU9/wGaO3yShsPleMIzmV\nuFaq3enOjqCLSwe+E7t8h1FUvelXNrTwRILoYgvJBDAG+x1ViM2X8bbXGW0Smy9hCDrtWFdXh7lz\n5yIhIQG2trasZU6dOoUdO3YgNTVVq3vj4+PRv39/AIC9vT0CAwMFRxxXjfCefuk8avOKYOcVgu6W\n5oIjwouRZtrkiFV/amoqavNyBZWnKOHzBa9opfzuA4ORX91I53//SyUWzJig9fxryldN/37hHJ1+\n83AuYhzu42HuHUjcA9XKSyTaz9/9s/+FTT9vzvyHt6/icatMKf/yPUu0RXvA3EyiNp5/7DmM2rxy\n2HmF4HGrTOP8iJWmXPzovqek1Aua/4TUIs75MfOfyDl/qSm1AOzo9IyPrmLLn+ewls9Jv4SUOke6\nP/sOn4CMorBgxgSl/gDytVxYWAgAiIuLA8F0ILY8BE2QNaKOhNLw87WlpQUzZszA1KlTsWrVKtYy\nGRkZmD17NpKTk+Ht7S343hMnTmDo0KE6dXxSYrratZeH9aW3RcLd7XGxiP0UmD7oSOBjLo4tDmUd\nJxsbpnoj1NWOt4yirvHePfHOOA8Ackezi/+rbItXm3cV+9+ej/4qYWiultbibnUTnvN3Yu0X0+WF\n0H6r3v/inkxUNarbr301a7BgJ7QKND2TblIzNLaoG/3H+Dvh1Qg3tet//TWP3rpcO9ETIw1knH/i\ndhX+uv0Q7LxC8H9j+mPyoF4AlOdY1d3I0h9voqCa/WTi7AAnTvcaBxcFIea7DM6+uDtY0T7VIvo7\n4F7tY/w50h2BLrZ0f47EhsCCxwAzLS0N48eP58zvSnTkHUZ4OnF0dAQAVFWpH1p61NiC+EM5eCAg\nQguTTc/6wN+ZXTFCEBex3l+8ezkURSEuLg5+fn6cgldhYSFmz56N3bt3KwleQu4VmyuMYL+GFLwA\nw/n54kKbrSmmuF3K4pzUzisEd6rVbcjePnIbW84X6zesDMc3W5cdLk3PhO20JQAcvCHA75cBDfOP\nZFfSY/n8TCEq6zW/mPm6x7ftqGmambuS5wsfIb+6Cf/3S65SmccCQz8RCATC0wqv8JWamordu3fj\n1KlTCA0NRWhoKI4ePYpt27Zh27ZtAIC1a9eiuroay5cvR2hoKMLCwjjvTU5O1utgKhu4HXSaOtrI\nJkXMsEpc32GeCvMqO2bcz4fCfYIq+vicu/dgDzAtBEMeilSNYpBdXq9mb6Vqq8Wl9QL4T3RqsuMS\nIuSL4YCXwI4x2O+oQmy+jLe9zmiT2HwJg9fmKyoqCjINsU0SExORmJio071iU1rTecKXPrYdtYFP\nGDh4oxwO1u2+nZo1fBxr866i2yRPzvwCFq2Y3tHhey72M+lMLxTMsZy8XY0RbvZK+UxP93xG8prQ\nJDdxyWbM05+tIofeIhg3xJ6HoAmyRtQxGQ/3mgjpZ9r74RIO0aCqoQVbzxdj/SmG53pK/rFuamnj\nFChsLbkdcVpZsC+bQ0K263REH64d+GpML6lVb5MxWWKF6NEFGSg0qmztKbpDURTucTiqVcA3ldps\nO3LV2dQqLGg6QXtM3YcSaa/rt2nq7YlFlxS+anTwdv6cn5MeetIOU8Pi06ubXttiQ9VTu4I6Fl9P\nFIDF/72Jmd9m4LMzhWr5dl4hvGoeLmPqLeflPt6MZdtJk9aLTwh55+htHMmuVLr2iHEQgDkD9c1t\nOJJdodO6FApzLA/qmvGxShgmiUQCiqLwf7/k4i9Hb3PW49RdyjpuB2u5ElzXbUemoCp20HkCgUAw\nNbqk8LXuZEFnd4GXF4KdO1xHbxupVuU/5YjJ2MKy9UuBQskT7QhX2J5PTt0FRVE4ebsK3zIcawKa\ng5bHfHtNSJfV+8Xz4V+RdEunOnnb06DnOX/3oVLajEPo/CK1CP9MKcJHJ9jjUopNbkUjrqr4GSt+\n1AQZBVy/X88r/Egk7ONWDE3XbUfmdeL+S38Yg/2OKsTmy3jb64w2ic2XMAT5+TI20kprNRcyMEyb\nHHMR4hxtelZYaCFNsAac1vBxrM27CniFIKe8AZ/8Ty7URXn0ENxms46ajyKWk5cdQZPNlyYhoY2S\nC4Q1j9vgYG0Ba8Z2K1P+vFj4CABwrUx/jlc1jeXHzAdYEemusR6KAms0hPZtS833syFTKkOkr6cJ\nYs9D0ARZI+p0Sc3X04AuJkVsHz22LUCu4NWq3GMEVFYIGADUNGFiUcWxdaovhGh5tpwvxrzdmbhQ\n+Ag9u7H/VulM+y8mQmXeviyxHc2ebKTKNEjmXPnMtUccTegPU7enIe11/TZNvT2xIMKXSDC1Ehl6\n0ID0sdW8DckmTLAJX1zbZwoUY2GW+kagwKXkxqKT0WTzpUkIlVEUkrIqAMg1S8z4ksy5MYToJeTU\npqq7CS5U18TrUe6CNV9crkDqmtttC4nmi0AgEPh5aoQvQ34PRnl03PO5an/HDOypUz1pJepbtOYC\nNTW6CBVxKt7ygXZjbk0YMli1EFQN6K3M2bcdmf9ubus8vY+Q+aMoZeHro0memDqkN23Hp+sz+MPe\nG0ptEPSDMdjvqEJsvoy3vc5ok9h8CePpEb70XD8ztmOAHsI8jOyvWaBj+3Duu3Zf7dooDWFx6LHo\nqNJRVay994yHoPs6ekhStV3mM9GFfBVHpdbS9j8XLru+reeL9aL5ETIWIZqvioYWtDAERIXbEKGa\nLyEYyWFXgoFYsWIFsekh8ELWiDq8wldRURGio6Ph7++PgIAAVsl1z549CA4ORlBQECIjI5GR0R4X\nLjY2Fs7OzggMDBS/51qiTfidjiKGwX13S/mj+Wy6D94c0x8Demr2xi50hHZWwjRRXL7DNNFDRdPl\n2E3Yyc29V9UFRW1gExy8RHT7wRSqmG0xZ+lIdiXOFiifkjQUQm2+Ugra7fcUQpfQ045CINuO+sPU\n7WlMqb02GaX2X8SoSN58TSYhumBKc2oM7YkF71dYKpVi06ZNCAkJQV1dHYYNG4aJEyfC19eXLuPp\n6YkzZ87AwcEBycnJWLp0KS5cuAAAeOWVV/Daa69h0aJF+h2FAMx4BImFoS7YnX6vQ/WL7d3e9omA\nFNTXFkF9bVH7WIAPKYHfPE2CKJvNlza497BGVWO73ZtQe3TVMDodxc4rBH8c2hd/O35HlPq43Cmo\nGtxfLqrReZuYC03r61Z5A5paOuLcVD6GuuaO+yojbr4IBCC9tBZ7eL4rbx7OVbtGUUC5lkG1CV0T\nXs2Xi4sLQkLkL31bW1v4+vqitLRUqUxERAQcHOTbWOHh4SguLqbzRo8ejZ49xf0I6UpgX+6twEXD\n+mL9FC8D9kZ7NPnWAoSfMhOqmND1G6rqckFI342da2V1+CHzAZ3mE2CFzu+1slr86UA2bosQqPxR\nUysudSCYvOLwwePWjktOhtQyP20Yg/2OKsTmi51HTa24cb9e6b8L51LpfNW8G/frkfWgXvS/HmOY\nU2LzpY5gm6+CggKkp6cjPDycs8z27dsxbdo0UTomJiH9bDUafQ9zs8fXc4bo3EZH7Ys0YS5EfhH4\n1ddkVK0Yi1jbR+YGsCx8Y3R/tZeWPp8J34lWobP21uHbuFPViLUCnLMKGYtHT+23WBXLasCTIONi\naL64lk1eZQPu1Yrry43Q+RB7HoImyBpRR5DxT11dHebOnYuEhATY2rJrkE6dOoUdO3YgNTWVNZ+L\n+Ph49O/fHwBgb2+PwMBAeg9XIdGqpoHuANo/SIotGa60rcdY3nwgFABQfOMKGvJvw2ZgsFb1c9Wn\n6/2KNHP8ZhKJxvKpqamwsjBTmq/avFy18rLB4zX0X863ScdRe79e5/631+eHNRM98c7XP6FFRnW4\nPra0n3N3tfyG0tvI+P0CgD6it/f91fvwbpJvZ0rgoDxen2cAcK/fqKgoUBRFl3cMGM5bXuh6T798\nHrV5JVqN5+qlCgQ9NxF3HzahNu8q1pRcB1wDOjQ/MspLpf/AidNnsft/12AmkWDvJ2+BoBumbk9j\n6u2JbZ4iBFOfU5O0+QKAlpYWzJkzBwsXLkRMTAxrmYyMDCxZsgTJyclabzNu2bKFM091Uul0djoA\n9YVs5xUCM0m70bAinwI4y6vW3yPXlvbQrqk8M832R6XN/Vz9USCRaC4/clQkujMCYkdFRcEuu7ta\neYXmS1N9RbY+sLPlzheabpNRiBjggEXPTcR/Mh5ofT9XesK4Mbj4ZKvN0lyilu88ei6CRnjiv8fu\niNIe1/P58m4mb75q+vSdanx2+i5dvupJzEi+9a5xfUmA4OEjYVeRx5pvzrF+QsJ8lNKUSj5nezxp\nhear16BQ9LWzRI9uUvT1HYpU55wnJcm2JIFAeLrh3RCiKApxcXHw8/PDqlWrWMsUFhZi9uzZ2L17\nN7y9vfXSSW0IdFHXzGmze6ZP66QjsSHYOc9Xc0EWhNhNCd0mFOqMUywUIY7699B8YlMbXB2s8OdR\nbnghqA9cWLy2GwrVJ6PpOXx8skAp/qKzrSUuFj5CQbV62B9t4HusNgyhXN+U17cg6349VibdwqL9\nWQZr92nAGOx3VCE2X8LRt3kKG8Ywp8TmSx1e4Ss1NRW7d+/GqVOnEBoaitDQUBw9ehTbtm3Dtm3b\nAABr165FdXU1li9fjtDQUISFhdH3z58/H6NGjcKtW7fg7u6OnTt36nc0YHfz8IyXXBsX2s9O4/0e\njrq5JhDyR2VhJoGTrSX9b20QUlyoSMUa75GB2C8I9ydC1wQfR7wyvK9o9ZpJJJjp54S4MFfWfIO9\n6FSejbai7f26Zrx/7A7e/EX99JMCTWMxg0QnfZKDtfhC2cazhXj/mFwD19SqOAZimEMXfO5tPv/8\nc5iZmaGqqoq+tn79evj4+GDIkCE4duwYff3KlSsIDAyEj48PVq5caZC+d1WIPQ9BE2SNqMO77RgV\nFQWZjP8MXWJiIhITE1nz9u7dq3WHmlplkJpJdPaVxWaYHjWwBwBgcVg/xB/MUS/A4LVR7vjqQjFu\n3K/XqX0Fz/k54WReFdpkFBpa2ufQ0twMSX8MQnMbhbm7MwXXJyR+oFANX3crw2lBgHaB2EwiwfwQ\nF+z8XZzYkMZyhlJXf2iq1Dxuw7FblWhoaUOMfx/t+iDR/oDEikh3DNDBSF8ItY874vZCd7jc2xQV\nFeH48eMYMGAAfS0rKwv79+9HVlYWSkpKMGHCBOTm5kIikWD58uXYvn07wsLCMG3aNCQnJ2PKlCmG\nHo4apm5PY+rtEZuvrt+eWBiVh/uHjS14cU8m3kvO4yzToiF8C5uTOsWWnbWF5uEOcrLBpmcHaSyn\niuofVfwoN/z4UhCGOHVXK2stNYeloOOL2nG24KGgD7Cm+IvavCD0MQ4FMf5OvPma5FE7rxC9Cmhx\n/81CdWMLy7Zj+7/rHrdqtc372ZlCbD1foubXTdMz6WUj1Urz1ctGihm+vbW4o2MYytsIl3ubN954\nA//4xz+Urh06dAjz58+HVCqFh4cHvL29cfHiRZSVlaG2tpbW4i9atAgHDx40SP8JBMLTgTBX5wbi\n5oMGNLTIkFaqHo8QAOqb2/Di99d56+DbzhPLeXCMvxOeD+qDBYx4diPc7HC5WL3fXB9EIZosbUlI\nKUKf7pYY4W7PWy7zXse0egoszcXS+agT6NIdz/r2xsEb5ZxlBGkDxeyUCkUPH2M/S/gmBQ8bW/D8\nnutwd7DC9nl+WtWtiL8oVHAb4W6vlW3j0+SL69ChQ3Bzc0NQUJDS9dLSUowcOZJOu7m5oaSkBFKp\nFG5ubvR1V1dXlJSUcNavy4ltXdNfffWVXuvXpb0DBw7Aw8MDK1asMMnxdSSteiL4/tn/golYJ7AB\nH87+ZGZmYvny5QaZT6720tLSAABDhw41SHti119TIz/YVVhYiLi4OIiBUQhfu9LKcPNBPSb59KKv\nPWpqVfPN9WPmAzxu1aD54vkgiyXwDO1nB0uG86q1kzzRcOca3vxDhFLwZYD7I6dLTzwdrXGnil9r\ndSa/mha+yuubdWhF/gctRPu1+hkPrD9ZoFMbmoj2cmTYC7HT1MKfX5t3FTJqoJjdUqNNpq7VUTxx\nxdZ10SPdfFv9/UQ+zuQ/BKD5mZhJJFoJVFUNypo1awszjfPdETpri7ihoQHr1q3D8ePH6Wtihz/S\n6cS2jmmmoKCP+nVpT8z+GOP4OpJW/Zu16efNmy/mCXljSnNtDRpL//jSqtcUgmRHMYptx11p9/B7\ncS2uMjReL+27oVYup1yzxsbliUE7G9povpaG9+PMC+9vr/SZG9nfAZYWZujZTap2qozzPc/oC9sJ\nTTY+mOCpsQxTIPnDXvU5FBPHblK97SdRFKUxJmSLBntEAGjtorFuJAAteAnB2sKsQ0GxVW0sHbsp\n//B5PqgPpHqIO6dv8vLyUFBQgODgYAwcOBDFxcUYNmwY7t+/D1dXVxQVFdFli4uL4ebmBldXV6VI\nHcXFxXB1ZT/UYWhM3Z7G1NsjNl9dvz2xMArhS8GRnEr63+y/wrlf/rEj+mFpeD/eLTdtNsnmBjrj\nwEuBWBImF8IG9rTG5pjB+GFhICQSidqHqCML4PMZPpoLAegm1fy4xAjqrc0L4uPJXnC00Y8CtVd3\nKd4Y3Z8zX5OwYecVgl7dhQX17gjdpOwC94M6dc2jrloXTc9k28UStKnU7WxriXmBcsP9F4Kdee/v\nbaM8T/bWFkpzb24mEW3b3pAEBgbi/v37yM/PR35+Ptzc3JCWlgZnZ2fMnDkT+/btQ3NzM/Lz85Gb\nm4uwsDC4uLjA3t4eFy9eBEVR2LVrF6ePQwKBQNAFoxK+NMH28n9zTH/MC+qDF4L6YG6gM+9WFJuS\nhu97YmtlgRh/J/xppCvee2YgBvW2obdCbSzN8cbo/lj9jAdvn7k+teY6aIz0YSfWEcwkEgT1tcW+\nBerH+sViSB8bzjwhxv5SM/0v8aGuyi5MFNt/X19UtxO6q+GwQ0fIUjmhGzuiLxaH9cM3z/vRQhgX\nr4xQdgFiJpFgyuBeytdU/gAHO3E/GyYZZbUG23bU5N6G+Tfk5+eH559/Hn5+fpg6dSq2bt1K52/d\nuhWLFy+Gj48PvL29jeKkI2AcPptUIX6+hEP8fBmmva5Ap9t8aaMJYJM9xnn1VLK/qmtWPuKuSVuk\nSZ6RmpthdgD7h4v5cUpJSWHVfnn0tEZGWZ2aCwxzMwn+Mc1bq6DTQjQPJ/Oq8ZdoD8F1siHU5ssQ\nmhC+AxQ9NGxL1uZdRU8bf7G7pAKlLuA9WdJsO56abBYVlNQo24kJeSaqdQe62EIikaCfvWYHtP7O\nylvfbHKt6lqdF9gHfxdg8/dlajHeG++hsZwYaHJvc+fOHaX06tWrsXr1arVyw4YNQ2amcFcwTzPE\nfxNBE2SNqNPpwlfsDzcFlTuaXYELhTVq11W/EaqyzEeT2u2kNAWU1gevDO8HW0tzjPd2VMsLEeD0\nlYk2gpohEKKJ66EhoDkXCo/1QgQHNiYPcoSNQ184dee2ARQL1VWlSJtL1AUwoc8wX8PBCjZqVHxr\nOdoI33JVFbbYXLY0tijX7yLw2ZSSYNqiYer2NKbeHrH56vrtiQWvWqioqAjR0dHw9/dHQEAAq9pw\nz549CA4ORlBQECIjI5GRkUHnJScnY8iQIfDx8cGGDRtY21D9hc/GDxn3sSmliDVPVQBgpt4aOwBB\nfdsFnB7WFrCyMIMzwyhfLHGGawF0tzTHy8P70V7eubBhaOi4ttOE9rWhuWMOLoW+IJjdVEQRYDJ5\nkCO2zBqsUx+Gucmfm64Cp7+zLZbPM8xWEZdMb2Gu/uclVFuoWo75TGI5ogScVTHQ52sq0sNBKa1q\nK1inIshRlHr4IqFPRlNEBQKBQHja4BW+pFIpNm3ahBs3buDChQvYsmULbt5U1lR5enrizJkzyMjI\nwPvvv4+lS5cCANra2vDnP/8ZycnJyMrKwt69e9XuFcJ/rt3Hvy+Van0fAEz0UdY2WUvN8c3zftjK\nEAiMxY7q6zm+eGN0f3w1