diff --git a/.buildinfo b/.buildinfo new file mode 100644 index 0000000..424e71c --- /dev/null +++ b/.buildinfo @@ -0,0 +1,4 @@ +# Sphinx build info version 1 +# This file hashes the configuration used when building these files. When it is not found, a full rebuild will be done. +config: 754fdb1a4387a656c1665f163a740f04 +tags: 645f666f9bcd5a90fca523b33c5a78b7 diff --git a/.gitignore b/.gitignore deleted file mode 100644 index b6643e2..0000000 --- a/.gitignore +++ /dev/null @@ -1,4 +0,0 @@ -.ipynb_checkpoints -/_build -*/.ipynb_checkpoints/* -*/_build/* diff --git a/.nojekyll b/.nojekyll new file mode 100644 index 0000000..e69de29 diff --git a/README.md b/README.md deleted file mode 100644 index b3befef..0000000 --- a/README.md +++ /dev/null @@ -1,9 +0,0 @@ -# Economic Dynamics, Theory and Computation - -This is the GH repo for the second edition of -[Economic Dynamics, Theory and Computation](http://johnstachurski.net/personal/edtc.html) by [John Stachurski](http://johnstachurski.net). - -The repo contains the source for the corresponding [Jupyter Book](https://jstac.github.io/edtc-code/intro.html) - -If you find problems, please feel free to get in touch via the issue tracker. -All feedback is appreciated. 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I will not spend time explaining concepts\n", + "here, since both programming and dynamics are dealt with more systematically\n", + "later.\n", + "\n", + "Rather, the code is included here for completeness, and so that readers can\n", + "circle back to it once they have read other chapters.\n", + "\n", + "We begin with some imports." + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "id": "209a2e4d", + "metadata": {}, + "outputs": [], + "source": [ + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "from matplotlib.colors import ListedColormap\n", + "import quantecon as qe\n", + "from numpy.random import uniform, randint\n", + "from numba import njit\n" + ] + }, + { + "cell_type": "markdown", + "id": "80b1db12", + "metadata": {}, + "source": [ + "## Markov Dynamics\n", + "\n", + "Here is the class transition model from chapter 1 expressed as a stochastic\n", + "matrix." + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "id": "87336e54", + "metadata": {}, + "outputs": [], + "source": [ + "P = ((0.9, 0.1, 0.0),\n", + " (0.4, 0.4, 0.2),\n", + " (0.1, 0.1, 0.8))\n", + "\n", + "mc = qe.MarkovChain(P)\n" + ] + }, + { + "cell_type": "markdown", + "id": "c3bed7da", + "metadata": {}, + "source": [ + "The following function simulates dynamics of a large group of households from\n", + "some fixed distribution `init`." + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "id": "acc92459", + "metadata": {}, + "outputs": [], + "source": [ + "def sim_population(init=None, sim_length=100, pop_size=1000):\n", + "\n", + " cdf = np.cumsum(init)\n", + " obs = qe.random.draw(cdf, pop_size)\n", + " updated_obs = mc.simulate(sim_length, init=obs)[:, -1]\n", + " return updated_obs\n" + ] + }, + { + "cell_type": "markdown", + "id": "23c0b7c0", + "metadata": {}, + "source": [ + "This function creates distribution plots." + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "id": "e7949569", + "metadata": {}, + "outputs": [], + "source": [ + "def generate_plot(initial_dist, title, ax):\n", + " population = 1000\n", + "\n", + " draws = sim_population(init=initial_dist, pop_size=population) \n", + " histogram = [np.mean(draws == i) for i in range(3)]\n", + "\n", + " names = 'poor', 'middle', 'rich'\n", + " ax.bar(names, histogram, edgecolor='k', alpha=0.4)\n", + " ax.set_title(title)\n" + ] + }, + { + "cell_type": "markdown", + "id": "e19ff916", + "metadata": {}, + "source": [ + "Now let us generate the first figure." + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "id": "925021e1", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "filenames": { + "image/png": "/home/john/gh_synced/books/sed2/edtc-code/code_book/_build/jupyter_execute/ch1_9_0.png" + }, + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "initial_dists = ((1, 0, 0),\n", + " (0, 1, 0),\n", + " (0, 0, 1),\n", + " (0.33, 0.33, 0.34))\n", + "\n", + "titles = ('$\\\\psi_0 = (1, 0, 0)$', \n", + " '$\\\\psi_0 = (0, 1, 0)$',\n", + " '$\\\\psi_0 = (0, 0, 1)$',\n", + " '$\\\\psi_0 = (1/3, 1/3, 1/3)$')\n", + "\n", + "fig, axes = plt.subplots(2, 2)\n", + "axes = axes.flatten()\n", + "\n", + "for psi, title, ax in zip(initial_dists, titles, axes):\n", + " generate_plot(psi, title, ax)\n", + "\n", + "plt.tight_layout()\n", + "plt.show()\n" + ] + }, + { + "cell_type": "markdown", + "id": "636f798e", + "metadata": {}, + "source": [ + "Finally, here is a histogram of states produced by a single very long time\n", + "series.\n", + "\n", + "For large samples, the histogram is essentially identical to the ones we\n", + "produced above.\n", + "\n", + "This is ergodicity." + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "id": "3c2f13f0", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "filenames": { + "image/png": "/home/john/gh_synced/books/sed2/edtc-code/code_book/_build/jupyter_execute/ch1_11_0.png" + }, + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "sim_length = 100_000\n", + "draws = mc.simulate(sim_length, init=0)\n", + "histogram = [np.mean(draws == i) for i in range(3)]\n", + "\n", + "fig, ax = plt.subplots()\n", + "names = 'poor', 'middle', 'rich'\n", + "ax.bar(names, histogram, edgecolor='k', alpha=0.4)\n", + "ax.set_title('time series average')\n", + "ax.set_yticks((0, 0.2, 0.4, 0.6))\n", + "plt.show()\n" + ] + }, + { + "cell_type": "markdown", + "id": "3d9a1bcc", + "metadata": {}, + "source": [ + "Here is the code that produced the lattice figure in chapter 1." + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "id": "5c28c267", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "filenames": { + "image/png": "/home/john/gh_synced/books/sed2/edtc-code/code_book/_build/jupyter_execute/ch1_13_0.png" + }, + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "xx, yy = np.meshgrid(np.arange(10), np.arange(10), indexing='ij')\n", + "\n", + "\n", + "cols = np.random.randint(0, high=2, size=100)\n", + "\n", + "cmap = ListedColormap(('lavender', 'navy'))\n", + "\n", + "fig, ax = plt.subplots()\n", + "plt.axis('off')\n", + "ax.get_xaxis().set_visible(False)\n", + "ax.get_yaxis().set_visible(False)\n", + "\n", + "ax.scatter(xx,yy, c=cols, cmap=cmap, alpha=0.6, edgecolor='k')\n", + "plt.show()\n" + ] + }, + { + "cell_type": "markdown", + "id": "de1901f9", + "metadata": {}, + "source": [ + "## The Schelling Model\n", + "\n", + "Next I provide the code for the Schelling model simulations.\n", + "\n", + "\n", + "I omit most explanations.\n", + "\n", + "Hopefully readers will find the code transparent after building some\n", + "experience reading other chapters." + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "id": "59834339", + "metadata": {}, + "outputs": [], + "source": [ + "n = 1000 # number of agents (agents = 0, ..., n-1)\n", + "k = 10 # number of agents regarded as neighbors\n", + "require_same_type = 5 # want >= require_same_type neighbors of the same type\n", + "\n", + "def initialize_state():\n", + " locations = uniform(size=(n, 2))\n", + " types = randint(0, high=2, size=n) # label zero or one\n", + " return locations, types\n", + "\n", + "@njit\n", + "def compute_distances_from_loc(loc, locations):\n", + " \" Compute distance from location loc to all other points. \"\n", + " distances = np.empty(n)\n", + " for j in range(n):\n", + " distances[j] = np.linalg.norm(loc - locations[j, :])\n", + " return distances\n", + "\n", + "def get_neighbors(loc, locations):\n", + " \" Get all neighbors of a given location. \"\n", + " all_distances = compute_distances_from_loc(loc, locations)\n", + " indices = np.argsort(all_distances) # sort agents by distance to loc\n", + " neighbors = indices[:k] # keep the k closest ones\n", + " return neighbors\n", + "\n", + "def is_happy(i, locations, types):\n", + " happy = True\n", + " agent_loc = locations[i, :]\n", + " agent_type = types[i]\n", + " neighbors = get_neighbors(agent_loc, locations)\n", + " neighbor_types = types[neighbors]\n", + " if sum(neighbor_types == agent_type) < require_same_type:\n", + " happy = False\n", + " return happy\n", + "\n", + "def count_happy(locations, types):\n", + " \" Count the number of happy agents. \"\n", + " happy_sum = 0\n", + " for i in range(n):\n", + " happy_sum += is_happy(i, locations, types)\n", + " return happy_sum\n", + " \n", + "def update_agent(i, locations, types):\n", + " \" Move agent if unhappy. \"\n", + " moved = False\n", + " while not is_happy(i, locations, types):\n", + " moved = True\n", + " locations[i, :] = uniform(), uniform()\n", + " return moved\n", + "\n", + "def plot_distribution(locations, types, title, savepdf=False):\n", + " \" Plot the distribution of agents after cycle_num rounds of the loop.\"\n", + " fig, ax = plt.subplots()\n", + " colors = 'lavender', 'navy'\n", + " for agent_type, color in zip((0, 1), colors):\n", + " idx = (types == agent_type)\n", + " ax.plot(locations[idx, 0], \n", + " locations[idx, 1], \n", + " 'o', \n", + " markersize=8,\n", + " markerfacecolor=color, \n", + " alpha=0.8)\n", + " ax.set_title(title)\n", + " if savepdf:\n", + " plt.savefig(title + '.pdf')\n", + " plt.show()\n", + "\n", + "\n", + "def sim_sequential(max_iter=100):\n", + " \"\"\"\n", + " Simulate by sequentially stepping through the agents, one after\n", + " another.\n", + "\n", + " \"\"\"\n", + "\n", + " locations, types = initialize_state()\n", + " current_iter = 0\n", + "\n", + " while current_iter < max_iter:\n", + " print(\"Entering iteration \", current_iter)\n", + "\n", + " plot_distribution(locations, types, f'cycle_{current_iter}')\n", + "\n", + " # Update all agents\n", + " num_moved = 0\n", + " for i in range(n):\n", + " num_moved += update_agent(i, locations, types)\n", + "\n", + " if num_moved == 0:\n", + " print(f\"Converged at iteration {current_iter}\")\n", + " break\n", + "\n", + " current_iter += 1\n", + "\n", + "\n", + "def sim_random_select(max_iter=100_000, flip_prob=0.01, test_freq=10_000):\n", + " \"\"\"\n", + " Simulate by randomly selecting one household at each update.\n", + "\n", + " Flip the color of the household with probability `flip_prob`.\n", + "\n", + " \"\"\"\n", + "\n", + " locations, types = initialize_state()\n", + " current_iter = 0\n", + "\n", + " while current_iter <= max_iter:\n", + "\n", + " # Choose a random agent and update them\n", + " i = randint(0, n)\n", + " moved = update_agent(i, locations, types)\n", + "\n", + " if flip_prob > 0: \n", + " # flip agent i's type with probability epsilon\n", + " U = uniform()\n", + " if U < flip_prob:\n", + " current_type = types[i]\n", + " types[i] = 0 if current_type == 1 else 1\n", + "\n", + " # Every so many updates, plot and test for convergence\n", + " if current_iter % test_freq == 0: \n", + " cycle = current_iter / n\n", + " plot_distribution(locations, types, f'iteration {current_iter}')\n", + " if count_happy(locations, types) == n:\n", + " print(f\"Converged at iteration {current_iter}\")\n", + " break\n", + "\n", + " current_iter += 1\n", + "\n", + " if current_iter > max_iter:\n", + " print(f\"Terminating at iteration {current_iter}\")\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "id": "a806a0fc", + "metadata": {}, + "source": [ + "This code creates figures 1.6 -- 1.7, modulo randomness." + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "id": "d2ce380b", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", 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" + ] + }, + "metadata": { + "filenames": { + "image/png": "/home/john/gh_synced/books/sed2/edtc-code/code_book/_build/jupyter_execute/ch1_17_2.png" + }, + "needs_background": "light" + }, + "output_type": "display_data" + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Converged at iteration 20000\n" + ] + } + ], + "source": [ + "sim_random_select(max_iter=50_000, flip_prob=0.0, test_freq=10_000)\n" + ] + }, + { + "cell_type": "markdown", + "id": "81eac610", + "metadata": {}, + "source": [ + "This code creates figures 1.8 -- 1.9." + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "id": "9d60eaeb", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "filenames": { + "image/png": "/home/john/gh_synced/books/sed2/edtc-code/code_book/_build/jupyter_execute/ch1_19_4.png" + }, + "needs_background": "light" + }, + "output_type": "display_data" + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Terminating at iteration 200001\n" + ] + } + ], + "source": [ + "sim_random_select(max_iter=200_000, flip_prob=0.01, test_freq=50_000)\n" + ] + }, + { + "cell_type": "markdown", + "id": "0d702645", + "metadata": {}, + "source": [ + "## Linear AR(1) Simulation\n", + "\n", + "In this section we generate the time path figures for the Gaussian AR(1) model\n", + "(figures 1.10, 1.12 and 1.13)." + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "id": "92fc4527", + "metadata": {}, + "outputs": [], + "source": [ + "a = 0.9\n", + "b = 1.0\n", + "\n", + "mu_0, v_0 = 1, 1\n", + "\n", + "def compute_mean_and_var(t):\n", + " mu, v = mu_0, v_0\n", + " for i in range(t):\n", + " mu = a * mu + b\n", + " v = a**2 * v + 1\n", + "\n", + " return mu, v\n", + "\n", + "def norm_pdf(x, mu, v):\n", + " return np.sqrt(1/(2 * np.pi * v)) * np.exp(-(x - mu)**2 / (2*v))\n" + ] + }, + { + "cell_type": "markdown", + "id": "c3b742bc", + "metadata": {}, + "source": [ + "Here is the density sequence." + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "id": "32776a05", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "filenames": { + "image/png": "/home/john/gh_synced/books/sed2/edtc-code/code_book/_build/jupyter_execute/ch1_23_0.png" + }, + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "dates = 1, 2, 4, 8, 16, 32, 64\n", + "y_grid = np.linspace(-5, 20, 200)\n", + "greys = [str(g) for g in np.linspace(0.2, 0.8, len(dates))]\n", + "greys.reverse()\n", + "\n", + "fig, ax = plt.subplots()\n", + "\n", + "for t, g in zip(dates, greys):\n", + " mu, v = compute_mean_and_var(t)\n", + " ax.plot(y_grid, \n", + " [norm_pdf(y, mu, v) for y in y_grid], \n", + " color=g, \n", + " lw=2, \n", + " alpha=0.6,\n", + " label=f'$t={t}$')\n", + "\n", + "ax.set_xlabel('$x$')\n", + "ax.legend()\n", + "\n", + "plt.show()\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "id": "3480d4ed", + "metadata": {}, + "source": [ + "Here is the time series." + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "id": "cd5eb309", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "filenames": { + "image/png": "/home/john/gh_synced/books/sed2/edtc-code/code_book/_build/jupyter_execute/ch1_25_0.png" + }, + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "def generate_time_series(X_0=14, ts_length=250):\n", + " X = np.empty(ts_length)\n", + " X[0] = X_0\n", + " for t in range(ts_length-1):\n", + " X[t+1] = a * X[t] + b + np.random.randn()\n", + " return X\n", + "\n", + "mu_star = b / (1 - a)\n", + "\n", + "X = generate_time_series()\n", + "\n", + "fig, ax = plt.subplots()\n", + "\n", + "ax.plot(X, label='$X_t$', alpha=0.8)\n", + "ax.plot(np.full(len(X), mu_star), 'k--', label='$\\\\mu^*$', alpha=0.8)\n", + "\n", + "ax.legend()\n", + "\n", + "plt.show()\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "id": "89eb9871", + "metadata": {}, + "source": [ + "Finally, here is the evolution of the mean." + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "id": "0eea6a3f", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "filenames": { + "image/png": "/home/john/gh_synced/books/sed2/edtc-code/code_book/_build/jupyter_execute/ch1_27_0.png" + }, + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "\n", + "X = generate_time_series(ts_length=5000)\n", + "X_bar_series = np.cumsum(X) / np.arange(1, len(X)+1)\n", + "\n", + "fig, ax = plt.subplots()\n", + "\n", + "ax.plot(X_bar_series, label='$\\\\bar X_t$', alpha=0.8)\n", + "ax.plot(np.full(len(X_bar_series), mu_star), 'k--', label='$\\\\mu^*$', alpha=0.8)\n", + "\n", + "ax.legend()\n", + "plt.show()\n" + ] + } + ], + "metadata": { + "jupytext": { + "cell_metadata_filter": "-all", + "formats": "md:myst", + "text_representation": { + "extension": ".md", + "format_name": "myst", + "format_version": 0.13, + "jupytext_version": "1.10.3" + } + }, + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.8.5" + }, + "source_map": [ + 14, + 28, + 37, + 44, + 51, + 58, + 67, + 72, + 84, + 88, + 109, + 120, + 133, + 138, + 154, + 168, + 301, + 305, + 308, + 312, + 315, + 324, + 341, + 345, + 368, + 372, + 395, + 399 + ] + }, + "nbformat": 4, + "nbformat_minor": 5 +} \ No newline at end of file diff --git a/code_book/ch1.md b/_sources/ch1.md similarity index 100% rename from code_book/ch1.md rename to _sources/ch1.md diff --git a/_sources/ch10.ipynb b/_sources/ch10.ipynb new file mode 100644 index 0000000..3a6c42b --- /dev/null +++ b/_sources/ch10.ipynb @@ -0,0 +1,48 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "id": "91de7285", + "metadata": {}, + "source": [ + "# Chapter 10 Code\n", + "\n", + "No code used in this chapter." + ] + } + ], + "metadata": { + "jupytext": { + "cell_metadata_filter": "-all", + "formats": "md:myst", + "text_representation": { + "extension": ".md", + "format_name": "myst", + "format_version": 0.13, + "jupytext_version": "1.10.3" + } + }, + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.8.5" + }, + "source_map": [ + 14 + ] + }, + "nbformat": 4, + "nbformat_minor": 5 +} \ No newline at end of file diff --git a/code_book/ch10.md b/_sources/ch10.md similarity index 100% rename from code_book/ch10.md rename to _sources/ch10.md diff --git a/_sources/ch11.ipynb b/_sources/ch11.ipynb new file mode 100644 index 0000000..04524b1 --- /dev/null +++ b/_sources/ch11.ipynb @@ -0,0 +1,253 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "id": "44ee240c", + "metadata": {}, + "source": [ + "# Chapter 11 Code\n", + "\n", + "We begin with some imports" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "id": "359ea3eb", + "metadata": {}, + "outputs": [], + "source": [ + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "from numba import njit\n" + ] + }, + { + "cell_type": "markdown", + "id": "30c613ec", + "metadata": {}, + "source": [ + "Now we recreate figure 11.3. Our first step is to set the parameters." + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "id": "430fd7e0", + "metadata": {}, + "outputs": [], + "source": [ + "alpha = 0.6\n", + "Q = 2\n", + "R = 1\n", + "sigma = 0.1 # variance\n", + "mu = - sigma**2 / 2\n" + ] + }, + { + "cell_type": "markdown", + "id": "2a3d968c", + "metadata": {}, + "source": [ + "Next we introduce useful functions." + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "id": "336ae793", + "metadata": {}, + "outputs": [], + "source": [ + "@njit\n", + "def wage(k, z):\n", + " return (1 - alpha) * (k**alpha) * z\n", + "\n", + "@njit\n", + "def theta(w, lda):\n", + " if (w < 1 - lda):\n", + " return lda / (1 - w)\n", + " else:\n", + " return 1\n", + "\n", + "@njit\n", + "def g(y): \n", + " return (y/alpha)**(1/(alpha-1)) \n", + "\n", + "@njit\n", + "def update(k, z, lda):\n", + " \" Update the state.\"\n", + " return g(R / (Q * theta(wage(k, z), lda)))\n", + "\n", + "@njit\n", + "def a(lda): \n", + " return g(R / (lda * Q))\n", + "\n", + "@njit\n", + "def generate_ts(lda, init=None, seed=1234, ts_length=10_000):\n", + " \" Generate a time series from the model.\"\n", + " np.random.seed(seed)\n", + " K = np.empty(ts_length) \n", + " if init is None:\n", + " init = a(lda)\n", + " K[0] = init\n", + " for t in range(ts_length-1):\n", + " z = np.exp(mu + sigma * np.random.randn())\n", + " K[t+1] = update(K[t], z, lda) \n", + " return K\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "id": "e9837668", + "metadata": {}, + "source": [ + "Now we recreate the plot." + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "id": "d5e23157", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "filenames": { + "image/png": "/home/john/gh_synced/books/sed2/edtc-code/code_book/_build/jupyter_execute/ch11_7_0.png" + }, + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "b = g(R / Q)\n", + "\n", + "lambdas = 0.48, 0.5, 0.52\n", + "line_type = '-', '--', '-.'\n", + "mc_size = 5000\n", + "grid_size = 150\n", + "\n", + "fig, ax = plt.subplots()\n", + "\n", + "for lda, lt in zip(lambdas, line_type): \n", + " xvec = np.linspace(a(lda), b, grid_size)\n", + " obs = generate_ts(lda, ts_length=mc_size)\n", + " def ecdf(y):\n", + " return sum(obs <= y) / mc_size\n", + " yvec = [ecdf(x) for x in xvec]\n", + " ax.plot(xvec, yvec, lt, label=f'$\\\\lambda={lda}$')\n", + "\n", + "ax.set_xlabel('capital')\n", + "ax.legend()\n", + "\n", + "plt.show()\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "id": "8ba2738c", + "metadata": {}, + "source": [ + "Now we address exercise 11.26.\n", + "\n", + "We need to determine the fraction of time the sample spends at the point $b$\n", + "in the state space over a long horizon, for different values of $\\lambda$." + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "id": "a9368669", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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+ "text/plain": [ + "
" + ] + }, + "metadata": { + "filenames": { + "image/png": "/home/john/gh_synced/books/sed2/edtc-code/code_book/_build/jupyter_execute/ch11_9_0.png" + }, + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "grid_size = 80\n", + "lambdas = np.linspace(0.4, 0.6, grid_size)\n", + "mc_size = 5000\n", + "\n", + "prob_at_b = np.empty_like(lambdas)\n", + "\n", + "for i, lda in enumerate(lambdas):\n", + " obs = generate_ts(lda, ts_length=mc_size)\n", + " prob_at_b[i] = np.mean(obs == b)\n", + "\n", + "fig, ax = plt.subplots()\n", + "ax.plot(lambdas, prob_at_b, label='$\\\\psi^*(\\{b\\})$')\n", + "ax.set_xlabel('$\\\\lambda$')\n", + "ax.legend()\n", + "\n", + "plt.show()\n", + "\n" + ] + } + ], + "metadata": { + "jupytext": { + "cell_metadata_filter": "-all", + "formats": "md:myst", + "text_representation": { + "extension": ".md", + "format_name": "myst", + "format_version": 0.13, + "jupytext_version": "1.10.3" + } + }, + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.8.5" + }, + "source_map": [ + 14, + 20, + 25, + 30, + 38, + 43, + 82, + 86, + 111, + 120 + ] + }, + "nbformat": 4, + "nbformat_minor": 5 +} \ No newline at end of file diff --git a/code_book/ch11.md b/_sources/ch11.md similarity index 100% rename from code_book/ch11.md rename to _sources/ch11.md diff --git a/_sources/ch2.ipynb b/_sources/ch2.ipynb new file mode 100644 index 0000000..7570aad --- /dev/null +++ b/_sources/ch2.ipynb @@ -0,0 +1,428 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "id": "d7aa3ec4", + "metadata": {}, + "source": [ + "# Chapter 2 Code" + ] + }, + { + "cell_type": "markdown", + "id": "43cf0bc7", + "metadata": {}, + "source": [ + "We'll use Python's NumPy library in what follows, as well as Matplotlib for plotting." + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "id": "79f29bd4", + "metadata": {}, + "outputs": [], + "source": [ + "import numpy as np\n", + "import matplotlib.pyplot as plt" + ] + }, + { + "cell_type": "markdown", + "id": "3342f579", + "metadata": {}, + "source": [ + "## Bisection" + ] + }, + { + "cell_type": "markdown", + "id": "ff8b2c21", + "metadata": {}, + "source": [ + "Here's an implementation of the bisection algorithm. We will test it on this function:" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "id": "328bd0f3", + "metadata": {}, + "outputs": [], + "source": [ + "f = lambda x: np.sin(4 * (x - 1/4)) + x + x**20 - 1" + ] + }, + { + "cell_type": "markdown", + "id": "8283b964", + "metadata": {}, + "source": [ + "The implementation:" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "id": "1c98caa0", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "0.408293504267931\n" + ] + } + ], + "source": [ + "M = 1000\n", + "ϵ = 1e-8\n", + "α, β = 0, 1\n", + "\n", + " \n", + "i = 1\n", + "a, b = α, β\n", + "while i <= M:\n", + " c = (a + b) / 2\n", + " if abs(f(c)) < ϵ:\n", + " print(c)\n", + " break\n", + " i += 1\n", + " if f(a) * f(c) < 0:\n", + " b = c\n", + " else:\n", + " a = c\n", + " \n", + "if i > M:\n", + " print(\"Failed to converge.\")" + ] + }, + { + "cell_type": "markdown", + "id": "d12f37b9", + "metadata": {}, + "source": [ + "## User Defined Functions" + ] + }, + { + "cell_type": "markdown", + "id": "07c83a47", + "metadata": {}, + "source": [ + "Here's the basic implementation of the function $\\tau$." + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "id": "0cb7b064", + "metadata": {}, + "outputs": [], + "source": [ + "def tau(z, S, phi):\n", + " \"\"\"\n", + " Evaluates the function tau(z) given data S, phi, where\n", + " S and phi are assumed to be arrays.\n", + " \"\"\"\n", + " a = 0\n", + " for i, x in enumerate(S):\n", + " b = a + phi[i]\n", + " if a < z <= b:\n", + " return x\n", + " a = b" + ] + }, + { + "cell_type": "markdown", + "id": "d3f8e645", + "metadata": {}, + "source": [ + "Here's a more efficient implementation." + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "id": "a3de9966", + "metadata": {}, + "outputs": [], + "source": [ + "def tau(z, S, phi):\n", + " i = np.searchsorted(np.cumsum(phi), z)\n", + " return S[i]" + ] + }, + { + "cell_type": "markdown", + "id": "40d50c6d", + "metadata": {}, + "source": [ + "And here's a closure that generates the function $\\tau$." + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "id": "632e24d0", + "metadata": {}, + "outputs": [], + "source": [ + "def tau_factory(S, phi):\n", + " Φ = np.cumsum(phi)\n", + " \n", + " def tau(z):\n", + " i = np.searchsorted(Φ, z)\n", + " return S[i]\n", + " \n", + " return tau" + ] + }, + { + "cell_type": "markdown", + "id": "e031cd43", + "metadata": {}, + "source": [ + "We generate a function $\\tau$ that acts on $z$ alone by calling the function factory:" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "id": "82918c54", + "metadata": {}, + "outputs": [], + "source": [ + "phi = 0.2, 0.5, 0.3\n", + "S = 0, 1, 2\n", + "tau = tau_factory(S, phi)" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "id": "03540fd8", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "0" + ] + }, + "execution_count": 8, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "tau(0.1) # Should be 0" + ] + }, + { + "cell_type": "markdown", + "id": "afbd06eb", + "metadata": {}, + "source": [ + "All of these functions work as expected. To illustrate, here $\\tau$ is used to generate draws from a given distribution $\\phi$." + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "id": "e933c432", + "metadata": {}, + "outputs": [], + "source": [ + "size = 100_000\n", + "\n", + "draws = np.empty(size)\n", + "for j in range(size):\n", + " W = np.random.uniform()\n", + " draws[j] = tau(W)\n", + " \n", + "# Compute fraction of draws with each possible value\n", + "frequency = [np.mean(draws==j) for j in S]\n", + " " + ] + }, + { + "cell_type": "markdown", + "id": "0f5ac849", + "metadata": {}, + "source": [ + "Let's check that the empirical frequency approximately coincides with the probabilities in $\\phi$." + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "id": "6c644bed", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "filenames": { + "image/png": "/home/john/gh_synced/books/sed2/edtc-code/code_book/_build/jupyter_execute/ch2_21_0.png" + }, + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "fig, ax = plt.subplots()\n", + "\n", + "ax.bar(S, frequency, \n", + " edgecolor='k',\n", + " facecolor='b',\n", + " alpha=0.25, \n", + " label=\"histogram\")\n", + "\n", + "ax.stem(S, phi, label='$\\\\phi$')\n", + "\n", + "ax.legend()\n", + "\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "id": "ab473117", + "metadata": {}, + "source": [ + "## Object Oriented Programming" + ] + }, + { + "cell_type": "markdown", + "id": "ce6c34a4", + "metadata": {}, + "source": [ + "Here's a class that implements the function $\\tau$ as a method, as well as a method to generate draws from $\\phi$." + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "id": "77a4a1d0", + "metadata": {}, + "outputs": [], + "source": [ + "class Tau:\n", + " \n", + " def __init__(self, S, phi):\n", + " self.S = S\n", + " self.Φ = np.cumsum(phi)\n", + " \n", + " def tau(self, z):\n", + " i = np.searchsorted(self.Φ, z)\n", + " return self.S[i]\n", + " \n", + " def draw(self):\n", + " W = np.random.uniform()\n", + " return self.tau(W)" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "id": "39ad665b", + "metadata": {}, + "outputs": [], + "source": [ + "tau = Tau(S, phi)" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "id": "e5049f6c", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "0\n", + "1\n", + "1\n", + "1\n", + "1\n" + ] + } + ], + "source": [ + "for i in range(5):\n", + " print(tau.draw())" + ] + } + ], + "metadata": { + "jupytext": { + "cell_metadata_filter": "-all", + "formats": "md:myst", + "text_representation": { + "extension": ".md", + "format_name": "myst", + "format_version": 0.13, + "jupytext_version": "1.10.3" + } + }, + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.8.5" + }, + "source_map": [ + 14, + 18, + 22, + 25, + 29, + 33, + 35, + 39, + 60, + 64, + 68, + 80, + 84, + 88, + 92, + 101, + 105, + 111, + 113, + 117, + 129, + 133, + 147, + 151, + 155, + 171, + 175 + ] + }, + "nbformat": 4, + "nbformat_minor": 5 +} \ No newline at end of file diff --git a/code_book/ch2.md b/_sources/ch2.md similarity index 100% rename from code_book/ch2.md rename to _sources/ch2.md diff --git a/_sources/ch3.ipynb b/_sources/ch3.ipynb new file mode 100644 index 0000000..aed2fab --- /dev/null +++ b/_sources/ch3.ipynb @@ -0,0 +1,48 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "id": "6db4b1f2", + "metadata": {}, + "source": [ + "# Chapter 3 Code\n", + "\n", + "No code used in this chapter." + ] + } + ], + "metadata": { + "jupytext": { + "cell_metadata_filter": "-all", + "formats": "md:myst", + "text_representation": { + "extension": ".md", + "format_name": "myst", + "format_version": 0.13, + "jupytext_version": "1.10.3" + } + }, + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.8.5" + }, + "source_map": [ + 14 + ] + }, + "nbformat": 4, + "nbformat_minor": 5 +} \ No newline at end of file diff --git a/code_book/ch3.md b/_sources/ch3.md similarity index 100% rename from code_book/ch3.md rename to _sources/ch3.md diff --git a/_sources/ch4.ipynb b/_sources/ch4.ipynb new file mode 100644 index 0000000..781e5f7 --- /dev/null +++ b/_sources/ch4.ipynb @@ -0,0 +1,1683 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "id": "c22d6206", + "metadata": {}, + "source": [ + "# Chapter 4 Code\n", + "\n", + "Let's start with some imports." + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "id": "947e0f53", + "metadata": {}, + "outputs": [], + "source": [ + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "from numba import jit\n", + "from quantecon import MarkovChain" + ] + }, + { + "cell_type": "markdown", + "id": "7d641af9", + "metadata": {}, + "source": [ + "## Introduction to Dynamics\n", + "\n", + "Here's the code that generated figure 4.1." + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "id": "15c9f41c", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "filenames": { + "image/png": "/home/john/gh_synced/books/sed2/edtc-code/code_book/_build/jupyter_execute/ch4_3_0.png" + }, + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "def draw_arrow(x, y, xp, yp, ax):\n", + " \"\"\"\n", + " Draw an arrow from (x, y) to (xp, yp).\n", + " \"\"\"\n", + " v1, v2 = xp - x, yp - y\n", + " eps = 1.0\n", + " nrm = np.sqrt(v1**2 + v2**2)\n", + " scale = 1.0\n", + " ax.arrow(x, y, scale * v1, scale * v2,\n", + " antialiased=True, \n", + " alpha=0.5,\n", + " head_length=0.025*(xmax - xmin), \n", + " head_width=0.012*(xmax - xmin),\n", + " fill=False)\n", + "\n", + "xmin, xmax = -10.0, 10.0\n", + "ymin, ymax = -5.0, 5.0\n", + "\n", + "A1 = np.asarray([[0.55, -0.6],\n", + " [0.5, 0.4]])\n", + "\n", + "def f(x, y): \n", + " return A1 @ (x, y)\n", + "\n", + "xgrid = np.linspace(xmin * 0.95, xmax * 0.95, 10)\n", + "ygrid = np.linspace(ymin * 0.95, ymax * 0.95, 10)\n", + "\n", + "fig, ax = plt.subplots()\n", + "\n", + "#ax.set_xlim(xmin, xmax)\n", + "#ax.set_ylim(ymin, ymax)\n", + "\n", + "ax.set_xticks((0,))\n", + "ax.set_yticks((0,))\n", + "ax.grid()\n", + "\n", + "for x in xgrid:\n", + " for y in ygrid:\n", + " xp, yp = f(x, y)\n", + " draw_arrow(x, y, xp, yp, ax)\n", + "\n", + "#plt.savefig(\"sdsdiagram.pdf\") # Uncomment to save figure\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "id": "ae3d898a", + "metadata": {}, + "source": [ + "And here's the code that generated figure 4.2." + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "id": "3967fcf7", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "filenames": { + "image/png": "/home/john/gh_synced/books/sed2/edtc-code/code_book/_build/jupyter_execute/ch4_5_0.png" + }, + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "def draw_trajectory(x, y, ax, n=10):\n", + " \"\"\"\n", + " Draw the trajectory of length n starting from (x, y).\n", + " \"\"\"\n", + " for i in range(n):\n", + " x_new, y_new = f(x, y)\n", + " draw_arrow(x, y, x_new, y_new, ax)\n", + " x, y = x_new, y_new\n", + " \n", + "xgrid = np.linspace(xmin * 0.95, xmax * 0.95, 3)\n", + "ygrid = np.linspace(ymin * 0.95, ymax * 0.95, 3)\n", + "\n", + "fig, ax = plt.subplots()\n", + "\n", + "#ax.set_xlim(xmin, xmax)\n", + "#ax.set_ylim(ymin, ymax)\n", + "\n", + "ax.set_xticks((0,))\n", + "ax.set_yticks((0,))\n", + "ax.grid()\n", + "\n", + "for x in xgrid:\n", + " for y in ygrid:\n", + " draw_trajectory(x, y, ax)\n", + "\n", + "#plt.savefig(\"sdsstable.pdf\") # Uncomment to save figure\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "id": "51244aa9", + "metadata": {}, + "source": [ + "## Chaotic Dynamics\n", + "\n", + "Just for fun, here's a little class that allows us to simulate trajectories\n", + "from a specified dynamical system:" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "id": "03ecb1d9", + "metadata": {}, + "outputs": [], + "source": [ + "class DS:\n", + "\n", + " def __init__(self, h=None, x=None):\n", + " \"\"\"Parameters: h is a function and x is an \n", + " element of S representing the current state.\"\"\"\n", + " self.h, self.x = h, x\n", + "\n", + " def update(self):\n", + " \"Update the state of the system by applying h.\"\n", + " self.x = self.h(self.x)\n", + "\n", + " def trajectory(self, n):\n", + " \"\"\"Generate a trajectory of length n, starting \n", + " at the current state.\"\"\"\n", + " traj = []\n", + " for i in range(n):\n", + " traj.append(self.x)\n", + " self.update()\n", + " return traj" + ] + }, + { + "cell_type": "markdown", + "id": "056d7bed", + "metadata": {}, + "source": [ + "As in the textbook, let's plot a trajectory starting from 0.11." + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "id": "d62bb435", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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p55+UFQtl1eeBRu+572h99vUrQrkIzllLJOTisopl+8M2TtdePiWWc+rSNGL1L1L2tEKXqEGbQJW4JmxDn0wUrhhfAEP72h8dM0QRpkzdqWLa5aAlzTSNjZ9mBYTt9DwEk8lMf56YmT2sOFfYn3f96b2479hp9X3+1X1P4yt/4o9welKy53ffNwi9/5nyOfS8gZp37vHfS/7ZJVZpCt0lUFUR5ZxKLMp1Kvahfwkq+uvu5G9aKRkSZpgT5bLo6o2a7GmFLqMENOWsKanHT2zjD+5saoXTBJWTbhqNctmp+dZ/zU5T7zXkl6NkteJH0SgThafv+01KtOzWpt86zVBlOtzIauNtb00r/PSH7sZ/+tzjKod+/1On8cTJCZ49M1UtgRgXLaVPAedmUsrr5+XQq9o5Rf/ii0/hkw89mwQR24wGq8QaI8nj0NN9onvHkDU9b/8pWenNfxk0KUlOHHq54tDTIhebtqNqSurXP/4l/Pe/9ilYa53nXCyqmIKZNwsyJ4Z4CEeaoly0RTYEoauZtsHGFp/s82x6PKrokw89i3/ZOuMIUQYcfuamMWOQVG78vEyENmeq2qqhhbXNK2bVR3MN3fh2GuVSsY3op/7TF/CuP703OY4T5uiL0R0pFJtHM7oG43QbvHb4VLjv2Gm8+ef/Aie2Zv3+loGKdBAFmhWHnr9BzCt7W6ELpcK5425XV14KDT6f4AHlMtN3053Xcsm5Jl9ZpCJQ+Fc5aEnypfzf4UKePxRQE6K4yrrGn37hSfzrv3jAC7OTbcUWrxRPYXSZxdTPmoEC/hun+LXEo9z64X2b/9AFvtM45opRRbOq9mrma/NoMgsVepxD1xB6/pzXrpNta2v5rsdO4vajJ3D02c3o+pm/HnoeJVbXTbnqPm48x4+1U9njiUX+ZOMFk6wFjNEXPr8+5lyLRZHMi5KGcOhZCD2hULWJM4xDD/sUUCFZHPp8CN2Z9zZqZi8Coc+8DSMcK06tSGvHT+XSpY9SGZp1vNNaLpVnkTZjm1K6k7Lyrud/SaaJfIgca7ZU3k/3nXjHsSgsaid+puicNGnmRtCFJPci9Pjmtyg5LxA6TZgZ4026xatksvEFG0t+oIla1hZffOIUbvrR38fDz2zuwGOegVYGKMKUx9wlYFj2WX/bWu0KN1a+VtKU///9R/fgd25/dE6E7vrM7xk3o/OUYcnmhIziqSLv31MSERpqGIeuX5szl+ra4jc+8SVMmYNyHn1OceSkP6u6Ue4ppbs9c5FHMRptmkCdqYqc3TV1uGZJZC0YjTrhc6XPgT5UcsFbbvTK6oCLHgkQOtvtJfJWeWFW9yUW5VJbi6PPbmFa1Xj0+NbcHHoMUd5x9ARe8S/+AE+fngxC/6ndXjPlc5RsV0pB2QiCY72UBf7/ffIo/uDzT8wVh+42ULcwZwxBxiyEfsolRICdBcDev4fAmYWgOQ1jcduxe8euzXnfn33kBH7kN+/AR+97au65B4TRLJW13klOMYRO/XQ0la5056ZchFXtfSesQG28OnrMszb8hoasq+1ZhbseOyl+l/4NzV1r0+9mpgCtRcueVuhusdP/cweLfw1/Kc7krqOTjtdy4QpmbsolouQeePoMnt2c4YmTkyyem/pE16Sq3OlnisYb1+JuYxyrplDr2npHAA5xQk045cI26th4xzZiKdxq6+ZE5VCd6gjuykXUqrWTQuhVbfHPfutzuP/Y6WQkEO9H6hlOthUoJ7NqbuuQ+gX4CjA1voB7J2XtUzVcZmX8XQ+h+bTr4olF+nM5Z7Z+j5w1+/5PPYK/9fN/gc1pmW0xc1ovZbmtqi32CA2Mo1wUNKa8FHrhMZMa8MMW6cWmNgBNPnTn4/jef/2fm3tFkhRoEvLEhFwTL3atpiiyELqiJGPFyDSevqwtZlUdfdaUcITuolD6zehehK7MCcel6wjcV3r+b4GWFoo83GMntvArH3sIf/7Fp3rfZ844bU5LADsDE0BIV9TWenNOQ5ceqCEAEfM1sc/f/u8/hV/4s3uzyueWHk3qPqdzcenf/Bm0PIlm3unjM4QCPLk9w6yy2JpWWZQR4K/H2Lyovbm2PIW+p52iMiGhVHZKzalHSDTFu6kIvaxVFBuT2x58plvYscVYKhOyr+2pwgtz0czgHKesmuauUBLetbU/5tMEjRWTurbMyes23BkfN4G6chcHt9okSq1iYYuewvetJuKiY9bHmUlDU/gKRu9bjoIe0l5KeOQO/T8HK4ALJKD78bVTRRF6aFV+4oFnYK3FDZccjD7fX933NJ7dnOKFzzncfaZx482//WeQDmr627f55yhSje7LqRXvnkG/ZubNw95uzC17G6GLCc4HjT7TFoGG0IM4dO6kYwt8yOQ4PSF0VUdD1GihTAdQFZ7zV7lWC1vMaVszWTmPOatqPH164iXreONqG8plaJiY3KAqhtD7inP1j5WvsJrnaxcts7g0v0HJkGmHEns2q9OTWfdMfQo7J2zRIXQOJoZrdLlWSJlz5cj7OeGoM2KpAHq01elJiWkZ57QB4N989AH87B/eE41yUX0fSns6Herfyzn7g24EwhH/PBZzDKGnonkWKXtaocsJU3qL11/w/iTg3KD+0vhEpeuHvGQAOLXdLMatqTv1KDQH0fU9VxH2TaAYHdLXtrZZ1Wwcf/VjD+EbfvbDKrUFNAt/6BgBQnnUtYfItMQwr1+RW/zvv38X3v5rn1IXEkd1WvtuY3NKVFp8tdUV62lC1KVFH6WShdCnhNBtFuceE4luq9p/V4A/lyazyvtt7MStID2/tticVpgy6k17R1VtMS1rEZkWttt87vddAyrc2o7HofePG43TdE6LOUqv8Xk4j4mVKXtaocvzJr0QNWFea6Vky9olVoSUS9Vd21EAPXG7Ugihb7HFEZ5IPnyzmCnPCQCPHt/C9sxxf3q1xXjb2ubH0epTpyd4dnPmbVByXPkY5eodb4Oq2YZbxS2iPkfXHUdP4K7HT6pWG58byfmhoD4f0Yb3Pd1u4tOq6lUkOTTYmQlH6PlzT0pAQda+U7Tph7t+Ivw08vf0725c2h93VmnpLDXt+cpWoccsBF8B+veIR7noG8iQcZvHp5WymB89voW/+OJTQun392Ne2dMKXZrLM2WxadwfR/QxBc1T6+dF6LS4Nz2Erj+D70zMn0B0qbUWb/q5P8e/+eiD3SkymqMv6aDSaBS2kOn70y0NEFxr50Xobnw8J3RCiWlojcuJrZmX6SifBWgAQCqs1Xea+gCBX8fFKeA05dDcv1/REIeeCsvLES0Gf8aUoGx3O0Do4b35RmyFQp/2bEC1tR6K520Akj6lPocKm/s7YnWZhtCk3dwr4xuEFB+Q+Bff+pH78fd/7ZO+L+dcUy7GmDcYY+42xtxrjHmn8v2FxpjfMcbcboy50xjz/YvvaigyM6yswsmhldR0YWvDolzKAWYYwBB6knJp/n/aExPMZaJMoFOTEsc3Zzh2auIQuqJ80mGL7TWR31E43+akDL6nf8+jeOSC0KJQ+kLapJzYmmEiTHqplKm/zb/dbzWFriFU7d6nSKGVaYXWJOv0jxNx6FxBzqMP5GHXDTr3a3jzfgYcOhu7E1sz3P7wcd/30f6TQMyscrXUY5FYU4bi5f01qsy9KxtcV3oUj77Gcuaj6tPaAYf+9JkpzkyrLrwztx/zSq9CN8aMALwLwBsB3Azgu4wxN4vL3g7g89balwH4OgA/Y4xZX3BfA3ElPQnRMeUidnWNFy4TKIJHufD2h6QRn+oQuo5oqX2gNVGzTbzwOY+faZxxW7NK59CrfrSRcjo1oWs+CuPXkqOUO+9yTcuJWBBu4cYXVa1s1FwahV6pCsNDdaz/JE7hh/ND2yS5cIokhQx9lKk/A8A59LjCyhGJ0Mu69vw2sl35TiqmTH/1Yw/hO/7VX3k8u5sbrVO4rFGxsMWQarRe9qu8fyrc1AtbZNZ5bC3nIu2mX83fvvcHAH9295P447ueSEa5HN+coqottss47bpIyUHorwJwr7X2fmvtFMB7AbxZXGMBHDbNacWHADwDoMSSRdZHLjW+VHGeeVEMkZemxqF7ERw5Cr2Z3JspDp31PReha5zds5tTAI0zq0NGHMkMQehW+8yN1abHocP7DY8cab7vH6cYQueUgGwmpdyq2uLUdtnW8w5Nd4fqdJTMN/BYPRFAN51PT8KoFO19pqoMcqENQuPzhwinHq1tuO9Z7VNSlikjT1l7RcwsNqclpmWNk9tsYydLcdtZFKks0KqlXGYRZehRLiJs0Z+fLiIqFoE0D0LfnlXRsr4kt37kfvzcn9ybROi0LkkXNPfo7cbckqPQrwbwMPv/o+1nXH4ewJcBeBTAHQB+2FobdNsY84PGmNuMMbcdO3Zszi47kS9K8ySnUKfvSPG/5/w8N8H7oitIrLV5lEvb52nCAShlplAuz7QTZ7us1NjgrFouCadTVbt/awi9y74tZShc8lEAhBQSd3RJVM2viz0PLZ5pWWOqmLp6ZIT7Padk5H0qRfFzOc0ol5zSsrF2SDTEP19ikbuXZnXJdrfZO5HUE/XjxBZXUv7cmFVx9E1tAvG1oSJ0dS27+8dqpQyhSWk8uA8h5QPZmpZJp+izreV8ajtcM8uQHIWuFZaTPfomAJ8BcBWAlwP4eWPMBcGPrL3VWnuLtfaWyy67bGBXQ5GcbyrUSTOVZ7UrSs93TS8Tk01mv0BS+qVszaqubW/Sim3OOWHyObuJ4jE/Tgp9psdW56C7VGIRjwg6o3DovCzr0JhbidCpTX9RxfoatscVjUd3iWiJaD10hcPvFEei3CvAOeQ0ovaVXfi9678LW4xFZOWIl1DELaAY5TLzHdV8rVE/TmxNg992UT5BBIvfH0LCZxRrr+mbYlmpCp0CFmygD3j/5e9iQtduJeYeSVnXODOpkk7R4x1CD62ZZUiOQj8K4Fr2/9egQeJcvh/A+20j9wJ4AMCLFtPFuMgFoy0SbXfuYk0jKfRTgU54mKNUYDE5zV7gpsI1yvs2ijCP65sp/SYksD2rOk6PFr6fCBRvvFaezZ2y4saNK3TbjXMYCdR3PxIe5cKpHRk6xyX1PFyhn1EQoJqHwPrsMklDM17bJLmcmYSUQ+pUp9gzuP4rCH0Ok51vZvzesazjmNXUlOANEXqn0HmUT2Jjp9tuTXXkqq3llDXFKZd43aH+uUjXbk37KbHKNoo/NobTsu7mn2/V9nZjbslR6J8AcKMx5obW0fkWAB8Q13wJwNcDgDHmCgAvBHD/IjuqiRaGRiIRusaR8knLX9qkqrxrPU41c3KcYi+QT9pYSFUqyUmKVgzIIfQq2BhyKRAdobdtMEVAyTP82oqPEbtJDpiMbaCeoo+hLuWBPIWu0EPcTNeP3WNoVlIuiXKvgHvvPoceXudHZPnfTcoKv/Tn92NW1ZE49PkROkfbzb30fkzEO/FOcWr/fXKLW2rN31MMoWvF8tz1IUL3snUHrmX/Xcl7he84Jt0xhRmUS1U370da9CS0JgEf4J1TysVaWwJ4B4APAbgLwH+w1t5pjHmbMeZt7WX/EsBrjDF3APhjAD9irX1qWZ0mkYttlsmhk8KImfR0WhHgI5IhyR0eQk/Eoet0TrrtaRUugmc45SLCu3KdlPpYEUJ346BF7fi8dFrpSZmIBVF37yeklly/4u8hrtCpr86a0M34UEm43yK47slT23jFv/gDfOLBZzwFnDz3NYHQP/HAs/jx37sLH3/gGWxOHOUyJKlNCleKnkKPKC65mfJxUjl0gdClUzTGoW9OdLCjgZaUNUVRO/q9wki3mOTQfV27lcWkrL1r+ab07KYbH+4UXaZCzyrOZa39IIAPis/ezf79KIDXL7Zr/SJLm6pRLoqZSgMaM+llfK2BU+i5HDo3sVK7vUO2AzLTuKOv/Q1Nnu3SmYBaZMbQKJdaQbOaU5Qj9FkPzyxFcpD6hhtB6D2Ui+7AdX12oXBh21z5aXOMvrvtwWfx7OYMdxw94TlF6dljkTiuX/53xB8fOzXxKJeUI7hPOP3B57e/Btz1fDOVvgSaB8eZwuoSizhCT6TEUxsxsKOhe+dDYO0wf4gMbyQZgtD7nLVau3wcqtrizkdP4OFnNnHkgIvcPqXMw2XIns4UdSU9m7+p8rmaB30S2YV9BVMLJ1peLDB3gmxlIvRcha6lER/vwhYZUlEQempSpxA6P75MpTEi/OtQDp1HEsUosVhxMJIoQhdWG4+MUJ3myiarAYPPHj0BAHjy1IRx6OkSCJrTj4R+d/TZTeYLWkwcOuDPb2/T9KgY4RRl6yknyqVpu9/C8nwcHHlriUV1ONfoupQFMyQ6iPrgl+vQr+1yQLgvoQZ++aMP4n9832c9yoXrg2WGLe7p8rnyyLRU+VzNpI5y6KK2iDH9k0YKn9ibkdongFOY22W/iUeiedWfYU7RWZJDz0foFK8MwIv20RYhH3uuJMLg1VDkBtBtuJEx4f/W0Kqv0MM2eJSTtkHrYYv0XTj2nz16HADw5MntbuHOyhpF4Z5Jihf/HUGUDz292X02LV1yzzyUC78fBz5RDp0p41lVs5hsxqFvhwqdf5aa9100SSTpTqtXpCFwt87jFsw8CH0zstFo7XoI3TbJdacmJe47dqb7/Gxx6HtcodNf2sHDyakmIxACjKATGf3Cs8dyUTTnzLYSk4Pa5mhmSC0X6gehgS2WWKTRBKmmpaORKwFuduu8tI7uhnLoftiijmJT51AC7pQfwN9Y5UEJPKXd3zAcIizFWMjwxrq2uOORBqE/emKre5ZZVWNkTbSPKaupU+jPOIW+8zh0fX7HrCn+eYwSS0W5AP7GLiOCNHCgZes2n/ufaWs5VTt/SC2XoRw64Idv8vH59JeOd59r83AZsscVuo9ENcoltav76c2uXT/qogYxU/zIsr534jtFU6n/zb08nr0H1Wro5VkW5UJhjVKBNW0nELoYK5l04hxZSpQLuzaHf+QSxKF3lIu+qPqidmKUS5j+rmcK8/ogMplFlhJ46JlNnNouURjggaccIptVNWw7b7QhSFlNtGE99PQZ77NYFEeOxDbc2ObLFZrccGlMTnoKvfmbP+8JoevvOF0+N1T8ZQJsDYkO0vuVj9C5BfOZh5/tPt9NmaK7VuSL0k54Tx3Hth1Jyff5Q7fApqUNFnhMTk+aRQ5Ix49cvG1fBihBaUFsTStsz2ocXB+htm5zcOGcaQUo+6I5UzlyPq3EofNrU9ypJjGEHqPE+iikE1szrI+LoK/0M630gxZfzhF695ziOqJbvuK5F+GJkxMAzak/fT6RWB1wfn9qD6Dqf/MjdI54+b0nESsojdCb/5fOQCA+72PhuprTGhD0qbSsFICSKp/Lcyn6pFPoiXId8hmOC18CtfHU6SkOrI8ArJyiWRIodM9M8xcqf5mawoglFjXccfPvIWbvqUnZeblTDhbNCdOnBKfCV0Do/DkX7mvu3aIkjQ5Jc+hx7p2bkmemIerlCzBnMXjPIwtBqWavrtC15k9ulbj88AYAfTPlAEALhfMqEkqrRYzJHUdPYGNc4DXPv7T7/ML9a61TVFcw4TPoyo7k4PrIq7syj0LwHZ6ccomE7rLPwxOlWoTOQ/FIQW/r8z62aW1GE4sSEWusLb45x8rnDhm3UrOYIz+j9k5s+uPA3+2VYk3m9mNe2dsKXSwyDfWkIjdiIVuxI9Fik1+T09slLtg3xrgwWQh9iBKUz0kK/aoj+wH45h0v09rXNq/30fy/vxFoqf8apTVkcwKUiAp1w3XXp+KbgQahk0I/o3CXPLJFozE0SkZFh9biS89s4rmXHMDV7dgDwMUH1ht/S6qWS+IZJN98pG1vSNXA1P08Dj2B0Ol8UQlwNMdh1c6P09MSFx9sFXpG2ejY2vCPDgzHXn6WigIaUsuFNoW8Wi6t5S70BR/rKy7YB2OEU3SeF5gpe1uhi2I8qSgXf8E2f2P8IU3ywvjIdIjj8vSkxKF9Y6yNiqywxZgDUBNZDIjS/gkNxCgM7f5+X/wFwSdmrDiXdFgB8WSVmEzLGuPWTucmfaydHMrl8sP7gr662vgtAKituuE7qqq/fG5ZW6yPC1x+wUb3+ZEDa72HfqdoMInQL9y/5hU9m+tM0YgF6id1uesnswoH1kbB9bJ0gPutxWZbofDiFqGngIyq0Nn9U6ePNe35301LXsjN79tcCD2xZmW78jP++UUH1rExLjyQUw1/fdmytxW6ROjqKSfWu7b5jBRGJGSrnUwH1seeEyjH801yervEoY0x1sXLjE3sIW3LBeYol/3BtbXtjwqRfekWhqAh1M1HQa45adNcJmWN/S3XyKOKYiF1qQ2qri1Obs9wWYvQNVpNC0uslfa1E3nkZlLWFqOi6DYQoFnEffRc6p1IBHfkwJpXlnguhB4JVYyCmrLGgY0mZmIqAISq0K1DoR1CT1CN9PxxykVT3qGS795VpJ5K7kEi7rdQ+h5B6KyPoxaQWLHejhxYw752Y+xrbxGytxW6UNb+IdHN31Rqt0w5J6GFvH995JlQOWYYyalJicP71rA2KrxJG4/HHeAUrerO6VfVtgtZvOrCfcG1PK67+f94uxIBeghdFN2S7cWcojlzd1rW2N9Oep68NVE2DnkvOZ6nJiWsRUe5cAnCFpn1pTlFpwpK9BF6o2TGhcEVDKFfdHC9zZjVKYDwGfzvJEI/cmANk5kfCz5U+PN5TtFEHPrBdpOVlRdl/8aFQWVtd7jFRT2UC89viDnQdcoF7Fr/fcQCHHibORthpSJ0/Yf8831sPUqEvm88iv5u0XJeKHSngJRkBJVyIYWedgjtXxuhYinFQ6I3Tk9mOLwxxsa4SP5OKwbU975nle0mUG1tl/Z/RUyhJxSg1hdp+TSfRUxMZeyHI/SqiwbgYV+xZCsPvYnIBQql4xSIbIM/B23eWhSN9t6CUM7KYlQYXHRgvaONCKGSktHmik9nyU3e3bcwwKGN8SD/jSbaM/M+0vOQNO+kQegTD/36ba2PCowKg7q2nePvEgWhaxaQFD90VNtMw81HB2euzdyDRNx9w/UYG2/+DsnCJABIPpUGoftqdhW2GBGZ9KHFoasHWCgKWkuN3r828o5EG+K4PL1NHLpfTj6PculB6GXVmXF1bTEpK4wLg0MbLq1gPYIYkpSLKCYlw8NKqT3hxoF/NYQ+AhokvL9VHtwRGSt6lCr+RTHoRw6sR8fe4/vLUOlq1R5jMf1VbTEuDIrCdDTPkQNrANx8VE+9T5SW5f07uB76YeYx2T2FHq3l4ltZBzdCDl1SLmsjg1FhUNXuQBdC6FxidIp/jfu3euC7h7b99Z3nb1Fvq/azD5TUtfWAF1+PVW3xgssP4Z+8/ia86SVXdt/RfFwh9IjI0qdaSVINlWkI3QqFPi4M1sbGm8C5StfaBq0Qh+71WZrXXZr7EKeo7SZJZdHyuMYz7TY6BK+HgGkSxKGLTVD7rVxYwLDNCWjMe0Lo3KSPx6Hz+4u22ne6b22EDWHqSquN30NTAlq9fN9qsd3YA8DlF+zDxrjonImxPgLp7F3aWI0BDmyMGoU+cEylxBB6PMrFIfSUU3RtXGBkjMehX6IodO1MXyl+HLo29spnlvo7X0SUFM2Rrf1MbkpuPTYAcG1k8I7X3YirjuzHRvsdzcdVlEtEpAKatQMJ+OFMgH7ARSrteaOdqJXlmYu6WSdl0pbCPbjRoCsusTNFufS971nlOOe6bmp8rI0Kz7TjkycXocsQxDCiw3/o9VGhbpga/5mSaeUUel2z4lwZqf9BDHd773Fhuk2NNlXpV+H3sDZE4VomsaRKCKEDDW9/eN8Ya8EmHo5B6p3QPS49tNHOIeNzwXOY7Px+eXHoOkKXHPraqIAxzTNQ8gxZKFxiSta/xkfxHaKlteyVx6b+hAjd2/wHVv7U/UT9n9F6rNr5S5s84Pj1dQayliV7OvVfKqBZVWN9VGBWVe47EarGTaVJhNuelo3TsWhNydS9NSGn0/qoUBC6UOhK+31KcFLWnfLmKJF70zcYx67VxdBERlEE9AJbHKPCoCigRrlwyZm8k1mN/ReMuj50Tuis1H99PEdMoW+MiracrQ1+IxXayLhNVttQanFvinIBgL/50itxw6UHg01cG5v0aT7N+7zs0AZGhQnaWyRC1yKWgDbKZT0W5eL+f31UdOGd9EyH94VqpY4oWaCxRJoN1X3mr+WwDQc62ueIgLNc/1HXt0yFLjelDmC1c2JcuHe2r0Pobk0uS84LhM7jVOUuKDl0joi3IyFbpNBHxgQcNEnqnXClEi5G/RlS10iZVXWHwDlK9BT6mhuHKqE8tH6n6AWScWFQGKNe6z9LHkLftzaCaeP+9Q1XX6Sx8VwbGWfqrok5EQnhk8+iUXIyNp+iXADgzS+/Gv/zm74M64FVFj5z3zOMCoOvvvFS/LXrL8Y4o70+8XxEVT9C355VLMrFXc83XKBBnaM2yoXWmgzTA3yrQlqltEZ8yoWv5XDsJQ0T89vkWqfa9Vp73XViU6I51swJgdDb77g1syzZswidI223UEnRzYLFKSszAok49LLCxnjUOXu04U+9FJp445FDiUCjBPtijvvaBhqFfnjfWttvjtDdvdZHOkJPbRYuasj/f/o379e4MDDGUQEadQTk0QOTWdVtoFzZbJd65I9EydozjIrCUS40FrWvBIC0QtfKFEuuvawtRsL52meV8T6MChMgx9o2G/T//KYvAwD8/J98sbe9Poly6IkS0mocurXe+K+Nmo3dWofQCdkDzTwpxdyRSnNjXASHSpd1jbFQgJqDs48+zfUfues18KYhdH9icwq0ZJt883zNd+ORD4KWIXsWoXvhY+1LmCm7ugxt9LnESPncNs6bFHquGdb1jRR6UXgIfTwyvTHHTdvRppv+lTWLe202shChh2GAuf3mFg//zkPoicXmP0seQt9oKS4/mYe14y12q17DvxsXppsLwZzgikupcqmGwinonsaWL14A/jtXNnHA+RnWRiYs91r5CG+5lEuIbIlC2a9litYhhy7XCflDeN81HxbJxji8ZlZZrBWmdbhqCr3dYBXKj7czFKGrAEsBJXK+87DFqtIR+vqIrP7ebswte1ehCzoAaHbNkHLxkVUMrfJ/T8u6i6+Npjon5oanVNoJPaLJKX5YKbOlv5aL7RQ29W80Mt3iAtwi4c5MDQ36ffHHSoZ6cjOTwtU6R2MknzlH90xmzXsbF8ZTolxyzWiOfKVTtLMmBFcs29Jq/VhlTHgcOhceLrnGHMd+Py37PnwG3uYiKJdYLRd/Dfgb2b41eid++KgXhz4uULRKiu6x31PoYaieXAM65dIg9IJbgcp71wFR3uaviWxvXXk/gNM5tJnvG/tRWuMRV+gOoTf+ghVCD0Q1vyrrHA+knDolBe//pQRRLmsuYWKo45IU36gwXcSD45zjzwHEJxCXaVl3CpWKJZEThpA7Rz1OeYRokIsM2fKjCqyHbMcFLeQQ9QLoCjvphJUvk5YqGxkfoXOJc+h++3wzJVM3ZrUBukKnMdL45VSUCwnn0NdG+iZK7WyMQ4VfijbXmXIYRRB/n0gLVL2mbZdQO9GOWnEuml9ro6JxjlvnLOXhs+vjkdc2PR8XLfpjVtlOAerF4sLnks/Bf5OzruQ9mucL1yyAwAG8XyTGFSZU6AS4VpSLIirl4iF0fwdP7ej8e6BZ5J15ZPVU5xRCp5oy45FD6A3nHOd8SfqULkBOURZWWTuUuE/EvHITWUODJBov7S8MCMrFoEhQLg51pZ/FWutFFcWUjVXet9Z+yTbTgEPvnQNtG+0L0E6elyiRR7mQ8LDF9fEogtCbe6yNCrUcRAyhxxRMn8QQOheJ0Dda2lEeyVjXtvPhOBrBHQ7OLdP1DqHz5/PvryH0WVVjrfAVoJ8hnELo7LmpT6M8RRrM43H4fvh1NA7OKWqDDZlA1lrhrJllyd5V6FpWaGXZ4m2vC5B6v0LnCqasrGoi5nDRo8JgfWy6fxcK5aGhlV6EXtXOY177Tph9QWSHFShFb1NLRZdI2M8QLDynqGaq0u/6ngVolMe4MN1pS1K8ReqZ0TGEXnRjsB6x2qRYa706I/79Q4Uuo1xIOEJfjygSx6GH71uGva2N/H/Px6HrjlAuzjJp30lrpUqnaFnbDpmujZp57ZApUBSmo1rWOksxgdBH+jXOiejuTWKVz9xzhHN5bVQMOuCCJDbe9AwdQl/zo874Jr8hKJcVQldEU0CcW+7MtA5thr/jwj9uEotGnUNGerT7UJJLbim6ybrW8oGSmtA2i773PStrz3yrGGdHSszPFHWTOkYV+dxw85crAToCbd2jkHjqv7BiRlR9Lv0wHA2mELpvLRC61SislkMfccqFzGF6Fr1PMQd48xzhbzu6ayQ5dKaAx4WXtMTvNSpa2ix4BukU5fRL//zQhA9r3xhTlubaqOXQeYmMdoyozARx6DL+ej2wjvzn47KmUi4uyqUDGMopRv0cetwS0iSVPKfd44IWoe/z4tBrlUNfUS4J0Xbrsq49ZOiHNrYKPuq84wi9aszNkWnD9fxr1yNmGImLcnFx6KOCKAr/WjkhcxAYRfOMmDNq1HHoIs3YWlS0QMfxyaShXr7uZ2XzGUUwjEeFF4GgPUdz/+SjdOY/PQ/nrUmk0ktRSN13CcollQQVDb9UNi6iuwKEPg4jVGSzFGoao+HGRdgG/XunCL3PCuLUiUToFG/uEDrP13CKbI0BmabtEIDRe9mIxKGvFcZz5EuHNBCuZ7nG3L36qSrNOotZzJJD51FndQ1vQ3Zx6KuwxaiUYmEBwikqFif9U1uw48LnrbuwxXaihgg9vahKhhI5ojVGjznm0ke5WGs7yoWbuqQAyDmjZYrGIi4APYKAKwFa1AdYoSHD+ECJ0GXsd0xmDA2OCtNtHFykY7FKPI+aKbrmK9U4Co8j9FQoZ8ChCwUMKM7bNtS0ieEO7xULW0xtyimJJRYBvJa3v+GNWg5bOkXr2imy9RFlVLtNCnAIfW2sKOu2fZqrmlOUUG4RofXkEZMkEol3cz+DyqTnJn+mMRQZFr+WOHTuFJVx6ASyxisOPS6eY6yjXGoXrscWJ4UfAnqYoFTQVWU7dELhehIxJSkXhtA7hT4qGvQgY45r6yUf9dE5hJ7WWZW7WeXC3PYJyoXTCClPP5/MMhkLYAq9NbXHbeq/zKDsuFPFGaZJKdDgRJnta0UhuGt3r3gtl8Jlio7cnOC/J6Gx4/SUFI2zzYlDj9XvIOVXKAi9DMIW8+deTGL5F02b/rsiQDIeGYyLQj0k+tDGWtefUeE2QxoLib75I9J6PSAUOn+Xs7Y+UWH898bfVdPXEEhoCD1n3Og+xIePI++Hj1GH0Fk9/9pKhN6CoHHh0ZTLkD2r0LXQtbK2DI05RcaTO0hfsKiiQInOauaQqZsXHSrdBELnYYssymWkmFsVq5zYtJ2mc7o6MWM32flCcpSLW0g+hx7ps8c1+p8Bjho5yCgXP/XfD1lzVEN68vKsWo4GPYQqQvtSlEu3iY+0OHQd1XXH39nQAQ74G6E85lCiaX6/5rd6ydSqJoWlzAnRpu9kzeOCpXCFTlYQrQFpRXBAUhThQR+1ZQidRVvNKmetOIQePn+A0EcOfLhr6m58uOUgi+/VdeOIJZHRLDn+IzlGpNBHRZwi6Tj0/T6HPq2azdJD6ES5JNpblOxZhc6VdWVtp8C5qU8vkxxJ1jr6hCtoSXNUrXNnzDLgQqXb37e1kUs/HxV+qnx3rbVeyv7aqEhGbpPC45Odm7ouyoWFLWaEbpHu5spLRv4AbhGuCXOY1vzGmq/Qe1ERocHOvKcY6HgsdypyoQsZVRKLOOXiK119zvD7V8qY0OaaQuj9HHo4J2TYW8ihY7B4YYuVvwaCsE5m5YyFdUQWFOfQDefQixiH7voiM0o1p2jZWsUEquh3fPOhuS/Xpn+vFgBlhC3SGHWJQEWhvh8+Ri+9+kJ86yuvxi3PvQjGgAES986kU3RFuSgiFzVRES6DkjlE2IKmycEnwbgogoVKYYZlRKFncegcobcJGFqY3X7Wdl8ChOScZXJLGOVimdJMOUVd5Ig80m99VDCETpSLNId9JaFxp/rzMMqF1XJJvR8vUUqxeADi0IU/oXbPtcGVpDc/rPcb+p7TETSfusUra7kM4tDjETDd83uUy/yJRbLf+4LNlxC6o1ykpcA39lFLKVLkhsaha+GrnUJfG0evmZGfSFAu62yDpHeSsnBLLzy0f4ya9vxAhlQc+qF9Y/zsd74clxzawMiYbj6zKdC1t8oUTYhc1GW3EyuUy8iZ1BpCbxxNftsNp+ucij6KTi8qbj34YX66ee1NyHE6sWjGnrtLuWamrlaqkxCflqlKQvfkE5/6uj4uOkVLCN059JyZPmbxxzGqQQr3c/BaLim/At/MNeRL/ZNx6PyIvQ3xPqmvXQantJoYZUdzjPoaIvQQXauRLCP9nTToNLQgqL15DkgomTKkUNEu6a2rO+6uBVy5Cv5c/Jl/8ltfgu+45Zq2pIVPiaTi0DtqI8Ghd3HoDITwEFGeF5GiQ30OPQ+hyzmuInQ2z0iKwiVheXHoY4HQz7VCN8a8wRhztzHmXmPMOyPXfJ0x5jPGmDuNMR9ebDdD4ei7ti5Lbd1Dpu5lys/4aTZrAgGWlcV45MxNFaFnpNBzhD5SJgdtOkPQv0OgIg494NBd7DVXHvETzMN43ZKNMS1kF7YozGHboDPKaoxRDbGxophniR7peLcYLxrjn41xlIs0+6va+u+fOU1lSB39m/sKSFkR/SCjXMgBDvj5APK5ycoJnsHGEfr6eL449NpyhF55czMI6yRUWxQ+QmfzYFQU+I5brsXzLzuEoiCwxBG6z4/753y2inONrgkd6LSp8SigquXV6VpdoUf8LRnjRu3t86oj6qCElDIfH166wufQdZpyGdJbPtcYMwLwLgDfCOAogE8YYz5grf08u+YIgF8A8AZr7ZeMMZcvqb+d0ICujwpMK9slQ7joDv8awK9rQte50CSuMFxImabQ++LQvcSiTqmEMcfOZJRoMP7cM0aNFMZFHdCi76JcKFO0dgkfRQHYMMy77Qu3eND9lj5zCr2lXEai2mJbpCoVf6xJ2SlFHaHTRsib8ROLQgrLFShzyIibzo1CDxEwt+o2vE3W8Z5VjYC6kAid7jkpnfIPqbY67lepLTbWQ9qG/j0P5cKzqKdVjZFxdIrcfDllKDcTzW9QGIOyqlsaiTYJP9pFpVyCsEVJubg5Tr/jDlRa33Jz5mWX/Tj0PGvRIfQ4h16xNU4yKkw3Plocehfpdo4R+qsA3Gutvd9aOwXwXgBvFtd8N4D3W2u/BADW2icX281QukXdKleOJgFKqEkgdBpk4XhpjkAj/hBMoec7pviCoImtKSbtQIAUz908t5tIWhy6pFx4rZeUh52jXhlzzRcyHUvmPPbu9yNGueQ6Rb0oFxM67LTQPlKuehy6c8xtROgu6RTlfeVFs0jGHuXiUKIWkUOyHmxs4rk7p5/uV+HFnaSDdh6E5yP02lPWnMag+9O9vH4w6s1DpkVYUyiMcnF9CRSnMkYa5cKdopatb0mHWtFO83l+HPo+L8olVg+9+YwbZ4XRN3nuqyiUiquLlByFfjWAh9n/H20/43ITgIuMMX9mjPmkMeatWkPGmB80xtxmjLnt2LFj8/W4Fb6om5ApF84HtC+cUCebVPQZmVWF8ZGzH7LlinPtG/uILUfprnmJReHuTJvI/gS9IIUjAAqD5OFilx3ewL61AgfbeHFrncURQxt+n0O0SmgT8BE6T2OuLXHoxFvncegyokI6t7WNKFXYykPoHBkVHGVbD4FzhUb3Cc34VqnYfg4dcNxxzDnsc+jyOz8xRcah51SwlFLW/mle48JgrYhTUkCL0EW0jbaJkZLiHLejc5pxlhYw4Ob9mqI4Zy3a9ygXa7217PxhPkL3cxbcXMkFFx7dFwFBHFiR8KxaNQ69B1QtQnIUejhbEcyoMYCvAPBfAfgmAP/MGHNT8CNrb7XW3mKtveWyyy4b3FkunPPloXmuyqAfEtd8Fjq9KKFFTuZxy+mWStRFbmKRzqHHJ7aG4oO22cEIWpTLt73yGnzoH/z1zpzlsdIxtMGfm4eQcT65c4p6fKC/EXIFkB+H7iIqONrh6FpuRBxBanSFQ+h+X2OUS6fQagTzqHl+Via4pUoKA9W8dm3GKQegcW6PisKzDrvnSxxwsZPEIo70i8IEaJr6OGObbCzKRSL0zldT+M8tHdLUF8BRLt04CD+WRrnQWq4ZYOMObBmCPF8culizir+MW+F8HLpNnm3CB9dH+NZXXo3XvOASD1gsQ3KOoDsK4Fr2/9cAeFS55ilr7RkAZ4wxHwHwMgD3LKSXiri4adOhUMCfnDKmmJtptGClouVxzCOmSLxJ0zM5+O7tTO9QMUm+NpWZRsI3C36wAIXOrY8LPPeSg3j6zNSNQ9Uf5eLGikURkA+COcOIcpH8Yt0qdOczyKRcRKYoScrsrWrb+j5CM5pbKxuedcSjJWqVQ+dthVEu7t5UVIs2OVmcC2BheyIG3j0DWU1x9N7d36u8mD6kJCZVbb2yvjwiSfL8FdtkpVP09KTsfk9CviYenUP30svnEuVC1p6byyR0BJ3/3vw8Ey3AYSx8UC54op+q0iiXWHVE+kyOgxaHbozBz37ny9trzn3Y4icA3GiMucEYsw7gLQA+IK75bQBfY4wZG2MOAPhKAHcttqu+SITelSMtXKynQ50h5RLjaCumYApFwdA905miLA5d3EcL39onEUESobPEosLFmUuzn8LNiGMfJTz2AHeAMqeTEod+wFuEfur/yHCnaCblwjY/P9QrPiaEBJvn8dvjY+HKLsgyrMJMZ/SQxqF7lAvzR2iLl/8mNQ58kw2VvV8fZk0U+5oXoW9EEDp/50BYnIskhtBpXvGSBdKHoIYt8qJVhbvGtjQi99NQoT1vLQtru7lviPSpH/1z0bdCXWSYci3LdyDhpSs0Go6uWSbl0ovQrbWlMeYdAD4EYATgPdbaO40xb2u/f7e19i5jzH8C8FkANYBfstZ+bmm9Bo/KKDoUCriUdB6CpoctksLwkSYh9NGo8GJw9wkFkEO58EL/DiW662SqsYwc0YTHuLvyvmH6OTmz6tqFyKU49FKMVWP1MIROtVy6TFGfQ6dNQ1Iu/bwlQ4PsETa8gkZhlISjp4SirLUoF990L+s6QODUV5mMBsBLLOIIfZLg0Pucog2P33zHD9IAGtCx+GqLDYfegJ2mz2M2N3kfkxx6zClaU76Gv5lqESw0rwgcSMqF054daLH9a1kbH5mzYK2FMbqylUmHozYyTL4fOUYkfJMvIvcwxiBS8HUhkkO5wFr7QQAfFJ+9W/z/TwP46cV1LS3dzktx6J5iMN7idBypRWhW+WZQ95vCeBmA3JMuMxel8IQmHyXqE3vfAA59xtouFA6dhACeH+USN/d4iCLgHIQU1skV3YX713Dh/rUu5ZueeVwUzhmYyaHzhaGFehUFVA59ZEy32GV79AzXXXwAf/2my/Cya454h4vUtYhiKTQloXPorqiWXneGJAjfFBp9VlscKIq2ZGuI3r04dEF79CkmTcraYn8LAkrr+zukA7tkCpUshcIIjpgrssJFW8UQOueh6T6xMhJ+5JPx3gtX6HL9UJ/lXOG/s9av4+SPkZIDEXFiaolFvHRFDKEvm3LJUui7UbosxtYx1in4wqHcKlBSYRx6wK8yU8pD6GsUFRMvqUnCaQR+SHSMQ9/nhVD2cOidSVcIhO6b/YQQqH5NanLyPssFI83uUWHw229/LS47vIE//+IxD9UVptkIZTspmbH3xu8TIHQ2cDx5qBKKkiP0/esj/Lv/9lXdeDiF0dTNJ7TaKbRazyQeF85nUtt2MzEuxFKPQzdeOxqHvlYYzGodvfO5Z0zDd88qt1mlFJMmtXWWRefADmiRdnzYc5FxQGGyGs1EAIpoJN6mWj63IoSuc9VdeQtmVYZr2RVSS9f9oazYdtx6xghwVFAqMoyuDZyiZMEofhUAXUnuZUkOh74rRcZNl8xBxcOo6BpApnYLp2gdtqsmB0Sy+7hw1OkfEh3j0Puru8nnpkQcQuhrYgJR32kx9PHzgUlbo61k529sI2Nw/aUHcXBjLFL/mzAzF67mKJ+U8BOGtPHWwxZtR60FilKkzZN4fpLaoih0eoj6G63lUjGnaCoOPXAO6yhcQ2zcyU3SORszN0oppGyprxyhcwuF7g+gK59L149MJOXdgFmKPtWilc+VVCOdtWnZGNP9R4XxDij3IpJUa0pH6OOMcaP77veyoSNx6EpiUWFcJcs4Qj/3YYu7UqQJNu2chS4MUTr6tF1dogPu0IxHXeTFinsc+igMzepi4pmJl+K5m/65Z+ILKeTQ3TgR0k7x81oSVlcDhpv/I76Q/WqLGurLdYqSA4yki0IyWrhnqpZ4OBaAT9sQRaUpyQ6hi0xRHm9Pc2PGrCUpfRmzXeKMmikaOrlpw6bPh4K82vqb88holEvbNyVsUa4HjzvuOPS624hcLZfQKdzVHV/3I5mCSLORA0/JJEEvCSzc/Mmqlv2QEgKs0O8lr+WvPhaHzqUo+kHOTuS8UejOQeUolwChe7s6Qx6MQuExzp5CH+crXQqrK7hCF5YAf4aczDQSWQkvltxC/CrnNlP8vHOAhr/zEDpHJEUYn73eLWSdagjuyygu/gwba3LDdb+p6poper89fgwalxHL0IvFzMcSi7x66JkcOg9XbdqW/aQ49LxNaX1ceJvrYITebiCkcHmORHhEHzn24Cn0wugKfWRcGWeZpas5hWnOXH3Rflx6aB03XHZQpT3XurWmWdvh+gFa/xa7mauZ46iqmGgAK2aNc1qVhM8JbZOna85plMtuFamAeEA/US6ulgtTUupLM6hs83unYIpgAo8L04X/pZWu7WKH1yOWAL/XetumFgkTtM3DKo3BlPWXCw9bdFl3ibBF609Q7kzl5r80td1RYDtD6JTNSbKPOZM5GqbfxGKEYwidP3vdctQSTfqJRRL1wf1WUC7aBuIyZnXncNly6NvqphQ6uQkt5ygmTSR9xmPMxyO/j2VL4RnjUzQxhD4qmqgyw5y5sc0CcGN8ycEN3Pa/fCMA34LiEWvEOddiLfNyH7LEg6R3CCjJfkiRRcM4bSlF49D7Nnn6fEW5KEK7sCwJ6sLpWEw5N9NErZAw9V9PqhiPTMsp9seKcwqE1zaRk81NiqLrd0rp+v3zD4QIolxY2KLPoetta9EATdU/P3yzEP92NEbtp/5HkGlwX+6A45RL54QOx7tmdIV8HO6Y4+IpjJpCLMPNxyF05gTn6LG2bDNNRLm0IYIyJJCk6uPQ5TmlY9MhRurrEJEO7pFxtVxcHDq/v0/xkM+GREa5VLXIFBWlDzzfUftvPmx8HLwCdIVvbdNarvi76iKilEgyFu8PpOejqw3jI/Q0h+5vbClHObD8sMU9q9ClAuLUQ8e7SUeKRTeYG16JTCVkSkEk2UqXKRUqIdCYy3rYInHtY8omTcw6r38JpcLDFsncNoLy4dL5GzjlUlmMCgQbW3cPz/fQOBrD4ly5CN2v7Oen/ofjFnsP3DEnx4OHpnIOWXeaMyd44YdnFiYvDj2lgL1jDsV3tYLQ1wRCH6rQyRGsOUVl8lNZOQuTlDgfL/o9Cb0HvhGFCJ33xVWa5O11oaGMw6fxCf1h7jpOh5K14N1rZLqIoCSHTtx+hr+so6XExqaND5c+636nsmcVepdYNCaE3iDVtVHR8W6uFokz07qTdSKnksTCFikLkhJ0rE3VRak9muKnv+Ol+M5brlWiNdykWBu7BZt63xwZGBM3+3nYIs+sjNdD9y2e2lKCS0g9kXip/9YvzpVdy0UsXpLQCe1+QwpZW2xlgkPnB1zwDdvND79+DdBsBH5NblLEPdUWx8ZTWtrGoz0bUQmFaHNtVLSJZ3mWjxQ3B5hCF4lFPGKJ5i9H6KPIPCBahNeKf/XzLsF3f+V1uPHyQ8HzxxLh6JlmImKtsmFpCh6/7/tbwpwF/tw24ZDkuRaF4XHo4bWlsunyaafNweaa5YYt7l0OXXi9uWKjE1Qkiie0CjCnqFAMvKRAiNBNwGMa5b3NxMv+lldcAyA0t8jEJQQ/pJZLQ7nElQr9Pz/RKEUVBQioti2qa5KvunbFJscdjfvWmBkfOdhBiuaAA8LSDPI0G23xNu3FOHQ/hTxmTch0cul7qGyD0AvPvNajXOi3QMh5z8q6BR/++6bnCRD62HRj0bQ3EKFbij0PEbpLemuu5crKc4rGEHpBKNp9ftnhDfzEt7wEJ7Zm3nMBugXi0540F92751UTm/b4Wk7X/RnKoY8Kt4HO6iqC0MN5Jjc5TfoCKnYqe1ahSycJj3KhBVgz5Qe42GrAj0PnVISM8yahmFxpRhdKMcqqijvmtDKiHp1T5NVyIYQZj3JxfezQWRGf0FrMPtEX8XA1P7Z7VLiontwj6GaKAw5Ih4k6Dl3nn3UO3afhOELveNk6VBKF8SMTaCxHDLVr7/qbXvwcXLh/LUqRzLxT7Xn/9Q3azb35ETpH2VSuuHlGf4x5LL+73kfoXtnYdmOvrebLaf4GG7KR1/E4dL6WydpuviOgwKuphnXvXbvucJf++Vh3a79glJluMavZ2RELhsuoWFEuqsQ4dFIOHI2rZ0aOfAQYhkwVIqLDtE4aHjoW75ue3BLGyFIfmrC0/lounHPmjjl5P1owlCk6Uqo9cuGnANGzUQwvn6jclDSKohtay4UjHc8pKsvnepX44hZHCqHzgm0jptD4M8s8BYq+4SfPcy6a+ijltS+4FP/49S/sfBmyn/yAC21OyDbXmf+maW84h84VG7dQpCKcsSJbRL3weQ/oUS6yqBgAdUOjuj/+dSwOnSUWkcO1VBA6KXkZ9hvcy6O+4mPUgTljcGjfGAfWx8mwRUmL+XMiHra4yhRVJIxDb6M92olvlcVJnxUGXhVEur5p1yGkQiCStXbX7nOwxGKhC+MnFXgZpS2dY5BZD71Fznzy+/ciysUyzjmjHrqC0D1nmIhy4dxyYVhm7AAOnRxwPuXCkzuURWqgLjYK0ZRCTjc35m7MeGhhiNBFNU7Bycp+S9E4dLpPd4KN4igPEHobYRXj5PuE3o/LDvUdpNJpLBOZeBkA2T/acKnEBBfNotCsKFmaAXDJc7alcwDdH9ZlFRsT+Lcch47ud/ExclnLv/R9t+BtX/e8hFNU4dD5Oolw6Ks49Ih0CqhzioZRLlqok0wqcXHoPjqQiUXkROKINfZe0tmKOho7sD7G/rVRVtiiMRSiFVcqfCHNqnhEBe9z89yOQycUEuVOpaIb8VNw8hQPd8BR24UB43oRbHJUZkCLCIohdLJOnMIsVGtCOtpkDRx6t7HIHyncOU3C55i0PiolHI76uJM4dOfMpTF2TlFJa/H5O2LX+5QLnxPNO6ltOBYa+KmVd+Rx6CLXorYug5cfV0cIvcv1GPnjY4yLqMkKW2Q+rRdfdWHXL22sU/WTqA1N+ijVncqeV+i0Y09Lvqu3aMzqqLNR6HrCD0fNMkyL7tVn9sZioTnvCjjlUhiDn/q2l2LfWoH33Xa0l3JZY9wnSYB4OlO/SSxaH/U4Ra1TMs3/u8iVFHdasXEbFUUX9qiFq8WeZywQemMNuX9bWKEQnBKSQxXj0Anpde/X8Pu11oy1QWIRj0SxrV8m5SDU7ivHgSsnaTVpp8kDXKFTe/MhdP7MXoy5cQdM8MOeSWkR/UEiHYD0fDGELue9zqETqOI1/33LSivTQH4z7oQm/9asyneKOge9boVy0Ry7MV+T/5zD390Q2dMKnaPlSVl3pV6LlkKpKp8XpgXNkyqkYuBIVU5gOiy4LxZY270BBE5J57Q1eOFzDjfXmB6er2L8pmcCx7lLF4fe7xSVJz5JvpibktKZPDKOqqC/vQi9cmZ6hx4LeEq+svBii5t65jq/SUhUCinlTqG3UQz8mbnCXxcKvfneKSMvRC3Cl/Jn4pbEjEVojQRi4xw/l+/+ymvx1Klp9/9DUR7RIV4cOlsDEtTIA6Rl2KJMLCIJ52HbX9ZhnUMPAxN48lhQbbF2m/yYW8+Fj8TLqm7rwPdbjLHCYzEOPWYVyza48CS1ZcjeVejWj8CYljVDrj7lwtEivQiOAPlL84pzCUrjgn1jVBa9DhYej8tFUi7cCcOvAeL1rok+oT6RxNBCVbsQuVSMu1bIjLI/vQVr/MnuJesUBb7uhZfhX7z5xbjxikPtc+j342PQKQ+G0LnisXVYrY9CBwNnY2wzNfCQHkeoPD3dnWjlZwvS9zVzyHZjkkDojnJwn80Y0CAHPu8/HwuS173oCgDA+25rzmsfcnJ8E7ONaGKRAzWOdpSb7Mj4G7uXUJOyFJW1oiV/8cPRZ5WPvP2ckjCxaFQYrLVWt6R4ZpXv80jNR7fZ+88WSywKwxb5v/U5kUruW4TsXYVe2y7pA2icouORm4S8/gM/Yqu21i/cr/CHAJmY7n7jwuDHv+UlsNbiDz//BIB0kk480sL9P91zpCyO2vqJCvy56XlSSoVPbAqR0w5T4H2m5wTgSgaYeEKJn/rfZJUeWB/jrV91fbco+xQPp6cKpmD44dqy36nqkZqzitrmCnvEOGQe1ior+MmoprJ9zlgafHBfhUP3k6kE5aIcbaa3F71lIHwT42GIpFSd38ldL+moIIw3Rr8k5iHvj3w8H1Q5NE60XurEIvJpcL8S3W5W1Z1zVfYjNk4SYGlTWE0s8sZHt9pGidDhRcieVug8DGtS+qY7d4CNO164pRGEt9+jDhg68PjiwuDqI/u79pv2Un3TFLr/MmM1lamvIyXGnZ/bmEJGPGyRDkYoq1RkjvWckTzKJV7Dw1EhEhnnxks35r3PoXM6YFwY1HXoTI5y6FWInKg/DQ3nlIBMfefHFsrY5m5MbFjfJs2hh+MgMyF1fj2i0JlvJFc4L9/NnSKkHXlynfZOUhs7SegUdWf88mcMEDobB+5jcBE0ci3DyymgCDSpuGdV3YYf9s9HzX8hN1yS2qYplxgLtwpbjIjj0Jv/n7S0AuDqdsgCXrSgx8Fk9sOcgDbjNGJC0T+jCD2aWKTzpfzl9yVA0OG5sk+xyVXWTjGn49BlvK7tuNQYX8rNdHKguu+QfA73PLW3udKz8FoiQSRI7RKLshG68R1pXLm5+cFyF1jxNv4sZIn0xaGnxoFTgfIZOOrU20vPD00kkqU+cz8Fp6+41eSHNuoIlK+TeP4F7482X8M49DW2NuVa5sdJ0ubE/R0caKzl1nJRIoyiqf/KGs9B6MvOFN3TCp3KawINh+5RLsridAiLTWbjDsQAfOohRmn0cegaAml+JxZvhzAK7xogblJzh1IKGXHLBXD1KVJx6H54l1UjI7x7cFQlkDH3BaSEm/ceX+slvYTp3DK7kWSmONyoPzWjbrgfhZcpoCgW2lB4qF8X01+EDvOYaM44jtBl6GWMQw/bi94yEE4laAhdjnEZsZo8/wkHIT3OwHDTCq0oI+YS4HJKomvZ84eIsM4WADR6gddDjw+clgOggYbmGRSFLvxLmiybctmzCp2oE5rgDeXiUFVtm0GnyBcA3Wd8MY+EY8pNkgIxFNY3OdLZiv4zADEOPYbQa5aI4z6PHbs2mfH4/DRC98O+yPHsF3SS7VM/axv7Xr8fSUx5SIddLcato8pE+zGELuv7NGiVYub9yB4ZAULK21OM7S24VaOJs+bcZ77TL6zf3fwuhtCpvUUgdLeRBpSL2MS5VUt9d31Kb27qId/KXNGs5PBMUR6HzuizDqGj/d61tc4Uemo+1rax+vn7jFU/VZOj2FjF5sSyE4v2rEKnOFCaGJOy6pQ0TQ6Z1Udmmhe+ZXx0wo+Pi/GEXOlpQmaelACpKKVv+9rmIWV9KLEwxqtCGUMb1OfCOJRR17YriUsbh4qq6lAJ8PvnJBZJ8348Yk5RE9agmbWhaFK5uXceDxnV8gw6R7Bt0SNzBNP8ANih0CM/WiQl2gbdHWwyTqT+JzINqa+5wp+Zb87OKSzj0JnVJJS+64dr3wM+kXnPNyBJz1H7IeVSeGsZ0Mt40LvkEVmcQyd6jn+uiVayIxYZlkLofT6VIRFKQ2XPKnReExtwphXgHA/ONG+u6WiEwo+ikNEahfFDvAB/ovah6BRC9ykXdH3IbXtWOedjinIBmmeYiBo31sadPLI8Ky28GELnVBWNq3zevqmr8rWGSs9CrUHjIhd85Rarg0J9Cc305rou9r5u6oOQYiiMrwRJ0XDlluLP6VreR4A5/VrqRqLXZiz0pZmjmKRomxivb14Ix6Wa+s98ShKB5gALuaFpPp8gMKHdOLXEIis2Z4rpl5SUq2pJQCU9TnLYYyBID71s/vZFPa04dEXIy6xGuRRu8fpRCmERKV4qAKC4VYcOSfxQJtcHTWLFuaRiqmpnDfBrgHjd5pLFuMcSPUgK45/klAp5K5XNTyYWhahKJKMECD4jsYhZHBLhXH1kP64+sj9AeNNSD0XrlGGUQ+eO6PDEHoq9d6azn53JK13GNrnwvn4fm/5zSiGC0CPtzlPLRaswORrxNeDXlOERS9y/Ed3Ye+ehUs8+MVdmwo+lUS5V7VNg3Zmrwmprqnnmhy3q8fH6tbFAhDRCX4UtqtLV1GgHccqjXIyLGeaxqTxskZvMZe3MIF5YKxZF0hcLHA+dC8uIhm2j66smnhPR61+4gYyMwWTmipbxtmXZX4r+cf4GG9BaWjYqXVfbkPdNJTKRaKn/9PdP/vHXYVwY/Njv3CkoF6tm/6WU4ciEjjS6j1dhktEBHS9bEEJ3B5LENjkpahx67W+yvl8lfSblPHHoRPHwmPowW9qhWjrvlPdDZpn6fXL/zg0G0Kw96idlD1PIo3xvQNses3D/p296EfavF7jnidPt9813jTWXn1iU2mi4lHWN9bGvPh1lGMfJZHEsS/asQpdFd2RiUVnVjjKg2N3adgrbmCbz84L9a3j69JQlIlh14npOoJ5Y4Hg9kfBsTHmfQU7RDGTEKZdU2V9aZNxk7dLcu/Hwf9OhXqsr0sLkJBaFHHoXTshCB0PKJVykKbqCNh+enSvPFO1KQ7B+8DnWIWuuGBNp/wCfK/yZHdqUiK0Poc9DuXgp8kxB09FtjT+CIXS2BrjVG1XoHFhEyi5Ix6/GoXcHtQurjQrFAXQimct+pTn71TdeCgC490lS6O5ZmjIe/lhoUirRN0M49ByEbiLtLUr2LOVCWYz0oiZl7ZVh5RELHuVi3YC//++/Bt/3muuj1EEsUSArsSjDKaql/rsF2992X6pxURivaFmKKnJhi+6a7oT7ji8O63R4XKZWn6Nn8vrPo6NejpJocauUS+KAXopl55uoSyxymcQyS5Kb8R5Cbz/L59AZ5VLJyKO01aa3l7ytJ96hLZ3SKfCqGy7GT3/7S/GKa4909Y/oevdOwgSrWBKb9l3TZ3ioVOPQPcqFgRaiPHjSD08clEW+pNU2rRyA459r0hcf712rOHa5Dygmq0zRiMi4aWudY7BDjkqlNYpiAIAXXN4UxOLOPS1LDpCx4unJEasnIkOgKKySI5y++O1Z1Rz1Bvi/i3PoPMolbnZqEUHdhhhBZtJhFS6u3MQiwdcqyIfGbVaHPgHpFI3RXTIyYtRx6MIqYaYzt1pK5vOIjYl2X95HwEfo0q+iWW1c+vw3mvA2XcRS83zfccu1XT99UOMUufutbpXEqEmSIBgggm67NcjqFXWUC4sIK0yjUFPZmt3mxCqNAumNkOuGWN9JUolFfVEu1RIV+t5G6IWMROEceptEZMLsRy38rsssY1EXsXoV9M9UHHqMAskxPZu+6s9d1txXkF5Io4KdTN8TukVRKo5Dd47nWDiWpFw0U3yexCLd+dr8268l7j9PKimni3JhfV0TlIucH8QbOz+N27g6qyVRCx3QN2ie3i/nUi5CHxKHzi1B5+zU/SFAs8nKzdWfB6JPEeBDEgQDWC080D+kugNV3XtD9/+UJKZHyzR/6V3Wlpy+zed9iUWxOS4lRbmk5kTfAfM7lT2L0GXYIgDnyGlf+KyqsTZ22aT0ktdGqcnUH+fdp3RnCaeoRCqhIxFdX9Xn5hw/N3UVR4xhHLqPUiKUi/GVpDzMIbZ4SiVluvm+n3Lh1SM1qgtwUUtAE4YGoC021nxPEUEuhltxEBfOamvuVeC1L7gUT57a7p5L59Ad/zpjKDEHjfFnkU5dQL6TxnHLE9vS7SVv64mfWIT23/41xrg4dA40vEgY9m+/T+7fOXHosRBXHmm2xuZCbVmFyrE7zzWF0OVvshKLFKqUbwQ8VFONQ4/ka3jXiPe9aNmzCl3GSAOCcqmVeOU2U5AoCxLP3Kv1sEX+jvqUbhShF76Cix3FlWqbJy0NoVx47LA2qZvNj1NY1lFWisXC+8oVnbx/HzXAx8pRHeF9nNPaKXTizHMQOpnu3aEiBfBVz78EX/X8SzqFR6Fw9N5fdf3FuPmqC9TnjI2JlG6usDBUvzgXumcYwWQgdGovX6N7Cp1x6LLdVOp/ExkGtW99HDr5tEi0JDRZIE9a2zMPmBAlqDgx2/+vatuN8/rIxXT1JRZplEvzO18Bqxx6xML023P90Irv7VSyKBdjzBuMMXcbY+41xrwzcd1fM8ZUxphvX1wXdXFZjCFKpUkwLRv+jKNO7aQRrni8AxeYovFTed0GofaNLQguklOOhUkB6VoubsNxn6uUizFd6v+aklnJZSq4xqpGR1nxY8i4UHvkeJVKIqcQER+rWOQIfz9TtkhlVmCVCPmjTcFFfPDUdXTt8Hfys//Ny/F3v+Z5ukJvf9Mb5aJs0LyiZxh6GXfsAvPVctHKHaQyNbXII17TJpbyzq8P23b/TydO+df4cejcSrZWHGBj+KHUcUTNLcccp6iO+N13XMoq9JPlRD71Fd/bqfQqdGPMCMC7ALwRwM0AvssYc3Pkup8C8KFFd1ITDaHz2NnaWkwr2yiyzqSO82TEa3lOsR6qYTBCVzj0uMkYc4qGi433VT5XF7ZYpB1DFMdP+1BHubA091gBMKfo5PNmHBKt1A2RpqgMqQMaM1oqtzSH3oy3U27uO17iNfVOpqz0bg4aa9pu/vJh0CgX58TLQ+hDOFgaO065hJRH6zch3llEHvHcjeC0ew+h9wOZMuJ85I5MeczipKxacEbvqt8H5SgXDmbUIWrvq+uGpj3/h1R1k0seQk+DwZ1KDkJ/FYB7rbX3W2unAN4L4M3KdT8E4DcBPLnA/kVFhiQCHKE3iGBaVthgFRnju7pbVJxjj4XRpaJFYkqh+Z2WYKGnD0edol4EQBoZNU7RNsplnHaKTpWjusLEIn0cZp0SijvaYlKxzFweUseFI33vvEmh3FLKkHh4F/Gh9TVGg6FtP6Rc5uPQ447q3louHcJL3tYTPi4xhN45GsWmyP/GFBYfypR1RMIrhvLf8U3b5ZQ032/P6q50Lr1LShL079X8bQAdAzMZyLhPN3BRD4nOmBMcMC1DchT61QAeZv9/tP2sE2PM1QC+BcC7Uw0ZY37QGHObMea2Y8eODe2rJ+6wXvfZGg91qtuDHcYybDFtVnkeflIwgZPOXS+lr54ID1mqqvk4dJmWHVJC7rm6KBfFvOcyq2R4l2WJRVCfif6XFzSTz9LrFFUyczWkDzSKe+op9AhCTyS3aLH/dI/a6qFwptu46u63uQhds4rkmZnaM8RimfusQ006hM55cNH+qPDP7pT1grws08icBeLWkaQaU7kGM4WG255V7pxX4zZn7UANemZuzblxC7rn+qXw4rHxrpVrYwDQb8+By2VIjkLXeid7838D+BFrbZVqyFp7q7X2FmvtLZdddllmF3Vxh/WG5l5HuXQculs0VWJnpe9lYSKJJlKKsa+eCA9ZitE/QOp4u7CWS9Q8Lxwy0sx7LtPSr2BYMtTdLeqIw4gn3PjPMqdTVEHPAJnRnK5A+7nk0LVMUZeHAOjvtLJ6KBz9f0e5DKq26PcRYFZGESZ7cXpEk3lquXiHtkTmDI2PK0tgut8AYZYpF9+PpW+mckNLx6HXXpQLAGyz0h5ksaWcmNZyoJF3SHSaAvWv1cp7jNjmF5O+Wk07lZwol6MArmX/fw2AR8U1twB4b9vZSwG8yRhTWmt/axGd1IQUEEemPPWfODRpmuu7sL+rS65wSKx4H4/b9MMpu7i1oD+3R1H0IAIZAZRCd1QfJaRR4tEnRlyrjVNK79DxeLHUf9eO6zenXOQi7RBZxDpqFDrUvlIonFZnpLNESofQi8iYSFHj0Fn0UCEWuHYsodde+3cIwOM0U0e5KO+So1rNj1SIdUEylEOvVEXsv0dJuUwYQi8MulLY6bnSzofcAy4iGazUHheVv89A6DTsy0LoOQr9EwBuNMbcAOARAG8B8N38AmvtDfRvY8wvA/jdZSpzwHG+/AW4HbwZcIc624VftzW+E7xbWdc4uOaGRfL0/HptclSJBck3jqINURtKufgUheujJnzRaBQFl66CYdtWydBuLNSNJue8YYvUj45CiqBHrrhnvDaNsDiSmaKFacMSW2tCUyitklhb0y0EnikaG5PgvsoGzR3boZURt/B4X+ZB6Jxy0Z+fo3np10hx6O7/4xy6UOhqmQiiXGocategj9CNd20fonabPwMzqfK56mauI2rNyuCHnsRk2VEuvQrdWlsaY96BJnplBOA91to7jTFva79P8ubLEqJT+Ni5KAnT8a3rLMqlsjr3xSeBfFG8brR2vZTUIb9ycfNSrfKa2PvmmazUD5koRcLXrJdZqXR8IigXF4rInD3ikejzKeOW/WdJc+jcOdjcK4bQneKessgF6WBKc+h+3ZkY35+i5Lp66MWQOPRwAc8q53iXC7zvCLqdJhalrM7S1t6m1fx1m23f+4n1uzDKmbDKpl0zK0XO8YZDH3X3d+8qjqhpE1kbpZPqeL/W10ai7649eW2MmsuKcjmHCB3W2g8C+KD4TFXk1tq/s/Nu9YtE30AY5VIKpU9hiRrXCzjKxT8A1yh8q7teSgolauVetYkda5v6Lyd7PMRNR+jaXCKnKCllHrnizO4w+gRgfLsyTn0LCAjDQzVzHPDNaK0+h3To+W34URwxvr+hA+Rvm7/Owczj0HMVuvuM+0Fk6GUqlp762VyfrxC0Ay5imZqSchmxzdbFoctaLuzfqu/I9bcLDVbeMT81jOeUAC3lIuu7JMCZtbYr1eAXplMGqBVNN8QQtXrvyDrR+ncuwxZ3pZBC9yiXbrI2A+6OKnMvRU8scmaVzGLjpqa8XuWiEwiL+sopgtwwKboecBtXHyKQzqpUdI70SbiIjpQvAeLa8FlyDuV1z9P2WzHHm34jzaH3RBjV1l2rLcYusifilN1ua8tvjEf5cehtU3wcmnIHvsIKarkYvd0cLliKrFSo9btRkvwgCX9zbUIe45sBSWrsgZBm066h8sh0X6ANW+TllGt3+pjWl8ba1ui5BAWYBFj+ddbqzxAbA3dN28Y5jHLZlTKp0gjdtlEukjuOHVDbfG+9Wi703SClG4nJlvcB+vsiRVIK/Qjd/dtPLNKcorXHNfKY6xi3PRLKX6UxEkhElruNx0g3f3k6N++ri0OPo1tj4NXV1p4ltuHT/Umhcxpv3jh0GcXBrQxjQqXZtdeTp6AJR/0p2sSyKBd6FxfuX8OVF+7DDZcejIav+gluyrwv/OPtAC1JzV8X1A4p1O2yCg+wUcN+m7917TvQc6iqVFy7fjCN//tunSQc5fLA8UXLnqzlQsp6gxWuByCcJixyo71G1rsm4WaVnCR8EXTXJ5WuH/bl/85f3EPCpJq2dYoiyrey64oiXsuFFN36aOQ5oQB4VlA0g7LUFWk25SLQoFxUzrKxXn33aBy6Zh2RIy2SfORC4eLhaFtTQuhF79iTuLniPpO1Sprv4zSc3158U44Jj+yJZT8TL90dJNF+v399hL/6p18PAPj0l55Vf5uH0H2FroXAurBFG4CWbS/KxVXOjK9l/6i/HGRcRQ46p/bcdTpoy/GrpMDgImRPIvSOR5UIvUM9zaKZiuJc7lT4uFnVHLjAOfQieHGpehp5HLq7Vqsh3lyjbBYsrpaeM3av5nt/gmloA2D1URjyJOXFxziGXGcRJdnrFBUKOHbIrhqHzhy4rrhWfOyDgxIUJEZp7zElscUQen6Ui4LQa6tw6PFNXvazuT55W09o3qSTg/xknFjmMRB/PzHLgmf6Sqcrb4Nz6O6wmub77VntOZJtxCnqJ8ax4lyZTtGQ7kPwu9gJXVnVFndBpuiuE66AtBKyRWG6azbGPpLTeDdeXpeHlAHNC8jNHgNy49BTlIvxrlHbFtUWYzHL9FzrjIpq+u1fN1VojC3OF/cg9GjYYpHmLGWIpzzowt0Hbb974tA7/jceCx2jNJzTVDuGrPmrUS5z1XIpw5r2tlN4+gHjrr34/IgJXwvdRhQACR+hxxKEAB3dA6nIHJY4Vfu/0a7htGdHucg49C5sMSzkBvhzhZ+nmxo2HWCFG0HMyisiY6tdcy4zRXedTJUa34BPuWzPQiUV94yz7+swbDHmeFGVbpJD9xWqXn85jv5l0klfpigNjUzSkBsRjSff/JwDsIgiD1knXMvwTCGRmQjxLCL3MWLDBWJx6Olqi/R+4yVeEakESGPCFWP7u57EIp4DQeLV3BfvpB+h9yNNKRPeb1K+ChKlM3cBHSTENvY+ZMoTzGKHYDf12BlCFxvepKw9YNLRp+KW3Armh6HkjFsqL4T/LBaaHBtbvb2VQu+kU+jjkcehSyoCEOYWecYV/g5wURQc4Y1GiTh0xeEXMyl5vzgSiSY5KRpdTqS+CUTf85Rpfn8SzXnE0aisHeP62vz/tDPp/fv3lc+VhzlEE1fYovJrucB7nn4OXT9UpOmrM9NjUU0e5ZLNoYcbtKawOCWREyUxRB84hM6tLX3zjWX9Nr9JW2prEcuCo+8YLeYpfS972F2zzuYxvcschJ57BF2tbKYq5RLxA/QBLP6bStEdi5A9rtBllItD6CRrY6eMppHJ2vHWitOUJ1QE1yfi0DUlOywOPfh5cDJQX5iUTDyKOWS88WxnxFZGiB61F0tX5wtZE0nVyJIGvB2gXaQstjgeh65vpl0UUwTBd7xsxGrq/AoMJPRHubi+k5SV7ZSfnEv5CD15W08mswrGNEg1HuvvLBggbuUA8XkQs1aorAAQ5599yqWGzFQFmiJbTd/i/jCOgLt5OUofkE6SokA9p2gi9LX5PBWH3t+PncieVOhUEjaW+s8VgjPTWFhbZMFa6xfXp7ZSp5hISZ04E1IEcYShc+iOE+TXRut+tN93Drj28xjlwpUkj+ig5mPUUzz1P13LRSYW5TlFaxSmuZdcpKk6KMbEHWnNPSgs0ga1YOg+22XVxernInRea51kVtUB+OAlgFMKPUcxSZmUNTZEvzWQYj0OPUW5yMSiPmDBLJAY/9xSXlTfRzqNAWB9NGrbS/k72rlSi9T/wh9nTbTaStp4x54hC6EXPqhbtOxRha5z6DKaA0DnSDHGOUpj9Zw1jnVkjBozC0RqudRxpaLzpeKa7oUHP4+GLcYmkKNkaKOjfvvXeVEuHb0Qhi3GfA/TqELvQ+i+NUMZffTOSLgFpdEV/HBhQEeKfKPaEOndACkUi0lZYZ/4vktumTb19QFkR7nQvT3KpbYBAu2sDEWpaM8xhIPl/POLnnMBvvzqC3D1Rfu9a0YFZYrGKUONBgEQjZzhfZZx6LEQ1xgNBziE3lTG1AMcuAL2i3PR52oXAfRx6CHlEuXQcyysc1htcdeJH8HiPl8bh2YaR+ibLeqUC5Z7nvkRb0Abw71ghM4Xb+zAXT1sUSJaUtjxhQT0c+g+hdV85jlFI8qryyot/X7x7/NS/5t2962NcOv33oJXXndEfQ7i0GNRO0kOve365qzCvjVts236uj1r0Kx2/61ZhY013wrsQ+jN7yXCq7s0dm2Tz4tD771tJ5PSbWIvuPwQfveHvkZttzfKJUIpOEouxqEbb84DcWsuTJ5z12ywtdzlokTeFVlzwIBaLlU685SkKx8h9ULPxtZ8h95+7ET2pkJXkl4ABMdWAU6ZjYzxaAQuMt2dL6gjB9Zw5MCad31a6cYRDkeaQKy4UHziybC83nronUL3zXupDHh9FKIIurFaG7GJ6v+O7hurh85NbU20aIFvvPmK8DnYImgOsxZJOTSeCYcejevWtMTGWEHohkWDRAo0bc0qXHxgHUBezDG/t6cQqjATsitMlR2HPpxySffRj0NXo1wi8y0WnSTbBuIWLG16nCZp2g7Xcrf5lnWwOXPruazcOaQOuUcGAPkHXMSeIaccBL3vc1k+d9cJV+ixeugkPLtsc1oCCBE6vQhql/OHP/eWVwR8YtYBFxkcuox5167x2hbURg53CfCFgLbtOEKnPmyXzgGYOike4A7UEC1VCdtSWhwx4ehqVmpJOW17GWO/lUDomz0b/vas7pR9n0PabzvFoaN7NsCvd6/JPIdE5yh0h5AToZ89Po6UpRhy6P41lMkrNxRtLY9MU1JiMquCzZmDlimvaplBVemF+0KKJBqp021sKadofz92IntaoW+wCBZ+0pBHw7Aa6XHF47fLJ+zlF+wL7p9SupVA0d7vhLnFFYTsi15vxTdHaa73cuidb0FXBtOq8vrM6akNpvxiCzlm+fRlispiYzHxY4vr6AZFFk/sOD7qq4bQjTHYnDmrhAsfX6J7uk21Jw69ubdPPc3qkDbiiUU5CH0Qhz6r1WeW7VJsN6CXroidyNOHTPmGRuMQOzeWchOkFdb0ya3lKEJn60etmROZkI7C6V+PsRLMDviot/CuWYUtMuFOPCCM9vCiXMbuM04jcCEF0DlNe5NFmr/zInT63URBiymONHAYRThN2ZZzDOv9ppoXXMnw5K34wRPNX9oopeXDTW1NYkW9wudo/lprMautd1hw8zzN9yllSJ9vTisVrY6KxukJxDd8wEeJOX1vfq9QLiKZylESdVZiSkwxaTIpq8DRrPdxztT/zmJMcehNu6lCbs337YYi/ESAb0FOqxpVbbEvitAbyiWg5yLDRoEWsfWoJRbFMmbTCJ36sULonXBlA9CghwV95DUxkzqF0DVJK90Uh+7/bluJqIgpXSDMrMw5U5T3JeYYchtkOH4b4wK1BV5y9YV40XMO++0bUpIlRoUJrJJ8hJ4e7w7VWCvS5uE9j1ZciaTj0GfhmFNft2Y6JSfHg7eXE+UiNza/3rf/TrRkM60vQygXzXkY9lEU51ItTH2+9VF//PCKLts2gqwnLTjQ4tDdRs59PDFAZD3Kpa+WCwUBBBuE4sSMUy79m/w5P7FoN4rG+QIhVyyv6YtymbFEhJQklW4C4XCkSTHPMYSROt5uTVgice6y+duXWDTrNsiR97su5toAv/NDXx20z1HvPkVhSO5YSqp2PBfOYzZOUeN/3qG/OEL3KZewrya14SsoMTcOvbm3H4/PY9215KikU22OKIlJWeOC/WvJa+hdpTj0eIIZor+h7x3NGFmDhW8la/QpX8sxq5CHBfqHTatd64Q2mhBghQq4n3LJsbDS/ZlX9iTlMhGUi1xcfrKRe6HbMQ69/d9YGVgpSaWbCvtii9dN7HzKRS62fu5S3+jiCN1X/BuZG9vmNI56+8qVNs/TRwe4fk/VOHRqL64MvTj0yOaz1TrNsyiXAVEuXKEBraKJOOtyM0WHALwcp6iLQ49vsuvjAoc3xrjk0Ibap9TYBwp9rFumzkr2qS3AByZxB3bzN4yIykToGeuxS/2PWSoJi3MVtqhI5xQViFKaV4CvpE5Folxk2KLmEOKSE4fel1gURSoZ6F+GIaa4S359LELCZYq27badkOZsrP2tiELnprYmqboh2n1sxCnK6Yr4WDR/NyOUyygD9QFOgQyLcpFO0fDEIl4CODXu83Cwk1LfxMI+ph3Va6MCf/xPvhYXtaGbJH2KrDm8ovk3RU/tX9fH2EWa+XMW8H1mWzFru2BzhW3wfVQV9Su2Hjl4m4igDPkM6Uzf5rtVtUUmAeUiJpSHqNjCSYXX8XaHIEYpVTIO3aGE7cikGFJrPRZGJvsZO0yBZBZxMvdHRhDlUkZRb1ZiUd8GylDNrLLRxKKKndUZtmG6e+p9dXx/DPUB8A4q5n9TIuPQ+RFrWuhl1pmUQxA6O74t3sd2fBM+IAC4/PC+gF/vSyziCWaO2kj7sfSINaecN3usqVr4W1I0abpf4XgTGAs2pZ71yNtbVVtkIhW6nFBemJlQ+kCoqOj3ROXIWh5SkgW0SOmmKJfaOX9yEAEJz3wD8lP/+2JxJ2WtXtcfGdH83Yyl05t0LZeUNcNFls9dE2GbPkJPUy5AOOa8LSA+P5rvxJzLClv0KRVr47kBTbXHeFt9ikmTaZUTttjWusm0mrzf9sxDPg+izkexBlNrmW+QYdivW5tlrcWh68/QRwXx8d6KXJtTDmLEdMAyZG8q9KrCqHCFhmjBqwV9lHIAfeggt4Je8hCKhFOUUsz1vsS5vtiRbX2RHUGmqJhMvMwo/12vmd7ed6LEAzffpxVPKqvWa4ct0mmZ5p/7rBVAf670/IgDhOxaLu2Yz0RorAy9nMzqAPlpfRkWh55DubTFyRJht32/zzngIuZ8zKJcOiDjftfLocsErohpsx3JQdDW41YEodMzpcaa+rfKFGUyZcWGAPeCJbUA6JEvEq2EHHoed6xNjpzyow3l0jOBlB1cLrZOqUTroTd/+8zOadmE+8kU/xzelUSileZ+mbVcMuP+bdTR1XyfQuhcMWjWBP9d7J0AYWLR0Fou7sxOnQaLOZhlXwZnimb4Q5riWHU0OSslHGDF2gbyk/v6ItZIYhsDJQrFiqBJ6QNYfBrH+PtrLz6AX/jbr8TrXnS5fhO4ebPKFGUyLX1OUDqoCLkahhromsKETs/hCD1BuSRLuKL7HZUAzjHxXNtECeU55mRKdjRTNDKeuZQLEC4Eaic1b2eJsZLtAJQpaj2/SPN5i9ATafMabcLFp1z0KCjAOYr7QvX8th1FMIsgUB4Fsj+p0OFd3yfW2jbKJU25UHnhWL34PilMmIfg2nYAhayFoO5PIRC6GrEWKvRUca6ytt1Y9lFVkx6nKP8dUZTae3rTS65U25f9W2WKMplWugKSL5yfO9lFboxHAfqg73IzF1OxwFXtCgJJ4ehhEkMEzEsftu3z832cXaeYg/K5oVNUG89cp2js2n6naF5mbsyMDh2KYX3sri+eUtb5fpJklEs7lhSz37fp0b27A5Br3V9Bw7TVo9CH1nLhlUmTfTSuONc8Cr0PoVu2YcUionh/NeUtM56BtAKWc8WYODKOhTRr4701rdpEunk2Pte/ZcieVOgTQbkUBTwlSi+cx1HTQOpIsvmrFefSJOVgSSEcPQ59jrDFwlfQMSeuQ/Bps5PHdvN2B1EuMYSe+H2XhNVj3nOqKlXLhZ/VmeprLCIn9r332/Z9vfiqC/B/fPtL8drnX5rsO/1eHsIRcLvWwlqLrVmFAwkOnX6Ta7LLukcxoTj0vjj4eJ/Coxq7tpmFsj2L+Fvan7pMUX8tAyHdBaQV8Kyy3lpOZS7HuX207fkc+j5RGDBXVpmiishU5pEx3nmGXXRHJuqU6GCeY8VIUguCh9/F417jCEwiWsmlx/q5Ng6VB5dpaf0NMpdyYV/HIkf6OPTCxPsv+2MjTtGcWuLG23ziCF1z7mlKpSgMvvOWa5P95m13lIuI4uDve1LWsBbY16vQ074JLrGYaSku9b/u9SHpfUqVoGCUklLuovm9vwaTEWuJd8k56lklgF9iPsYpF9ceydasSjquU9KX4LRT2ZMIPeB8C/9UIUk1AG5Bx5AktQvsLLFoluBxPadohHJJcX0yEefA+hj/5PU34Q1f/hz1ft3GJmtvK5miOuUyBKFHMkVTiUXs7Mj0fZq/FIcei9ppnLvzcei0qexbCyk5TakMEb6xdVaWUjCNnG0pygVII00pTqH3o36gOaxkHoQ+KsKTvUi4D2FrWqkO9NAp6r/j5rOQcok5V6u6Kc7F+5Q6tLxbjzFOvubXph3XKVl22OLeROiKAuKoil44IdPmmuavNrFlPfS+CZ1WuonkFoY0Jx1nl1/LpVQiEN7xuhsT/WwVenB+pX/dtKzE5tf8HeIU1aIo+qiBKpOv5aF9nHKR72FrVuHig+t6GwnelX/fF9LYt8np92Yn2hOHXsh3Yl04XI+y6LN8uHTzLDPrd1bNh9Bfcd1FuPmqCyNtu3mglbwFmJUsaM95o1yIclkTCD3FoY8Lo5x9gLY9613b945iQu2twhaZBGGLwsNOCnld+UyfTG27A8MWtclxZlriwLo+rBxpUqbosFouw9BTLJwzzBS13uZHG1xOZASJ7hRNI8nciAoXGVD7ySLCgbw5rXDtRfrYmx6lnKLkNKUyRLywRVEAjr/vWHyz1tdcfcDP3+3rI9Ak9syD0N/zd/5aom2/lkuKcpHJfT5C96lDrcJnzIEu+yGl4fbj/ZJO0bkR+pLDFrNmpzHmDcaYu40x9xpj3ql8/7eNMZ9t//tLY8zLFt9VJ5JyMQYq5bKmUC4xxQPET6+PXa8pq81JhYMb+svmDpt4xhzaa7SwxfBE+px+xlLlSeQGmUu5jDykpG+UycSigZTLhB1czT/vYrgnZVQZppyezfepDX9nlAtXJLLmPn+GfMolniAjpXOK9iB0jpDniXJJCd/YJ7FaOm33QoTOxl44RVPvsctZyHWKlpGTrJTIsL5IpJTMk0cwqP2+C4wxIwDvAvBGADcD+C5jzM3isgcAfK219qUA/iWAWxfdUS6SchkVxuNONfO5+yzx0uigh7XeuOjmr6asshH6rFGi0SOvImGLOQrQ3a9pS0YM9HHo+ZQLU+jRxKL47/tKxcr7TCL8Kt3jzLTCwahCj5vpALywVk1GPd+nhI8DIXSZlTsUoS+eQ3cKfR6EnhK+scejXCTl4r/jtZGjGp0/LI2oS0G5pADGtnKcnWzPXVv3Oq5jwjn+ZUiOdngVgHuttfdba6cA3gvgzfwCa+1fWmufbf/3YwCuWWw3fdEQpTStAAS7M5BG6F2US29cdAKhT+MInaOHbXaCvH8NumukaGeQpsQpdBnzLKNcQiQD5FAu7t8xXjpZDz2TQ6f7UCRClEOfVjiwoW+mqVA36isQR7L0/byUSxdaKXId+PvOReiDOPRSj6+WQq9/cxq3cuYVThHFolwkhy5Dc2W0CpB+j1RqWVrusWGb9IRThhz6fPEkjiY8dwr9agAPs/8/2n4Wkx8A8PvaF8aYHzTG3GaMue3YsWP5vRSiR7mkw+46Xjjx0jYnTQW3HHMqpqzOTFIIvd0I6mahpRGGTrnkFIMiGXWLQUe0JEEYaBEfK6+vTEnGUFdK8WxN88K/QoQeblDTssa0qnEg8u68yIjEuGuWRvP7PBoq1v8ubFGUp+XvO1a+N2ivMNkKgWiqXIR+arvEwcj8nVe4D6E3yiWgpFpwpkRhpTYGcqDnhi32JTwFceg7pFzOJULXNIjaG2PM30Cj0H9E+95ae6u19hZr7S2XXXZZfi+FTIRCHxk/drhLuFEiN2LUANBMZgBRhM0lpqw2E2Y/R5R9pqcaElnHw/L0+7UIPVI3pGs34Bqbv7mONCARtpiYt6cmJQ5FELVsB2AcuuZQbNFtDKH79FDcMR7bxEYKSMgVrkhmZeQZavYMS6Bc+svnMoWe8U6GSOgUzaBchFN0iI+nMI0lVFsIKjbhFO0BWLKWy7wc+iixvhchOW/uKACeQXENgEflRcaYlwL4JQBvtNY+vZju6SJPYClElIuG0LtJkJhMp7ZnWBuZLJ40tqg2p2WvUqFaLvrmgvYaZbNIOFxT93MxzxGEHnDoeQg9pz5KCqGfmZQ4tC9HoTd/O8pFSZQ609bHzuHQ1eJcPTRT7ianicehi+Qw/r6n7YbVz6HnUy7TKo9yoec7uT3DoQFzLEf482+XOv/s3nFDK7qSHc3nKiUYUaqFcYec8+itvjj0IZTLvAh9niMEh0jO7PwEgBuNMTcYY9YBvAXAB/gFxpjrALwfwPdaa+9ZfDd9kXHTOYlFNDE0JUqL+eQAdBJTVmcmCccc85hvz/QKeLFYcQA4nYloSbpqiwpfy2UWcOjN3yFhizF0k5q3ZyZ55n3AryoOxc0+hM6GWj//NL2JpaJg+oTTc8GpUyz0Mp9DH4DQI4cyh31s+nF6sgyE3jx/XTfUWMpKbiokhmtZDXCIInTjQpBFsEQqDl2ngkIQtN1T4jgly84U7X1z1trSGPMOAB8CMALwHmvtncaYt7XfvxvAPwdwCYBfaF9Maa29ZSk9RogoLz6w3pUlBYYjdNJLpyclrrlof1YfNGVV11SLox+hxyeQa0vKqUmJC3sO+9XuF5SbFW1rUUPAIqotpidu7gbF0RugHw5BJ9jEOHR69pGSPAKgt35NF/kzGr6Quakfpv431wzh0A3ynWpDM0WtxSDQkCNkzU663ItEHHpZqWh8TQC4WDtA865oIwvi0CMZmnEOvfnr8ggaX03M19Inu4FygbX2gwA+KD57N/v33wXwdxfbtbhIp+hPfftLPVbfmWnhTq8qUaaZciezFgtMCzIe5dL8pTNFNcWfiqA5MylxzZG8Dae5H3HoPh8p25bFzrIPuPAolxiHnlboOWhQOkVDDt3izIQQelqhxxV2WknkOopj9yZFUorUf+kHKEzeuC86yoVbW8tA6P6GFac2Tm6VOMzur/kuOn9H5JlGhWHO1dywxT6LufUBUOnc9fmiXKjvy3KK7rlMUXJ2cKQkUauO0Ju/qSgXIH8yaxw68bgxhO6dKTqrcfHBPM6O5PT2MMqF2uooigh/F5bPbf7utJZLHzWQz6E79AaEUS4N5UIcejoHIKqwex1tIY2XK1yRzETqP0eAlLDSV8WvUZB595bHNcbbXJ5Cp1rrsQqjgANVJ7Zm3no2Cjgb9Wy+hTHdXJHO1Ni49UedNf+/nVmeISa7IlN0NwntvKkJmopDT/GnQD5C13b7zUkfQnd86Xapn8NpTPyFD+U342eK+teFJ0BlUi7s61hMcGziTsoKs8rmUS5t09KM5sqQOPTo2CeyC6mvzffpsMV5M0W7Wi6R1H+q5ZLDzfadBMVlUtYoTH+Nf75PLdopSs+4OU0hdKfQD7NNPkmfJuixbq54TtEUh67TKBJgxU4ryhUXtjjXz/vbX06zy5Oc+s5d/LUauRHnyYABlIsSC9yH0PnkmEQmEF0nkURd24ZzzkC0JGFxLnd/kqq2qG1+Epbfz36naAwREUUScyBr9+k49HG4QRFC39/jv+inXGJmPJK/TwkvHxurJlhbYDuzRkhzYEbevem0oj7Uv2zKBUg7fbtrZpWn0EcqOGv+xt5Vg9B9XwV9no5D1/xrEYS+w0zRVfncVnJMyA5NKeeOptABkBeDTr+RyqpDiblO0cSElC+cNovDC0DovN/aeM7DoQ91ip7uYv6HUy7BEXS17d0g+iiXvk2sMKZBunPVCnfv89T2DMa4OcIX+Oa0/3AL2V6fTCIZyVqbJAtX6AUh9Oad950YdXgfo1wU+i9Vl6lpK6Tn6HP92Mim6FuqCieBt61IDaZc6Ts5aaey5xR6TqJEOhkhPZkObeRFkWjK6kybaRpzzHGKYFLq1d2oP3LinW7bHoLQb77yArzsmgtx2eGN4P4krsKkG4NcDp2DvhiHbm2cPgLgobGYUH+2ZzLKJeTQ+yKM+imX+CY7D90C+L6EE1szXLBvrVNyspZLXpbysMSiHKuCMzKLjnKhebKZUIZ8LmmUi1ZNNQeh51RbTB0CIiPDtjNzBVJSGLMqn0uSc0ai5hlPLeiRp9DzXpTm8MtF6FTLJTYhtR2cEO2Qxfaya4/gt9/x1er9STQKK7d8Li0srYypfz9/wQLO4shBg6T0HOoKOfTJtCmVGlO6HdLriWJJhcLNU5gL8H0J0unn1XLJTFhJRWtIkRFh8T4yhL7w1P8WoU/6OXTAR+iaP6ezthL+juObMwDABft9tK8NW9JZK6za3NDSlIwGbMhDZc8h9KkIXdOE5oaa+q8hSdZUfpRLqHQ7hN6TrTitLMraJs17uWDnQeix+3uUi+JkznUA5qJeNWJnMoRyaf7KOHQyX4muSKHbVMlVaiv1/aiYH6FzRB0qdHonzSafW9tmSBx6zkY0jx8pV7paSe0mnlKcgETozV+1FHaikNqzZ6YAgCNirLW5GDubAAgjw3KTv1Lytq99Hl79vEvm/n1K9h5CH0K5ZCJ0j3LJVJgG4eTY7KnF4ZxDNLHjEzJGuQzh0GP35/2eCSXJr8tNF49SR0W4gZAMsTi6LMZtcnyOvO+aOPR0BFA/R978TWWKzuMQpbbrKELntFGFay7KKwyXe4TZpKwyKZfhfqRcobZT6JZTPhewNaiBC5e1GwdEp9r1cuGBDIWegdC7apGJWPpc+Uevf+Hcv+2TvYfQM8IW0ycWpSfToMSiSBx6TLHQ5DwzSZttKkLf3jlC15KWtPHsS4OX7WmhoM33aO+nlUgYrtCfVlGXU4Yph2JOZASQMuPnC1lsfis49P1cYTV/6YCLrCiXIU7RbA59eU5RmiebCXRrPITu+7FGhckun8u/B/wcFRNxipKSTp1WxYuLATvj0JcpexehJyiXrpBSZnbZPPyhFgu8OUln+vHQLCCtPOR6PTVAAaZEUkWyPgqgb4ip9voiR2J1aYBMDr3tBqHbsTC/6zb1P9VWb2RETyZoYczcJ/n4HHqpInRKvMkx5YfWcsmhXLrjCov5LZGYOMoljm55vXrpKC/EZtrv72i+P7A+8p49RlXFDmyn3wAhh74TymWZsvcQegblcu3FB/C3XnYVbrn+ou6zlJnm8YeZCFiLBT4zbYpNxWJ+XYIFhW9FlIcS404I/XBmFE5MJLrTzGBj4jVPpIwKk6h61/yNFTEDhsWhA8BFB2RWcPMezvRx6Bm8K5A4scjEn7NP+Jif3J55jjoeepkf5TKglkuV5xSlOXtwIz5/5xXnFE1x6O7fEqH/wFc/D9/wZVcEfY0Cp/bjIzKDvNAR+iRBuUgrcxFO0WXKnkPoOWGL+9ZG+LnveoX3WcpMmydTVNvtNydVNGSR32drGi9SRNfFOPSd8puy7adPNzTGJQfXvWtyUZoxppfG0J2iM+xbKwadKQoAF7F+0j3qukHolx/el2gjTam4DT9OH23MEYPe9bFF4NOyVhF6Zamw2xLi0Nuw1b42gcU7RJu2m79npvG6MjGnKAC8840vUtuLRiy1bV14QJkrqlM0h0NvKZdp1UY87U4svDt7lZDCAEcOrA3eIV1xpbSHfae1XFKUDVEHW7M4UmnaDpXg6UmZrQBTIkPenjo9AQBcesgt+iERHSmKKVVo7PSkGhDz797Pxeoi7efQXdjifAi9MGauwlx079panNhqQukkrws0yM9aZJ1VObSWS45lQc+/aIco4ObB1rTExrhQLQD+UV9uQn90VfO9ROgxqmoI5bLdlv9dtBWzKNlzCP31L34OXv/i5wz+XcpM84tz5cahK7VcpnkIveMSE4pQTrxT22W2AkwJrysCOIR+MUO+QxBIYUxyYwLiR/Xlx/y7fx8RCr0LW5xUyc20K7nax6FHnvuqI/u7BK2hQmOuK/Qm9JJitPM59OU4RRftEOVtbyaOHIzFoavXZuQMAMBFBzV6LhHlklnLZbc6RIE9qNDnlRTl4tJx8zlqqRiB9HmigDMFSaGnuGctxj0nq7JPmpA3H6FfuH/NQ+SvvO4iGPXkQa0900tj6Ag9v9AYT/y6OFikDfV1pudw434OPa0k3v09r8zqq952UzNHU+h0b4qQyufQ8+7dnGafw6E3f5dJuWxFzgBorsmnPXOyegHgwv2ZlMssToFKKzPXz3Gu5L8ghW6i5h59b2Gz40s1WmRzWuHSQ+uRXzDzOuHtp75olMsiFlvAoZ+ZBH3+nlc/F9/z6udmtpeOpwfiiUVD6C0SyaGPiiaNenOaPp4vN9Qt9v1OqC56nyc2YwrdhXHmJhblIPRZVeOZzSkuOZTPoS86S5S3vTlN1S9q/h7aGHsRL6n2+qKrjigOdC1+vy+2nAOsrczaOOdKdm/PFiyXHdrAlRemnGbDPPzaokqdJ0q/oeuAtIMucIoOrIUek5BDz1vwMSmKOOWinZhOcmZSZidJ8VcScuhNaF5V26R1dOGBNbz82iN46TUXqt9/xXMvxutvvsKLQFmUUE0bQugX7Au53VSMtpRchX7s1ATWAs+5ID7veZvAcigXen9nJmXvXMmxQg/vG6Mw4TjK++kc+jCnKOCP92SF0HeH/L2vfT7e+prro98bYwZlYcZquaTC8Ah4nNzuL+IlJ96pAcfjpUSGRD51eoIXPefw3O191fMuwSuuO6LfKxGH3pfZyYVTYiGHbroIoJRTdGM8wm+9/bXR77/iuRfh1rcu59REsubilMswhG4ynaKPn9wGgCSQ6frQQrtF10IHWHTXrAren7um+Zuj0L/pxc/B7/7Q10R9GkMROuWPxPIuOMBaUS67RNbHRU+5gGHoJMZzp1AiTbRjpyZYHxe49GB8QkoleHoyw+GN+RUvb1uGLV66A4T+i9/zFYl7NX93Srk0bTXUysVB2CIL6VwCXbAI6SiXrbBgFNDw+0MRes4RZo+faBT6FecYodNmcezUBM+79KB6DdEsfQ5RoEmCu/mqC3rvp3HopQ01+qPHt3Dlhfu9oyi5cIC1Na2WMkaLkv9iKJc+KYwZrGD4mrIZPC6nDq45Ep9Aatji9rDDLWLC256WNU5szXBJZGPZ+b3STtEhaJCGSnOKnuqxeM61UELLye0ZDiscccGsjNwDLnIoF1LoWQj9LEW5XHvxgeQ1i3H8xxC6TrkcfXYLVyesXw6wnjo9jVoZu0FWCr2VwphBk0kq3WlbJD+F0Ik6ANA7geRmsSinKKeKnmlro1x6eDkTlJ5VHqZdVjW2Z/WgMEziWC9S4tDP7HKEbtpInKaOS/jMxgxH0zkK/YmT21gfF4Fi09ts/uZk7g4V7pe69iJdoS8yysZEFHqMqjr67GaSzqTIsFlV45HjW7j+Ev0ZdoOsFHorxgxTCJJD38xMZSf0kJpAkkOflDVmlV0IeuJUESUVLRuhhyUS0ud/6m01fyX/bAw6hL5b44MpEeikqLTYfV8YlLXF4Y1xMkqKJLeWy2MntvGcC/ZlOfrNEhE6Dzu99mJ93juEvohci+bvEYVykTTptKzx+MltXBPZaOh3tQUeeXYLVW1xXcTK2A2yUuitjIqhlIvPoT9yfAsAcGlP8glNtr4JxNsmBLooc7QWCj1Hicx1L1FLmuT0HIXGCmOCwlz0+ROnGnR79ZGdO42XIZxDVxV6q8yuv/RglvLNreXy+MltPCeDbqE2geXGoQPxeU9jcMEC5vgogtC1DNvHT2yjtnkA66FnNgEAz71E9wPsBlkp9FauPrIfL7j8UPb10uy954lTANAbMWIyEHpTn8T9P0XFLIJS4HQOZYnuxCnady8gVOjHTjUbyRAusjAmcIg2nzcWwIH10e5W6LUNSue675u/10cchmp7OVEuLULPkRuvOIw3fvlz8BWsoN2ixKNcohx683dRoGVjXAT+CI2qOvpso6ST67GNDHvo6TMAsKspl91JOp4D+d0f+ur+i5hIpXv3E6ewPip6d2+H0PMpl3ufPA0AuP7SnU8k3vbTZ1rKZUkIPVbL5c5HTwAAXpyIVAjbChEX4DaNG684HHUyn2uhkMsYQqdxuiFbofc7Ra21gxD6oY1xMmJpJ0Kv5YJ9Y/X5gSastDCLARexuaJRVUefbSzrGLcPUNIh8NDTm9i/Npq7BMTZkJVCb2VosR2pdO95/BSed9lB9WxNLqSArj7Sz9mR3HH0OAoD3HylnhQzRKTHfn1cLMXMbu7V/JX0wJ2PnsQF+8aD4uoLY4KkIsA5024aYF2dbSlMw5Ef34xRLs3fGzI37BwO/fjmDNOyzkboyxSa8zF0DjSJX+9722sGbfKp+0n+vPk8nItHn91EYZDc+GgDfejpTVx38YFdW5gLWCn0uUXGAt/zxGmv/nrqd2sjg8sTu3xTa921/dlHTuCmKw4vxOnH0d1Tpye47NDG0iZoLGzxzkdP4sVXXTjovoUJ0/75PV64g+SoZUthXB1tLX666BB63qaUw6E/1kbN5CL0ZQr5UlIoGGiSuxYhz7/8IK6ahmBBp1yaGPQUEKMN9KGnz2RbUedKVgp9TikKYFY1k+PU9gyPHN/Cd19xXe/vjGn4+hQ9wCeetRZ3HD2Br/+yyxfTb4bunjw5WRrd0tyr+csXUVnV+MJjJ/G9mbViSN72tc/HS685otzDUS67VXgtmq+8ITwcuFPomc62nLDFJ07mh0EuW0yH0M+Oj+PHv/kl6ufaARd9MehAM4+ryuJLz2zi61542aK6uRRZOUXnFL6o7nmi4bhzUugLY5IRLoBvUj96YhtPn5niJYoym0tadHdmUuITDz6Dl1+7oHa1Wylhi/cdO4NJWePFVw8zrf/e1z4fX/X8UBl2lMsVu5dyoXF47iUHcJXiuDWmOYnpwox4cSDPKfroiYYbzkkqWrbkUC5nQ7RaLn0x6EDT/8dObmNS1rhuF0e4ACuFPrdwpUsRLjdloMSNcYHrerzknBa54+hxAMBLr945f9603XDof/yFJzEpa/zNl161kHZj9wJ8hE4O0S+/anHPc3jfeFdwxTEhS+XVCjpvvjeDTHnpv9HkQ3c+gSsu2NgVCJ3CCPsol2WLLKlxYnPWG4NOv3vgqQa0PXcXx6ADK8plbuE85u0PH8fBzLC5X/yer+i9jk+8zx49gbWRwYuuXAylQJvF7332UVx+eAO3LIi3jN0L8BH65x45iX1rBZ532WIQ9agwuOmKw7vaUUUb26uff7H6/XUXHxhksWi1frg8+NQZfOSeY/iH33BTbynasyG3XH8R/vE33oTXvEDf0M6WyOigX/7LB1Fb4I1fnj4wxxjg4We2sD5O15DZDZKl0I0xbwDw/wAYAfgla+1Piu9N+/2bAGwC+DvW2k8tuK+7Ssjsvf3h43jfJ4/i2155dVbYXI7jhybe4ye28b5PHsVLrzmSdXJ7jhTG4OT2DJ948Fl896uuW2qon0ToDz51Bu+77WF85Q2XLEzR/KPX34QDu7j6HYBujDX+HAB+5QdeNay9HoT+a//5IYwLg7e86tpB7S5L9q2N8ENff+O57oZHk57anuE9H30A33jzFfiyK9NKmubx97/m+qXlbCxKehW6MWYE4F0AvhHAUQCfMMZ8wFr7eXbZGwHc2P73lQB+sf173kphgKdPT/AP/8NncNmhDfzof3Xzwto2xuDp01P8vV/9JM5MSvzv36o7eeZt+6P3Pg0A+OZXXL2wdvV7NX8ra3H7w8fxzvffgdHI4CcW+Dx/44WLcRYvU7755Vfh8sMbKn8ODA+ZjTlFz0xKvO+2h/GrH/sSXv/iK3YF3bKbxJimfO79x07jp/7TF3Bia4Yfet0Len/X1F4f47//uuefhV7uTHIQ+qsA3GutvR8AjDHvBfBmAFyhvxnAv7MNB/ExY8wRY8yV1trHFt7jXSLr4wKPntjGwfURbn3rLdGEiXlkbWRw9xOnMC4Mfv67X5HFzefKoY0RLtg3xv/5HS9bqkMUcMjmO9/9Vyhri/VxgX/1vf2U0/kmz7vs0MIoJqDZAB49vo2v/ek/RVlZlHVT64eKrX3NjZfin//NFy/sfueLjIzBI8e38Lqf+TA2xgX+0TfepEZOSfm+11yP51ywb1dXWSTJUehXA3iY/f9RhOhbu+ZqAJ5CN8b8IIAfBIDrrusP8dvN8g+/4Sa88cuvxOtedPnCCxr9T9/0Itz98lN43YsuX7iJ9/+85RVYGxVnJdvtFdcdwfe/9nqsjQrcdMVhfOOXXZEdybGSuHzbV1yN7bLCuDAYFwXGhcFoZHDVhfvwsmuP4KtfcOmu9imcK/nbr34ujhxYw9VH9uONL7ky24L5/tfesOSeLU5yNJE2M6S9l3MNrLW3ArgVAG655ZbMY253p9x4xeGlxT6/7NojeNmS0HPM7F+GHN63hv/1v14hxUXLa55/KV7z/EvPdTf2nLz82iNLt0rPteSELR4FwL0r1wB4dI5rVrKSlaxkJUuUHIX+CQA3GmNuMMasA3gLgA+Iaz4A4K2mkVcDOHE+8+crWclKVrIbpZdysdaWxph3APgQmrDF91hr7zTGvK39/t0APogmZPFeNGGL37+8Lq9kJStZyUo0yfLmWWs/iEZp88/ezf5tAbx9sV1byUpWspKVDJFV6v9KVrKSlZwnslLoK1nJSlZynshKoa9kJStZyXkiK4W+kpWsZCXniZic08OXcmNjjgF4aM6fXwrgqQV2Z5GyW/u26tcw2a39AnZv31b9Gibz9uu51lr1pI1zptB3IsaY26y1t5zrfmiyW/u26tcw2a39AnZv31b9GibL6NeKclnJSlaykvNEVgp9JStZyUrOE9mrCv3Wc92BhOzWvq36NUx2a7+A3du3Vb+GycL7tSc59JWsZCUrWUkoexWhr2QlK1nJSoSsFPpKVrKSlZwnsucUujHmDcaYu40x9xpj3nkO+3GtMeZPjTF3GWPuNMb8cPv5jxljHjHGfKb9703noG8PGmPuaO9/W/vZxcaYPzTGfLH9239a9eL79UI2Lp8xxpw0xvyDczFmxpj3GGOeNMZ8jn0WHSNjzD9t59zdxphvOsv9+mljzBeMMZ81xvxHY8yR9vPrjTFbbNzeHW14Of2KvrezNV6Jvv0G69eDxpjPtJ+flTFL6IflzjFr7Z75D0353vsAPA/AOoDbAdx8jvpyJYBXtv8+DOAeADcD+DEA/+Qcj9ODAC4Vn/0fAN7Z/vudAH5qF7zLxwE891yMGYC/DuCVAD7XN0bte70dwAaAG9o5ODqL/Xo9gHH7759i/bqeX3cOxkt9b2dzvGJ9E9//DIB/fjbHLKEfljrH9hpC7w6sttZOAdCB1WddrLWPWWs/1f77FIC70JyjulvlzQD+bfvvfwvgm89dVwAAXw/gPmvtvNnCOxJr7UcAPCM+jo3RmwG811o7sdY+gKbu/6vOVr+stX9grS3b//0YmhPBzqpExismZ228+vpmmsNVvxPAry/r/pE+xfTDUufYXlPoscOoz6kYY64H8AoA/7n96B2tefyec0FtoDnP9Q+MMZ9sD+YGgCtse4pU+/fyc9AvLm+Bv8jO9ZgB8THaTfPuvwXw++z/bzDGfNoY82FjzNecg/5o7203jdfXAHjCWvtF9tlZHTOhH5Y6x/aaQs86jPpsijHmEIDfBPAPrLUnAfwigOcDeDmAx9CYe2dbXmutfSWANwJ4uzHmr5+DPkTFNEcZ/i0A72s/2g1jlpJdMe+MMT8KoATwa+1HjwG4zlr7CgD/CMC/N8ZccBa7FHtvu2K8Wvku+MDhrI6Zoh+ilyqfDR6zvabQd9Vh1MaYNTQv69este8HAGvtE9baylpbA/h/sURTMybW2kfbv08C+I9tH54wxlzZ9vtKAE+e7X4xeSOAT1lrnwB2x5i1Ehujcz7vjDHfB+BvAvjbtiVdW/P86fbfn0TDu950tvqUeG/nfLwAwBgzBvCtAH6DPjubY6bpByx5ju01hZ5zYPVZkZab+9cA7rLW/iz7/Ep22bcA+Jz87ZL7ddAYc5j+jcah9jk04/R97WXfB+C3z2a/hHio6VyPGZPYGH0AwFuMMRvGmBsA3Ajg42erU8aYNwD4EQB/y1q7yT6/zBgzav/9vLZf95/FfsXe2zkdLybfAOAL1tqj9MHZGrOYfsCy59iyvb1L8B6/CY3H+D4AP3oO+/HVaEyizwL4TPvfmwD8CoA72s8/AODKs9yv56Hxlt8O4E4aIwCXAPhjAF9s/158jsbtAICnAVzIPjvrY4ZmQ3kMwAwNOvqB1BgB+NF2zt0N4I1nuV/3ouFXaZ69u73229p3fDuATwH4r89yv6Lv7WyNV6xv7ee/DOBt4tqzMmYJ/bDUObZK/V/JSlaykvNE9hrlspKVrGQlK4nISqGvZCUrWcl5IiuFvpKVrGQl54msFPpKVrKSlZwnslLoK1nJSlZynshKoa9kJStZyXkiK4W+kpWsZCXnifz/3pXgwVliJTQAAAAASUVORK5CYII=\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "filenames": { + "image/png": "/home/john/gh_synced/books/sed2/edtc-code/code_book/_build/jupyter_execute/ch4_9_0.png" + }, + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "q = DS(h=lambda x: 4 * x * (1 - x), x=0.11)\n", + "t = q.trajectory(200)\n", + "\n", + "fig, ax = plt.subplots()\n", + "ax.plot(t)\n", + "\n", + "plt.show()\n" + ] + }, + { + "cell_type": "markdown", + "id": "06806e4c", + "metadata": {}, + "source": [ + "Now let's generate a histograms from a long trajectory, to address exercise\n", + "4.16." + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "id": "146c5baa", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "filenames": { + "image/png": "/home/john/gh_synced/books/sed2/edtc-code/code_book/_build/jupyter_execute/ch4_11_0.png" + }, + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "q.x = 0.11\n", + "t = q.trajectory(5000)\n", + "\n", + "fig, ax = plt.subplots()\n", + "ax.hist(t, bins=40, alpha=0.5, edgecolor='k')\n", + "\n", + "plt.show()\n" + ] + }, + { + "cell_type": "markdown", + "id": "649d698f", + "metadata": {}, + "source": [ + "If you experiment with different initial conditions you will find that, for\n", + "all most all choices, the histogram looks the same." + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "id": "f518b173", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "filenames": { + "image/png": "/home/john/gh_synced/books/sed2/edtc-code/code_book/_build/jupyter_execute/ch4_13_0.png" + }, + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "q.x = 0.65\n", + "t = q.trajectory(5000)\n", + "\n", + "fig, ax = plt.subplots()\n", + "ax.hist(t, bins=40, alpha=0.5, edgecolor='k')\n", + "\n", + "plt.show()\n" + ] + }, + { + "cell_type": "markdown", + "id": "222c5078", + "metadata": {}, + "source": [ + "What we have learned is that, although the trajectories seem very random, when\n", + "we take a statistical perspective we can make predictions.\n", + "\n", + "In particular, we can say what will happen \"one average, in the long run.\"\n", + "\n", + "\n", + "Here's the set of maps." + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "id": "eed3c4b7", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "filenames": { + "image/png": "/home/john/gh_synced/books/sed2/edtc-code/code_book/_build/jupyter_execute/ch4_15_0.png" + }, + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "xgrid = np.linspace(0, 1, 100)\n", + "\n", + "h = lambda x, r: r * x * (1 - x)\n", + "\n", + "fig, ax = plt.subplots()\n", + "\n", + "ax.plot(xgrid, xgrid, '-', color='grey')\n", + "\n", + "r = 0\n", + "step = 0.3\n", + "\n", + "while r <= 4:\n", + " y = [h(x, r) for x in xgrid]\n", + " ax.plot(xgrid, y)\n", + " r = r + step\n", + "\n", + "plt.show()\n" + ] + }, + { + "cell_type": "markdown", + "id": "6e754c9f", + "metadata": {}, + "source": [ + "Here's the bifurcation diagram." + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "id": "5a741047", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "filenames": { + "image/png": "/home/john/gh_synced/books/sed2/edtc-code/code_book/_build/jupyter_execute/ch4_17_0.png" + }, + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "q = DS(h=None, x=0.1)\n", + "\n", + "fig, ax = plt.subplots()\n", + "\n", + "r = 2.5\n", + "while r < 4:\n", + " q.h = lambda x: r * x * (1 - x)\n", + " t = q.trajectory(1000)[950:]\n", + " ax.plot([r] * len(t), t, 'k.', ms=0.4)\n", + " r = r + 0.005\n", + "\n", + "ax.set_xlabel('$r$', fontsize=16)\n", + "plt.show()\n" + ] + }, + { + "cell_type": "markdown", + "id": "1b45504b", + "metadata": {}, + "source": [ + "## Markov Chains\n", + "\n", + "\n", + "Our first task is to simulate time series from Hamilton's Markov chain" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "id": "4fa2d905", + "metadata": {}, + "outputs": [], + "source": [ + "p_H = ((0.971, 0.029, 0.000), # Hamilton's kernel\n", + " (0.145, 0.778, 0.077),\n", + " (0.000, 0.508, 0.492))\n", + "\n", + "p_H = np.array(p_H) # Convert to numpy array\n", + "\n", + "S = np.array((0, 1, 2))" + ] + }, + { + "cell_type": "markdown", + "id": "5d632673", + "metadata": {}, + "source": [ + "We'll borrow this code from Chapter 2." + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "id": "c6ce79ee", + "metadata": {}, + "outputs": [], + "source": [ + "@jit\n", + "def tau(z, S, phi):\n", + " i = np.searchsorted(np.cumsum(phi), z)\n", + " return S[i]" + ] + }, + { + "cell_type": "markdown", + "id": "242fcc91", + "metadata": {}, + "source": [ + "(We have targeted the function for JIT compilation via `@jit` because we need\n", + "fast execution below.)\n", + "\n", + "As discussed in that chapter, if we create a function `tau` using this code and feed it uniform draws on $(0,1]$, we get draws from `S` distributed according to `phi`.\n", + "\n", + "Here's some code to generate a trajectory starting at $x \\in S$, using\n", + "stochastic kernel $p$." + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "id": "de847ead", + "metadata": {}, + "outputs": [], + "source": [ + "def trajectory(x, p, S, n=100):\n", + "\n", + " X = np.empty(n, dtype=int)\n", + " X[0] = x\n", + " for t in range(n-1):\n", + " W = np.random.rand()\n", + " X[t+1] = tau(W, S, p[X[t], :])\n", + " return X" + ] + }, + { + "cell_type": "markdown", + "id": "ab27ec69", + "metadata": {}, + "source": [ + "Let's plot a trajectory." + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "id": "d654bc0f", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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JsFkL4BrTtgLAl0Tkmw2cQ6305RdcGY9g9ACzg5mp6eGohUeCRiwbfcyjNFHQi8hFE9a/H8D7Pe17AZxe3CNs7KibmH/BlfEMbY0eHTpj1UYfNEMRy5TbcWeWgc6MdUhzoABxFwNWxpNG3QDJeHdZSlDj6MNFAMt0E+8gqaB3UI1+NhDrB33QgaC1SwlqUrNwGQ7FMuV23JlloILeIafRxzyyyljE0ugT00m7xx/aGj3i1hb7jK0QxDxGKugdBMCKufh/wZXxpIVHAJOCoO3wSmia4hgQwJop321floMKegfJOV8iHlllLEOT6wZInbHtHt9OgUBNUxwsw1xKlI47swxU0DuIQOPoZwCRUfqDwaD94tz2hClqKcFgsSfWxRycoYLeYaga/UwwFIxs9OiylGCavVLvtRAZ9iQ4QwW9w9DW6Dvui9IcdlbCLsIr7cIjXUT9KNWwfTkxK34q6B2S8MrR/0o/saMpujCduGmKYxYifUZEehGcoYLewU5qFvPAKuOxJ0x1YToZzYxlJ6YjpRrDnDyId5BU0DsI+mGTU8YjQC5NcRe5bgbZD037zmClGnZSs5hHSAW9Q18KDSjjyYdXdmOjpx3Hr7dakNgafa9LCc4ao0IDcf+CK+NxUyC0/QwX8+EroZGFwPbgDV8FvYtAa8bOAG4KhPZz3eSzZ+rbY3ikQ5LZ6CP+OVZB79CXmXDKeOycRl05Y7PsmQNNgRAi6ZD0QR6ooHewc1uoltVfBPk0xa2HVyL/Q6P3WnikYzITgp7k5SQPkPSWAWTCp0juIXk7yTOtdVtI3mvWXVJnx5uiL4UGlPEMh24pwZadsUPLdATV6EPEFfQx/xhX0eivALBlzPrzAGwyf1sBfA4ASM4BuMys3wzgIpKbl9PZNsjnuol3YJXJ5JyhnYRXWuGdEdt/+4pdHAaIOzijSinBG0luGLPJBQC+IIlUvJnksSRPBLABwB5TUhAkrzLb3rXsXjfAcCj4q6/dhYeffCbT6D9zwx6873UbszC4kLlj3+PY9p37clrHkc9ZgUvP34znP3dlhz3rnoOHhvj4jt341VMHs7aHn3wml+vmlvsfxQe/uCtbf9r6Y/HBc17SWJ9y4Z0Enj0s+OHeR/DqFx/f2DH7hIjgr79xD4ZDwUff+vJantEv3vwAXrHuGJxx0rEAgG/fuwgA2Uz5y27Yg+OPXIVXrDsGn/32Htyx73Hv9xyxagUufdtmHHNEOM9dHTb6dQAetJb3mbaydi8kt5JcILmwuLhYQ7emY/HJZ3DFTffjmOetxLmnrgUA/OqpZ/HE04da78tS2HnnQ/j6HQ/hvsUncd/ik7jjF4/j/+7ah92/eKLrrnXOA4/8Blf+6Oe49cFfZddnw/FH4uyXrgYAvPnUtTj6uSuydT/Y+wg+9+09jfZJrKRqr96YCPev3PqLRo/ZJ35z8DC237gXn//ez2p7Rj/2lTvx9su+ny3/4+37AQDvOHM9XnXKcfjRzx7Ftbt/CQD47A334Qd7H8numfTvzv2P4+of78Nt+35VS5/qYqJGXwHfT6mMafciItsBbAeA+fn51t+SUk34w7//MvyrM9fj8aefxV/+413RvFIPRbBqxQDX/fkbAAA/uO8RXPQ/b46m/02S+lo+9tbNeOtpJxbWf+S8l+Mj5708W/4vO3bj6h/va7RPYk2Yev3L1mDt85+jdvopsN9cG7vHBXjpCUfh3FNfiHNPfSFe/JGvZ2M0FME7zzwJH3tb3hq964FH8Y7P/SC4p64OQb8PwEnW8noA+wGsKmkPklFpt+STTnvo2BNwACuHdiT9b5JRpshq27dhsx8649XF7NyYkeHo/6aeUdu8BuSTzw2t1Ag2ZJiO2zpMNzsAvMdE37wGwOMi8hCAWwBsIrmR5CoAF5ptg8ROMgXE55AVa0YvoMVTbEaZIqtJ+kELcfUCZ7w0DcJU2Fp8U2Nlz54G8mG4tunNJts+sLGcqNGTvBLAOQBWk9wH4OMAVgKAiGwDsBPAWwDsAfAUgPeadYdIXgzgWgBzAC4Xkd0NnEMtZMIA+c9YNPpkpuWIUf8jOYEGGWY/4tW2ZwspEYaOoOiiQHnM2NeqUY3eeajSe0msmc3Ib5LtGxJVom4umrBeAHyoZN1OJD8EweOGUjELqQprwMpwtQ/2ICSsbgaVNXo2Pu52KUOgmwLlMWNr8U1dNzvDKWBMbTI6ps8UmIViBjaUOjPW4Gp92RtYYANWxlDyKn3a/9A0iy7IxrbqDi1o9OLYfzWD5XTY49PUdSuMEWwbvf8NMdTnTgW9IR2W0SSWMH+Zx+HaEwGoSg/rba3i3T5I1OtGsbOkpseMxR8UAnkbfUPHkPw9Y/tRXJ9YSqiPnQp6g6vRDwL9ZS7DtSeGaivsgpFGX02nbyObpOvMG6iNfirs4WlqrNwfY9uP4vrEsm0QZhCHCnqDG3WTDlgsgtKnISbtXfUoHNJrUNUZ20YNVzt7JqCpiqfFvlbNCXoUzGtDkYKssEnfAEJ77lTQG0bO2OQzNhu9G0c/6n8kJ9AoaRz9FOGVTXYH+eyZQOqMVapi39aNmW7gOmPz5lzf/RSqyVcFvSHT+rKMhmEOWBlJ//NRHKP22WZajR4tTJhyTTdaN3Y6cjNjm3TGOj/GQ5Gx4bqhmkxV0Bsk0/qQ+4wn5C0f7jXSNmLpf3OM08B8DFp4GypMcNOom6nIafQ13OO+sfZOmBI7cKP4PaGGNaugNwzNlGo3vDIWjXg4dDVE0x5J/5tk2vDKkX+moQ7BN8FNUyBMQ94ZW+/3jb7XDa90NfoxUTeBjaUKeoM7eCNnZlgDVka5MzaO/jfJuAfTRxsRV8WIDv1Rnoa6nbG+7yiLuhml1Ch+T6jPnQp6hywFQmQ2eoE/BUIs/W+UKW30bTjiBfn+dFH8JGbsS1XHdfN9RdGPkmw5SpdSngIhtLFUQW8YZThMwysTQnsFKyOJoy+mQAhNs+iCUWbSinH0LVw7KYxXPPdaCOSdsc1o9MW5DomJdFw21FDDmlXQG9zZk9GVD/PM4lMSXEf7JKr+ICwHNxy2iwLlMZN3xtb7faPv9cxetly/Y2fGBvajrYLe4M6eDDVnRRmJ40g1eh/Thle2MfbF8dKxmgZbkNZx3fzOWMd0Y9rGhlcGOv9GBb0hHRc3BUJoA1aGQAuPlDFuJqOPNq6dP46+ueP1jfpt9D7TTdEZKzln7JgJU4G9n6mgNxRSIESmESfahz2lPkxbYReMnGfVaCP9hTteA9Xop6L+qBt/m8+PkskKz/eEGtasgt5QVkowlmevkNQsMtNTk7iO9km08bAm2qJ1TMRzr4XA0ColWMd18ztj/aUEXVkBZ5uy7+uSSoKe5BaS95LcQ/ISz/q/IHmr+buT5GGSLzDr7id5h1m3UPcJ1IU7ezLUnBWluLP4RlN7Z57pZ8Y2f+3E6U8bxU76RN1piv3O2KI5VDB6+/fXjK2vT3VSpZTgHIDLALwZSSHwW0juEJG70m1E5BMAPmG2Px/An4vIo9bXvFFEHq615zXjzp6MTSP2zeJL22edpZQStPdrAt8bmK2lKuPJz4ytwxnrnzDlhiwnzliz7PmemNMUnwVgj4jsFZGDAK4CcMGY7S8CcGUdnWsT18ESW3ilLy8HEE//m8R1tE+ijWsnBfuvavTT0Ep4pRMCm9noUe7cD/VFuoqgXwfgQWt5n2krQPIIAFsAXG01C4DrSO4iubXsICS3klwgubC4uFihW/UirtYXo0avNnovI+fZtDb6psMrrWMiPAdeyLSTAgHIZYQFnKib4vdkQRyBDWYVQe97OsrO4nwA33fMNmeLyJkAzgPwIZKv9+0oIttFZF5E5tesWVOhW/XiToKIzUYvKEYIAPH0v0ncyXCTaCP9hW/CVHBqYMDUH17paZNiRlixUiD489GXf1+XVLn19wE4yVpeD2B/ybYXwjHbiMh+83kAwDVITEHBUVZKMDRbWxm+QsZp+6zj1hqYRBvpL5LCI7bzXN++pqGtFAiFxHPDoj/PJtSw5iqC/hYAm0huJLkKiTDf4W5E8hgAbwDwVavtSJJHp/8DOBfAnXV0vG6K4ZVhDlgZQ/GnQIil/00yLjeJjzbylQyHjv1X0xRPRX5mbB3fV2xzzaGj8MrycF0Oiv0LgYlRNyJyiOTFAK4FMAfgchHZTfIDZv02s+kfArhORH5j7b4WwDVGc1kB4Esi8s06T6Au3AlTMWr0XmdsJP1vkpEzdsqZsQ2+gLsavVpupiPnjG0oBYIbAkuTj2icjT5Uk+9EQQ8AIrITwE6nbZuzfAWAK5y2vQBOX1YPW6IwezIyjdhXyDhtn3UKjvYJtHHtiuNFHaspsK9VHdetLB89cm9d6cxYs+zT6Md8X5fozFjDKMOhG14Z1oCVUXTGanhlyrQTptjG21AhHBbhqYEBY49NLaUESxoHjh9FxJYVxV1CDWtWQW8olBI07bE8e75Cxmn7rDN9KcGEJi9dIRwW+vY1Dfa1qiUFgufiF0Ng8ykQxmWvVI0+UFwHSzq9ObQBK0NLCZYzbeGRNq6db7x0rKrTVppiNwWCnaZ4fD76ZXepVlTQG9xxiS3Nr2NOjO6NpEmWaqNv2HKjaYqXQf1x9J7wSqfwCBxnrI9Qw5pV0Buk8Csdl0ZcrtF31aNwGBcl4aMdjb44wS2Wey0EWklTPEROexqkKRDGaPShhjWroDe4sydDneFWRpI7ZbQ8SsAYyxk0h+ton0QLySuBwqzLJg/WP+rPdeP/lkKGUSnOovdtH9pvtgp6gzt7spXIixopFfRxdL9Rpi8l2PzYF8IrdcLUVNQ/M9Z/DNccak+YUmdshLghU9HZ6D2FjIF4fqiaZNrwylZKCbrjNYjnXguBum30vvcCNwVCptFn91PxW0INa1ZBb3C1vhhTILjhemn7rDN9eGU7KRDy46Ua/TTUnQKhVKN3VHpboy+7o9J0xiGhgt5QrBmbtMfy8Gl4ZTlLLQ7efOERJwWCDlVl7CItTaYpduv6TtLok/bwfrRV0Bvc1/tQnSpliCeKI22fdUbOs2rbt5GmGCimKdahqk7t4ZUlU2OnTVOctIf33KmgN5SVEgztFayMQppitdFnpLMeq2r07RUe0fDKpdJGmuKCOdSZMFV2OyVmuGV3qVZU0BtKNfquOjQlgqLGmhYznnWm1eirOm2Xg4ibVlonTE1D/eGVvraiOTQpJTha9pFkIg1rMFXQG9xf6Rht9K7GygBthV2w1MIjrWr0DR+vb7SVAsG9Y2yNvux2CtHfooLekPnRYw2vlBKNPpL+N0nmjK14tw+y4hENdQi+eQ+q0U9D7TZ6b3ilUwXMSYFQbqNncCbTSrc+yS0k7yW5h+QlnvXnkHyc5K3m79Kq+4ZCMeomrqgVt5BxshSerbALJihgBUbhlc1dvMTU5kZ06GBVpY0UCG4cfRo2OSo274cl39clEwuPkJwDcBmANyOpH3sLyR0icpez6XdF5G1L3LdziqUEE2J59txCxkCY8bxdMC7boI92Co8U00qHJhxCpvY0xV5nbFkpwdGyj1jDK88CsEdE9orIQQBXAbig4vcvZ99WKXfGhjVgZbjaB6AheymTnGcuo+0a1Oh9sy51tCpTe+ERn0aPYpriJI5esmUfsdro1wF40FreZ9pcXkvyNpLfIHnqlPuC5FaSCyQXFhcXK3SrXsrCK+2JGSFTmMUHoyWqmjgxHM6lNY3eOaYOVXVsQVrHM+p78y0GONA4Y7NFL4zURu87HfcsfgzgFBE5HcCnAXxlin2TRpHtIjIvIvNr1qyp0K16GTljYw6vVI3eR2ajnzK8snlnrG3/VWfsNNhafC3hlb42x2GepSmekA01xLDmKoJ+H4CTrOX1APbbG4jIEyLypPl/J4CVJFdX2TcUyopThGZrK8MtZAxoyF7KyHkWTnhlofQj1J8yDbWnQPC8TiWPVDFNxSTnfohhzVUE/S0ANpHcSHIVgAsB7LA3IPlCGvWE5Fnmex+psm8opAPtlhKM5eHz2ehDtBV2geton0QbEVfFMnXhCYeQaStNsW+MMud+yQ2VlhwMiYlRNyJyiOTFAK4FMAfgchHZTfIDZv02AO8E8EGShwA8DeBCSa6+d9+GzmVZjBx2+c9Ynj1f1M1gEJ6tsAsmxT27ZNexSdNNIa10eK/7IdNKHD18DvPJSc1CNMNNFPRAZo7Z6bRts/7/DIDPVN03RAqFR2JMU+y0hRjP2wXTO2ObH/tiHhWq43wK6k5T7J8Zu8Q0xQjPEqAzYw3u7MlRKcGwBqyMQiFjaMheiuton0QbY190xqpGPw35XDcNhVc6YzQwg+S+/buEmLdIBb2h4GBpIcSuTtxCxoCG7KW4js9JtBFeWcg2ivCEQ8jYY1NP4ZH8l/hmv6bBDZPqG4SYiVQFvcENmcq048AGbBxFZ6wKD8DvqB5HGymei/bf8F73QyanxdeR1Mxd9vh1Uj/KJBt9iGHNKugNxVKC+fbQcSfgAGHaCrvAd23G0Ub6C02BsDya1uh9fp00bLJKNlTV6APFzYcSWyk+t5QgoCF7KcMpNfo2xn44LOY617GqTv1pil1Bn3wO3B/j4WTnfoiF3lXQG9zZkzGWEhw4o6lpihME09noW5kZC0+a4uYO1ztyztgGom5S01DBGQu/Wccm2jTFs0Bh9mTmkAtrwMrwpimmpikGilPZJ9FG0Rn/rEsdrKo0nabYlzaj6Iz1f1eIYc0q6A2ug6XqLMpwKElTrHpioSTcJDI/fEP9AYoT3PTtazrqvlbuj6zfGZsENwiK62zUGRswI2csc58xafS+7JWRdL9RfJPJxpFq2k1q2IUJU1Ab/TQ0rdG72WyBUdjkxAl4Gl4ZLiNnLHKfob2ClaHO2HJ812Ycqa+j6TTFbuheLPdaCNi3dT0zY/1RN/kKU/k0xeMnTIU1mCroDe7syRidsf7wyi56ExYimEqlH2n0zfQHSJ2xeSGSHFMHrAq5NMV1CPqSZTcEFhBrjMalQFh+n+pEBb2hbPZkLBpxsUiCavQp09roR29zTTpji3H0SXtjh+wV+Tj6Okw3jo3epEGm562ryoSp0J47FfQGd/bkNIIhCDyx4po/JSGZhVp9+0y7bqY7yXdLMU1x08fsE/U7Y53lbKb8qC01yUwqPBKib0wFvcFX2g2IpxSfv5RgeLbCLvC97YxjpF036YyVfHil1a5MJueMreEZLc6MTT6LuW5GRU9KwysDDGtWQW9ItD7P5IiO+jMtPq1VQ/YSXO15Em1NmMppi4Pmj9lX6r5kYsXK28VFmGn0CeNKCYYmOVTQG9xSfLFpWD6tVUP2EnyTycbR9NgnggRelVDHqxq2Fl+3jd6OrHHf8kUmHy/EvEWVBD3JLSTvJbmH5CWe9e8iebv5u4nk6da6+0neQfJWkgt1dr5OXK2vjVS1dVIWRx9L/5vEV31rHKNcN031Jz1O8Zgq56tRe1IzpwatLxVx6mT1afs2ITpjJ1aYIjkH4DIAb0ZS7PsWkjtE5C5rs58BeIOIPEbyPADbAbzaWv9GEXm4xn7XjhuZQTIRnIENWCkeZ2yIBRC6wHW0T6JpG73v1T+2Qjdd02Sa4rLZr1XTFIeYHryKRn8WgD0isldEDgK4CsAF9gYicpOIPGYWbwawvt5uNk/spfi8aYo1fwoAv6N6HE2HOpbNukzWNXPMvmFPWqo7TXHZ7NeqaYrTnDghUUXQrwPwoLW8z7SV8T4A37CWBcB1JHeR3Fq2E8mtJBdILiwuLlboVr34tL6YSvG5zmQgzJwbXeC7NuMYOeKbstGb4wzyZoFknY5YJYw5rrZn1A2v9GjtqY3eF3ppE2KerCrFwX3d9l5Zkm9EIuhfZzWfLSL7SZ4A4HqS94jIjYUvFNmOxOSD+fn51u921xkLxGXj9odXhqdZdMG016Bp7Xpcf2K537om8Umxtme0VKPPhcDSOGOzBi8M0EZfRaPfB+Aka3k9gP3uRiRPA/B5ABeIyCNpu4jsN58HAFyDxBQUJDGX4hMp1rCMqf+NIsVc/eNoyzHqnaCn41UJMdla67rHCzb61DyTc5gbbd6TB8cmxLDmKrf/LQA2kdxIchWACwHssDcgeTKALwN4t4j8xGo/kuTR6f8AzgVwZ12drxOvRow4XqV9hYzT5dA0iy5wJydNounwSr/9t9lj9o3Ep8banlFXox8JejtAozz00ibEsOaJphsROUTyYgDXApgDcLmI7Cb5AbN+G4BLARwP4LPmwhwSkXkAawFcY9pWAPiSiHyzkTNZJjFnfxw5ptz+h6dZdMFwyglTTScY82U/jK10Zdekilldz6gbrulms03+Z86sMy4FQmgmuCo2eojITgA7nbZt1v/vB/B+z357AZzutoeIb/ZkLIJSPDdlshyPM7lJpnfGjvZrAvEIiqaP2TvMvJHanlH7S0rCK1MzkZQoVrD2ORyYpNeZsYaYS/GNiqbk28n8RJBZxedoH0dWdKahwfd+rWr0U5G+gdf1jLrZML3mNWt9rsEhxCAIFfQZ8Zbi8xUyTpdj6H/jTDlhqnHt2qMRZveeDlcl0nDoup5R20xnT4ryFQf3mXVsQgxrVkFvGA49GjFiMd0kn77+x/BG0jS+yWTjSB23TYdX5rXFZo/ZN9IJjnU9o65G7wtwSMfr0NCvWNnbqUYfKF5n7CAWZ6zfORRiSbMumLaUIM1T0ZwzttxGH8P9FgKZM7amZ7QYR5/87x2j4XiNPkSTrwp6g89hF0uumLLcG4NBHG8kTSMyppCzh6bj6EeOPs8xmzlkLyHZzDMq/tmvqQZ/2Pi9xqYpDuzBU0Fv8GkFscSh+2bxpcsx9L9p0lmUVWkrjt7n6Yul0E3XDE0KhLqe0UKaYk9xkfT/wxOOF6LJVAV9imf2JAN0qvhI++iLuomh/82ztDTFzTtji8dUqjFyxtbzjOajK8Ub4JA5YzPTTXl4ZWhBECroDb7Zk7Fkf/QVMk6XQ9MsusCXq38cTc9S9WU/bPotom+kNvq6nlF3wpQvgjL9P9Xoy+6pEMOaVdAbEht9vi2aCVMl2fRCtBV2gVtrYBJNpyn2Fp7OHMDNHLNvCFIbfT3XzNbAswpg8OcjmqTRh2gJUEFv8NlxY7Fxl+XeCNFW2AW+WgPjSDXtplMg+MMrdcCqICZktq5nNGe6kfH5iLLwypLvIsKzBKigN/iSmtVV1KBpsnA9R6WPJVdP0/jq6Y5jFOrYUH88cdhNp0buG8Nhcn/XVnjEqUHrC4EdRd2MN92E+NypoE/xzJ6MJc2vbxZfuhxD/9tgSc7Yhq+dN01xcC/9YdJ4mmLzv5umGLD9AyXO2ADDmlXQG2IuxVeapjjAGXpdMK1G37wztnzWpWr01bALjzSTptjz1mU+Dw/Hz7QO0eSrgt4gHo0+xJwVPkYTcNz+t9+XEPFlJh1Hlqa4wf4A+XDett4i+kI6Ca6uZ9RJXumdhJiaRifNtA4xrFkFvSHmUnw+xxEQpmbRBdMWHgGafZvzl6nLr1PGI1Z4ZT3O2HzUzbgQ2MPD8cXmQzSZqqA3pOFaNpoCoR9MmwIBaHbsffZfqkY/FUk4dH0pEAo2ek+GSjsFwjhT4CBAk28lQU9yC8l7Se4heYlnPUl+yqy/neSZVfcNhTRcy0ZTIPSDpQj6Jsfea/9t2C/QN1KfWmMpELJf49E2WQqE4XCCjT48X8tEQU9yDsBlAM4DsBnARSQ3O5udB2CT+dsK4HNT7BsEQ/GlQIhDw/KlTkmXY+h/00ybvRJIQ+Sa6k96jPzxAB2vqgzFykdfR3hlbmaswF8FzGj0Hn+eTYjhlVVKCZ4FYI8pCwiSVwG4AMBd1jYXAPiCJFfnZpLHkjwRwIYK+9bG+Z/+Hn777OEl7fuLXz2Nl6w5Ktc2IPGdnyzizZ/8Th3da4xnTTo9n+npwceeCr7/TfPgY0/hVaccN9U+JPC/b/k5vnX3P9fen2cOmfGCLUSSz3/3pV147oq52o/ZNx56/Lc44fnPqe0ZffjJZ7L//+3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+ "text/plain": [ + "
" + ] + }, + "metadata": { + "filenames": { + "image/png": "/home/john/gh_synced/books/sed2/edtc-code/code_book/_build/jupyter_execute/ch4_25_0.png" + }, + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "fig, ax = plt.subplots()\n", + "\n", + "X = trajectory(0, p_H, S, n=500)\n", + "\n", + "ax.plot(X)\n", + "plt.show()\n" + ] + }, + { + "cell_type": "markdown", + "id": "5d693b52", + "metadata": {}, + "source": [ + "Another option is to use existing code from QuantEcon. This code is\n", + "JIT-compiled and very fast." + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "id": "409d87c2", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "filenames": { + "image/png": "/home/john/gh_synced/books/sed2/edtc-code/code_book/_build/jupyter_execute/ch4_27_0.png" + }, + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "mc = MarkovChain(p_H, state_values=S)\n", + "X = mc.simulate(init=0, ts_length=500)\n", + "\n", + "fig, ax = plt.subplots()\n", + "ax.plot(X)\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "id": "b199ec2e", + "metadata": {}, + "source": [ + "Here's a solution to exercise 4.23." + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "id": "97744f53", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "0.59668" + ] + }, + "execution_count": 15, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "@jit\n", + "def compute_marginal(n=100_000, T=10):\n", + " X_vals = np.empty(n)\n", + "\n", + " for i in range(n):\n", + " X = 2 # start in state SR\n", + " for t in range(T):\n", + " W = np.random.rand()\n", + " X = tau(W, S, p_H[X, :])\n", + " X_vals[i] = X\n", + " return np.mean(X_vals == 0)\n", + "\n", + "compute_marginal()" + ] + }, + { + "cell_type": "markdown", + "id": "66b8358b", + "metadata": {}, + "source": [ + "The answer is close to 0.6, as expected.\n", + "\n", + "\n", + "Here's a solution to exercise 4.24." + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "id": "bc401ebe", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "0.59518" + ] + }, + "execution_count": 16, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "@jit\n", + "def compute_marginal_2(n=100_000, T=10):\n", + " counter = 0\n", + "\n", + " for i in range(n):\n", + " X = 2 # start in state SR\n", + " for t in range(T):\n", + " W = np.random.rand()\n", + " X = tau(W, S, p_H[X, :])\n", + " if X == 0:\n", + " counter += 1\n", + "\n", + " return counter / n\n", + "\n", + "compute_marginal_2()" + ] + }, + { + "cell_type": "markdown", + "id": "5c9e09f1", + "metadata": {}, + "source": [ + "Here's a solution to exercise 4.29." + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "id": "0954a7cc", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "885.347632676323\n" + ] + } + ], + "source": [ + "T = 5\n", + "psi = (1, 0, 0) # start in NG\n", + "h = (1000, 0, -1000) # profits\n", + "\n", + "for t in range(T):\n", + " psi = psi @ p_H\n", + "\n", + "print(psi @ h)" + ] + }, + { + "cell_type": "markdown", + "id": "24cf3c8f", + "metadata": {}, + "source": [ + "Now let's see what happens when we start in severe recession." + ] + }, + { + "cell_type": "code", + "execution_count": 18, + "id": "c878889c", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "217.74304876607997\n" + ] + } + ], + "source": [ + "psi = (0, 0, 1) \n", + "\n", + "for t in range(T):\n", + " psi = psi @ p_H\n", + "\n", + "print(psi @ h)" + ] + }, + { + "cell_type": "markdown", + "id": "bc27c624", + "metadata": {}, + "source": [ + "Profits are much lower because the Markov chain is relatively persistent,\n", + "implying that starting in recession increases the probability of recession at\n", + "date $t=5$.\n", + "\n", + "\n", + "Here's a solution to exercise 4.30." + ] + }, + { + "cell_type": "code", + "execution_count": 19, + "id": "d4981bbf", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Profits in state 0 at date 1000 equals 788.1599999999967\n", + "Profits in state 1 at date 1000 equals 788.1599999999974\n", + "Profits in state 2 at date 1000 equals 788.1599999999972\n" + ] + } + ], + "source": [ + "T = 1000\n", + "\n", + "for i in (0, 1, 2):\n", + " psi = np.zeros(3)\n", + " psi[i] = 1\n", + " for t in range(T):\n", + " psi = psi @ p_H\n", + " print(f\"Profits in state {i} at date {T} equals {psi @ h}\")" + ] + }, + { + "cell_type": "markdown", + "id": "0cb8c9b3", + "metadata": {}, + "source": [ + "Notice that profits are almost invariant with respect to the initial\n", + "condition.\n", + "\n", + "This is due to inherent stability of the kernel, which implies that initial\n", + "conditions become irrelevant after sufficient time has elapsed.\n", + "\n", + "Here's a solution to exercise 4.31." + ] + }, + { + "cell_type": "code", + "execution_count": 20, + "id": "6297b423", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "385.45189053788556\n" + ] + } + ], + "source": [ + "T = 5\n", + "psi = (0.2, 0.2, 0.6) \n", + "\n", + "for t in range(T):\n", + " psi = psi @ p_H\n", + "\n", + "print(psi @ h)" + ] + }, + { + "cell_type": "markdown", + "id": "97ab3c55", + "metadata": {}, + "source": [ + "Here's a solution to exercise 4.32." + ] + }, + { + "cell_type": "code", + "execution_count": 21, + "id": "025ca85c", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "0.0008410000000000001\n" + ] + } + ], + "source": [ + "def path_prob(p, psi, X): # X gives a time path\n", + " prob = psi[X[0]]\n", + " for t in range(len(X)-1):\n", + " prob = prob * p[X[t], X[t+1]]\n", + " return prob\n", + "\n", + "psi = np.array((0.2, 0.2, 0.6))\n", + "prob = path_prob(p_H, psi, (0, 1, 0))\n", + "\n", + "print(prob)" + ] + }, + { + "cell_type": "markdown", + "id": "779519b1", + "metadata": {}, + "source": [ + "Here's a solution to exercise 4.33." + ] + }, + { + "cell_type": "code", + "execution_count": 22, + "id": "215ea02b", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "0.704242\n" + ] + } + ], + "source": [ + "counter = 0\n", + "recession_states = 1, 2\n", + "for x0 in recession_states:\n", + " for x1 in recession_states:\n", + " for x2 in recession_states:\n", + " path = x0, x1, x2\n", + " counter += path_prob(p_H, psi, path)\n", + "\n", + "print(counter)" + ] + }, + { + "cell_type": "markdown", + "id": "cda97749", + "metadata": {}, + "source": [ + "Here's a solution to exercise 4.34." + ] + }, + { + "cell_type": "code", + "execution_count": 23, + "id": "44710126", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "0.6893\n" + ] + } + ], + "source": [ + "counter = 0\n", + "m = 10_000\n", + "mc = MarkovChain(p_H)\n", + "\n", + "for i in range(m):\n", + " x0 = tau(np.random.rand(), S, psi)\n", + " X = mc.simulate(init=x0, ts_length=3)\n", + " if 0 not in X:\n", + " counter += 1\n", + "\n", + "print(counter / m)" + ] + }, + { + "cell_type": "markdown", + "id": "f8c713af", + "metadata": {}, + "source": [ + "Next we turn to exercise 4.36." + ] + }, + { + "cell_type": "code", + "execution_count": 24, + "id": "ad162649", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "filenames": { + "image/png": "/home/john/gh_synced/books/sed2/edtc-code/code_book/_build/jupyter_execute/ch4_47_0.png" + }, + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "max_T = 12\n", + "T_vals = range(max_T)\n", + "profits = []\n", + "r = 0.05\n", + "rho = 1 / (1+r)\n", + "\n", + "psi = (0.2, 0.2, 0.6) \n", + "h = (1000, 0, -1000) \n", + "current_profits = np.inner(psi, h)\n", + "discount = rho\n", + "Q = np.identity(3)\n", + "\n", + "for t in T_vals:\n", + " Q = Q @ p_H\n", + " discount = discount * rho\n", + " current_profits += discount * np.inner(psi, Q @ h)\n", + " profits.append(current_profits)\n", + "\n", + "fig, ax = plt.subplots()\n", + "ax.plot(profits, label='profits')\n", + "ax.plot(np.zeros(max_T), '--', label='break even')\n", + "ax.set_xlabel('time')\n", + "ax.legend()\n", + "\n", + "plt.show()\n" + ] + }, + { + "cell_type": "markdown", + "id": "cbb12129", + "metadata": {}, + "source": [ + "Here's figure 4.11." + ] + }, + { + "cell_type": "code", + "execution_count": 25, + "id": "c3d81b09", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "filenames": { + "image/png": "/home/john/gh_synced/books/sed2/edtc-code/code_book/_build/jupyter_execute/ch4_49_0.png" + }, + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "p_Q = ((0.97 , 0.03 , 0.00 , 0.00 , 0.00),\n", + " (0.05 , 0.92 , 0.03 , 0.00 , 0.00),\n", + " (0.00 , 0.04 , 0.92 , 0.04 , 0.00),\n", + " (0.00 , 0.00 , 0.04 , 0.94 , 0.02),\n", + " (0.00 , 0.00 , 0.00 , 0.01 , 0.99))\n", + "\n", + "p_Q = np.array(p_Q)\n", + "states = 0, 1, 2, 3, 4\n", + "dates = 10, 60, 160\n", + "initial_states = 0, 4\n", + "\n", + "rows, cols = 2, 3\n", + "fig, axes = plt.subplots(rows, cols)\n", + "\n", + "for row, init in enumerate(initial_states):\n", + " psi = np.zeros(5)\n", + " psi[init] = 1\n", + " for col, d in enumerate(dates):\n", + " ax = axes[row, col]\n", + " ax.bar(states, \n", + " psi @ np.linalg.matrix_power(p_Q, d), \n", + " alpha=0.5,\n", + " edgecolor='k')\n", + " ax.set_title(f\"$X_0 = {init}, t = {d}$\")\n", + " ax.set_ylabel(\"prob\")\n", + " ax.set_xlabel(\"state\")\n", + "\n", + "plt.tight_layout()\n", + "\n", + "#plt.savefig(\"dds2.pdf\")\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "id": "6e1836cf", + "metadata": {}, + "source": [ + "And here's figure 4.12." + ] + }, + { + "cell_type": "code", + "execution_count": 26, + "id": "7494edd3", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "filenames": { + "image/png": "/home/john/gh_synced/books/sed2/edtc-code/code_book/_build/jupyter_execute/ch4_51_0.png" + }, + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "dates = 160, 500, 1000\n", + "\n", + "fig, axes = plt.subplots(rows, cols)\n", + "\n", + "for row, init in enumerate(initial_states):\n", + " psi = np.zeros(5)\n", + " psi[init] = 1\n", + " for col, d in enumerate(dates):\n", + " ax = axes[row, col]\n", + " ax.bar(states, \n", + " psi @ np.linalg.matrix_power(p_Q, d), \n", + " alpha=0.5,\n", + " edgecolor='k')\n", + " ax.set_title(f\"$X_0 = {init}, t = {d}$\")\n", + " ax.set_ylabel(\"prob\")\n", + " ax.set_xlabel(\"state\")\n", + "\n", + "plt.tight_layout()\n", + "\n", + "#plt.savefig(\"dds3.pdf\")\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "id": "2bdb627f", + "metadata": {}, + "source": [ + "Next we turn to exercise 4.42.