azD2LghgLcOmjWBjG4utkT7QNHXTh/TWqHlSFQIUdDSWJV8em/CyYapu\ncUlP3K5Wc/FQUd8CAOjG4tRXqPKVb/wvhrgIqoNvbQ/urWyvpdqeqvF+RzGOv7KujzHY76hCbL6E\nQ2y+DNNeV4BX+HJxcUFIiPwXt62tLXx9fVFaqiwIRUREwMFB/gENDw+nj2hfunQJ3t7e8PDwgFQq\nxYsvvohDhw5p1TmKopB4mV/w0rTtqEovGynsrNq3wsT6KHR0AfSxtcSUwb3g1ctGqX9MhJqOF+vo\nV1JBzEgAACAASURBVEqB0BcE8+PONu9cAsTsgHbP9Rb6clUB9mfi6WjNKrw4dNNte1TVxhAAbJ+E\nbxrr2UMtT6gnLVU5W/SXtsq8q2q+VG3t2EQxIlARABK3j6AZskbUEXwUrKCgAOnp6QgPD+css337\ndkybNg0AUFJSAnd3dzpP4T1aG3TZrdDW57qRKL4EIbSvmffqWK/PC+yjtL3ZUbozfJqxdo2jvy8y\n3B6wafOceXy1MeFbHgHO7L7TuE6ZDuxpjakqp/uEoqokUqRVHeI+bGwR7JRWDJchfKjWrtqc2D69\nyMajOJi6PY2pt0dsvrp+e2Ih6Od+XV0d5s6di4SEBNjasn/UTp06hR07diA1NRWA8O28/P0bYOUo\n10SYW3eHTT9veoFu+U8yavPu8YZWSE2tw5jRowHINR3Xy2oBuNBpgD/0g9xHU4ig8nzpqKgovYdu\nOH8uFbV5t3UORWFbfhO1eaUw7x+o0/3M9OwAJ9xMu0j3TyKRqJW/euk8HthbqY0nYFg4XV9Jkx1g\n7aVU/4TJ0UrlPR17405VI2rzriLayxG/Q+5/KvfaJaQ09GIN5dG/pzUK6Tq60/n3K6wADIGrvRWy\n0y/S5SUSCUZICvGfvFyt54Pyn6iUbusnX4/nUlOUyq/66ifklNcLqv+XmxVKaTuvEIb2KxRvjumP\nD3Ym8faPL9SJRCXfTOX5NbTIkJKSgton89HNwkyt/rRL51GbVygg9AmwLeEw8lOfhAYb+jYIBALh\naUaj8NXS0oI5c+Zg4cKFnI4GMzIysGTJEiQnJ9NBbVW9RxcVFSnFS1Mw8IV3ONsOGB4Ou7q7dJot\ntMKY0aF0OioqCm13qpH0RLvAFzpgsJMNchCCcZ49WfONMT06Kgp2Oe3Cr7ahJ0aMHIUDD/PwqKlV\np/uZ6cmDemGgoxtv+dlTnlHavlKM52FjC11+4URP/O34Hdb7FeWrs8rx5bli2HmFYOyY/vj9TCEA\nwCc4DFFD2+23FPcrfLEp7h/bnI/Tdx7CzisEzr27AQD+NNIV79eot2eX3V2tPk1phaaLFkqeRGpQ\nLV/Tewjs7NvU7mdL365o4M2fNKgXxn30R9S3tOGFPddZ6+MNdSLhz58+pBeiQvyxvp8/fsutwqwA\nJ3xzRbn+YeERsCttt6ucOSkap/KqWetbOvtFXHHLfpIiejBd4XJp05ntKWx5xNhWMsbxiUln2Xx1\n9pyKuUaEtNcV4BW+KIpCXFwc/Pz8sGrVKtYyhYWFmD17Nnbv3g1v73aj5eHDhyM3NxcFBQXo168f\n9u/fr9EHjyqatj6C+qpr4YRulqyZ6In/3anG5EG6bTWpYogF0NHDAU4Ct/OE+JQS0hUuH6jMcQxy\nssHGGT5445dcznqYn2pmlZpswhXPxJXFJQKXXZ2+aGxpY7UP40L1ZCHbM7G0MBNVjBnQ0xp3q+Vb\npVZPDguM8+yp9ANFGeUHzHbAgGD6EFsegibIGlGH9wuUmpqK3bt3IygoCKGhcg3TunXrUFgo1zws\nW7YMa9euRXV1NR1VXCqV4tKlS7CwsMDmzZsxefJktLW1IS4uDr6+vlp1Lq+qkTf/02ksJ9QEyieO\nNlJO56mmyJaYwXCwtqC1Xh3FUsWNAtu0cwmLEqUyciGCj/4MNx3MOoUKHlMH98b3V++r9E3gzYLQ\n3JN6Ld1/CD1tKMTLPxtsdykEL0D7+ZkyuBcGO9kohQhjomuQd4Iypm5PY+rtEZuvrt+eWPAKX1FR\nUZBpCF6cmJiIxMRE1rypU6di6tSpOncu50EDbz7bx11bg3uxMLYFUPdYWcjy6S0sFAwAvDRzIg7e\nKFe77mpvRftlUzXc11WYEXJbT8ZJRCF24IoiimfibGeJ6UN64XB2JeYFyY39xfSkoFoVm8ZW2+ZU\nNV9cL21dtaGaXHkI+TtiVjHBm0s7Juevv97hzScQCISnCaPeJ+CLg7cghD1QcBc6vKhXVL2dCyVh\n5iD0tWPfnrRgaFnE8rYvkUg0SiZMQaScEayay5cXW9dWRLpj34IAegtN1TcXH+4O/J7cVbvBprXq\nhOAKvIS68kdX0PR4rSzMlLaVu1uaw4/jhClBPIzBZ5MqxM+XcIifL8O01xUwauGrd3fu8CgvBLML\nX52FsS0AXT0FuNpb4caTU4yqMI3n+WIuaoL5YZdAO61Zq6pKiK3+J/9nPhOJRKIcboejGlXfXOYS\nYPs8PwSz2BdyIaOAZpU4i/dqO7btJuZLe/IgR3g6dutQHRLIt4NfDHbGi8HO8HTsBgszCT6b7iNO\nJwldBuLDiaAJskbUMWrhi+lHiomZBE9cRKjTlfx2dYRBGrYRddl+XTyiH+x5YjEyBS5VP1TabH+p\n1uPVqxtGuLVrYtRCRjGFNSHtCCjCJcK9GuGG10a1n+JUtMcn8rHlfX62UCn91YVizZ0yEK4O7KGu\nHJW2d4VsO0oQO6IfYkf0o+eJJaISQURM3Z7G1NsjNl9dvz2xMOpXJZeRMl+w5s4Svgy9AKTmEvj0\natdeDHZSFsZO5lWx3rcs3JWzThd7+XbjkNAw9jb5hC/+7irRTWqOVyNc8aeRruhuaQ4ziQQfT+EO\n72PGUTuXQKQQPPmeCde9PbtJ8axfuwd+RcvahDJy6i5VcrkAAHmV/IdHNMH30pbqaHSvSiBDu6ep\nRq7ZsOX4wUQgEAiEdoxa+MopZze4F8veqKujdPJP5Wu48/cy1nvmBHKf8FQILVxaM6bA1dHvfYx/\nH8GnTc04VqkVh5pFSNeYAtP/jenPXe7J/717cWsar9+vV0qXP4ntaCjeGjNAq/Jc81PV0KK5kAb6\nCHRnQtANY7DfUYXYfAmH2HwZpr2ugGGdHYkEn+zVWacdDe3oTQJluy4ri46PW1FDTvolAOoaMiV/\nW6pbgx1unRvVZ/r22AE4nluFGH8n9vJPigt9Jg4CfH714In96GpvpeSmQR/0rMyGdEAgFrDEpbSx\nFOc3VH1zu52ars+TyxyAYLoQWx6CJsgaUadLCl98mq+nRSdGQTku4vwQF2Qm53WoTsW0ck2vu4MV\nRva3h60ly7IRYeIVrixG9ndQut5TRfCZ4OOICT6O6AhMQZItvqRaeR6jLyGHADpKLxsptr4YwJEr\nzqpnagM1u6IgdAambk9j6u0Rm6+u355YGKXw5elorRaUmIl3b56TWk+JzRegvGesyQBfG4aEhuHU\nBfUg6LZWFpgbqL9TpgkzByG/uhFBLsonC220tCNSOJLleya3GFvafEbiQrZXr3MEMhcTj8DhnHl6\njsFNIBAIBJHh3a8oKipCdHQ0/P39ERAQwLpnm52djYiICFhbW+Pzzz9XyktISEBgYCACAgKQkJAg\nuFMj3B148xeP4DYaf1q+QxIoa2zENIPjqovvI28jwnaTvbUFgvvadTiMkqr3fTaYnv65DPqB9jnm\n0201tPA7IhaDVp4mtJ0trvLK28rq+cwDHsTssnMwBvsdVYjNl3CIzZdh2usK8Gq+pFIpNm3ahJCQ\nENTV1WHYsGGYOHGiUpigXr164csvv8TBgweV7r1+/ToSExNx+fJlSKVSTJkyBTNmzICXl5fGTmn6\nJe/K4/Sysz4Khrb5oqA8T3zDXj6SW1hl4v4kjE82h80XXxsvBjvjVkUDymoeG9zgXBVFyB2+Z6JJ\n0DA2zpw9i9XPeLDmidV/5tYqW5UjBzgg98mpzeeDjMvPHqHzIPY8BE2QNaIOr4rAxcUFISHyPWpb\nW1v4+vqitLRUqYyTkxOGDx8OqVTZIWp2djbCw8NhbW0Nc3NzjB07FgcOHBDUqfsdcEgZ0tcO7j2s\nMMO3t851dBWYGhs+bdEsAacKP5/hQ8dQZNa0fW67oK3qXoKJvbUFPpvug/HeHbPFEgVBxx0ZxXkP\ncBgHMh6jM7EOmfAdqFBlXtDTExfVmDB1expTb4/YfHX99sRCsM1XQUEB0tPTER4eLqh8QEAA3nvv\nPVRVVcHa2hqHDx9GWJi6/6j8/Rtg5Sg/wWVu3R02/bzROnAcgHYVrWLBtqts5UG+FepGxeQr0olz\nIiGRSDjz9ZGOiooySHu1ebmw8wqBBMC97CuoLW9Qmx9N8/VutB/Wn7qrVD7QxZbO9x0ajhPnilGb\ndxV3r9cD6A4AuJNxGSkNjrz9y8upBNBfL+OvzbuKXPMiIHQmZz4A9AocAQVM7RezvHsPa7q8BN6c\n9TVbmAEI5p1fRVpWlIn65jaNz0OXtKNPKOf82Hqy949rfhDWjzX/QU4aauuaYecVAjOJen7utUuo\nzauCnVcILM3NOPujWC/MLZbaO9fwuOqePDH0bRAIBMLTjCDhq66uDnPnzkVCQgJsbYWFWRkyZAje\neecdTJo0Cd27d0doaCjMWBw2fZ7wJTafY/f+rforQTWtKvE+DWm7bPmHrUc3C0gGhcLOvt3HlDbz\n1U1qjl1XutHbSMz8pKxy+v6oqFDE9yzHsdxKvDltulLUAbb+3bYuxeWr9/UyfjuvEPiE9OUtf62s\nDuH97TXWN3mQIzbyzM97z3hgHYCPJsu3yUf2d8C3XiFwsLag7cVU5/ftP0zHZ2faPdtreh7apCme\n8Vwrq2W9n23+AGBgz26s+b0HhaLpkTxwurmZRC3fOygMF9rucdZPp7PT1fqj3DcjC3TZhTC0eYOQ\n9hS2PGJsLRnj+MSks2y+OntOxVwjQtrrCmgUvlpaWjBnzhwsXLgQMTExWlUeGxuL2NhYAMDq1avR\nv7+6M0s255XGstWjDYZaABtn+ODH6w8QP8odOy+XIvOeXPjqJtXO19PI/g74MfMBa15VbjqAdh9a\nz/k74TkOn1qGhm9t/G3CQFwsrEHUQHl8Rr5nwtxWY9tiG+vZE6MH9qBdLnj16oY98/3Rw9oCbTIK\nH58swMWiGqV7hrnJhT4bqZnoRvjlOekAAlnzhP697Jznh9uVDRjuxh5Um7mz2duGO64qgcCE2PMQ\nNEHWiDq8whdFUYiLi4Ofnx9WrVrFWxFb+JUHDx6gT58+KCwsxE8//YSLF9UDNpNj8toR4GKLgCeu\nGDx7dQNy5dfNJBIkzvHF4h9vCq7LnMOux7uXDVYHeOgUfLmjJxU7gp2VhU7+v7h6rOrryqm73Hu7\n1JzdD5bNEwFYH26/pgzmG5ewOXd1sOI9rDLIyQYlNXLNl8L+jwnRV3U+pm5PY+rtEZuvrt+eWPAK\nX6mpqdi9ezeCgoIQGiq3G1q3bh0KC+VbK8uWLcO9e/cwYsQI1NTUwMzMDAkJCcjKyoKtrS3mzp2L\nyspKSKVSbN26Ffb29mpt9Oqu/gu7K77kO2MBPOvbG+V1LRjlIXfNwWcQrw0dGYu+Ra8BPdmDQrMh\ndBzaag0B9ZBHYe729Nib+PxC6Mjbf5jBmfewUZzTpbHD5bZg0V49WQOs88W3JBAIBIJweIWvqKgo\nyGT8HxIXFxcUFRWx5p05c0ZjB5y6W2LdFC+sFuidnWyHtCM1N8MyhhuJ+hb2QOSGRF+Kr+1zfXHz\nQT1GDeD3AacN74wbgLvVTfDiidvIheowJeg8rZ9YW5zOdpZ4N9pDlLoI+sEY7HdUITZfwiE2X8Tm\nS4FReLgf7mavZMjM9/v63wzXB8ZEV1wAXPPckbHoS/xw72FN+yETiqZxdMQthlpsS4n+xu7v3N0o\n1hfRexHYIPY8BE2QNaKOOBF5RYDNxoSN7lqGmnmaEBIKR990ps2XIVH9w5FAohet3/NBffDhRE/e\nMk/JlAsiNjYWzs7OCAxsP5zw1ltvwdfXF8HBwZg9ezYePXpE561fvx4+Pj4YMmQIjh07Rl+/cuUK\nAgMD4ePjg5UrVxp0DHyYuj2NqbdHbL66fntiYTTC1xuj3dsTXfAntnEsAO2+whTHRBvHWDqOXseh\nMtUSiX4Cvg/qbQMHawvesRhK9orykJ8i9evTXVD5BSHOWBXlrrmgiLzyyitITk5WujZp0iTcuHED\n165dw6BBg7B+/XoAQFZWFvbv34+srCwkJyfj1Vdfpe3ali9fju3btyM3Nxe5ublqdRII/8/encdF\nXe2PH3+B4C7uQgJGCQqjqCDuLe6KJXXdbdGbuNzSzJafeu3e782+N8E2r2V2vZbmV29Iq5oLGaRW\neNUUMRJMNJBFocgNBQWG+f3BZXJkmxk+M5+ZD+/n4+Hj4WfmM5/3Ocxh5nDO+3OOEPXhMJ0vr1YV\nd2E1cau5SPIHfu2q++4P9qr5i9IW+XMD/7vGlp8FifHO6PaO1tlb1kuzxOA7W7Pzid41n+BAjT6g\nQ3M+nN6DNx4MqPW85+7tQkD7ZjzUoyPjAu2708S9995L27ZtTR4bNWqUcY3BAQMGkJNTsa7g9u3b\nmT59Ou7u7vj5+eHv78/hw4e5cOEChYWFxkWhZ8yYUWX7NLU4wj59t5O9Hc0nezvaJ54zcIicL6i4\nU2/HH3vjCkTvz1S7OBZzhJwc31qWEajO3AHelBtgvM70C7I+denavjmbp/agbXP1m5Yt35Pb+0T5\n10pqXTbl9jHGUQHtGN2tHYEdW9S6EXjl1kHm1qVjC3eb7q3Z4b/LbdRmbPf2jO3e3mZlqI8NGzYw\nffp0AM6fP8/AgQONz/n4+JCbm4u7uzs+Pj7Gx729vcnNzbV7WZ2F5POIukgbqUr9b8hbNK1l1EvU\nzb2WL/HqtGnmztJhfoqXw7NV3V/Qzq66jpYl+W5/GuhNqyZ1//pZOvA1oWcn1h2WjkJ1XnnlFRo3\nbswjjzyi6HXnz59vXEDaw8OD4OBgm20xVvmYPbZMk3jKbIkGNed6KbUFGQTUWp5b66pk/RpCvJSU\nFK5erVhQOysri8jISJTgYlBx8Z6EhARCQ0OrPL48/mcSM69UedwF+HJ2iB1K5rxGv3fc5DjYq2Wd\n00TCcq8dOMdX6RdNHts7O6TKz786EboOLBhsmgtV0+v+NvIuhvw316omX6Vf5LUD5wD4y3A/urRt\nSuumbrRt5hjLsly7WcaEzSnG4+hQAyNGjLBZvMzMTMaPH09Kyu8xP/jgA9avX09CQgJNm1ZMiUdH\nRwOwdOlSAMaOHcvy5cu58847GTZsGGlpFQsWx8TEcODAAf75z39WiVXTZ5gQCWcusnL/uSqPH11c\n0fbDXk1QLNaq8QH08DRv6z9RP0lJSYp8fslQkxBWsCYV6+9jujKoS2tmhN5R63mNLbxt9dazDYBf\n22YO0/ECaGnGCJ8txcXF8dprr7F9+3ZjxwsgIiKCrVu3UlJSQkZGBunp6fTv3x8vLy88PDw4fPgw\nBoOBzZs3W7y1mq04Qv7O7STny3yS82WfeM6g1k/F7OxsZsyYwS+//IKLiwtz586tMnd76tQpnnji\nCY4fP84rr7zC888/b3wuKiqKLVu24OrqSnBwMBs3bqRJk7rzkmoai3PkW+odIedLKVqpi01zvmpo\ni0GdmpP2S1G1z/X39aC/b9VdHsB0P8hbL12Z2F9bXcxdpqUhmD59OgcOHKCgoABfX1+WL19OVFQU\nJSUljBo1CoBBgwaxdu1adDodU6ZMQafT4ebmxtq1a41Tx2vXruWPf/wjxcXFjBs3jrFjx6pZLYem\n9Xye/MKbJJ6rOhNTl/+cu2yD0jgnrbcRa9Ta+XJ3d2fVqlX06dOHa9eu0bdvX0aNGkVQ0O8LnbZv\n35633367yt1AmZmZrF+/nrS0NJo0acLUqVPZunUrM2fOtLiQod6tSMotJMyn+i