\n", + "\n", + "First here's a function to compute the stationary distribution, assuming it is\n", + "unique." + ] + }, + { + "cell_type": "code", + "execution_count": 27, + "id": "80d25174", + "metadata": {}, + "outputs": [], + "source": [ + "from numpy.linalg import solve\n", + "\n", + "def compute_stationary(p):\n", + " N = p.shape[0]\n", + " I = np.identity(N)\n", + " O = np.ones((N, N))\n", + " A = I - p + O\n", + " return solve(A.T, np.ones((N, 1))).flatten()\n" + ] + }, + { + "cell_type": "markdown", + "id": "dc5dd5b7", + "metadata": {}, + "source": [ + "Now let's apply it to `p_Q`." + ] + }, + { + "cell_type": "code", + "execution_count": 28, + "id": "75a1c2b4", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": "iVBORw0KGgoAAAANSUhEUgAAAXoAAAD4CAYAAADiry33AAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjQuMiwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy8rg+JYAAAACXBIWXMAAAsTAAALEwEAmpwYAAAO2UlEQVR4nO3dcYhdaX2H8efbWUPLVhHM6Eom24Q2aMNi7DJEYaWyUiWxtbG00Cx2BesSAgYVKmvqH8oiSJFSihANIQ1FWhsKNRDb6LpYy1LWbTNpt2vibmSIWzLEkIlarViMqb/+MTd4O3uz99xk7tydd54PDHPPOe975z0seXL35N4zqSokSe36uUkvQJI0XoZekhpn6CWpcYZekhpn6CWpcXdMegGDbNy4sbZs2TLpZUjSmnHmzJmrVTU96NiLMvRbtmxhbm5u0suQpDUjyX/e7JiXbiSpcZ1Cn2RXkvNJ5pMcHHB8T5KnkzyVZC7Jm7rOlSSN19DQJ5kCDgG7ge3AA0m2Lxv2FWBHVb0e+EPg6AhzJUlj1OUV/U5gvqouVNU14Diwp39AVf2wfnYvhTuB6jpXkjReXUK/CbjYt73Q2/f/JPmdJM8C/8DSq/rOcyVJ49Ml9Bmw73l3QquqE1X1WuCdwMdHmQuQZF/v+v7c4uJih2VJkrroEvoFYHPf9gxw6WaDq+px4JeTbBxlblUdqarZqpqdnh74VlBJ0i3oEvrTwLYkW5NsAPYCJ/sHJPmVJOk9vhfYAHyny1xJ0ngN/cBUVV1PcgB4FJgCjlXVuST7e8cPA78LvDvJT4D/AX6/94+zA+eO6VwkSQPkxfiLR2ZnZ+tWPxn7sU98koXLV1d4RZMxc9dGHvnIw5NehqQ1IMmZqpoddOxFeQuE27Fw+Sr3vOOhSS9jRZz9wtFJL0FSA7wFgiQ1ztBLUuMMvSQ1ztBLUuMMvSQ1ztBLUuMMvSQ1ztBLUuMMvSQ1ztBLUuMMvSQ1ztBLUuMMvSQ1ztBLUuMMvSQ1ztBLUuMMvSQ1ztBLUuOa+1WCktYXf0/0cIZe0prm74kezks3ktQ4Qy9JjTP0ktQ4Qy9JjTP0ktQ4Qy9JjesU+iS7kpxPMp/k4IDj70rydO/riSQ7+o49l+TrSZ5KMreSi5ckDTf0ffRJpoBDwFuBBeB0kpNV9Y2+Yd8C3lxV30uyGzgCvKHv+P1V1cYnGiRpjenyin4nMF9VF6rqGnAc2NM/oKqeqKrv9TafBGZWdpmSpFvVJfSbgIt92wu9fTfzXuCLfdsFfDnJmST7bjYpyb4kc0nmFhcXOyxLktRFl1sgZMC+GjgwuZ+l0L+pb/d9VXUpySuBx5I8W1WPP+8Jq46wdMmH2dnZgc8vSRpdl1f0C8Dmvu0Z4NLyQUleBxwF9lTVd27sr6pLve9XgBMsXQqSJK2SLqE/DWxLsjXJBmAvcLJ/QJK7gc8DD1bVN/v235nkpTceA28Dzq7U4iVJww29dFNV15McAB4FpoBjVXUuyf7e8cPAR4FXAJ9OAnC9qmaBVwEnevvuAD5XVV8ay5lIkgbqdJviqjoFnFq273Df44eA590ntKouADuW75ckrR4/GStJjTP0ktQ4Qy9JjTP0ktQ4Qy9JjTP0ktQ4Qy9JjTP0ktQ4Qy9JjTP0ktQ4Qy9JjTP0ktQ4Qy9JjTP0ktQ4Qy9JjTP0ktQ4Qy9JjTP0ktQ4Qy9JjTP0ktQ4Qy9JjTP0ktQ4Qy9JjTP0ktQ4Qy9JjTP0ktS4TqFPsivJ+STzSQ4OOP6uJE/3vp5IsqPrXEnSeA0NfZIp4BCwG9gOPJBk+7Jh3wLeXFWvAz4OHBlhriRpjLq8ot8JzFfVhaq6BhwH9vQPqKonqup7vc0ngZmucyVJ49Ul9JuAi33bC719N/Ne4Iujzk2yL8lckrnFxcUOy5IkddEl9BmwrwYOTO5nKfQfHnVuVR2pqtmqmp2enu6wLElSF3d0GLMAbO7bngEuLR+U5HXAUWB3VX1nlLmSpPHp8or+NLAtydYkG4C9wMn+AUnuBj4PPFhV3xxlriRpvIa+oq+q60kOAI8CU8CxqjqXZH/v+GHgo8ArgE8nAbjeuwwzcO6YzkWSNECXSzdU1Sng1LJ9h/sePwQ81HWuJGn1+MlYSWqcoZekxhl6SWqcoZekxhl6SWqcoZekxhl6SWqcoZekxhl6SWqcoZekxhl6SWpcp3vdaG342Cc+ycLlq5NexoqYuWsjj3zk4UkvQ2qCoW/IwuWr3POOgfeWW3POfuHopJcgNcNLN5LUOEMvSY0z9JLUOEMvSY0z9JLUOEMvSY0z9JLUOEMvSY0z9JLUOEMvSY0z9JLUOEMvSY0z9JLUuE6hT7Iryfkk80kODjj+2iRfS/LjJB9aduy5JF9P8lSSuZVauCSpm6G3KU4yBRwC3gosAKeTnKyqb/QN+y7wfuCdN3ma+6uqjRulS9Ia0+UV/U5gvqouVNU14Diwp39AVV2pqtPAT8awRknSbegS+k3Axb7thd6+rgr4cpIzSfbdbFCSfUnmkswtLi6O8PSSpBfSJfQZsK9G+Bn3VdW9wG7gfUl+fdCgqjpSVbNVNTs9PT3C00uSXkiX0C8Am/u2Z4BLXX9AVV3qfb8CnGDpUpAkaZV0Cf1pYFuSrUk2AHuBk12ePMmdSV564zHwNuDsrS5WkjS6oe+6qarrSQ4AjwJTwLGqOpdkf+/44SR3AXPAy4CfJvkgsB3YCJxIcuNnfa6qvjSWM5EkDTQ09ABVdQo4tWzf4b7Hl1m6pLPcD4Adt7NASdLt8ZOxktQ4Qy9JjTP0ktQ4Qy9JjTP0ktQ4Qy9JjTP0ktS4Tu+jl9aCj33ikyxcXvt3w565ayOPfOThkea0cu5wa+evF2bo1YyFy1e55x0PTXoZt+3sF46OPKeVc4dbO3+9MC/dSFLjDL0kNc7QS1LjDL0kNc7QS1LjDL0kNc7QS1LjDL0kNc7QS1LjDL0kNc7QS1LjDL0kNc7QS1LjDL0kNc7QS1LjDL0kNc7QS1LjOoU+ya4k55PMJzk44Phrk3wtyY+TfGiUuZKk8Roa+iRTwCFgN7AdeCDJ9mXDvgu8H/jTW5grSRqjLq/odwLzVXWhqq4Bx4E9/QOq6kpVnQZ+MupcSdJ4dQn9JuBi3/ZCb18Xnecm2ZdkLsnc4uJix6eXJA3TJfQZsK86Pn/nuVV1pKpmq2p2enq649NLkobpEvoFYHPf9gxwqePz385cSdIK6BL608C2JFuTbAD2Aic7Pv/tzJUkrYA7hg2oqutJDgCPAlPAsao6l2R/7/jhJHcBc8DLgJ8m+SCwvap+MGjumM5FkjTA0NADVNUp4NSyfYf7Hl9m6bJMp7mSpNXjJ2MlqXGGXpIaZ+glqXGGXpIaZ+glqXGGXpIaZ+glqXGGXpIaZ+glqXGGXpIaZ+glqXGGXpIaZ+glqXGGXpIaZ+glqXGGXpIaZ+glqXGGXpIaZ+glqXGGXpIaZ+glqXGGXpIaZ+glqXGGXpIaZ+glqXGGXpIa1yn0SXYlOZ9kPsnBAceT5FO9408nubfv2HNJvp7kqSRzK7l4SdJwdwwbkGQKOAS8FVgATic5WVXf6Bu2G9jW+3oD8Jne9xvur6qrK7ZqSVJnXV7R7wTmq+pCVV0DjgN7lo3ZA3y2ljwJvDzJq1d4rZKkW9Al9JuAi33bC719XccU8OUkZ5Lsu9WFSpJuzdBLN0AG7KsRxtxXVZeSvBJ4LMmzVfX4837I0l8C+wDuvvvuDsuSJHXR5RX9ArC5b3sGuNR1TFXd+H4FOMHSpaDnqaojVTVbVbPT09PdVi9JGqpL6E8D25JsTbIB2AucXDbmJPDu3rtv3gh8v6q+neTOJC8FSHIn8Dbg7AquX5I0xNBLN1V1PckB4FFgCjhWVeeS7O8dPwycAt4OzAM/At7Tm/4q4ESSGz/rc1X1pRU/C0nSTXW5Rk9VnWIp5v37Dvc9LuB9A+ZdAHbc5holSbfBT8ZKUuMMvSQ1ztBLUuMMvSQ1ztBLUuMMvSQ1ztBLUuMMvSQ1ztBLUuMMvSQ1ztBLUuMMvSQ1ztBLUuMMvSQ1ztBLUuMMvSQ1ztBLUuMMvSQ1ztBLUuMMvSQ1ztBLUuMMvSQ1ztBLUuMMvSQ1ztBLUuMMvSQ1ztBLUuM6hT7JriTnk8wnOTjgeJJ8qnf86ST3dp0rSRqvoaFPMgUcAnYD24EHkmxfNmw3sK33tQ/4zAhzJUlj1OUV/U5gvqouVNU14DiwZ9mYPcBna8mTwMuTvLrjXEnSGKWqXnhA8nvArqp6qLf9IPCGqjrQN+bvgT+pqn/ubX8F+DCwZdjcvufYx9L/DQC8Bjh/e6c2VhuBq5NexASt5/P33NevF/v5/1JVTQ86cEeHyRmwb/nfDjcb02Xu0s6qI8CRDuuZuCRzVTU76XVMyno+f899fZ47rO3z7xL6BWBz3/YMcKnjmA0d5kqSxqjLNfrTwLYkW5NsAPYCJ5eNOQm8u/fumzcC36+qb3ecK0kao6Gv6KvqepIDwKPAFHCsqs4l2d87fhg4BbwdmAd+BLznheaO5UxW15q4xDRG6/n8Pff1a82e/9B/jJUkrW1+MlaSGmfoJalxhn5E6/mWDkmOJbmS5Oyk17LakmxO8tUkzyQ5l+QDk17Takny80n+Ncl/9M79kUmvabUlmUry773PDK05hn4E3tKBvwR2TXoRE3Id+KOq+lXgjcD71tF/+x8Db6mqHcDrgV29d9etJx8Anpn0Im6VoR/Nur6lQ1U9Dnx30uuYhKr6dlX9W+/xf7P0h37TZFe1Onq3Nvlhb/Mlva918y6OJDPAbwJHJ72WW2XoR7MJuNi3vcA6+cOun0myBfg14F8mvJRV07t08RRwBXisqtbNuQN/DjwM/HTC67hlhn40nW/poDYl+UXg74APVtUPJr2e1VJV/1tVr2fp0+07k9wz4SWtiiS/BVypqjOTXsvtMPSj6XI7CDUqyUtYivxfV9XnJ72eSaiq/wL+ifXzbzX3Ab+d5DmWLtW+JclfTXZJozP0o/GWDutUkgB/ATxTVX826fWspiTTSV7ee/wLwG8Az050Uaukqv64qmaqagtLf97/sar+YMLLGpmhH0FVXQdu3NLhGeBvG7mlQydJ/gb4GvCaJAtJ3jvpNa2i+4AHWXpF91Tv6+2TXtQqeTXw1SRPs/Ri57GqWpNvM1yvvAWCJDXOV/SS1DhDL0mNM/SS1DhDL0mNM/SS1DhDL0mNM/SS1Lj/A72hb9YCqbDBAAAAAElFTkSuQmCC\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "filenames": { + "image/png": "/home/john/gh_synced/books/sed2/edtc-code/code_book/_build/jupyter_execute/ch4_55_0.png" + }, + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "psi_star = compute_stationary(p_Q)\n", + "\n", + "fig, ax = plt.subplots()\n", + "ax.bar(states, psi_star, alpha=0.5, edgecolor='k')\n", + "\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "id": "30a3043c", + "metadata": {}, + "source": [ + "As expected, the distribution is very similar to the time 1,000 distribution\n", + "we obtained above by shifting forward in time.\n", + "\n", + "\n", + "Now let's look at exercise 4.43." + ] + }, + { + "cell_type": "code", + "execution_count": 29, + "id": "05e0e21e", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "788.1600000000004\n" + ] + } + ], + "source": [ + "psi_star = compute_stationary(p_H) \n", + "print(np.inner(psi_star, h))" + ] + }, + { + "cell_type": "markdown", + "id": "e17bba44", + "metadata": {}, + "source": [ + "If we compute profits at $t=1000$, starting from a range of initial\n", + "conditions, we get very similar results." + ] + }, + { + "cell_type": "code", + "execution_count": 30, + "id": "5df8ace9", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "788.1599999999779\n", + "788.1599999999786\n", + "788.1599999999784\n" + ] + } + ], + "source": [ + "pT = np.linalg.matrix_power(p_H, 1000)\n", + "psi_vecs = (1, 0, 0), (0, 1, 0), (0, 0, 1)\n", + "\n", + "for psi in psi_vecs:\n", + " print(np.inner(psi, pT @ h))" + ] + }, + { + "cell_type": "markdown", + "id": "dcc40e49", + "metadata": {}, + "source": [ + "This is not surprising, since `p_H` is globally stable.\n", + "\n", + "\n", + "Here's the solution to exercise 4.57, which computes mean return time.\n", + "\n", + "I'll use JIT compilation to make the code fast." + ] + }, + { + "cell_type": "code", + "execution_count": 31, + "id": "683a5cd3", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "[1.22511, 6.1233, 40.81569]" + ] + }, + "execution_count": 31, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "@jit\n", + "def compute_return_time(x, p, max_iter=100_000):\n", + " X = x\n", + " t = 0\n", + " while t < max_iter:\n", + " W = np.random.rand()\n", + " X = tau(W, S, p_H[X, :])\n", + " t += 1\n", + " if X == x:\n", + " return t\n", + "\n", + "@jit\n", + "def compute_mean_return_time(x, p, n=100_000):\n", + " counter = 0\n", + " for i in range(n):\n", + " counter += compute_return_time(x, p)\n", + " return counter / n\n", + "\n", + "\n", + "[compute_mean_return_time(i, p_H) for i in range(3)]\n" + ] + }, + { + "cell_type": "markdown", + "id": "bc16c65b", + "metadata": {}, + "source": [ + "For comparison:" + ] + }, + { + "cell_type": "code", + "execution_count": 32, + "id": "58105c7e", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array([ 1.23031496, 6.1515748 , 40.58441558])" + ] + }, + "execution_count": 32, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "psi_star = compute_stationary(p_H)\n", + "1/ psi_star\n" + ] + }, + { + "cell_type": "markdown", + "id": "1386856b", + "metadata": {}, + "source": [ + "As predicted by the theory, the values are approximately equal.\n", + "\n", + "\n", + "Now let's turn to the inventory model." + ] + }, + { + "cell_type": "code", + "execution_count": 33, + "id": "b369f23c", + "metadata": {}, + "outputs": [], + "source": [ + "def b(d):\n", + " \" Returns probability that demand = d.\"\n", + " return (d >= 0) * (1/2)**(d + 1)\n", + "\n", + "def h(x, q, Q):\n", + " return x + (Q - x) * (x <= q)\n", + "\n", + "def build_p(q=2, Q=5): \n", + " p = np.empty((Q+1, Q+1))\n", + " for x in range(Q+1):\n", + " for y in range(Q+1):\n", + " if y == 0:\n", + " p[x,y] = (1/2)**h(x, q, Q) # prob D >= h(x, q)\n", + " else:\n", + " p[x,y] = b(h(x, q, Q) - y) # prob h(x, q) - D = y\n", + "\n", + " return p\n" + ] + }, + { + "cell_type": "markdown", + "id": "30719f22", + "metadata": {}, + "source": [ + "Let's verify that the stationary distribution at $q=2$ and $Q=5$ matches the\n", + "one shown in the text." + ] + }, + { + "cell_type": "code", + "execution_count": 34, + "id": "056da0c0", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array([0.0625, 0.0625, 0.125 , 0.25 , 0.25 , 0.25 ])" + ] + }, + "execution_count": 34, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "p = build_p()\n", + "compute_stationary(p)\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "id": "19cda144", + "metadata": {}, + "source": [ + "Yep, looks good.\n", + "\n", + "Now let's check that the optimal policy agrees with $q=7$, as claimed in the text." + ] + }, + { + "cell_type": "code", + "execution_count": 35, + "id": "114d1bfc", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "7" + ] + }, + "execution_count": 35, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "Q = 20 # inventory upper bound\n", + "C = 0.1 # cost of restocking\n", + "\n", + "# profit given state x, demand d, policy q\n", + "def profit(x, d, q):\n", + " stock = h(x, q, Q)\n", + " revenue = stock if stock < d else d\n", + " cost = C * (x <= q)\n", + " return revenue - cost\n", + "\n", + "# expected profit given x and policy q\n", + "def g(x, q):\n", + " counter = 0\n", + " for d in range(1000):\n", + " counter += profit(x, d, q) * b(d)\n", + " return counter\n", + "\n", + "def profit_at_stationary(q):\n", + " p = build_p(q=q, Q=Q)\n", + " stationary = compute_stationary(p)\n", + " counter = 0\n", + " for x in range(Q+1):\n", + " counter += g(x, q) * stationary[x]\n", + " return counter\n", + " \n", + "def compute_optimal_policy():\n", + " running_max = -np.inf\n", + " for q in range(Q+1):\n", + " counter = profit_at_stationary(q)\n", + " if counter > running_max:\n", + " running_max = counter\n", + " argmax = q\n", + " return(argmax)\n", + "\n", + "compute_optimal_policy()" + ] + }, + { + "cell_type": "markdown", + "id": "f88b1e4b", + "metadata": {}, + "source": [ + "Here's a solution for exercise 4.61. From preceding calculations we have\n", + "the stationary probability assigned to normal growth:" + ] + }, + { + "cell_type": "code", + "execution_count": 36, + "id": "0c619563", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "0.8128000000000003" + ] + }, + "execution_count": 36, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "psi_star = compute_stationary(p_H) \n", + "psi_star[0]" + ] + }, + { + "cell_type": "markdown", + "id": "f8067b0a", + "metadata": {}, + "source": [ + "The fraction of the time a long path spends in this state can be calculated as\n", + "follows." + ] + }, + { + "cell_type": "code", + "execution_count": 37, + "id": "87670c46", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "0.812896" + ] + }, + "execution_count": 37, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "T = 1_000_000\n", + "mc = MarkovChain(p_H)\n", + "X = mc.simulate(init=0, ts_length=T)\n", + "np.mean(X == 0)" + ] + }, + { + "cell_type": "markdown", + "id": "abfd153d", + "metadata": {}, + "source": [ + "As expected given the LLN results for stable Markov chains, the two numbers are approximately equal.\n", + "\n", + "\n", + "Finally, let's look at the expected profits question in exercise 4.63.\n", + "\n", + "Previously we calculated steady state profits via" + ] + }, + { + "cell_type": "code", + "execution_count": 38, + "id": "b2505c77", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "788.1600000000004\n" + ] + } + ], + "source": [ + "h = (1000, 0, -1000)\n", + "psi_star = compute_stationary(p_H) \n", + "print(np.inner(psi_star, h))" + ] + }, + { + "cell_type": "markdown", + "id": "6efb7b10", + "metadata": {}, + "source": [ + "To check that we get approximately the same results when simulating a long\n", + "time series, we can calculate as follows." + ] + }, + { + "cell_type": "code", + "execution_count": 39, + "id": "7f2744f1", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "788.24" + ] + }, + "execution_count": 39, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "y = [h[x] for x in X]\n", + "np.mean(y)" + ] + } + ], + "metadata": { + "jupytext": { + "cell_metadata_filter": "-all", + "formats": "md:myst", + "text_representation": { + "extension": ".md", + "format_name": "myst", + "format_version": 0.13, + "jupytext_version": "1.10.3" + } + }, + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.8.5" + }, + "source_map": [ + 14, + 20, + 25, + 32, + 77, + 82, + 111, + 120, + 140, + 145, + 155, + 161, + 171, + 177, + 187, + 198, + 218, + 224, + 240, + 249, + 257, + 263, + 268, + 278, + 287, + 291, + 299, + 305, + 313, + 318, + 332, + 340, + 356, + 361, + 370, + 374, + 381, + 391, + 400, + 410, + 418, + 422, + 433, + 437, + 447, + 452, + 464, + 468, + 495, + 500, + 532, + 538, + 560, + 568, + 578, + 582, + 590, + 599, + 602, + 607, + 613, + 622, + 644, + 648, + 652, + 659, + 678, + 684, + 690, + 696, + 732, + 739, + 742, + 748, + 753, + 763, + 767, + 773 + ] + }, + "nbformat": 4, + "nbformat_minor": 5 +} \ No newline at end of file diff --git a/code_book/ch4.md b/_sources/ch4.md similarity index 100% rename from code_book/ch4.md rename to _sources/ch4.md diff --git a/_sources/ch5.ipynb b/_sources/ch5.ipynb new file mode 100644 index 0000000..cf39676 --- /dev/null +++ b/_sources/ch5.ipynb @@ -0,0 +1,828 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "id": "30c2c7da", + "metadata": {}, + "source": [ + "# Chapter 5 Code\n", + "\n", + "\n", + "We will use the following imports." + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "id": "27c49cad", + "metadata": {}, + "outputs": [], + "source": [ + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "from numba import jit" + ] + }, + { + "cell_type": "markdown", + "id": "7e78e95b", + "metadata": {}, + "source": [ + "## The Optimal Savings Problem\n", + "\n", + "First we set parameters and construct the state and action spaces." + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "id": "2d9dd3c6", + "metadata": {}, + "outputs": [], + "source": [ + "beta, rho = 0.5, 0.9\n", + "z_bar, s_bar = 10, 5\n", + "\n", + "S = np.arange(z_bar + s_bar + 1) # State space = 0,...,z_bar + s_bar\n", + "Z = np.arange(z_bar + 1) # Shock space = 0,...,z_bar " + ] + }, + { + "cell_type": "markdown", + "id": "df533cdb", + "metadata": {}, + "source": [ + "Next we write down the primitives of the problem, such as the utility function." + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "id": "d8b56e6f", + "metadata": {}, + "outputs": [], + "source": [ + "def U(c): \n", + " \"Utility function.\"\n", + " return c**beta\n", + "\n", + "def phi(z): \n", + " \"Probability mass function, uniform distribution.\"\n", + " return 1.0 / len(Z) if 0 <= z <= z_bar else 0\n", + "\n", + "def Gamma(x): \n", + " \"The correspondence of feasible actions.\"\n", + " return range(min(x, s_bar) + 1)" + ] + }, + { + "cell_type": "markdown", + "id": "bb6392b9", + "metadata": {}, + "source": [ + "### Value Function Iteration\n", + "\n", + "To implement VFI, we first construct the Bellman operator $T$." + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "id": "310d7ae6", + "metadata": {}, + "outputs": [], + "source": [ + "def T(v): \n", + " Tv = np.empty_like(v)\n", + " for x in S:\n", + " # Compute the value of the objective function for each \n", + " # a in Gamma(x) and record highest value.\n", + " running_max = -np.inf\n", + " for a in Gamma(x):\n", + " y = U(x - a) + rho * sum(v[a + z]*phi(z) for z in Z)\n", + " if y > running_max:\n", + " running_max = y\n", + " # Store the maximum reward for this x in Tv\n", + " Tv[x] = running_max\n", + " return Tv " + ] + }, + { + "cell_type": "markdown", + "id": "5667ebbf", + "metadata": {}, + "source": [ + "The next function computes a $w$-greedy policy." + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "id": "8a982711", + "metadata": {}, + "outputs": [], + "source": [ + "def get_greedy(w): \n", + " sigma = np.empty_like(w)\n", + " for x in S:\n", + " running_max = -np.inf\n", + " for a in Gamma(x):\n", + " y = U(x - a) + rho * sum(w[a + z]*phi(z) for z in Z)\n", + " # Record the action that gives highest value\n", + " if y > running_max:\n", + " running_max = y\n", + " sigma[x] = a\n", + " return sigma" + ] + }, + { + "cell_type": "markdown", + "id": "190ff1e4", + "metadata": {}, + "source": [ + "The following function implements value function iteration, starting with the\n", + "utility function as the initial condition.\n", + "\n", + "Iteration continues until the sup deviation between iterates is less than\n", + "`tol`." + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "id": "c13ec96b", + "metadata": {}, + "outputs": [], + "source": [ + "def compute_value_function(tol=1e-4,\n", + " max_iter=1000,\n", + " verbose=True,\n", + " print_skip=5):\n", + "\n", + " # Set up loop\n", + " v = [U(x) for x in S] # Initial condition\n", + " i = 0\n", + " error = tol + 1\n", + "\n", + " while i < max_iter and error > tol:\n", + " v_new = T(v)\n", + " error = np.max(np.abs(v - v_new))\n", + " i += 1\n", + " if verbose and i % print_skip == 0:\n", + " print(f\"Error at iteration {i} is {error}.\")\n", + " v = v_new\n", + "\n", + " if i == max_iter:\n", + " print(\"Failed to converge!\")\n", + "\n", + " if verbose and i < max_iter:\n", + " print(f\"\\nConverged in {i} iterations.\")\n", + "\n", + " return v_new" + ] + }, + { + "cell_type": "markdown", + "id": "c47989dd", + "metadata": {}, + "source": [ + "Let's run the code and plot the result." + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "id": "2b077e15", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Error at iteration 5 is 1.2573668687016468.\n", + "Error at iteration 10 is 0.741211643809562.\n", + "Error at iteration 15 is 0.4376689170549888.\n", + "Error at iteration 20 is 0.2584390462574362.\n", + "Error at iteration 25 is 0.15260567184870055.\n", + "Error at iteration 30 is 0.09011212316537609.\n", + "Error at iteration 35 is 0.05321030760788403.\n", + "Error at iteration 40 is 0.0314201545393793.\n", + "Error at iteration 45 is 0.018553287053961753.\n", + "Error at iteration 50 is 0.010955530472493535.\n", + "Error at iteration 55 is 0.0064691311887052905.\n", + "Error at iteration 60 is 0.003819957275620567.\n", + "Error at iteration 65 is 0.002255646571679648.\n", + "Error at iteration 70 is 0.0013319367441120278.\n", + "Error at iteration 75 is 0.0007864953280325437.\n", + "Error at iteration 80 is 0.00046441762625448746.\n", + "Error at iteration 85 is 0.0002742339641272906.\n", + "Error at iteration 90 is 0.00016193241347650655.\n", + "Error at iteration 95 is 9.561947083724931e-05.\n", + "\n", + "Converged in 95 iterations.\n" + ] + }, + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "filenames": { + "image/png": "/home/john/gh_synced/books/sed2/edtc-code/code_book/_build/jupyter_execute/ch5_13_1.png" + }, + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "v_star = compute_value_function()\n", + "\n", + "fig, ax = plt.subplots()\n", + "ax.plot(S, v_star, 'k-', label='approximate value function')\n", + "ax.legend()\n", + "ax.set_xlabel(\"$x$\")\n", + "ax.set_ylabel(\"value\")\n", + "\n", + "#plt.savefig(\"vfiv.pdf\")\n", + "\n", + "plt.show()\n" + ] + }, + { + "cell_type": "markdown", + "id": "88f6913a", + "metadata": {}, + "source": [ + "Now we can compute the $v^*$-greedy policy, which is approximately optimal." + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "id": "c40b62e3", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "filenames": { + "image/png": "/home/john/gh_synced/books/sed2/edtc-code/code_book/_build/jupyter_execute/ch5_15_0.png" + }, + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "sigma_star = get_greedy(v_star)\n", + "\n", + "fig, ax = plt.subplots()\n", + "ax.plot(S, sigma_star, 'k-', label='optimal policy')\n", + "ax.legend()\n", + "\n", + "plt.show()\n" + ] + }, + { + "cell_type": "markdown", + "id": "723cd2bc", + "metadata": {}, + "source": [ + "Even though value function iteration only guarantees an approximately optimal\n", + "policy, since computation of the value function is only up to a certain degree\n", + "of precision, it turns out that our policy is exactly optimal.\n", + "\n", + "This becomes clear in the next section.\n", + "\n", + "Before that, let's check that the Markov chain for wealth is globally stable\n", + "by calculating the Dobrushin coefficient.\n", + "\n", + "Here's a function to compute the Dobrushin coefficient." + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "id": "38092a35", + "metadata": {}, + "outputs": [], + "source": [ + "def dobrushin(p):\n", + " running_min = 1\n", + " for x in S:\n", + " for xp in S:\n", + " a = sum((min(p[x,y], p[xp, y]) for y in S))\n", + " if a < running_min:\n", + " running_min = a\n", + " return running_min" + ] + }, + { + "cell_type": "markdown", + "id": "222d1e0a", + "metadata": {}, + "source": [ + "Now we construct the stochastic kernel at the optimal policy and check the\n", + "Dobrushin coefficient." + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "id": "618571a3", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "0.5454545454545455" + ] + }, + "execution_count": 10, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "p_sigma = np.empty((len(S), len(S)))\n", + "\n", + "for x in S:\n", + " for y in S:\n", + " p_sigma[x, y] = phi(y - sigma_star[x])\n", + "\n", + "dobrushin(p_sigma)" + ] + }, + { + "cell_type": "markdown", + "id": "08f2a293", + "metadata": {}, + "source": [ + "The Dobrushin coefficient is positive so global stability holds.\n", + "\n", + "We'll borrow some earlier code to compute the stationary distribution." + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "id": "d0f580d6", + "metadata": {}, + "outputs": [], + "source": [ + "from numpy.linalg import solve\n", + "\n", + "def compute_stationary(p):\n", + " N = p.shape[0]\n", + " I = np.identity(N)\n", + " O = np.ones((N, N))\n", + " A = I - p + O\n", + " return solve(A.T, np.ones((N, 1))).flatten()\n" + ] + }, + { + "cell_type": "markdown", + "id": "1c40e777", + "metadata": {}, + "source": [ + "Now let's compute it." + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "id": "88277ef5", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": "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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "filenames": { + "image/png": "/home/john/gh_synced/books/sed2/edtc-code/code_book/_build/jupyter_execute/ch5_23_0.png" + }, + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "fig, ax = plt.subplots()\n", + "psi_star = compute_stationary(p_sigma)\n", + "\n", + "ax.bar(S, psi_star, edgecolor='k', alpha=0.5, label=r'$\\psi^*$')\n", + "ax.set_xlabel('wealth')\n", + "ax.legend()\n", + "\n", + "# plt.savefig(\"opt_wealth_dist.pdf\")\n", + "\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "id": "a4e682c1", + "metadata": {}, + "source": [ + "### Policy Iteration\n", + "\n", + "Now we turn to the Howard policy iteration algorithm.\n", + "\n", + "In the finite state setting, this algorithm converges to the exact optimal\n", + "policy.\n", + "\n", + "To implement the algorithm, we need to be able to evaluate the lifetime reward\n", + "of any given policy.\n", + "\n", + "The next function does this using the algebraic method suggested in the\n", + "textbook." + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "id": "79dbb1a1", + "metadata": {}, + "outputs": [], + "source": [ + "def compute_policy_value(sigma):\n", + " \n", + " # Construct r_sigma and p_sigma = M_sigma\n", + " n = len(S)\n", + " r_sigma = np.empty(n)\n", + " p_sigma = np.empty((n, n))\n", + " for x in S:\n", + " r_sigma[x] = U(x - sigma[x])\n", + " for y in S:\n", + " p_sigma[x, y] = phi(y - sigma[x])\n", + "\n", + "\n", + " # Solve sigma = (I - rho p_sigma)^{-1} r_sigma\n", + " I = np.identity(n)\n", + " sigma = np.linalg.solve(I - rho * p_sigma, r_sigma)\n", + " return sigma" + ] + }, + { + "cell_type": "markdown", + "id": "f4c6db93", + "metadata": {}, + "source": [ + "Now we can implement policy iteration." + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "id": "227476f5", + "metadata": {}, + "outputs": [], + "source": [ + "def policy_iteration(max_iter=1e6, verbose=True):\n", + "\n", + " sigma = np.zeros(len(S)) # Starting point\n", + " i = 1\n", + "\n", + " while i < max_iter:\n", + " v_sigma = compute_policy_value(sigma)\n", + " new_sigma = get_greedy(v_sigma)\n", + " if np.all(new_sigma == sigma):\n", + " break\n", + " else:\n", + " sigma = new_sigma\n", + " i += 1\n", + "\n", + " if i == max_iter:\n", + " print(\"Failed to converge!\")\n", + "\n", + " if verbose and i < max_iter:\n", + " print(f\"\\nConverged in {i} iterations.\")\n", + "\n", + " return sigma\n" + ] + }, + { + "cell_type": "markdown", + "id": "d4e86d02", + "metadata": {}, + "source": [ + "Now let's compute using policy iteration and plot." + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "id": "0b5fcfad", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "\n", + "Converged in 4 iterations.\n" + ] + }, + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "filenames": { + "image/png": "/home/john/gh_synced/books/sed2/edtc-code/code_book/_build/jupyter_execute/ch5_29_1.png" + }, + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "sigma_star_pi = policy_iteration()\n", + "\n", + "fig, ax = plt.subplots()\n", + "ax.plot(S, sigma_star_pi, 'k-', label='optimal policy via PI')\n", + "ax.legend()\n", + "ax.set_xlabel(\"$x$\")\n", + "ax.set_ylabel(\"savings\")\n", + "\n", + "# plt.savefig(\"wealth_opt_pol.pdf\")\n", + "\n", + "plt.show()\n" + ] + }, + { + "cell_type": "markdown", + "id": "6b4c7c49", + "metadata": {}, + "source": [ + "Let's check that the two ways of computing the optimal policy are\n", + "equivalent up." + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "id": "40a5b96e", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "True" + ] + }, + "execution_count": 16, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "np.all(sigma_star == sigma_star_pi)" + ] + }, + { + "cell_type": "markdown", + "id": "be4f58ff", + "metadata": {}, + "source": [ + "Success! We have found the optimal policy and both methods of computing lead\n", + "us to it.\n", + "\n", + "\n", + "\n", + "\n", + "## Equilibrium Selection\n", + "\n", + "\n", + "Here are the parameter values." + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "id": "c523fa8b", + "metadata": {}, + "outputs": [], + "source": [ + "N = 12\n", + "u = 2\n", + "w = 1" + ] + }, + { + "cell_type": "code", + "execution_count": 18, + "id": "bd3f86e9", + "metadata": {}, + "outputs": [], + "source": [ + "@jit\n", + "def reward1(z):\n", + " return (z/N) * u\n", + "\n", + "@jit\n", + "def reward2(z):\n", + " return ((N - z)/N) * w\n", + "\n", + "@jit\n", + "def B(z):\n", + " if reward1(z) > reward2(z):\n", + " return N\n", + " elif reward1(z) < reward2(z):\n", + " return 0\n", + " else:\n", + " return z\n", + "\n", + "@jit\n", + "def update(z, epsilon): \n", + " Vu = np.random.binomial(N - B(z), epsilon)\n", + " Vw = np.random.binomial(B(z), epsilon)\n", + " return B(z) + Vu - Vw" + ] + }, + { + "cell_type": "markdown", + "id": "7dcce006", + "metadata": {}, + "source": [ + "Plot the function $B$ as a 45 degree diagram." + ] + }, + { + "cell_type": "code", + "execution_count": 19, + "id": "ff6e713b", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "filenames": { + "image/png": "/home/john/gh_synced/books/sed2/edtc-code/code_book/_build/jupyter_execute/ch5_36_0.png" + }, + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "fig, ax = plt.subplots()\n", + "state = np.arange(0, N+1)\n", + "ax.plot(state, state, 'k--', label='45 degrees') \n", + "ax.scatter(state, [B(x) for x in state], label='$B(x)$')\n", + "ax.legend()\n", + "ax.set_xlabel('$x$')\n", + "# plt.savefig(\"os_rewards.pdf\")\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "id": "8c1e344b", + "metadata": {}, + "source": [ + "Now we barplot the fraction of time sample paths spend at $N$ as epsilon varies." + ] + }, + { + "cell_type": "code", + "execution_count": 20, + "id": "0a50056c", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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+ "text/plain": [ + "
" + ] + }, + "metadata": { + "filenames": { + "image/png": "/home/john/gh_synced/books/sed2/edtc-code/code_book/_build/jupyter_execute/ch5_38_0.png" + }, + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "@jit\n", + "def compute_time_at_state(s, epsilon, sim_length=1_000_000, x_init=5):\n", + " X = x_init\n", + " counter = 0\n", + " for t in range(sim_length):\n", + " X = update(X, epsilon)\n", + " if X == s:\n", + " counter += 1\n", + " return counter / sim_length\n", + "\n", + "epsilons = np.arange(0.001, 0.1, step=0.01)\n", + "sample_frac = np.empty(len(epsilons))\n", + "for i, eps in enumerate(epsilons): \n", + " sample_frac[i] = compute_time_at_state(N, eps)\n", + "\n", + "fig, ax = plt.subplots()\n", + "ax.bar(epsilons, sample_frac, width=0.005, edgecolor='k', alpha=0.5)\n", + "ax.set_ylim(0, 1.01)\n", + "ax.set_xlabel('$\\\\epsilon$')\n", + "ax.set_ylabel('fraction')\n", + "#plt.savefig(\"mutation_ess.pdf\")\n", + "plt.show()\n" + ] + } + ], + "metadata": { + "jupytext": { + "cell_metadata_filter": "-all", + "formats": "md:myst", + "text_representation": { + "extension": ".md", + "format_name": "myst", + "format_version": 0.13, + "jupytext_version": "1.10.3" + } + }, + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.8.5" + }, + "source_map": [ + 14, + 21, + 25, + 31, + 37, + 42, + 54, + 61, + 75, + 79, + 91, + 100, + 126, + 130, + 143, + 147, + 156, + 169, + 178, + 183, + 191, + 198, + 208, + 212, + 223, + 239, + 256, + 261, + 284, + 288, + 301, + 307, + 309, + 322, + 328, + 351, + 355, + 364, + 368 + ] + }, + "nbformat": 4, + "nbformat_minor": 5 +} \ No newline at end of file diff --git a/code_book/ch5.md b/_sources/ch5.md similarity index 100% rename from code_book/ch5.md rename to _sources/ch5.md diff --git a/_sources/ch6.ipynb b/_sources/ch6.ipynb new file mode 100644 index 0000000..57b1a2b --- /dev/null +++ b/_sources/ch6.ipynb @@ -0,0 +1,1830 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "id": "28e7b9af", + "metadata": {}, + "source": [ + "# Chapter 6 Code\n", + "\n", + "We start with some imports." + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "id": "19e15a04", + "metadata": {}, + "outputs": [], + "source": [ + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "from numba import jit, vectorize\n", + "from interpolation import interp\n", + "from scipy.interpolate import interp1d\n", + "from scipy.optimize import minimize_scalar, brentq\n", + "from scipy.stats import beta\n" + ] + }, + { + "cell_type": "markdown", + "id": "c0861b0b", + "metadata": {}, + "source": [ + "## First Steps\n", + "\n", + "Here is the code that generated figure 6.1." + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "id": "5b4a3a46", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "filenames": { + "image/png": "/home/john/gh_synced/books/sed2/edtc-code/code_book/_build/jupyter_execute/ch6_3_0.png" + }, + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "alpha = 0.5 # capital intensity\n", + "sigma = 0.2 # shock parameter\n", + "s = 0.5 # savings rate\n", + "delta = 0.1 # depreciation\n", + "\n", + "default_params = alpha, sigma, s, delta\n", + "\n", + "@jit\n", + "def f(k, params=default_params):\n", + " alpha, sigma, s, delta = params\n", + " return k**alpha\n", + "\n", + "@jit\n", + "def update(k, params=default_params):\n", + " alpha, sigma, s, delta = params\n", + " w = np.exp(sigma * np.random.randn())\n", + " new_k = s * f(k) * w + (1 - delta) * k\n", + " return new_k\n", + "\n", + "@jit\n", + "def generate_solow_ts(init=1, ts_length=200, params=default_params):\n", + " \" A function to generate time series. \"\n", + " k = np.empty(ts_length)\n", + " k[0] = init\n", + " for t in range(ts_length-1):\n", + " k[t+1] = update(k[t], params=params)\n", + " return k\n", + "\n", + "fig, ax = plt.subplots()\n", + "\n", + "ax.plot(generate_solow_ts(init=1), label='$k_0 = 1$')\n", + "ax.plot(generate_solow_ts(init=60), '--', label='$k_0 = 60$')\n", + "ax.legend()\n", + "ax.set_xlabel('time')\n", + "#plt.savefig('solow_ts.pdf')\n", + "plt.show()\n" + ] + }, + { + "cell_type": "markdown", + "id": "bbca9c68", + "metadata": {}, + "source": [ + "Here is a function to generate draws from the time $t$ marginal distribution of\n", + "capital." + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "id": "c178c28f", + "metadata": {}, + "outputs": [], + "source": [ + "@jit\n", + "def sim_from_marginal(t=10, init=1, sim_size=1000, params=default_params):\n", + " k_draws = np.empty(sim_size)\n", + " for i in range(sim_size):\n", + " k = init\n", + " for j in range(t):\n", + " k = update(k, params=params)\n", + " k_draws[i] = k\n", + " return k_draws" + ] + }, + { + "cell_type": "markdown", + "id": "4a2234b2", + "metadata": {}, + "source": [ + "Now we generate some draws for date $t=20$ under the default parameters and\n", + "take the mean, which solves exercise 6.2." + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "id": "8940ee19", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "12.820298089686927" + ] + }, + "execution_count": 4, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "draws = sim_from_marginal(t=20)\n", + "draws.mean()" + ] + }, + { + "cell_type": "markdown", + "id": "01d2c825", + "metadata": {}, + "source": [ + "Here is the solution to exercise 6.3." + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "id": "06eb5624", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "26.53508930557267" + ] + }, + "execution_count": 5, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "new_s = 3/4\n", + "new_params = alpha, sigma, new_s, delta\n", + "draws = sim_from_marginal(t=20, params=new_params)\n", + "draws.mean()" + ] + }, + { + "cell_type": "markdown", + "id": "fdae8479", + "metadata": {}, + "source": [ + "Not surprisingly, mean capital stock at this (and any given) date is higher,\n", + "due to higher savings.\n", + "\n", + "\n", + "Here is the solution to exercise 6.4." + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "id": "60653d8b", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Mean capital from initial condition 5 is 16.50\n", + "Mean capital from initial condition 10 is 19.38\n", + "Mean capital from initial condition 20 is 23.77\n" + ] + } + ], + "source": [ + "init_values = 5, 10, 20\n", + "for init_k in init_values:\n", + " draws = sim_from_marginal(t=20, init=init_k)\n", + " print(f\"Mean capital from initial condition {init_k} is {draws.mean():.2f}\")" + ] + }, + { + "cell_type": "markdown", + "id": "4579551e", + "metadata": {}, + "source": [ + "Higher initial capital leads to higher mean capital at $t=20$.\n", + "\n", + "This is as expected, since the law of motion for capital is increasing in\n", + "lagged capital.\n", + "\n", + "\n", + "Here is the solution to exercise 6.5." + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "id": "0540ae57", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Mean capital at 50 is 22.75\n", + "Mean capital at 100 is 25.71\n", + "Mean capital at 200 is 26.08\n" + ] + } + ], + "source": [ + "dates = 50, 100, 200\n", + "for date in dates:\n", + " draws = sim_from_marginal(t=date)\n", + " print(f\"Mean capital at {date} is {draws.mean():.2f}\")" + ] + }, + { + "cell_type": "markdown", + "id": "1cc2283e", + "metadata": {}, + "source": [ + "Mean capital is slightly increasing, although it stabilizes as $t \\to \\infty$.\n", + "\n", + "The initial increase is due to the fact that the initial condition is\n", + "relatively small. Hence we see growth on average, as shown in the time series\n", + "plot starting from $k_0=1$ above.\n", + "\n", + "For exercise 6.6 we compute the 95% confidence interval as follows" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "id": "f7c110b1", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Sample mean is 12.8343\n", + "The 95% Confidence interval is [12.7693, 12.8992]\n" + ] + } + ], + "source": [ + "draws = sim_from_marginal(t=20)\n", + "n = len(draws)\n", + "k_bar = draws.mean()\n", + "sigma_hat = draws.std()\n", + "c = 1.96\n", + "\n", + "lower = k_bar - (sigma_hat / np.sqrt(n)) * c\n", + "upper = k_bar + (sigma_hat / np.sqrt(n)) * c\n", + "\n", + "print(f\"Sample mean is {k_bar:.4f}\")\n", + "print(\"The 95% Confidence interval is \", [round(x, 4) for x in (lower, upper)])\n" + ] + }, + { + "cell_type": "markdown", + "id": "a7d5a81f", + "metadata": {}, + "source": [ + "For exercise 6.7 we approximate steady state consumption at a range of savings\n", + "values using the method described in the exercise." + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "id": "c8174417", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "filenames": { + "image/png": "/home/john/gh_synced/books/sed2/edtc-code/code_book/_build/jupyter_execute/ch6_17_0.png" + }, + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "m = 100_000\n", + "min_s, max_s, grid_size = 0.2, 0.8, 20\n", + "savings_rates = np.linspace(min_s, max_s, grid_size)\n", + "expected_consumption = np.empty_like(savings_rates)\n", + "\n", + "for i, s in enumerate(savings_rates):\n", + " params = alpha, sigma, s, delta\n", + " draws = sim_from_marginal(t=100, sim_size=m, params=params)\n", + " w_vec = np.exp(sigma * np.random.randn(m))\n", + " c_bar = np.mean( (1-s) * f(draws) * w_vec )\n", + " expected_consumption[i] = c_bar\n", + "\n", + "fig, ax = plt.subplots()\n", + "\n", + "ax.plot(savings_rates, expected_consumption, label='expected consumption')\n", + "ax.legend()\n", + "ax.set_xlabel('savings rate')\n", + "#plt.savefig('solow_golden.pdf')\n", + "plt.show()\n" + ] + }, + { + "cell_type": "markdown", + "id": "0ae3c8db", + "metadata": {}, + "source": [ + "Exercise 6.8 asks us to compute the empirical distribution of $\\psi_t$ when\n", + "$t=20$ at different sample sizes." + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "id": "340ca972", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "filenames": { + "image/png": "/home/john/gh_synced/books/sed2/edtc-code/code_book/_build/jupyter_execute/ch6_19_0.png" + }, + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "fig, axes = plt.subplots(2, 2)\n", + "axes = axes.flatten()\n", + "sample_sizes = 4, 25, 100, 5000\n", + "grid_points = np.linspace(0, 25, 100)\n", + "\n", + "for ax, n in zip(axes, sample_sizes):\n", + " draws = sim_from_marginal(t=20, sim_size=n)\n", + " ecdf_vals = [np.mean(draws <= x) for x in grid_points]\n", + " ax.plot(grid_points, ecdf_vals)\n", + " ax.set_title(f\"$n={n}$\")\n", + "\n", + "plt.tight_layout()\n", + "#plt.savefig('solow_ecdf.pdf')\n", + "plt.show()\n" + ] + }, + { + "cell_type": "markdown", + "id": "0d9ccd71", + "metadata": {}, + "source": [ + "Our next task is to simulate from the \"threshold exernalities\" model.\n", + "\n", + "The following code generates figures 6.6 and 6.7." + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "id": "0714896c", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "filenames": { + "image/png": "/home/john/gh_synced/books/sed2/edtc-code/code_book/_build/jupyter_execute/ch6_21_0.png" + }, + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "alpha = 0.5 # capital intensity\n", + "s = 0.25 # savings rate\n", + "sigma = 0.14 # shock parameter\n", + "delta = 1.0 # depreciation\n", + "A1, A2 = 15, 25\n", + "k_b = 21.6\n", + "\n", + "\n", + "@jit\n", + "def A(k):\n", + " return A1 if k < k_b else A2\n", + "\n", + "@jit\n", + "def f(k):\n", + " return k**alpha\n", + "\n", + "@jit\n", + "def update(k):\n", + " w = np.exp(sigma * np.random.randn())\n", + " new_k = s * A(k) * f(k) * w + (1 - delta) * k\n", + " return new_k\n", + "\n", + "@jit\n", + "def generate_ad_ts(init=1, ts_length=400):\n", + " k = np.empty(ts_length)\n", + " k[0] = init\n", + " for t in range(ts_length-1):\n", + " k[t+1] = update(k[t])\n", + " return k\n", + "\n", + "fig, ax = plt.subplots()\n", + "\n", + "ax.plot(generate_ad_ts(init=1), label='$k_0 = 1$')\n", + "ax.plot(generate_ad_ts(init=80), '--', label='$k_0 = 80$')\n", + "ax.legend()\n", + "ax.set_xlabel('time')\n", + "#plt.savefig('adtssim.pdf')\n", + "plt.show()\n" + ] + }, + { + "cell_type": "markdown", + "id": "702d1004", + "metadata": {}, + "source": [ + "The next piece of code computes an approximation of the first passage time\n", + "above $k_b$ using simulation." + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "id": "450c0727", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "12.825768361534907\n" + ] + } + ], + "source": [ + "@jit\n", + "def draw_tau():\n", + " tau = 0\n", + " k = 1\n", + " while k < k_b: \n", + " k = update(k)\n", + " tau += 1\n", + " return tau\n", + "\n", + "def tau_draws(m=10_000):\n", + " draws = np.empty(m)\n", + " for i in range(m):\n", + " draws[i] = draw_tau()\n", + "\n", + "print(np.mean(draws))" + ] + }, + { + "cell_type": "markdown", + "id": "66e83b26", + "metadata": {}, + "source": [ + "Here is a solution to Exercise 6.11, which implements a kernel density\n", + "estimator and tests it on some data.\n", + "\n", + "The kernel density estimator uses a Gaussian kernel and is implemented via a closure.\n", + "\n", + "We use the `vectorize` decorator from Numba to ensure that the function can act\n", + "correctly on arrays as well as scalars." + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "id": "3c347859", + "metadata": {}, + "outputs": [], + "source": [ + "k0 = np.sqrt(1 / (2 * np.pi)) # for Gaussian kernel\n", + "@jit\n", + "def K(z):\n", + " return k0 * np.exp(-z**2)\n", + "\n", + "def kde_factory(data, delta):\n", + "\n", + " @vectorize\n", + " def kde(x):\n", + " return (1 / delta) * np.mean( K((x - data) / delta) )\n", + "\n", + " return kde" + ] + }, + { + "cell_type": "markdown", + "id": "136c0a2e", + "metadata": {}, + "source": [ + "Now we produce the figure." + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "id": "af174ee6", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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+ "text/plain": [ + "
" + ] + }, + "metadata": { + "filenames": { + "image/png": "/home/john/gh_synced/books/sed2/edtc-code/code_book/_build/jupyter_execute/ch6_27_0.png" + }, + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "Y = np.random.randn(100)\n", + "deltas = 0.01, 0.05, 0.1, 0.5\n", + "x_grid = np.linspace(-2, 2, 200)\n", + "\n", + "fig, axes = plt.subplots(2, 2)\n", + "axes = axes.flatten()\n", + "\n", + "for delta, ax in zip(deltas, axes):\n", + " f = kde_factory(Y, delta)\n", + " ax.plot(x_grid, f(x_grid))\n", + " ax.set_title(f\"$\\delta_n = {delta}$\")\n", + "\n", + "plt.tight_layout()\n", + "#plt.savefig(\"kdes.pdf\")\n", + "plt.show()\n" + ] + }, + { + "cell_type": "markdown", + "id": "9894681d", + "metadata": {}, + "source": [ + "Next we turn to exercise~6.12, which concerns the STAR model.\n", + "\n", + "We will use a `jitclass`, which requires us to set up parameters." + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "id": "b73ab44f", + "metadata": {}, + "outputs": [], + "source": [ + "from numba import float64\n", + "from numba.experimental import jitclass\n", + "\n", + "star_data = (\n", + " ('alpha_0', float64),\n", + " ('alpha_1', float64),\n", + " ('beta_0', float64),\n", + " ('beta_1', float64)\n", + ")" + ] + }, + { + "cell_type": "markdown", + "id": "41817481", + "metadata": {}, + "source": [ + "Next we set up the class, which implements the law of motion and the\n", + "stochastic kernel." + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "id": "33267e10", + "metadata": {}, + "outputs": [], + "source": [ + "@jitclass(star_data)\n", + "class STAR:\n", + "\n", + " def __init__(self, alpha_0=-4.0, alpha_1=0.4, beta_0=5.0, beta_1=0.6):\n", + "\n", + " self.alpha_0, self.alpha_1 = alpha_0, alpha_1\n", + " self.beta_0, self.beta_1 = beta_0, beta_1\n", + "\n", + " def G(self, x):\n", + " \" Logistic function \"\n", + " return 1 / (1 + np.exp(-x))\n", + "\n", + " def g(self, x):\n", + " \" Smooth transition function \"\n", + " a = (self.alpha_0 + self.alpha_1 * x) * (1-self.G(x)) \n", + " b = (self.beta_0 + self.beta_1 * x) * self.G(x)\n", + " return a + b\n", + "\n", + " def update(self, x):\n", + " \" Update by one time step. \"\n", + " W = np.random.randn()\n", + " return self.g(x) + W\n", + "\n", + " def draws_from_marginal(self, t_date, init=0, n=10_000):\n", + " draws = np.empty(n)\n", + " for i in range(n):\n", + " X = init\n", + " for t in range(t_date):\n", + " X = self.update(X)\n", + " draws[i] = X\n", + " return draws\n", + "\n", + " def phi(self, z):\n", + " \" Standard normal density \"\n", + " return k0 * np.exp(-z**2)\n", + "\n", + " def p(self, x, y):\n", + " \" Stochastic kernel \"\n", + " return self.phi(y - self.g(x))" + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "id": "e057ff83", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "filenames": { + "image/png": "/home/john/gh_synced/books/sed2/edtc-code/code_book/_build/jupyter_execute/ch6_32_0.png" + }, + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "s = STAR()\n", + "x_grid = np.linspace(-10, 20, 200)\n", + "\n", + "fig, ax = plt.subplots()\n", + "ax.plot(x_grid, x_grid, '--', label='45 degrees')\n", + "ax.plot(x_grid, s.g(x_grid), label='$g$')\n", + "ax.legend()\n", + "\n", + "#plt.savefig(\"star_g.pdf\")\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "id": "c9268a5a", + "metadata": {}, + "source": [ + "Now we use a closure to produce a look ahead estimator of the time $t$\n", + "marginal given a stochastic kernel and a set of draws from time $t+1$." + ] + }, + { + "cell_type": "code", + "execution_count": 18, + "id": "eb64c661", + "metadata": {}, + "outputs": [], + "source": [ + "def lae_factory(p, x_data):\n", + " \n", + " def f(y):\n", + " return np.mean(p(x_data, y))\n", + "\n", + " return f\n", + " " + ] + }, + { + "cell_type": "markdown", + "id": "212043e0", + "metadata": {}, + "source": [ + "This code solves exercise 6.12." + ] + }, + { + "cell_type": "code", + "execution_count": 19, + "id": "2b797135", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "filenames": { + "image/png": "/home/john/gh_synced/books/sed2/edtc-code/code_book/_build/jupyter_execute/ch6_36_0.png" + }, + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "dates = 1, 2, 4, 8, 16, 32\n", + "y_grid = np.linspace(-20, 20, 200)\n", + "greys = [str(g) for g in np.linspace(0.2, 0.8, len(dates))]\n", + "greys.reverse()\n", + "\n", + "s = STAR()\n", + "\n", + "fig, ax = plt.subplots()\n", + "\n", + "for t, g in zip(dates, greys):\n", + " x_obs = s.draws_from_marginal(t)\n", + " f = lae_factory(s.p, x_obs)\n", + " ax.plot(y_grid, \n", + " [f(y) for y in y_grid], \n", + " color=g, \n", + " lw=2, \n", + " alpha=0.6,\n", + " label=f'$t={t}$')\n", + "\n", + "ax.set_xlabel('$x$')\n", + "ax.legend()\n", + "\n", + "#plt.savefig(\"starseq.pdf\")\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "id": "f64d289e", + "metadata": {}, + "source": [ + "Solutions to exercises 6.13 -- 6.15 are omitted. They can be solved using\n", + "techniques similar to those described above and immediately below.\n", + "\n", + "We complete section 6.1 by solving exercise 6.16." + ] + }, + { + "cell_type": "code", + "execution_count": 20, + "id": "2e60cf0b", + "metadata": {}, + "outputs": [], + "source": [ + "ad_data = (\n", + " ('alpha', float64),\n", + " ('s', float64),\n", + " ('sigma', float64),\n", + " ('A1', float64),\n", + " ('A2', float64),\n", + " ('k_b', float64),\n", + ")\n", + "\n", + "\n", + "@jitclass(ad_data)\n", + "class AD:\n", + "\n", + " def __init__(self, \n", + " alpha=0.5,\n", + " s=0.25, \n", + " sigma=0.14,\n", + " A1=15, \n", + " A2=25,\n", + " k_b = 21.6):\n", + "\n", + " self.alpha, self.s, self.sigma = alpha, s, sigma\n", + " self.A1, self.A2, self.k_b = A1, A2, k_b\n", + "\n", + " def A(self, k):\n", + " return self.A1 * (k < self.k_b) + self.A2 * (k >= self.k_b)\n", + "\n", + " def f(self, k):\n", + " return k**self.alpha\n", + "\n", + " def update(self, k):\n", + " w = np.exp(self.sigma * np.random.randn())\n", + " new_k = self.s * self.A(k) * self.f(k) * w \n", + " return new_k\n", + "\n", + " def generate_ts(self, init=1, ts_length=100_000):\n", + " k = np.empty(ts_length)\n", + " k[0] = init\n", + " for t in range(ts_length-1):\n", + " k[t+1] = self.update(k[t])\n", + " return k\n", + "\n", + " def phi(self, z):\n", + " \" Lognormal density for N(0, sigma^2) \"\n", + " a = k0 / (z * self.sigma)\n", + " b = np.exp(- np.log(z)**2 / (2 * self.sigma**2))\n", + " return a * b\n", + "\n", + " def p(self, x, y):\n", + " z = y / (self.s * self.A(x) * self.f(x))\n", + " return self.phi(z) / z\n", + " " + ] + }, + { + "cell_type": "markdown", + "id": "f3002462", + "metadata": {}, + "source": [ + "Now we use the class to generate the figure." + ] + }, + { + "cell_type": "code", + "execution_count": 21, + "id": "4e94b9f6", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "filenames": { + "image/png": "/home/john/gh_synced/books/sed2/edtc-code/code_book/_build/jupyter_execute/ch6_40_0.png" + }, + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "sigmas = 0.1, 0.12, 0.14, 0.16, 0.18\n", + "y_grid = np.linspace(0, 60, 140)\n", + "greys = [str(g) for g in np.linspace(0.2, 0.8, len(sigmas))]\n", + "greys.reverse()\n", + "\n", + "fig, ax = plt.subplots()\n", + "\n", + "for sigma, g in zip(sigmas, greys):\n", + " ad = AD(sigma=sigma)\n", + " x_obs = ad.generate_ts()\n", + " f = lae_factory(ad.p, x_obs)\n", + " ax.plot(y_grid, \n", + " [f(y) for y in y_grid], \n", + " color=g, \n", + " lw=2, \n", + " alpha=0.6,\n", + " label=f'$\\sigma={sigma}$')\n", + "\n", + "ax.set_xlabel('$k$')\n", + "ax.legend()\n", + "\n", + "#plt.savefig(\"ad_sdla.pdf\")\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "id": "ed2bb5e5", + "metadata": {}, + "source": [ + "## Optimal Savings\n", + "\n", + "Optimization routines in the Python numerical tool set typically perform\n", + "minimization.\n", + "\n", + "It is useful for us to have a function \n", + "maximizises a map g over an interval [a, b].\n", + "\n", + "We use the fact that the maximizer of g on any interval is also the minimizer\n", + "of -g." + ] + }, + { + "cell_type": "code", + "execution_count": 22, + "id": "83cf8303", + "metadata": {}, + "outputs": [], + "source": [ + "def maximize(g, a, b, args):\n", + " \"\"\"\n", + " Returns the maximal value and the maximizer.\n", + " The tuple args collects any extra arguments to g.\n", + " \"\"\"\n", + " objective = lambda x: -g(x, *args)\n", + " result = minimize_scalar(objective, bounds=(a, b), method='bounded')\n", + " maximizer, maximum = result.x, -result.fun\n", + " return maximizer, maximum" + ] + }, + { + "cell_type": "code", + "execution_count": 23, + "id": "c0a7cb57", + "metadata": {}, + "outputs": [], + "source": [ + "class OptimalSaving:\n", + "\n", + " def __init__(self,\n", + " U, # utility function\n", + " R=1.05, # gross return on saving\n", + " rho=0.96, # discount factor\n", + " b=0.1, # shock scale parameter\n", + " grid_max=2,\n", + " grid_size=120,\n", + " shock_size=250,\n", + " seed=1234):\n", + "\n", + " self.U, self.R, self.rho, self.b = U, R, rho, b\n", + "\n", + " # Set up grid\n", + " self.grid = np.linspace(1e-4, grid_max, grid_size)\n", + "\n", + " # Store shocks (with a seed, so results are reproducible)\n", + " np.random.seed(seed)\n", + " self.shocks = np.exp(b * np.random.randn(shock_size))\n", + "\n", + " def state_action_value(self, s, a, v_array):\n", + " \"\"\"\n", + " Right hand side of the Bellman equation.\n", + " \"\"\"\n", + "\n", + " U, R, rho, shocks = self.U, self.R, self.rho, self.shocks\n", + "\n", + " v = interp1d(self.grid, \n", + " v_array, \n", + " fill_value=(v_array[0], v_array[-1]),\n", + " bounds_error=False)\n", + "\n", + " return U(a-s) + rho * np.mean(v(R * s + shocks))\n" + ] + }, + { + "cell_type": "markdown", + "id": "c1daa39c", + "metadata": {}, + "source": [ + "In the last line, the expectation is computed via Monte Carlo.\n", + "\n", + "\n", + "Now we write up the Bellman operator." + ] + }, + { + "cell_type": "code", + "execution_count": 24, + "id": "245c084b", + "metadata": {}, + "outputs": [], + "source": [ + "def T(v, os):\n", + " \"\"\"\n", + " The Bellman operator. Updates the guess of the value function\n", + " and also computes a v-greedy policy.\n", + "\n", + " * os is an instance of OptimalSaving\n", + " * v is an array representing a guess of the value function\n", + "\n", + " \"\"\"\n", + " v_new = np.empty_like(v)\n", + " v_greedy = np.empty_like(v)\n", + "\n", + " for i in range(len(os.grid)):\n", + " a = os.grid[i]\n", + "\n", + " # Maximize RHS of Bellman equation at state a\n", + " c_star, v_max = maximize(os.state_action_value, 1e-10, a, (a, v))\n", + " v_new[i] = v_max\n", + " v_greedy[i] = c_star\n", + "\n", + " return v_greedy, v_new" + ] + }, + { + "cell_type": "markdown", + "id": "eb87186b", + "metadata": {}, + "source": [ + "Here is a figure showing the function sequence generated by value function\n", + "iteration, starting at the utility function." + ] + }, + { + "cell_type": "code", + "execution_count": 25, + "id": "e121c391", + "metadata": {}, + "outputs": [], + "source": [ + "def solve_model(os,\n", + " tol=1e-4,\n", + " max_iter=1000,\n", + " verbose=True,\n", + " print_skip=25):\n", + " \"\"\"\n", + " Solve the model by iterating with the Bellman operator.\n", + "\n", + " * os is an instance of OptimalSaving\n", + "\n", + " \"\"\"\n", + "\n", + " # Set up loop\n", + " v = U(os.grid) # Initial condition\n", + " i = 0\n", + " error = tol + 1\n", + "\n", + " while i < max_iter and error > tol:\n", + " v_greedy, v_new = T(v, os)\n", + " error = np.max(np.abs(v - v_new))\n", + " i += 1\n", + " if verbose and i % print_skip == 0:\n", + " print(f\"Error at iteration {i} is {error}.\")\n", + " v = v_new\n", + "\n", + " if i == max_iter:\n", + " print(\"Failed to converge!\")\n", + "\n", + " if verbose and i < max_iter:\n", + " print(f\"\\nConverged in {i} iterations.\")\n", + "\n", + " return v_greedy, v_new" + ] + }, + { + "cell_type": "markdown", + "id": "970ceb33", + "metadata": {}, + "source": [ + "Let us put this code to work." + ] + }, + { + "cell_type": "code", + "execution_count": 26, + "id": "0365e9eb", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "filenames": { + "image/png": "/home/john/gh_synced/books/sed2/edtc-code/code_book/_build/jupyter_execute/ch6_49_0.png" + }, + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "@jit \n", + "def U(c, gamma=0.5):\n", + " \"The utility function.\"\n", + " return c**(1 - gamma) / (1 - gamma)\n", + "\n", + "os = OptimalSaving(U)\n", + "\n", + "#v = U(os.grid) # Initial condition\n", + "v = np.zeros_like(os.grid) # Initial condition\n", + "n = 40 # Number of iterations\n", + "greys = [str(g) for g in np.linspace(0.0, 0.8, n)]\n", + "greys.reverse()\n", + "\n", + "fig, ax = plt.subplots()\n", + "\n", + "for i in range(n):\n", + " v_greedy, v = T(v, os) # Apply the Bellman operator\n", + " ax.plot(os.grid, v, color=greys[i], lw=1.0, alpha=0.6)\n", + "\n", + "ax.set_xlabel('assets')\n", + "ax.set_ylabel('value')\n", + "ax.set(xlim=(np.min(os.grid), np.max(os.grid)))\n", + "plt.show()\n" + ] + }, + { + "cell_type": "markdown", + "id": "fa202558", + "metadata": {}, + "source": [ + "The next code block uses a more systematic method to find a good approximation\n", + "to the value function and then computes the associated greedy policy." + ] + }, + { + "cell_type": "code", + "execution_count": 27, + "id": "ec272ab0", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Error at iteration 25 is 0.7349889566690351.\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Error at iteration 50 is 0.2648838502200732.\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Error at iteration 75 is 0.09546326991188181.\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Error at iteration 100 is 0.0344046490568104.\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Error at iteration 125 is 0.012399322564725423.\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Error at iteration 150 is 0.004468675143598944.\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Error at iteration 175 is 0.001610495850478344.\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Error at iteration 200 is 0.000580417417040735.\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Error at iteration 225 is 0.00020918053152030325.\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "\n", + "Converged in 244 iterations.\n" + ] + }, + { + "data": { + "image/png": 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CLVu20KNHD5588kl+9rOfsWTJkpqyusHBwWzduvWa16uoqCAhIQGLxcL7778PwF//+leeeOIJoqOjMZvNjBo1ijfffPOac2tbtGgRc+fOJTo6mk6dOrFkyRIAFi5cyD333MPgwYMZPXo0oaHXToSIiYlh0KBBRERE0Lt375oVmYqLi7n99tspLy9Ha81f/vIXAJ577jlOnTqF1prx48cTExNDdHQ0qampDB48GK01/v7+fPLJJ0RHR+Pi4kJMTEzNnf+yZctwdXUlKCiIBQsW3NTXQ4hrmMrg9BY4uw0sJlBOEDocS58JbN11gJiAMsaOHUtiYiJOTu3zXrbJ8rnK+LvdQ2tdopRyBXYAP9Na76rVZgzGWqPTrX3jtlQ+t7mFhYWxd+/eetchdWSO8vUXLaA4E75+HUyXje3gGBgwnfQiM0uWLMHNzY2f/OQn7eJn7qbK51Y/VS2p3nSt/rBNEXUhhKiPhz909AGvQBg4E7r2wmQy8eabv2LChAmMHDmyVRZptjWr/u5QSjkrpQ4CWcAmrfXuepoNU0odUkptUEpFNPA6jyil9iql9mZnZ9941G1campqu7hTEMJm8s/Drn9CWfWzIScnuPV/YPhTpBYpPvjgA1xcXFi4cCGjRo1yiGQOViZ0rXWV1joW6A7EK6Ui6zTZD/TUWscAfwM+aeB1Fmut47TWcf7+/vU1EUKIpp3daiwicWpTza5K5cZHq1fz97//nV69egHGSDVHcl3DFrXWBUqpbcBk4HCt/UW1Pl+vlPqHUspPa916xUOEEO2XqRwqS8Cj+i/bATOgY1e45fvVgvbv309+fj4LFizAy8urgRdq36wZ5eIPmKqTeUdgAvD7Om2CgEyttVZKxWPc+ee2RMBCCAdisUDaHjieBB27wG3/zyiS5eEL4TMpKytj9fLlDBgwgISEBG699VZbR2xT1tyhBwNLlFLOGIl6pdY6SSn1GIDW+k3gLuBxpZQZKAPu1k0NnxFCiMbknIYjH0NRmrHdyde4S69eTCI5OZn33nuPqKgowsPDHaafvDHWjHJJBgbVs//NWp+/AbTcMvStrKqqiri4OLp160ZSUhJgjPf+97//zZW+/9/+9reNr/SNsf7n9OnTueuuu1o8ZiHajdI8OPrJ9zM83X0gfCaEDAalamZH79u3j7lz59K/f3+bhWpv7Hvqv428/vrrDBw4kKKioqv2P/PMMzWVB1uT2WzGxUW+VKKdM1fA6c1w5gujrK2zm9FH3mccOLuitWbvt9/y2Wef8eKLLzJ37lxbR2x32ud0qZuQlpbGunXrmDdv3nWfq7XmySefJDw8nGnTppGVlVVzbN++fYwePZohQ4aQmJhIRkYGAN9++y3R0dEMGzaM5557jshIYwDRO++8w+zZs5kxYwaTJk3i8uXLPPjggwwdOpRBgwaxZs0aoOHytRkZGYwaNYrY2FgiIyPZvn37zV4aIVqG1pC2F7b+Bk5tNJJ5tzgY+xL0SwRnVwoKCvjHP/7B+vXrue++++QGpwFyVep4+umn+cMf/lBvHZY33niDpUuXEhcXx//93/9dU8Hw448/5sSJE6SkpJCZmUl4eDgPPvggJpOJn/70p6xZswZ/f38++OADXn75Zd5++23mzp3L4sWLGT58OL/4xS+uer2dO3eSnJxM165deemllxg3bhxvv/02BQUFxMfHM2HCBJYvX463tzfffvstFRUVjBgxgkmTJrF69WoSExN5+eWXqaqqarHVk4S4KQUX4PBqyK+uGuITChGzoKsx7FBrjdlsprS0lJ49e/Loo49KMm+EXV+ZTz/9tKYPG+Cll14CjP7rK6ZPn86MGTN4/vnnKSwsBCA0NJSXX36ZZcuWXXVn+vvf/x4fH58G3y8pKYmAgACGDBlyTbXAxx9/nPnz56OUYv78+fz85z/n7bffvqrNV199xT333IOzszMhISE11QRPnDjB4cOHmThxImDcVQcHB1NQUEBxcTHDhw8HjIqEtf+/EydOpGvXroBRpnbt2rX86U9/AqC8vJwLFy40WL526NChNb9M7rjjjpqSwELYlYxkI5l38DKGIvaIr1nqLSsri3fffZfw8HCmTJlCSEiIjYO1f3ad0GfMmMGMGTOu2X+lW6G2P/zhD9fsmzNnDnPmzLH6/b7++mvWrl3L+vXrKS8vp6ioiDlz5rBs2TICAwNr2j388MM1NcLrqu9Ju9aaiIgIdu7cedX++iog1la7ZK7Wmo8++uiaB0ANla8F4xfMunXruO+++3juuee4//77G30/IVqcpQou5xhT9AH6TjSWees9Flzda5pt2bKFdevWMXXqVCmzfB2kD72W3/3ud6SlpZGamsqKFSsYN24cy5YtA6jp8waja+VKX3dto0aNYsWKFVRVVZGRkVFTZbF///5kZ2fXJHSTycSRI0fo0qULXl5e7Npl1DlbsWJFg7ElJibyt7/9reYJ/4EDB2r211e+9vz58wQEBPDwww/z0EMPsX///pu9PELcnLIC+PIPsOvvxgNQAJcO0H9KTTK/8le2h4cHL730EhMmTGi3lRFbgl3foduT559/noMHD6KUIiwsrN6/Eu68806++OILoqKi6NevH6NHjwbAzc2NVatW8dRTT1FYWIjZbObpp58mIiKCt956i4cffhgPDw/GjBmDt7d3ve8/f/58nn76aaKjo9FaExYWRlJSEvPmzau3fO22bdv44x//iKurK56enixdurRFr48QTXL3Bhc346FnaR50Dq45ZDab2bBhA19++SWLFi1y+AlCN6rJ8rktxZHL59ZWUlKCp6cnAP/7v/9LRkYGr79+kys1tVGO+PVv16pMcGYrdI+DTsazIErzjP5yZ9eaZjk5ObzxxhsEBATw4x//uNHnXOImy+eKlrVu3Tp+97vfYTab6dmzJ++8846tQxLi5mgNmYeNWZ6lucZMz7gHjWNXEjvGIi+FhYV06dKFO+64g5iYGJnteZMkodvYj370I370ox/ZOgwhmkdJljEMMfuYse0VDGGjrml2/Phx3n33XRISEpg5c6aMwmomdpfQtdbyW9oBSemfNs5cASc/N5Z/01Xg0hEGTIWetxm1ymv59NNP+frrr5kzZ069gwvEjbOrhO7u7k5ubi6+vr6S1B2I1prc3Fzc3d2bbizsi9aQfsCovVJeCCjocSsMnF5TROuKI0eO0L9/f4YMGcLEiRPl690C7Cqhd+/enbS0NBx5NSNH5e7uTvfu3W0dhrgexZfg8EeQc9LY9gmFyLugS8+rmhUVFbFixQouXrzIz372M5kg1ILsKqG7urrWrDQihLBTWsOxtdXdKxZw9TDuyEOH1czyvKK4uJhXX32V4cOHM3fuXFxdXet/TdEs7CqhCyHaAKWMSUJaQ88RMGAauHlc1SQvL69mfsSLL76Ir6+vbWJ1MJLQhRBNK75kTNv37mZsh98Ovcdc072itebLL7/k008/rSlHIcm89VizBJ078BXQobr9Kq31wjptFPA6MBUoBR7QWstccyHag6xjsGcxeIXAyJ8bo1Y6+hgfdWzYsIGUlBSeffZZgoODrzkuWpY1d+gVwDitdYlSyhXYoZTaoLXeVavNFKBv9UcC8M/qf4UQbV3X3saqQT6hYDGBU4erDlssFjZt2sTgwYMZP348kydPlvorNmLNEnQaKKnedK3+qDto+HZgaXXbXUopH6VUsNY6AyFE21KSDSc/g6jZRtEslw4w5hfGv3VcvHiRpUuX4uHhwdChQ+nQ4do2ovVY1YdevUD0PuAW4O9a6911mnQDLtbaTqved1VCV0o9AjwCRs1yIYQdqTLBqU1wZotRQMvd21jLE+pN5iaTiX//+98kJiYyfPhwmTtiB6xK6FrrKiBWKeUDfKyUitRaH67VpL6v5DVT/7TWi4HFYBTnuv5whRAt4tJhOLLaqL0C0CMB+oytt+mZM2fYvXs399xzD4sWLZLuFTtyXaNctNYFSqltwGSgdkJPA3rU2u4OpN90dEKIllWaZyTySynGduduEHWX0W9eR0VFBR9//DH79++vqT8kydy+WDPKxR8wVSfzjsAE4Pd1mq0FnlRKrcB4GFoo/edC2LEqszEx6ORnxoNO5w5G7ZWwUdfUXrni4MGDlJWVsXDhwqtW0xL2w5o79GBgSXU/uhOwUmudpJR6DEBr/SawHmPI4mmMYYtzWyheIcTNyjkFKR9CSaaxHTIIwu+odxhiaWkpH374IRERESQkJJCQIIPX7Jk1o1ySgUH17H+z1ucaeKJ5QxNCNCtzBSSvhO+qF5bxCDC6V/z719v8wIEDrFixgtjYWKmK2EbITFEhHIWzG5TmgJMr9J0EfcaB87UpwGKxoJQiJSWFhx9+mFtuucUGwYobIQldiPYs/7xRxrZTV6MGS+y9oJzB49rp+Fprdu3axcaNG3n55Ze5//77bRCwuBmS0IVory7shkPvQ2AEDJ1nJHTPgHqb5uXl8e6771JcXMyDDz6Ii4ukhrZIvmpCtFcBA8C1E3gGGpUR65n4o7XGZDJRUVFBv379mDRpEs7OzjYIVjQHSehCtBfFmXDuS2ORCScnY6bn+AXG9P16XLp0iaVLlxIVFcWUKVOkmFY7IAldiLbOXAmnNsKZL4z1PL2CoFf1wswNJPONGzfy+eefM2PGDEaPHt2KwYqWJAldiLYs8wikrIKyPGM7dBh0G9Jg8/z8fLp06YKPjw8vvfSS1CpvZyShC9EWleXD4dVwKdnY9gqB6Nn1TtkHo5BWUlIS33zzDYsWLSI+Pr4VgxVXFJRWcjqrBFdnJ2J6+DT760tCF6ItsVQZ/eQnPoOqCmPKfv8p0Gt0g1P2s7KyeOONN+jWrRvz58+XafutLLekgm9T8zmSXkhOSSUA3bt0lIQuhEPLO2t0rxR9Z2wHx0DEndCxS73Ny8vLKSwspGvXrsyePZuoqKhWDNYxlZuqyCwqJ6u4guziCr7LL+NszuWa4x1cnOjj70HfQC+01s1eclgSuhD2zlQOR9fAhW+M7Y5djcUnAsMbPOXw4cMsX76cESNGMH36dEnmzUxrTd7lStILykkvLCOjoIxLRRUUlpmuaevqrIjs5k1czy6E+Xrg5NRydeMloQth75QT5JwwZnj2GWdM23dxa7D5J598wp49e7j//vsZOHBgKwba/l0qLGfn2RxS0oooM1Vdc9zVWeHv2YHAzu74e3XA36sDffw96ejWOmP7JaELYY+KM8G9M7h2NJL3oDnGJCGvoHqba61JSUkhPDychIQEpkyZIsvBNYOyyipOZhaTll9Gau5l0vLLao55ubsQ4u1OiE9Hgr07EuTtjq+HW4vegTdFEroQ9ubCbkj+AHoON6ohQoOjVwAKCwt5//33uXTpEt26dZMJQs0g73Il35zJYW9qPhVmS83+Di5ODO7ZhVt7dSWgc/1j/G1JEroQ9sa7u/GvparBKftXFBUV8atf/YqRI0cyb948qcFyE0oqzCSnFZCSVkhqbmnN/l5+nejj70mPrp0I7doJd1f7LY2gjFLmjTRQqgewFAgCLMBirfXrddqMAdYA56p3rdZav9rY68bFxem9e/feWNRCtCflRUaN8t5jv0/epXlGhcQG5OTkkJqaSlxcXM1kIXFj8i9X8tWpbPadz8dUZeRDFydFVHdvbrvFjxCfjjaO8GpKqX1a67j6jlnz69wM/FxrvV8p5QXsU0pt0lofrdNuu9Z6+s0GK4TDsFjg/NdwfB2Yy6CTHwRHG8caSOYWi4WtW7eybt06pk2bBiDJ/AZlFZez7UQ2hy4WYKm+r+0f6Mmg0C70D/Ky6zvxhlizYlEGkFH9ebFS6hjQDaib0IUQ1ipMM/rJCy4Y2wHhxgLNTVi/fj3Hjx/nhRdeIDAwsIWDbJ++Kyhj24ksjqQXoTU4KRjUw4dR/fwJ8ra/fvHr0WSXy1WNlQoDvgIitdZFtfaPAT4C0oB04Fmt9ZF6zn8EeAQgNDR0yPnz528idCHaIHMFnNhgzPbUFqMiYsQsY5JQA33lZrOZjRs3EhcXh7e3N25ubs0+IcURnM+9zBfHsziZWQIY3SpDenZhVD9/uno0PAzU3txsl8uVF/HESNpP107m1fYDPbXWJUqpqcAnQN+6r6G1XgwsBqMP3dr3FqJduJRizPQsLwCUURGx/7QGKyICnD9/nqVLl+Lj48OwYcNkKOINOJ97mc3HsjidZSTyDi5OxPfqyohb/PDu6Grj6JqXVQldKeWKkcyXa61X1z1eO8Frrdcrpf6hlPLTWuc0X6hCtFFl+XD4IyOhA3j3gOgfgk9oo6eZTCb++9//MmXKFOLj4+Wu/DpdyC1l87FMTtVK5MP7+HJbXz86ubXP0UBN/q+U8V30FnBMa/3nBtoEAZlaa62UigecgNxmjVSItsZiqS6ktcEopOXiDgOmQc/bGiykBXDy5En27NnDvffey4IFC3BqpK241ncFZWw6cokTmY6TyK+w5n83ArgPSFFKHaze9xIQCqC1fhO4C3hcKWUGyoC79fV0zgvRHlWWwMnPjWQeHGP0lXf0abB5eXk5H330EcnJyfz4xz9GKSV35dchq6icTccyOfyd0WHQwcWJYX18GekAifwKa0a57AAa/a7SWr8BvNFcQQnRZpnKwdmtegm4zkaNcucOEBTZ5KmHDh3CYrGwcOFCOnXq1ArBtg95lyvZfCyTgxcL0NqopzKsty8j+/nj2cExEvkVjvW/FaIlZR2DQ+9D7zFGES1odPUggJKSElauXEl0dDQJCQkkJCS0fJztRHG5ia0nstlzLpcqCzg7wdBeXRnTP6DdPey0liR0IZqL1lBeaCT22rM+622q2bdvHx988AHx8fFS3vY6lJuq+OpkNt+cyaXCbEEpGBTqw4SBgW1q+GFLkIQuxI2yWCD3NPj3M7YDwyHhMfDr32gyt1gsKKU4fvw4//M//0OvXr1aKeC2zVRlYeeZXL48mU1ppVG6dmCwF4kRQQTaYaEsW5CELsSNyD9vzPQsSoeR/+/7IYgBDdcf11qzY8cOtmzZwiuvvMKcOXNaKdi2zWLRHLiYz6ajWTULSPTy60RiRBA9fWU5vdokoQtxPUxlRu2V1B2ANlYPqrp2lZq6cnJyWLp0KeXl5Tz88MNSFdEKWmtOZpaw4XAGmUUVAAR7u5MYEUS/QE8ZAVQP+a4SwhpaQ8YhOLLa6CdXTtB7HPSb3OjqQRaLBZPJhNlsJjIykgkTJsi4ciuk5Zfy2eFLnMk21uPs0smVCeGBDOrhI4m8EZLQhWhKaZ4xZT+rujxRlzCI+iF4N15MKz09nSVLljB48GASExMJCqp/tSHxvfzLlXx+5BKH0goB6OjqzLgBAST07oqrs/wibIokdCEaYrHAuW3VMz0rwaUjDJwOPUc0+tATYMOGDWzevJk77riD2267rXXibcPKKqvYeiKLnWdyMVs0Lk6K4X18GdM/oNXW42wPJKELUZ/885C8EorSjO2QQRBxp1EdsRG5ubn4+vri7+/PK6+8IrXKm2CusrDrbB5fHM+qWXR5UA8fJoYH0sXBhyDeCEnoQtRVXgTf/BUsZuOhZ9RsY0hiIyorK1m7di27d+9m0aJFxMXVW91UVNNacyS9iA2HM8i7bDxU7uPvwZSoYLrZ2QpBbYkkdCGuuLJ+p3tnY6anxVz90LPxkrVZWVm8/vrr9OrViwULFuDhIUPpGnMht5T1hzM4X71uZ4BXB6ZEBdE/0EseeN4kSehClOUbDz27D4WQWGPfgGlNn1ZWRkFBAX5+ftx7772Ehzd+F+/o6j7w9OzgzPiBgcSHdcXJSRJ5c5CELkTmEcg8DJezG105qLbk5GTee+89Ro0axdSpUyWZN6LcVMW2E9l8fToHs0Xj6qwYcYsfo/v5t8l1O+2ZJHThmCpLwa26omHPEVBWAGG3WZXMV69ezf79+3nwwQfp169fy8bZhlksmm9T89h8LJOSiu8feE6KCMSnkzzwbAmS0IVjubKm54VdMPp56NTVSOIDpzd6mtaagwcPEhUVxYgRI5g+fTpubpKUGnIys5j1Kd/P8Ozp24lpUcH06CplgVuSJHThODKPQsqHUJYHKMg5BaFNl6vNz89n+fLl5OXlERoaSmBgYMvH2kZlFpWzPiWjZiHmrh6uTI4IJrJbZ3ng2QqsWYKuB7AUCAIswGKt9et12ijgdWAqUAo8oLXe3/zhCnEDyouMKfvpB4ztzt0h5kdNrukJUFRUxG9+8xvGjh3LY489JjVYGlBSYWbz0Uz2pOahtbFa0LgBAQzr4yszPFuRNd+dZuDnWuv9SikvYJ9SapPW+mitNlOAvtUfCcA/q/8Vwna0hvPfwLFPwVxmrCTUfyr0Gt3omp5gDEU8d+4cCQkJzJ8/H2/vxicUOSpzlYVvzuTyxfEsKswWnBQk9O7K+IGBDrdakD2wZgm6DCCj+vNipdQxoBtQO6HfDiytXkd0l1LKRykVXH2uEK2vKMMob5t/ztgOCDcmCHXq2uhpFouFzZs389lnnzFjxgwASeb10FpzLKOYDYczyCmpBKB/oCdTo4IJkNrkNnNdv0KVUmHAIGB3nUPdgIu1ttOq912V0JVSjwCPAISGNv3nrhDXrcoEpzbC6S2gq6CDl7E4c8ggq0awrFu3jtOnT/PSSy/h5+fXCgG3PZcKy0lKTq+phOjv1YFpUcH0D/KycWTC6oSulPIEPgKe1loX1T1czyn6mh1aLwYWA8TFxV1zXIibUlkKO/5sjCcHYzjigOnfD09sgNlsZsOGDcTHxzN58mRcXFzkAV496vaTd3JzZvzAABJ6+eIsE4PsglUJXSnlipHMl2utV9fTJA3oUWu7O5B+8+EJcR3cOoF3D1DOxkPPrr2bPOXs2bMsXbqUgIAARo0ahaurYy4u3BhzlYWdZ3PZcuz7fvJb+/gyYWAAndykn9yeWDPKRQFvAce01n9uoNla4Eml1AqMh6GF0n8uWpzWkLYXvAK/H7ESNdt4+OncdKIxmUwsW7aMGTNmMHjwYLkrr0NrzfFLxnhy6SdvG6z59ToCuA9IUUodrN73EhAKoLV+E1iPMWTxNMawxbnNHqkQdZ3/BlJWQuduMPJZY+RKE90rAMeOHWPPnj3cf//9zJ8/XxJ5PTKLyklKzuB0ljGe3N/TjWnRIdJPbuesGeWyg/r7yGu30cATzRWUEFbpHgcXdhrDEK1IyqWlpaxatYqjR48yZ84cSeT1KK00s/lYFrvP5mLRxopB4wcGcGtv6SdvC6QDTLQdeefg5Ocw5AFwdTfK2o78uVXJXGvN4cOHcXFxYdGiRbi7S5dBbRaLZvc5o+5KaWUVSkFCr65MDA/EQ8aTtxnylRL2z1QGx9dB6g5Aw9mt0H+KcayJZF5UVMSKFSsYPHgw8fHxxMfHt3y8bczprBKSktNr6q708fdgWnQwwd6y0ERbIwld2C+tIeMQHP4IKopAOUGfCXDLBCtO1ezevZtVq1YxfPhwYmJiWiHgtiXvciXrUzI4km6MQu7q4cqUyGAiQqTuSlslCV3YpyuLTmQeNra7hEH0j6BzSJOnVlVV4eTkxLlz5/jpT39Kz549WzbWNqbCbNQn33HKqE/ewcWJ0f39ue0WP6m70sZJQhf2xWKB1O1GF0tVBbi4w8AZxiShJu4atdZ8+eWXbN26lfnz53PPPfe0UtBtg9aagxcL+OzIJYrKzAAMCvUhMSII744y/r49kIQu7Efhd5C8AgouGNtB0RD5A+jo0+Sp2dnZvPPOO2itpSpiPS7mlZKUnMGFPGMdz+5dOjIjOoRQX6lP3p7Id72wvSoznFhvPOzUFnD3hsi7IDi66VOrqjCbzVgsFoYMGcKYMWNwaqKSoiMpLjfx+ZFM9p3PB8DL3YXEiEAGh3aRfvJ2SBK6sD0nZ8g7YzwEDRtp1F9xbXpY4cWLF1myZAnx8fFMmjRJFp6oxVxlYddZYxhihdmCsxPcdosfY/oHyDqe7ZgkdGEbFSVGNUR3b6NvPOYeY3hi115WnZ6UlMS2bduYNWsWw4YNa+Fg25aTmcUkHUonu3q6/oAgL6ZFB+Pn2cHGkYmWJgldtL6c07D3bWPkSvzDRkL3CrLq1OzsbPz9/QkJCZGFJ+rIKalgfUoGxzKKAfDzdGO6TNd3KJLQRevz9Df6yi0mqKo0Znw2oaKigo8//pgDBw6wYMECBg8e3AqBtg0V5iq2Hs/m69PfD0McNyCA4X18cZFhiA5FErpoeZYquLgHeiQYBbTcvY0p+x5+Vk3bz8zM5PXXX6dfv34sWLAADw+PVgja/tU3DHFIzy4kRgTi5S7DEB2RJHTRsvLPG0vBFX0H5nLoM9bY7+nf5KmXL1+msLCQgIAAfvKTn9C/f/8WDrbtSMs3hiGez/1+GOLMmBB6dJVhiI5MErpoGaZyYyjiua8ADZ18rZrlecX+/ftZsWIF48aNY/LkyZLMq5VUmNl09BLfpuajtQxDFFeThC6aX+YRSF4J5QVG/ZXeY6HfFHBxs+r0VatWkZyczKOPPkqfPn1aNtY2osqi2X02l03HMik3GasGjezrx9gBMgxRfE8Sumg+5UVwZDWkHzC2vXtAzN3g3b3JU7XW7Nu3j5iYGEaNGsXtt98uy8FVq1sNsV+gJ9OigwnwkhLA4mrWLEH3NjAdyNJaR9ZzfAywBjhXvWu11vrVZoxR2Dut4cIuOLYWTKXGEnD9pxoLT1gxazM3N5d3332XkpIS+vTpQ0BAQCsEbf8KSitZl5LB4e++r4Y4PTqEAUFe0r0i6mXNHfo7wBvA0kbabNdaT2+WiETbUpIFh1YYMz0B/AdC9A+hU1erTi8qKuK3v/0tEydOZOLEiTg7S/eBqcrC9lPZbDuRjalK4+asGDMgQKohiiZZswTdV0qpsFaIRbQ1WsO3/4GSTHDzhMhZEDLYqqGIGRkZnD9/nltvvZVFixbh5SWTX7TWHMsoZl1KOnmXTQBEd/dmamQw3p2k+0k0rbn60IcppQ4B6cCzWusj9TVSSj0CPAIQGhraTG8tWp3WRtJWCiJmQfp+CL8d3JoeH15VVcXGjRvZvHkzd9xxB4AkcyC7uIKk5HROZhqLMgd27sDMmBB6+3vaODLRlihjfecmGhl36EkN9KF3Bixa6xKl1FTgda1136ZeMy4uTu/du/cGQhY2c2UpOOVk3I3fgE8//ZRz584xZ84cuna1rlumPSs3VbH1eBZfn8mhymIsyjwhPIBbe/niJIsyi3oopfZprePqO3bTd+ha66Jan69XSv1DKeWntc652dcWdqY0D85/Xb0U3Dir6pQDmEwmkpKSGDZsGJMnT8bFxcXhH+rVzPI8fImicjNKQVzPLiRGBuEpizKLG3TT3zlKqSAgU2utlVLxgBOQe9ORCftQefn7rhTvbhA1G3x6Wp3MT506xdKlS+nRowedOnWSoYhAekEZnx5KJ7V6lmePrsZiEzLLU9wsa4Ytvg+MAfyUUmnAQsAVQGv9JnAX8LhSygyUAXdra/pxhH3TGs5/A8c+hdh7ILh6keWew61+CZPJxAcffMCsWbMYNGhQCwXadpRWmtl0NJPd5/LQGjw7ODM5MkhmeYpmY1UfekuQPnQ7Vpxp1F+5MhQxdJgxQchKhw8fZs+ePcydOxfA4ZOVxaLZez6fz49corSyCicFw/r4MmFgoMzyFNetRfvQRTtSZYbTm+H0JrCYoYOXMYolxLq768uXL7Ny5UpOnz7NnDlzHD6RA1zILeXT5HTS8ssA6OPvwYyYEAI7yyxP0fwkoQtD3lk49AGUXDK2Q4fBwJng1nS/7pW/8o4ePYqHhwcLFiygQwfHXh2n7lqe3h1dmRoVRFQ3b/lFJ1qMJHRHZyqDY0lwfoex7eEP0XeD3y1WnV5QUMB7773H0KFDaz4cmcWi2Xk2l01HjbU8XZwUt/X1Y0x/fzq4SPeKaFmS0B1ZxiE4/BGUFxpDEW+ZAH0ngXPTI1G01nzzzTesXr2aUaNGyUNP4Gx2CWsPfV9Eq3+gJ9NjQmQtT9FqJKE7qoPvwcXdxuc+PY2HnlbWKzebzTg7O/Pdd9/xzDPP0L1709UU27PCUhMbDmdwKK0QMIpoTYsKYWCwFNESrUsSuqPy6QnpB2HgdOh5m1VVES0WC1u3buXLL79kwYIF/PCHP2z5OO2YucrC12dy2Xo8iwqzBVdnxeh+/ozq5y9FtIRNSEJ3FMWZUJwBIbHGds/hEBhh9QShzMxM/vvf/+Li4sKTTz6Ji4tjf+ucyizm00PpZJdUAhAR0plpUcF08bBuEQ8hWoJj/1Q6isu58NUfjH5yn1CjtK1SViVzs9mM2WxGKcXw4cMZOXKkQ3cj5F82apQfSTcqXvh7ujE9JoR+gVJgTNieJHRH4OELQdHGwhMu1o9/Tk1NZenSpQwfPpwJEyY49MITpioLO07lsPVEFqYqTQcXJ8YOCGBEH19cpHtF2AlJ6O2RqRyOJ0GPeOOOHGDQfVb1k1+xZs0aduzYwezZsx1+KOKxjCKSkr+vUR7T3ZspUcF4d5S6NMK+SEJvby6lQMqHxlDE/FQY+XOje8XKZJ6ZmUlgYCBhYWGMGzfOoWuV55ZUsC4lg2MZxYBRo3xGTAh9pEa5sFOS0NuL8kJjTHnGIWPbJ9SYIGRlf3dZWRmrV68mJSWFBQsWEBMT04LB2jdTlYUvT2Tz5clszBaje2XCwECG9fHFWWqUCzsmCb2t0xou7ISja8FcBs4dYMBUCBtl9V35pUuXeO2114iMjGTBggV06uSYZVy11hzNKGJdcgb5pUb3yqBQH6ZEBuHlLt0rwv5JQm/L6i7QHBBu1Cu3coHm4uJiCgsLCQoKYt68edxyi3XT/dujnJIKPj30/RJwwd7uzIgJoZdf08vqCWEvJKG3RVVmOLMFTm00qiJe5wLNWmv27t3LypUrmThxIt27d3fYZF5hrmLbiWx2nMrBbNG4uzoxMTxQloATbZI1C1y8DUwHshpYU1QBrwNTgVLgAa31/uYOVFTLOwvJK41JQgA9boXwmVYt0HzFhx9+yLFjx3jiiScICwtrmTjtnNaaI+lFJCVnUFhmdK/IEnCirbPmO/cd4A1gaQPHpwB9qz8SgH9W/ytaQuZRI5l7+EP0j8CvyfW4ASOB7dmzh8GDBzNu3DhmzZrlsLM9s4uN7pVTWUb3Sjcfd2bGdCPU1zGfHYj2o8mfaK31V0qpsEaa3A4srV52bpdSykcpFay1zmiuIK+RsgpSt1/fOSOehq69rj4/8i7oNdLYd2EXHHr/+l6zvvN7JEDsj419hd8ZMzSvR33nd+4Go5839vWdZEwO6j3aqqqIAFlZWbz77rtUVlbSr18//Pz8ri+mdqLCXMXW49nsOJ1NlQU6ujozKSKQ+LCu0r0i2oXmuEXrBlystZ1Wve+ahK6UegR4BCA0NLQZ3toBubhB3wlWNy8sLOT3v/89kydPZvz48Thdx+Si9kK6V4SjsGpN0eo79KQG+tDXAb/TWu+o3t4CPK+13tfYa97UmqI3ug7qlQeGtc+vb589v6aVvvvuO1JTUxkxYgSXL1/Gw8MxR2tkF1ew9lA6p6V7RbQTLb2maBrQo9Z2dyC9GV63YTdbHKq+89vKazbBbDazYcMGtm3bxqxZswAcMpkb3StZ7DidU9O9khgRyFDpXhHtWHMk9LXAk0qpFRgPQwtbtP9cNGr9+vVcvHiR+fPn4+PjY+twWp3WmsPfFZGUkk5RmRmlYGhYFxIjgvCQ7hXRzlkzbPF9YAzgp5RKAxYCrgBa6zeB9RhDFk9jDFuc21LBivpVVFSQlJTE8OHDmTp1Ks7Ozg5Z4jaruJxPD2XUdK9079KRmTEh9Ogq3SvCMVgzyuWeJo5r4Ilmi0hcl+PHj/Puu+/Sp08fvLy8HHIoYt3ulU5uzkwKl+4V4Xgc76e/HamsrGT16tXcfffdREVF2TqcVqe1JuW7QtalZNR0r8T36sKkcOleEY5JvuvboEOHDvHtt9/y0EMP8eKLLzpm90pROWsPpXMm+zIg3StCgCT0NqW4uJgVK1Zw4cIF7rvvPodM5Fe6V7afysGije6VxIgg4np2ke4V4fAkobcBV+YKnDhxgq5du/LAAw/g6upY5VyvjF5Zl2JMDrrSvZIYEUQnN/k2FgIkodu9/Px8li1bxq233srQoUOJi6t3PkG7JqNXhLCOJHQ7pbVm+/btrFmzhvHjxzNo0CBbh9Tq6tZekdErQjROErodMplMuLi4kJ2dzbPPPktwcLCtQ2pVdWuvyOgVIawjPx12xGKxsGnTJr7++msWLlzID37wA1uH1Orq1l6R7hUhrCcJ3U5kZGTw9ttv4+HhwVNPPYWzs7OtQ2pVV1YO2n4qW2qvCHGDJKHbmNlsxmQy4ezszJgxYxg+fLhDDUe80r2yLiWDglIpbSvEzZCfGBs6c+YMS5cuZdSoUYwfP56AgABbh9SqckoqSDqUzonqhZlDvN25PVZK2wpxoySh28jq1avZuXMnd999N4MHD7Z1OK3KVGVh24lsvjqZXbMw86TwIBJ6SfeKEDdDEnorS09PJyQkhL59+5KYmOhwtcqPZRSRlJxO3mWje2VwqA+TI4PwcnesiVJCtARJ6K2ktLSUVatWcfz4cV555RWHK6aVd7mSpOR0jmUUAxDs7c7MmBDC/BzrF5oQLUkSeivIyMjgtddeIzY2lgULFuDu7m7rkFqNqcrC9lPZbDuRjalK08HFiUnhgdza21e6V4RoZpLQW1BRURGFhYUEBwfz6KOP0rt3b1uH1KpOZhbz6aF0ckoqARjUw4fJUUF0lu4VIVqEVQldKTUZeB1wBv6jtf7fOsfHAGuAc9W7VmutX22+MNsWrTW7d+9m1apVTJkyhR49ejhUMi8orSQpOYMj6UUABHh14PbYEHr7e9o4MiHaN2uWoHMG/g5MxFgQ+lul1Fqt9dE6Tbdrrae3QIxtzgcffMCpU6d46qmnCA0NtXU4rcZcZWHH6Ry2Hs+isrp7ZdyAAEbc4oezdK8I0eKsuUOPB05rrc8CVC8GfTtQN6E7NK01O3fuZOjQoUycOJHZs2c71GzP01klrD2UTnZxBQBR3byZFhWMdyfpXhGitViT0LsBF2ttpwEJ9bQbppQ6BKQDz2qtj9RtoJR6BHgEaFd3rpmZmSxZsgSA8PBwfH19bRxR6yksM7E+JYPktEIA/D3dmBkbwi0BXjaOTAjHY01Cr+9vZV1nez/QU2tdopSaCnwC9L3mJK0XA4sB4uLi6r5Gm1RYWMgf//hHpk2bxpgxYxxm2n6VRfPNmRy2HMuiwmzB1VkxdkAAI2/xw8XZydbhCeGQrEnoaUCPWtvdMe7Ca2iti2p9vl4p9Q+llJ/WOqd5wrQ/Fy9eJDU1lZEjR/Lqq6/SqZPjTFc/l3OZNQe/I7PI6F4JD+nM9Khguni42TgyIRybNQn9W6CvUqoX8B1wN/Dj2g2UUkFAptZaK6XiAScgt7mDtQcmk4l169axY8cO7rrrLgCHSebF5SY2pFziwMUCAHw93JgRE0L/IOleEcIeNJnQtdZmpdSTwOcYwxbf1lofUUo9Vn38TeAu4HGllBkoA+7WVxbCbGfWr19PZmYmCxYsoHPnzrYOp1VYLJpd53LZeCSTCrMFFyfFmP7+jOrnj6t0rwhhN5St8m5cXJzeu3evTd77epWXl7NmzRpGjhxJYGCgQ41euZBbypqD35FeWA5A/0BPZsSE4OvZwcaRCeGYlFL7tNb1Li4sM0WbcOTIEZYvX07//v3x8fFxmGR+ucLMZ4cvsfd8PgA+nVyZHh1MeHBnh3nwK0RbIwm9EZWVlSQlJTFnzhzCw8NtHU6r0FrzbWo+nx+5RGllFc5OMLKvP2P6+9PBxTF+mQnRVklCr0NrzYEDB9i7dy8PP/wwzz//vMPckabll7LmYDpp+WUA9PH3YGZsCAFejlNMTIi2TBJ6LYWFhbz//vtkZGRw//33O0wiL6usYuPRS+w+l4fW0LmjC9Oigonq5u0w10CI9kASOsZdOcDp06cJCgrioYcewtW1/U9Z11pz4GIBG1IyKKmowknBiFv8GD8wAHdX6V4Roq1x+ISek5PDsmXLuO2224iLi2PIkCG2DqlVZBaVs+bgd5zLKQUgzLcTt8d2I8hbuleEaKscNqFrrdm6dStJSUkkJiY6zLqe5aYqvjiexdenc7Bo8OzgzOTIYAaH+kj3ihBtnEMm9MrKSlxdXSksLOSFF14gMDDQ1iG1OK01h78rIiklnaIyM0rBrb27Mik8iI5u0r0iRHvgUAm9qqqKzz//nJ07d7Jo0SLuvPNOW4fUKnJKKlh7MJ1TWSUAdO/SkdtjQ+jexTFKFgjhKBwmoaenp/PWW2/h7e3NM8884xAThCrNFradyGL7qRzMFk1HV2cSIwIZGtZV1vMUoh1q9wndZDJhMplwc3Nj4sSJJCQkOERf8bGMIj49lE5+qQmAIT27MDkyCM8O7f5LLoTDatc/3adOnWLp0qWMGzeOsWPH4ufnZ+uQWlz+5UqSktM5mlEMQLC3O7fHhtDT18PGkQkhWlq7Tegffvghe/fu5Z577iE2NtbW4bQ4c5WF7dXreZqq1/OcGB7IsN6+0r0ihINodwk9LS2N7t27Ex4ezrRp0xyiVvnprGLWHkwnu6QSgJju3kyJCsa7Y/ufHCWE+F67SeglJSWsXLmSM2fO8PLLLxMREWHrkFrcNet5enVgZkwItwR42jgyIYQttIuEnp6ezl/+8hfi4+NZsGABHTq071rdddfzdKtez/M2Wc9TCIdmVUJXSk0GXsdYseg/Wuv/rXNcVR+fCpQCD2it9zdzrNcoKCigsLCQ7t278+STT9KzZ8+WfkubO5tdwtpD6bKepxDiGk0mdKWUM/B3YCLGgtHfKqXWaq2P1mo2Behb/ZEA/LP632ZXbqrCVGVh5zdf8+naNUyZMg3foG74BnWjpMLcEm9pF8oqq9h8LLOme0XW8xRC1GXNHXo8cFprfRZAKbUCuB2ondBvB5ZWryO6Synlo5QK1lpnNHfAnx+5xFtL3qUwK53IMTPYfjmQ7euONffb2C1XZ8XofrKepxDiWtYk9G7AxVrbaVx7911fm27AVQldKfUI8AhAaGjo9cYKQAcXJ6ISRtOhkxdOTo6T0JSCPv6eJEYESfeKEKJe1iT0+gYx111Z2po2aK0XA4vBWCTaive+xuTIYCZHBt/IqUII0a5Zc4ubBvSotd0dSL+BNkIIIVqQNQn9W6CvUqqXUsoNuBtYW6fNWuB+ZbgVKGyJ/nMhhBANa7LLRWttVko9CXyOMWzxba31EaXUY9XH3wTWYwxZPI0xbHFuy4UshBCiPlaNQ9dar8dI2rX3vVnrcw080byhCSGEuB6OM0xECCHaOUnoQgjRTkhCF0KIdkISuhBCtBPKeJ5pgzdWKhs4f4On+wE5zRhOc7HXuMB+Y5O4ro/EdX3aY1w9tdb+9R2wWUK/GUqpvVrrOFvHUZe9xgX2G5vEdX0kruvjaHFJl4sQQrQTktCFEKKdaKsJfbGtA2iAvcYF9hubxHV9JK7r41Bxtck+dCGEENdqq3foQggh6pCELoQQ7YRdJ3Sl1GSl1Aml1Gml1C/qOa6UUn+tPp6slBpsJ3GNUUoVKqUOVn8saKW43lZKZSmlDjdw3FbXq6m4Wv16KaV6KKW2KqWOKaWOKKV+Vk+bVr9eVsZli+vlrpTao5Q6VB3XL+tpY4vrZU1cNvl5rH5vZ6XUAaVUUj3Hmv96aa3t8gOjVO8ZoDfgBhwCwuu0mQpswFgx6VZgt53ENQZIssE1GwUMBg43cLzVr5eVcbX69QKCgcHVn3sBJ+3k+8uauGxxvRTgWf25K7AbuNUOrpc1cdnk57H6vf8f8F59798S18ue79BrFqfWWlcCVxanrq1mcWqt9S7ARynV0uvTWROXTWitvwLyGmlii+tlTVytTmudobXeX/15MXAMYx3c2lr9elkZV6urvgYl1Zuu1R91R1TY4npZE5dNKKW6A9OA/zTQpNmvlz0n9IYWnr7eNraIC2BY9Z+BG5RSES0ck7Vscb2sZbPrpZQKAwZh3N3VZtPr1UhcYIPrVd19cBDIAjZpre3ielkRF9jm++s14HnA0sDxZr9e9pzQm21x6mZmzXvux6i3EAP8DfikhWOyli2ulzVsdr2UUp7AR8DTWuuiuofrOaVVrlcTcdnkemmtq7TWsRhrBscrpSLrNLHJ9bIirla/Xkqp6UCW1npfY83q2XdT18ueE7q9Lk7d5HtqrYuu/BmojdWeXJVSfi0clzXscjFvW10vpZQrRtJcrrVeXU8Tm1yvpuKy9feX1roA2AZMrnPIpt9fDcVlo+s1ApiplErF6JYdp5RaVqdNs18ve07o9ro4dZNxKaWClFKq+vN4jOuc28JxWcMuF/O2xfWqfr+3gGNa6z830KzVr5c1cdnoevkrpXyqP+8ITACO12lmi+vVZFy2uF5a6xe11t211mEYOeILrfWcOs2a/XpZtaaoLWg7XZzayrjuAh5XSpmBMuBuXf1YuyUppd7HeKLvp5RKAxZiPCSy2fWyMi5bXK8RwH1ASnX/K8BLQGituGxxvayJyxbXKxhYopRyxkiIK7XWSbb+ebQyLpv8PNanpa+XTP0XQoh2wp67XIQQQlwHSehCCNFOSEIXQoh2QhK6EEK0E5LQhRCinZCELoQQ7YQkdCGEaCf+PzxZvMzZjpMeAAAAAElFTkSuQmCC\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "filenames": { + "image/png": "/home/john/gh_synced/books/sed2/edtc-code/code_book/_build/jupyter_execute/ch6_51_10.png" + }, + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "os = OptimalSaving(U, grid_max=4)\n", + "sigma_star, v_star = solve_model(os)\n", + "\n", + "fig, ax = plt.subplots()\n", + "\n", + "ax.plot(os.grid, sigma_star, \n", + " label='optimal policy', lw=2, alpha=0.6)\n", + "ax.plot(os.grid, os.R * sigma_star + 1.01, '-.', \n", + " label='next period assets', lw=2, alpha=0.6)\n", + "ax.plot(os.grid, os.grid, 'k--', \n", + " label='45 degrees', lw=1, alpha=0.6)\n", + "\n", + "ax.legend()\n", + "plt.show()\n" + ] + }, + { + "cell_type": "markdown", + "id": "274a6f6d", + "metadata": {}, + "source": [ + "Now we use the look-ahead estimator to compute asset density dynamics under\n", + "the optimal policy." + ] + }, + { + "cell_type": "code", + "execution_count": 28, + "id": "31c60aef", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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YtVyMzzFmt2TT2NgIQAR9uSNZLrWJCHqNYtVyAa4OuCgk6OKjC4BsitYqIug1ilXLBbgq6IW8cSXoKhtGWJ6UEqGL5VJ5RNBrlFIsl1QqBeBqX5dcNDQ0gIiQSCT0i4aw/LATocvdXeUQQa9BrDbmAuYvAJlMBkRUMKr3eDwIBoNgZom0ljGStlibiKDXIFYbcwHQGy35/f6ikbd8MAU7gi4tmCtHUTUgorVEtJ+IThDRe0T0RI5jiIi+QURniOgdIrrRneUKQGkbokZBLzYsWqbPLG+YuSTLJRAIwOPxIJlMykDyCmFGEdIA/gsz9wO4BcDjRHR91jGfALB54etRAH/n6CqFRVhtzAXMC7rH45EIXShKKpVCJpPRe5ybxdhqt15+d+wOuPj85z+PFStWLOrWCABTU1N46KGHcN1116G/vx+//vWv7S4VgAlBZ+ZhZn574e9RACcArMk67FMAvsfzHAAQJqIeR1YoLKGUCF1F2z6fTyJ0oSCl2C2Kest0sTPgAgA++9nPYu/evUu+/8QTT+C+++7DyZMncfToUfT399tZpo4lD52I1gPYCeCNrIfWALho+Pcgloo+iOhRIjpIRAfVTEvBOqWkLCYSCXg8HlOCbvRC62mcmGCOUjotKuopQndiwMWdd96Jjo6ORd+LRCJ45ZVX8MgjjwCYt6qMw2bsYPp+ioiaAfwUwBeYOXusTa4O+EuUgJmfAfAMAOzevVuUokSspiwyM5LJJID5HHSVJZPv+cZxYqlUqmAhklB/lOKfK9yw655++mnHzmXkscceK/i43QEX+Th37hy6u7vxuc99DkePHsWuXbvw1FNPOdKy2pSgE5Ef82L+j8z8LzkOGQSw1vDvXgCXbK9OyEmpKYter1ffFC0k6MDV6TOJREIEfZkhlstV7Ay4yEc6ncbbb7+Nb37zm7j55pvxxBNP4Mknn8SXv/xlW+cFTAg6zXdx+g6AE8z8N3kOexbAHxHRjwDcDGCamYdtr07IiVXLRXnhqpuiEvhCG17BYNCVcWJC9VNKp0WFG8VFxSJpt7A74CIfvb296O3txc033wwAeOihh/Dkk086smYzEfptAH4fwDEiOrLwvf8GoA8AmPlpAM8D+CSAMwDmAHzOkdUJObFquShBDwQC+kXAio8uLC/sWC71tKFud8BFPlatWoW1a9fq0f++fftw/fXZiYOlUVTQmflXyO2RG49hAI87siKhKFYtF+WfqwjdeI581NMHU7CGnU3RerJcjAMunnnmGXzkIx+xfI6HH34YL7/8Mq5cuYLe3l586UtfwiOPPIJvfvOb+PSnP41kMomNGzfi7//+7x1Zswy4qEFKtVxU4QdQPEJXvrkI+vLDjodeT/1cnBhw8cMf/jDn93fs2IGDBw/aOncuRNBrEKuWizFCzz5HPtSxyWRSbzMgLA+qLctFMI8Ieo1RSmMuY4SuhLyY5eL1evXUxXQ6bWkcHTPj8uXLiMfjaG1tRXt7u1wQaggnInS5s6sMIug1htXGXMyMVCoFIkIgENA/aGZ6bQQCAaTTaSSTSdOCnslkcPLkSQwPX01y6u3txXXXXWfq+ULlcSJCrwfLpRaRbos1RikboswMv98Pj8djOssFKM1HP336NIaHh+Hz+bBmzRp4PB4MDg7i4sWLxZ8sVAXq5y0Reu0hgl5jWG3MpfxzJc7qQmBmeIXRRzfD7OwshoaGQETYuXMn+vv79R4Vp0+fFl+1RhAPvXYRQa8xrEboakqRskyMEXqxPi1WI/SzZ8+CmbF69Wq0tbUBAHp6erBy5UpomiZReg2QyWSQSCQWdU60gjHdVfoAlR8R9BrDaspidoRu9N7N5qKbidBnZ2cxOjoKr9eLDRs2LHps3bp1AIChoSH9AiNUJ8Yq0VI2so0Tr8R2KT8i6DWG1ZTF7AgdgGkf3UqEPjIyAgBYuXLlklv11tZWdHR0IJ1O49IlafFTzdjJcFGI7VI5RNBrjFKrRI0NtsxG6IFAAESEVCpV8PaZmXVBX7VqVc5j1q6d792mjhOqEzv+uaKeBN3OgIt4PI4Pf/jD2L59O7Zu3Yq/+Iu/AABcvHgRe/bsQX9/P7Zu3YqnnnrKsfWKoNcYdi0X43OLRehqwpGx/W4uIpEIYrEYgsEg2tvbcx7T0dEBn8+HaDSKubk5U2sXyo9E6IuxM+AiGAzipZdewtGjR3HkyBHs3bsXBw4cgM/nw9e+9jWcOHECBw4cwLe//W0cP37ckfWKoNcY5bRcgKsXgkKCbozO8/muXq8XXV1dAIDR0VETKxcqgZ1Oi4p6EXS7Ay6ICM3NzQDmP4eqHqSnpwc33jg/drmlpQX9/f0YGhpyZM1SWFRjWLFcNE1DOp3WJxUprKQumhH08fFxAMCKFSsKnmvFihUYGRnB6Ogo1q9fX/S1hfJTjZbLX/3VXzlynmz+/M//vODjTgy4yGQy2LVrF86cOYPHH39cb5mruHDhAg4fPrzk+6Uigl5jWLFcjFOKjJGzlQi9WNfFWCyGubk5+P1+tLa2FjxXZ2cnfD4fIpEI4vG4LdEQ3MFOp0VFvUTogP0BF16vF0eOHMHU1BR++7d/G++++65+cZiZmcGDDz6Ir3/960U/O2YRQa8xrFguufxzoDTLJZ+gq+jcTL8Wr9eL9vZ2jI2NYWJiImevaaGyVKOgF4uk3cLJARfhcBh333039u7di23btiGVSuHBBx/Epz/9aTzwwAOOrVkEvYaw2pgrl38OwHRPdKC45TIxMQFgPvo2Q0dHhwh6FSMe+lXsDrgYGxuD3+9HOBxGLBbDiy++iD/90z8FM+ORRx5Bf38/vvjFLzq6ZtkUrSGsNubKF6Gb7YkOFC4u0jRNF/Tsyeb5UMdNTExIJWEVUo0ReqUwDrh4/fXXLT9/eHgYe/bswQ033ICbbroJ99xzD+6//3689tpr+P73v4+XXnoJO3bswI4dO/D88887smaJ0GsIu2X/CiuWi/LfU6nUksHS0WgU6XQajY2NpgWgsbERwWAQiUQCMzMzMq+0ypC0xavYHXBxww034PDhw0u+f/vtt7sWzIig1xB2G3MpiAhEpFs4hS4Qxra7iURi0Qd9enoawLw/aBYiQkdHB4aHhzExMSGCXgYymQxOnz6N9957D6lUCu3t7di9e3dOm0wsl9pGBL2GcCpCJyJ4vV6k02lkMpmi51MRdTKZXCToU1NTAKwJOgBd0KempvQ+L4I7pNNpvPDCC4vynKempjAwMIA77rhjSZ96EfTaRgS9hnCiSlRhNxedmfUIXXVWNIu6AExNTcl4OxfJZDLYu3cvhoaG0NDQgFtvvRWdnZ04duwYTp48iX//939Ha2urvvHHzI7koTs1YHy5/26UYsvIpmgNYSVlMZPJ6NF3rguA3dTFeDyORCKBQCCAxsZGU+tXhEIhBINBpFIpaQPgIu+88w4GBwfR0NCA3/zN38S1116Lzs5O3H333di5cyeYGS+++KIu4olEApqmIRAILCpEs4q6i4vH4yV7xaFQCOPj48t245yZMT4+bvnCWvSnRkTfBXA/gFFm3pbj8bsB/CsAVRf7L8z8l5ZWIZjCiuVijM5zRTmlFBcZI3Rlt7S1tVmOoogIbW1tGB0dxfT0NJqamiw9XyjO1NSUPlX+ox/96JIeOzfddBOGh4cxMjKCN998E3fddZdukVi9QGfj8/n0ebSZTKaki0Nvby8GBwcxNjZmay21TCgUQm9vr6XnmPmf/gcA3wLwvQLHvMrM91t6ZcEyViyXfP65wm4ueql2iyIcDmN0dBRTU1Nlz0dX0c/s7Cy8Xi96enpM21i1wmuvvYZMJoMtW7bonS6NeDwe3HXXXfjxj3+MkydPYufOnfrdkhMVvKFQCDMzM4jFYiVtfPv9/iV99YXiFBV0Zn6FiNaXYS1CEZyoElVYyUV3Q9DV89R5ykU8HsehQ4cWbRI2NTVhx44dWLNmTVnX4haXL1/GxYsX4ff7ccstt+Q9rr29HZs3b8apU6dw6NAh9PX1AbCXsqhQgh6PxyWTqYw45aHfSkRHiegFItqa7yAiepSIDhLRweV8K1UqpVguxSJ0M4Lu8/ng8Xj0W+hMJoOZmRkQUckf1paWFni9XszOzpqeWWqXVCqF/fv3Y2hoCD6fD2vXrkVraytmZ2fx+uuvY3BwsCzrcJtDhw4BALZt21ZUnHft2gUiwqlTp/QiMScE3amNUcEaTgj62wDWMfN2AN8E8PN8BzLzM8y8m5l3d3d3O/DSy4tSLJd8EboVQVe56AD0giBmRlNTU8mbZx6PR29IFIlESjqHFZgZb775JqLRKFpbW/Hxj38ct956K+6991709/eDmXHgwAFcuXLF9bW4yfj4OAYGBuDz+XDDDTcUPb6trQ3r168HM+P06dMAnIvQgauVp0J5sC3ozBxh5pmFvz8PwE9EXbZXJizBDcvFjIcOLN4YVQJs91ZaPT9XoyOn+eCDDzA0NAS/34/bbrtN34j1eDzYtm0brrnmGmiahrfeesvURa5aee+99wDMl62bFeb+/n4AwJkzZwA4K+gSoZcX24JORKtoIc2BiD68cM5xu+cVFuNUYy6FlQgdWOyjKwG22/KzXBF6JpPBsWPHAAA7d+5cciEiImzfvh2tra2IRqO6KNYayWRSj7Kvv/5608/r7e1Fc3MzotEoZmdnJUKvYYoqAxH9EMCvAWwhokEieoSIHiOixxYOeQjAu0R0FMA3APweL9fkURex0pjLODLOTIRu5sdlFHQlwLUi6GfOnEEsFkM4HM5bmer1erF7924AwKlTp2oyP/7MmTNIpVLo6ekx3SwNmP9d2LJlC1KpFKanp22nLQJSLVopzGS5PFzk8W9hPq1RcBEr0Xkmk4GmafB6vXn9dlX+rzY5i3nhStBjsRhmZ2cXjdcqlYaGBvh8PiQSCdcGXmQyGZw8eRIA8KEPfahgznxXVxf6+vowMDCAEydOYNeuXY6vx03U+1QWihWuueYapNNpRKPRvEGAFdRFQSL08iKVojWClcZcxaJzRSnVotFoFMyM5uZm27nbRKRH6W756IODg0gkEgiHw1i1alXR47dunU/SOnfuHGZmZlxZkxtMT09jdHQUfr8fGzdutPz89vZ2+P1+aJrmyB2Tsm1E0MuLCHqN4KR/riiln4sSXqdyi922XZSnvGnTJlMVrS0tLVi3bt2irI9aQG1obtiwoeTMI7VRrIZ+20E89Moggl4jlFr2X4hSctHn5ub0CN0J3Mx0mZiYwMTEBPx+v6WujmqG5Pnz5/WLYzVjvPhcc801JZ9HZTKNjIyYzn7Kh7Gfi1A+RNBrhFIsl2IReim56IlEAplMxpUI3em99AsXLgAA1q9fbylqDYfD6O7uRjqd1s9RzUxMTGBqagqhUKjkalfVyM3v9yOVStnuoSIRemUQQa8RSrFcikXoVnPR/X4/kskkNE1zLEIPhUL6eZ3MWdY0DRcvXgSAknquq0j3zJkzVd/x79y5cwCAjRs3lryvoSLpjo4OEJH+f1cq4qFXBhH0GsFKlagblgtwNRfe5/MVjf7NYtwYddJHHx0dRSKRQEtLy5JOg2ZYs2YNQqEQotEoxseru6zi/Pn5Rqfr168v+RxKeFUFt1OCbqeFrmAdEfQawUqVqNlNUauCnk6nARS/UFjFDUEfGBgAAPT19ZU0JMHj8egCqQSzGpmentb3Cew0FzMKOhHpF8RS8Xg8CAaDYGapFi0jIug1glnLxUxRkcJKC13AvDdvFeXHOyXomUxGb7SlOgiWgrJqLl68qF/Mqg3l8a9bt85WGqkS9JaWFvT09ICZbTcrE9ul/Iig1whmLZd0Og1m1rNSCmGlhS5wtS+HnWk2uTDmojtxez46Oop0Oo1wOGxr87atrQ0dHR1Ip9OL2u1WE07YLQAWjZ5T/dPt2i6yMVp+RNBrBLOWi9kNUWCx5WJGSNXGmdPDIILBoD6SzokP/6VLlwDAkcEZSijtipsbxONxXL58GUSUc4iFFdT/e2Njo27dDA8P2zqnROjlRwS9BrDSmMuKLWLsC1PMdkkmk0ilUvB6vSAiRzsSGvuq281HZ2Y9mnZiYIUaATYyMlK2vu1mGRwcBDOjp6dHzyEvFdW7pqGhAV1dXfD7/ZienrZVLSu56OVHBL0GsNKYy6x/rjC7Mao+2I2NjSAix8XNKUEfHx9HPB5HU1MTwuGw7XWFQiGsWLECmqZVne1i3Pi1ixL0pqYmeDwe9PT0ALh6t1MKEqGXHxH0GsCNsn+F2QhdCa3KP69WQVc2werVq0vKbsmFsjOUgFYDzKyvp5Q8+2xmZ2cBXG2qpewqO4IuHnr5EUGvAdzIQVdYjdCV8Dot6E5tjCpBN9OIyyy9vb16Kl+12C5jY2P6vE4n7kRUhJ4t6HZ8dLFcyo8Ieg3gRg66wqygq8hZDXd2Orc4GAzarhiNx+OYmpqC1+vFihUrHF1bd3c3mNn2RqFTqE3atWvXOnInYrRcACzy0VX0bhWJ0MuPCHoN4EZjLoUZQdc0Te+BrgTd6UjViY1R1SWwu7vb8UwcJywIJ1E54mrT1i7ZEbrH48HKlSsBAJcvXy7pnOKhlx8R9BrAbGMuZnYlQp+dnQUzo7GxUf+QumE92O2NrgRdbeg5idGCqPTM0WQyiZGRERCRI5k8qVQKyWQSPp9vUSBgV9BlyEX5EUGvAcxG6KlUCswMv99vKpoHzAm6cUNUfeATiYTjPTrsROiapumC7qR/rmhubkZrayvS6TSuXLni+PmtcOnSJTAzuru7bacrAos3RI32jV1BlzF05UcEvQYwG6Fbjc6N5ywk6GpDtLm5GT6fb9HoOiex0wJgcnISyWQSTU1NjnWCzEZFw5VOX1Sv75TdYiwqMqIEfWxsrKSftRL0WpzPWquIoNcAZrNcrPrnxnOaidBbWlr0vujG13MK44xRqxujRrvFqXTFbIyCXskOgk775ypCVxuiimAwiPb2dmQymZLuSqTjYvkRQa8BzGa5lCLoxjz0XB86Zl4UoQNXJ9s4neliZ2PUjXTFbNrb2xEKhRCLxTA1NeXa6xRiZmYGk5OT8Pv9egRtl+wNUSN2bBev14tQKARmFh+9TIig1wBmI/RSLBciKhilJxIJpFIp+P1+XcjdEnSgNB89kUhgYmICHo/H0XTFbIio4tkuKjrv6elxLJPHLUEHrkb9YruUBxH0GsDNCB242j0xl6Bn2y3G87uR6VKKoCux6erqcrwTZDbKdqm0oDtltwBLq0SNKEEvdXC0sl1KzWUXrFFU0Inou0Q0SkTv5nmciOgbRHSGiN4hohudX+byxUpjrlIidOBq5J+r53e23QK4G6GXkrroZnZLNitWrIDP58Pk5GTZbQRj4zG73RWNFIrQ29vbEQgEMDs7W5IoqwhdLJfyYCZC/wcA9xV4/BMANi98PQrg7+wvS1AY7ZZim32lRuiFLBdjhK4wpi46TWNjI7xeL2KxmH6BKgQzu5p/no2xCrXcVaMTExOIxWKONR5T5NsUBeZtJvV+S7Fd1EXCTtdGwTxFBZ2ZXwEwUeCQTwH4Hs9zAECYiNz/ZC0TzNotmqYhnU6DiEqO0HMJeq4IPRAIgIj0vHcnISL9tcxE6VNTU4jH42hoaNCje7dRF45yC7oq91+zZo2jmTz50hYVdmwXKS4qL0546GsAGLv/Dy58bwlE9CgRHSSig2NjYw68dP1jJQddFRVZ/bDnE/R0Oo1YLAaPx7MoevN4PPD7/YvG3TmJFR/daLe4la6YjbJ2Ll++XNaqUTf8c2BpH5ds7GyMqnOKh14enBD0XJ+inGEbMz/DzLuZebeaLi4Uxm3/HMgv6KrkX/XINlItPno5/XNFU1OTXjU6Pj5eltdMp9P6HYHTgq7EVm1gZqME/cqVK5YvYCpClyyX8uCEoA8CMO7Q9AKojg5GdYDZCL1U/9x47uwPa3YPdCPVkLqYTCZx5coVEJFjOdlmKbftMjIygkwmg87OzrzWSCkY01Lz/e7YKTASQS8vTgj6swD+YCHb5RYA08xcHT1G6wCzEboSVicFPbsHuhE3BV3dEczOzubMvFGMjo6CmdHV1VXS+7ZDuQXdLbvF+DMuZFmpjdHR0VFL5xdBLy9m0hZ/CODXALYQ0SARPUJEjxHRYwuHPA/gHIAzAP4fAP+ra6tdhliN0Etp1uTxeEBE0DRt0eSiSkXoHo/H1MZoJewWhcp5j0QiZfGH3RL0Qj9jI6UKuhQWlZeiVRjM/HCRxxnA446tSFiEm31cFKpaNJ1OI5PJwOPxLCr5LxShu9VJr6WlBZFIBNFoFO3t7UseNw6bqISgq37hQ0NDGBkZwaZNm1x7rVgshvHxcXi9Xsffa64splwoS8uqoCtffm5uTp+LK7iHVIpWOW5XiSpUhaWyOObm5pDJZBAKhXJutAaDQX1YtBuNl4r56JFIBLFYDKFQyNGcbCuUy3YZHBwEM6Onp6ekTe9CFLpoG2lvb4fX68X09LSli7j0cykvIuhVjhnLxZg+WKqgZ/voxSI3Y+qimxuj+VrpKrtl5cqVFYv6lKC7nb5oHDfnNGYjdK/XC5WZJrZL9SKCXuWY2RQtZbBFNtkReq4K0WzcznTxeDyYm5vLuTGqouJyVIfmo6GhAeFwuOT2smZg5qoQdKB0H136uZQPEfQqRvVxIaKCQm03OgeWCrqKjAtVX7q9MdrS0gJmXhKlp1IpqMK0cqcrZqMuKG416xofH9fL/XPtJdjF7KYoYH9jVCwX9xFBr2KMdkshW8EJQTdaLsxsKkJXE2ncEHTg6sVkenp60fdHRkb0dEUnRrDZQW1SltqNsBjG6NwNa6nUCN3Kvon0cykfIuhVTDmKihTGCD0ejyOVSiEYDBYUTDcjdABoa2sDsNRHrwa7RdHZ2Qm/349oNOqKYClBdzpdUWF2U1Qd09DQgHg8bqkbpuSilw8R9CqmnIJujNBVRFys2MTt1EUl6NPT03pEWO7uisXweDx6lO50tksqlcLIyAiIyBVBTyQSSCaTBatEjRBRSRuj6mIhEbr7iKBXMeUUdI/Ho+efGwW9EMFgEB6PB8lk0pUsj1AohEAggGQyqV80Jicn9e6KSvArjVvpi0NDQ9A0Dd3d3bq95SRmq0SNlNKoq9SxgoJ1RNCrGLOCriwPu36ysl2UoBdrR0tErtouRLTER1eiuXr16qopUlER+tjYmKMXNjezWwBrG6IKFaFb6ZYqgl4+RNCrGJVxYiYHnYhs9zPxer2LskrM+KoqcnTbdlFrqib/XBEKhfTmVVYzQAqhyv3dEnQrG6IKtTFq5eKlzi+Wi/uIoFcxZiL0RCJhOwdd4fP5kEwmTW2IKpSgu5WSZvTR4/F4WYZBl4LTtsvk5CSmp6cRDAZde69WNkQVoVAIbW1tyGQymJgoNPfmKk1NTSCios3WBPuIoFcxZgTdTlOubHw+H+bm5qBpmmlf1e0I3Xi7ruZpqrme1YRxY9SJVggXLlwAAKxbt872hTofpVgugPV8dGOzNSkuchcR9CrGbIQOOCvozGw6anNb0P1+P5qamqBpmi5y1WS3KDo6OvRhyk5YC+fPnwcArF+/3va58jE1NQUAlnvhlFJgZGWsoFA6IuhViqoSBQqX/Tst6LFYDJqmmZ7PaWzSZWy96yStra3QNE33lFevXu3K69jB4/E4VjU6OzuL0dFReL1e1/xz4OpGs9VsoVIEXVIXy4MIepVitkrUSUH3er265WL2Ntzj8SAYDIKZXd0YnZmZQTweR3t7e97Zl5XGqapRdSeydu1ax7srGilV0Lu6uuDxeDA1NWU6u0kEvTyIoFcpVlMWnZjYo6Jsn89nyaMuR6ZLJBJBIpHAmjU5549XBcb0RTubf+WwW+LxOOLxOAKBQN5Zovnwer3o6uoCM5tOXxTLpTyIoFcpVtvmOhGhRyIReDweNDY2WsqnVoLgVqZLY2MjZmZmkMlk0NXV5cprOEEwGERnZyc0TbNUeGMkkUhgaGgIRIR169Y5vMKrGGsNSsnnt2q7SC56eRBBr1LMCHoqlYKmafD7/UUjeTNEIhEQERobGy1FmG4LuprWEwgEXO077gR22wBcvHhRH2ZhNXK2Qql2i0IEvToRQa9Syp3hAsxnPXg8HjQ1NSGVSpl+nlHQ3ZheNDg4iEAggNbW1iWdF6sNtWGryvatUg67BSg9w0WhBP3y5cumfubioZcHEfQqRUXIhbxs5Vk7IeiapiEajeqWi5UIPRAIwOv1IpVKOV44wswYGhpCIBBAW1sbJicnHT2/04TDYTQ3NyORSFgeepFOpzEwMAAA2LBhgxvL01EXxlIFva2tDcFgELFYzFRuuXjo5UEEvUqxIuhONG6KRqN6dovP57MkzMqmAZxvkTo5OYlYLIa2tjY0NzdjdnZW3zeoRohITzVUvVjMMjAwgFQqhe7ubkvVm6Vgtl9PPqx2XlSzaROJhGub54IIetVSbkFXt+BqKo4aa2cWt3x0VR3a29urR5NqrdWKanVr1XY5ffo0AOCaa65xZV1G7FouwGLbpRhEVDM/v1rGlKAT0X1E9D4RnSGiP8vx+N1ENE1ERxa+/rvzS10+MLMpD91JQVcRW3t7u95G14oYuSHoxnmaa9as0S82ZnuIVIpwOIympibE43HTtksikcDAwACIqCyCbndTFFjcqMsMIujuU1TQicgL4NsAPgHgegAPE9H1OQ59lZl3LHz9pcPrXFaYKSpKp9NIpVLweDy2c9CNPdDb2tr0YpZSN0adYnJyEjMzMwiFQuju7kZHRweA6hd0o+2iqluLcf78eWQyGfT09LheOKVy0H0+n26VlYJR0M1c/NUFWQTdPcxE6B8GcIaZzzFzEsCPAHzK3WUtb6zaLXb7gsdiMSQSCQQCATQ2NpYk6KFQCB6PB/F43LGN0Q8++ADAfMWkx+NBa2ur3m+m2gcOK9tlcHDQlNidOnUKALB582ZX1wVAv2vo7Oy09bvT2NiIlpYWpFIpU5vVStCrfWO7ljEj6GsAGHd3Bhe+l82tRHSUiF4goq25TkREjxLRQSI6aKVB/nKj3P65+oCFw2EQkS7oVjYfVXYM4MzGqKZput3S19cHYD7yrZUoXbUoiMfjGB8fL3js9PQ0Ll26BK/Xi02bNrm+NrUeJ4q0VJRupt2BWC7uY0bQc13Cs3fL3gawjpm3A/gmgJ/nOhEzP8PMu5l5t9ohF5ZS6Q1RZeFYidAB6FaBEy1Sx8bGEI/H0dTUpIs4AP3vxUSy0ljJdnn//fcBAJs2bXKkhUMxVITuhKBb6QOvBF0idPcwI+iDAIwt33oBLGonx8wRZp5Z+PvzAPxEVL012lVOOTdEmVmPdpWgGy0XK5kuKkJ3QtBVPnZfX98iW0AJ+uTkpCtFTE5iFPR8Fa6apumCft1115VlXU5G6KqQykwfeCXo09PTrnXmXO6YEfS3AGwmog1EFADwewCeNR5ARKto4VNHRB9eOG91h1BVjJkIXXnIdgXd6J+rCNvr9cLr9ULTNEul9sYI3Y7YZjIZfTNR2S2KxsZGvZK12m/dw+EwWltbkUgk8kawAwMDmJ2dRUtLS9n6vBs9dLu0t7cjGAxidna2aNGQz+dDS0sLNE3TRwoKzlJU0Jk5DeCPAPxPACcA/JiZ3yOix4josYXDHgLwLhEdBfANAL/H1R4+VTHFBD2VSiGVSsHr9dquEs32zxWlbIwGAgG934qd4pGRkRGkUimEw+GcaXUqsrRaiVluiEiv+FQtcbM5fvw4AGDr1q1lGXqdTqcxNTUFItLvyOxARJZsF8l0cRdTeejM/DwzX8vMm5j5rxa+9zQzP73w928x81Zm3s7MtzDz624uup4xk4OuNh0bGxtti0C23aIoRdDVmoxrLAWV3ZIdnSuUoNfCxvq6detARBgeHl5ykZuensbFixfh9XqxZcuWsqxnfHwczIz29nbHxviJj149SKVolZFOp8HM8Hq9eScVKbG0243P6J9n+6mlZLoA9nt2JBIJfeJPPkEPh8Pw+/2Ym5ur+hmVoVAIq1evBjPj3Llzix47fvw4mBmbNm1ytbOiESf9c4USdFXVWwgRdHcRQa8yVERcaFKN8s/tFIUA8xFiKpVCY2PjEkFR2RZWBd3YJrUU1+2DDz6ApmlYtWpV3vdHRDUVpavKz7Nnz+qbgclkEidOnAAAbNu2rWxrcdI/V3R1dSEYDCIajRbthmml/4tgHRH0KsOMoBstFzuoaC3XhzsQCICIkEqlLG2MqiZMqVTKso9ujGI3btxY8FgrfUQqzYoVK9DS0oJYLKZHsSdPnkQymcSqVav091IO1P+Xk6/p8XgWFVIVopR5pIJ5RNCrjGKCnkqlkEwmHdkQLSToRFRSlE5EJQ8zGB8fRyQSQTAYLJrx0dnZCZ/Ph2g0WvW2i7E/y+nTp6FpGo4dOwYA2L59e9nWwcy6neX0oG2zOffKLotGo1Vf7VuLiKBXGcUEXX0IGhoabG2IxuNxRCIReL3evNkO6oJhdhCwolRBP3PmDID5XuDFJjB5PJ6aitLXr18Pv9+PK1eu4NChQ4hGo2hra3N1zFw20WhU743jRIaLETXrdWhoqOAdXa393GoNEfQqgpmLCrqa+GLXblHec0dHR17xVIJeqo8+MzNjuoAkFovh4sWLICLT5e8rV64EYH5qTiXx+/245pprwMzYv38/AGDnzp15N77dwBidO50i2dLSgnA4jFQqVVSoxXZxDxH0KiKTyegZLvlEVgm63QEI6sNUyEtVlksikbAkmGqSfCaTMR2lnz17FsyMNWvWmO422NHRoRe1VPtoOmC+8VYkEsHY2Bj8fn9ZGnEZUYLuVgGTsl1U2mk+RNDdQwS9iigWnWuahrm5ORCRrRariURCnx9aqKeOz+fTK0at5qNbacSUTqd1u8WKyBmLWsykzFWaQCCwaEPbicHeVlCCruwRpzEWURUKANSdlQi684igVxFKNPMVfMzOzkLTNDQ0NNgqChkbGwMzo6Ojo+h5VGsBqxkrxr4dxaL7s2fPIplMorOz03J+tBKn0dFRyxedcnPq1Cn4fD59/6OcgqZpml7441aEvmrVKjQ0NGB6erpgN0wVRJjtoy6YRwS9ilBedb6Oe8q+UMU7paI+2CpSKkSpgytCoRCCwSDS6XTBSe+ZTEZvTtXf32/Z221oaEBHRwcymYypSsVKkU6n8dZbb8Hr9eL222+Hx+PB0aNHyyZoIyMjSCaT+hBrN/B4PPom7/nz5/MeFwqF0NHRgXQ6bartrmAeEfQqQmWT5EtHVMJo5wM5MzOD6elp+Hw+U7nIKkJPJBKWxMfYK6RQtHb27FnE43GEw+GSI0fl3Q4MDFRtxHf48GHMzs6iq6sLe/bsQUNDAyYnJ5dUj7rF2bNnAcD1fuuqfqDY+1LCX8xvF6whgl4lZDIZpNPpRQMmjKTTaczOzoKIbAm68lFXrVplysNV+e7MbNl2Mba6zZXKlkwm9eZU27ZtKznzoqurSx8mUY0R3/T0NI4cOQIAuP322+H3+7Fz504AwLFjx2w1MjOL2qNwW9DXrFmDYDCIiYmJglW8StDzNS0TSkMEvUowRue5hE150S0tLSX750ZbwsrGmIrSS7FdVLvUXFH6iRMnkEwm0d3dbcvXJaJFEV81pTAyM1599VVkMhls2bIFq1atAjD//9/T04NUKoW33nrL1TXPzs5ieHgYPp/P9bx3r9eLa6+9FsB8NWw+1DoGBgYcG1koiKBXDcXsFpUtojYbS+HSpUtIpVJobW21lPZo7KBoVXhUFeqVK1cWPXdqakqfo7l9+3bbedFqQ06JV7Xw3nvvYXBwEMFgELfccov+fSLCrl274Pf7MTw8rFsibnDu3DkwM9atW1eWiUhqUMfp06fzinVzczO6u7uRTqf1u0bBPiLoVUIhQVf53ESUsz+4GTRN0/3K9evXW3qu3+9HIBCApmmWo3RV6h2LxfShBpqm4eDBg3qnQeOIuVLxeDy6nXD27NmqiPomJydx4MABAMBdd921pAFaY2Mjdu3aBQA4cuSIa3NS1aZzsf44TtHZ2Ynu7m4kk8mCFyqxXZxHBL0K0DRNz3DJJehTU1PQNA1NTU0Fm3YVYmRkRJ/RaXWeqzHvvVDGSi6Mpd5qTNnJkycxMTGBhoYG3HDDDZbOV4iVK1eira0NiUSiYJZFOUgmk9i7dy/S6TQ2b96cV0z7+vqwadMmaJqG1157zXE/PRqN4vTp0/B4PLj++usdPXchtm6dnxN/+PDhvHd16gKs2ggL9hFBrwJisRiYGcFgcEkpODMvKtMvhXQ6rUdK69evL8neaGpqAhEhFotZjn67u7v1/uXnzp3Du+++CwDYvXt3yReoXBARrr32WhARBgYGKjYVR9M07Nu3D9PT0+jo6MCdd95Z8PgdO3ags7MTsVgMr7zyiuVWC4U4cuQINE3Dtdde61q6Yi42b96MlpYWTE1N5c142bhxI5qbmzE+Pl4ThWG1gAh6FaC6Beaq/pydncXc3Bx8Pl/Jgn7u3DkkEgm0tbXpm3JW8Xq9updutcze4/Fg5cqViMViePnll8HM6O/vd6XARTW8YmYcP3687MVGzIyXX34ZH3zwAYLBID7+8Y8XvWh5vV7cdtttugC++uqrjoi6pml6do2ydsqF1+vFjh07AACHDh3KmU7q8Xj0XvDvvPNOOZdXt4igVxhN0/Tb7FwNt1Q1YVdXV0mNnKampvSmV1u2bLG1+aj8+5mZGctC2dzcjLNnzyKRSCAUCum35G6wceNGtLS0YG5uDseOHStbbnomk8H+/fv1itBPfOITpvc8QqEQ7rzzTjQ2NmJ8fBz79++33V72yJEjiEQi6OjoKGtXR8V1112HlpYWTExM5BVs1T74+PHjlrt6CksRQa8wKnMkFAotyQuPRqOmeq7kI5lM4tixY2Bm9PX1obW11dZa/X6/fts+OTlp2vecmZnB/v374fP50NzcjNWrV7tqh3g8Htxwww0IBAKYmJjA8ePHXRf1eDyOF154AadOnYLf78d9991n+W6oqakJe/bsQUtLC6anp/HLX/6y5IlM6m4IAPbs2VOWAdTZeL1e3HHHHQCAt956S98UN9LV1YW+vj4kEgn8+te/LvcS6w4R9ArCzLp9kW23aJqmDwtYuXKlZa85lUrhyJEjSCQSCIfDjhWUtLW1wePxIBaLmeqkODw8jH379mF2dhbd3d3Ys2cPvF4vBgYGSp47aoaGhgZs374dPp8PIyMjOHbsmGuZL4ODg/jJT36CwcFBhEIh/MZv/IY+wccqTU1N+OhHP4oVK1YgHo9j//79eOeddyxNjWJm7Nu3D7FYDOvWrSvbAOpc9PX14ZprrkEmk8HevXtzWkl79uwBALzxxhsV2/eoF0TQK0g0GkU6nYbf718k6MyMixcvIh6PIxQKmeq5YiQej+Pw4cOIRCJoaGjAtm3bHOu77fP59NzyyclJvXtgNolEAocOHcKrr76KRCKBVatW4e6770Zvby+6u7uhaRrOnj3r6rDgtrY27Ny5E36/H2NjY3jzzTcdFYxIJIJ9+/bhueeew8zMDFauXImHHnrI9ni3YDCIO++8U8/nPnnyJPbu3avPWy3GG2+8gaNHj8Ln8+HjH/94RaJzI3fccQfC4TAmJibwb//2b0vsut7eXmzbtg3pdBrPPvtsVaSc1ipUqXSh3bt388GDByvy2tVAKpXCyMgINE1Dd3e37p8zM4aGhjA6OgqPx4PNmzebbpXLzLh8+TLef/99pFIpNDQ0YNeuXXqlp5NMTk7qt9AdHR1obm4GEWF2dhbnzp3DmTNnkEqlQETYunXrosZb6oJlHFi8evVqRzNejMzOzuLdd9/V7whWrlyJdevWlWRBMTNGRkZw/Phxfeiz1+vFjTfeiB07djjeEldNOFJ3cs3NzdiwYQPWrl27JGtFVaW++uqrAIAHHngA/f39jq6nVCKRCH72s58hFouhs7MT99xzz6IiuZmZGXz3u99FNBrFtddei9/6rd9y7feh1iGiQ8y8O+djZgSdiO4D8BQAL4D/wcxPZj1OC49/EsAcgM8y89uFzrmcBT2ZTGJ0dBSZTAYNDQ3o7u4GEWFubg6Dg4OYmZkBEWHjxo2mNtXU+YaGhnTR6uzsxNatW12rDFR20ejoKGZmZnQLZnp6WhfuFStWYOfOnTnfg0rHvHTpEjRNg8fjQWdnJ9rb2/UUSSfJZDK4cOHCoii3paUF3d3daGtrQ2tra94eOlNTU5iYmMDw8DAGBgb0rCQiwubNm7F7927b+xOF0DQNFy5cwMmTJxfVAXR0dGDlypVob29HJBLBm2++iaGhIRAR7rnnHtx0002urakUpqam8MILL+i/I9dffz22bt2qZ2+NjY3he9/7HuLxODo6OvCxj30MmzZtKutUp1rAlqATkRfAKQD3ABgE8BaAh5n5uOGYTwL4z5gX9JsBPMXMNxc6b6mCPjw8rIuWWrv603g7mv2+8r1PZl5yG5t9rHqcmYtuBOZ6XNM0ZDIZaJqGRCKh+4hEpE/2mZub03f5vV4vVqxYgcbGxkXvMZPJ6E284vG4/mXMhvD5fFi9enXBvuLZ/2/5jkmn0/rrpdNpJJNJJBIJxONxJBIJxGIxzM7OIpVK6f83Xq8X3d3dWLt2Ldrb2+H1euHxeHSBJqJFYp1IJHDlypVFQkVECAaDCAaD8Pv98Pl88Hg8+pc6hzHiN2I8f/ZjyWQSIyMjGBsbQzKZ1H82mUwGXq9X/31QxV7qZ2J8vcbGRqxduxabNm3S70yyL0AmPlcFH8+FpmkYGxvDwMAALl26hLm5OczMzGBychKJREJPLf3IRz6CdevW6RW+fr8ffr9/0f+h8Svfmqz+2wzJZBJvv/32ogpSVezW1NSEVCqFgwcPIhKJ6I3o1O9SU1MTmpqaEAgE4PF49N8Lr9ebcy1W11tOayoQCFiu2FYUEnQzXZ4+DOAMM59bONmPAHwKwHHDMZ8C8D2e/y0+QERhIuphZsebanz5y18uW8vRSmAUPqtkf0DLhfpA2X19JaTlQtM0/UJUSIDVSECfz6dfYI4ePVq2deYjnU7rFySfz4fW1lZ0dXXh3LlzVf8ZSSaTmJmZwdzcXM6AKhqN6ntM9Zj90tLSgn/+5392/LxmBH0NgIuGfw9iPgovdswaAIsEnYgeBfAoML/7XQrqA2UGt6+4pZ7f+Lzs6M5sFKEENDtadWqtxnOqv2dHdir6zkZFuWbuBHKhBLbYOcyeN9d7N0b72XcQxu8rTzxb9CtZqq6i7mAwiKamJrS1taGpqQmapul3U+qO0Hh3qNad/VUMN96rz+fT70CTySSSyeSitTc2NqK7u1u/AzXeLRp/P0pdX6VbDbhlhZpRxlxKkP2/YeYYMPMzAJ4B5i0XE6+9hKeeeqqUpwmCINQ9Zu6PBwGsNfy7F0B2v0szxwiCIAguYkbQ3wKwmYg2EFEAwO8BeDbrmGcB/AHNcwuAaTf8c0EQBCE/RS0XZk4T0R8B+J+YT1v8LjO/R0SPLTz+NIDnMZ/hcgbzaYufc2/JgiAIQi5M7S4y8/OYF23j9542/J0BPO7s0gRBEAQrSMa+IAhCnSCCLgiCUCeIoAuCINQJIuiCIAh1QsW6LRLRGIAPSnx6F4ArDi6nFpD3vDyQ97w8sPOe1zFzzok3FRN0OxDRwXzNaeoVec/LA3nPywO33rNYLoIgCHWCCLogCEKdUKuC/kylF1AB5D0vD+Q9Lw9cec816aELgiAIS6nVCF0QBEHIQgRdEAShTqg5QSei+4jofSI6Q0R/Vun1uA0RfZeIRono3UqvpVwQ0Voi2k9EJ4joPSJ6otJrchsiChHRm0R0dOE9f6nSayoHROQlosNE9Fyl11IOiOgCER0joiNEZH2ocrHz15KHbmZgdb1BRHcCmMH8zNZtlV5POSCiHgA9zPw2EbUAOATgt+r850wAmph5hoj8AH4F4AlmPlDhpbkKEX0RwG4Arcx8f6XX4zZEdAHAbmZ2pZCq1iJ0fWA1MycBqIHVdQszvwJgotLrKCfMPMzMby/8PQrgBOZn1NYtPM/Mwj/9C1+1E22VABH1AvgPAP5HpddSL9SaoOcbRi3UKUS0HsBOAG9UeCmus2A/HAEwCuCXzFzv7/nrAP53AFqF11FOGMC/EdEhInrU6ZPXmqCbGkYt1AdE1AzgpwC+wMyRSq/HbZg5w8w7MD+T98NEVLcWGxHdD2CUmQ9Vei1l5jZmvhHAJwA8vmCpOkatCboMo14mLPjIPwXwj8z8L5VeTzlh5ikALwO4r7IrcZXbAPzmgqf8IwAfJaIfVHZJ7sPMlxb+HAXwM8zbyI5Ra4JuZmC1UOMsbBB+B8AJZv6bSq+nHBBRNxGFF/7eAOBjAE5WdFEuwsz/lZl7mXk95j/HLzHzZyq8LFchoqaFTX4QUROAewE4mr1WU4LOzGkAamD1CQA/Zub3KrsqdyGiHwL4NYAtRDRIRI9Uek1l4DYAv4/5qO3IwtcnK70ol+kBsJ+I3sF84PJLZl4WqXzLiJUAfkVERwG8CeAXzLzXyReoqbRFQRAEIT81FaELgiAI+RFBFwRBqBNE0AVBEOoEEXRBEIQ6QQRdEAShThBBFwQLENGOZZBCKdQoIuiCYI0dAETQhapEBF2oW4jo5wtNkN4jokcXml/9AxG9u9CT+n9bOO6Pieg4Eb1DRD9a+F7TQi/6txb6dX9qoTr5LwH8x4Vip/9IRHcZip8Oq0pAQagEUlgk1C1E1MHMEwul9G8B+E8AnmTmexYeDzPzFBFdArCBmROG7/2fAI4z8w8WSvLfxHzXx9/BfD/rP1o4x/+3cM7XFpqJxRcqmgWh7EiELtQzf7xQZn0A803dAgA2EtE3ieg+AKqD4zsA/pGIPgNAifG9AP5soZ3tywBCAPpyvMZrAP6GiP4YQFjEXKgkIuhCXUJEd2O+wdWtzLwdwGEAQQDbMS/Qj+PqYIX/AODbAHYBOEREPsy3an6QmXcsfPUx84ns12HmJwH8IYAGAAeI6Do335cgFEIEXahX2gBMMvPcgsjeAqALgIeZfwrg/wBwIxF5AKxl5v2YH7YQBtCM+QZw/3mh8yOIaOfCeaMAdJ+ciDYx8zFm/r8AHAQggi5UDPHQhbqEiIIAfo75iVbvA+jGfP/p/4Srgcx/BfAigP2YvwAQgB8w85MLvvvXAXxk4fsXmPl+IurAvNj7AXwFwO0A9gDIADgO4LPMnCjDWxSEJYigC4Ig1AliuQiCINQJIuiCIAh1ggi6IAhCnSCCLgiCUCeIoAuCINQJIuiCIAh1ggi6IAhCnfD/A+4Gm+GQ0zfdAAAAAElFTkSuQmCC\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "filenames": { + "image/png": "/home/john/gh_synced/books/sed2/edtc-code/code_book/_build/jupyter_execute/ch6_53_0.png" + }, + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "# Turn the policy array into a function\n", + "sigma = lambda x: interp(os.grid, sigma_star, x)\n", + "\n", + "@vectorize\n", + "def phi(z, b):\n", + " \" Lognormal density for N(0, b^2) \"\n", + " if z <= 0:\n", + " return 0\n", + " else:\n", + " c1 = k0 / (z * b)\n", + " c2 = np.exp(- np.log(z)**2 / (2 * b**2))\n", + " return c1 * c2\n", + "\n", + "def p(x, y):\n", + " return phi(y - os.R * sigma(x), os.b)\n", + "\n", + "def draws_from_marginal(t_date, init=0, n=10_000):\n", + " draws = np.empty(n)\n", + " for i in range(n):\n", + " a = init\n", + " for t in range(t_date):\n", + " xi = np.exp(os.b * np.random.randn())\n", + " a = os.R * sigma(a) + xi\n", + " draws[i] = a\n", + " return draws\n", + "\n", + "dates = 1, 2, 4, 8, 16, 32\n", + "greys = [str(g) for g in np.linspace(0.2, 0.8, len(dates))]\n", + "greys.reverse()\n", + "grid = np.linspace(0, 5, 200)\n", + "\n", + "fig, ax = plt.subplots()\n", + "\n", + "for t, g in zip(dates, greys):\n", + " a_obs = draws_from_marginal(t)\n", + " f = lae_factory(p, a_obs)\n", + " ax.plot(grid, \n", + " [f(y) for y in grid], \n", + " color=g, \n", + " lw=2, \n", + " alpha=0.6,\n", + " label=f'$t={t}$')\n", + "\n", + "ax.set_xlabel('assets')\n", + "ax.legend()\n", + "\n", + "plt.show()\n" + ] + }, + { + "cell_type": "markdown", + "id": "0dc5a1cd", + "metadata": {}, + "source": [ + "Finally we turn to policy function iteration, in order to solve exercise 6.19.\n", + "\n", + "We need to compute the value of any feasible policy $\\sigma$.\n", + "\n", + "To do so we will iterate with the policy value operator $T_\\sigma$." + ] + }, + { + "cell_type": "code", + "execution_count": 29, + "id": "9f4620f8", + "metadata": {}, + "outputs": [], + "source": [ + "def T_sigma(v, sigma, os):\n", + " \"\"\"\n", + " Here os is an instance of OptimalSaving and v and sigma\n", + " are both arrays defined on the grid.\n", + " \"\"\"\n", + " v_new = np.empty_like(v)\n", + "\n", + "\n", + " sigma_interp = interp1d(os.grid, \n", + " sigma, \n", + " fill_value=(sigma[0], sigma[-1]),\n", + " bounds_error=False)\n", + "\n", + " for i in range(len(os.grid)):\n", + " a = os.grid[i]\n", + " v_new[i] = os.state_action_value(sigma_interp(a), a, v)\n", + "\n", + " return v_new" + ] + }, + { + "cell_type": "markdown", + "id": "5bd23bcd", + "metadata": {}, + "source": [ + "To compute the policy value we iterate until convergence, starting\n", + "from some guess of $v_\\sigma$ represented by `v_guess`." + ] + }, + { + "cell_type": "code", + "execution_count": 30, + "id": "b139f105", + "metadata": {}, + "outputs": [], + "source": [ + "def compute_policy_value(os,\n", + " sigma,\n", + " v_guess=None,\n", + " tol=1e-3,\n", + " max_iter=1000):\n", + "\n", + " if v_guess is None:\n", + " v_guess = U(os.grid) \n", + " v = v_guess\n", + " i = 0\n", + " error = tol + 1\n", + "\n", + " while i < max_iter and error > tol:\n", + " v_new = T_sigma(v, sigma, os)\n", + " error = np.max(np.abs(v - v_new))\n", + " i += 1\n", + " v = v_new\n", + "\n", + " return v_new" + ] + }, + { + "cell_type": "markdown", + "id": "bd583b2e", + "metadata": {}, + "source": [ + "We will use existing code to get a greedy policy from a guess $v$ of the value\n", + "function." + ] + }, + { + "cell_type": "code", + "execution_count": 31, + "id": "b62bddf4", + "metadata": {}, + "outputs": [], + "source": [ + "def get_greedy(v, os):\n", + " sigma, _ = T(v, os)\n", + " return sigma" + ] + }, + { + "cell_type": "code", + "execution_count": 32, + "id": "f78bdfe0", + "metadata": {}, + "outputs": [], + "source": [ + "def policy_iteration(os, tol=1e-3, max_iter=1e5, verbose=True):\n", + "\n", + " sigma = np.zeros_like(os.grid) # Initial condition is consume everything\n", + " v_guess = U(os.grid) # Starting guess for value function\n", + " i = 1\n", + "\n", + " while i < max_iter:\n", + " v_sigma = compute_policy_value(os, sigma, v_guess=v_guess)\n", + " new_sigma = get_greedy(v_sigma, os)\n", + " if np.abs(np.max(new_sigma - sigma)) < tol:\n", + " break\n", + " else:\n", + " sigma = new_sigma\n", + " v_guess = v_sigma # Use last computed value to start iteration\n", + " i += 1\n", + "\n", + " if i == max_iter:\n", + " print(\"Failed to converge!\")\n", + "\n", + " if verbose and i < max_iter:\n", + " print(f\"\\nConverged in {i} iterations.\")\n", + "\n", + " return sigma\n" + ] + }, + { + "cell_type": "markdown", + "id": "cad242ae", + "metadata": {}, + "source": [ + "Running the following code produces essentially the same figure we obtained\n", + "for the optimal policy when using value function iteration, just as we hoped." + ] + }, + { + "cell_type": "code", + "execution_count": 33, + "id": "c3deb5b7", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "\n", + "Converged in 7 iterations.\n" + ] + }, + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "filenames": { + "image/png": "/home/john/gh_synced/books/sed2/edtc-code/code_book/_build/jupyter_execute/ch6_62_1.png" + }, + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "os = OptimalSaving(U, grid_max=4)\n", + "sigma_star = policy_iteration(os)\n", + "\n", + "fig, ax = plt.subplots()\n", + "\n", + "ax.plot(os.grid, sigma_star, \n", + " label='optimal policy', lw=2, alpha=0.6)\n", + "ax.plot(os.grid, os.R * sigma_star + 1.01, '-.', \n", + " label='next period assets', lw=2, alpha=0.6)\n", + "ax.plot(os.grid, os.grid, 'k--', \n", + " label='45 degrees', lw=1, alpha=0.6)\n", + "\n", + "ax.legend()\n", + "plt.show()\n" + ] + }, + { + "cell_type": "markdown", + "id": "1875b9a0", + "metadata": {}, + "source": [ + "## Stochastic Speculative Price\n", + "\n", + "\n", + "Finally, to conclude code for this chapter, we turn to the commodity pricing\n", + "model.\n", + "\n", + "The next code block computes figure 6.16 and hence solves exercise 6.26." + ] + }, + { + "cell_type": "code", + "execution_count": 34, + "id": "d4657659", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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MmTO2DksIIfokCWAAKaXw9vbG39+fpKQkPvroI+69916amppsHZoQQvyAJIAB5urqSmdnJ08//TQLFy5kw4YNrFy5UvoLEkIMO5IABphSiquvvprMzEzefPNNVqxYQXh4OK+++ipGo9HW4QkhhIUkgEEQGxtLbGwsnZ2dvPLKK0RHR/PSSy+xZMkSGT9ACDFsWJUAlFLzlVLHlVJ5Sqmn+1g+Tin1jVKqVSn1y17zo5RS25VSx5RSR5RSP++17HmlVKlS6qD5Z8HAnNLwcNNNN+Hr64uTkxP33nsvK1asIDMzk+uvv57c3FxbhyeEEBdOAEopR+CvwA3ABOAupdSEs1arA34GvHzW/A7g37TW44HLgEfP2vaPWusU88/miz2J4WrHjh3s2LEDV1dXXnnlFZ555hkKCwt56aWXOHz4sK3DE0KMctY8AaQDeVrrk1rrNmA1sLj3ClrrKq11BtB+1vxyrfV+82cTcAyIGJDI7cD06dPZv38/RqMRJycnnn32Wf77v/+b0NBQ7rvvPrZu3WrrEIUQo5g1CSACKO41XcJF3MSVUrFAKvBtr9krlVKHlFJvKaUM59juAaVUplIqs7q6ur+HtSlvb29mzpzJtm3bgO4K4gULFjBr1ixKSkpYtmwZ7777LlprG0cqhBiNrEkAqo95/bpjKaW8gP8FHtdaN5pn/x1IAFKAcuAPfW2rtX5Na52mtU4LCgrqz2GHhZkzZzJt2jTLtFKKa6+9ls2bN+Pr68vPfvYz/vznP9Pe3n6evQghxMCzJgGUAFG9piOBMmsPoJRypvvm/0+t9dqe+VrrSq11p9a6C3id7qKmEcfZ2Zm4uDgOHDjwvW/6qampbNmyhWnTplFdXc1f//pXGhsbz7MnIYQYWNYkgAxgjFIqTinlAiwF1luzc6WUAt4EjmmtXzlrWVivySVAtnUh2x+lFPv27ePgwYPfm5+UlMTq1avx8fHh17/+NYsWLaK0tNQ2QQohRp0LJgCtdQewEthKdyXuh1rrI0qph5RSDwEopUKVUiXAE8CvlFIlSikf4Argx8DcPpp7vqiUOqyUOgRcDfxi4E9veOgp+//8889/0DdQcHAwK1eu5J577mH//v3MnTuXAwcO2ChSIcRoouypAjItLU1nZmbaOoyLtmXLFoKCgr5XJ9Cjs7OTVatW8R//8R8sXLiQ5cuXM3fuXLofooQQ4uIppfZprdPOni9vAg+h66+/nmnTptHV1fWDZY6OjjzyyCOsX7+e6OhoHn74YX7zm99Il9JCiEEjCWAIKaWoq6vj9ddf73MAeaUUM2bM4K677sLb25uXXnqJ22+/nYqKChtEK4QY6SQBDDF/f398fX3Zs2fPOdcZO3Ys27Zt4+abb2b79u088MADUi8ghBhwkgBs4IYbbuDbb7897wDy/v7+vPPOO7z00kukpKTw61//Wt4XEEIMKEkANuDr68uSJUtwc3M773rOzs48/PDD3HLLLRQUFPDss8+yYsWK8yYOIYSwliQAGxkzZgwdHR0cOXLkguumpKTw+eefM3fuXD755BNuvvlmsrKypAsJIcQlkQRgQ1prNm3aZNUYASEhIaxZs4ann36a+Ph43n77bV544QWam5uHIFIhxEgkCcCG/Pz8uO6661i3bh2dnZ0XXN/V1ZVf/epXPP744xw+fJjf/va33HTTTZw6dWoIohVCjDSSAGwsJSWFkJAQqqqqrFpfKUVqaipr1qzhjjvuYO/evcyZM4cNGzbQ2to6yNEKIUYSSQA2ppRiyZIlhIaGcvr0aau38/f358033+Stt95izJgx7Nu3j0ceeYScnJxBjFYIMZJIAhgmiouLeeONN/r15q+DgwO33347//znP3F3d+fDDz/k2muv5S9/+Uu/kokQYnSSBDBMREdHM2bMGD755JN+t+4JCQnh3//933n33Xdxdnbm6aef5oEHHmDv3r1W1S0IIUYnSQDDyLx586ivr+f48eP93tbBwYFbbrmFjIwMli1bRkREBC+//DL33XcfJ0+eHIRohRD2TnoDHWbOnDmDu7s7wEX3BKq1Jjc319KFhL+/P8uXL+eRRx4hPDx8IMMVQtgB6Q3UTnh4eHDmzJl+1wf0ppQiKSmJzz77jOeeew6AN954g1WrVvHee+9Z9d6BEGLkkwQwDHl6ehIREcHHH398SW/7uri48MQTT7Bz505eeeUVnJ2deeaZZ5g7dy6//e1vKSoqkreJhRjFJAEMU9dffz1nzpxh165dl7yv6Oholi1bxtKlS7nqqqvo6Ojgj3/8I7fccgtvvvkmR44c6XOMAiHEyCZ1AMPY6dOnaWlpISAgYMD22dTUxMcff8z27dtxc3PD19eX1atXM2HCBB566CFmzZqFj4/PgB1PCGF756oDkARgBzZs2MD06dMJDQ0dsH1WVVXh5+fHhx9+yNq1azlw4AAmk4lp06Zxzz33kJaWRkJCAg4O8pAohL27pEpgpdR8pdRxpVSeUurpPpaPU0p9o5RqVUr90pptlVL+SqltSqlc82/DxZzYaBAXF8fq1asH9OWu4OBgXFxciI2NZcaMGbzwwgv88pe/JCYmhoyMDObNm8ett97Kli1bMJlMA3ZcIcTwccEnAKWUI3ACuA4oATKAu7TWR3utEwzEADcDRq31yxfaVin1IlCntX7BnBgMWuunzhfLaH0CAPjiiy8oLCxkxYoVODo6Dui+6+vr2bp1KwEBAVx22WV8++23/O1vf2Pfvn00NTVxxRVXcNddd5GamkpiYuKAH18IMbjO9QTgZMW26UCe1vqkeUergcWAJQForauAKqXUwn5suxiYY17vXWAHcN4EMJrNnTuXY8eODUqRjJ+fH3feeSddXV0YjUaqq6tZtWoVjY2NrF69moqKCnbu3MmTTz7J+PHjueeee5g7dy4hISEDHosQYuhYkwAigOJe0yXADCv3f75tQ7TW5QBa63LzU4Q4B6UUEyZMoKioiNzcXK655poBP4aDgwN+fn5ER0fz9ttvk5yczBNPPEFHRwcZGRk0NDTw3XffsXLlSi6//HIWLFjAlClTSElJwcPDY8DjEUIMLmsSQF+vo1pbc3wp23bvQKkHgAeguznjaBcUFMSGDRvw8PBg5syZA75/R0dHLr/8clJSUti9e7dl/qxZs7j66qspKyvjs88+Iy8vj7179/Lcc88RExPDkiVLuO2220hMTJSKYyHshDUJoASI6jUdCZRZuf/zbVuplAozf/sPA/rsEF9r/RrwGnTXAVh53BHL3d2dH/3oR7z55pv4+fkxfvz4QTmOh4cH8+bNA2Dnzp0cOHCAa665huTkZO699146Ojo4fvw4ERERbN68mVdeeYW9e/dy2WWXERkZydVXX01kZORFd2chhBh81lQCO9FdkXsNUEp3Re4yrfUPBrNVSj0PNPWqBD7ntkqpl4DaXpXA/lrrJ88Xy2iuBD5bZWUlrq6u+Pn5DcnxCgsL2bp1K15eXixbtux7y0wmE9999x1ZWVns37+fzZs34+/vz6RJk7j33nu57LLLCA6WEj4hbOWS3gNQSi0A/gtwBN7SWv9OKfUQgNZ6lVIqFMgEfIAuoAmYoLVu7Gtb8z4DgA+BaKAIuF1rXXe+OCQB/NC6detISUkhLi5u0I+ltaahoQFfX182b97MxIkTiY2N/d7yiooKdu3axbvvvsvRo0dJTU0lPj6e6upq7r77bqZNmzZkSUsI0U1eBBuhCgoKWLNmDUuXLiUqKurCGwwArTWHDh1ix44d+Pv7c+211xIWFva9dbq6uigqKuLw4cNs2rSJTZs20dzcTFhYGEuWLGHRokWMHz8eLy+vIYlZiNFMEsAIlpeXx7p163jooYfw9vYesuN2dnZy4MABvL29GTNmDLW1tQQFBf1gvY6ODvLz81m/fj3r1q1j7NixuLu788033zB79mzuvPNOkpOThzR2IUYTSQAjXG1tLQEBAbS3t+Ps7Dzkx6+uruadd94hLi6Oq6666pzvCLS2tpKTk8OXX37J6tWrKSoqorOzk1mzZjF//nzGjRvHpEmT8PX1HeIzEGLkkgQwCjQ3N7Nq1Spuv/12IiMjh/z4ra2tZGZm8s0337B8+XJCQ0PP2wqopaWFEydOsHbtWkwmE7W1tWzatInQ0FAuv/xyli9fzqRJkzAYpJcQIS6FJIBRIjc3l48//pg77riDmJgYm8TQ3t6Ok5MTmZmZ5OTkMGvWrAvG0traaol98+bNFBYWMmHCBNLT0ykpKeH2228nNTWV8PBwaVoqRD9JAhhFTp48yZdffsl9991n05eyOjs7ycrKYvfu3Xh7e/OjH/3IquKptrY28vLyyM7O5uuvv2bt2rWcPn0af39/rrzySpYsWcLYsWOJj4+3SXGXEPZGEsAo09XVRWdnJyUlJUPSRPRCsRQWFhIXF8e+fftwcXFhwoQJVnUq19HRQUFBAV999RVr167Fx8eHiIgIPvzwQ6Kjo5k3bx433HAD48aNkxZFQpyDJIBRqLa2lnfeeYdZs2Yxffp0W4cDQH5+Prt27cJoNDJz5kwuu+wyq7fVWlNZWUlWVhYffPAB+/bto7KykoSEBObPn09tbS3XX389ycnJREVFSa+lQphJAhiljEYj77//PsnJycydO9fW4ViUlZVRVlZGWloa2dnZREZG9vsFMZPJxNGjRzl8+DBFRUW89dZbNDc34+/vT3JyMnfccQeJiYkkJCTg7+8/OCcihB2QBDCKnT59mhMnTpCamorWethVon755ZdkZGQQHx/PFVdcQXh4eL/30d7ebikq2rhxIx0dHUydOpX33nsPX19fJk2axPXXX09qaioxMTFSXCRGFUkAgrKyMr788ktuvfVW3N3dbR3O97S2tnLgwAE6Ozu54ooryMvLIyYm5qIreRsaGsjLy+Ojjz5i586dFBcX4+npydKlS8nMzCQiIoLZs2czZcoUYmNj8fT0HOAzEmL4kAQg6OrqYtu2bZw4cYJly5YN6GDzA6mzs5PVq1dTWlpKamoqaWlpl/QuQFdXFyUlJZw4cYLy8nL+8pe/UFJSQkdHBwEBAdxxxx04ODiQlJTEhAkTiIqKws/Pb9g9KQlxsSQBCIt9+/Zx+PBhVqxYMaxvcnV1dWRmZmIwGEhLS6OwsJCYmJhLjrmzs5P8/Hy++uorDh8+TFBQEGvXrqWsrAxPT09CQkJYtGgRERERxMfHEx0dTXh4OE5O1vSeLsTwIwlAfE9nZyednZ0cO3aMyZMnD+tEAN1vOb/33nu0trYydepUUlJSBqwcv6Ojg0OHDrF3716++uor8vPzWbhwIXv27OHEiRMEBgYSEhLCNddcw/jx4wkPDycsLIygoCAZ/EbYBUkA4gcaGxv54IMPCAoKYtGiRbi4uNg6pPPSWlNaWsr+/fuJj49nwoQJ5Ofnk5CQMKA34p6xkT///HO2bt3KkSNHOH36NPPmzaO6upqMjAwMBgNBQUHMnDmTlJQUwsPDCQ8PJyAgQJKCGHYkAYg+tbe3s3HjRiorK/nJT35iV8UcDQ0NrFmzhoaGBlJTU5k2bdqgdCLX0tLCyZMncXNzY/PmzXz22Wc0NjbS1NREcnIyISEhrF+/Hj8/P0JCQkhNTSU9PZ2QkBBCQ0MJDg62q7+rGHkkAYhz0lpTXl5OeHg4NTU1BAYG2jqkfqmqqmL//v2MHTuW8PBwjh8/zrhx4wbtiaahoYHCwkJycnJITk7m4MGDbNmyhZqaGhoaGggODmbKlCmsX78eJycn/P39SUpKYs6cOZakEBoaKi2PxJCRBCAuqL29nVWrVhEfH8+8efPssp8do9HI5s2bKS4uZuzYsVx55ZV9jlEwkE6fPk1eXh4FBQUcP36c9PR0Ojo62Lp1K1VVVZSXl6OUYubMmXz55Zc0Njbi5+dHREQE8+bNIyIiwpIU/P39pQhJDDhJAMIqLS0tbNy4kerqau666y67Hb6xqamJ7Oxs4uPjcXV1JSMjg8mTJw/J2MQ9Q2fu3LmTgoICmpubueyyy/D29ua7777j1KlT5ObmUldXx5w5czhw4AD5+fn4+PgQFBTErFmzSExMJDg42FKEJC+uiUshCUBYTWtNdnY2Y8eOpb29HQ8Pj2HfSuh8TCYTe/fu5fDhw3h6enLjjTcSERExZMdvaGjAyckJBwcH3nnnHYxGI+Hh4YwZMwZ/f38KCgo4dOgQR44coaSkhJSUFEsC8fb2xtfXlylTpjB16lS8vLyIjY0lODiY4OBgXF1dh+w8hP2SBCAuyscff4zJZOKmm26y+1G6urq6KCgoICgoiKamJj799FMmTpzIxIkTh/QbdktLC8XFxbi5uREZGcmf/vQn3NzciI6OJioqCm9vb8rLy8nNzeXw4cPk5+cTGBhIcHAw//rXv3BycsLb25vo6GhmzZqFg4OD5X2F4OBgAgMDpdJZfM8lJQCl1HzgT4Aj8IbW+oWzlivz8gXAGeAerfV+pdRY4H96rRoP/Fpr/V9KqeeBnwLV5mXPaq03ny8OSQBDr6uriz179vDNN9+wcOFCJk6caOuQBkTPy2BHjhzh+PHj3HrrrSQkJNDS0oKHh8eQxtLR0UF5eTnFxcWWuoL169fT0dFBVFQUEREReHp6UlVVRUVFBdnZ2Rw5coTm5maioqL49NNPqa6uxs3NjYCAAK677jrLW87JycmEhoYSFBSEv7+/JIZR6qITgFLKETgBXAeUABnAXVrro73WWQA8RncCmAH8SWs9o4/9lAIztNaF5gTQpLV+2dqTkARgOxUVFbS1tREZGcmZM2dGVJl0R0cH0N199ttvv01ERATJycmMHz8eNzc3m8RUW1tLQUEBJSUlNDU1sXz5cg4cOEB1dTWRkZFERkbi5eVFXV0dVVVVlJaWcvjwYQoKCggICGDfvn3k5ubS2tqKh4cHCxYsoL29HZPJxJgxY0hOTiYyMpLAwEACAwOlKGmEO1cCsObrQDqQp7U+ad7RamAxcLTXOouB93R3NtmrlPJTSoVprct7rXMNkK+1LrzosxA2ExoaCkBBQQFr1qxh3rx5dvEGsTV6vhWHhITwxBNPkJubS3Z2Nt7e3kRGRnLo0CHGjRuHj4/PkMUUEBBAQEAA06ZNs8wLDQ3FZDJx8OBBNm3axMqVK2ltbcVoNFqamTo7O9Pe3k5NTQ1VVVUUFxeTnZ2Nu7s7R48eJTs7m2+++Ybm5mZmzpxJTEwM3333HWFhYSQmJjJp0iSio6MJCgoiMDBQmqqOcNYkgAiguNd0Cd3f8i+0TgTQOwEsBf511nYrlVJ3A5nAv2mtjWcfXCn1APAAQHR0tBXhisEUGxvL8uXL2bBhAwcPHmTZsmV22Vz0XFxcXCz1AtD9tnRpaSnbt2/H39+fa6+91mYjrIWFhREWFgZg6dbb0dGRxsZGPvvsM6qqqrj77rsJCAigsrKS8PBwJk2axI033gh0P+nU1tZSXV1NeXm55berqysnT54kKyuLr7/+mpkzZ/LFF1/g5OREcHAwSUlJpKenExgYaElMfn5+MuDOCGBNEdDtwPVa65+Yp38MpGutH+u1zibgP7XWu83TXwBPaq33maddgDJgota60jwvBKgBNPD/gDCt9X3ni0WKgIaPrq4u8vLySEpKoqioaMR3ltbZ2UlhYSF+fn44OTnx/vvvM3bsWEvfQMPhSaijowOlFA0NDWzfvp2ysjJMJhMLFy5kypQpHDlyhJCQEAICAr4Xb0/XFzU1NVRXV1NTU8NXX33FyZMnqa2txdHRkTlz5rBz507q6urw8vLC19eXa6+9Fl9fXwICAoiMjLQkB29v72Hx9xD/51LqAGYCz2utrzdPPwOgtf7PXuv8A9ihtf6Xefo4MKenCEgptRh4VGs97xzHiAU2aq2TzxeLJIDhad26dRQXF7Nw4UISEhJsHc6g01pTVlZGTk4Ox44dIy0tjRkzZljGMBhOfSq1tLSgtcbZ2Zl169ZRVlbGmTNnmDFjBnPnzqWwsBBvb28MBsMPbtpaa0wmkyUpnDp1ipycHE6ePElFRQUzZ87k6NGj7Nu3D2dnZ7y8vJg+fTqhoaEYjUYSExMZN24cwcHBluQw3MahGC0uJQE40V0JfA3dlbgZwDKt9ZFe6ywEVvJ/lcB/1lqn91q+GtiqtX6717ywXgniF3RXDi89XyySAIavEydOsHnzZi6//HLS09MvvMEI0tXVRVtbG//zP/9DaWkpUVFRzJgxg6SkJFuH1qczZ87Q1taGn58fGzdutFQWjx07liVLllBVVYWDg8N530pub2/HaDRSW1tLVVUVx48f58SJE3h4eNDY2MiuXbs4ffo0bW1tTJgwgbS0NDIyMvDx8SE6OpqkpCQSEhIwGAwYDAb8/f3x9PSUJ4dBcqnNQBcA/0V3M9C3tNa/U0o9BKC1XmVuBvoXYD7dzUDv1Vpnmrf1oLt+IF5r3dBrn+8DKXQXARUAD55VafwDkgCGt/b2dtrb22ltbWX//v1ceeWVo651SWtrKydPnsTd3Z3o6GjeeustoqKiSEpKIjo6etiWm58+fZrGxkbCwsLYvXs3+/bt4/Tp0wQHB7NixQpOnz5tmb5QnU9zczO1tbXU1tZSVlZGZWUlLS0tfPrpp9TW1tLU1ISbmxvz589nz549NDY24uXlhcFgYM6cOfj4+ODv709ISAj+/v4YDAZ8fX2H7d/OHsiLYGLINDU1sW3bNvLz87n66qtJTU0dlf3b9HSyl5uby4kTJwgNDWXRokUcP36coKCgPotdhpOWlhaqq6uJiori+PHj7Nixg5qaGvz8/Lj11lvx8/OjtLTU6o7teoqU6urqMBqN1NXVkZ2dzYkTJygtLcVoNDJnzhwOHz5MVlYWLi4ueHp6kp6ejsFgoKamhtjYWBISEggNDcVgMODn54efnx9eXl7D+m9pa5IAxJArKytj+/bt3Hzzzbi4uIyo1kIXo6urCwcHBzZt2kROTg6Ojo6kpqYye/Zsy7LhrrOzk+rqagwGAyaTiY0bN1JRUYGLiwvXXXcdkyZNIicnx1Lm359zam5uxmg0YjQaKSsrIzc3l/z8fPz8/Kirq2P37t2WYqWelklfffUVzs7O+Pr6EhMTw6RJk/Dw8CAwMNCSIHx9ffHx8bGLv+9gkQQgbGrjxo3U1tYyd+5coqKibB2OzWmtqa6u5vTp08TFxfHee+/R1tZGQkICiYmJdvU36un8ztHREQ8PD9asWUNVVRUmk4lp06Yxf/58jh07hpOTEyEhIRfVSqijo4P6+nqMRiOVlZXU1dXR0tLC559/TllZGXV1dbi6ujJ79mx27NhBZWUl7u7ueHp6Mnv2bJqbm+ns7LQM3BMSEoLBYMDHx8fy4+7uPmKfIiQBCJvq7OwkKyuLnTt3Eh8fz+LFi20d0rDS0dFBcXEx+fn5NDY2csstt7B//37OnDlDbGws4eHhdvcNtq2tjdbWVry9vdm1axenTp2iqqoKd3d3Hn30UfLy8jAajYSEhBAcHHxJb123tbXR0NBAQ0MDxcXFnDp1ioKCAsrKyhg3bhwHDx7k0KFDtLe3AzBz5kwCAgL45ptv8PT0xMvLi4iICBITE+nq6sJgMFiKmXonCXutqJYEIIaFjo4OqqurCQ0NZefOnUyaNImAgABbhzUs9TS7LCgooKmpiSeeeIK6ujra29sJDQ21u4TQo7W1FVdXV3Jzczl27BhVVVVUVVXx2GOPWbrxDgwMJCgoiODg4AFpVtvR0UFDQ4Pl7WiAmpoadu7cSVVVFTU1NQQHBzNp0iQ+/fRTWltbATAYDMyePZvi4mJOnz6Np6cn/v7+JCYm4u3tjbu7OwEBAfj4+ODl5YW3t7dl/nBKFJIAxLDSu5O5+Ph4Zs+ePegDt9iznpvm4cOH+eqrrzCZTMTExLBo0SLc3d1xcHAYVjec/uq5D9XV1XH06FGqq6uprq5m7ty5REZG8tFHH1m6p+jp9XSgtba2YjKZyMnJoaysjPLycs6cOUNMTAxbt24lJyeHjo4OHBwcuO6666iqqiIrKwtHR0fc3d0ZP348QUFB5OXl4e7ujq+vL2FhYURGRuLm5obBYLAkiJ5kMVRPFJIAxLDU2tpKZmYmfn5+jB8/nsrKSkt3B+LcmpqaKCgoYPz48eTk5LBhwwaioqKIjo5mypQpQ9pv0WBrb2+noKDAkhQiIyOZNm0ar7/+Ok5OTgQFBREVFcWUKVNob2/HyclpUG6qXV1d1NXVUVpaiq+vL3l5eRw8eJCKigqqqqoYP348jo6ObNq0ia6uLpRShISEMHHiRDIyMjCZTLi7u+Ph4cGUKVMwGo2YTCZ8fX3x9/cnJiYGX19fvL29LU8UvX8u5U17SQBi2Kurq+Pdd98lMDCQq666ipiYGLv+VjuUmpqaKC4upqioiGnTpqG1Zv369URHR1t+RtpbuD1vKVdXd/coP2PGDNavX8+RI0csTws33ngjzc3NNDc3D0l32J2dnVRWVlJTU0NFRYWli+41a9ZQXFxMQ0MDnp6ezJgxgwMHDlBUVIRSCq01kydPprOzkwMHDuDs7IyLiwuRkZGWN6sXLFjA9ddff1FxSQIQdqGnsnjPnj0sWrTI0hpGXgLqn55K5aKiIoqKipg8eTKTJk1i8+bNREZGEh0dPezfQ7hYZ86coaamhpqaGlJTU8nJyeHzzz+noaEBb29vbr31VgIDAzl8+LCluaqPj8+Q/C3a2tpobm7G19eX/Px88vPzLU8Q1113HceOHWP79u1orenq6rIMEHTixAmWLVvGrFmzLuq4kgCEXen5d5mTk8OWLVuYMWMGU6dOtVn//CNBe3s7+/fvtySGcePGsWDBAg4ePIi3tzcREREj+u/b2dlJfX09Xl5etLW1sWPHDssby9OmTWPOnDls3LgRDw8PAgICCAkJsXSDPlS6urpoamqisbGRhoYGyzXJy8uzFDFdDEkAwm6VlZWxd+9ecnNzeeSRR+StzwHS2dmJo6MjO3bs4NSpU5SXlxMfH8/SpUspLi7G2dmZ4OBgu21t1B893WtnZ2dTU1NDbW0tHh4e3HDDDWzYsIGqqir8/f3x9/fnqquuorW1Fa31sGvtcy6SAITd62mGt3v3bk6dOsX06dNJSkoaFTeoodDz7dPHx4fdu3eTlZVl+RZ6991309jYSGdn54gtOjqXpqYmamtrqauro6GhgTlz5nDw4EG2bNkCgL+/v2XM7JycHEvndsOpW2xJAGLE6Ojo4OjRo5aWFY8++uigtfwY7Xr3B3TgwAG2b99OW1sbYWFh3Hzzzbi6utLc3Iyfn9+o+/trrS3dVwQEBNDa2sqXX35p6esoPT2dWbNm8fHHH+Pu7o6/vz+hoaFERUVZnjiGiiQAMSLV19fj5+fH1q1bqa+vJyUlhTFjxshTwSA6ffo0ZWVlxMbGUlpaytq1ay1J4eqrryYqKspyXUZbUuit5yZ/7Ngx6urqqKurw8PDg2uuuYY1a9ZQVlaGn58fBoOBG2+8EZPJhMlkwmAw4OHhMaB/O0kAYkRrbW3lyJEjHDhwgDNnzvDoo4/S1dU1okcpG06ampooLy8nODgYR0dHXnvtNdrb2wkLC2PatGlMnDgRo9GIj4+PtOji/95MNhqNNDY2MnXqVI4dO8auXbswGo10dnby4x//GIPBwK5duxg7dizx8fEXfTxJAGLU6Kkr+OSTT6iuriY1NZXk5ORRNzaBrfUkBQ8PDyIiInjjjTeorKwkMDCQpKQkrr76aoxGI25ubiPuHYVL1dLSgpOTE21tbWRlZREUFERiYuJF708SgBh1esYtPnDgADU1NTzyyCOWwUfkW6httLW1UVVVRXt7O3FxcWzZsoUDBw7g5uZGWFgYd955J42NjXR0dODv7z+qi5AGkiQAMar1NHn89NNPOXToEOPHjyc5OZm4uDi5ydiY1toyvOSYMWPIyspi+/btnDlzhsDAQG699Vbc3d0pLS0lODh4yF7aGkkkAQhh1tDQwJEjRygvL+fWW28lPz8fV1dXIiIi5MYyjPS0QAoNDaWuro6tW7dSXV1NW1sbN954I8nJyXz33XcEBgYSHBws74echyQAIc5h3759fPPNN7S3tzNx4kSuu+46uZEMY83NzSilcHR0ZNu2bZbupMeNG8dNN93E3r17cXBwICgoiKCgILy8vGwdss2dKwFIEwkx6k2bNo2pU6dSXV1NWVkZSim2b9+OyWRi/PjxxMXFSWuiYaR3hfGCBQssnzs6OgBwc3OjuLiY7OxstNbcf//9ZGRkUFJSQmBgIIGBgSQmJo76IUrByicApdR84E+AI/CG1vqFs5Yr8/IFwBngHq31fvOyAsAEdAIdPVlIKeUP/A8QCxQAd2itjeeLQ54AxFAxGo0cO3aMnJwc6uvrefzxxzGZTLi6uo7o/nJGqurqakpKSiydxC1ZsoSCggK2bdtmSQopKSkEBgbS0tIy4lolXXQRkFLKETgBXAeUABnAXVrro73WWQA8RncCmAH8SWs9w7ysAEjTWtectd8XgTqt9QtKqacBg9b6qfPFIglA2ELPYCx79uxh586dhIeHWwYllycD+9XZ2UldXZ0lKSQlJeHp6cmrr76Kk5MTAQEBpKamkpqayqlTpyxv8w7ECGVD7VKKgNKBPK31SfOOVgOLgaO91lkMvKe7s8lepZSfUipMa11+nv0uBuaYP78L7ADOmwCEsIWe9weuuOIK0tPTOXXqFKdOncLR0ZHs7GyKiopISkoiNjZWEoIdcXR0tNQT9Pb000/T1NRETU2N5Wnv8OHDlJSUYDQaCQ8P59577+XIkSPU1dVZOokLCQmxuzfQrfnXGgEU95ouoftb/oXWiQDKAQ18ppTSwD+01q+Z1wnpSRBa63KlVJ9jvCmlHgAeAIiOjrYiXCEGj7OzM0lJSSQlJQEQHh5OfX09X331FWvWrGHlypVA98toISEhUplsh5RSlqEbe9x0001Ad5PVlpYWoLuuoaWlhezsbGpra7n//vspKChgz549BAQE4O/vz8SJEzEYDLS1tQ3LFxGtSQB9/Qs+u9zofOtcobUuM9/gtymlcrTWX1kboDlhvAbdRUDWbifEUPD39+fKK6/kyiuvpKWlBVdXV06ePMnmzZtpaWkhLi6OuXPnjroeNEcqpZSlfiAhIYGEhITvLY+OjsbV1dXSe2h7ezsmk4lXX30VZ2dnDAYDqamppKWlkZOTg4uLCwaDwWZdZFiTAEqAqF7TkUCZtetorXt+Vyml1tFdpPQVUNlTTKSUCgOqLu4UhBgeeooLEhISeOyxx6ivr+fkyZO4urpSVFTE+vXrSUhIID4+ntjYWKlMHoHc3d2JjY0lNjb2e/OfffZZTp8+TX19vaUOobCwkIqKCoxGI+7u7jz44INkZGRQXl5u6SRu3LhxODo6opQalC8Q1iSADGCMUioOKAWWAsvOWmc9sNJcPzADaDDf2D0BB621yfx5HvAfvbZZAbxg/v3JJZ+NEMOIn58fU6dOBcDDw4Pbb7+d/Px8MjIycHBwICYmhi+++IKYmBhiYmKkvfoIppSyDO7eo/f4vj2NcSIjI1FKUV9fT05ODmPHjuXYsWOUl5dz7bXXDnxcVjYDXQD8F93NQN/SWv9OKfWQOfBV5magfwHm090M9F6tdaZSKh5YZ96NE/CB1vp35n0GAB8C0UARcLvWuu58cUgrIDGStLS0sG/fPgoLCykqKuKqq67iiiuuICcnh7CwMHx9fW0dohgmurq6LqmCWd4EFmIY6+rqoqOjAycnJz766CMKCgpwcXEhLS2NK6+80jKgub21MhHDg7wJLMQw5uDgYCkbvuOOO9BaU1NTQ3t7OwCbNm2ioKCA8PBwEhISuOqqqywd3AlxsSQBCDEMKaW+1z592bJltLS0UFpaSlNTEwAbN26koKCAqKgoIiIiSEtLk4Qg+kUSgBB2ws3N7XvNDm+66SZqamooLi6msrISBwcHvvvuO/bt20d4eDjh4eFMnDgRDw8PG0YthjNJAELYqZ6nhN5PClOnTiUyMpKysjLKyspISkqiuLiYTZs2WZLCmDFjpIJZAJIAhBhRnJycLDf6Hp6enixatIiysjJKS0sxGAy4u7vz5ptvEhISQkhICHFxcd/bRowOkgCEGOGcnJyIiIggIiLCMq+rq4vFixdTWVlJRUUFZWVlhIeH8+677+Lg4EBoaCiRkZGMHz/ehpGLwSYJQIhRyMHB4QdPCgA333yzJSlUVFQwfvx4Nm7cSElJCcHBwQQFBTFz5kzLPqRZqn2TBCCEsPD19cXX19fS2R10v7FaVVVFdXU1NTU1ODo6kpWVxaZNmwgICCAoKIhZs2ZhMBior6/H399fEoOdkAQghDgvZ2fnHxQhpaSkMGHCBGpqaqiursbNzY2GhgY++OADGhsbLZ3kTZ48mRMnTuDt7U1AQIBd9qU/kkkCEEJcFBcXlx8UI/3sZz+jvb2dmpoaXF1d0Vpz6NAhqqqqqKurIykpiTvuuIMDBw7Q0tJCQECApetk6S116EkCEEIMKGdnZ8LCwizTt912G/D9vvRdXV2pqKggPz+fxsZGHn74YQ4dOkR2drYlKYwfP97S9bIUKQ0OSQBCiCHRuy/9CRMmMGHChO8tj4uLw8XFhdraWsrKyoiPj6ehoYE333wTX19fDAYD06dPZ9y4ceTm5uLt7Y3BYBiWA63YC0kAQohhwdvbm3Hjxv1g/jPPPEN9fT1GoxE/Pz+01hw4cIDa2lqMRiMJCQnceeedfPvttzQ1NWEwGDAYDMTGxkqx0gVIAhBCDGtOTk4EBgYSGBhomXfHHXcA3cVKPR3mBQQE0NLSQlFREUeOHCE2NpZvv/2Wr7/+Gl9fX/z8/Jg9ezZeXl4UFxdbWjyN5oppSQBCCLullLLcwBMTE0lMTPze8rS0NJKSkmhoaKC+vh5XV1fOnDnD119/TUNDAw0NDcyePZurrrqK9evX4+Ligp+fH8HBwcTHx9Pe3o6Tk9OIfZKQBCCEGLEcHR0tRUK93X333UD3E0RnZycAY8aMwWg0YjQaaWlpIT4+nk2bNnH48GF8fHzw9vbm7rvvpqamhlOnTuHj44OPjw/BwcF2Ww8hCUAIMWoppXBy6r4N9tXtxc0338zChQsxmUyYTCacnJzo7Oykvr6eoqIiTCYT1157LQaDgTfeeANvb298fHyYOHEikyZNIjc3FycnJ7y9vfH29h52iUISgBBCnIezszP+/v74+/sD/OClOOh+kvjpT39KY2MjjY2N+Pj4AJCXl0dFRQUmkwl3d3d++tOfsmvXLvLy8vDy8sLb25vZs2fT2dlJZWWlZZ67u/uQFDtJAhBCiEuklLIUCfV2ww03/GDdKVOmEBUVRVNTEyaTCUdHR2pra9mzZw8mk4mmpibmzZvH5MmTefvtt/Hy8iI5OZnk5OSBj1vGBBZCiOFFa43WmrKyMkwmE76+vpfUXfe5xgS26vU6pdR8pdRxpVSeUurpPpYrpdSfzcsPKaWmmudHKaW2K6WOKaWOKKV+3mub55VSpUqpg+afBRd9dkIIMYIopXBwcLB0yT1YYzVcsAhIKeUI/BW4DigBMpRS67XWR3utdgMwxvwzA/i7+XcH8G9a6/1KKW9gn1JqW69t/6i1fnngTkcIIYS1rHkCSAfytNYntdZtwGpg8VnrLAbe0932An5KqTCtdbnWej+A1toEHAMiEEIIYXPWJIAIoLjXdAk/vIlfcB2lVCyQCnzba/ZKc5HRW0qp7zfU/b/tHlBKZSqlMqurq60IVwghhDWsSQB9tUU6u+b4vOsopbyA/wUe11o3mmf/HUgAUoBy4A99HVxr/ZrWOk1rndZ78GshhBCXxpoEUAJE9ZqOBMqsXUcp5Uz3zf+fWuu1PStorSu11p1a6y7gdbqLmoQQQgwRaxJABjBGKRWnlHIBlgLrz1pnPXC3uTXQZUCD1rpcdb/J8CZwTGv9Su8NlFJhvSaXANkXfRZCCCH67YKtgLTWHUqplcBWwBF4S2t9RCn1kHn5KmAzsADIA84A95o3vwL4MXBYKXXQPO9ZrfVm4EWlVArdRUUFwIMDdE5CCCGsIC+CCSHECHeuF8HsKgEopaqBwovcPBCoGcBwbEnOZfgZKecBci7D1aWcS4zW+getaOwqAVwKpVRmXxnQHsm5DD8j5TxAzmW4GoxzkZGWhRBilJIEIIQQo9RoSgCv2TqAASTnMvyMlPMAOZfhasDPZdTUAQghhPi+0fQEIIQQohdJAEIIMUqNigSglCpQSh02DzxjV2+SmXtKrVJKZfea56+U2qaUyjX/7rMn1eHkHOdhl4MCnWugI3u7Luc5D7u7LkopN6XUd0qpLPO5/MY8366uCZz3XAb8uoyKOgClVAGQprW2uxdClFKzgCa6x1tINs97EajTWr9gHqHNoLV+ypZxXsg5zuN5oMneBgUy92MV1nugI+Bm4B7s6Lqc5zzuwM6ui7nfMU+tdZO5A8rdwM+BW7CjawLnPZf5DPB1GRVPAPZMa/0VUHfW7MXAu+bP79L9n3ZYO8d52KXzDHRkV9dlJA3YZB6Mqsk86Wz+0djZNYHznsuAGy0JQAOfKaX2KaUesHUwAyBEa10O3f+JgWAbx3MpLjgo0HB21kBHdntd+hiwye6ui1LK0dzpZBWwTWttt9fkHOcCA3xdRksCuEJrPZXusYsfNRdHCNuzalCg4eocAx3ZnT7Owy6vi3l8kRS6xyNJV0ol2ziki3aOcxnw6zIqEoDWusz8uwpYh/0PPlPZM56C+XeVjeO5KPY8KJDqe6Aju7sufZ2HPV8XAK11PbCD7jJzu7smvfU+l8G4LiM+ASilPM0VXCilPIF52P/gM+uBFebPK4BPbBjLRbPXQYHMlXR9DXRkV9flXOdhj9dFKRWklPIzf3YHrgVysLNrAuc+l8G4LiO+FZBSKp7ub/3QPQDOB1rr39kwpH5RSv0LmEN3V7CVwHPAx8CHQDRQBNyutR7WFaznOI85dD/OWgYF6imvHc6UUlcCu4DDQJd59rN0l5/bzXU5z3nchZ1dF6XUZLoreR3p/mL7odb6P5RSAdjRNYHznsv7DPB1GfEJQAghRN9GfBGQEEKIvkkCEEKIUUoSgBBCjFKSAIQQYpSSBCCEEKOUJAAhhBilJAEIIcQo9f8BjUENeU3USQcAAAAASUVORK5CYII=\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "filenames": { + "image/png": "/home/john/gh_synced/books/sed2/edtc-code/code_book/_build/jupyter_execute/ch6_64_0.png" + }, + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "alpha, a, c = 0.8, 5.0, 2.0 \n", + "beta_a, beta_b = 5, 5\n", + "mc_draw_size = 250\n", + "gridsize = 150\n", + "grid_max = 35\n", + "grid = np.linspace(a, grid_max, gridsize)\n", + "\n", + "beta_dist = beta(5, 5)\n", + "W = a + beta_dist.rvs(mc_draw_size) * c # Shock observations\n", + "D = P = lambda x: 1.0 / x \n", + "tol = 1e-4\n", + "\n", + "def fix_point(h, lower, upper):\n", + " \"Computes the fixed point of h on [upper, lower].