8uIeytZePqf3Vq\n6njVpemtnS8XFypT9M35e6Nbx99X6HfCVVoUFRMTU+WxWbNm1Xj+smXLWLZsWZXH+/btazJt6Si0\nvoaSI8Yr0Rv45yFl8ihttc5XIxcXrhSXVftccN+BNT7XqmmjWpfIsYYjvoeOqNbOl5eXF15eXgC0\nbNmSoKAgzp8/b9L56tixIx07dmTXrl0mr/Xw8MDd3Z2ioiIaNWpEUVER3t7eWGPZMD/2/3yJYV3b\n1nmuWpy1AVRHK3WxZT2m9u7Epz/+otj1XG7pZpl8Fv73/2bXpaH3voRogP6692eLb1jr2r4Zy4bd\nSWM3WbhcDWYnY2RmZnL8+HEGDBhg1vnt2rXj+eefp0uXLjRr1owxY8YwcuTIKudVd6cQVGzwWzk/\n7tE0hAhdR7vdOeHMx4Vn003uhLlwqRk8WPudMHJs+XGLxo2q3HlU3c//9udrup7LLec3Dww1vj7l\n6C8M7DLGrPIVnk3mR488hnYNV/3nc+sxwPmvPuHmxbyKg9DFCOvYOyXAnHiyt6P5bJXzdeVGGTVN\njBaeTa52xK11U9vkYlb3M5W9Hasy627Ha9euMXToUP7yl7/UmHi6fPlyWrZsacz5Onv2LOPHj+fb\nb7+ldevWTJ48mUmTJvHoo48aX1PTnUIvffUzB2+ZY9/rBHc4OkoDuF6i5w//94Px2Jq7HR2lLvVl\ny3qUlRsYt8H0g7Suux1ra8dPfJRK7tWbQMUWWtdLKjZJ//uYu+nv27rOulTGXTbMj6EOOEJ868/F\n1nc72pO973bUeufEEeNlX75B5CdpisQrPJvMT+sqviOVvNuxrpjVdb66dWjOmw/6Kz7y5YjvoZLs\ndrdjaWkpEydO5LHHHrPojp+jR48yePBg2rdvj5ubGxMmTODgwYMWF3D9xECLX9OQ3b73ZYm+XKWS\naJvS9348EXYHLsCc/p1vW0PMskiucv+ypmk9n0br8dTY29HeMbX+Hiql1o9qg8FAZGQkOp2ORYsW\n1Xqh2wfQAgMDOXToEMXFxRgMBuLj49HpdGYVqtEt3z53tm1m1mvU5qgNoOi/IyiWcNS6WErteni2\nNH+x2fvubstnM3oxuZenyeOVvwl11WXugM6EerdiUJfWlhZTCCGEndXa+UpMTGTLli3s27ePkJAQ\nQkJC2LNnD+vWrWPdunUA5OXl4evry6pVq/j73/9Oly5duHbtGr1792bGjBmEhYXRq1cvAObOnWtW\noZ4e7EPX9s3svimvFjWWXQNsorathCpZuOGAcdSy8ObvHWZzb0SaFOxJdLi/xbsc2ItHE0nqVYIj\nrNl0O1nny3xqrPNl75iyzpd5as24u+eeeygvr33aysvLi+zs7GqfW7x4MYsXW55c26aZO+/+wbmm\nGx01T8qa/QsctS6Wsu06Xy58PqOXSX7d7ZS4hbty2tjZ35M1D3dn64l8dp/6Te2iCIXJGk6iLtJG\nqnLMP5OFgmTtAVtp0bhRrSNgOVdu1jvGjVJt5Ox5tWrChJ6d1C6G09N6Po3W40nOl/PHU4p0vhTi\nqA3AmpEvR62LpexRD1vvjFp5ea28J0IIIaTzpXky7mVf700MqvukhkoaY705Yk6U5HyZT3K+7BPP\nGUjnSyGO2gCs+b5z1LpYyh71uP3n26Xt7/ssDr1bufW2tPKeCO1ZuHChpnN6LN3oXlSl9TZiDdss\ncSsch4w2qMazlflLTdSkXEPvX6umcsdjfWk9n8bW8XafKuBI9q1rwd9B/Fdna31NUYlyeZeS8+X8\n8ZQinS+FOGoDKLei9+WodbGU2vUoV6Dn1Pq/HRa166KEts3c1S6CaOB+/q2Yg+euql0MIWTaUfM0\nNHLibMxZC6wutk7oF87FEXOinDnny975UJLzZZ94zkA6Xwpx1Aag82xh8WsctS6Wsmc9WlWziKiL\nAut8Vfa9tPKeCO2RfB5RF2kjVdXa+crOzmbYsGH06NGDnj17VttzPXXqFIMGDaJp06a88cYbxsd/\n+ukn46r4ISEhtG7d2mY9X2Fq2XA/WjRuxPigDvxpoI/axWmwrt4ss+p144M6KFwSoRVaz6fR+rpb\nkvPl/PGUUmvOl7u7O6tWraJPnz5cu3aNvn37MmrUKIKCfr+dvn379rz99tts27bN5LXdu3fn+PHj\nAJSXl+Pt7c0f/vAHG1TBMThSAxh6d9t63WnnSHWpD7Xr0bFFY3p6tuDH/OsWvc4kUf+/Q19q10UI\nIYRyah358vLyok+fil5zy5YtCQoK4vz58ybndOzYkbCwMNzda06mjY+Pp2vXrvj6yl6NomGx5o7H\nVo1/n8IM6NhcyeIIJyc5X8qSnC/lSc6Xecy+2zEzM5Pjx48zYMAAi4Ns3bqVRx55pNrn5s+fT5cu\nXQDw8PAgODjY+Fd+5Q/VGY5vbQCOUJ76HN9eJ7XLY+3xu+++a/P21Kf8V5Jd/ZjSy/OWn19Fnl16\n8hEaN3IFvC26vkvHipHlwrPJpCVdd/r2BZCYmEhWVhYZp3+DUMv3exWOS3J5RF2kjVTlYjDUfT/V\ntWvXGDp0KH/5y194+OGHqz1n+fLltGzZkueff97k8ZKSEry9vUlNTaVjx44mzyUkJBAaGlqP4jsO\nZ9/4+FZaqYs96lFuMHD+6k28PZoYE+xHv1cx3T6z7x1M7e3JrrQCwnw88G7dxKxrfnn6N974JguA\nvbNDAO28J6PfO050qIERI0aoXRRFaOkzrCFYk5jNjrQCVctwdHFF2w97NUHVcnTr0Jw3H/SnsZus\nv2eJpKQkRT6/6hz5Ki0tZeLEiTz22GM1drxqs2fPHvr27Vul46U1WvhirKSVutijHq4uLvi0blrj\n826uLjzUw7K2X909klp5T4QQQtSR82UwGIiMjESn07Fo0aJaL1TTAFpMTAzTp0+3voRCOClrF5pQ\nYokKR/W3kXepXQSnJjlfypKcL+VJzpd5ah35SkxMZMuWLfTq1YuQkIrpjxUrVpCVVTElMm/ePPLy\n8ujXrx9Xr17F1dWV1atXk5qaSsuWLbl+/Trx8fGsX7/e9jVRmVamhUA7dXHWelS3OKuz1uV2Q/za\nkHRR7VIIJUk+j6iLtJGqau183XPPPZSX176vlZeXF9nZ2dU+16JFCwoK1J1fF0It1g5gdetQcYej\ndse/hLW0voaSrPPl/DG13maUIns7KsRZG0B1tFIXtethbefJt01T/jkhkPbNf1++Re26CCGEUI5s\nLySEA7q7XTNaN5W/jYQpyflSluR8KU9yvswjnS+FOGsDqI5W6qJ6PRRMnFe9LkLUQPbtE3WRCAxv\ntQAAIABJREFUNlKVdL6EEMJJaD2fRnK+nD+m1tuMUqTzpRBnbQDV0Upd1K5HGwWnDdWui7OYNWsW\nnp6eBAcHGx+7ePEio0aNolu3bowePZrLly8bn4uKiiIgIIDAwED27t1rfPzYsWMEBwcTEBDAM888\nY9c6CCG0TzpfQijs72Pu5sGgDowMaKd2URqcJ554gri4OJPHoqOjGTVqFKdPn2bEiBFER0cDkJqa\nSmxsLKmpqcTFxfHUU08Z1yt88sknef/990lPTyc9Pb3KNdUiOV/Kkpwv5UnOl3mk86UQZ20A1dFK\nXdSqR3/f1iwc4otbdQt2WUkr74mt3XvvvbRt29bksR07djBz5kwAZs6cybZt2wDYvn0706dPx93d\nHT8/P/z9/Tl8+DAXLlygsLCQ/v37AzBjxgzja0RVks8j6iJtpCrpfCkkJSVF7SIoRit10Uo9QFt1\nsbf8/Hw8PT0B8PT0JD8/H4Dz58/j4+NjPM/Hx4fc3Nwqj3t7e5Obm2vfQtdA6/k0kvPl/DG13maU\nUmtSSnZ2NjNmzOCXX37BxcWFuXPnVum9njp1iieeeILjx4/zyiuvmGysffnyZWbPns3JkydxcXFh\nw4YNDBw40DY1UdnVq1fVLoJitFIXrdQDtFUXNbm4uCi+fdP8+fPp0qULAB4eHgQHBxu/ECpHLOXY\nMY4zUr6n8NwVY4ekckrO3seV1IpfeXwwMRG3Rq4O8/444nFKSorx8zcrK4vIyEiU4GKoaVNGIC8v\nj7y8PPr06cO1a9fo27cv27ZtIygoyHjOr7/+yrlz59i2bRtt27Y16XzNnDmT+++/n1mzZlFWVsb1\n69dp3bq18fmEhARCQ0MVqYjaVq5cyZIlS9QuhiK0Uhet1AO0VZekpCRGjBhhs+tnZmYyfvx442hh\nYGAg+/fvx8vLiwsXLjBs2DBOnTplzP1aunQpAGPHjmX58uXceeedDBs2jLS0NKBif9oDBw7wz3/+\ns0ose3+G2XubKXPiVebyKDGtZOv6rUnMZkfa77uuFJ5NtuvIUOHZZH5aV/EdGfZqgt1iVlfHbh2a\n8+aD/jR2a6RovOreQyXbiDnxbEmpz69apx29vLzo06fiTWvZsiVBQUGcP3/e5JyOHTsSFhaGu7u7\nyeNXrlzh22+/ZdasWQC4ubmZdLy0pnK/Sy3QSl20Ug/QVl3sLSIigk2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7WIQchukY0guq8JyXneqGBuSLUw9x/mElvnzeF7KPekntnCok97z4sFKp89Xd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DBmHy5MmIiIjQvEUSKCtsZ2slua+psfjHxawn2NRKQSBj+mTM8fv4/HKO+LE7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z/3hw84Gu8Fmu9dngPEIWDH5IZXI8aZTB1cWRV3nB8lSJYIjTlDxVVU+XZbl8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\nwrlz5xAREYGkpCR88803AIAmTZrg/v376Ny5MxiGgZ2dHdtjV/N8NY+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xiG9jwY3BMAxK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HWEwPN7w9NhAA8z2N7NYRH00Ooa3beq4U312mJ3wdHtAJHZzsMTbEAxHeHQW3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B1DiC1vzYUbakHS7IER9UAsuRkk+T8JlzPqQkiz1wSWXOnKF/u9ZUmiGLkKls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+ } + ], + "prompt_number": 19 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "mcplot?" + ], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 20 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [], + "language": "python", + "metadata": {}, + "outputs": [] + } + ], + "metadata": {} + } + ] } \ No newline at end of file diff --git a/sandbox/github_events.py b/sandbox/github_events.py index 85dd9a4a..03b405e1 100644 --- a/sandbox/github_events.py +++ b/sandbox/github_events.py @@ -1,27 +1,27 @@ -#github_events.py - -try: - from json import loads - - import numpy as np - from requests import get - -except ImportError as e: - raise e - - -URL = "https://api.github.com/events" - -#github allows up to 10 pages of 30 events, but we will only keep the unique ones. -ids = np.empty(300, dtype=int) - -k = 0 -for page in range(10,0, -1): - - r = get( URL, params = {"page":page} ) - data = loads(r.text) - for event in data: - ids[k] = ( event["actor"]["id"] ) - k+=1 - +#github_events.py + +try: + from json import loads + + import numpy as np + from requests import get + +except ImportError as e: + raise e + + +URL = "https://api.github.com/events" + +#github allows up to 10 pages of 30 events, but we will only keep the unique ones. +ids = np.empty(300, dtype=int) + +k = 0 +for page in range(10,0, -1): + + r = get( URL, params = {"page":page} ) + data = loads(r.text) + for event in data: + ids[k] = ( event["actor"]["id"] ) + k+=1 + ids = np.unique( ids.astype(int) ) \ No newline at end of file diff --git a/styles/bmh_matplotlibrc.json b/styles/bmh_matplotlibrc.json index 773b86fa..4e040896 100644 --- a/styles/bmh_matplotlibrc.json +++ b/styles/bmh_matplotlibrc.json @@ -1,23 +1,23 @@ -{ - "lines.linewidth": 2.0, - "examples.download": true, - "axes.edgecolor": "#bcbcbc", - "patch.linewidth": 0.5, - "legend.fancybox": true, - "axes.color_cycle": [ - "#348ABD", - "#A60628", - "#7A68A6", - "#467821", - "#CF4457", - "#188487", - "#E24A33" - ], - "axes.facecolor": "#eeeeee", - "axes.labelsize": "large", - "axes.grid": true, - "patch.edgecolor": "#eeeeee", - "axes.titlesize": "x-large", - "svg.embed_char_paths": "path", - "examples.directory": "" -} +{ + "lines.linewidth": 2.0, + "examples.download": true, + "axes.edgecolor": "#bcbcbc", + "patch.linewidth": 0.5, + "legend.fancybox": true, + "axes.color_cycle": [ + "#348ABD", + "#A60628", + "#7A68A6", + "#467821", + "#CF4457", + "#188487", + "#E24A33" + ], + "axes.facecolor": "#eeeeee", + "axes.labelsize": "large", + "axes.grid": true, + "patch.edgecolor": "#eeeeee", + "axes.titlesize": "x-large", + "svg.embed_char_paths": "path", + "examples.directory": "" +} diff --git a/styles/custom.css b/styles/custom.css index ac5a409f..2adac375 100644 --- a/styles/custom.css +++ b/styles/custom.css @@ -1,76 +1,76 @@ - - + + diff --git a/styles/matplotlibrc b/styles/matplotlibrc index 0152865a..abcae8d4 100644 --- a/styles/matplotlibrc +++ b/styles/matplotlibrc @@ -1,438 +1,438 @@ -### MATPLOTLIBRC FORMAT - -# This is a sample matplotlib configuration file - you can find a copy -# of it on your system in -# site-packages/matplotlib/mpl-data/matplotlibrc. If you edit it -# there, please note that it will be overwritten in your next install. -# If you want to keep a permanent local copy that will not be -# overwritten, place it in HOME/.matplotlib/matplotlibrc (unix/linux -# like systems) and C:\Documents and Settings\yourname\.matplotlib -# (win32 systems). -# -# This file is best viewed in a editor which supports python mode -# syntax highlighting. Blank lines, or lines starting with a comment -# symbol, are ignored, as are trailing comments. Other lines must -# have the format -# key : val # optional comment -# -# Colors: for the color values below, you can either use - a -# matplotlib color string, such as r, k, or b - an rgb tuple, such as -# (1.0, 0.5, 0.0) - a hex string, such as ff00ff or #ff00ff - a scalar -# grayscale intensity such as 0.75 - a legal html color name, eg red, -# blue, darkslategray - -#### CONFIGURATION BEGINS HERE - -# the default backend; one of GTK GTKAgg GTKCairo GTK3Agg GTK3Cairo -# CocoaAgg FltkAgg MacOSX QtAgg Qt4Agg TkAgg WX WXAgg Agg Cairo GDK PS -# PDF SVG Template -# You can also deploy your own backend outside of matplotlib by -# referring to the module name (which must be in the PYTHONPATH) as -# 'module://my_backend' -backend : TkAgg - -# If you are using the Qt4Agg backend, you can choose here -# to use the PyQt4 bindings or the newer PySide bindings to -# the underlying Qt4 toolkit. -#backend.qt4 : PyQt4 # PyQt4 | PySide - -# Note that this can be overridden by the environment variable -# QT_API used by Enthought Tool Suite (ETS); valid values are -# "pyqt" and "pyside". The "pyqt" setting has the side effect of -# forcing the use of Version 2 API for QString and QVariant. - -# if you are running pyplot inside a GUI and your backend choice -# conflicts, we will automatically try to find a compatible one for -# you if backend_fallback is True -#backend_fallback: True - -#interactive : False -#toolbar : toolbar2 # None | toolbar2 ("classic" is deprecated) -#timezone : UTC # a pytz timezone string, eg US/Central or Europe/Paris - -# Where your matplotlib data lives if you installed to a non-default -# location. This is where the matplotlib fonts, bitmaps, etc reside -#datapath : /home/jdhunter/mpldata - - -### LINES -# See http://matplotlib.org/api/artist_api.html#module-matplotlib.lines for more -# information on line properties. -lines.linewidth : 2.0 # line width in points -#lines.linestyle : - # solid line -#lines.color : blue # has no affect on plot(); see axes.color_cycle -#lines.marker : None # the default marker -#lines.markeredgewidth : 0.5 # the line width around the marker symbol -#lines.markersize : 6 # markersize, in points -#lines.dash_joinstyle : miter # miter|round|bevel -#lines.dash_capstyle : butt # butt|round|projecting -#lines.solid_joinstyle : miter # miter|round|bevel -#lines.solid_capstyle : projecting # butt|round|projecting -#lines.antialiased : True # render lines in antialised (no jaggies) - -### PATCHES -# Patches are graphical objects that fill 2D space, like polygons or -# circles. See -# http://matplotlib.org/api/artist_api.html#module-matplotlib.patches -# information on patch properties -patch.linewidth : 0.5 # edge width in points -patch.facecolor : blue -patch.edgecolor : eeeeee -patch.antialiased : True - -### FONT -# -# font properties used by text.Text. See -# http://matplotlib.org/api/font_manager_api.html for more -# information on font properties. The 6 font properties used for font -# matching are given below with their default values. -# -# The font.family property has five values: 'serif' (e.g. Times), -# 'sans-serif' (e.g. Helvetica), 'cursive' (e.g. Zapf-Chancery), -# 'fantasy' (e.g. Western), and 'monospace' (e.g. Courier). Each of -# these font families has a default list of font names in decreasing -# order of priority associated with them. -# -# The font.style property has three values: normal (or roman), italic -# or oblique. The oblique style will be used for italic, if it is not -# present. -# -# The font.variant property has two values: normal or small-caps. For -# TrueType fonts, which are scalable fonts, small-caps is equivalent -# to using a font size of 'smaller', or about 83% of the current font -# size. -# -# The font.weight property has effectively 13 values: normal, bold, -# bolder, lighter, 100, 200, 300, ..., 900. Normal is the same as -# 400, and bold is 700. bolder and lighter are relative values with -# respect to the current weight. -# -# The font.stretch property has 11 values: ultra-condensed, -# extra-condensed, condensed, semi-condensed, normal, semi-expanded, -# expanded, extra-expanded, ultra-expanded, wider, and narrower. This -# property is not currently implemented. -# -# The font.size property is the default font size for text, given in pts. -# 12pt is the standard value. -# -#font.family : monospace -#font.style : normal -#font.variant : normal -#font.weight : medium -#font.stretch : normal -# note that font.size controls default text sizes. To configure -# special text sizes tick labels, axes, labels, title, etc, see the rc -# settings for axes and ticks. Special text sizes can be defined -# relative to font.size, using the following values: xx-small, x-small, -# small, medium, large, x-large, xx-large, larger, or smaller -#font.size : 12.0 -#font.serif : Bitstream Vera Serif, New Century Schoolbook, Century Schoolbook L, Utopia, ITC Bookman, Bookman, Nimbus Roman No9 L, Times New Roman, Times, Palatino, Charter, serif -#font.sans-serif : Bitstream Vera Sans, Lucida Grande, Verdana, Geneva, Lucid, Arial, Helvetica, Avant Garde, sans-serif -#font.cursive : Apple Chancery, Textile, Zapf Chancery, Sand, cursive -#font.fantasy : Comic Sans MS, Chicago, Charcoal, Impact, Western, fantasy -#font.monospace : Andale Mono, Nimbus Mono L, Courier New, Courier, Fixed, Terminal, monospace - - -### TEXT -# text properties used by text.Text. See -# http://matplotlib.org/api/artist_api.html#module-matplotlib.text for more -# information on text properties - -#text.color : black - -### LaTeX customizations. See http://www.scipy.org/Wiki/Cookbook/Matplotlib/UsingTex -#text.usetex : False # use latex for all text handling. The following fonts - # are supported through the usual rc parameter settings: - # new century schoolbook, bookman, times, palatino, - # zapf chancery, charter, serif, sans-serif, helvetica, - # avant garde, courier, monospace, computer modern roman, - # computer modern sans serif, computer modern typewriter - # If another font is desired which can loaded using the - # LaTeX \usepackage command, please inquire at the - # matplotlib mailing list -#text.latex.unicode : False # use "ucs" and "inputenc" LaTeX packages for handling - # unicode strings. -#text.latex.preamble : # IMPROPER USE OF THIS FEATURE WILL LEAD TO LATEX FAILURES - # AND IS THEREFORE UNSUPPORTED. PLEASE DO NOT ASK FOR HELP - # IF THIS FEATURE DOES NOT DO WHAT YOU EXPECT IT TO. - # preamble is a comma separated list of LaTeX statements - # that are included in the LaTeX document preamble. - # An example: - # text.latex.preamble : \usepackage{bm},\usepackage{euler} - # The following packages are always loaded with usetex, so - # beware of package collisions: color, geometry, graphicx, - # type1cm, textcomp. Adobe Postscript (PSSNFS) font packages - # may also be loaded, depending on your font settings - -#text.dvipnghack : None # some versions of dvipng don't handle alpha - # channel properly. Use True to correct - # and flush ~/.matplotlib/tex.cache - # before testing and False to force - # correction off. None will try and - # guess based on your dvipng version - -#text.hinting : 'auto' # May be one of the following: - # 'none': Perform no hinting - # 'auto': Use freetype's autohinter - # 