\"\n", + " return brentq(lambda x: x - h(x), lower, upper)\n", + "\n", + "def T(p_array):\n", + "\n", + " new_p = np.empty_like(p_array)\n", + "\n", + " # Interpolate to obtain p as a function.\n", + " p = interp1d(grid, \n", + " p_array, \n", + " fill_value=(p_array[0], p_array[-1]),\n", + " bounds_error=False)\n", + "\n", + " for i, x in enumerate(grid):\n", + " y = alpha * np.mean(p(W))\n", + " if y <= P(x): \n", + " new_p[i] = P(x) \n", + " continue\n", + " h = lambda r: alpha * np.mean(p(alpha*(x - D(r)) + W))\n", + " new_p[i] = fix_point(h, P(x), y)\n", + "\n", + " return new_p\n", + "\n", + "\n", + "fig, ax = plt.subplots()\n", + "\n", + "price = P(grid)\n", + "error = tol + 1\n", + "while error > tol:\n", + " ax.plot(grid, price, 'k--', alpha=0.5, lw=1)\n", + " new_price = T(price)\n", + " error = max(np.abs(new_price - price))\n", + " price = new_price\n", + "\n", + "ax.plot(grid, price, 'k-', alpha=0.5, lw=2, label=r'$p^*$')\n", + "ax.legend()\n", + "\n", + "plt.show()\n" + ] + }, + { + "cell_type": "markdown", + "id": "dbcec582", + "metadata": {}, + "source": [ + "Our final task for this chapter is to solve exercise 6.28, which involves\n", + "computing the stationary density of the associated state process for\n", + "quantities.\n", + "\n", + "To do so we use the look ahead estimator." + ] + }, + { + "cell_type": "code", + "execution_count": 35, + "id": "fee47eb9", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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+ "text/plain": [ + "
" + ] + }, + "metadata": { + "filenames": { + "image/png": "/home/john/gh_synced/books/sed2/edtc-code/code_book/_build/jupyter_execute/ch6_66_0.png" + }, + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "# Turn the price array into a price function\n", + "p_star = lambda x: interp(grid, price, x)\n", + "\n", + "def carry_over(x):\n", + " return alpha * (x - D(p_star(x)))\n", + "\n", + "def phi(z):\n", + " \"Shock distribution computed by change of variables.\"\n", + " return beta_dist.pdf((z - a)/c) / c\n", + "\n", + "def p(x, y):\n", + " return phi(y - carry_over(x))\n", + "\n", + "def generate_cp_ts(init=0, n=1000):\n", + " X = np.empty(n)\n", + " X[0] = init\n", + " for t in range(n-1):\n", + " W = a + c * beta_dist.rvs()\n", + " X[t+1] = carry_over(X[t]) + W\n", + " return X\n", + "\n", + "fig, ax = plt.subplots()\n", + "\n", + "plot_grid = np.linspace(a, a * 1.5, 200)\n", + "\n", + "x_ts = generate_cp_ts()\n", + "f = lae_factory(p, x_ts)\n", + "ax.plot(plot_grid, \n", + " [f(y) for y in plot_grid], \n", + " lw=2, \n", + " alpha=0.6,\n", + " label=r'$\\psi^*$')\n", + "ax.plot(plot_grid, \n", + " phi(plot_grid),\n", + " '--',\n", + " lw=2, \n", + " alpha=0.6,\n", + " label=r'$\\phi$')\n", + "\n", + "ax.set_xlabel('$x$')\n", + "ax.legend()\n", + "\n", + "plt.show()\n" + ] + }, + { + "cell_type": "markdown", + "id": "ab318322", + "metadata": {}, + "source": [ + "As claimed in the statement of the exercise, the two distributions line up\n", + "exactly.\n", + "\n", + "Hence, for these particular parameters, speculation has no impact on long run\n", + "average outcomes.\n", + "\n", + "If we change parameters to make storage more attractive, then we will see\n", + "differences between the distributions." + ] + } + ], + "metadata": { + "jupytext": { + "cell_metadata_filter": "-all", + "formats": "md:myst", + "text_representation": { + "extension": ".md", + "format_name": "myst", + "format_version": 0.13, + "jupytext_version": "1.10.3" + } + }, + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.8.5" + }, + "source_map": [ + 14, + 20, + 29, + 35, + 73, + 78, + 89, + 94, + 97, + 102, + 107, + 116, + 121, + 132, + 137, + 147, + 160, + 166, + 187, + 193, + 209, + 216, + 256, + 262, + 278, + 288, + 302, + 306, + 323, + 329, + 339, + 345, + 387, + 398, + 403, + 411, + 416, + 441, + 449, + 502, + 508, + 532, + 546, + 559, + 595, + 602, + 624, + 630, + 663, + 668, + 693, + 700, + 716, + 723, + 772, + 780, + 799, + 804, + 824, + 830, + 837, + 862, + 867, + 883, + 894, + 947, + 955, + 1001 + ] + }, + "nbformat": 4, + "nbformat_minor": 5 +} \ No newline at end of file diff --git a/code_book/ch6.md b/_sources/ch6.md similarity index 100% rename from code_book/ch6.md rename to _sources/ch6.md diff --git a/_sources/ch7.ipynb b/_sources/ch7.ipynb new file mode 100644 index 0000000..a21a3ae --- /dev/null +++ b/_sources/ch7.ipynb @@ -0,0 +1,48 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "id": "55da7328", + "metadata": {}, + "source": [ + "# Chapter 7 Code\n", + "\n", + "No code for this chapter." + ] + } + ], + "metadata": { + "jupytext": { + "cell_metadata_filter": "-all", + "formats": "md:myst", + "text_representation": { + "extension": ".md", + "format_name": "myst", + "format_version": 0.13, + "jupytext_version": "1.10.3" + } + }, + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.8.5" + }, + "source_map": [ + 14 + ] + }, + "nbformat": 4, + "nbformat_minor": 5 +} \ No newline at end of file diff --git a/code_book/ch7.md b/_sources/ch7.md similarity index 100% rename from code_book/ch7.md rename to _sources/ch7.md diff --git a/_sources/ch8.ipynb b/_sources/ch8.ipynb new file mode 100644 index 0000000..0b37c70 --- /dev/null +++ b/_sources/ch8.ipynb @@ -0,0 +1,193 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "id": "661ab925", + "metadata": {}, + "source": [ + "# Chapter 8 Code\n", + "\n", + "Let us start with some imports." + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "id": "4d20a90f", + "metadata": {}, + "outputs": [], + "source": [ + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "from mpl_toolkits.mplot3d.axes3d import Axes3D\n", + "from matplotlib import cm\n" + ] + }, + { + "cell_type": "markdown", + "id": "49ab6a8d", + "metadata": {}, + "source": [ + "Here is the code for figure 8.1." + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "id": "08de2de9", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "filenames": { + "image/png": "/home/john/gh_synced/books/sed2/edtc-code/code_book/_build/jupyter_execute/ch8_3_0.png" + }, + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "a, b = 0.8, 1.0 # parameters\n", + "\n", + "def phi(z):\n", + " \"Standard normal density.\"\n", + " return (1/np.sqrt(2 * np.pi)) * np.exp(-z**2/2)\n", + "\n", + "def p(x, y):\n", + " return phi(y - a * x - b)\n", + "\n", + "xgrid = np.linspace(-3, 3, 50)\n", + "ygrid = xgrid\n", + "x, y = np.meshgrid(xgrid, ygrid)\n", + "\n", + "fig = plt.figure()\n", + "ax = fig.add_subplot(111, projection='3d')\n", + "\n", + "ax.plot_surface(x,\n", + " y,\n", + " p(x, y),\n", + " rstride=2, cstride=2,\n", + " cmap=cm.Blues_r,\n", + " alpha=0.9,\n", + " linewidth=0.25)\n", + "ax.set_zticks((0.0, 0.05, 0.1, 0.15))\n", + "ax.set_xlabel('$x$')\n", + "ax.set_ylabel('$y$')\n", + "ax.zaxis.set_rotate_label(False)\n", + "ax.set_zlabel('$p(x,y)$', rotation=0, labelpad=20)\n", + "\n", + "azimuth, elevation = -128, 25\n", + "ax.view_init(elevation, azimuth)\n", + "\n", + "plt.show()\n" + ] + }, + { + "cell_type": "markdown", + "id": "de9ad922", + "metadata": {}, + "source": [ + "Here is the code for the time series in figure 8.2." + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "id": "b8dc09f6", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "filenames": { + "image/png": "/home/john/gh_synced/books/sed2/edtc-code/code_book/_build/jupyter_execute/ch8_5_0.png" + }, + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "\n", + "ts_length = 100\n", + "\n", + "X = np.zeros(ts_length)\n", + "\n", + "for t in range(ts_length-1):\n", + " Z = np.random.randn()\n", + " X[t+1] = a * X[t] + b + Z\n", + "\n", + "fig, ax = plt.subplots()\n", + "\n", + "ax.plot(X, alpha=0.7, label='$X_t$')\n", + "ax.legend()\n", + "ax.set_xlabel(\"time\")\n", + "\n", + "plt.show()\n" + ] + }, + { + "cell_type": "markdown", + "id": "2237d0ec", + "metadata": {}, + "source": [ + "Other figures from this chapter were written using different tools and are\n", + "omitted." + ] + } + ], + "metadata": { + "jupytext": { + "cell_metadata_filter": "-all", + "formats": "md:myst", + "text_representation": { + "extension": ".md", + "format_name": "myst", + "format_version": 0.13, + "jupytext_version": "1.10.3" + } + }, + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.8.5" + }, + "source_map": [ + 14, + 20, + 26, + 30, + 65, + 69, + 89 + ] + }, + "nbformat": 4, + "nbformat_minor": 5 +} \ No newline at end of file diff --git a/code_book/ch8.md b/_sources/ch8.md similarity index 100% rename from code_book/ch8.md rename to _sources/ch8.md diff --git a/_sources/ch9.ipynb b/_sources/ch9.ipynb new file mode 100644 index 0000000..bc51695 --- /dev/null +++ b/_sources/ch9.ipynb @@ -0,0 +1,48 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "id": "498df039", + "metadata": {}, + "source": [ + "# Chapter 9 Code\n", + "\n", + "No code used in this chapter." + ] + } + ], + "metadata": { + "jupytext": { + "cell_metadata_filter": "-all", + "formats": "md:myst", + "text_representation": { + "extension": ".md", + "format_name": "myst", + "format_version": 0.13, + "jupytext_version": "1.10.3" + } + }, + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.8.5" + }, + "source_map": [ + 14 + ] + }, + "nbformat": 4, + "nbformat_minor": 5 +} \ No newline at end of file diff --git a/code_book/ch9.md b/_sources/ch9.md similarity index 100% rename from code_book/ch9.md rename to _sources/ch9.md diff --git a/code_book/intro.md b/_sources/intro.md similarity index 100% rename from code_book/intro.md rename to _sources/intro.md diff --git a/_sphinx_design_static/design-tabs.js b/_sphinx_design_static/design-tabs.js new file mode 100644 index 0000000..b25bd6a --- /dev/null +++ b/_sphinx_design_static/design-tabs.js @@ -0,0 +1,101 @@ +// @ts-check + +// Extra JS capability for selected tabs to be synced +// The selection is stored in local storage so that it persists across page loads. + +/** + * @type {Record} + */ +let sd_id_to_elements = {}; +const storageKeyPrefix = "sphinx-design-tab-id-"; + +/** + * Create a key for a tab element. + * @param {HTMLElement} el - The tab element. + * @returns {[string, string, string] | null} - The key. + * + */ +function create_key(el) { + let syncId = el.getAttribute("data-sync-id"); + let syncGroup = el.getAttribute("data-sync-group"); + if (!syncId || !syncGroup) return null; + return [syncGroup, syncId, syncGroup + "--" + syncId]; +} + +/** + * Initialize the tab selection. + * + */ +function ready() { + // Find all tabs with sync data + + /** @type {string[]} */ + let groups = []; + + document.querySelectorAll(".sd-tab-label").forEach((label) => { + if (label instanceof HTMLElement) { + let data = create_key(label); + if (data) { + let [group, id, key] = data; + + // add click event listener + // @ts-ignore + label.onclick = onSDLabelClick; + + // store map of key to elements + if (!sd_id_to_elements[key]) { + sd_id_to_elements[key] = []; + } + sd_id_to_elements[key].push(label); + + if (groups.indexOf(group) === -1) { + groups.push(group); + // Check if a specific tab has been selected via URL parameter + const tabParam = new URLSearchParams(window.location.search).get( + group + ); + if (tabParam) { + console.log( + "sphinx-design: Selecting tab id for group '" + + group + + "' from URL parameter: " + + tabParam + ); + window.sessionStorage.setItem(storageKeyPrefix + group, tabParam); + } + } + + // Check is a specific tab has been selected previously + let previousId = window.sessionStorage.getItem( + storageKeyPrefix + group + ); + if (previousId === id) { + // console.log( + // "sphinx-design: Selecting tab from session storage: " + id + // ); + // @ts-ignore + label.previousElementSibling.checked = true; + } + } + } + }); +} + +/** + * Activate other tabs with the same sync id. + * + * @this {HTMLElement} - The element that was clicked. + */ +function onSDLabelClick() { + let data = create_key(this); + if (!data) return; + let [group, id, key] = data; + for (const label of sd_id_to_elements[key]) { + if (label === this) continue; + // @ts-ignore + label.previousElementSibling.checked = true; + } + window.sessionStorage.setItem(storageKeyPrefix + group, id); +} + +document.addEventListener("DOMContentLoaded", ready, false); diff --git a/_sphinx_design_static/sphinx-design.5ea377869091fd0449014c60fc090103.min.css b/_sphinx_design_static/sphinx-design.5ea377869091fd0449014c60fc090103.min.css new file mode 100644 index 0000000..a325746 --- /dev/null +++ b/_sphinx_design_static/sphinx-design.5ea377869091fd0449014c60fc090103.min.css @@ 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Multiple values per key are supported, + * it will always return arrays of strings for the value parts. + */ +jQuery.getQueryParameters = function(s) { + if (typeof s === 'undefined') + s = document.location.search; + var parts = s.substr(s.indexOf('?') + 1).split('&'); + var result = {}; + for (var i = 0; i < parts.length; i++) { + var tmp = parts[i].split('=', 2); + var key = jQuery.urldecode(tmp[0]); + var value = jQuery.urldecode(tmp[1]); + if (key in result) + result[key].push(value); + else + result[key] = [value]; + } + return result; +}; + +/** + * highlight a given string on a jquery object by wrapping it in + * span elements with the given class name. + */ +jQuery.fn.highlightText = function(text, className) { + function highlight(node, addItems) { + if (node.nodeType === 3) { + var val = node.nodeValue; + var pos = val.toLowerCase().indexOf(text); + if (pos >= 0 && + !jQuery(node.parentNode).hasClass(className) && + !jQuery(node.parentNode).hasClass("nohighlight")) { + var span; + var isInSVG = jQuery(node).closest("body, svg, foreignObject").is("svg"); + if (isInSVG) { + span = document.createElementNS("http://www.w3.org/2000/svg", "tspan"); + } else { + span = document.createElement("span"); + span.className = className; + } + span.appendChild(document.createTextNode(val.substr(pos, text.length))); + node.parentNode.insertBefore(span, node.parentNode.insertBefore( + document.createTextNode(val.substr(pos + text.length)), + node.nextSibling)); + node.nodeValue = val.substr(0, pos); + if (isInSVG) { + var rect = document.createElementNS("http://www.w3.org/2000/svg", "rect"); + var bbox = node.parentElement.getBBox(); + rect.x.baseVal.value = bbox.x; + rect.y.baseVal.value = bbox.y; + rect.width.baseVal.value = bbox.width; + rect.height.baseVal.value = bbox.height; + rect.setAttribute('class', className); + addItems.push({ + "parent": node.parentNode, + "target": rect}); + } + } + } + else if (!jQuery(node).is("button, select, textarea")) { + jQuery.each(node.childNodes, function() { + highlight(this, addItems); + }); + } + } + var addItems = []; + var result = this.each(function() { + highlight(this, addItems); + }); + for (var i = 0; i < addItems.length; ++i) { + jQuery(addItems[i].parent).before(addItems[i].target); + } + return result; +}; + +/* + * backward compatibility for jQuery.browser + * This will be supported until firefox bug is fixed. + */ +if (!jQuery.browser) { + jQuery.uaMatch = function(ua) { + ua = ua.toLowerCase(); + + var match = /(chrome)[ \/]([\w.]+)/.exec(ua) || + /(webkit)[ \/]([\w.]+)/.exec(ua) || + /(opera)(?:.*version|)[ \/]([\w.]+)/.exec(ua) || + /(msie) ([\w.]+)/.exec(ua) || + ua.indexOf("compatible") < 0 && /(mozilla)(?:.*? rv:([\w.]+)|)/.exec(ua) || + []; + + return { + browser: match[ 1 ] || "", + version: match[ 2 ] || "0" + }; + }; + jQuery.browser = {}; + jQuery.browser[jQuery.uaMatch(navigator.userAgent).browser] = true; +} diff --git a/_static/basic.css b/_static/basic.css new file mode 100644 index 0000000..c5dde73 --- /dev/null +++ b/_static/basic.css @@ -0,0 +1,899 @@ +/* + * basic.css + * ~~~~~~~~~ + * + * Sphinx stylesheet -- basic theme. + * + * :copyright: Copyright 2007-2022 by the Sphinx team, see AUTHORS. + * :license: BSD, see LICENSE for details. + * + */ + +/* -- main layout ----------------------------------------------------------- */ + +div.clearer { + clear: both; +} + +div.section::after { + display: block; + content: ''; + clear: left; +} + +/* -- relbar ---------------------------------------------------------------- */ + +div.related { + width: 100%; + font-size: 90%; +} + +div.related h3 { + display: none; +} + +div.related ul { + margin: 0; + padding: 0 0 0 10px; + list-style: none; +} + +div.related li { + display: inline; +} + +div.related li.right { + float: right; + margin-right: 5px; +} + +/* -- sidebar --------------------------------------------------------------- */ + +div.sphinxsidebarwrapper { + padding: 10px 5px 0 10px; +} + +div.sphinxsidebar { + float: left; + width: 270px; + margin-left: -100%; + font-size: 90%; + word-wrap: break-word; + overflow-wrap : break-word; +} + +div.sphinxsidebar ul { + list-style: none; +} + +div.sphinxsidebar ul ul, +div.sphinxsidebar ul.want-points { + margin-left: 20px; + list-style: square; +} + +div.sphinxsidebar ul ul { + margin-top: 0; + margin-bottom: 0; +} + +div.sphinxsidebar form { + margin-top: 10px; +} + +div.sphinxsidebar input { + border: 1px solid #98dbcc; + font-family: sans-serif; + font-size: 1em; +} + +div.sphinxsidebar #searchbox form.search { + overflow: hidden; +} + +div.sphinxsidebar #searchbox input[type="text"] { + float: left; + width: 80%; + padding: 0.25em; + box-sizing: border-box; +} + +div.sphinxsidebar #searchbox input[type="submit"] { + float: left; + width: 20%; + border-left: none; + padding: 0.25em; + box-sizing: border-box; +} + + +img { + border: 0; + max-width: 100%; +} + +/* -- search page ----------------------------------------------------------- */ + +ul.search { + margin: 10px 0 0 20px; + padding: 0; +} + +ul.search li { + padding: 5px 0 5px 20px; + background-image: url(http://github.com/file.png); + background-repeat: no-repeat; + background-position: 0 7px; +} + +ul.search li a { + font-weight: bold; +} + +ul.search li p.context { + color: #888; + margin: 2px 0 0 30px; + text-align: left; +} + +ul.keywordmatches li.goodmatch a { + font-weight: bold; +} + +/* -- index page ------------------------------------------------------------ */ + +table.contentstable { + width: 90%; + margin-left: auto; + margin-right: auto; +} + +table.contentstable p.biglink { + line-height: 150%; +} + +a.biglink { + font-size: 1.3em; +} + +span.linkdescr { + font-style: italic; + padding-top: 5px; + font-size: 90%; +} + +/* -- general index --------------------------------------------------------- */ + +table.indextable { + width: 100%; +} + +table.indextable td { + text-align: left; + vertical-align: top; +} + +table.indextable ul { + margin-top: 0; + margin-bottom: 0; + list-style-type: none; +} + +table.indextable > tbody > tr > td > ul { + padding-left: 0em; +} + +table.indextable tr.pcap { + height: 10px; +} + +table.indextable tr.cap { + margin-top: 10px; + background-color: #f2f2f2; +} + +img.toggler { + margin-right: 3px; + margin-top: 3px; + cursor: pointer; +} + +div.modindex-jumpbox { + border-top: 1px solid #ddd; + border-bottom: 1px solid #ddd; + margin: 1em 0 1em 0; + padding: 0.4em; +} + +div.genindex-jumpbox { + border-top: 1px solid #ddd; + border-bottom: 1px solid #ddd; + margin: 1em 0 1em 0; + padding: 0.4em; +} + +/* -- domain module index --------------------------------------------------- */ + +table.modindextable td { + padding: 2px; + border-collapse: collapse; +} + +/* -- general body styles --------------------------------------------------- */ + +div.body { + min-width: 360px; + max-width: 800px; +} + +div.body p, div.body dd, div.body li, div.body blockquote { + -moz-hyphens: auto; + -ms-hyphens: auto; + -webkit-hyphens: auto; + hyphens: auto; +} + +a.headerlink { + visibility: hidden; +} +a.brackets:before, +span.brackets > a:before{ + content: "["; +} + +a.brackets:after, +span.brackets > a:after { + content: "]"; +} + + +h1:hover > a.headerlink, +h2:hover > a.headerlink, +h3:hover > a.headerlink, +h4:hover > a.headerlink, +h5:hover > a.headerlink, +h6:hover > a.headerlink, +dt:hover > a.headerlink, +caption:hover > a.headerlink, +p.caption:hover > a.headerlink, +div.code-block-caption:hover > a.headerlink { + visibility: visible; +} + +div.body p.caption { + text-align: inherit; +} + +div.body td { + text-align: left; +} + +.first { + margin-top: 0 !important; +} + +p.rubric { + margin-top: 30px; + font-weight: bold; +} + +img.align-left, figure.align-left, .figure.align-left, object.align-left { + clear: left; + float: left; + margin-right: 1em; +} + +img.align-right, figure.align-right, .figure.align-right, object.align-right { + clear: right; + float: right; + margin-left: 1em; +} + +img.align-center, figure.align-center, .figure.align-center, object.align-center { + display: block; + margin-left: auto; + margin-right: auto; +} + +img.align-default, figure.align-default, .figure.align-default { + display: block; + margin-left: auto; + margin-right: auto; +} + +.align-left { + text-align: left; +} + +.align-center { + text-align: center; +} + +.align-default { + text-align: center; +} + +.align-right { + text-align: right; +} + +/* -- sidebars -------------------------------------------------------------- */ + +div.sidebar, +aside.sidebar { + margin: 0 0 0.5em 1em; + border: 1px solid #ddb; + padding: 7px; + background-color: #ffe; + width: 40%; + float: right; + clear: right; + overflow-x: auto; +} + +p.sidebar-title { + font-weight: bold; +} +div.admonition, div.topic, blockquote { + clear: left; +} + +/* -- topics ---------------------------------------------------------------- */ +div.topic { + border: 1px solid #ccc; + padding: 7px; + margin: 10px 0 10px 0; +} + +p.topic-title { + font-size: 1.1em; + font-weight: bold; + margin-top: 10px; +} + +/* -- admonitions ----------------------------------------------------------- */ + +div.admonition { + margin-top: 10px; + margin-bottom: 10px; + padding: 7px; +} + +div.admonition dt { + font-weight: bold; +} + +p.admonition-title { + margin: 0px 10px 5px 0px; + font-weight: bold; +} + +div.body p.centered { + text-align: center; + margin-top: 25px; +} + +/* -- content of sidebars/topics/admonitions -------------------------------- */ + +div.sidebar > :last-child, +aside.sidebar > :last-child, +div.topic > :last-child, +div.admonition > :last-child { + margin-bottom: 0; +} + +div.sidebar::after, +aside.sidebar::after, +div.topic::after, +div.admonition::after, +blockquote::after { + display: block; + content: ''; + clear: both; +} + +/* -- tables ---------------------------------------------------------------- */ + +table.docutils { + margin-top: 10px; + margin-bottom: 10px; + border: 0; + border-collapse: collapse; +} + +table.align-center { + margin-left: auto; + margin-right: auto; +} + +table.align-default { + margin-left: auto; + margin-right: auto; +} + +table caption span.caption-number { + font-style: italic; +} + +table caption span.caption-text { +} + +table.docutils td, table.docutils th { + padding: 1px 8px 1px 5px; + border-top: 0; + border-left: 0; + border-right: 0; + border-bottom: 1px solid #aaa; +} + +th { + text-align: left; + padding-right: 5px; +} + +table.citation { + border-left: solid 1px gray; + margin-left: 1px; +} + +table.citation td { + border-bottom: none; +} + +th > :first-child, +td > :first-child { + margin-top: 0px; +} + +th > :last-child, +td > :last-child { + margin-bottom: 0px; +} + +/* -- figures --------------------------------------------------------------- */ + +div.figure, figure { + margin: 0.5em; + padding: 0.5em; +} + +div.figure p.caption, figcaption { + padding: 0.3em; +} + +div.figure p.caption span.caption-number, +figcaption span.caption-number { + font-style: italic; +} + +div.figure p.caption span.caption-text, +figcaption span.caption-text { +} + +/* -- field list styles ----------------------------------------------------- */ + +table.field-list td, table.field-list th { + border: 0 !important; +} + +.field-list ul { + margin: 0; + padding-left: 1em; +} + +.field-list p { + margin: 0; +} + +.field-name { + -moz-hyphens: manual; + -ms-hyphens: manual; + -webkit-hyphens: manual; + hyphens: manual; +} + +/* -- hlist styles ---------------------------------------------------------- */ + +table.hlist { + margin: 1em 0; +} + +table.hlist td { + vertical-align: top; +} + +/* -- object description styles --------------------------------------------- */ + +.sig { + font-family: 'Consolas', 'Menlo', 'DejaVu Sans Mono', 'Bitstream Vera Sans Mono', monospace; +} + +.sig-name, code.descname { + background-color: transparent; + font-weight: bold; +} + +.sig-name { + font-size: 1.1em; +} + +code.descname { + font-size: 1.2em; +} + +.sig-prename, code.descclassname { + background-color: transparent; +} + +.optional { + font-size: 1.3em; +} + +.sig-paren { + font-size: larger; +} + +.sig-param.n { + font-style: italic; +} + +/* C++ specific styling */ + +.sig-inline.c-texpr, +.sig-inline.cpp-texpr { + font-family: unset; +} + +.sig.c .k, .sig.c .kt, +.sig.cpp .k, .sig.cpp .kt { + color: #0033B3; +} + +.sig.c .m, +.sig.cpp .m { + color: #1750EB; +} + +.sig.c .s, .sig.c .sc, +.sig.cpp .s, .sig.cpp .sc { + color: #067D17; +} + + +/* -- other body styles ----------------------------------------------------- */ + +ol.arabic { + list-style: decimal; +} + +ol.loweralpha { + list-style: lower-alpha; +} + +ol.upperalpha { + list-style: upper-alpha; +} + +ol.lowerroman { + list-style: lower-roman; +} + +ol.upperroman { + list-style: upper-roman; +} + +:not(li) > ol > li:first-child > :first-child, +:not(li) > ul > li:first-child > :first-child { + margin-top: 0px; +} + +:not(li) > ol > li:last-child > :last-child, +:not(li) > ul > li:last-child > :last-child { + margin-bottom: 0px; +} + +ol.simple ol p, +ol.simple ul p, +ul.simple ol p, +ul.simple ul p { + margin-top: 0; +} + +ol.simple > li:not(:first-child) > p, +ul.simple > li:not(:first-child) > p { + margin-top: 0; +} + +ol.simple p, +ul.simple p { + margin-bottom: 0; +} +dl.footnote > dt, +dl.citation > dt { + float: left; + margin-right: 0.5em; +} + +dl.footnote > dd, +dl.citation > dd { + margin-bottom: 0em; +} + +dl.footnote > dd:after, +dl.citation > dd:after { + content: ""; + clear: both; +} + +dl.field-list { + display: grid; + grid-template-columns: fit-content(30%) auto; +} + +dl.field-list > dt { + font-weight: bold; + word-break: break-word; + padding-left: 0.5em; + padding-right: 5px; +} +dl.field-list > dt:after { + content: ":"; +} + + +dl.field-list > dd { + padding-left: 0.5em; + margin-top: 0em; + margin-left: 0em; + margin-bottom: 0em; +} + +dl { + margin-bottom: 15px; +} + +dd > :first-child { + margin-top: 0px; +} + +dd ul, dd table { + margin-bottom: 10px; +} + +dd { + margin-top: 3px; + margin-bottom: 10px; + margin-left: 30px; +} + +dl > dd:last-child, +dl > dd:last-child > :last-child { + margin-bottom: 0; +} + +dt:target, span.highlighted { + background-color: #fbe54e; +} + +rect.highlighted { + fill: #fbe54e; +} + +dl.glossary dt { + font-weight: bold; + font-size: 1.1em; +} + +.versionmodified { + font-style: italic; +} + +.system-message { + background-color: #fda; + padding: 5px; + border: 3px solid red; +} + +.footnote:target { + background-color: #ffa; +} + +.line-block { + display: block; + margin-top: 1em; + margin-bottom: 1em; +} + +.line-block .line-block { + margin-top: 0; + margin-bottom: 0; + margin-left: 1.5em; +} + +.guilabel, .menuselection { + font-family: sans-serif; +} + +.accelerator { + text-decoration: underline; +} + +.classifier { + font-style: oblique; +} + +.classifier:before { + font-style: normal; + margin: 0 0.5em; + content: ":"; + display: inline-block; +} + +abbr, acronym { + border-bottom: dotted 1px; + cursor: help; +} + +/* -- code displays --------------------------------------------------------- */ + +pre { + overflow: auto; + overflow-y: hidden; /* fixes display issues on Chrome browsers */ +} + +pre, div[class*="highlight-"] { + clear: both; +} + +span.pre { + -moz-hyphens: none; + -ms-hyphens: none; + -webkit-hyphens: none; + hyphens: none; + white-space: nowrap; +} + +div[class*="highlight-"] { + margin: 1em 0; +} + +td.linenos pre { + border: 0; + background-color: transparent; + color: #aaa; +} + +table.highlighttable { + display: block; +} + +table.highlighttable tbody { + display: block; +} + +table.highlighttable tr { + display: flex; +} + +table.highlighttable td { + margin: 0; + padding: 0; +} + +table.highlighttable td.linenos { + padding-right: 0.5em; +} + +table.highlighttable td.code { + flex: 1; + overflow: hidden; +} + +.highlight .hll { + display: block; +} + +div.highlight pre, +table.highlighttable pre { + margin: 0; +} + +div.code-block-caption + div { + margin-top: 0; +} + +div.code-block-caption { + margin-top: 1em; + padding: 2px 5px; + font-size: small; +} + +div.code-block-caption code { + background-color: transparent; +} + +table.highlighttable td.linenos, +span.linenos, +div.highlight span.gp { /* gp: Generic.Prompt */ + user-select: none; + -webkit-user-select: text; /* Safari fallback only */ + -webkit-user-select: none; /* Chrome/Safari */ + -moz-user-select: none; /* Firefox */ + -ms-user-select: none; /* IE10+ */ +} + +div.code-block-caption span.caption-number { + padding: 0.1em 0.3em; + font-style: italic; +} + +div.code-block-caption span.caption-text { +} + +div.literal-block-wrapper { + margin: 1em 0; +} + +code.xref, a code { + background-color: transparent; + font-weight: bold; +} + +h1 code, h2 code, h3 code, h4 code, h5 code, h6 code { + background-color: transparent; +} + +.viewcode-link { + float: right; +} + +.viewcode-back { + float: right; + font-family: sans-serif; +} + +div.viewcode-block:target { + margin: -1px -10px; + padding: 0 10px; +} + +/* -- math display ---------------------------------------------------------- */ + +img.math { + vertical-align: middle; +} + +div.body div.math p { + text-align: center; +} + +span.eqno { + float: right; +} + +span.eqno a.headerlink { + position: absolute; + z-index: 1; +} + +div.math:hover a.headerlink { + visibility: visible; +} + +/* -- printout stylesheet --------------------------------------------------- */ + +@media print { + div.document, + div.documentwrapper, + div.bodywrapper { + margin: 0 !important; + width: 100%; + } + + div.sphinxsidebar, + div.related, + div.footer, + #top-link { + display: none; + } +} \ No newline at end of file diff --git a/_static/check-solid.svg b/_static/check-solid.svg new file mode 100644 index 0000000..92fad4b --- /dev/null +++ b/_static/check-solid.svg @@ -0,0 +1,4 @@ + + + + diff --git a/_static/clipboard.min.js b/_static/clipboard.min.js new file mode 100644 index 0000000..54b3c46 --- /dev/null +++ b/_static/clipboard.min.js @@ -0,0 +1,7 @@ +/*! + * clipboard.js v2.0.8 + * https://clipboardjs.com/ + * + * Licensed MIT © Zeno Rocha + */ +!function(t,e){"object"==typeof exports&&"object"==typeof module?module.exports=e():"function"==typeof define&&define.amd?define([],e):"object"==typeof exports?exports.ClipboardJS=e():t.ClipboardJS=e()}(this,function(){return n={686:function(t,e,n){"use strict";n.d(e,{default:function(){return o}});var e=n(279),i=n.n(e),e=n(370),u=n.n(e),e=n(817),c=n.n(e);function a(t){try{return document.execCommand(t)}catch(t){return}}var f=function(t){t=c()(t);return a("cut"),t};var l=function(t){var e,n,o,r=1 + + + + diff --git a/_static/copybutton.css b/_static/copybutton.css new file mode 100644 index 0000000..f1916ec --- /dev/null +++ b/_static/copybutton.css @@ -0,0 +1,94 @@ +/* Copy buttons */ +button.copybtn { + position: absolute; + display: flex; + top: .3em; + right: .3em; + width: 1.7em; + height: 1.7em; + opacity: 0; + transition: opacity 0.3s, border .3s, background-color .3s; + user-select: none; + padding: 0; + border: none; + outline: none; + border-radius: 0.4em; + /* The colors that GitHub uses */ + border: #1b1f2426 1px solid; + background-color: #f6f8fa; + color: #57606a; +} + +button.copybtn.success { + border-color: #22863a; + color: #22863a; +} + +button.copybtn svg { + stroke: currentColor; + width: 1.5em; + height: 1.5em; + padding: 0.1em; +} + +div.highlight { + position: relative; +} + +/* Show the copybutton */ +.highlight:hover button.copybtn, button.copybtn.success { + opacity: 1; +} + +.highlight button.copybtn:hover { + background-color: rgb(235, 235, 235); +} + +.highlight button.copybtn:active { + background-color: rgb(187, 187, 187); +} + +/** + * A minimal CSS-only tooltip copied from: + * https://codepen.io/mildrenben/pen/rVBrpK + * + * To use, write HTML like the following: + * + *

Short

+ */ + .o-tooltip--left { + position: relative; + } + + .o-tooltip--left:after { + opacity: 0; + visibility: hidden; + position: absolute; + content: attr(data-tooltip); + padding: .2em; + font-size: .8em; + left: -.2em; + background: grey; + color: white; + white-space: nowrap; + z-index: 2; + border-radius: 2px; + transform: translateX(-102%) translateY(0); + transition: opacity 0.2s cubic-bezier(0.64, 0.09, 0.08, 1), transform 0.2s cubic-bezier(0.64, 0.09, 0.08, 1); +} + +.o-tooltip--left:hover:after { + display: block; + opacity: 1; + visibility: visible; + transform: translateX(-100%) translateY(0); + transition: opacity 0.2s cubic-bezier(0.64, 0.09, 0.08, 1), transform 0.2s cubic-bezier(0.64, 0.09, 0.08, 1); + transition-delay: .5s; +} + +/* By default the copy button shouldn't show up when printing a page */ +@media print { + button.copybtn { + display: none; + } +} diff --git a/_static/copybutton.js b/_static/copybutton.js new file mode 100644 index 0000000..2ea7ff3 --- /dev/null +++ b/_static/copybutton.js @@ -0,0 +1,248 @@ +// Localization support +const messages = { + 'en': { + 'copy': 'Copy', + 'copy_to_clipboard': 'Copy to clipboard', + 'copy_success': 'Copied!', + 'copy_failure': 'Failed to copy', + }, + 'es' : { + 'copy': 'Copiar', + 'copy_to_clipboard': 'Copiar al portapapeles', + 'copy_success': '¡Copiado!', + 'copy_failure': 'Error al copiar', + }, + 'de' : { + 'copy': 'Kopieren', + 'copy_to_clipboard': 'In die Zwischenablage kopieren', + 'copy_success': 'Kopiert!', + 'copy_failure': 'Fehler beim Kopieren', + }, + 'fr' : { + 'copy': 'Copier', + 'copy_to_clipboard': 'Copier dans le presse-papier', + 'copy_success': 'Copié !', + 'copy_failure': 'Échec de la copie', + }, + 'ru': { + 'copy': 'Скопировать', + 'copy_to_clipboard': 'Скопировать в буфер', + 'copy_success': 'Скопировано!', + 'copy_failure': 'Не удалось скопировать', + }, + 'zh-CN': { + 'copy': '复制', + 'copy_to_clipboard': '复制到剪贴板', + 'copy_success': '复制成功!', + 'copy_failure': '复制失败', + }, + 'it' : { + 'copy': 'Copiare', + 'copy_to_clipboard': 'Copiato negli appunti', + 'copy_success': 'Copiato!', + 'copy_failure': 'Errore durante la copia', + } +} + +let locale = 'en' +if( document.documentElement.lang !== undefined + && messages[document.documentElement.lang] !== undefined ) { + locale = document.documentElement.lang +} + +let doc_url_root = DOCUMENTATION_OPTIONS.URL_ROOT; +if (doc_url_root == '#') { + doc_url_root = ''; +} + +/** + * SVG files for our copy buttons + */ +let iconCheck = ` + ${messages[locale]['copy_success']} + + +` + +// If the user specified their own SVG use that, otherwise use the default +let iconCopy = ``; +if (!iconCopy) { + iconCopy = ` + ${messages[locale]['copy_to_clipboard']} + + + +` +} + +/** + * Set up copy/paste for code blocks + */ + +const runWhenDOMLoaded = cb => { + if (document.readyState != 'loading') { + cb() + } else if (document.addEventListener) { + document.addEventListener('DOMContentLoaded', cb) + } else { + document.attachEvent('onreadystatechange', function() { + if (document.readyState == 'complete') cb() + }) + } +} + +const codeCellId = index => `codecell${index}` + +// Clears selected text since ClipboardJS will select the text when copying +const clearSelection = () => { + if (window.getSelection) { + window.getSelection().removeAllRanges() + } else if (document.selection) { + document.selection.empty() + } +} + +// Changes tooltip text for a moment, then changes it back +// We want the timeout of our `success` class to be a bit shorter than the +// tooltip and icon change, so that we can hide the icon before changing back. +var timeoutIcon = 2000; +var timeoutSuccessClass = 1500; + +const temporarilyChangeTooltip = (el, oldText, newText) => { + el.setAttribute('data-tooltip', newText) + el.classList.add('success') + // Remove success a little bit sooner than we change the tooltip + // So that we can use CSS to hide the copybutton first + setTimeout(() => el.classList.remove('success'), timeoutSuccessClass) + setTimeout(() => el.setAttribute('data-tooltip', oldText), timeoutIcon) +} + +// Changes the copy button icon for two seconds, then changes it back +const temporarilyChangeIcon = (el) => { + el.innerHTML = iconCheck; + setTimeout(() => {el.innerHTML = iconCopy}, timeoutIcon) +} + +const addCopyButtonToCodeCells = () => { + // If ClipboardJS hasn't loaded, wait a bit and try again. This + // happens because we load ClipboardJS asynchronously. + if (window.ClipboardJS === undefined) { + setTimeout(addCopyButtonToCodeCells, 250) + return + } + + // Add copybuttons to all of our code cells + const COPYBUTTON_SELECTOR = 'div.highlight pre'; + const codeCells = document.querySelectorAll(COPYBUTTON_SELECTOR) + codeCells.forEach((codeCell, index) => { + const id = codeCellId(index) + codeCell.setAttribute('id', id) + + const clipboardButton = id => + `` + codeCell.insertAdjacentHTML('afterend', clipboardButton(id)) + }) + +function escapeRegExp(string) { + return string.replace(/[.*+?^${}()|[\]\\]/g, '\\$&'); // $& means the whole matched string +} + +/** + * Removes excluded text from a Node. + * + * @param {Node} target Node to filter. + * @param {string} exclude CSS selector of nodes to exclude. + * @returns {DOMString} Text from `target` with text removed. + */ +function filterText(target, exclude) { + const clone = target.cloneNode(true); // clone as to not modify the live DOM + if (exclude) { + // remove excluded nodes + clone.querySelectorAll(exclude).forEach(node => node.remove()); + } + return clone.innerText; +} + +// Callback when a copy button is clicked. Will be passed the node that was clicked +// should then grab the text and replace pieces of text that shouldn't be used in output +function formatCopyText(textContent, copybuttonPromptText, isRegexp = false, onlyCopyPromptLines = true, removePrompts = true, copyEmptyLines = true, lineContinuationChar = "", hereDocDelim = "") { + var regexp; + var match; + + // Do we check for line continuation characters and "HERE-documents"? + var useLineCont = !!lineContinuationChar + var useHereDoc = !!hereDocDelim + + // create regexp to capture prompt and remaining line + if (isRegexp) { + regexp = new RegExp('^(' + copybuttonPromptText + ')(.*)') + } else { + regexp = new RegExp('^(' + escapeRegExp(copybuttonPromptText) + ')(.*)') + } + + const outputLines = []; + var promptFound = false; + var gotLineCont = false; + var gotHereDoc = false; + const lineGotPrompt = []; + for (const line of textContent.split('\n')) { + match = line.match(regexp) + if (match || gotLineCont || gotHereDoc) { + promptFound = regexp.test(line) + lineGotPrompt.push(promptFound) + if (removePrompts && promptFound) { + outputLines.push(match[2]) + } else { + outputLines.push(line) + } + gotLineCont = line.endsWith(lineContinuationChar) & useLineCont + if (line.includes(hereDocDelim) & useHereDoc) + gotHereDoc = !gotHereDoc + } else if (!onlyCopyPromptLines) { + outputLines.push(line) + } else if (copyEmptyLines && line.trim() === '') { + outputLines.push(line) + } + } + + // If no lines with the prompt were found then just use original lines + if (lineGotPrompt.some(v => v === true)) { + textContent = outputLines.join('\n'); + } + + // Remove a trailing newline to avoid auto-running when pasting + if (textContent.endsWith("\n")) { + textContent = textContent.slice(0, -1) + } + return textContent +} + + +var copyTargetText = (trigger) => { + var target = document.querySelector(trigger.attributes['data-clipboard-target'].value); + + // get filtered text + let exclude = '.linenos'; + + let text = filterText(target, exclude); + return formatCopyText(text, '', false, true, true, true, '', '') +} + + // Initialize with a callback so we can modify the text before copy + const clipboard = new ClipboardJS('.copybtn', {text: copyTargetText}) + + // Update UI with error/success messages + clipboard.on('success', event => { + clearSelection() + temporarilyChangeTooltip(event.trigger, messages[locale]['copy'], messages[locale]['copy_success']) + temporarilyChangeIcon(event.trigger) + }) + + clipboard.on('error', event => { + temporarilyChangeTooltip(event.trigger, messages[locale]['copy'], messages[locale]['copy_failure']) + }) +} + +runWhenDOMLoaded(addCopyButtonToCodeCells) \ No newline at end of file diff --git a/_static/copybutton_funcs.js b/_static/copybutton_funcs.js new file mode 100644 index 0000000..dbe1aaa --- /dev/null +++ b/_static/copybutton_funcs.js @@ -0,0 +1,73 @@ +function escapeRegExp(string) { + return string.replace(/[.*+?^${}()|[\]\\]/g, '\\$&'); // $& means the whole matched string +} + +/** + * Removes excluded text from a Node. + * + * @param {Node} target Node to filter. + * @param {string} exclude CSS selector of nodes to exclude. + * @returns {DOMString} Text from `target` with text removed. + */ +export function filterText(target, exclude) { + const clone = target.cloneNode(true); // clone as to not modify the live DOM + if (exclude) { + // remove excluded nodes + clone.querySelectorAll(exclude).forEach(node => node.remove()); + } + return clone.innerText; +} + +// Callback when a copy button is clicked. Will be passed the node that was clicked +// should then grab the text and replace pieces of text that shouldn't be used in output +export function formatCopyText(textContent, copybuttonPromptText, isRegexp = false, onlyCopyPromptLines = true, removePrompts = true, copyEmptyLines = true, lineContinuationChar = "", hereDocDelim = "") { + var regexp; + var match; + + // Do we check for line continuation characters and "HERE-documents"? + var useLineCont = !!lineContinuationChar + var useHereDoc = !!hereDocDelim + + // create regexp to capture prompt and remaining line + if (isRegexp) { + regexp = new RegExp('^(' + copybuttonPromptText + ')(.*)') + } else { + regexp = new RegExp('^(' + escapeRegExp(copybuttonPromptText) + ')(.*)') + } + + const outputLines = []; + var promptFound = false; + var gotLineCont = false; + var gotHereDoc = false; + const lineGotPrompt = []; + for (const line of textContent.split('\n')) { + match = line.match(regexp) + if (match || gotLineCont || gotHereDoc) { + promptFound = regexp.test(line) + lineGotPrompt.push(promptFound) + if (removePrompts && promptFound) { + outputLines.push(match[2]) + } else { + outputLines.push(line) + } + gotLineCont = line.endsWith(lineContinuationChar) & useLineCont + if (line.includes(hereDocDelim) & useHereDoc) + gotHereDoc = !gotHereDoc + } else if (!onlyCopyPromptLines) { + outputLines.push(line) + } else if (copyEmptyLines && line.trim() === '') { + outputLines.push(line) + } + } + + // If no lines with the prompt were found then just use original lines + if (lineGotPrompt.some(v => v === true)) { + textContent = outputLines.join('\n'); + } + + // Remove a trailing newline to avoid auto-running when pasting + if (textContent.endsWith("\n")) { + textContent = textContent.slice(0, -1) + } + return textContent +} diff --git a/_static/css/index.c5995385ac14fb8791e8eb36b4908be2.css b/_static/css/index.c5995385ac14fb8791e8eb36b4908be2.css new file mode 100644 index 0000000..655656d --- /dev/null +++ b/_static/css/index.c5995385ac14fb8791e8eb36b4908be2.css @@ -0,0 +1,6 @@ +/*! + * Bootstrap v4.5.0 (https://getbootstrap.com/) + * Copyright 2011-2020 The Bootstrap Authors + * Copyright 2011-2020 Twitter, Inc. + * Licensed under MIT (https://github.com/twbs/bootstrap/blob/master/LICENSE) + */:root{--blue:#007bff;--indigo:#6610f2;--purple:#6f42c1;--pink:#e83e8c;--red:#dc3545;--orange:#fd7e14;--yellow:#ffc107;--green:#28a745;--teal:#20c997;--cyan:#17a2b8;--white:#fff;--gray:#6c757d;--gray-dark:#343a40;--primary:#007bff;--secondary:#6c757d;--success:#28a745;--info:#17a2b8;--warning:#ffc107;--danger:#dc3545;--light:#f8f9fa;--dark:#343a40;--breakpoint-xs:0;--breakpoint-sm:540px;--breakpoint-md:720px;--breakpoint-lg:960px;--breakpoint-xl:1200px;--font-family-sans-serif:-apple-system,BlinkMacSystemFont,"Segoe UI",Roboto,"Helvetica Neue",Arial,"Noto Sans",sans-serif,"Apple Color Emoji","Segoe UI Emoji","Segoe UI Symbol","Noto Color 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a{color:#130754}.xr-wrap[hidden]{display:block!important}.toctree-checkbox{position:absolute;display:none}.toctree-checkbox~ul{display:none}.toctree-checkbox~label i{transform:rotate(0deg)}.toctree-checkbox:checked~ul{display:block}.toctree-checkbox:checked~label i{transform:rotate(180deg)}.bd-sidebar li{position:relative}.bd-sidebar label{position:absolute;top:0;right:0;height:30px;width:30px;cursor:pointer;display:flex;justify-content:center;align-items:center}.bd-sidebar label:hover{background:rgba(var(--pst-color-sidebar-expander-background-hover),1)}.bd-sidebar label i{display:inline-block;font-size:.75rem;text-align:center}.bd-sidebar label i:hover{color:rgba(var(--pst-color-sidebar-link-hover),1)}.bd-sidebar li.has-children>.reference{padding-right:30px}div.doctest>div.highlight span.gp,span.linenos,table.highlighttable td.linenos{user-select:none!important;-webkit-user-select:text!important;-webkit-user-select:none!important;-moz-user-select:none!important;-ms-user-select:none!important} \ No newline at end of file diff --git a/_static/css/theme.css b/_static/css/theme.css new file mode 100644 index 0000000..3f6e79d --- /dev/null +++ b/_static/css/theme.css @@ -0,0 +1,117 @@ +:root { + /***************************************************************************** + * Theme config + **/ + --pst-header-height: 60px; + + /***************************************************************************** + * Font size + **/ + --pst-font-size-base: 15px; /* base font size - applied at body / html level */ + + /* heading font sizes */ + --pst-font-size-h1: 36px; + --pst-font-size-h2: 32px; + --pst-font-size-h3: 26px; + --pst-font-size-h4: 21px; + --pst-font-size-h5: 18px; + --pst-font-size-h6: 16px; + + /* smaller then heading font sizes*/ + --pst-font-size-milli: 12px; + + --pst-sidebar-font-size: .9em; + --pst-sidebar-caption-font-size: .9em; + + /***************************************************************************** + * Font family + **/ + /* These are adapted from https://systemfontstack.com/ */ + --pst-font-family-base-system: -apple-system, BlinkMacSystemFont, Segoe UI, "Helvetica Neue", + Arial, sans-serif, Apple Color Emoji, Segoe UI Emoji, Segoe UI Symbol; + --pst-font-family-monospace-system: "SFMono-Regular", Menlo, Consolas, Monaco, + Liberation Mono, Lucida Console, monospace; + + --pst-font-family-base: var(--pst-font-family-base-system); + --pst-font-family-heading: var(--pst-font-family-base); + --pst-font-family-monospace: var(--pst-font-family-monospace-system); + + /***************************************************************************** + * Color + * + * Colors are defined in rgb string way, "red, green, blue" + **/ + --pst-color-primary: 19, 6, 84; + --pst-color-success: 40, 167, 69; + --pst-color-info: 0, 123, 255; /*23, 162, 184;*/ + --pst-color-warning: 255, 193, 7; + --pst-color-danger: 220, 53, 69; + --pst-color-text-base: 51, 51, 51; + + --pst-color-h1: var(--pst-color-primary); + --pst-color-h2: var(--pst-color-primary); + --pst-color-h3: var(--pst-color-text-base); + --pst-color-h4: var(--pst-color-text-base); + --pst-color-h5: var(--pst-color-text-base); + --pst-color-h6: var(--pst-color-text-base); + --pst-color-paragraph: var(--pst-color-text-base); + --pst-color-link: 0, 91, 129; + --pst-color-link-hover: 227, 46, 0; + --pst-color-headerlink: 198, 15, 15; + --pst-color-headerlink-hover: 255, 255, 255; + --pst-color-preformatted-text: 34, 34, 34; + --pst-color-preformatted-background: 250, 250, 250; + --pst-color-inline-code: 232, 62, 140; + + --pst-color-active-navigation: 19, 6, 84; + --pst-color-navbar-link: 77, 77, 77; + --pst-color-navbar-link-hover: var(--pst-color-active-navigation); + --pst-color-navbar-link-active: var(--pst-color-active-navigation); + --pst-color-sidebar-link: 77, 77, 77; + --pst-color-sidebar-link-hover: var(--pst-color-active-navigation); + --pst-color-sidebar-link-active: var(--pst-color-active-navigation); + --pst-color-sidebar-expander-background-hover: 244, 244, 244; + --pst-color-sidebar-caption: 77, 77, 77; + --pst-color-toc-link: 119, 117, 122; + --pst-color-toc-link-hover: var(--pst-color-active-navigation); + --pst-color-toc-link-active: var(--pst-color-active-navigation); + + /***************************************************************************** + * Icon + **/ + + /* font awesome icons*/ + --pst-icon-check-circle: '\f058'; + --pst-icon-info-circle: '\f05a'; + --pst-icon-exclamation-triangle: '\f071'; + --pst-icon-exclamation-circle: '\f06a'; + --pst-icon-times-circle: '\f057'; + --pst-icon-lightbulb: '\f0eb'; + + /***************************************************************************** + * Admonitions + **/ + + --pst-color-admonition-default: var(--pst-color-info); + --pst-color-admonition-note: var(--pst-color-info); + --pst-color-admonition-attention: var(--pst-color-warning); + --pst-color-admonition-caution: var(--pst-color-warning); + --pst-color-admonition-warning: var(--pst-color-warning); + --pst-color-admonition-danger: var(--pst-color-danger); + --pst-color-admonition-error: var(--pst-color-danger); + --pst-color-admonition-hint: var(--pst-color-success); + --pst-color-admonition-tip: var(--pst-color-success); + --pst-color-admonition-important: var(--pst-color-success); + + --pst-icon-admonition-default: var(--pst-icon-info-circle); + --pst-icon-admonition-note: var(--pst-icon-info-circle); + --pst-icon-admonition-attention: var(--pst-icon-exclamation-circle); + --pst-icon-admonition-caution: var(--pst-icon-exclamation-triangle); + --pst-icon-admonition-warning: var(--pst-icon-exclamation-triangle); + --pst-icon-admonition-danger: var(--pst-icon-exclamation-triangle); + --pst-icon-admonition-error: var(--pst-icon-times-circle); + --pst-icon-admonition-hint: var(--pst-icon-lightbulb); + --pst-icon-admonition-tip: var(--pst-icon-lightbulb); + --pst-icon-admonition-important: var(--pst-icon-exclamation-circle); + +} diff --git a/_static/design-tabs.js b/_static/design-tabs.js new file mode 100644 index 0000000..b25bd6a --- /dev/null +++ b/_static/design-tabs.js @@ -0,0 +1,101 @@ +// @ts-check + +// Extra JS capability for selected tabs to be synced +// The selection is stored in local storage so that it persists across page loads. + +/** + * @type {Record} + */ +let sd_id_to_elements = {}; +const storageKeyPrefix = "sphinx-design-tab-id-"; + +/** + * Create a key for a tab element. + * @param {HTMLElement} el - The tab element. + * @returns {[string, string, string] | null} - The key. + * + */ +function create_key(el) { + let syncId = el.getAttribute("data-sync-id"); + let syncGroup = el.getAttribute("data-sync-group"); + if (!syncId || !syncGroup) return null; + return [syncGroup, syncId, syncGroup + "--" + syncId]; +} + +/** + * Initialize the tab selection. + * + */ +function ready() { + // Find all tabs with sync data + + /** @type {string[]} */ + let groups = []; + + document.querySelectorAll(".sd-tab-label").forEach((label) => { + if (label instanceof HTMLElement) { + let data = create_key(label); + if (data) { + let [group, id, key] = data; + + // add click event listener + // @ts-ignore + label.onclick = onSDLabelClick; + + // store map of key to elements + if (!sd_id_to_elements[key]) { + sd_id_to_elements[key] = []; + } + sd_id_to_elements[key].push(label); + + if (groups.indexOf(group) === -1) { + groups.push(group); + // Check if a specific tab has been selected via URL parameter + const tabParam = new URLSearchParams(window.location.search).get( + group + ); + if (tabParam) { + console.log( + "sphinx-design: Selecting tab id for group '" + + group + + "' from URL parameter: " + + tabParam + ); + window.sessionStorage.setItem(storageKeyPrefix + group, tabParam); + } + } + + // Check is a specific tab has been selected previously + let previousId = window.sessionStorage.getItem( + storageKeyPrefix + group + ); + if (previousId === id) { + // console.log( + // "sphinx-design: Selecting tab from session storage: " + id + // ); + // @ts-ignore + label.previousElementSibling.checked = true; + } + } + } + }); +} + +/** + * Activate other tabs with the same sync id. + * + * @this {HTMLElement} - The element that was clicked. + */ +function onSDLabelClick() { + let data = create_key(this); + if (!data) return; + let [group, id, key] = data; + for (const label of sd_id_to_elements[key]) { + if (label === this) continue; + // @ts-ignore + label.previousElementSibling.checked = true; + } + window.sessionStorage.setItem(storageKeyPrefix + group, id); +} + +document.addEventListener("DOMContentLoaded", ready, false); diff --git a/_static/doctools.js b/_static/doctools.js new file mode 100644 index 0000000..527b876 --- /dev/null +++ b/_static/doctools.js @@ -0,0 +1,156 @@ +/* + * doctools.js + * ~~~~~~~~~~~ + * + * Base JavaScript utilities for all Sphinx HTML documentation. + * + * :copyright: Copyright 2007-2022 by the Sphinx team, see AUTHORS. + * :license: BSD, see LICENSE for details. + * + */ +"use strict"; + +const BLACKLISTED_KEY_CONTROL_ELEMENTS = new Set([ + "TEXTAREA", + "INPUT", + "SELECT", + "BUTTON", +]); + +const _ready = (callback) => { + if (document.readyState !== "loading") { + callback(); + } else { + document.addEventListener("DOMContentLoaded", callback); + } +}; + +/** + * Small JavaScript module for the documentation. + */ +const Documentation = { + init: () => { + Documentation.initDomainIndexTable(); + Documentation.initOnKeyListeners(); + }, + + /** + * i18n support + */ + TRANSLATIONS: {}, + PLURAL_EXPR: (n) => (n === 1 ? 0 : 1), + LOCALE: "unknown", + + // gettext and ngettext don't access this so that the functions + // can safely bound to a different name (_ = Documentation.gettext) + gettext: (string) => { + const translated = Documentation.TRANSLATIONS[string]; + switch (typeof translated) { + case "undefined": + return string; // no translation + case "string": + return translated; // translation exists + default: + return translated[0]; // (singular, plural) translation tuple exists + } + }, + + ngettext: (singular, plural, n) => { + const translated = Documentation.TRANSLATIONS[singular]; + if (typeof translated !== "undefined") + return translated[Documentation.PLURAL_EXPR(n)]; + return n === 1 ? singular : plural; + }, + + addTranslations: (catalog) => { + Object.assign(Documentation.TRANSLATIONS, catalog.messages); + Documentation.PLURAL_EXPR = new Function( + "n", + `return (${catalog.plural_expr})` + ); + Documentation.LOCALE = catalog.locale; + }, + + /** + * helper function to focus on search bar + */ + focusSearchBar: () => { + document.querySelectorAll("input[name=q]")[0]?.focus(); + }, + + /** + * Initialise the domain index toggle buttons + */ + initDomainIndexTable: () => { + const toggler = (el) => { + const idNumber = el.id.substr(7); + const toggledRows = document.querySelectorAll(`tr.cg-${idNumber}`); + if (el.src.substr(-9) === "minus.png") { + el.src = `${el.src.substr(0, el.src.length - 9)}plus.png`; + toggledRows.forEach((el) => (el.style.display = "none")); + } else { + el.src = `${el.src.substr(0, el.src.length - 8)}minus.png`; + toggledRows.forEach((el) => (el.style.display = "")); + } + }; + + const togglerElements = document.querySelectorAll("img.toggler"); + togglerElements.forEach((el) => + el.addEventListener("click", (event) => toggler(event.currentTarget)) + ); + togglerElements.forEach((el) => (el.style.display = "")); + if (DOCUMENTATION_OPTIONS.COLLAPSE_INDEX) togglerElements.forEach(toggler); + }, + + initOnKeyListeners: () => { + // only install a listener if it is really needed + if ( + !DOCUMENTATION_OPTIONS.NAVIGATION_WITH_KEYS && + !DOCUMENTATION_OPTIONS.ENABLE_SEARCH_SHORTCUTS + ) + return; + + document.addEventListener("keydown", (event) => { + // bail for input elements + if (BLACKLISTED_KEY_CONTROL_ELEMENTS.has(document.activeElement.tagName)) return; + // bail with special keys + if (event.altKey || event.ctrlKey || event.metaKey) return; + + if (!event.shiftKey) { + switch (event.key) { + case "ArrowLeft": + if (!DOCUMENTATION_OPTIONS.NAVIGATION_WITH_KEYS) break; + + const prevLink = document.querySelector('link[rel="prev"]'); + if (prevLink && prevLink.href) { + window.location.href = prevLink.href; + event.preventDefault(); + } + break; + case "ArrowRight": + if (!DOCUMENTATION_OPTIONS.NAVIGATION_WITH_KEYS) break; + + const nextLink = document.querySelector('link[rel="next"]'); + if (nextLink && nextLink.href) { + window.location.href = nextLink.href; + event.preventDefault(); + } + break; + } + } + + // some keyboard layouts may need Shift to get / + switch (event.key) { + case "/": + if (!DOCUMENTATION_OPTIONS.ENABLE_SEARCH_SHORTCUTS) break; + Documentation.focusSearchBar(); + event.preventDefault(); + } + }); + }, +}; + +// quick alias for translations +const _ = Documentation.gettext; + +_ready(Documentation.init); diff --git a/_static/documentation_options.js b/_static/documentation_options.js new file mode 100644 index 0000000..05f76e7 --- /dev/null +++ b/_static/documentation_options.js @@ -0,0 +1,14 @@ +var DOCUMENTATION_OPTIONS = { + URL_ROOT: document.getElementById("documentation_options").getAttribute('data-url_root'), + VERSION: '', + LANGUAGE: 'en', + COLLAPSE_INDEX: false, + BUILDER: 'html', + FILE_SUFFIX: '.html', + LINK_SUFFIX: '.html', + HAS_SOURCE: true, + SOURCELINK_SUFFIX: '', + NAVIGATION_WITH_KEYS: false, + SHOW_SEARCH_SUMMARY: true, + ENABLE_SEARCH_SHORTCUTS: true, +}; \ No newline at end of file diff --git a/_static/file.png b/_static/file.png new file mode 100644 index 0000000..a858a41 Binary files /dev/null and b/_static/file.png differ diff --git a/_static/images/logo_binder.svg b/_static/images/logo_binder.svg new file mode 100644 index 0000000..45fecf7 --- /dev/null +++ b/_static/images/logo_binder.svg @@ -0,0 +1,19 @@ + + + + +logo + + + + + + + + diff --git a/_static/images/logo_colab.png b/_static/images/logo_colab.png new file mode 100644 index 0000000..b7560ec Binary files /dev/null and b/_static/images/logo_colab.png differ diff --git a/_static/images/logo_deepnote.svg b/_static/images/logo_deepnote.svg new file mode 100644 index 0000000..fa77ebf --- /dev/null +++ b/_static/images/logo_deepnote.svg @@ -0,0 +1 @@ + diff --git a/_static/images/logo_jupyterhub.svg b/_static/images/logo_jupyterhub.svg new file mode 100644 index 0000000..60cfe9f --- /dev/null +++ b/_static/images/logo_jupyterhub.svg @@ -0,0 +1 @@ +logo_jupyterhubHub diff --git a/_static/jquery-3.5.1.js b/_static/jquery-3.5.1.js new file mode 100644 index 0000000..5093733 --- /dev/null +++ b/_static/jquery-3.5.1.js @@ -0,0 +1,10872 @@ +/*! + * jQuery JavaScript Library v3.5.1 + * https://jquery.com/ + * + * Includes Sizzle.js + * https://sizzlejs.com/ + * + * Copyright JS Foundation and other contributors + * Released under the MIT license + * https://jquery.org/license + * + * Date: 2020-05-04T22:49Z + */ +( function( global, factory ) { + + "use strict"; + + if ( typeof module === "object" && typeof module.exports === "object" ) { + + // For CommonJS and CommonJS-like environments where a proper `window` + // is present, execute the factory and get jQuery. + // For environments that do not have a `window` with a `document` + // (such as Node.js), expose a factory as module.exports. + // This accentuates the need for the creation of a real `window`. + // e.g. var jQuery = require("jquery")(window); + // See ticket #14549 for more info. + module.exports = global.document ? + factory( global, true ) : + function( w ) { + if ( !w.document ) { + throw new Error( "jQuery requires a window with a document" ); + } + return factory( w ); + }; + } else { + factory( global ); + } + +// Pass this if window is not defined yet +} )( typeof window !== "undefined" ? window : this, function( window, noGlobal ) { + +// Edge <= 12 - 13+, Firefox <=18 - 45+, IE 10 - 11, Safari 5.1 - 9+, iOS 6 - 9.1 +// throw exceptions when non-strict code (e.g., ASP.NET 4.5) accesses strict mode +// arguments.callee.caller (trac-13335). But as of jQuery 3.0 (2016), strict mode should be common +// enough that all such attempts are guarded in a try block. +"use strict"; + +var arr = []; + +var getProto = Object.getPrototypeOf; + +var slice = arr.slice; + +var flat = arr.flat ? function( array ) { + return arr.flat.call( array ); +} : function( array ) { + return arr.concat.apply( [], array ); +}; + + +var push = arr.push; + +var indexOf = arr.indexOf; + +var class2type = {}; + +var toString = class2type.toString; + +var hasOwn = class2type.hasOwnProperty; + +var fnToString = hasOwn.toString; + +var ObjectFunctionString = fnToString.call( Object ); + +var support = {}; + +var isFunction = function isFunction( obj ) { + + // Support: Chrome <=57, Firefox <=52 + // In some browsers, typeof returns "function" for HTML elements + // (i.e., `typeof document.createElement( "object" ) === "function"`). + // We don't want to classify *any* DOM node as a function. + return typeof obj === "function" && typeof obj.nodeType !== "number"; + }; + + +var isWindow = function isWindow( obj ) { + return obj != null && obj === obj.window; + }; + + +var document = window.document; + + + + var preservedScriptAttributes = { + type: true, + src: true, + nonce: true, + noModule: true + }; + + function DOMEval( code, node, doc ) { + doc = doc || document; + + var i, val, + script = doc.createElement( "script" ); + + script.text = code; + if ( node ) { + for ( i in preservedScriptAttributes ) { + + // Support: Firefox 64+, Edge 18+ + // Some browsers don't support the "nonce" property on scripts. + // On the other hand, just using `getAttribute` is not enough as + // the `nonce` attribute is reset to an empty string whenever it + // becomes browsing-context connected. + // See https://github.com/whatwg/html/issues/2369 + // See https://html.spec.whatwg.org/#nonce-attributes + // The `node.getAttribute` check was added for the sake of + // `jQuery.globalEval` so that it can fake a nonce-containing node + // via an object. + val = node[ i ] || node.getAttribute && node.getAttribute( i ); + if ( val ) { + script.setAttribute( i, val ); + } + } + } + doc.head.appendChild( script ).parentNode.removeChild( script ); + } + + +function toType( obj ) { + if ( obj == null ) { + return obj + ""; + } + + // Support: Android <=2.3 only (functionish RegExp) + return typeof obj === "object" || typeof obj === "function" ? + class2type[ toString.call( obj ) ] || "object" : + typeof obj; +} +/* global Symbol */ +// Defining this global in .eslintrc.json would create a danger of using the global +// unguarded in another place, it seems safer to define global only for this module + + + +var + version = "3.5.1", + + // Define a local copy of jQuery + jQuery = function( selector, context ) { + + // The jQuery object is actually just the init constructor 'enhanced' + // Need init if jQuery is called (just allow error to be thrown if not included) + return new jQuery.fn.init( selector, context ); + }; + +jQuery.fn = jQuery.prototype = { + + // The current version of jQuery being used + jquery: version, + + constructor: jQuery, + + // The default length of a jQuery object is 0 + length: 0, + + toArray: function() { + return slice.call( this ); + }, + + // Get the Nth element in the matched element set OR + // Get the whole matched element set as a clean array + get: function( num ) { + + // Return all the elements in a clean array + if ( num == null ) { + return slice.call( this ); + } + + // Return just the one element from the set + return num < 0 ? this[ num + this.length ] : this[ num ]; + }, + + // Take an array of elements and push it onto the stack + // (returning the new matched element set) + pushStack: function( elems ) { + + // Build a new jQuery matched element set + var ret = jQuery.merge( this.constructor(), elems ); + + // Add the old object onto the stack (as a reference) + ret.prevObject = this; + + // Return the newly-formed element set + return ret; + }, + + // Execute a callback for every element in the matched set. + each: function( callback ) { + return jQuery.each( this, callback ); + }, + + map: function( callback ) { + return this.pushStack( jQuery.map( this, function( elem, i ) { + return callback.call( elem, i, elem ); + } ) ); + }, + + slice: function() { + return this.pushStack( slice.apply( this, arguments ) ); + }, + + first: function() { + return this.eq( 0 ); + }, + + last: function() { + return this.eq( -1 ); + }, + + even: function() { + return this.pushStack( jQuery.grep( this, function( _elem, i ) { + return ( i + 1 ) % 2; + } ) ); + }, + + odd: function() { + return this.pushStack( jQuery.grep( this, function( _elem, i ) { + return i % 2; + } ) ); + }, + + eq: function( i ) { + var len = this.length, + j = +i + ( i < 0 ? len : 0 ); + return this.pushStack( j >= 0 && j < len ? [ this[ j ] ] : [] ); + }, + + end: function() { + return this.prevObject || this.constructor(); + }, + + // For internal use only. + // Behaves like an Array's method, not like a jQuery method. + push: push, + sort: arr.sort, + splice: arr.splice +}; + +jQuery.extend = jQuery.fn.extend = function() { + var options, name, src, copy, copyIsArray, clone, + target = arguments[ 0 ] || {}, + i = 1, + length = arguments.length, + deep = false; + + // Handle a deep copy situation + if ( typeof target === "boolean" ) { + deep = target; + + // Skip the boolean and the target + target = arguments[ i ] || {}; + i++; + } + + // Handle case when target is a string or something (possible in deep copy) + if ( typeof target !== "object" && !isFunction( target ) ) { + target = {}; + } + + // Extend jQuery itself if only one argument is passed + if ( i === length ) { + target = this; + i--; + } + + for ( ; i < length; i++ ) { + + // Only deal with non-null/undefined values + if ( ( options = arguments[ i ] ) != null ) { + + // Extend the base object + for ( name in options ) { + copy = options[ name ]; + + // Prevent Object.prototype pollution + // Prevent never-ending loop + if ( name === "__proto__" || target === copy ) { + continue; + } + + // Recurse if we're merging plain objects or arrays + if ( deep && copy && ( jQuery.isPlainObject( copy ) || + ( copyIsArray = Array.isArray( copy ) ) ) ) { + src = target[ name ]; + + // Ensure proper type for the source value + if ( copyIsArray && !Array.isArray( src ) ) { + clone = []; + } else if ( !copyIsArray && !jQuery.isPlainObject( src ) ) { + clone = {}; + } else { + clone = src; + } + copyIsArray = false; + + // Never move original objects, clone them + target[ name ] = jQuery.extend( deep, clone, copy ); + + // Don't bring in undefined values + } else if ( copy !== undefined ) { + target[ name ] = copy; + } + } + } + } + + // Return the modified object + return target; +}; + +jQuery.extend( { + + // Unique for each copy of jQuery on the page + expando: "jQuery" + ( version + Math.random() ).replace( /\D/g, "" ), + + // Assume jQuery is ready without the ready module + isReady: true, + + error: function( msg ) { + throw new Error( msg ); + }, + + noop: function() {}, + + isPlainObject: function( obj ) { + var proto, Ctor; + + // Detect obvious negatives + // Use toString instead of jQuery.type to catch host objects + if ( !obj || toString.call( obj ) !== "[object Object]" ) { + return false; + } + + proto = getProto( obj ); + + // Objects with no prototype (e.g., `Object.create( null )`) are plain + if ( !proto ) { + return true; + } + + // Objects with prototype are plain iff they were constructed by a global Object function + Ctor = hasOwn.call( proto, "constructor" ) && proto.constructor; + return typeof Ctor === "function" && fnToString.call( Ctor ) === ObjectFunctionString; + }, + + isEmptyObject: function( obj ) { + var name; + + for ( name in obj ) { + return false; + } + return true; + }, + + // Evaluates a script in a provided context; falls back to the global one + // if not specified. + globalEval: function( code, options, doc ) { + DOMEval( code, { nonce: options && options.nonce }, doc ); + }, + + each: function( obj, callback ) { + var length, i = 0; + + if ( isArrayLike( obj ) ) { + length = obj.length; + for ( ; i < length; i++ ) { + if ( callback.call( obj[ i ], i, obj[ i ] ) === false ) { + break; + } + } + } else { + for ( i in obj ) { + if ( callback.call( obj[ i ], i, obj[ i ] ) === false ) { + break; + } + } + } + + return obj; + }, + + // results is for internal usage only + makeArray: function( arr, results ) { + var ret = results || []; + + if ( arr != null ) { + if ( isArrayLike( Object( arr ) ) ) { + jQuery.merge( ret, + typeof arr === "string" ? + [ arr ] : arr + ); + } else { + push.call( ret, arr ); + } + } + + return ret; + }, + + inArray: function( elem, arr, i ) { + return arr == null ? -1 : indexOf.call( arr, elem, i ); + }, + + // Support: Android <=4.0 only, PhantomJS 1 only + // push.apply(_, arraylike) throws on ancient WebKit + merge: function( first, second ) { + var len = +second.length, + j = 0, + i = first.length; + + for ( ; j < len; j++ ) { + first[ i++ ] = second[ j ]; + } + + first.length = i; + + return first; + }, + + grep: function( elems, callback, invert ) { + var callbackInverse, + matches = [], + i = 0, + length = elems.length, + callbackExpect = !invert; + + // Go through the array, only saving the items + // that pass the validator function + for ( ; i < length; i++ ) { + callbackInverse = !callback( elems[ i ], i ); + if ( callbackInverse !== callbackExpect ) { + matches.push( elems[ i ] ); + } + } + + return matches; + }, + + // arg is for internal usage only + map: function( elems, callback, arg ) { + var length, value, + i = 0, + ret = []; + + // Go through the array, translating each of the items to their new values + if ( isArrayLike( elems ) ) { + length = elems.length; + for ( ; i < length; i++ ) { + value = callback( elems[ i ], i, arg ); + + if ( value != null ) { + ret.push( value ); + } + } + + // Go through every key on the object, + } else { + for ( i in elems ) { + value = callback( elems[ i ], i, arg ); + + if ( value != null ) { + ret.push( value ); + } + } + } + + // Flatten any nested arrays + return flat( ret ); + }, + + // A global GUID counter for objects + guid: 1, + + // jQuery.support is not used in Core but other projects attach their + // properties to it so it needs to exist. + support: support +} ); + +if ( typeof Symbol === "function" ) { + jQuery.fn[ Symbol.iterator ] = arr[ Symbol.iterator ]; +} + +// Populate the class2type map +jQuery.each( "Boolean Number String Function Array Date RegExp Object Error Symbol".split( " " ), +function( _i, name ) { + class2type[ "[object " + name + "]" ] = name.toLowerCase(); +} ); + +function isArrayLike( obj ) { + + // Support: real iOS 8.2 only (not reproducible in simulator) + // `in` check used to prevent JIT error (gh-2145) + // hasOwn isn't used here due to false negatives + // regarding Nodelist length in IE + var length = !!obj && "length" in obj && obj.length, + type = toType( obj ); + + if ( isFunction( obj ) || isWindow( obj ) ) { + return false; + } + + return type === "array" || length === 0 || + typeof length === "number" && length > 0 && ( length - 1 ) in obj; +} +var Sizzle = +/*! + * Sizzle CSS Selector Engine v2.3.5 + * https://sizzlejs.com/ + * + * Copyright JS Foundation and other contributors + * Released under the MIT license + * https://js.foundation/ + * + * Date: 2020-03-14 + */ +( function( window ) { +var i, + support, + Expr, + getText, + isXML, + tokenize, + compile, + select, + outermostContext, + sortInput, + hasDuplicate, + + // Local document vars + setDocument, + document, + docElem, + documentIsHTML, + rbuggyQSA, + rbuggyMatches, + matches, + contains, + + // Instance-specific data + expando = "sizzle" + 1 * new Date(), + preferredDoc = window.document, + dirruns = 0, + done = 0, + classCache = createCache(), + tokenCache = createCache(), + compilerCache = createCache(), + nonnativeSelectorCache = createCache(), + sortOrder = function( a, b ) { + if ( a === b ) { + hasDuplicate = true; + } + return 0; + }, + + // Instance methods + hasOwn = ( {} ).hasOwnProperty, + arr = [], + pop = arr.pop, + pushNative = arr.push, + push = arr.push, + slice = arr.slice, + + // Use a stripped-down indexOf as it's faster than native + // https://jsperf.com/thor-indexof-vs-for/5 + indexOf = function( list, elem ) { + var i = 0, + len = list.length; + for ( ; i < len; i++ ) { + if ( list[ i ] === elem ) { + return i; + } + } + return -1; + }, + + booleans = "checked|selected|async|autofocus|autoplay|controls|defer|disabled|hidden|" + + "ismap|loop|multiple|open|readonly|required|scoped", + + // Regular expressions + + // http://www.w3.org/TR/css3-selectors/#whitespace + whitespace = "[\\x20\\t\\r\\n\\f]", + + // https://www.w3.org/TR/css-syntax-3/#ident-token-diagram + identifier = "(?:\\\\[\\da-fA-F]{1,6}" + whitespace + + "?|\\\\[^\\r\\n\\f]|[\\w-]|[^\0-\\x7f])+", + + // Attribute selectors: http://www.w3.org/TR/selectors/#attribute-selectors + attributes = "\\[" + whitespace + "*(" + identifier + ")(?:" + whitespace + + + // Operator (capture 2) + "*([*^$|!~]?=)" + whitespace + + + // "Attribute values must be CSS identifiers [capture 5] + // or strings [capture 3 or capture 4]" + "*(?:'((?:\\\\.|[^\\\\'])*)'|\"((?:\\\\.|[^\\\\\"])*)\"|(" + identifier + "))|)" + + whitespace + "*\\]", + + pseudos = ":(" + identifier + ")(?:\\((" + + + // To reduce the number of selectors needing tokenize in the preFilter, prefer arguments: + // 1. quoted (capture 3; capture 4 or capture 5) + "('((?:\\\\.|[^\\\\'])*)'|\"((?:\\\\.|[^\\\\\"])*)\")|" + + + // 2. simple (capture 6) + "((?:\\\\.|[^\\\\()[\\]]|" + attributes + ")*)|" + + + // 3. anything else (capture 2) + ".*" + + ")\\)|)", + + // Leading and non-escaped trailing whitespace, capturing some non-whitespace characters preceding the latter + rwhitespace = new RegExp( whitespace + "+", "g" ), + rtrim = new RegExp( "^" + whitespace + "+|((?:^|[^\\\\])(?:\\\\.)*)" + + whitespace + "+$", "g" ), + + rcomma = new RegExp( "^" + whitespace + "*," + whitespace + "*" ), + rcombinators = new RegExp( "^" + whitespace + "*([>+~]|" + whitespace + ")" + whitespace + + "*" ), + rdescend = new RegExp( whitespace + "|>" ), + + rpseudo = new RegExp( pseudos ), + ridentifier = new RegExp( "^" + identifier + "$" ), + + matchExpr = { + "ID": new RegExp( "^#(" + identifier + ")" ), + "CLASS": new RegExp( "^\\.(" + identifier + ")" ), + "TAG": new RegExp( "^(" + identifier + "|[*])" ), + "ATTR": new RegExp( "^" + attributes ), + "PSEUDO": new RegExp( "^" + pseudos ), + "CHILD": new RegExp( "^:(only|first|last|nth|nth-last)-(child|of-type)(?:\\(" + + whitespace + "*(even|odd|(([+-]|)(\\d*)n|)" + whitespace + "*(?:([+-]|)" + + whitespace + "*(\\d+)|))" + whitespace + "*\\)|)", "i" ), + "bool": new RegExp( "^(?:" + booleans + ")$", "i" ), + + // For use in libraries implementing .is() + // We use this for POS matching in `select` + "needsContext": new RegExp( "^" + whitespace + + "*[>+~]|:(even|odd|eq|gt|lt|nth|first|last)(?:\\(" + whitespace + + "*((?:-\\d)?\\d*)" + whitespace + "*\\)|)(?=[^-]|$)", "i" ) + }, + + rhtml = /HTML$/i, + rinputs = /^(?:input|select|textarea|button)$/i, + rheader = /^h\d$/i, + + rnative = /^[^{]+\{\s*\[native \w/, + + // Easily-parseable/retrievable ID or TAG or CLASS selectors + rquickExpr = /^(?:#([\w-]+)|(\w+)|\.([\w-]+))$/, + + rsibling = /[+~]/, + + // CSS escapes + // http://www.w3.org/TR/CSS21/syndata.html#escaped-characters + runescape = new RegExp( "\\\\[\\da-fA-F]{1,6}" + whitespace + "?|\\\\([^\\r\\n\\f])", "g" ), + funescape = function( escape, nonHex ) { + var high = "0x" + escape.slice( 1 ) - 0x10000; + + return nonHex ? + + // Strip the backslash prefix from a non-hex escape sequence + nonHex : + + // Replace a hexadecimal escape sequence with the encoded Unicode code point + // Support: IE <=11+ + // For values outside the Basic Multilingual Plane (BMP), manually construct a + // surrogate pair + high < 0 ? + String.fromCharCode( high + 0x10000 ) : + String.fromCharCode( high >> 10 | 0xD800, high & 0x3FF | 0xDC00 ); + }, + + // CSS string/identifier serialization + // https://drafts.csswg.org/cssom/#common-serializing-idioms + rcssescape = /([\0-\x1f\x7f]|^-?\d)|^-$|[^\0-\x1f\x7f-\uFFFF\w-]/g, + fcssescape = function( ch, asCodePoint ) { + if ( asCodePoint ) { + + // U+0000 NULL becomes U+FFFD REPLACEMENT CHARACTER + if ( ch === "\0" ) { + return "\uFFFD"; + } + + // Control characters and (dependent upon position) numbers get escaped as code points + return ch.slice( 0, -1 ) + "\\" + + ch.charCodeAt( ch.length - 1 ).toString( 16 ) + " "; + } + + // Other potentially-special ASCII characters get backslash-escaped + return "\\" + ch; + }, + + // Used for iframes + // See setDocument() + // Removing the function wrapper causes a "Permission Denied" + // error in IE + unloadHandler = function() { + setDocument(); + }, + + inDisabledFieldset = addCombinator( + function( elem ) { + return elem.disabled === true && elem.nodeName.toLowerCase() === "fieldset"; + }, + { dir: "parentNode", next: "legend" } + ); + +// Optimize for push.apply( _, NodeList ) +try { + push.apply( + ( arr = slice.call( preferredDoc.childNodes ) ), + preferredDoc.childNodes + ); + + // Support: Android<4.0 + // Detect silently failing push.apply + // eslint-disable-next-line no-unused-expressions + arr[ preferredDoc.childNodes.length ].nodeType; +} catch ( e ) { + push = { apply: arr.length ? + + // Leverage slice if possible + function( target, els ) { + pushNative.apply( target, slice.call( els ) ); + } : + + // Support: IE<9 + // Otherwise append directly + function( target, els ) { + var j = target.length, + i = 0; + + // Can't trust NodeList.length + while ( ( target[ j++ ] = els[ i++ ] ) ) {} + target.length = j - 1; + } + }; +} + +function Sizzle( selector, context, results, seed ) { + var m, i, elem, nid, match, groups, newSelector, + newContext = context && context.ownerDocument, + + // nodeType defaults to 9, since context defaults to document + nodeType = context ? context.nodeType : 9; + + results = results || []; + + // Return early from calls with invalid selector or context + if ( typeof selector !== "string" || !selector || + nodeType !== 1 && nodeType !== 9 && nodeType !== 11 ) { + + return results; + } + + // Try to shortcut find operations (as opposed to filters) in HTML documents + if ( !seed ) { + setDocument( context ); + context = context || document; + + if ( documentIsHTML ) { + + // If the selector is sufficiently simple, try using a "get*By*" DOM method + // (excepting DocumentFragment context, where the methods don't exist) + if ( nodeType !== 11 && ( match = rquickExpr.exec( selector ) ) ) { + + // ID selector + if ( ( m = match[ 1 ] ) ) { + + // Document context + if ( nodeType === 9 ) { + if ( ( elem = context.getElementById( m ) ) ) { + + // Support: IE, Opera, Webkit + // TODO: identify versions + // getElementById can match elements by name instead of ID + if ( elem.id === m ) { + results.push( elem ); + return results; + } + } else { + return results; + } + + // Element context + } else { + + // Support: IE, Opera, Webkit + // TODO: identify versions + // getElementById can match elements by name instead of ID + if ( newContext && ( elem = newContext.getElementById( m ) ) && + contains( context, elem ) && + elem.id === m ) { + + results.push( elem ); + return results; + } + } + + // Type selector + } else if ( match[ 2 ] ) { + push.apply( results, context.getElementsByTagName( selector ) ); + return results; + + // Class selector + } else if ( ( m = match[ 3 ] ) && support.getElementsByClassName && + context.getElementsByClassName ) { + + push.apply( results, context.getElementsByClassName( m ) ); + return results; + } + } + + // Take advantage of querySelectorAll + if ( support.qsa && + !nonnativeSelectorCache[ selector + " " ] && + ( !rbuggyQSA || !rbuggyQSA.test( selector ) ) && + + // Support: IE 8 only + // Exclude object elements + ( nodeType !== 1 || context.nodeName.toLowerCase() !== "object" ) ) { + + newSelector = selector; + newContext = context; + + // qSA considers elements outside a scoping root when evaluating child or + // descendant combinators, which is not what we want. + // In such cases, we work around the behavior by prefixing every selector in the + // list with an ID selector referencing the scope context. + // The technique has to be used as well when a leading combinator is used + // as such selectors are not recognized by querySelectorAll. + // Thanks to Andrew Dupont for this technique. + if ( nodeType === 1 && + ( rdescend.test( selector ) || rcombinators.test( selector ) ) ) { + + // Expand context for sibling selectors + newContext = rsibling.test( selector ) && testContext( context.parentNode ) || + context; + + // We can use :scope instead of the ID hack if the browser + // supports it & if we're not changing the context. + if ( newContext !== context || !support.scope ) { + + // Capture the context ID, setting it first if necessary + if ( ( nid = context.getAttribute( "id" ) ) ) { + nid = nid.replace( rcssescape, fcssescape ); + } else { + context.setAttribute( "id", ( nid = expando ) ); + } + } + + // Prefix every selector in the list + groups = tokenize( selector ); + i = groups.length; + while ( i-- ) { + groups[ i ] = ( nid ? "#" + nid : ":scope" ) + " " + + toSelector( groups[ i ] ); + } + newSelector = groups.join( "," ); + } + + try { + push.apply( results, + newContext.querySelectorAll( newSelector ) + ); + return results; + } catch ( qsaError ) { + nonnativeSelectorCache( selector, true ); + } finally { + if ( nid === expando ) { + context.removeAttribute( "id" ); + } + } + } + } + } + + // All others + return select( selector.replace( rtrim, "$1" ), context, results, seed ); +} + +/** + * Create key-value caches of limited size + * @returns {function(string, object)} Returns the Object data after storing it on itself with + * property name the (space-suffixed) string and (if the cache is larger than Expr.cacheLength) + * deleting the oldest entry + */ +function createCache() { + var keys = []; + + function cache( key, value ) { + + // Use (key + " ") to avoid collision with native prototype properties (see Issue #157) + if ( keys.push( key + " " ) > Expr.cacheLength ) { + + // Only keep the most recent entries + delete cache[ keys.shift() ]; + } + return ( cache[ key + " " ] = value ); + } + return cache; +} + +/** + * Mark a function for special use by Sizzle + * @param {Function} fn The function to mark + */ +function markFunction( fn ) { + fn[ expando ] = true; + return fn; +} + +/** + * Support testing using an element + * @param {Function} fn Passed the created element and returns a boolean result + */ +function assert( fn ) { + var el = document.createElement( "fieldset" ); + + try { + return !!fn( el ); + } catch ( e ) { + return false; + } finally { + + // Remove from its parent by default + if ( el.parentNode ) { + el.parentNode.removeChild( el ); + } + + // release memory in IE + el = null; + } +} + +/** + * Adds the same handler for all of the specified attrs + * @param {String} attrs Pipe-separated list of attributes + * @param {Function} handler The method that will be applied + */ +function addHandle( attrs, handler ) { + var arr = attrs.split( "|" ), + i = arr.length; + + while ( i-- ) { + Expr.attrHandle[ arr[ i ] ] = handler; + } +} + +/** + * Checks document order of two siblings + * @param {Element} a + * @param {Element} b + * @returns {Number} Returns less than 0 if a precedes b, greater than 0 if a follows b + */ +function siblingCheck( a, b ) { + var cur = b && a, + diff = cur && a.nodeType === 1 && b.nodeType === 1 && + a.sourceIndex - b.sourceIndex; + + // Use IE sourceIndex if available on both nodes + if ( diff ) { + return diff; + } + + // Check if b follows a + if ( cur ) { + while ( ( cur = cur.nextSibling ) ) { + if ( cur === b ) { + return -1; + } + } + } + + return a ? 1 : -1; +} + +/** + * Returns a function to use in pseudos for input types + * @param {String} type + */ +function createInputPseudo( type ) { + return function( elem ) { + var name = elem.nodeName.toLowerCase(); + return name === "input" && elem.type === type; + }; +} + +/** + * Returns a function to use in pseudos for buttons + * @param {String} type + */ +function createButtonPseudo( type ) { + return function( elem ) { + var name = elem.nodeName.toLowerCase(); + return ( name === "input" || name === "button" ) && elem.type === type; + }; +} + +/** + * Returns a function to use in pseudos for :enabled/:disabled + * @param {Boolean} disabled true for :disabled; false for :enabled + */ +function createDisabledPseudo( disabled ) { + + // Known :disabled false positives: fieldset[disabled] > legend:nth-of-type(n+2) :can-disable + return function( elem ) { + + // Only certain elements can match :enabled or :disabled + // https://html.spec.whatwg.org/multipage/scripting.html#selector-enabled + // https://html.spec.whatwg.org/multipage/scripting.html#selector-disabled + if ( "form" in elem ) { + + // Check for inherited disabledness on relevant non-disabled elements: + // * listed form-associated elements in a disabled fieldset + // https://html.spec.whatwg.org/multipage/forms.html#category-listed + // https://html.spec.whatwg.org/multipage/forms.html#concept-fe-disabled + // * option elements in a disabled optgroup + // https://html.spec.whatwg.org/multipage/forms.html#concept-option-disabled + // All such elements have a "form" property. + if ( elem.parentNode && elem.disabled === false ) { + + // Option elements defer to a parent optgroup if present + if ( "label" in elem ) { + if ( "label" in elem.parentNode ) { + return elem.parentNode.disabled === disabled; + } else { + return elem.disabled === disabled; + } + } + + // Support: IE 6 - 11 + // Use the isDisabled shortcut property to check for disabled fieldset ancestors + return elem.isDisabled === disabled || + + // Where there is no isDisabled, check manually + /* jshint -W018 */ + elem.isDisabled !== !disabled && + inDisabledFieldset( elem ) === disabled; + } + + return elem.disabled === disabled; + + // Try to winnow out elements that can't be disabled before trusting the disabled property. + // Some victims get caught in our net (label, legend, menu, track), but it shouldn't + // even exist on them, let alone have a boolean value. + } else if ( "label" in elem ) { + return elem.disabled === disabled; + } + + // Remaining elements are neither :enabled nor :disabled + return false; + }; +} + +/** + * Returns a function to use in pseudos for positionals + * @param {Function} fn + */ +function createPositionalPseudo( fn ) { + return markFunction( function( argument ) { + argument = +argument; + return markFunction( function( seed, matches ) { + var j, + matchIndexes = fn( [], seed.length, argument ), + i = matchIndexes.length; + + // Match elements found at the specified indexes + while ( i-- ) { + if ( seed[ ( j = matchIndexes[ i ] ) ] ) { + seed[ j ] = !( matches[ j ] = seed[ j ] ); + } + } + } ); + } ); +} + +/** + * Checks a node for validity as a Sizzle context + * @param {Element|Object=} context + * @returns {Element|Object|Boolean} The input node if acceptable, otherwise a falsy value + */ +function testContext( context ) { + return context && typeof context.getElementsByTagName !== "undefined" && context; +} + +// Expose support vars for convenience +support = Sizzle.support = {}; + +/** + * Detects XML nodes + * @param {Element|Object} elem An element or a document + * @returns {Boolean} True iff elem is a non-HTML XML node + */ +isXML = Sizzle.isXML = function( elem ) { + var namespace = elem.namespaceURI, + docElem = ( elem.ownerDocument || elem ).documentElement; + + // Support: IE <=8 + // Assume HTML when documentElement doesn't yet exist, such as inside loading iframes + // https://bugs.jquery.com/ticket/4833 + return !rhtml.test( namespace || docElem && docElem.nodeName || "HTML" ); +}; + +/** + * Sets document-related variables once based on the current document + * @param {Element|Object} [doc] An element or document object to use to set the document + * @returns {Object} Returns the current document + */ +setDocument = Sizzle.setDocument = function( node ) { + var hasCompare, subWindow, + doc = node ? node.ownerDocument || node : preferredDoc; + + // Return early if doc is invalid or already selected + // Support: IE 11+, Edge 17 - 18+ + // IE/Edge sometimes throw a "Permission denied" error when strict-comparing + // two documents; shallow comparisons work. + // eslint-disable-next-line eqeqeq + if ( doc == document || doc.nodeType !== 9 || !doc.documentElement ) { + return document; + } + + // Update global variables + document = doc; + docElem = document.documentElement; + documentIsHTML = !isXML( document ); + + // Support: IE 9 - 11+, Edge 12 - 18+ + // Accessing iframe documents after unload throws "permission denied" errors (jQuery #13936) + // Support: IE 11+, Edge 17 - 18+ + // IE/Edge sometimes throw a "Permission denied" error when strict-comparing + // two documents; shallow comparisons work. + // eslint-disable-next-line eqeqeq + if ( preferredDoc != document && + ( subWindow = document.defaultView ) && subWindow.top !== subWindow ) { + + // Support: IE 11, Edge + if ( subWindow.addEventListener ) { + subWindow.addEventListener( "unload", unloadHandler, false ); + + // Support: IE 9 - 10 only + } else if ( subWindow.attachEvent ) { + subWindow.attachEvent( "onunload", unloadHandler ); + } + } + + // Support: IE 8 - 11+, Edge 12 - 18+, Chrome <=16 - 25 only, Firefox <=3.6 - 31 only, + // Safari 4 - 5 only, Opera <=11.6 - 12.x only + // IE/Edge & older browsers don't support the :scope pseudo-class. + // Support: Safari 6.0 only + // Safari 6.0 supports :scope but it's an alias of :root there. + support.scope = assert( function( el ) { + docElem.appendChild( el ).appendChild( document.createElement( "div" ) ); + return typeof el.querySelectorAll !== "undefined" && + !el.querySelectorAll( ":scope fieldset div" ).length; + } ); + + /* Attributes + ---------------------------------------------------------------------- */ + + // Support: IE<8 + // Verify that getAttribute really returns attributes and not properties + // (excepting IE8 booleans) + support.attributes = assert( function( el ) { + el.className = "i"; + return !el.getAttribute( "className" ); + } ); + + /* getElement(s)By* + ---------------------------------------------------------------------- */ + + // Check if getElementsByTagName("*") returns only elements + support.getElementsByTagName = assert( function( el ) { + el.appendChild( document.createComment( "" ) ); + return !el.getElementsByTagName( "*" ).length; + } ); + + // Support: IE<9 + support.getElementsByClassName = rnative.test( document.getElementsByClassName ); + + // Support: IE<10 + // Check if getElementById returns elements by name + // The broken getElementById methods don't pick up programmatically-set names, + // so use a roundabout getElementsByName test + support.getById = assert( function( el ) { + docElem.appendChild( el ).id = expando; + return !document.getElementsByName || !document.getElementsByName( expando ).length; + } ); + + // ID filter and find + if ( support.getById ) { + Expr.filter[ "ID" ] = function( id ) { + var attrId = id.replace( runescape, funescape ); + return function( elem ) { + return elem.getAttribute( "id" ) === attrId; + }; + }; + Expr.find[ "ID" ] = function( id, context ) { + if ( typeof context.getElementById !== "undefined" && documentIsHTML ) { + var elem = context.getElementById( id ); + return elem ? [ elem ] : []; + } + }; + } else { + Expr.filter[ "ID" ] = function( id ) { + var attrId = id.replace( runescape, funescape ); + return function( elem ) { + var node = typeof elem.getAttributeNode !== "undefined" && + elem.getAttributeNode( "id" ); + return node && node.value === attrId; + }; + }; + + // Support: IE 6 - 7 only + // getElementById is not reliable as a find shortcut + Expr.find[ "ID" ] = function( id, context ) { + if ( typeof context.getElementById !== "undefined" && documentIsHTML ) { + var node, i, elems, + elem = context.getElementById( id ); + + if ( elem ) { + + // Verify the id attribute + node = elem.getAttributeNode( "id" ); + if ( node && node.value === id ) { + return [ elem ]; + } + + // Fall back on getElementsByName + elems = context.getElementsByName( id ); + i = 0; + while ( ( elem = elems[ i++ ] ) ) { + node = elem.getAttributeNode( "id" ); + if ( node && node.value === id ) { + return [ elem ]; + } + } + } + + return []; + } + }; + } + + // Tag + Expr.find[ "TAG" ] = support.getElementsByTagName ? + function( tag, context ) { + if ( typeof context.getElementsByTagName !== "undefined" ) { + return context.getElementsByTagName( tag ); + + // DocumentFragment nodes don't have gEBTN + } else if ( support.qsa ) { + return context.querySelectorAll( tag ); + } + } : + + function( tag, context ) { + var elem, + tmp = [], + i = 0, + + // By happy coincidence, a (broken) gEBTN appears on DocumentFragment nodes too + results = context.getElementsByTagName( tag ); + + // Filter out possible comments + if ( tag === "*" ) { + while ( ( elem = results[ i++ ] ) ) { + if ( elem.nodeType === 1 ) { + tmp.push( elem ); + } + } + + return tmp; + } + return results; + }; + + // Class + Expr.find[ "CLASS" ] = support.getElementsByClassName && function( className, context ) { + if ( typeof context.getElementsByClassName !== "undefined" && documentIsHTML ) { + return context.getElementsByClassName( className ); + } + }; + + /* QSA/matchesSelector + ---------------------------------------------------------------------- */ + + // QSA and matchesSelector support + + // matchesSelector(:active) reports false when true (IE9/Opera 11.5) + rbuggyMatches = []; + + // qSa(:focus) reports false when true (Chrome 21) + // We allow this because of a bug in IE8/9 that throws an error + // whenever `document.activeElement` is accessed on an iframe + // So, we allow :focus to pass through QSA all the time to avoid the IE error + // See https://bugs.jquery.com/ticket/13378 + rbuggyQSA = []; + + if ( ( support.qsa = rnative.test( document.querySelectorAll ) ) ) { + + // Build QSA regex + // Regex strategy adopted from Diego Perini + assert( function( el ) { + + var input; + + // Select is set to empty string on purpose + // This is to test IE's treatment of not explicitly + // setting a boolean content attribute, + // since its presence should be enough + // https://bugs.jquery.com/ticket/12359 + docElem.appendChild( el ).innerHTML = "" + + ""; + + // Support: IE8, Opera 11-12.16 + // Nothing should be selected when empty strings follow ^= or $= or *= + // The test attribute must be unknown in Opera but "safe" for WinRT + // https://msdn.microsoft.com/en-us/library/ie/hh465388.aspx#attribute_section + if ( el.querySelectorAll( "[msallowcapture^='']" ).length ) { + rbuggyQSA.push( "[*^$]=" + whitespace + "*(?:''|\"\")" ); + } + + // Support: IE8 + // Boolean attributes and "value" are not treated correctly + if ( !el.querySelectorAll( "[selected]" ).length ) { + rbuggyQSA.push( "\\[" + whitespace + "*(?:value|" + booleans + ")" ); + } + + // Support: Chrome<29, Android<4.4, Safari<7.0+, iOS<7.0+, PhantomJS<1.9.8+ + if ( !el.querySelectorAll( "[id~=" + expando + "-]" ).length ) { + rbuggyQSA.push( "~=" ); + } + + // Support: IE 11+, Edge 15 - 18+ + // IE 11/Edge don't find elements on a `[name='']` query in some cases. + // Adding a temporary attribute to the document before the selection works + // around the issue. + // Interestingly, IE 10 & older don't seem to have the issue. + input = document.createElement( "input" ); + input.setAttribute( "name", "" ); + el.appendChild( input ); + if ( !el.querySelectorAll( "[name='']" ).length ) { + rbuggyQSA.push( "\\[" + whitespace + "*name" + whitespace + "*=" + + whitespace + "*(?:''|\"\")" ); + } + + // Webkit/Opera - :checked should return selected option elements + // http://www.w3.org/TR/2011/REC-css3-selectors-20110929/#checked + // IE8 throws error here and will not see later tests + if ( !el.querySelectorAll( ":checked" ).length ) { + rbuggyQSA.push( ":checked" ); + } + + // Support: Safari 8+, iOS 8+ + // https://bugs.webkit.org/show_bug.cgi?id=136851 + // In-page `selector#id sibling-combinator selector` fails + if ( !el.querySelectorAll( "a#" + expando + "+*" ).length ) { + rbuggyQSA.push( ".#.+[+~]" ); + } + + // Support: Firefox <=3.6 - 5 only + // Old Firefox doesn't throw on a badly-escaped identifier. + el.querySelectorAll( "\\\f" ); + rbuggyQSA.push( "[\\r\\n\\f]" ); + } ); + + assert( function( el ) { + el.innerHTML = "" + + ""; + + // Support: Windows 8 Native Apps + // The type and name attributes are restricted during .innerHTML assignment + var input = document.createElement( "input" ); + input.setAttribute( "type", "hidden" ); + el.appendChild( input ).setAttribute( "name", "D" ); + + // Support: IE8 + // Enforce case-sensitivity of name attribute + if ( el.querySelectorAll( "[name=d]" ).length ) { + rbuggyQSA.push( "name" + whitespace + "*[*^$|!~]?=" ); + } + + // FF 3.5 - :enabled/:disabled and hidden elements (hidden elements are still enabled) + // IE8 throws error here and will not see later tests + if ( el.querySelectorAll( ":enabled" ).length !== 2 ) { + rbuggyQSA.push( ":enabled", ":disabled" ); + } + + // Support: IE9-11+ + // IE's :disabled selector does not pick up the children of disabled fieldsets + docElem.appendChild( el ).disabled = true; + if ( el.querySelectorAll( ":disabled" ).length !== 2 ) { + rbuggyQSA.push( ":enabled", ":disabled" ); + } + + // Support: Opera 10 - 11 only + // Opera 10-11 does not throw on post-comma invalid pseudos + el.querySelectorAll( "*,:x" ); + rbuggyQSA.push( ",.*:" ); + } ); + } + + if ( ( support.matchesSelector = rnative.test( ( matches = docElem.matches || + docElem.webkitMatchesSelector || + docElem.mozMatchesSelector || + docElem.oMatchesSelector || + docElem.msMatchesSelector ) ) ) ) { + + assert( function( el ) { + + // Check to see if it's possible to do matchesSelector + // on a disconnected node (IE 9) + support.disconnectedMatch = matches.call( el, "*" ); + + // This should fail with an exception + // Gecko does not error, returns false instead + matches.call( el, "[s!='']:x" ); + rbuggyMatches.push( "!=", pseudos ); + } ); + } + + rbuggyQSA = rbuggyQSA.length && new RegExp( rbuggyQSA.join( "|" ) ); + rbuggyMatches = rbuggyMatches.length && new RegExp( rbuggyMatches.join( "|" ) ); + + /* Contains + ---------------------------------------------------------------------- */ + hasCompare = rnative.test( docElem.compareDocumentPosition ); + + // Element contains another + // Purposefully self-exclusive + // As in, an element does not contain itself + contains = hasCompare || rnative.test( docElem.contains ) ? + function( a, b ) { + var adown = a.nodeType === 9 ? a.documentElement : a, + bup = b && b.parentNode; + return a === bup || !!( bup && bup.nodeType === 1 && ( + adown.contains ? + adown.contains( bup ) : + a.compareDocumentPosition && a.compareDocumentPosition( bup ) & 16 + ) ); + } : + function( a, b ) { + if ( b ) { + while ( ( b = b.parentNode ) ) { + if ( b === a ) { + return true; + } + } + } + return false; + }; + + /* Sorting + ---------------------------------------------------------------------- */ + + // Document order sorting + sortOrder = hasCompare ? + function( a, b ) { + + // Flag for duplicate removal + if ( a === b ) { + hasDuplicate = true; + return 0; + } + + // Sort on method existence if only one input has compareDocumentPosition + var compare = !a.compareDocumentPosition - !b.compareDocumentPosition; + if ( compare ) { + return compare; + } + + // Calculate position if both inputs belong to the same document + // Support: IE 11+, Edge 17 - 18+ + // IE/Edge sometimes throw a "Permission denied" error when strict-comparing + // two documents; shallow comparisons work. + // eslint-disable-next-line eqeqeq + compare = ( a.ownerDocument || a ) == ( b.ownerDocument || b ) ? + a.compareDocumentPosition( b ) : + + // Otherwise we know they are disconnected + 1; + + // Disconnected nodes + if ( compare & 1 || + ( !support.sortDetached && b.compareDocumentPosition( a ) === compare ) ) { + + // Choose the first element that is related to our preferred document + // Support: IE 11+, Edge 17 - 18+ + // IE/Edge sometimes throw a "Permission denied" error when strict-comparing + // two documents; shallow comparisons work. + // eslint-disable-next-line eqeqeq + if ( a == document || a.ownerDocument == preferredDoc && + contains( preferredDoc, a ) ) { + return -1; + } + + // Support: IE 11+, Edge 17 - 18+ + // IE/Edge sometimes throw a "Permission denied" error when strict-comparing + // two documents; shallow comparisons work. + // eslint-disable-next-line eqeqeq + if ( b == document || b.ownerDocument == preferredDoc && + contains( preferredDoc, b ) ) { + return 1; + } + + // Maintain original order + return sortInput ? + ( indexOf( sortInput, a ) - indexOf( sortInput, b ) ) : + 0; + } + + return compare & 4 ? -1 : 1; + } : + function( a, b ) { + + // Exit early if the nodes are identical + if ( a === b ) { + hasDuplicate = true; + return 0; + } + + var cur, + i = 0, + aup = a.parentNode, + bup = b.parentNode, + ap = [ a ], + bp = [ b ]; + + // Parentless nodes are either documents or disconnected + if ( !aup || !bup ) { + + // Support: IE 11+, Edge 17 - 18+ + // IE/Edge sometimes throw a "Permission denied" error when strict-comparing + // two documents; shallow comparisons work. + /* eslint-disable eqeqeq */ + return a == document ? -1 : + b == document ? 1 : + /* eslint-enable eqeqeq */ + aup ? -1 : + bup ? 1 : + sortInput ? + ( indexOf( sortInput, a ) - indexOf( sortInput, b ) ) : + 0; + + // If the nodes are siblings, we can do a quick check + } else if ( aup === bup ) { + return siblingCheck( a, b ); + } + + // Otherwise we need full lists of their ancestors for comparison + cur = a; + while ( ( cur = cur.parentNode ) ) { + ap.unshift( cur ); + } + cur = b; + while ( ( cur = cur.parentNode ) ) { + bp.unshift( cur ); + } + + // Walk down the tree looking for a discrepancy + while ( ap[ i ] === bp[ i ] ) { + i++; + } + + return i ? + + // Do a sibling check if the nodes have a common ancestor + siblingCheck( ap[ i ], bp[ i ] ) : + + // Otherwise nodes in our document sort first + // Support: IE 11+, Edge 17 - 18+ + // IE/Edge sometimes throw a "Permission denied" error when strict-comparing + // two documents; shallow comparisons work. + /* eslint-disable eqeqeq */ + ap[ i ] == preferredDoc ? -1 : + bp[ i ] == preferredDoc ? 