'native': Use the hinting information in the - # font file, if available, and if your - # freetype library supports it - # 'either': Use the native hinting information, - # or the autohinter if none is available. - # For backward compatibility, this value may also be - # True === 'auto' or False === 'none'. -text.hinting_factor : 8 # Specifies the amount of softness for hinting in the - # horizontal direction. A value of 1 will hint to full - # pixels. A value of 2 will hint to half pixels etc. - -#text.antialiased : True # If True (default), the text will be antialiased. - # This only affects the Agg backend. - -# The following settings allow you to select the fonts in math mode. -# They map from a TeX font name to a fontconfig font pattern. -# These settings are only used if mathtext.fontset is 'custom'. -# Note that this "custom" mode is unsupported and may go away in the -# future. -#mathtext.cal : cursive -#mathtext.rm : serif -#mathtext.tt : monospace -#mathtext.it : serif:italic -#mathtext.bf : serif:bold -#mathtext.sf : sans -mathtext.fontset : cm # Should be 'cm' (Computer Modern), 'stix', - # 'stixsans' or 'custom' -#mathtext.fallback_to_cm : True # When True, use symbols from the Computer Modern - # fonts when a symbol can not be found in one of - # the custom math fonts. - -#mathtext.default : it # The default font to use for math. - # Can be any of the LaTeX font names, including - # the special name "regular" for the same font - # used in regular text. - -### AXES -# default face and edge color, default tick sizes, -# default fontsizes for ticklabels, and so on. See -# http://matplotlib.org/api/axes_api.html#module-matplotlib.axes -#axes.hold : True # whether to clear the axes by default on -axes.facecolor : eeeeee # axes background color -axes.edgecolor : bcbcbc # axes edge color -#axes.linewidth : 1.0 # edge linewidth -axes.grid : True # display grid or not -axes.titlesize : x-large # fontsize of the axes title -axes.labelsize : large # fontsize of the x any y labels -#axes.labelweight : normal # weight of the x and y labels -#axes.labelcolor : black -#axes.axisbelow : False # whether axis gridlines and ticks are below - # the axes elements (lines, text, etc) -#axes.formatter.limits : -7, 7 # use scientific notation if log10 - # of the axis range is smaller than the - # first or larger than the second -#axes.formatter.use_locale : False # When True, format tick labels - # according to the user's locale. - # For example, use ',' as a decimal - # separator in the fr_FR locale. -#axes.formatter.use_mathtext : False # When True, use mathtext for scientific - # notation. -#axes.unicode_minus : True # use unicode for the minus symbol - # rather than hyphen. See - # http://en.wikipedia.org/wiki/Plus_and_minus_signs#Character_codes -axes.color_cycle : 348ABD, A60628, 7A68A6, 467821,D55E00, CC79A7, 56B4E9, 009E73, F0E442, 0072B2 # color cycle for plot lines - # as list of string colorspecs: - # single letter, long name, or - # web-style hex - -#polaraxes.grid : True # display grid on polar axes -#axes3d.grid : True # display grid on 3d axes - -### TICKS -# see http://matplotlib.org/api/axis_api.html#matplotlib.axis.Tick -#xtick.major.size : 4 # major tick size in points -#xtick.minor.size : 2 # minor tick size in points -#xtick.major.width : 0.5 # major tick width in points -#xtick.minor.width : 0.5 # minor tick width in points -#xtick.major.pad : 4 # distance to major tick label in points -#xtick.minor.pad : 4 # distance to the minor tick label in points -#xtick.color : k # color of the tick labels -#xtick.labelsize : medium # fontsize of the tick labels -#xtick.direction : in # direction: in, out, or inout - -#ytick.major.size : 4 # major tick size in points -#ytick.minor.size : 2 # minor tick size in points -#ytick.major.width : 0.5 # major tick width in points -#ytick.minor.width : 0.5 # minor tick width in points -#ytick.major.pad : 4 # distance to major tick label in points -#ytick.minor.pad : 4 # distance to the minor tick label in points -#ytick.color : k # color of the tick labels -#ytick.labelsize : medium # fontsize of the tick labels -#ytick.direction : in # direction: in, out, or inout - - -### GRIDS -#grid.color : black # grid color -#grid.linestyle : : # dotted -#grid.linewidth : 0.5 # in points -#grid.alpha : 1.0 # transparency, between 0.0 and 1.0 - -### Legend -legend.fancybox : True # if True, use a rounded box for the - # legend, else a rectangle -#legend.isaxes : True -#legend.numpoints : 2 # the number of points in the legend line -#legend.fontsize : large -#legend.pad : 0.0 # deprecated; the fractional whitespace inside the legend border -#legend.borderpad : 0.5 # border whitespace in fontsize units -#legend.markerscale : 1.0 # the relative size of legend markers vs. original -# the following dimensions are in axes coords -#legend.labelsep : 0.010 # deprecated; the vertical space between the legend entries -#legend.labelspacing : 0.5 # the vertical space between the legend entries in fraction of fontsize -#legend.handlelen : 0.05 # deprecated; the length of the legend lines -#legend.handlelength : 2. # the length of the legend lines in fraction of fontsize -#legend.handleheight : 0.7 # the height of the legend handle in fraction of fontsize -#legend.handletextsep : 0.02 # deprecated; the space between the legend line and legend text -#legend.handletextpad : 0.8 # the space between the legend line and legend text in fraction of fontsize -#legend.axespad : 0.02 # deprecated; the border between the axes and legend edge -#legend.borderaxespad : 0.5 # the border between the axes and legend edge in fraction of fontsize -#legend.columnspacing : 2. # the border between the axes and legend edge in fraction of fontsize -#legend.shadow : False -#legend.frameon : True # whether or not to draw a frame around legend - -### FIGURE -# See http://matplotlib.org/api/figure_api.html#matplotlib.figure.Figure -figure.figsize : 11, 8 # figure size in inches -figure.dpi : 100 # figure dots per inch -#figure.facecolor : 0.75 # figure facecolor; 0.75 is scalar gray -#figure.edgecolor : white # figure edgecolor -#figure.autolayout : False # When True, automatically adjust subplot - # parameters to make the plot fit the figure - -# The figure subplot parameters. All dimensions are a fraction of the -# figure width or height -#figure.subplot.left : 0.125 # the left side of the subplots of the figure -#figure.subplot.right : 0.9 # the right side of the subplots of the figure -#figure.subplot.bottom : 0.1 # the bottom of the subplots of the figure -#figure.subplot.top : 0.9 # the top of the subplots of the figure -#figure.subplot.wspace : 0.2 # the amount of width reserved for blank space between subplots -#figure.subplot.hspace : 0.2 # the amount of height reserved for white space between subplots - -### IMAGES -#image.aspect : equal # equal | auto | a number -#image.interpolation : bilinear # see help(imshow) for options -#image.cmap : jet # gray | jet etc... -#image.lut : 256 # the size of the colormap lookup table -#image.origin : upper # lower | upper -#image.resample : False - -### CONTOUR PLOTS -#contour.negative_linestyle : dashed # dashed | solid - -### Agg rendering -### Warning: experimental, 2008/10/10 -#agg.path.chunksize : 0 # 0 to disable; values in the range - # 10000 to 100000 can improve speed slightly - # and prevent an Agg rendering failure - # when plotting very large data sets, - # especially if they are very gappy. - # It may cause minor artifacts, though. - # A value of 20000 is probably a good - # starting point. -### SAVING FIGURES -#path.simplify : True # When True, simplify paths by removing "invisible" - # points to reduce file size and increase rendering - # speed -#path.simplify_threshold : 0.1 # The threshold of similarity below which - # vertices will be removed in the simplification - # process -#path.snap : True # When True, rectilinear axis-aligned paths will be snapped to - # the nearest pixel when certain criteria are met. When False, - # paths will never be snapped. - -# the default savefig params can be different from the display params -# Eg, you may want a higher resolution, or to make the figure -# background white -savefig.dpi : 300 # figure dots per inch -#savefig.facecolor : white # figure facecolor when saving -#savefig.edgecolor : white # figure edgecolor when saving -#savefig.format : png # png, ps, pdf, svg -#savefig.bbox : standard # 'tight' or 'standard'. -#savefig.pad_inches : 0.1 # Padding to be used when bbox is set to 'tight' - -# tk backend params -#tk.window_focus : False # Maintain shell focus for TkAgg - -# ps backend params -#ps.papersize : letter # auto, letter, legal, ledger, A0-A10, B0-B10 -#ps.useafm : False # use of afm fonts, results in small files -#ps.usedistiller : False # can be: None, ghostscript or xpdf - # Experimental: may produce smaller files. - # xpdf intended for production of publication quality files, - # but requires ghostscript, xpdf and ps2eps -#ps.distiller.res : 6000 # dpi -#ps.fonttype : 3 # Output Type 3 (Type3) or Type 42 (TrueType) - -# pdf backend params -#pdf.compression : 6 # integer from 0 to 9 - # 0 disables compression (good for debugging) -#pdf.fonttype : 3 # Output Type 3 (Type3) or Type 42 (TrueType) - -# svg backend params -#svg.image_inline : True # write raster image data directly into the svg file -#svg.image_noscale : False # suppress scaling of raster data embedded in SVG -#svg.fonttype : 'path' # How to handle SVG fonts: -# 'none': Assume fonts are installed on the machine where the SVG will be viewed. -# 'path': Embed characters as paths -- supported by most SVG renderers -# 'svgfont': Embed characters as SVG fonts -- supported only by Chrome, -# Opera and Safari - -# docstring params -#docstring.hardcopy = False # set this when you want to generate hardcopy docstring - -# Set the verbose flags. This controls how much information -# matplotlib gives you at runtime and where it goes. The verbosity -# levels are: silent, helpful, debug, debug-annoying. Any level is -# inclusive of all the levels below it. If your setting is "debug", -# you'll get all the debug and helpful messages. When submitting -# problems to the mailing-list, please set verbose to "helpful" or "debug" -# and paste the output into your report. -# -# The "fileo" gives the destination for any calls to verbose.report. -# These objects can a filename, or a filehandle like sys.stdout. -# -# You can override the rc default verbosity from the command line by -# giving the flags --verbose-LEVEL where LEVEL is one of the legal -# levels, eg --verbose-helpful. -# -# You can access the verbose instance in your code -# from matplotlib import verbose. -#verbose.level : silent # one of silent, helpful, debug, debug-annoying -#verbose.fileo : sys.stdout # a log filename, sys.stdout or sys.stderr - -# Event keys to interact with figures/plots via keyboard. -# Customize these settings according to your needs. -# Leave the field(s) empty if you don't need a key-map. (i.e., fullscreen : '') - -#keymap.fullscreen : f # toggling -#keymap.home : h, r, home # home or reset mnemonic -#keymap.back : left, c, backspace # forward / backward keys to enable -#keymap.forward : right, v # left handed quick navigation -#keymap.pan : p # pan mnemonic -#keymap.zoom : o # zoom mnemonic -#keymap.save : s # saving current figure -#keymap.quit : ctrl+w # close the current figure -#keymap.grid : g # switching on/off a grid in current axes -#keymap.yscale : l # toggle scaling of y-axes ('log'/'linear') -#keymap.xscale : L, k # toggle scaling of x-axes ('log'/'linear') -#keymap.all_axes : a # enable all axes - -###ANIMATION settings -#animation.writer : ffmpeg # MovieWriter 'backend' to use -#animation.codec : mp4 # Codec to use for writing movie -#animation.bitrate: -1 # Controls size/quality tradeoff for movie. - # -1 implies let utility auto-determine -#animation.frame_format: 'png' # Controls frame format used by temp files -#animation.ffmpeg_path: 'ffmpeg' # Path to ffmpeg binary. Without full path - # $PATH is searched -#animation.ffmpeg_args: '' # Additional arugments to pass to mencoder -#animation.mencoder_path: 'ffmpeg' # Path to mencoder binary. Without full path - # $PATH is searched -#animation.mencoder_args: '' # Additional arugments to pass to mencoder +### MATPLOTLIBRC FORMAT + +# This is a sample matplotlib configuration file - you can find a copy +# of it on your system in +# site-packages/matplotlib/mpl-data/matplotlibrc. If you edit it +# there, please note that it will be overwritten in your next install. +# If you want to keep a permanent local copy that will not be +# overwritten, place it in HOME/.matplotlib/matplotlibrc (unix/linux +# like systems) and C:\Documents and Settings\yourname\.matplotlib +# (win32 systems). +# +# This file is best viewed in a editor which supports python mode +# syntax highlighting. Blank lines, or lines starting with a comment +# symbol, are ignored, as are trailing comments. Other lines must +# have the format +# key : val # optional comment +# +# Colors: for the color values below, you can either use - a +# matplotlib color string, such as r, k, or b - an rgb tuple, such as +# (1.0, 0.5, 0.0) - a hex string, such as ff00ff or #ff00ff - a scalar +# grayscale intensity such as 0.75 - a legal html color name, eg red, +# blue, darkslategray + +#### CONFIGURATION BEGINS HERE + +# the default backend; one of GTK GTKAgg GTKCairo GTK3Agg GTK3Cairo +# CocoaAgg FltkAgg MacOSX QtAgg Qt4Agg TkAgg WX WXAgg Agg Cairo GDK PS +# PDF SVG Template +# You can also deploy your own backend outside of matplotlib by +# referring to the module name (which must be in the PYTHONPATH) as +# 'module://my_backend' +backend : TkAgg + +# If you are using the Qt4Agg backend, you can choose here +# to use the PyQt4 bindings or the newer PySide bindings to +# the underlying Qt4 toolkit. +#backend.qt4 : PyQt4 # PyQt4 | PySide + +# Note that this can be overridden by the environment variable +# QT_API used by Enthought Tool Suite (ETS); valid values are +# "pyqt" and "pyside". The "pyqt" setting has the side effect of +# forcing the use of Version 2 API for QString and QVariant. + +# if you are running pyplot inside a GUI and your backend choice +# conflicts, we will automatically try to find a compatible one for +# you if backend_fallback is True +#backend_fallback: True + +#interactive : False +#toolbar : toolbar2 # None | toolbar2 ("classic" is deprecated) +#timezone : UTC # a pytz timezone string, eg US/Central or Europe/Paris + +# Where your matplotlib data lives if you installed to a non-default +# location. This is where the matplotlib fonts, bitmaps, etc reside +#datapath : /home/jdhunter/mpldata + + +### LINES +# See http://matplotlib.org/api/artist_api.html#module-matplotlib.lines for more +# information on line properties. +lines.linewidth : 2.0 # line width in points +#lines.linestyle : - # solid line +#lines.color : blue # has no affect on plot(); see axes.color_cycle +#lines.marker : None # the default marker +#lines.markeredgewidth : 0.5 # the line width around the marker symbol +#lines.markersize : 6 # markersize, in points +#lines.dash_joinstyle : miter # miter|round|bevel +#lines.dash_capstyle : butt # butt|round|projecting +#lines.solid_joinstyle : miter # miter|round|bevel +#lines.solid_capstyle : projecting # butt|round|projecting +#lines.antialiased : True # render lines in antialised (no jaggies) + +### PATCHES +# Patches are graphical objects that fill 2D space, like polygons or +# circles. See +# http://matplotlib.org/api/artist_api.html#module-matplotlib.patches +# information on patch properties +patch.linewidth : 0.5 # edge width in points +patch.facecolor : blue +patch.edgecolor : eeeeee +patch.antialiased : True + +### FONT +# +# font properties used by text.Text. See +# http://matplotlib.org/api/font_manager_api.html for more +# information on font properties. The 6 font properties used for font +# matching are given below with their default values. +# +# The font.family property has five values: 'serif' (e.g. Times), +# 'sans-serif' (e.g. Helvetica), 'cursive' (e.g. Zapf-Chancery), +# 'fantasy' (e.g. Western), and 'monospace' (e.g. Courier). Each of +# these font families has a default list of font names in