1 : + /* eslint-enable eqeqeq */ + 0; + }; + + return document; +}; + +Sizzle.matches = function( expr, elements ) { + return Sizzle( expr, null, null, elements ); +}; + +Sizzle.matchesSelector = function( elem, expr ) { + setDocument( elem ); + + if ( support.matchesSelector && documentIsHTML && + !nonnativeSelectorCache[ expr + " " ] && + ( !rbuggyMatches || !rbuggyMatches.test( expr ) ) && + ( !rbuggyQSA || !rbuggyQSA.test( expr ) ) ) { + + try { + var ret = matches.call( elem, expr ); + + // IE 9's matchesSelector returns false on disconnected nodes + if ( ret || support.disconnectedMatch || + + // As well, disconnected nodes are said to be in a document + // fragment in IE 9 + elem.document && elem.document.nodeType !== 11 ) { + return ret; + } + } catch ( e ) { + nonnativeSelectorCache( expr, true ); + } + } + + return Sizzle( expr, document, null, [ elem ] ).length > 0; +}; + +Sizzle.contains = function( context, elem ) { + + // Set document vars if needed + // Support: IE 11+, Edge 17 - 18+ + // IE/Edge sometimes throw a "Permission denied" error when strict-comparing + // two documents; shallow comparisons work. + // eslint-disable-next-line eqeqeq + if ( ( context.ownerDocument || context ) != document ) { + setDocument( context ); + } + return contains( context, elem ); +}; + +Sizzle.attr = function( elem, name ) { + + // Set document vars if needed + // Support: IE 11+, Edge 17 - 18+ + // IE/Edge sometimes throw a "Permission denied" error when strict-comparing + // two documents; shallow comparisons work. + // eslint-disable-next-line eqeqeq + if ( ( elem.ownerDocument || elem ) != document ) { + setDocument( elem ); + } + + var fn = Expr.attrHandle[ name.toLowerCase() ], + + // Don't get fooled by Object.prototype properties (jQuery #13807) + val = fn && hasOwn.call( Expr.attrHandle, name.toLowerCase() ) ? + fn( elem, name, !documentIsHTML ) : + undefined; + + return val !== undefined ? + val : + support.attributes || !documentIsHTML ? + elem.getAttribute( name ) : + ( val = elem.getAttributeNode( name ) ) && val.specified ? + val.value : + null; +}; + +Sizzle.escape = function( sel ) { + return ( sel + "" ).replace( rcssescape, fcssescape ); +}; + +Sizzle.error = function( msg ) { + throw new Error( "Syntax error, unrecognized expression: " + msg ); +}; + +/** + * Document sorting and removing duplicates + * @param {ArrayLike} results + */ +Sizzle.uniqueSort = function( results ) { + var elem, + duplicates = [], + j = 0, + i = 0; + + // Unless we *know* we can detect duplicates, assume their presence + hasDuplicate = !support.detectDuplicates; + sortInput = !support.sortStable && results.slice( 0 ); + results.sort( sortOrder ); + + if ( hasDuplicate ) { + while ( ( elem = results[ i++ ] ) ) { + if ( elem === results[ i ] ) { + j = duplicates.push( i ); + } + } + while ( j-- ) { + results.splice( duplicates[ j ], 1 ); + } + } + + // Clear input after sorting to release objects + // See https://github.com/jquery/sizzle/pull/225 + sortInput = null; + + return results; +}; + +/** + * Utility function for retrieving the text value of an array of DOM nodes + * @param {Array|Element} elem + */ +getText = Sizzle.getText = function( elem ) { + var node, + ret = "", + i = 0, + nodeType = elem.nodeType; + + if ( !nodeType ) { + + // If no nodeType, this is expected to be an array + while ( ( node = elem[ i++ ] ) ) { + + // Do not traverse comment nodes + ret += getText( node ); + } + } else if ( nodeType === 1 || nodeType === 9 || nodeType === 11 ) { + + // Use textContent for elements + // innerText usage removed for consistency of new lines (jQuery #11153) + if ( typeof elem.textContent === "string" ) { + return elem.textContent; + } else { + + // Traverse its children + for ( elem = elem.firstChild; elem; elem = elem.nextSibling ) { + ret += getText( elem ); + } + } + } else if ( nodeType === 3 || nodeType === 4 ) { + return elem.nodeValue; + } + + // Do not include comment or processing instruction nodes + + return ret; +}; + +Expr = Sizzle.selectors = { + + // Can be adjusted by the user + cacheLength: 50, + + createPseudo: markFunction, + + match: matchExpr, + + attrHandle: {}, + + find: {}, + + relative: { + ">": { dir: "parentNode", first: true }, + " ": { dir: "parentNode" }, + "+": { dir: "previousSibling", first: true }, + "~": { dir: "previousSibling" } + }, + + preFilter: { + "ATTR": function( match ) { + match[ 1 ] = match[ 1 ].replace( runescape, funescape ); + + // Move the given value to match[3] whether quoted or unquoted + match[ 3 ] = ( match[ 3 ] || match[ 4 ] || + match[ 5 ] || "" ).replace( runescape, funescape ); + + if ( match[ 2 ] === "~=" ) { + match[ 3 ] = " " + match[ 3 ] + " "; + } + + return match.slice( 0, 4 ); + }, + + "CHILD": function( match ) { + + /* matches from matchExpr["CHILD"] + 1 type (only|nth|...) + 2 what (child|of-type) + 3 argument (even|odd|\d*|\d*n([+-]\d+)?|...) + 4 xn-component of xn+y argument ([+-]?\d*n|) + 5 sign of xn-component + 6 x of xn-component + 7 sign of y-component + 8 y of y-component + */ + match[ 1 ] = match[ 1 ].toLowerCase(); + + if ( match[ 1 ].slice( 0, 3 ) === "nth" ) { + + // nth-* requires argument + if ( !match[ 3 ] ) { + Sizzle.error( match[ 0 ] ); + } + + // numeric x and y parameters for Expr.filter.CHILD + // remember that false/true cast respectively to 0/1 + match[ 4 ] = +( match[ 4 ] ? + match[ 5 ] + ( match[ 6 ] || 1 ) : + 2 * ( match[ 3 ] === "even" || match[ 3 ] === "odd" ) ); + match[ 5 ] = +( ( match[ 7 ] + match[ 8 ] ) || match[ 3 ] === "odd" ); + + // other types prohibit arguments + } else if ( match[ 3 ] ) { + Sizzle.error( match[ 0 ] ); + } + + return match; + }, + + "PSEUDO": function( match ) { + var excess, + unquoted = !match[ 6 ] && match[ 2 ]; + + if ( matchExpr[ "CHILD" ].test( match[ 0 ] ) ) { + return null; + } + + // Accept quoted arguments as-is + if ( match[ 3 ] ) { + match[ 2 ] = match[ 4 ] || match[ 5 ] || ""; + + // Strip excess characters from unquoted arguments + } else if ( unquoted && rpseudo.test( unquoted ) && + + // Get excess from tokenize (recursively) + ( excess = tokenize( unquoted, true ) ) && + + // advance to the next closing parenthesis + ( excess = unquoted.indexOf( ")", unquoted.length - excess ) - unquoted.length ) ) { + + // excess is a negative index + match[ 0 ] = match[ 0 ].slice( 0, excess ); + match[ 2 ] = unquoted.slice( 0, excess ); + } + + // Return only captures needed by the pseudo filter method (type and argument) + return match.slice( 0, 3 ); + } + }, + + filter: { + + "TAG": function( nodeNameSelector ) { + var nodeName = nodeNameSelector.replace( runescape, funescape ).toLowerCase(); + return nodeNameSelector === "*" ? + function() { + return true; + } : + function( elem ) { + return elem.nodeName && elem.nodeName.toLowerCase() === nodeName; + }; + }, + + "CLASS": function( className ) { + var pattern = classCache[ className + " " ]; + + return pattern || + ( pattern = new RegExp( "(^|" + whitespace + + ")" + className + "(" + whitespace + "|$)" ) ) && classCache( + className, function( elem ) { + return pattern.test( + typeof elem.className === "string" && elem.className || + typeof elem.getAttribute !== "undefined" && + elem.getAttribute( "class" ) || + "" + ); + } ); + }, + + "ATTR": function( name, operator, check ) { + return function( elem ) { + var result = Sizzle.attr( elem, name ); + + if ( result == null ) { + return operator === "!="; + } + if ( !operator ) { + return true; + } + + result += ""; + + /* eslint-disable max-len */ + + return operator === "=" ? result === check : + operator === "!=" ? result !== check : + operator === "^=" ? check && result.indexOf( check ) === 0 : + operator === "*=" ? check && result.indexOf( check ) > -1 : + operator === "$=" ? check && result.slice( -check.length ) === check : + operator === "~=" ? ( " " + result.replace( rwhitespace, " " ) + " " ).indexOf( check ) > -1 : + operator === "|=" ? result === check || result.slice( 0, check.length + 1 ) === check + "-" : + false; + /* eslint-enable max-len */ + + }; + }, + + "CHILD": function( type, what, _argument, first, last ) { + var simple = type.slice( 0, 3 ) !== "nth", + forward = type.slice( -4 ) !== "last", + ofType = what === "of-type"; + + return first === 1 && last === 0 ? + + // Shortcut for :nth-*(n) + function( elem ) { + return !!elem.parentNode; + } : + + function( elem, _context, xml ) { + var cache, uniqueCache, outerCache, node, nodeIndex, start, + dir = simple !== forward ? "nextSibling" : "previousSibling", + parent = elem.parentNode, + name = ofType && elem.nodeName.toLowerCase(), + useCache = !xml && !ofType, + diff = false; + + if ( parent ) { + + // :(first|last|only)-(child|of-type) + if ( simple ) { + while ( dir ) { + node = elem; + while ( ( node = node[ dir ] ) ) { + if ( ofType ? + node.nodeName.toLowerCase() === name : + node.nodeType === 1 ) { + + return false; + } + } + + // Reverse direction for :only-* (if we haven't yet done so) + start = dir = type === "only" && !start && "nextSibling"; + } + return true; + } + + start = [ forward ? parent.firstChild : parent.lastChild ]; + + // non-xml :nth-child(...) stores cache data on `parent` + if ( forward && useCache ) { + + // Seek `elem` from a previously-cached index + + // ...in a gzip-friendly way + node = parent; + outerCache = node[ expando ] || ( node[ expando ] = {} ); + + // Support: IE <9 only + // Defend against cloned attroperties (jQuery gh-1709) + uniqueCache = outerCache[ node.uniqueID ] || + ( outerCache[ node.uniqueID ] = {} ); + + cache = uniqueCache[ type ] || []; + nodeIndex = cache[ 0 ] === dirruns && cache[ 1 ]; + diff = nodeIndex && cache[ 2 ]; + node = nodeIndex && parent.childNodes[ nodeIndex ]; + + while ( ( node = ++nodeIndex && node && node[ dir ] || + + // Fallback to seeking `elem` from the start + ( diff = nodeIndex = 0 ) || start.pop() ) ) { + + // When found, cache indexes on `parent` and break + if ( node.nodeType === 1 && ++diff && node === elem ) { + uniqueCache[ type ] = [ dirruns, nodeIndex, diff ]; + break; + } + } + + } else { + + // Use previously-cached element index if available + if ( useCache ) { + + // ...in a gzip-friendly way + node = elem; + outerCache = node[ expando ] || ( node[ expando ] = {} ); + + // Support: IE <9 only + // Defend against cloned attroperties (jQuery gh-1709) + uniqueCache = outerCache[ node.uniqueID ] || + ( outerCache[ node.uniqueID ] = {} ); + + cache = uniqueCache[ type ] || []; + nodeIndex = cache[ 0 ] === dirruns && cache[ 1 ]; + diff = nodeIndex; + } + + // xml :nth-child(...) + // or :nth-last-child(...) or :nth(-last)?-of-type(...) + if ( diff === false ) { + + // Use the same loop as above to seek `elem` from the start + while ( ( node = ++nodeIndex && node && node[ dir ] || + ( diff = nodeIndex = 0 ) || start.pop() ) ) { + + if ( ( ofType ? + node.nodeName.toLowerCase() === name : + node.nodeType === 1 ) && + ++diff ) { + + // Cache the index of each encountered element + if ( useCache ) { + outerCache = node[ expando ] || + ( node[ expando ] = {} ); + + // Support: IE <9 only + // Defend against cloned attroperties (jQuery gh-1709) + uniqueCache = outerCache[ node.uniqueID ] || + ( outerCache[ node.uniqueID ] = {} ); + + uniqueCache[ type ] = [ dirruns, diff ]; + } + + if ( node === elem ) { + break; + } + } + } + } + } + + // Incorporate the offset, then check against cycle size + diff -= last; + return diff === first || ( diff % first === 0 && diff / first >= 0 ); + } + }; + }, + + "PSEUDO": function( pseudo, argument ) { + + // pseudo-class names are case-insensitive + // http://www.w3.org/TR/selectors/#pseudo-classes + // Prioritize by case sensitivity in case custom pseudos are added with uppercase letters + // Remember that setFilters inherits from pseudos + var args, + fn = Expr.pseudos[ pseudo ] || Expr.setFilters[ pseudo.toLowerCase() ] || + Sizzle.error( "unsupported pseudo: " + pseudo ); + + // The user may use createPseudo to indicate that + // arguments are needed to create the filter function + // just as Sizzle does + if ( fn[ expando ] ) { + return fn( argument ); + } + + // But maintain support for old signatures + if ( fn.length > 1 ) { + args = [ pseudo, pseudo, "", argument ]; + return Expr.setFilters.hasOwnProperty( pseudo.toLowerCase() ) ? + markFunction( function( seed, matches ) { + var idx, + matched = fn( seed, argument ), + i = matched.length; + while ( i-- ) { + idx = indexOf( seed, matched[ i ] ); + seed[ idx ] = !( matches[ idx ] = matched[ i ] ); + } + } ) : + function( elem ) { + return fn( elem, 0, args ); + }; + } + + return fn; + } + }, + + pseudos: { + + // Potentially complex pseudos + "not": markFunction( function( selector ) { + + // Trim the selector passed to compile + // to avoid treating leading and trailing + // spaces as combinators + var input = [], + results = [], + matcher = compile( selector.replace( rtrim, "$1" ) ); + + return matcher[ expando ] ? + markFunction( function( seed, matches, _context, xml ) { + var elem, + unmatched = matcher( seed, null, xml, [] ), + i = seed.length; + + // Match elements unmatched by `matcher` + while ( i-- ) { + if ( ( elem = unmatched[ i ] ) ) { + seed[ i ] = !( matches[ i ] = elem ); + } + } + } ) : + function( elem, _context, xml ) { + input[ 0 ] = elem; + matcher( input, null, xml, results ); + + // Don't keep the element (issue #299) + input[ 0 ] = null; + return !results.pop(); + }; + } ), + + "has": markFunction( function( selector ) { + return function( elem ) { + return Sizzle( selector, elem ).length > 0; + }; + } ), + + "contains": markFunction( function( text ) { + text = text.replace( runescape, funescape ); + return function( elem ) { + return ( elem.textContent || getText( elem ) ).indexOf( text ) > -1; + }; + } ), + + // "Whether an element is represented by a :lang() selector + // is based solely on the element's language value + // being equal to the identifier C, + // or beginning with the identifier C immediately followed by "-". + // The matching of C against the element's language value is performed case-insensitively. + // The identifier C does not have to be a valid language name." + // http://www.w3.org/TR/selectors/#lang-pseudo + "lang": markFunction( function( lang ) { + + // lang value must be a valid identifier + if ( !ridentifier.test( lang || "" ) ) { + Sizzle.error( "unsupported lang: " + lang ); + } + lang = lang.replace( runescape, funescape ).toLowerCase(); + return function( elem ) { + var elemLang; + do { + if ( ( elemLang = documentIsHTML ? + elem.lang : + elem.getAttribute( "xml:lang" ) || elem.getAttribute( "lang" ) ) ) { + + elemLang = elemLang.toLowerCase(); + return elemLang === lang || elemLang.indexOf( lang + "-" ) === 0; + } + } while ( ( elem = elem.parentNode ) && elem.nodeType === 1 ); + return false; + }; + } ), + + // Miscellaneous + "target": function( elem ) { + var hash = window.location && window.location.hash; + return hash && hash.slice( 1 ) === elem.id; + }, + + "root": function( elem ) { + return elem === docElem; + }, + + "focus": function( elem ) { + return elem === document.activeElement && + ( !document.hasFocus || document.hasFocus() ) && + !!( elem.type || elem.href || ~elem.tabIndex ); + }, + + // Boolean properties + "enabled": createDisabledPseudo( false ), + "disabled": createDisabledPseudo( true ), + + "checked": function( elem ) { + + // In CSS3, :checked should return both checked and selected elements + // http://www.w3.org/TR/2011/REC-css3-selectors-20110929/#checked + var nodeName = elem.nodeName.toLowerCase(); + return ( nodeName === "input" && !!elem.checked ) || + ( nodeName === "option" && !!elem.selected ); + }, + + "selected": function( elem ) { + + // Accessing this property makes selected-by-default + // options in Safari work properly + if ( elem.parentNode ) { + // eslint-disable-next-line no-unused-expressions + elem.parentNode.selectedIndex; + } + + return elem.selected === true; + }, + + // Contents + "empty": function( elem ) { + + // http://www.w3.org/TR/selectors/#empty-pseudo + // :empty is negated by element (1) or content nodes (text: 3; cdata: 4; entity ref: 5), + // but not by others (comment: 8; processing instruction: 7; etc.) + // nodeType < 6 works because attributes (2) do not appear as children + for ( elem = elem.firstChild; elem; elem = elem.nextSibling ) { + if ( elem.nodeType < 6 ) { + return false; + } + } + return true; + }, + + "parent": function( elem ) { + return !Expr.pseudos[ "empty" ]( elem ); + }, + + // Element/input types + "header": function( elem ) { + return rheader.test( elem.nodeName ); + }, + + "input": function( elem ) { + return rinputs.test( elem.nodeName ); + }, + + "button": function( elem ) { + var name = elem.nodeName.toLowerCase(); + return name === "input" && elem.type === "button" || name === "button"; + }, + + "text": function( elem ) { + var attr; + return elem.nodeName.toLowerCase() === "input" && + elem.type === "text" && + + // Support: IE<8 + // New HTML5 attribute values (e.g., "search") appear with elem.type === "text" + ( ( attr = elem.getAttribute( "type" ) ) == null || + attr.toLowerCase() === "text" ); + }, + + // Position-in-collection + "first": createPositionalPseudo( function() { + return [ 0 ]; + } ), + + "last": createPositionalPseudo( function( _matchIndexes, length ) { + return [ length - 1 ]; + } ), + + "eq": createPositionalPseudo( function( _matchIndexes, length, argument ) { + return [ argument < 0 ? argument + length : argument ]; + } ), + + "even": createPositionalPseudo( function( matchIndexes, length ) { + var i = 0; + for ( ; i < length; i += 2 ) { + matchIndexes.push( i ); + } + return matchIndexes; + } ), + + "odd": createPositionalPseudo( function( matchIndexes, length ) { + var i = 1; + for ( ; i < length; i += 2 ) { + matchIndexes.push( i ); + } + return matchIndexes; + } ), + + "lt": createPositionalPseudo( function( matchIndexes, length, argument ) { + var i = argument < 0 ? + argument + length : + argument > length ? + length : + argument; + for ( ; --i >= 0; ) { + matchIndexes.push( i ); + } + return matchIndexes; + } ), + + "gt": createPositionalPseudo( function( matchIndexes, length, argument ) { + var i = argument < 0 ? argument + length : argument; + for ( ; ++i < length; ) { + matchIndexes.push( i ); + } + return matchIndexes; + } ) + } +}; + +Expr.pseudos[ "nth" ] = Expr.pseudos[ "eq" ]; + +// Add button/input type pseudos +for ( i in { radio: true, checkbox: true, file: true, password: true, image: true } ) { + Expr.pseudos[ i ] = createInputPseudo( i ); +} +for ( i in { submit: true, reset: true } ) { + Expr.pseudos[ i ] = createButtonPseudo( i ); +} + +// Easy API for creating new setFilters +function setFilters() {} +setFilters.prototype = Expr.filters = Expr.pseudos; +Expr.setFilters = new setFilters(); + +tokenize = Sizzle.tokenize = function( selector, parseOnly ) { + var matched, match, tokens, type, + soFar, groups, preFilters, + cached = tokenCache[ selector + " " ]; + + if ( cached ) { + return parseOnly ? 0 : cached.slice( 0 ); + } + + soFar = selector; + groups = []; + preFilters = Expr.preFilter; + + while ( soFar ) { + + // Comma and first run + if ( !matched || ( match = rcomma.exec( soFar ) ) ) { + if ( match ) { + + // Don't consume trailing commas as valid + soFar = soFar.slice( match[ 0 ].length ) || soFar; + } + groups.push( ( tokens = [] ) ); + } + + matched = false; + + // Combinators + if ( ( match = rcombinators.exec( soFar ) ) ) { + matched = match.shift(); + tokens.push( { + value: matched, + + // Cast descendant combinators to space + type: match[ 0 ].replace( rtrim, " " ) + } ); + soFar = soFar.slice( matched.length ); + } + + // Filters + for ( type in Expr.filter ) { + if ( ( match = matchExpr[ type ].exec( soFar ) ) && ( !preFilters[ type ] || + ( match = preFilters[ type ]( match ) ) ) ) { + matched = match.shift(); + tokens.push( { + value: matched, + type: type, + matches: match + } ); + soFar = soFar.slice( matched.length ); + } + } + + if ( !matched ) { + break; + } + } + + // Return the length of the invalid excess + // if we're just parsing + // Otherwise, throw an error or return tokens + return parseOnly ? + soFar.length : + soFar ? + Sizzle.error( selector ) : + + // Cache the tokens + tokenCache( selector, groups ).slice( 0 ); +}; + +function toSelector( tokens ) { + var i = 0, + len = tokens.length, + selector = ""; + for ( ; i < len; i++ ) { + selector += tokens[ i ].value; + } + return selector; +} + +function addCombinator( matcher, combinator, base ) { + var dir = combinator.dir, + skip = combinator.next, + key = skip || dir, + checkNonElements = base && key === "parentNode", + doneName = done++; + + return combinator.first ? + + // Check against closest ancestor/preceding element + function( elem, context, xml ) { + while ( ( elem = elem[ dir ] ) ) { + if ( elem.nodeType === 1 || checkNonElements ) { + return matcher( elem, context, xml ); + } + } + return false; + } : + + // Check against all ancestor/preceding elements + function( elem, context, xml ) { + var oldCache, uniqueCache, outerCache, + newCache = [ dirruns, doneName ]; + + // We can't set arbitrary data on XML nodes, so they don't benefit from combinator caching + if ( xml ) { + while ( ( elem = elem[ dir ] ) ) { + if ( elem.nodeType === 1 || checkNonElements ) { + if ( matcher( elem, context, xml ) ) { + return true; + } + } + } + } else { + while ( ( elem = elem[ dir ] ) ) { + if ( elem.nodeType === 1 || checkNonElements ) { + outerCache = elem[ expando ] || ( elem[ expando ] = {} ); + + // Support: IE <9 only + // Defend against cloned attroperties (jQuery gh-1709) + uniqueCache = outerCache[ elem.uniqueID ] || + ( outerCache[ elem.uniqueID ] = {} ); + + if ( skip && skip === elem.nodeName.toLowerCase() ) { + elem = elem[ dir ] || elem; + } else if ( ( oldCache = uniqueCache[ key ] ) && + oldCache[ 0 ] === dirruns && oldCache[ 1 ] === doneName ) { + + // Assign to newCache so results back-propagate to previous elements + return ( newCache[ 2 ] = oldCache[ 2 ] ); + } else { + + // Reuse newcache so results back-propagate to previous elements + uniqueCache[ key ] = newCache; + + // A match means we're done; a fail means we have to keep checking + if ( ( newCache[ 2 ] = matcher( elem, context, xml ) ) ) { + return true; + } + } + } + } + } + return false; + }; +} + +function elementMatcher( matchers ) { + return matchers.length > 1 ? + function( elem, context, xml ) { + var i = matchers.length; + while ( i-- ) { + if ( !matchers[ i ]( elem, context, xml ) ) { + return false; + } + } + return true; + } : + matchers[ 0 ]; +} + +function multipleContexts( selector, contexts, results ) { + var i = 0, + len = contexts.length; + for ( ; i < len; i++ ) { + Sizzle( selector, contexts[ i ], results ); + } + return results; +} + +function condense( unmatched, map, filter, context, xml ) { + var elem, + newUnmatched = [], + i = 0, + len = unmatched.length, + mapped = map != null; + + for ( ; i < len; i++ ) { + if ( ( elem = unmatched[ i ] ) ) { + if ( !filter || filter( elem, context, xml ) ) { + newUnmatched.push( elem ); + if ( mapped ) { + map.push( i ); + } + } + } + } + + return newUnmatched; +} + +function setMatcher( preFilter, selector, matcher, postFilter, postFinder, postSelector ) { + if ( postFilter && !postFilter[ expando ] ) { + postFilter = setMatcher( postFilter ); + } + if ( postFinder && !postFinder[ expando ] ) { + postFinder = setMatcher( postFinder, postSelector ); + } + return markFunction( function( seed, results, context, xml ) { + var temp, i, elem, + preMap = [], + postMap = [], + preexisting = results.length, + + // Get initial elements from seed or context + elems = seed || multipleContexts( + selector || "*", + context.nodeType ? [ context ] : context, + [] + ), + + // Prefilter to get matcher input, preserving a map for seed-results synchronization + matcherIn = preFilter && ( seed || !selector ) ? + condense( elems, preMap, preFilter, context, xml ) : + elems, + + matcherOut = matcher ? + + // If we have a postFinder, or filtered seed, or non-seed postFilter or preexisting results, + postFinder || ( seed ? preFilter : preexisting || postFilter ) ? + + // ...intermediate processing is necessary + [] : + + // ...otherwise use results directly + results : + matcherIn; + + // Find primary matches + if ( matcher ) { + matcher( matcherIn, matcherOut, context, xml ); + } + + // Apply postFilter + if ( postFilter ) { + temp = condense( matcherOut, postMap ); + postFilter( temp, [], context, xml ); + + // Un-match failing elements by moving them back to matcherIn + i = temp.length; + while ( i-- ) { + if ( ( elem = temp[ i ] ) ) { + matcherOut[ postMap[ i ] ] = !( matcherIn[ postMap[ i ] ] = elem ); + } + } + } + + if ( seed ) { + if ( postFinder || preFilter ) { + if ( postFinder ) { + + // Get the final matcherOut by condensing this intermediate into postFinder contexts + temp = []; + i = matcherOut.length; + while ( i-- ) { + if ( ( elem = matcherOut[ i ] ) ) { + + // Restore matcherIn since elem is not yet a final match + temp.push( ( matcherIn[ i ] = elem ) ); + } + } + postFinder( null, ( matcherOut = [] ), temp, xml ); + } + + // Move matched elements from seed to results to keep them synchronized + i = matcherOut.length; + while ( i-- ) { + if ( ( elem = matcherOut[ i ] ) && + ( temp = postFinder ? indexOf( seed, elem ) : preMap[ i ] ) > -1 ) { + + seed[ temp ] = !( results[ temp ] = elem ); + } + } + } + + // Add elements to results, through postFinder if defined + } else { + matcherOut = condense( + matcherOut === results ? + matcherOut.splice( preexisting, matcherOut.length ) : + matcherOut + ); + if ( postFinder ) { + postFinder( null, results, matcherOut, xml ); + } else { + push.apply( results, matcherOut ); + } + } + } ); +} + +function matcherFromTokens( tokens ) { + var checkContext, matcher, j, + len = tokens.length, + leadingRelative = Expr.relative[ tokens[ 0 ].type ], + implicitRelative = leadingRelative || Expr.relative[ " " ], + i = leadingRelative ? 1 : 0, + + // The foundational matcher ensures that elements are reachable from top-level context(s) + matchContext = addCombinator( function( elem ) { + return elem === checkContext; + }, implicitRelative, true ), + matchAnyContext = addCombinator( function( elem ) { + return indexOf( checkContext, elem ) > -1; + }, implicitRelative, true ), + matchers = [ function( elem, context, xml ) { + var ret = ( !leadingRelative && ( xml || context !== outermostContext ) ) || ( + ( checkContext = context ).nodeType ? + matchContext( elem, context, xml ) : + matchAnyContext( elem, context, xml ) ); + + // Avoid hanging onto element (issue #299) + checkContext = null; + return ret; + } ]; + + for ( ; i < len; i++ ) { + if ( ( matcher = Expr.relative[ tokens[ i ].type ] ) ) { + matchers = [ addCombinator( elementMatcher( matchers ), matcher ) ]; + } else { + matcher = Expr.filter[ tokens[ i ].type ].apply( null, tokens[ i ].matches ); + + // Return special upon seeing a positional matcher + if ( matcher[ expando ] ) { + + // Find the next relative operator (if any) for proper handling + j = ++i; + for ( ; j < len; j++ ) { + if ( Expr.relative[ tokens[ j ].type ] ) { + break; + } + } + return setMatcher( + i > 1 && elementMatcher( matchers ), + i > 1 && toSelector( + + // If the preceding token was a descendant combinator, insert an implicit any-element `*` + tokens + .slice( 0, i - 1 ) + .concat( { value: tokens[ i - 2 ].type === " " ? "*" : "" } ) + ).replace( rtrim, "$1" ), + matcher, + i < j && matcherFromTokens( tokens.slice( i, j ) ), + j < len && matcherFromTokens( ( tokens = tokens.slice( j ) ) ), + j < len && toSelector( tokens ) + ); + } + matchers.push( matcher ); + } + } + + return elementMatcher( matchers ); +} + +function matcherFromGroupMatchers( elementMatchers, setMatchers ) { + var bySet = setMatchers.length > 0, + byElement = elementMatchers.length > 0, + superMatcher = function( seed, context, xml, results, outermost ) { + var elem, j, matcher, + matchedCount = 0, + i = "0", + unmatched = seed && [], + setMatched = [], + contextBackup = outermostContext, + + // We must always have either seed elements or outermost context + elems = seed || byElement && Expr.find[ "TAG" ]( "*", outermost ), + + // Use integer dirruns iff this is the outermost matcher + dirrunsUnique = ( dirruns += contextBackup == null ? 1 : Math.random() || 0.1 ), + len = elems.length; + + if ( outermost ) { + + // Support: IE 11+, Edge 17 - 18+ + // IE/Edge sometimes throw a "Permission denied" error when strict-comparing + // two documents; shallow comparisons work. + // eslint-disable-next-line eqeqeq + outermostContext = context == document || context || outermost; + } + + // Add elements passing elementMatchers directly to results + // Support: IE<9, Safari + // Tolerate NodeList properties (IE: "length"; Safari: ) matching elements by id + for ( ; i !== len && ( elem = elems[ i ] ) != null; i++ ) { + if ( byElement && elem ) { + j = 0; + + // Support: IE 11+, Edge 17 - 18+ + // IE/Edge sometimes throw a "Permission denied" error when strict-comparing + // two documents; shallow comparisons work. + // eslint-disable-next-line eqeqeq + if ( !context && elem.ownerDocument != document ) { + setDocument( elem ); + xml = !documentIsHTML; + } + while ( ( matcher = elementMatchers[ j++ ] ) ) { + if ( matcher( elem, context || document, xml ) ) { + results.push( elem ); + break; + } + } + if ( outermost ) { + dirruns = dirrunsUnique; + } + } + + // Track unmatched elements for set filters + if ( bySet ) { + + // They will have gone through all possible matchers + if ( ( elem = !matcher && elem ) ) { + matchedCount--; + } + + // Lengthen the array for every element, matched or not + if ( seed ) { + unmatched.push( elem ); + } + } + } + + // `i` is now the count of elements visited above, and adding it to `matchedCount` + // makes the latter nonnegative. + matchedCount += i; + + // Apply set filters to unmatched elements + // NOTE: This can be skipped if there are no unmatched elements (i.e., `matchedCount` + // equals `i`), unless we didn't visit _any_ elements in the above loop because we have + // no element matchers and no seed. + // Incrementing an initially-string "0" `i` allows `i` to remain a string only in that + // case, which will result in a "00" `matchedCount` that differs from `i` but is also + // numerically zero. + if ( bySet && i !== matchedCount ) { + j = 0; + while ( ( matcher = setMatchers[ j++ ] ) ) { + matcher( unmatched, setMatched, context, xml ); + } + + if ( seed ) { + + // Reintegrate element matches to eliminate the need for sorting + if ( matchedCount > 0 ) { + while ( i-- ) { + if ( !( unmatched[ i ] || setMatched[ i ] ) ) { + setMatched[ i ] = pop.call( results ); + } + } + } + + // Discard index placeholder values to get only actual matches + setMatched = condense( setMatched ); + } + + // Add matches to results + push.apply( results, setMatched ); + + // Seedless set matches succeeding multiple successful matchers stipulate sorting + if ( outermost && !seed && setMatched.length > 0 && + ( matchedCount + setMatchers.length ) > 1 ) { + + Sizzle.uniqueSort( results ); + } + } + + // Override manipulation of globals by nested matchers + if ( outermost ) { + dirruns = dirrunsUnique; + outermostContext = contextBackup; + } + + return unmatched; + }; + + return bySet ? + markFunction( superMatcher ) : + superMatcher; +} + +compile = Sizzle.compile = function( selector, match /* Internal Use Only */ ) { + var i, + setMatchers = [], + elementMatchers = [], + cached = compilerCache[ selector + " " ]; + + if ( !cached ) { + + // Generate a function of recursive functions that can be used to check each element + if ( !match ) { + match = tokenize( selector ); + } + i = match.length; + while ( i-- ) { + cached = matcherFromTokens( match[ i ] ); + if ( cached[ expando ] ) { + setMatchers.push( cached ); + } else { + elementMatchers.push( cached ); + } + } + + // Cache the compiled function + cached = compilerCache( + selector, + matcherFromGroupMatchers( elementMatchers, setMatchers ) + ); + + // Save selector and tokenization + cached.selector = selector; + } + return cached; +}; + +/** + * A low-level selection function that works with Sizzle's compiled + * selector functions + * @param {String|Function} selector A selector or a pre-compiled + * selector function built with Sizzle.compile + * @param {Element} context + * @param {Array} [results] + * @param {Array} [seed] A set of elements to match against + */ +select = Sizzle.select = function( selector, context, results, seed ) { + var i, tokens, token, type, find, + compiled = typeof selector === "function" && selector, + match = !seed && tokenize( ( selector = compiled.selector || selector ) ); + + results = results || []; + + // Try to minimize operations if there is only one selector in the list and no seed + // (the latter of which guarantees us context) + if ( match.length === 1 ) { + + // Reduce context if the leading compound selector is an ID + tokens = match[ 0 ] = match[ 0 ].slice( 0 ); + if ( tokens.length > 2 && ( token = tokens[ 0 ] ).type === "ID" && + context.nodeType === 9 && documentIsHTML && Expr.relative[ tokens[ 1 ].type ] ) { + + context = ( Expr.find[ "ID" ]( token.matches[ 0 ] + .replace( runescape, funescape ), context ) || [] )[ 0 ]; + if ( !context ) { + return results; + + // Precompiled matchers will still verify ancestry, so step up a level + } else if ( compiled ) { + context = context.parentNode; + } + + selector = selector.slice( tokens.shift().value.length ); + } + + // Fetch a seed set for right-to-left matching + i = matchExpr[ "needsContext" ].test( selector ) ? 0 : tokens.length; + while ( i-- ) { + token = tokens[ i ]; + + // Abort if we hit a combinator + if ( Expr.relative[ ( type = token.type ) ] ) { + break; + } + if ( ( find = Expr.find[ type ] ) ) { + + // Search, expanding context for leading sibling combinators + if ( ( seed = find( + token.matches[ 0 ].replace( runescape, funescape ), + rsibling.test( tokens[ 0 ].type ) && testContext( context.parentNode ) || + context + ) ) ) { + + // If seed is empty or no tokens remain, we can return early + tokens.splice( i, 1 ); + selector = seed.length && toSelector( tokens ); + if ( !selector ) { + push.apply( results, seed ); + return results; + } + + break; + } + } + } + } + + // Compile and execute a filtering function if one is not provided + // Provide `match` to avoid retokenization if we modified the selector above + ( compiled || compile( selector, match ) )( + seed, + context, + !documentIsHTML, + results, + !context || rsibling.test( selector ) && testContext( context.parentNode ) || context + ); + return results; +}; + +// One-time assignments + +// Sort stability +support.sortStable = expando.split( "" ).sort( sortOrder ).join( "" ) === expando; + +// Support: Chrome 14-35+ +// Always assume duplicates if they aren't passed to the comparison function +support.detectDuplicates = !!hasDuplicate; + +// Initialize against the default document +setDocument(); + +// Support: Webkit<537.32 - Safari 6.0.3/Chrome 25 (fixed in Chrome 27) +// Detached nodes confoundingly follow *each other* +support.sortDetached = assert( function( el ) { + + // Should return 1, but returns 4 (following) + return el.compareDocumentPosition( document.createElement( "fieldset" ) ) & 1; +} ); + +// Support: IE<8 +// Prevent attribute/property "interpolation" +// https://msdn.microsoft.com/en-us/library/ms536429%28VS.85%29.aspx +if ( !assert( function( el ) { + el.innerHTML = ""; + return el.firstChild.getAttribute( "href" ) === "#"; +} ) ) { + addHandle( "type|href|height|width", function( elem, name, isXML ) { + if ( !isXML ) { + return elem.getAttribute( name, name.toLowerCase() === "type" ? 1 : 2 ); + } + } ); +} + +// Support: IE<9 +// Use defaultValue in place of getAttribute("value") +if ( !support.attributes || !assert( function( el ) { + el.innerHTML = ""; + el.firstChild.setAttribute( "value", "" ); + return el.firstChild.getAttribute( "value" ) === ""; +} ) ) { + addHandle( "value", function( elem, _name, isXML ) { + if ( !isXML && elem.nodeName.toLowerCase() === "input" ) { + return elem.defaultValue; + } + } ); +} + +// Support: IE<9 +// Use getAttributeNode to fetch booleans when getAttribute lies +if ( !assert( function( el ) { + return el.getAttribute( "disabled" ) == null; +} ) ) { + addHandle( booleans, function( elem, name, isXML ) { + var val; + if ( !isXML ) { + return elem[ name ] === true ? name.toLowerCase() : + ( val = elem.getAttributeNode( name ) ) && val.specified ? + val.value : + null; + } + } ); +} + +return Sizzle; + +} )( window ); + + + +jQuery.find = Sizzle; +jQuery.expr = Sizzle.selectors; + +// Deprecated +jQuery.expr[ ":" ] = jQuery.expr.pseudos; +jQuery.uniqueSort = jQuery.unique = Sizzle.uniqueSort; +jQuery.text = Sizzle.getText; +jQuery.isXMLDoc = Sizzle.isXML; +jQuery.contains = Sizzle.contains; +jQuery.escapeSelector = Sizzle.escape; + + + + +var dir = function( elem, dir, until ) { + var matched = [], + truncate = until !== undefined; + + while ( ( elem = elem[ dir ] ) && elem.nodeType !== 9 ) { + if ( elem.nodeType === 1 ) { + if ( truncate && jQuery( elem ).is( until ) ) { + break; + } + matched.push( elem ); + } + } + return matched; +}; + + +var siblings = function( n, elem ) { + var matched = []; + + for ( ; n; n = n.nextSibling ) { + if ( n.nodeType === 1 && n !== elem ) { + matched.push( n ); + } + } + + return matched; +}; + + +var rneedsContext = jQuery.expr.match.needsContext; + + + +function nodeName( elem, name ) { + + return elem.nodeName && elem.nodeName.toLowerCase() === name.toLowerCase(); + +}; +var rsingleTag = ( /^<([a-z][^\/\0>:\x20\t\r\n\f]*)[\x20\t\r\n\f]*\/?>(?:<\/\1>|)$/i ); + + + +// Implement the identical functionality for filter and not +function winnow( elements, qualifier, not ) { + if ( isFunction( qualifier ) ) { + return jQuery.grep( elements, function( elem, i ) { + return !!qualifier.call( elem, i, elem ) !== not; + } ); + } + + // Single element + if ( qualifier.nodeType ) { + return jQuery.grep( elements, function( elem ) { + return ( elem === qualifier ) !== not; + } ); + } + + // Arraylike of elements (jQuery, arguments, Array) + if ( typeof qualifier !== "string" ) { + return jQuery.grep( elements, function( elem ) { + return ( indexOf.call( qualifier, elem ) > -1 ) !== not; + } ); + } + + // Filtered directly for both simple and complex selectors + return jQuery.filter( qualifier, elements, not ); +} + +jQuery.filter = function( expr, elems, not ) { + var elem = elems[ 0 ]; + + if ( not ) { + expr = ":not(" + expr + ")"; + } + + if ( elems.length === 1 && elem.nodeType === 1 ) { + return jQuery.find.matchesSelector( elem, expr ) ? [ elem ] : []; + } + + return jQuery.find.matches( expr, jQuery.grep( elems, function( elem ) { + return elem.nodeType === 1; + } ) ); +}; + +jQuery.fn.extend( { + find: function( selector ) { + var i, ret, + len = this.length, + self = this; + + if ( typeof selector !== "string" ) { + return this.pushStack( jQuery( selector ).filter( function() { + for ( i = 0; i < len; i++ ) { + if ( jQuery.contains( self[ i ], this ) ) { + return true; + } + } + } ) ); + } + + ret = this.pushStack( [] ); + + for ( i = 0; i < len; i++ ) { + jQuery.find( selector, self[ i ], ret ); + } + + return len > 1 ? jQuery.uniqueSort( ret ) : ret; + }, + filter: function( selector ) { + return this.pushStack( winnow( this, selector || [], false ) ); + }, + not: function( selector ) { + return this.pushStack( winnow( this, selector || [], true ) ); + }, + is: function( selector ) { + return !!winnow( + this, + + // If this is a positional/relative selector, check membership in the returned set + // so $("p:first").is("p:last") won't return true for a doc with two "p". + typeof selector === "string" && rneedsContext.test( selector ) ? + jQuery( selector ) : + selector || [], + false + ).length; + } +} ); + + +// Initialize a jQuery object + + +// A central reference to the root jQuery(document) +var rootjQuery, + + // A simple way to check for HTML strings + // Prioritize #id over to avoid XSS via location.hash (#9521) + // Strict HTML recognition (#11290: must start with <) + // Shortcut simple #id case for speed + rquickExpr = /^(?:\s*(<[\w\W]+>)[^>]*|#([\w-]+))$/, + + init = jQuery.fn.init = function( selector, context, root ) { + var match, elem; + + // HANDLE: $(""), $(null), $(undefined), $(false) + if ( !selector ) { + return this; + } + + // Method init() accepts an alternate rootjQuery + // so migrate can support jQuery.sub (gh-2101) + root = root || rootjQuery; + + // Handle HTML strings + if ( typeof selector === "string" ) { + if ( selector[ 0 ] === "<" && + selector[ selector.length - 1 ] === ">" && + selector.length >= 3 ) { + + // Assume that strings that start and end with <> are HTML and skip the regex check + match = [ null, selector, null ]; + + } else { + match = rquickExpr.exec( selector ); + } + + // Match html or make sure no context is specified for #id + if ( match && ( match[ 1 ] || !context ) ) { + + // HANDLE: $(html) -> $(array) + if ( match[ 1 ] ) { + context = context instanceof jQuery ? context[ 0 ] : context; + + // Option to run scripts is true for back-compat + // Intentionally let the error be thrown if parseHTML is not present + jQuery.merge( this, jQuery.parseHTML( + match[ 1 ], + context && context.nodeType ? context.ownerDocument || context : document, + true + ) ); + + // HANDLE: $(html, props) + if ( rsingleTag.test( match[ 1 ] ) && jQuery.isPlainObject( context ) ) { + for ( match in context ) { + + // Properties of context are called as methods if possible + if ( isFunction( this[ match ] ) ) { + this[ match ]( context[ match ] ); + + // ...and otherwise set as attributes + } else { + this.attr( match, context[ match ] ); + } + } + } + + return this; + + // HANDLE: $(#id) + } else { + elem = document.getElementById( match[ 2 ] ); + + if ( elem ) { + + // Inject the element directly into the jQuery object + this[ 0 ] = elem; + this.length = 1; + } + return this; + } + + // HANDLE: $(expr, $(...)) + } else if ( !context || context.jquery ) { + return ( context || root ).find( selector ); + + // HANDLE: $(expr, context) + // (which is just equivalent to: $(context).find(expr) + } else { + return this.constructor( context ).find( selector ); + } + + // HANDLE: $(DOMElement) + } else if ( selector.nodeType ) { + this[ 0 ] = selector; + this.length = 1; + return this; + + // HANDLE: $(function) + // Shortcut for document ready + } else if ( isFunction( selector ) ) { + return root.ready !== undefined ? + root.ready( selector ) : + + // Execute immediately if ready is not present + selector( jQuery ); + } + + return jQuery.makeArray( selector, this ); + }; + +// Give the init function the jQuery prototype for later instantiation +init.prototype = jQuery.fn; + +// Initialize central reference +rootjQuery = jQuery( document ); + + +var rparentsprev = /^(?:parents|prev(?:Until|All))/, + + // Methods guaranteed to produce a unique set when starting from a unique set + guaranteedUnique = { + children: true, + contents: true, + next: true, + prev: true + }; + +jQuery.fn.extend( { + has: function( target ) { + var targets = jQuery( target, this ), + l = targets.length; + + return this.filter( function() { + var i = 0; + for ( ; i < l; i++ ) { + if ( jQuery.contains( this, targets[ i ] ) ) { + return true; + } + } + } ); + }, + + closest: function( selectors, context ) { + var cur, + i = 0, + l = this.length, + matched = [], + targets = typeof selectors !== "string" && jQuery( selectors ); + + // Positional selectors never match, since there's no _selection_ context + if ( !rneedsContext.test( selectors ) ) { + for ( ; i < l; i++ ) { + for ( cur = this[ i ]; cur && cur !== context; cur = cur.parentNode ) { + + // Always skip document fragments + if ( cur.nodeType < 11 && ( targets ? + targets.index( cur ) > -1 : + + // Don't pass non-elements to Sizzle + cur.nodeType === 1 && + jQuery.find.matchesSelector( cur, selectors ) ) ) { + + matched.push( cur ); + break; + } + } + } + } + + return this.pushStack( matched.length > 1 ? jQuery.uniqueSort( matched ) : matched ); + }, + + // Determine the position of an element within the set + index: function( elem ) { + + // No argument, return index in parent + if ( !elem ) { + return ( this[ 0 ] && this[ 0 ].parentNode ) ? this.first().prevAll().length : -1; + } + + // Index in selector + if ( typeof elem === "string" ) { + return indexOf.call( jQuery( elem ), this[ 0 ] ); + } + + // Locate the position of the desired element + return indexOf.call( this, + + // If it receives a jQuery object, the first element is used + elem.jquery ? elem[ 0 ] : elem + ); + }, + + add: function( selector, context ) { + return this.pushStack( + jQuery.uniqueSort( + jQuery.merge( this.get(), jQuery( selector, context ) ) + ) + ); + }, + + addBack: function( selector ) { + return this.add( selector == null ? + this.prevObject : this.prevObject.filter( selector ) + ); + } +} ); + +function sibling( cur, dir ) { + while ( ( cur = cur[ dir ] ) && cur.nodeType !== 1 ) {} + return cur; +} + +jQuery.each( { + parent: function( elem ) { + var parent = elem.parentNode; + return parent && parent.nodeType !== 11 ? parent : null; + }, + parents: function( elem ) { + return dir( elem, "parentNode" ); + }, + parentsUntil: function( elem, _i, until ) { + return dir( elem, "parentNode", until ); + }, + next: function( elem ) { + return sibling( elem, "nextSibling" ); + }, + prev: function( elem ) { + return sibling( elem, "previousSibling" ); + }, + nextAll: function( elem ) { + return dir( elem, "nextSibling" ); + }, + prevAll: function( elem ) { + return dir( elem, "previousSibling" ); + }, + nextUntil: function( elem, _i, until ) { + return dir( elem, "nextSibling", until ); + }, + prevUntil: function( elem, _i, until ) { + return dir( elem, "previousSibling", until ); + }, + siblings: function( elem ) { + return siblings( ( elem.parentNode || {} ).firstChild, elem ); + }, + children: function( elem ) { + return siblings( elem.firstChild ); + }, + contents: function( elem ) { + if ( elem.contentDocument != null && + + // Support: IE 11+ + // elements with no `data` attribute has an object + // `contentDocument` with a `null` prototype. + getProto( elem.contentDocument ) ) { + + return elem.contentDocument; + } + + // Support: IE 9 - 11 only, iOS 7 only, Android Browser <=4.3 only + // Treat the template element as a regular one in browsers that + // don't support it. + if ( nodeName( elem, "template" ) ) { + elem = elem.content || elem; + } + + return jQuery.merge( [], elem.childNodes ); + } +}, function( name, fn ) { + jQuery.fn[ name ] = function( until, selector ) { + var matched = jQuery.map( this, fn, until ); + + if ( name.slice( -5 ) !== "Until" ) { + selector = until; + } + + if ( selector && typeof selector === "string" ) { + matched = jQuery.filter( selector, matched ); + } + + if ( this.length > 1 ) { + + // Remove duplicates + if ( !guaranteedUnique[ name ] ) { + jQuery.uniqueSort( matched ); + } + + // Reverse order for parents* and prev-derivatives + if ( rparentsprev.test( name ) ) { + matched.reverse(); + } + } + + return this.pushStack( matched ); + }; +} ); +var rnothtmlwhite = ( /[^\x20\t\r\n\f]+/g ); + + + +// Convert String-formatted options into Object-formatted ones +function createOptions( options ) { + var object = {}; + jQuery.each( options.match( rnothtmlwhite ) || [], function( _, flag ) { + object[ flag ] = true; + } ); + return object; +} + +/* + * Create a callback list using the following parameters: + * + * options: an optional list of space-separated options that will change how + * the callback list behaves or a more traditional option object + * + * By default a callback list will act like an event callback list and can be + * "fired" multiple times. + * + * Possible options: + * + * once: will ensure the callback list can only be fired once (like a Deferred) + * + * memory: will keep track of previous values and will call any callback added + * after the list has been fired right away with the latest "memorized" + * values (like a Deferred) + * + * unique: will ensure a callback can only be added once (no duplicate in the list) + * + * stopOnFalse: interrupt callings when a callback returns false + * + */ +jQuery.Callbacks = function( options ) { + + // Convert options from String-formatted to Object-formatted if needed + // (we check in cache first) + options = typeof options === "string" ? + createOptions( options ) : + jQuery.extend( {}, options ); + + var // Flag to know if list is currently firing + firing, + + // Last fire value for non-forgettable lists + memory, + + // Flag to know if list was already fired + fired, + + // Flag to prevent firing + locked, + + // Actual callback list + list = [], + + // Queue of execution data for repeatable lists + queue = [], + + // Index of currently firing callback (modified by add/remove as needed) + firingIndex = -1, + + // Fire callbacks + fire = function() { + + // Enforce single-firing + locked = locked || options.once; + + // Execute callbacks for all pending executions, + // respecting firingIndex overrides and runtime changes + fired = firing = true; + for ( ; queue.length; firingIndex = -1 ) { + memory = queue.shift(); + while ( ++firingIndex < list.length ) { + + // Run callback and check for early termination + if ( list[ firingIndex ].apply( memory[ 0 ], memory[ 1 ] ) === false && + options.stopOnFalse ) { + + // Jump to end and forget the data so .add doesn't re-fire + firingIndex = list.length; + memory = false; + } + } + } + + // Forget the data if we're done with it + if ( !options.memory ) { + memory = false; + } + + firing = false; + + // Clean up if we're done firing for good + if ( locked ) { + + // Keep an empty list if we have data for future add calls + if ( memory ) { + list = []; + + // Otherwise, this object is spent + } else { + list = ""; + } + } + }, + + // Actual Callbacks object + self = { + + // Add a callback or a collection of callbacks to the list + add: function() { + if ( list ) { + + // If we have memory from a past run, we should fire after adding + if ( memory && !firing ) { + firingIndex = list.length - 1; + queue.push( memory ); + } + + ( function add( args ) { + jQuery.each( args, function( _, arg ) { + if ( isFunction( arg ) ) { + if ( !options.unique || !self.has( arg ) ) { + list.push( arg ); + } + } else if ( arg && arg.length && toType( arg ) !== "string" ) { + + // Inspect recursively + add( arg ); + } + } ); + } )( arguments ); + + if ( memory && !firing ) { + fire(); + } + } + return this; + }, + + // Remove a callback from the list + remove: function() { + jQuery.each( arguments, function( _, arg ) { + var index; + while ( ( index = jQuery.inArray( arg, list, index ) ) > -1 ) { + list.splice( index, 1 ); + + // Handle firing indexes + if ( index <= firingIndex ) { + firingIndex--; + } + } + } ); + return this; + }, + + // Check if a given callback is in the list. + // If no argument is given, return whether or not list has callbacks attached. + has: function( fn ) { + return fn ? + jQuery.inArray( fn, list ) > -1 : + list.length > 0; + }, + + // Remove all callbacks from the list + empty: function() { + if ( list ) { + list = []; + } + return this; + }, + + // Disable .fire and .add + // Abort any current/pending executions + // Clear all callbacks and values + disable: function() { + locked = queue = []; + list = memory = ""; + return this; + }, + disabled: function() { + return !list; + }, + + // Disable .fire + // Also disable .add unless we have memory (since it would have no effect) + // Abort any pending executions + lock: function() { + locked = queue = []; + if ( !memory && !firing ) { + list = memory = ""; + } + return this; + }, + locked: function() { + return !!locked; + }, + + // Call all callbacks with the given context and arguments + fireWith: function( context, args ) { + if ( !locked ) { + args = args || []; + args = [ context, args.slice ? args.slice() : args ]; + queue.push( args ); + if ( !firing ) { + fire(); + } + } + return this; + }, + + // Call all the callbacks with the given arguments + fire: function() { + self.fireWith( this, arguments ); + return this; + }, + + // To know if the callbacks have already been called at least once + fired: function() { + return !!fired; + } + }; + + return self; +}; + + +function Identity( v ) { + return v; +} +function Thrower( ex ) { + throw ex; +} + +function adoptValue( value, resolve, reject, noValue ) { + var method; + + try { + + // Check for promise aspect first to privilege synchronous behavior + if ( value && isFunction( ( method = value.promise ) ) ) { + method.call( value ).done( resolve ).fail( reject ); + + // Other thenables + } else if ( value && isFunction( ( method = value.then ) ) ) { + method.call( value, resolve, reject ); + + // Other non-thenables + } else { + + // Control `resolve` arguments by letting Array#slice cast boolean `noValue` to integer: + // * false: [ value ].slice( 0 ) => resolve( value ) + // * true: [ value ].slice( 1 ) => resolve() + resolve.apply( undefined, [ value ].slice( noValue ) ); + } + + // For Promises/A+, convert exceptions into rejections + // Since jQuery.when doesn't unwrap thenables, we can skip the extra checks appearing in + // Deferred#then to conditionally suppress rejection. + } catch ( value ) { + + // Support: Android 4.0 only + // Strict mode functions invoked without .call/.apply get global-object context + reject.apply( undefined, [ value ] ); + } +} + +jQuery.extend( { + + Deferred: function( func ) { + var tuples = [ + + // action, add listener, callbacks, + // ... .then handlers, argument index, [final state] + [ "notify", "progress", jQuery.Callbacks( "memory" ), + jQuery.Callbacks( "memory" ), 2 ], + [ "resolve", "done", jQuery.Callbacks( "once memory" ), + jQuery.Callbacks( "once memory" ), 0, "resolved" ], + [ "reject", "fail", jQuery.Callbacks( "once memory" ), + jQuery.Callbacks( "once memory" ), 1, "rejected" ] + ], + state = "pending", + promise = { + state: function() { + return state; + }, + always: function() { + deferred.done( arguments ).fail( arguments ); + return this; + }, + "catch": function( fn ) { + return promise.then( null, fn ); + }, + + // Keep pipe for back-compat + pipe: function( /* fnDone, fnFail, fnProgress */ ) { + var fns = arguments; + + return jQuery.Deferred( function( newDefer ) { + jQuery.each( tuples, function( _i, tuple ) { + + // Map tuples (progress, done, fail) to arguments (done, fail, progress) + var fn = isFunction( fns[ tuple[ 4 ] ] ) && fns[ tuple[ 4 ] ]; + + // deferred.progress(function() { bind to newDefer or newDefer.notify }) + // deferred.done(function() { bind to newDefer or newDefer.resolve }) + // deferred.fail(function() { bind to newDefer or newDefer.reject }) + deferred[ tuple[ 1 ] ]( function() { + var returned = fn && fn.apply( this, arguments ); + if ( returned && isFunction( returned.promise ) ) { + returned.promise() + .progress( newDefer.notify ) + .done( newDefer.resolve ) + .fail( newDefer.reject ); + } else { + newDefer[ tuple[ 0 ] + "With" ]( + this, + fn ? [ returned ] : arguments + ); + } + } ); + } ); + fns = null; + } ).promise(); + }, + then: function( onFulfilled, onRejected, onProgress ) { + var maxDepth = 0; + function resolve( depth, deferred, handler, special ) { + return function() { + var that = this, + args = arguments, + mightThrow = function() { + var returned, then; + + // Support: Promises/A+ section 2.3.3.3.3 + // https://promisesaplus.com/#point-59 + // Ignore double-resolution attempts + if ( depth < maxDepth ) { + return; + } + + returned = handler.apply( that, args ); + + // Support: Promises/A+ section 2.3.1 + // https://promisesaplus.com/#point-48 + if ( returned === deferred.promise() ) { + throw new TypeError( "Thenable self-resolution" ); + } + + // Support: Promises/A+ sections 2.3.3.1, 3.5 + // https://promisesaplus.com/#point-54 + // https://promisesaplus.com/#point-75 + // Retrieve `then` only once + then = returned && + + // Support: Promises/A+ section 2.3.4 + // https://promisesaplus.com/#point-64 + // Only check objects and functions for thenability + ( typeof returned === "object" || + typeof returned === "function" ) && + returned.then; + + // Handle a returned thenable + if ( isFunction( then ) ) { + + // Special processors (notify) just wait for resolution + if ( special ) { + then.call( + returned, + resolve( maxDepth, deferred, Identity, special ), + resolve( maxDepth, deferred, Thrower, special ) + ); + + // Normal processors (resolve) also hook into progress + } else { + + // ...and disregard older resolution values + maxDepth++; + + then.call( + returned, + resolve( maxDepth, deferred, Identity, special ), + resolve( maxDepth, deferred, Thrower, special ), + resolve( maxDepth, deferred, Identity, + deferred.notifyWith ) + ); + } + + // Handle all other returned values + } else { + + // Only substitute handlers pass on context + // and multiple values (non-spec behavior) + if ( handler !