decreasing +# order of priority associated with them. +# +# The font.style property has three values: normal (or roman), italic +# or oblique. The oblique style will be used for italic, if it is not +# present. +# +# The font.variant property has two values: normal or small-caps. For +# TrueType fonts, which are scalable fonts, small-caps is equivalent +# to using a font size of 'smaller', or about 83% of the current font +# size. +# +# The font.weight property has effectively 13 values: normal, bold, +# bolder, lighter, 100, 200, 300, ..., 900. Normal is the same as +# 400, and bold is 700. bolder and lighter are relative values with +# respect to the current weight. +# +# The font.stretch property has 11 values: ultra-condensed, +# extra-condensed, condensed, semi-condensed, normal, semi-expanded, +# expanded, extra-expanded, ultra-expanded, wider, and narrower. This +# property is not currently implemented. +# +# The font.size property is the default font size for text, given in pts. +# 12pt is the standard value. +# +#font.family : monospace +#font.style : normal +#font.variant : normal +#font.weight : medium +#font.stretch : normal +# note that font.size controls default text sizes. To configure +# special text sizes tick labels, axes, labels, title, etc, see the rc +# settings for axes and ticks. Special text sizes can be defined +# relative to font.size, using the following values: xx-small, x-small, +# small, medium, large, x-large, xx-large, larger, or smaller +#font.size : 12.0 +#font.serif : Bitstream Vera Serif, New Century Schoolbook, Century Schoolbook L, Utopia, ITC Bookman, Bookman, Nimbus Roman No9 L, Times New Roman, Times, Palatino, Charter, serif +#font.sans-serif : Bitstream Vera Sans, Lucida Grande, Verdana, Geneva, Lucid, Arial, Helvetica, Avant Garde, sans-serif +#font.cursive : Apple Chancery, Textile, Zapf Chancery, Sand, cursive +#font.fantasy : Comic Sans MS, Chicago, Charcoal, Impact, Western, fantasy +#font.monospace : Andale Mono, Nimbus Mono L, Courier New, Courier, Fixed, Terminal, monospace + + +### TEXT +# text properties used by text.Text. See +# http://matplotlib.org/api/artist_api.html#module-matplotlib.text for more +# information on text properties + +#text.color : black + +### LaTeX customizations. See http://www.scipy.org/Wiki/Cookbook/Matplotlib/UsingTex +#text.usetex : False # use latex for all text handling. The following fonts + # are supported through the usual rc parameter settings: + # new century schoolbook, bookman, times, palatino, + # zapf chancery, charter, serif, sans-serif, helvetica, + # avant garde, courier, monospace, computer modern roman, + # computer modern sans serif, computer modern typewriter + # If another font is desired which can loaded using the + # LaTeX \usepackage command, please inquire at the + # matplotlib mailing list +#text.latex.unicode : False # use "ucs" and "inputenc" LaTeX packages for handling + # unicode strings. +#text.latex.preamble : # IMPROPER USE OF THIS FEATURE WILL LEAD TO LATEX FAILURES + # AND IS THEREFORE UNSUPPORTED. PLEASE DO NOT ASK FOR HELP + # IF THIS FEATURE DOES NOT DO WHAT YOU EXPECT IT TO. + # preamble is a comma separated list of LaTeX statements + # that are included in the LaTeX document preamble. + # An example: + # text.latex.preamble : \usepackage{bm},\usepackage{euler} + # The following packages are always loaded with usetex, so + # beware of package collisions: color, geometry, graphicx, + # type1cm, textcomp. Adobe Postscript (PSSNFS) font packages + # may also be loaded, depending on your font settings + +#text.dvipnghack : None # some versions of dvipng don't handle alpha + # channel properly. Use True to correct + # and flush ~/.matplotlib/tex.cache + # before testing and False to force + # correction off. None will try and + # guess based on your dvipng version + +#text.hinting : 'auto' # May be one of the following: + # 'none': Perform no hinting + # 'auto': Use freetype's autohinter + # 'native': Use the hinting information in the + # font file, if available, and if your + # freetype library supports it + # 'either': Use the native hinting information, + # or the autohinter if none is available. + # For backward compatibility, this value may also be + # True === 'auto' or False === 'none'. +text.hinting_factor : 8 # Specifies the amount of softness for hinting in the + # horizontal direction. A value of 1 will hint to full + # pixels. A value of 2 will hint to half pixels etc. + +#text.antialiased : True # If True (default), the text will be antialiased. + # This only affects the Agg backend. + +# The following settings allow you to select the fonts in math mode. +# They map from a TeX font name to a fontconfig font pattern. +# These settings are only used if mathtext.fontset is 'custom'. +# Note that this "custom" mode is unsupported and may go away in the +# future. +#mathtext.cal : cursive +#mathtext.rm : serif +#mathtext.tt : monospace +#mathtext.it : serif:italic +#mathtext.bf : serif:bold +#mathtext.sf : sans +mathtext.fontset : cm # Should be 'cm' (Computer Modern), 'stix', + # 'stixsans' or 'custom' +#mathtext.fallback_to_cm : True # When True, use symbols from the Computer Modern + # fonts when a symbol can not be found in one of + # the custom math fonts. + +#mathtext.default : it # The default font to use for math. + # Can be any of the LaTeX font names, including + # the special name "regular" for the same font + # used in regular text. + +### AXES +# default face and edge color, default tick sizes, +# default fontsizes for ticklabels, and so on. See +# http://matplotlib.org/api/axes_api.html#module-matplotlib.axes +#axes.hold : True # whether to clear the axes by default on +axes.facecolor : eeeeee # axes background color +axes.edgecolor : bcbcbc # axes edge color +#axes.linewidth : 1.0 # edge linewidth +axes.grid : True # display grid or not +axes.titlesize : x-large # fontsize of the axes title +axes.labelsize : large # fontsize of the x any y labels +#axes.labelweight : normal # weight of the x and y labels +#axes.labelcolor : black +#axes.axisbelow : False # whether axis gridlines and ticks are below + # the axes elements (lines, text, etc) +#axes.formatter.limits : -7, 7 # use scientific notation if log10 + # of the axis range is smaller than the + # first or larger than the second +#axes.formatter.use_locale : False # When True, format tick labels + # according to the user's locale. + # For example, use ',' as a decimal + # separator in the fr_FR locale. +#axes.formatter.use_mathtext : False # When True, use mathtext for scientific + # notation. +#axes.unicode_minus : True # use unicode for the minus symbol + # rather than hyphen. See + # http://en.wikipedia.org/wiki/Plus_and_minus_signs#Character_codes +axes.color_cycle : 348ABD, A60628, 7A68A6, 467821,D55E00, CC79A7, 56B4E9, 009E73, F0E442, 0072B2 # color cycle for plot lines + # as list of string colorspecs: + # single letter, long name, or + # web-style hex + +#polaraxes.grid : True # display grid on polar axes +#axes3d.grid : True # display grid on 3d axes + +### TICKS +# see http://matplotlib.org/api/axis_api.html#matplotlib.axis.Tick +#xtick.major.size : 4 # major tick size in points +#xtick.minor.size : 2 # minor tick size in points +#xtick.major.width : 0.5 # major tick width in points +#xtick.minor.width : 0.5 # minor tick width in points +#xtick.major.pad : 4 # distance to major tick label in points +#xtick.minor.pad : 4 # distance to the minor tick label in points +#xtick.color : k # color of the tick labels +#xtick.labelsize : medium # fontsize of the tick labels +#xtick.direction : in # direction: in, out, or inout + +#ytick.major.size : 4 # major tick size in points +#ytick.minor.size : 2 # minor tick size in points +#ytick.major.width : 0.5 # major tick width in points +#ytick.minor.width : 0.5 # minor tick width in points +#ytick.major.pad : 4 # distance to major tick label in points +#ytick.minor.pad : 4 # distance to the minor tick label in points +#ytick.color : k # color of the tick labels +#ytick.labelsize : medium # fontsize of the tick labels +#ytick.direction : in # direction: in, out, or inout + + +### GRIDS +#grid.color : black # grid color +#grid.linestyle : : # dotted +#grid.linewidth : 0.5 # in points +#grid.alpha : 1.0 # transparency, between 0.0 and 1.0 + +### Legend +legend.fancybox : True # if True, use a rounded box for the + # legend, else a rectangle +#legend.isaxes : True +#legend.numpoints : 2 # the number of points in the legend line +#legend.fontsize : large +#legend.pad : 0.0 # deprecated; the fractional whitespace inside the legend border +#legend.borderpad : 0.5 # border whitespace in fontsize units +#legend.markerscale : 1.0 # the relative size of legend markers vs. original +# the following dimensions are in axes coords +#legend.labelsep : 0.010 # deprecated; the vertical space between the legend entries +#legend.labelspacing : 0.5 # the vertical space between the legend entries in fraction of fontsize +#legend.handlelen : 0.05 # deprecated; the length of the legend lines +#legend.handlelength : 2. # the length of the legend lines in fraction of fontsize +#legend.handleheight : 0.7 # the height of the legend handle in fraction of fontsize +#legend.handletextsep : 0.02 # deprecated; the space between the legend line and legend text +#legend.handletextpad : 0.8 # the space between the legend line and legend text in fraction of fontsize +#legend.axespad : 0.02 # deprecated; the border between the axes and legend edge +#legend.borderaxespad : 0.5 # the border between the axes and legend edge in fraction of fontsize +#legend.columnspacing : 2. # the border between the axes and legend edge in fraction of fontsize +#legend.shadow : False +#legend.frameon : True # whether or not to draw a frame around legend + +### FIGURE +# See http://matplotlib.org/api/figure_api.html#matplotlib.figure.Figure +figure.figsize : 11, 8 # figure size in inches +figure.dpi : 100 # figure dots per inch +#figure.facecolor : 0.75 # figure facecolor; 0.75 is scalar gray +#figure.edgecolor : white # figure edgecolor +#figure.autolayout : False # When True, automatically adjust subplot + # parameters to make the plot fit the figure + +# The figure subplot parameters. All dimensions are a fraction of the +# figure width or height +#figure.subplot.left : 0.125 # the left side of the subplots of the figure +#figure.subplot.right : 0.9 # the right side of the subplots of the figure +#figure.subplot.bottom : 0.1 # the bottom of the subplots of the figure +#figure.subplot.top : 0.9 # the top of the subplots of the figure +#figure.subplot.wspace : 0.2 # the amount of width reserved for blank space between subplots +#figure.subplot.hspace : 0.2 # the amount of height reserved for white space between subplots + +### IMAGES +#image.aspect : equal # equal | auto | a number +#image.interpolation : bilinear # see help(imshow) for options +#image.cmap : jet # gray | jet etc... +#image.lut : 256 # the size of the colormap lookup table +#image.origin : upper # lower | upper +#image.resample : False + +### CONTOUR PLOTS +#contour.negative_linestyle : dashed # dashed | solid + +### Agg rendering +### Warning: experimental, 2008/10/10 +#agg.path.chunksize : 0 # 0 to disable; values in the range + # 10000 to 100000 can improve speed slightly + # and prevent an Agg rendering failure + # when plotting very large data sets, + # especially if they are very gappy. + # It may cause minor artifacts, though. + # A value of 20000 is probably a good + # starting point. +### SAVING FIGURES +#path.simplify : True # When True, simplify paths by removing "invisible" + # points to reduce file size and increase rendering + # speed +#path.simplify_threshold : 0.1 # The threshold of similarity below which + # vertices will be removed in the simplification + # process +#path.snap : True # When True, rectilinear axis-aligned paths will be snapped to + # the nearest pixel when certain criteria are met. When False, + # paths will never be snapped. + +# the default savefig params can be different from the display params +# Eg, you may want a higher resolution, or to make the figure +# background white +savefig.dpi : 300 # figure dots per inch +#savefig.facecolor : white # figure facecolor when saving +#savefig.edgecolor : white # figure edgecolor when saving +#savefig.format : png # png, ps, pdf, svg +#savefig.bbox : standard # 'tight' or 'standard'. +#savefig.pad_inches : 0.1 # Padding to be used when bbox is set to 'tight' + +# tk backend params +#tk.window_focus : False # Maintain shell focus for TkAgg + +# ps backend params +#ps.papersize : letter # auto, letter, legal, ledger, A0-A10, B0-B10 +#ps.useafm : False # use of afm fonts, results in small files +#ps.usedistiller : False # can be: None, ghostscript or xpdf + # Experimental: may produce smaller files. + # xpdf intended for production of publication quality files, + # but requires ghostscript, xpdf and ps2eps +#ps.distiller.res : 6000 # dpi +#ps.fonttype : 3 # Output Type 3 (Type3) or Type 42 (TrueType) + +# pdf backend params +#pdf.compression : 6 # integer from 0 to 9 + # 0 disables compression (good for debugging) +#pdf.fonttype : 3 # Output Type 3 (Type3) or Type 42 (TrueType) + +# svg backend params +#svg.image_inline : True # write raster image data directly into the svg file +#svg.image_noscale : False # suppress scaling of raster data embedded in SVG +#svg.fonttype : 'path' # How to handle SVG fonts: +# 'none': Assume fonts are installed on the machine where the SVG will be viewed. +# 'path': Embed characters as paths -- supported by most SVG renderers +# 'svgfont': Embed characters as SVG fonts -- supported only by Chrome, +# Opera and Safari + +# docstring params +#docstring.hardcopy = False # set this when you want to generate hardcopy docstring + +# Set the verbose flags. This controls how much information +# matplotlib gives you at runtime and where it goes. The verbosity +# levels are: silent, helpful, debug, debug-annoying. Any level is +# inclusive of all the levels below it. If your setting is "debug", +# you'll get all the debug and helpful messages. When submitting +# problems to the mailing-list, please set verbose to "helpful" or "debug" +# and paste the output into your report. +# +# The "fileo" gives the destination for any calls to verbose.report. +# These objects can a filename, or a filehandle like sys.stdout. +# +# You can override the rc default verbosity from the command line by +# giving the flags --verbose-LEVEL where LEVEL is one of the legal +# levels, eg --verbose-helpful. +# +# You can access the verbose instance in your code +# from matplotlib import verbose. +#verbose.level : silent # one of silent, helpful, debug, debug-annoying +#verbose.fileo : sys.stdout # a log filename, sys.stdout or sys.stderr + +# Event keys to interact with figures/plots via keyboard. +# Customize these settings according to your needs. +# Leave the field(s) empty if you don't need a key-map. (i.e., fullscreen : '') + +#keymap.fullscreen : f # toggling +#keymap.home : h, r, home # home or reset mnemonic +#keymap.back : left, c, backspace # forward / backward keys to enable +#keymap.forward : right, v # left handed quick navigation +#keymap.pan : p # pan mnemonic +#keymap.zoom : o # zoom mnemonic +#keymap.save : s # saving current figure +#keymap.quit : ctrl+w # close the current figure +#keymap.grid : g # switching on/off a grid in current axes +#keymap.yscale : l # toggle scaling of y-axes ('log'/'linear') +#keymap.xscale : L, k # toggle scaling of x-axes ('log'/'linear') +#keymap.all_axes : a # enable all axes + +###ANIMATION settings +#animation.writer : ffmpeg # MovieWriter 'backend' to use +#animation.codec : mp4 # Codec to use for writing movie +#animation.bitrate: -1 # Controls size/quality tradeoff for movie. + # -1 implies let utility auto-determine +#animation.frame_format: 'png' # Controls frame format used by temp files +#animation.ffmpeg_path: 'ffmpeg' # Path to ffmpeg binary. Without full path + # $PATH is searched +#animation.ffmpeg_args: '' # Additional arugments to pass to mencoder +#animation.mencoder_path: 'ffmpeg' # Path to mencoder binary. Without full path + # $PATH is searched +#animation.mencoder_args: '' # Additional arugments to pass to mencoder