== Identity ) { + that = undefined; + args = [ returned ]; + } + + // Process the value(s) + // Default process is resolve + ( special || deferred.resolveWith )( that, args ); + } + }, + + // Only normal processors (resolve) catch and reject exceptions + process = special ? + mightThrow : + function() { + try { + mightThrow(); + } catch ( e ) { + + if ( jQuery.Deferred.exceptionHook ) { + jQuery.Deferred.exceptionHook( e, + process.stackTrace ); + } + + // Support: Promises/A+ section 2.3.3.3.4.1 + // https://promisesaplus.com/#point-61 + // Ignore post-resolution exceptions + if ( depth + 1 >= maxDepth ) { + + // Only substitute handlers pass on context + // and multiple values (non-spec behavior) + if ( handler !== Thrower ) { + that = undefined; + args = [ e ]; + } + + deferred.rejectWith( that, args ); + } + } + }; + + // Support: Promises/A+ section 2.3.3.3.1 + // https://promisesaplus.com/#point-57 + // Re-resolve promises immediately to dodge false rejection from + // subsequent errors + if ( depth ) { + process(); + } else { + + // Call an optional hook to record the stack, in case of exception + // since it's otherwise lost when execution goes async + if ( jQuery.Deferred.getStackHook ) { + process.stackTrace = jQuery.Deferred.getStackHook(); + } + window.setTimeout( process ); + } + }; + } + + return jQuery.Deferred( function( newDefer ) { + + // progress_handlers.add( ... ) + tuples[ 0 ][ 3 ].add( + resolve( + 0, + newDefer, + isFunction( onProgress ) ? + onProgress : + Identity, + newDefer.notifyWith + ) + ); + + // fulfilled_handlers.add( ... ) + tuples[ 1 ][ 3 ].add( + resolve( + 0, + newDefer, + isFunction( onFulfilled ) ? + onFulfilled : + Identity + ) + ); + + // rejected_handlers.add( ... ) + tuples[ 2 ][ 3 ].add( + resolve( + 0, + newDefer, + isFunction( onRejected ) ? + onRejected : + Thrower + ) + ); + } ).promise(); + }, + + // Get a promise for this deferred + // If obj is provided, the promise aspect is added to the object + promise: function( obj ) { + return obj != null ? jQuery.extend( obj, promise ) : promise; + } + }, + deferred = {}; + + // Add list-specific methods + jQuery.each( tuples, function( i, tuple ) { + var list = tuple[ 2 ], + stateString = tuple[ 5 ]; + + // promise.progress = list.add + // promise.done = list.add + // promise.fail = list.add + promise[ tuple[ 1 ] ] = list.add; + + // Handle state + if ( stateString ) { + list.add( + function() { + + // state = "resolved" (i.e., fulfilled) + // state = "rejected" + state = stateString; + }, + + // rejected_callbacks.disable + // fulfilled_callbacks.disable + tuples[ 3 - i ][ 2 ].disable, + + // rejected_handlers.disable + // fulfilled_handlers.disable + tuples[ 3 - i ][ 3 ].disable, + + // progress_callbacks.lock + tuples[ 0 ][ 2 ].lock, + + // progress_handlers.lock + tuples[ 0 ][ 3 ].lock + ); + } + + // progress_handlers.fire + // fulfilled_handlers.fire + // rejected_handlers.fire + list.add( tuple[ 3 ].fire ); + + // deferred.notify = function() { deferred.notifyWith(...) } + // deferred.resolve = function() { deferred.resolveWith(...) } + // deferred.reject = function() { deferred.rejectWith(...) } + deferred[ tuple[ 0 ] ] = function() { + deferred[ tuple[ 0 ] + "With" ]( this === deferred ? undefined : this, arguments ); + return this; + }; + + // deferred.notifyWith = list.fireWith + // deferred.resolveWith = list.fireWith + // deferred.rejectWith = list.fireWith + deferred[ tuple[ 0 ] + "With" ] = list.fireWith; + } ); + + // Make the deferred a promise + promise.promise( deferred ); + + // Call given func if any + if ( func ) { + func.call( deferred, deferred ); + } + + // All done! + return deferred; + }, + + // Deferred helper + when: function( singleValue ) { + var + + // count of uncompleted subordinates + remaining = arguments.length, + + // count of unprocessed arguments + i = remaining, + + // subordinate fulfillment data + resolveContexts = Array( i ), + resolveValues = slice.call( arguments ), + + // the master Deferred + master = jQuery.Deferred(), + + // subordinate callback factory + updateFunc = function( i ) { + return function( value ) { + resolveContexts[ i ] = this; + resolveValues[ i ] = arguments.length > 1 ? slice.call( arguments ) : value; + if ( !( --remaining ) ) { + master.resolveWith( resolveContexts, resolveValues ); + } + }; + }; + + // Single- and empty arguments are adopted like Promise.resolve + if ( remaining <= 1 ) { + adoptValue( singleValue, master.done( updateFunc( i ) ).resolve, master.reject, + !remaining ); + + // Use .then() to unwrap secondary thenables (cf. gh-3000) + if ( master.state() === "pending" || + isFunction( resolveValues[ i ] && resolveValues[ i ].then ) ) { + + return master.then(); + } + } + + // Multiple arguments are aggregated like Promise.all array elements + while ( i-- ) { + adoptValue( resolveValues[ i ], updateFunc( i ), master.reject ); + } + + return master.promise(); + } +} ); + + +// These usually indicate a programmer mistake during development, +// warn about them ASAP rather than swallowing them by default. +var rerrorNames = /^(Eval|Internal|Range|Reference|Syntax|Type|URI)Error$/; + +jQuery.Deferred.exceptionHook = function( error, stack ) { + + // Support: IE 8 - 9 only + // Console exists when dev tools are open, which can happen at any time + if ( window.console && window.console.warn && error && rerrorNames.test( error.name ) ) { + window.console.warn( "jQuery.Deferred exception: " + error.message, error.stack, stack ); + } +}; + + + + +jQuery.readyException = function( error ) { + window.setTimeout( function() { + throw error; + } ); +}; + + + + +// The deferred used on DOM ready +var readyList = jQuery.Deferred(); + +jQuery.fn.ready = function( fn ) { + + readyList + .then( fn ) + + // Wrap jQuery.readyException in a function so that the lookup + // happens at the time of error handling instead of callback + // registration. + .catch( function( error ) { + jQuery.readyException( error ); + } ); + + return this; +}; + +jQuery.extend( { + + // Is the DOM ready to be used? Set to true once it occurs. + isReady: false, + + // A counter to track how many items to wait for before + // the ready event fires. See #6781 + readyWait: 1, + + // Handle when the DOM is ready + ready: function( wait ) { + + // Abort if there are pending holds or we're already ready + if ( wait === true ? --jQuery.readyWait : jQuery.isReady ) { + return; + } + + // Remember that the DOM is ready + jQuery.isReady = true; + + // If a normal DOM Ready event fired, decrement, and wait if need be + if ( wait !== true && --jQuery.readyWait > 0 ) { + return; + } + + // If there are functions bound, to execute + readyList.resolveWith( document, [ jQuery ] ); + } +} ); + +jQuery.ready.then = readyList.then; + +// The ready event handler and self cleanup method +function completed() { + document.removeEventListener( "DOMContentLoaded", completed ); + window.removeEventListener( "load", completed ); + jQuery.ready(); +} + +// Catch cases where $(document).ready() is called +// after the browser event has already occurred. +// Support: IE <=9 - 10 only +// Older IE sometimes signals "interactive" too soon +if ( document.readyState === "complete" || + ( document.readyState !== "loading" && !document.documentElement.doScroll ) ) { + + // Handle it asynchronously to allow scripts the opportunity to delay ready + window.setTimeout( jQuery.ready ); + +} else { + + // Use the handy event callback + document.addEventListener( "DOMContentLoaded", completed ); + + // A fallback to window.onload, that will always work + window.addEventListener( "load", completed ); +} + + + + +// Multifunctional method to get and set values of a collection +// The value/s can optionally be executed if it's a function +var access = function( elems, fn, key, value, chainable, emptyGet, raw ) { + var i = 0, + len = elems.length, + bulk = key == null; + + // Sets many values + if ( toType( key ) === "object" ) { + chainable = true; + for ( i in key ) { + access( elems, fn, i, key[ i ], true, emptyGet, raw ); + } + + // Sets one value + } else if ( value !== undefined ) { + chainable = true; + + if ( !isFunction( value ) ) { + raw = true; + } + + if ( bulk ) { + + // Bulk operations run against the entire set + if ( raw ) { + fn.call( elems, value ); + fn = null; + + // ...except when executing function values + } else { + bulk = fn; + fn = function( elem, _key, value ) { + return bulk.call( jQuery( elem ), value ); + }; + } + } + + if ( fn ) { + for ( ; i < len; i++ ) { + fn( + elems[ i ], key, raw ? + value : + value.call( elems[ i ], i, fn( elems[ i ], key ) ) + ); + } + } + } + + if ( chainable ) { + return elems; + } + + // Gets + if ( bulk ) { + return fn.call( elems ); + } + + return len ? fn( elems[ 0 ], key ) : emptyGet; +}; + + +// Matches dashed string for camelizing +var rmsPrefix = /^-ms-/, + rdashAlpha = /-([a-z])/g; + +// Used by camelCase as callback to replace() +function fcamelCase( _all, letter ) { + return letter.toUpperCase(); +} + +// Convert dashed to camelCase; used by the css and data modules +// Support: IE <=9 - 11, Edge 12 - 15 +// Microsoft forgot to hump their vendor prefix (#9572) +function camelCase( string ) { + return string.replace( rmsPrefix, "ms-" ).replace( rdashAlpha, fcamelCase ); +} +var acceptData = function( owner ) { + + // Accepts only: + // - Node + // - Node.ELEMENT_NODE + // - Node.DOCUMENT_NODE + // - Object + // - Any + return owner.nodeType === 1 || owner.nodeType === 9 || !( +owner.nodeType ); +}; + + + + +function Data() { + this.expando = jQuery.expando + Data.uid++; +} + +Data.uid = 1; + +Data.prototype = { + + cache: function( owner ) { + + // Check if the owner object already has a cache + var value = owner[ this.expando ]; + + // If not, create one + if ( !value ) { + value = {}; + + // We can accept data for non-element nodes in modern browsers, + // but we should not, see #8335. + // Always return an empty object. + if ( acceptData( owner ) ) { + + // If it is a node unlikely to be stringify-ed or looped over + // use plain assignment + if ( owner.nodeType ) { + owner[ this.expando ] = value; + + // Otherwise secure it in a non-enumerable property + // configurable must be true to allow the property to be + // deleted when data is removed + } else { + Object.defineProperty( owner, this.expando, { + value: value, + configurable: true + } ); + } + } + } + + return value; + }, + set: function( owner, data, value ) { + var prop, + cache = this.cache( owner ); + + // Handle: [ owner, key, value ] args + // Always use camelCase key (gh-2257) + if ( typeof data === "string" ) { + cache[ camelCase( data ) ] = value; + + // Handle: [ owner, { properties } ] args + } else { + + // Copy the properties one-by-one to the cache object + for ( prop in data ) { + cache[ camelCase( prop ) ] = data[ prop ]; + } + } + return cache; + }, + get: function( owner, key ) { + return key === undefined ? + this.cache( owner ) : + + // Always use camelCase key (gh-2257) + owner[ this.expando ] && owner[ this.expando ][ camelCase( key ) ]; + }, + access: function( owner, key, value ) { + + // In cases where either: + // + // 1. No key was specified + // 2. A string key was specified, but no value provided + // + // Take the "read" path and allow the get method to determine + // which value to return, respectively either: + // + // 1. The entire cache object + // 2. The data stored at the key + // + if ( key === undefined || + ( ( key && typeof key === "string" ) && value === undefined ) ) { + + return this.get( owner, key ); + } + + // When the key is not a string, or both a key and value + // are specified, set or extend (existing objects) with either: + // + // 1. An object of properties + // 2. A key and value + // + this.set( owner, key, value ); + + // Since the "set" path can have two possible entry points + // return the expected data based on which path was taken[*] + return value !== undefined ? value : key; + }, + remove: function( owner, key ) { + var i, + cache = owner[ this.expando ]; + + if ( cache === undefined ) { + return; + } + + if ( key !== undefined ) { + + // Support array or space separated string of keys + if ( Array.isArray( key ) ) { + + // If key is an array of keys... + // We always set camelCase keys, so remove that. + key = key.map( camelCase ); + } else { + key = camelCase( key ); + + // If a key with the spaces exists, use it. + // Otherwise, create an array by matching non-whitespace + key = key in cache ? + [ key ] : + ( key.match( rnothtmlwhite ) || [] ); + } + + i = key.length; + + while ( i-- ) { + delete cache[ key[ i ] ]; + } + } + + // Remove the expando if there's no more data + if ( key === undefined || jQuery.isEmptyObject( cache ) ) { + + // Support: Chrome <=35 - 45 + // Webkit & Blink performance suffers when deleting properties + // from DOM nodes, so set to undefined instead + // https://bugs.chromium.org/p/chromium/issues/detail?id=378607 (bug restricted) + if ( owner.nodeType ) { + owner[ this.expando ] = undefined; + } else { + delete owner[ this.expando ]; + } + } + }, + hasData: function( owner ) { + var cache = owner[ this.expando ]; + return cache !== undefined && !jQuery.isEmptyObject( cache ); + } +}; +var dataPriv = new Data(); + +var dataUser = new Data(); + + + +// Implementation Summary +// +// 1. Enforce API surface and semantic compatibility with 1.9.x branch +// 2. Improve the module's maintainability by reducing the storage +// paths to a single mechanism. +// 3. Use the same single mechanism to support "private" and "user" data. +// 4. _Never_ expose "private" data to user code (TODO: Drop _data, _removeData) +// 5. Avoid exposing implementation details on user objects (eg. expando properties) +// 6. Provide a clear path for implementation upgrade to WeakMap in 2014 + +var rbrace = /^(?:\{[\w\W]*\}|\[[\w\W]*\])$/, + rmultiDash = /[A-Z]/g; + +function getData( data ) { + if ( data === "true" ) { + return true; + } + + if ( data === "false" ) { + return false; + } + + if ( data === "null" ) { + return null; + } + + // Only convert to a number if it doesn't change the string + if ( data === +data + "" ) { + return +data; + } + + if ( rbrace.test( data ) ) { + return JSON.parse( data ); + } + + return data; +} + +function dataAttr( elem, key, data ) { + var name; + + // If nothing was found internally, try to fetch any + // data from the HTML5 data-* attribute + if ( data === undefined && elem.nodeType === 1 ) { + name = "data-" + key.replace( rmultiDash, "-$&" ).toLowerCase(); + data = elem.getAttribute( name ); + + if ( typeof data === "string" ) { + try { + data = getData( data ); + } catch ( e ) {} + + // Make sure we set the data so it isn't changed later + dataUser.set( elem, key, data ); + } else { + data = undefined; + } + } + return data; +} + +jQuery.extend( { + hasData: function( elem ) { + return dataUser.hasData( elem ) || dataPriv.hasData( elem ); + }, + + data: function( elem, name, data ) { + return dataUser.access( elem, name, data ); + }, + + removeData: function( elem, name ) { + dataUser.remove( elem, name ); + }, + + // TODO: Now that all calls to _data and _removeData have been replaced + // with direct calls to dataPriv methods, these can be deprecated. + _data: function( elem, name, data ) { + return dataPriv.access( elem, name, data ); + }, + + _removeData: function( elem, name ) { + dataPriv.remove( elem, name ); + } +} ); + +jQuery.fn.extend( { + data: function( key, value ) { + var i, name, data, + elem = this[ 0 ], + attrs = elem && elem.attributes; + + // Gets all values + if ( key === undefined ) { + if ( this.length ) { + data = dataUser.get( elem ); + + if ( elem.nodeType === 1 && !dataPriv.get( elem, "hasDataAttrs" ) ) { + i = attrs.length; + while ( i-- ) { + + // Support: IE 11 only + // The attrs elements can be null (#14894) + if ( attrs[ i ] ) { + name = attrs[ i ].name; + if ( name.indexOf( "data-" ) === 0 ) { + name = camelCase( name.slice( 5 ) ); + dataAttr( elem, name, data[ name ] ); + } + } + } + dataPriv.set( elem, "hasDataAttrs", true ); + } + } + + return data; + } + + // Sets multiple values + if ( typeof key === "object" ) { + return this.each( function() { + dataUser.set( this, key ); + } ); + } + + return access( this, function( value ) { + var data; + + // The calling jQuery object (element matches) is not empty + // (and therefore has an element appears at this[ 0 ]) and the + // `value` parameter was not undefined. An empty jQuery object + // will result in `undefined` for elem = this[ 0 ] which will + // throw an exception if an attempt to read a data cache is made. + if ( elem && value === undefined ) { + + // Attempt to get data from the cache + // The key will always be camelCased in Data + data = dataUser.get( elem, key ); + if ( data !== undefined ) { + return data; + } + + // Attempt to "discover" the data in + // HTML5 custom data-* attrs + data = dataAttr( elem, key ); + if ( data !== undefined ) { + return data; + } + + // We tried really hard, but the data doesn't exist. + return; + } + + // Set the data... + this.each( function() { + + // We always store the camelCased key + dataUser.set( this, key, value ); + } ); + }, null, value, arguments.length > 1, null, true ); + }, + + removeData: function( key ) { + return this.each( function() { + dataUser.remove( this, key ); + } ); + } +} ); + + +jQuery.extend( { + queue: function( elem, type, data ) { + var queue; + + if ( elem ) { + type = ( type || "fx" ) + "queue"; + queue = dataPriv.get( elem, type ); + + // Speed up dequeue by getting out quickly if this is just a lookup + if ( data ) { + if ( !queue || Array.isArray( data ) ) { + queue = dataPriv.access( elem, type, jQuery.makeArray( data ) ); + } else { + queue.push( data ); + } + } + return queue || []; + } + }, + + dequeue: function( elem, type ) { + type = type || "fx"; + + var queue = jQuery.queue( elem, type ), + startLength = queue.length, + fn = queue.shift(), + hooks = jQuery._queueHooks( elem, type ), + next = function() { + jQuery.dequeue( elem, type ); + }; + + // If the fx queue is dequeued, always remove the progress sentinel + if ( fn === "inprogress" ) { + fn = queue.shift(); + startLength--; + } + + if ( fn ) { + + // Add a progress sentinel to prevent the fx queue from being + // automatically dequeued + if ( type === "fx" ) { + queue.unshift( "inprogress" ); + } + + // Clear up the last queue stop function + delete hooks.stop; + fn.call( elem, next, hooks ); + } + + if ( !startLength && hooks ) { + hooks.empty.fire(); + } + }, + + // Not public - generate a queueHooks object, or return the current one + _queueHooks: function( elem, type ) { + var key = type + "queueHooks"; + return dataPriv.get( elem, key ) || dataPriv.access( elem, key, { + empty: jQuery.Callbacks( "once memory" ).add( function() { + dataPriv.remove( elem, [ type + "queue", key ] ); + } ) + } ); + } +} ); + +jQuery.fn.extend( { + queue: function( type, data ) { + var setter = 2; + + if ( typeof type !== "string" ) { + data = type; + type = "fx"; + setter--; + } + + if ( arguments.length < setter ) { + return jQuery.queue( this[ 0 ], type ); + } + + return data === undefined ? + this : + this.each( function() { + var queue = jQuery.queue( this, type, data ); + + // Ensure a hooks for this queue + jQuery._queueHooks( this, type ); + + if ( type === "fx" && queue[ 0 ] !== "inprogress" ) { + jQuery.dequeue( this, type ); + } + } ); + }, + dequeue: function( type ) { + return this.each( function() { + jQuery.dequeue( this, type ); + } ); + }, + clearQueue: function( type ) { + return this.queue( type || "fx", [] ); + }, + + // Get a promise resolved when queues of a certain type + // are emptied (fx is the type by default) + promise: function( type, obj ) { + var tmp, + count = 1, + defer = jQuery.Deferred(), + elements = this, + i = this.length, + resolve = function() { + if ( !( --count ) ) { + defer.resolveWith( elements, [ elements ] ); + } + }; + + if ( typeof type !== "string" ) { + obj = type; + type = undefined; + } + type = type || "fx"; + + while ( i-- ) { + tmp = dataPriv.get( elements[ i ], type + "queueHooks" ); + if ( tmp && tmp.empty ) { + count++; + tmp.empty.add( resolve ); + } + } + resolve(); + return defer.promise( obj ); + } +} ); +var pnum = ( /[+-]?(?:\d*\.|)\d+(?:[eE][+-]?\d+|)/ ).source; + +var rcssNum = new RegExp( "^(?:([+-])=|)(" + pnum + ")([a-z%]*)$", "i" ); + + +var cssExpand = [ "Top", "Right", "Bottom", "Left" ]; + +var documentElement = document.documentElement; + + + + var isAttached = function( elem ) { + return jQuery.contains( elem.ownerDocument, elem ); + }, + composed = { composed: true }; + + // Support: IE 9 - 11+, Edge 12 - 18+, iOS 10.0 - 10.2 only + // Check attachment across shadow DOM boundaries when possible (gh-3504) + // Support: iOS 10.0-10.2 only + // Early iOS 10 versions support `attachShadow` but not `getRootNode`, + // leading to errors. We need to check for `getRootNode`. + if ( documentElement.getRootNode ) { + isAttached = function( elem ) { + return jQuery.contains( elem.ownerDocument, elem ) || + elem.getRootNode( composed ) === elem.ownerDocument; + }; + } +var isHiddenWithinTree = function( elem, el ) { + + // isHiddenWithinTree might be called from jQuery#filter function; + // in that case, element will be second argument + elem = el || elem; + + // Inline style trumps all + return elem.style.display === "none" || + elem.style.display === "" && + + // Otherwise, check computed style + // Support: Firefox <=43 - 45 + // Disconnected elements can have computed display: none, so first confirm that elem is + // in the document. + isAttached( elem ) && + + jQuery.css( elem, "display" ) === "none"; + }; + + + +function adjustCSS( elem, prop, valueParts, tween ) { + var adjusted, scale, + maxIterations = 20, + currentValue = tween ? + function() { + return tween.cur(); + } : + function() { + return jQuery.css( elem, prop, "" ); + }, + initial = currentValue(), + unit = valueParts && valueParts[ 3 ] || ( jQuery.cssNumber[ prop ] ? "" : "px" ), + + // Starting value computation is required for potential unit mismatches + initialInUnit = elem.nodeType && + ( jQuery.cssNumber[ prop ] || unit !== "px" && +initial ) && + rcssNum.exec( jQuery.css( elem, prop ) ); + + if ( initialInUnit && initialInUnit[ 3 ] !== unit ) { + + // Support: Firefox <=54 + // Halve the iteration target value to prevent interference from CSS upper bounds (gh-2144) + initial = initial / 2; + + // Trust units reported by jQuery.css + unit = unit || initialInUnit[ 3 ]; + + // Iteratively approximate from a nonzero starting point + initialInUnit = +initial || 1; + + while ( maxIterations-- ) { + + // Evaluate and update our best guess (doubling guesses that zero out). + // Finish if the scale equals or crosses 1 (making the old*new product non-positive). + jQuery.style( elem, prop, initialInUnit + unit ); + if ( ( 1 - scale ) * ( 1 - ( scale = currentValue() / initial || 0.5 ) ) <= 0 ) { + maxIterations = 0; + } + initialInUnit = initialInUnit / scale; + + } + + initialInUnit = initialInUnit * 2; + jQuery.style( elem, prop, initialInUnit + unit ); + + // Make sure we update the tween properties later on + valueParts = valueParts || []; + } + + if ( valueParts ) { + initialInUnit = +initialInUnit || +initial || 0; + + // Apply relative offset (+=/-=) if specified + adjusted = valueParts[ 1 ] ? + initialInUnit + ( valueParts[ 1 ] + 1 ) * valueParts[ 2 ] : + +valueParts[ 2 ]; + if ( tween ) { + tween.unit = unit; + tween.start = initialInUnit; + tween.end = adjusted; + } + } + return adjusted; +} + + +var defaultDisplayMap = {}; + +function getDefaultDisplay( elem ) { + var temp, + doc = elem.ownerDocument, + nodeName = elem.nodeName, + display = defaultDisplayMap[ nodeName ]; + + if ( display ) { + return display; + } + + temp = doc.body.appendChild( doc.createElement( nodeName ) ); + display = jQuery.css( temp, "display" ); + + temp.parentNode.removeChild( temp ); + + if ( display === "none" ) { + display = "block"; + } + defaultDisplayMap[ nodeName ] = display; + + return display; +} + +function showHide( elements, show ) { + var display, elem, + values = [], + index = 0, + length = elements.length; + + // Determine new display value for elements that need to change + for ( ; index < length; index++ ) { + elem = elements[ index ]; + if ( !elem.style ) { + continue; + } + + display = elem.style.display; + if ( show ) { + + // Since we force visibility upon cascade-hidden elements, an immediate (and slow) + // check is required in this first loop unless we have a nonempty display value (either + // inline or about-to-be-restored) + if ( display === "none" ) { + values[ index ] = dataPriv.get( elem, "display" ) || null; + if ( !values[ index ] ) { + elem.style.display = ""; + } + } + if ( elem.style.display === "" && isHiddenWithinTree( elem ) ) { + values[ index ] = getDefaultDisplay( elem ); + } + } else { + if ( display !== "none" ) { + values[ index ] = "none"; + + // Remember what we're overwriting + dataPriv.set( elem, "display", display ); + } + } + } + + // Set the display of the elements in a second loop to avoid constant reflow + for ( index = 0; index < length; index++ ) { + if ( values[ index ] != null ) { + elements[ index ].style.display = values[ index ]; + } + } + + return elements; +} + +jQuery.fn.extend( { + show: function() { + return showHide( this, true ); + }, + hide: function() { + return showHide( this ); + }, + toggle: function( state ) { + if ( typeof state === "boolean" ) { + return state ? this.show() : this.hide(); + } + + return this.each( function() { + if ( isHiddenWithinTree( this ) ) { + jQuery( this ).show(); + } else { + jQuery( this ).hide(); + } + } ); + } +} ); +var rcheckableType = ( /^(?:checkbox|radio)$/i ); + +var rtagName = ( /<([a-z][^\/\0>\x20\t\r\n\f]*)/i ); + +var rscriptType = ( /^$|^module$|\/(?:java|ecma)script/i ); + + + +( function() { + var fragment = document.createDocumentFragment(), + div = fragment.appendChild( document.createElement( "div" ) ), + input = document.createElement( "input" ); + + // Support: Android 4.0 - 4.3 only + // Check state lost if the name is set (#11217) + // Support: Windows Web Apps (WWA) + // `name` and `type` must use .setAttribute for WWA (#14901) + input.setAttribute( "type", "radio" ); + input.setAttribute( "checked", "checked" ); + input.setAttribute( "name", "t" ); + + div.appendChild( input ); + + // Support: Android <=4.1 only + // Older WebKit doesn't clone checked state correctly in fragments + support.checkClone = div.cloneNode( true ).cloneNode( true ).lastChild.checked; + + // Support: IE <=11 only + // Make sure textarea (and checkbox) defaultValue is properly cloned + div.innerHTML = ""; + support.noCloneChecked = !!div.cloneNode( true ).lastChild.defaultValue; + + // Support: IE <=9 only + // IE <=9 replaces "; + support.option = !!div.lastChild; +} )(); + + +// We have to close these tags to support XHTML (#13200) +var wrapMap = { + + // XHTML parsers do not magically insert elements in the + // same way that tag soup parsers do. So we cannot shorten + // this by omitting or other required elements. + thead: [ 1, "", "
" ], + col: [ 2, "", "
" ], + tr: [ 2, "", "
" ], + td: [ 3, "", "
" ], + + _default: [ 0, "", "" ] +}; + +wrapMap.tbody = wrapMap.tfoot = wrapMap.colgroup = wrapMap.caption = wrapMap.thead; +wrapMap.th = wrapMap.td; + +// Support: IE <=9 only +if ( !support.option ) { + wrapMap.optgroup = wrapMap.option = [ 1, "" ]; +} + + +function getAll( context, tag ) { + + // Support: IE <=9 - 11 only + // Use typeof to avoid zero-argument method invocation on host objects (#15151) + var ret; + + if ( typeof context.getElementsByTagName !== "undefined" ) { + ret = context.getElementsByTagName( tag || "*" ); + + } else if ( typeof context.querySelectorAll !== "undefined" ) { + ret = context.querySelectorAll( tag || "*" ); + + } else { + ret = []; + } + + if ( tag === undefined || tag && nodeName( context, tag ) ) { + return jQuery.merge( [ context ], ret ); + } + + return ret; +} + + +// Mark scripts as having already been evaluated +function setGlobalEval( elems, refElements ) { + var i = 0, + l = elems.length; + + for ( ; i < l; i++ ) { + dataPriv.set( + elems[ i ], + "globalEval", + !refElements || dataPriv.get( refElements[ i ], "globalEval" ) + ); + } +} + + +var rhtml = /<|&#?\w+;/; + +function buildFragment( elems, context, scripts, selection, ignored ) { + var elem, tmp, tag, wrap, attached, j, + fragment = context.createDocumentFragment(), + nodes = [], + i = 0, + l = elems.length; + + for ( ; i < l; i++ ) { + elem = elems[ i ]; + + if ( elem || elem === 0 ) { + + // Add nodes directly + if ( toType( elem ) === "object" ) { + + // Support: Android <=4.0 only, PhantomJS 1 only + // push.apply(_, arraylike) throws on ancient WebKit + jQuery.merge( nodes, elem.nodeType ? [ elem ] : elem ); + + // Convert non-html into a text node + } else if ( !rhtml.test( elem ) ) { + nodes.push( context.createTextNode( elem ) ); + + // Convert html into DOM nodes + } else { + tmp = tmp || fragment.appendChild( context.createElement( "div" ) ); + + // Deserialize a standard representation + tag = ( rtagName.exec( elem ) || [ "", "" ] )[ 1 ].toLowerCase(); + wrap = wrapMap[ tag ] || wrapMap._default; + tmp.innerHTML = wrap[ 1 ] + jQuery.htmlPrefilter( elem ) + wrap[ 2 ]; + + // Descend through wrappers to the right content + j = wrap[ 0 ]; + while ( j-- ) { + tmp = tmp.lastChild; + } + + // Support: Android <=4.0 only, PhantomJS 1 only + // push.apply(_, arraylike) throws on ancient WebKit + jQuery.merge( nodes, tmp.childNodes ); + + // Remember the top-level container + tmp = fragment.firstChild; + + // Ensure the created nodes are orphaned (#12392) + tmp.textContent = ""; + } + } + } + + // Remove wrapper from fragment + fragment.textContent = ""; + + i = 0; + while ( ( elem = nodes[ i++ ] ) ) { + + // Skip elements already in the context collection (trac-4087) + if ( selection && jQuery.inArray( elem, selection ) > -1 ) { + if ( ignored ) { + ignored.push( elem ); + } + continue; + } + + attached = isAttached( elem ); + + // Append to fragment + tmp = getAll( fragment.appendChild( elem ), "script" ); + + // Preserve script evaluation history + if ( attached ) { + setGlobalEval( tmp ); + } + + // Capture executables + if ( scripts ) { + j = 0; + while ( ( elem = tmp[ j++ ] ) ) { + if ( rscriptType.test( elem.type || "" ) ) { + scripts.push( elem ); + } + } + } + } + + return fragment; +} + + +var + rkeyEvent = /^key/, + rmouseEvent = /^(?:mouse|pointer|contextmenu|drag|drop)|click/, + rtypenamespace = /^([^.]*)(?:\.(.+)|)/; + +function returnTrue() { + return true; +} + +function returnFalse() { + return false; +} + +// Support: IE <=9 - 11+ +// focus() and blur() are asynchronous, except when they are no-op. +// So expect focus to be synchronous when the element is already active, +// and blur to be synchronous when the element is not already active. +// (focus and blur are always synchronous in other supported browsers, +// this just defines when we can count on it). +function expectSync( elem, type ) { + return ( elem === safeActiveElement() ) === ( type === "focus" ); +} + +// Support: IE <=9 only +// Accessing document.activeElement can throw unexpectedly +// https://bugs.jquery.com/ticket/13393 +function safeActiveElement() { + try { + return document.activeElement; + } catch ( err ) { } +} + +function on( elem, types, selector, data, fn, one ) { + var origFn, type; + + // Types can be a map of types/handlers + if ( typeof types === "object" ) { + + // ( types-Object, selector, data ) + if ( typeof selector !== "string" ) { + + // ( types-Object, data ) + data = data || selector; + selector = undefined; + } + for ( type in types ) { + on( elem, type, selector, data, types[ type ], one ); + } + return elem; + } + + if ( data == null && fn == null ) { + + // ( types, fn ) + fn = selector; + data = selector = undefined; + } else if ( fn == null ) { + if ( typeof selector === "string" ) { + + // ( types, selector, fn ) + fn = data; + data = undefined; + } else { + + // ( types, data, fn ) + fn = data; + data = selector; + selector = undefined; + } + } + if ( fn === false ) { + fn = returnFalse; + } else if ( !fn ) { + return elem; + } + + if ( one === 1 ) { + origFn = fn; + fn = function( event ) { + + // Can use an empty set, since event contains the info + jQuery().off( event ); + return origFn.apply( this, arguments ); + }; + + // Use same guid so caller can remove using origFn + fn.guid = origFn.guid || ( origFn.guid = jQuery.guid++ ); + } + return elem.each( function() { + jQuery.event.add( this, types, fn, data, selector ); + } ); +} + +/* + * Helper functions for managing events -- not part of the public interface. + * Props to Dean Edwards' addEvent library for many of the ideas. + */ +jQuery.event = { + + global: {}, + + add: function( elem, types, handler, data, selector ) { + + var handleObjIn, eventHandle, tmp, + events, t, handleObj, + special, handlers, type, namespaces, origType, + elemData = dataPriv.get( elem ); + + // Only attach events to objects that accept data + if ( !acceptData( elem ) ) { + return; + } + + // Caller can pass in an object of custom data in lieu of the handler + if ( handler.handler ) { + handleObjIn = handler; + handler = handleObjIn.handler; + selector = handleObjIn.selector; + } + + // Ensure that invalid selectors throw exceptions at attach time + // Evaluate against documentElement in case elem is a non-element node (e.g., document) + if ( selector ) { + jQuery.find.matchesSelector( documentElement, selector ); + } + + // Make sure that the handler has a unique ID, used to find/remove it later + if ( !handler.guid ) { + handler.guid = jQuery.guid++; + } + + // Init the element's event structure and main handler, if this is the first + if ( !( events = elemData.events ) ) { + events = elemData.events = Object.create( null ); + } + if ( !( eventHandle = elemData.handle ) ) { + eventHandle = elemData.handle = function( e ) { + + // Discard the second event of a jQuery.event.trigger() and + // when an event is called after a page has unloaded + return typeof jQuery !== "undefined" && jQuery.event.triggered !== e.type ? + jQuery.event.dispatch.apply( elem, arguments ) : undefined; + }; + } + + // Handle multiple events separated by a space + types = ( types || "" ).match( rnothtmlwhite ) || [ "" ]; + t = types.length; + while ( t-- ) { + tmp = rtypenamespace.exec( types[ t ] ) || []; + type = origType = tmp[ 1 ]; + namespaces = ( tmp[ 2 ] || "" ).split( "." ).sort(); + + // There *must* be a type, no attaching namespace-only handlers + if ( !type ) { + continue; + } + + // If event changes its type, use the special event handlers for the changed type + special = jQuery.event.special[ type ] || {}; + + // If selector defined, determine special event api type, otherwise given type + type = ( selector ? special.delegateType : special.bindType ) || type; + + // Update special based on newly reset type + special = jQuery.event.special[ type ] || {}; + + // handleObj is passed to all event handlers + handleObj = jQuery.extend( { + type: type, + origType: origType, + data: data, + handler: handler, + guid: handler.guid, + selector: selector, + needsContext: selector && jQuery.expr.match.needsContext.test( selector ), + namespace: namespaces.join( "." ) + }, handleObjIn ); + + // Init the event handler queue if we're the first + if ( !( handlers = events[ type ] ) ) { + handlers = events[ type ] = []; + handlers.delegateCount = 0; + + // Only use addEventListener if the special events handler returns false + if ( !special.setup || + special.setup.call( elem, data, namespaces, eventHandle ) === false ) { + + if ( elem.addEventListener ) { + elem.addEventListener( type, eventHandle ); + } + } + } + + if ( special.add ) { + special.add.call( elem, handleObj ); + + if ( !handleObj.handler.guid ) { + handleObj.handler.guid = handler.guid; + } + } + + // Add to the element's handler list, delegates in front + if ( selector ) { + handlers.splice( handlers.delegateCount++, 0, handleObj ); + } else { + handlers.push( handleObj ); + } + + // Keep track of which events have ever been used, for event optimization + jQuery.event.global[ type ] = true; + } + + }, + + // Detach an event or set of events from an element + remove: function( elem, types, handler, selector, mappedTypes ) { + + var j, origCount, tmp, + events, t, handleObj, + special, handlers, type, namespaces, origType, + elemData = dataPriv.hasData( elem ) && dataPriv.get( elem ); + + if ( !elemData || !( events = elemData.events ) ) { + return; + } + + // Once for each type.namespace in types; type may be omitted + types = ( types || "" ).match( rnothtmlwhite ) || [ "" ]; + t = types.length; + while ( t-- ) { + tmp = rtypenamespace.exec( types[ t ] ) || []; + type = origType = tmp[ 1 ]; + namespaces = ( tmp[ 2 ] || "" ).split( "." ).sort(); + + // Unbind all events (on this namespace, if provided) for the element + if ( !type ) { + for ( type in events ) { + jQuery.event.remove( elem, type + types[ t ], handler, selector, true ); + } + continue; + } + + special = jQuery.event.special[ type ] || {}; + type = ( selector ? special.delegateType : special.bindType ) || type; + handlers = events[ type ] || []; + tmp = tmp[ 2 ] && + new RegExp( "(^|\\.)" + namespaces.join( "\\.(?:.*\\.|)" ) + "(\\.|$)" ); + + // Remove matching events + origCount = j = handlers.length; + while ( j-- ) { + handleObj = handlers[ j ]; + + if ( ( mappedTypes || origType === handleObj.origType ) && + ( !handler || handler.guid === handleObj.guid ) && + ( !tmp || tmp.test( handleObj.namespace ) ) && + ( !selector || selector === handleObj.selector || + selector === "**" && handleObj.selector ) ) { + handlers.splice( j, 1 ); + + if ( handleObj.selector ) { + handlers.delegateCount--; + } + if ( special.remove ) { + special.remove.call( elem, handleObj ); + } + } + } + + // Remove generic event handler if we removed something and no more handlers exist + // (avoids potential for endless recursion during removal of special event handlers) + if ( origCount && !handlers.length ) { + if ( !special.teardown || + special.teardown.call( elem, namespaces, elemData.handle ) === false ) { + + jQuery.removeEvent( elem, type, elemData.handle ); + } + + delete events[ type ]; + } + } + + // Remove data and the expando if it's no longer used + if ( jQuery.isEmptyObject( events ) ) { + dataPriv.remove( elem, "handle events" ); + } + }, + + dispatch: function( nativeEvent ) { + + var i, j, ret, matched, handleObj, handlerQueue, + args = new Array( arguments.length ), + + // Make a writable jQuery.Event from the native event object + event = jQuery.event.fix( nativeEvent ), + + handlers = ( + dataPriv.get( this, "events" ) || Object.create( null ) + )[ event.type ] || [], + special = jQuery.event.special[ event.type ] || {}; + + // Use the fix-ed jQuery.Event rather than the (read-only) native event + args[ 0 ] = event; + + for ( i = 1; i < arguments.length; i++ ) { + args[ i ] = arguments[ i ]; + } + + event.delegateTarget = this; + + // Call the preDispatch hook for the mapped type, and let it bail if desired + if ( special.preDispatch && special.preDispatch.call( this, event ) === false ) { + return; + } + + // Determine handlers + handlerQueue = jQuery.event.handlers.call( this, event, handlers ); + + // Run delegates first; they may want to stop propagation beneath us + i = 0; + while ( ( matched = handlerQueue[ i++ ] ) && !event.isPropagationStopped() ) { + event.currentTarget = matched.elem; + + j = 0; + while ( ( handleObj = matched.handlers[ j++ ] ) && + !event.isImmediatePropagationStopped() ) { + + // If the event is namespaced, then each handler is only invoked if it is + // specially universal or its namespaces are a superset of the event's. + if ( !event.rnamespace || handleObj.namespace === false || + event.rnamespace.test( handleObj.namespace ) ) { + + event.handleObj = handleObj; + event.data = handleObj.data; + + ret = ( ( jQuery.event.special[ handleObj.origType ] || {} ).handle || + handleObj.handler ).apply( matched.elem, args ); + + if ( ret !== undefined ) { + if ( ( event.result = ret ) === false ) { + event.preventDefault(); + event.stopPropagation(); + } + } + } + } + } + + // Call the postDispatch hook for the mapped type + if ( special.postDispatch ) { + special.postDispatch.call( this, event ); + } + + return event.result; + }, + + handlers: function( event, handlers ) { + var i, handleObj, sel, matchedHandlers, matchedSelectors, + handlerQueue = [], + delegateCount = handlers.delegateCount, + cur = event.target; + + // Find delegate handlers + if ( delegateCount && + + // Support: IE <=9 + // Black-hole SVG instance trees (trac-13180) + cur.nodeType && + + // Support: Firefox <=42 + // Suppress spec-violating clicks indicating a non-primary pointer button (trac-3861) + // https://www.w3.org/TR/DOM-Level-3-Events/#event-type-click + // Support: IE 11 only + // ...but not arrow key "clicks" of radio inputs, which can have `button` -1 (gh-2343) + !( event.type === "click" && event.button >= 1 ) ) { + + for ( ; cur !== this; cur = cur.parentNode || this ) { + + // Don't check non-elements (#13208) + // Don't process clicks on disabled elements (#6911, #8165, #11382, #11764) + if ( cur.nodeType === 1 && !( event.type === "click" && cur.disabled === true ) ) { + matchedHandlers = []; + matchedSelectors = {}; + for ( i = 0; i < delegateCount; i++ ) { + handleObj = handlers[ i ]; + + // Don't conflict with Object.prototype properties (#13203) + sel = handleObj.selector + " "; + + if ( matchedSelectors[ sel ] === undefined ) { + matchedSelectors[ sel ] = handleObj.needsContext ? + jQuery( sel, this ).index( cur ) > -1 : + jQuery.find( sel, this, null, [ cur ] ).length; + } + if ( matchedSelectors[ sel ] ) { + matchedHandlers.push( handleObj ); + } + } + if ( matchedHandlers.length ) { + handlerQueue.push( { elem: cur, handlers: matchedHandlers } ); + } + } + } + } + + // Add the remaining (directly-bound) handlers + cur = this; + if ( delegateCount < handlers.length ) { + handlerQueue.push( { elem: cur, handlers: handlers.slice( delegateCount ) } ); + } + + return handlerQueue; + }, + + addProp: function( name, hook ) { + Object.defineProperty( jQuery.Event.prototype, name, { + enumerable: true, + configurable: true, + + get: isFunction( hook ) ? + function() { + if ( this.originalEvent ) { + return hook( this.originalEvent ); + } + } : + function() { + if ( this.originalEvent ) { + return this.originalEvent[ name ]; + } + }, + + set: function( value ) { + Object.defineProperty( this, name, { + enumerable: true, + configurable: true, + writable: true, + value: value + } ); + } + } ); + }, + + fix: function( originalEvent ) { + return originalEvent[ jQuery.expando ] ? + originalEvent : + new jQuery.Event( originalEvent ); + }, + + special: { + load: { + + // Prevent triggered image.load events from bubbling to window.load + noBubble: true + }, + click: { + + // Utilize native event to ensure correct state for checkable inputs + setup: function( data ) { + + // For mutual compressibility with _default, replace `this` access with a local var. + // `|| data` is dead code meant only to preserve the variable through minification. + var el = this || data; + + // Claim the first handler + if ( rcheckableType.test( el.type ) && + el.click && nodeName( el, "input" ) ) { + + // dataPriv.set( el, "click", ... ) + leverageNative( el, "click", returnTrue ); + } + + // Return false to allow normal processing in the caller + return false; + }, + trigger: function( data ) { + + // For mutual compressibility with _default, replace `this` access with a local var. + // `|| data` is dead code meant only to preserve the variable through minification. + var el = this || data; + + // Force setup before triggering a click + if ( rcheckableType.test( el.type ) && + el.click && nodeName( el, "input" ) ) { + + leverageNative( el, "click" ); + } + + // Return non-false to allow normal event-path propagation + return true; + }, + + // For cross-browser consistency, suppress native .click() on links + // Also prevent it if we're currently inside a leveraged native-event stack + _default: function( event ) { + var target = event.target; + return rcheckableType.test( target.type ) && + target.click && nodeName( target, "input" ) && + dataPriv.get( target, "click" ) || + nodeName( target, "a" ); + } + }, + + beforeunload: { + postDispatch: function( event ) { + + // Support: Firefox 20+ + // Firefox doesn't alert if the returnValue field is not set. + if ( event.result !== undefined && event.originalEvent ) { + event.originalEvent.returnValue = event.result; + } + } + } + } +}; + +// Ensure the presence of an event listener that handles manually-triggered +// synthetic events by interrupting progress until reinvoked in response to +// *native* events that it fires directly, ensuring that state changes have +// already occurred before other listeners are invoked. +function leverageNative( el, type, expectSync ) { + + // Missing expectSync indicates a trigger call, which must force setup through jQuery.event.add + if ( !expectSync ) { + if ( dataPriv.get( el, type ) === undefined ) { + jQuery.event.add( el, type, returnTrue ); + } + return; + } + + // Register the controller as a special universal handler for all event namespaces + dataPriv.set( el, type, false ); + jQuery.event.add( el, type, { + namespace: false, + handler: function( event ) { + var notAsync, result, + saved = dataPriv.get( this, type ); + + if ( ( event.isTrigger & 1 ) && this[ type ] ) { + + // Interrupt processing of the outer synthetic .trigger()ed event + // Saved data should be false in such cases, but might be a leftover capture object + // from an async native handler (gh-4350) + if ( !saved.length ) { + + // Store arguments for use when handling the inner native event + // There will always be at least one argument (an event object), so this array + // will not be confused with a leftover capture object. + saved = slice.call( arguments ); + dataPriv.set( this, type, saved ); + + // Trigger the native event and capture its result + // Support: IE <=9 - 11+ + // focus() and blur() are asynchronous + notAsync = expectSync( this, type ); + this[ type ](); + result = dataPriv.get( this, type ); + if ( saved !== result || notAsync ) { + dataPriv.set( this, type, false ); + } else { + result = {}; + } + if ( saved !== result ) { + + // Cancel the outer synthetic event + event.stopImmediatePropagation(); + event.preventDefault(); + return result.value; + } + + // If this is an inner synthetic event for an event with a bubbling surrogate + // (focus or blur), assume that the surrogate already propagated from triggering the + // native event and prevent that from happening again here. + // This technically gets the ordering wrong w.r.t. to `.trigger()` (in which the + // bubbling surrogate propagates *after* the non-bubbling base), but that seems + // less bad than duplication. + } else if ( ( jQuery.event.special[ type ] || {} ).delegateType ) { + event.stopPropagation(); + } + + // If this is a native event triggered above, everything is now in order + // Fire an inner synthetic event with the original arguments + } else if ( saved.length ) { + + // ...and capture the result + dataPriv.set( this, type, { + value: jQuery.event.trigger( + + // Support: IE <=9 - 11+ + // Extend with the prototype to reset the above stopImmediatePropagation() + jQuery.extend( saved[ 0 ], jQuery.Event.prototype ), + saved.slice( 1 ), + this + ) + } ); + + // Abort handling of the native event + event.stopImmediatePropagation(); + } + } + } ); +} + +jQuery.removeEvent = function( elem, type, handle ) { + + // This "if" is needed for plain objects + if ( elem.removeEventListener ) { + elem.removeEventListener( type, handle ); + } +}; + +jQuery.Event = function( src, props ) { + + // Allow instantiation without the 'new' keyword + if ( !( this instanceof jQuery.Event ) ) { + return new jQuery.Event( src, props ); + } + + // Event object + if ( src && src.type ) { + this.originalEvent = src; + this.type = src.type; + + // Events bubbling up the document may have been marked as prevented + // by a handler lower down the tree; reflect the correct value. + this.isDefaultPrevented = src.defaultPrevented || + src.defaultPrevented === undefined && + + // Support: Android <=2.3 only + src.returnValue === false ? + returnTrue : + returnFalse; + + // Create target properties + // Support: Safari <=6 - 7 only + // Target should not be a text node (#504, #13143) + this.target = ( src.target && src.target.nodeType === 3 ) ? + src.target.parentNode : + src.target; + + this.currentTarget = src.currentTarget; + this.relatedTarget = src.relatedTarget; + + // Event type + } else { + this.type = src; + } + + // Put explicitly provided properties onto the event object + if ( props ) { + jQuery.extend( this, props ); + } + + // Create a timestamp if incoming event doesn't have one + this.timeStamp = src && src.timeStamp || Date.now(); + + // Mark it as fixed + this[ jQuery.expando ] = true; +}; + +// jQuery.Event is based on DOM3 Events as specified by the ECMAScript Language Binding +// https://www.w3.org/TR/2003/WD-DOM-Level-3-Events-20030331/ecma-script-binding.html +jQuery.Event.prototype = { + constructor: jQuery.Event, + isDefaultPrevented: returnFalse, + isPropagationStopped: returnFalse, + isImmediatePropagationStopped: returnFalse, + isSimulated: false, + + preventDefault: function() { + var e = this.originalEvent; + + this.isDefaultPrevented = returnTrue; + + if ( e && !this.isSimulated ) { + e.preventDefault(); + } + }, + stopPropagation: function() { + var e = this.originalEvent; + + this.isPropagationStopped = returnTrue; + + if ( e && !this.isSimulated ) { + e.stopPropagation(); + } + }, + stopImmediatePropagation: function() { + var e = this.originalEvent; + + this.isImmediatePropagationStopped = returnTrue; + + if ( e && !this.isSimulated ) { + e.stopImmediatePropagation(); + } + + this.stopPropagation(); + } +}; + +// Includes all common event props including KeyEvent and MouseEvent specific props +jQuery.each( { + altKey: true, + bubbles: true, + cancelable: true, + changedTouches: true, + ctrlKey: true, + detail: true, + eventPhase: true, + metaKey: true, + pageX: true, + pageY: true, + shiftKey: true, + view: true, + "char": true, + code: true, + charCode: true, + key: true, + keyCode: true, + button: true, + buttons: true, + clientX: true, + clientY: true, + offsetX: true, + offsetY: true, + pointerId: true, + pointerType: true, + screenX: true, + screenY: true, + targetTouches: true, + toElement: true, + touches: true, + + which: function( event ) { + var button = event.button; + + // Add which for key events + if ( event.which == null && rkeyEvent.test( event.type ) ) { + return event.charCode != null ? event.charCode : event.keyCode; + } + + // Add which for click: 1 === left; 2 === middle; 3 === right + if ( !event.which && button !== undefined && rmouseEvent.test( event.type ) ) { + if ( button & 1 ) { + return 1; + } + + if ( button & 2 ) { + return 3; + } + + if ( button & 4 ) { + return 2; + } + + return 0; + } + + return event.which; + } +}, jQuery.event.addProp ); + +jQuery.each( { focus: "focusin", blur: "focusout" }, function( type, delegateType ) { + jQuery.event.special[ type ] = { + + // Utilize native event if possible so blur/focus sequence is correct + setup: function() { + + // Claim the first handler + // dataPriv.set( this, "focus", ... ) + // dataPriv.set( this, "blur", ... ) + leverageNative( this, type, expectSync ); + + // Return false to allow normal processing in the caller + return false; + }, + trigger: function() { + + // Force setup before trigger + leverageNative( this, type ); + + // Return non-false to allow normal event-path propagation + return true; + }, + + delegateType: delegateType + }; +} ); + +// Create mouseenter/leave events using mouseover/out and event-time checks +// so that event delegation works in jQuery. +// Do the same for pointerenter/pointerleave and pointerover/pointerout +// +// Support: Safari 7 only +// Safari sends mouseenter too often; see: +// https://bugs.chromium.org/p/chromium/issues/detail?id=470258 +// for the description of the bug (it existed in older Chrome versions as well). +jQuery.each( { + mouseenter: "mouseover", + mouseleave: "mouseout", + pointerenter: "pointerover", + pointerleave: "pointerout" +}, function( orig, fix ) { + jQuery.event.special[ orig ] = { + delegateType: fix, + bindType: fix, + + handle: function( event ) { + var ret, + target = this, + related = event.relatedTarget, + handleObj = event.handleObj; + + // For mouseenter/leave call the handler if related is outside the target. + // NB: No relatedTarget if the mouse left/entered the browser window + if ( !related || ( related !== target && !jQuery.contains( target, related ) ) ) { + event.type = handleObj.origType; + ret = handleObj.handler.apply( this, arguments ); + event.type = fix; + } + return ret; + } + }; +} ); + +jQuery.fn.extend( { + + on: function( types, selector, data, fn ) { + return on( this, types, selector, data, fn ); + }, + one: function( types, selector, data, fn ) { + return on( this, types, selector, data, fn, 1 ); + }, + off: function( types, selector, fn ) { + var handleObj, type; + if ( types && types.preventDefault && types.handleObj ) { + + // ( event ) dispatched jQuery.Event + handleObj = types.handleObj; + jQuery( types.delegateTarget ).off( + handleObj.namespace ? + handleObj.origType + "." + handleObj.namespace : + handleObj.origType, + handleObj.selector, + handleObj.handler + ); + return this; + } + if ( typeof types === "object" ) { + + // ( types-object [, selector] ) + for ( type in types ) { + this.off( type, selector, types[ type ] ); + } + return this; + } + if ( selector === false || typeof selector === "function" ) { + + // ( types [, fn] ) + fn = selector; + selector = undefined; + } + if ( fn === false ) { + fn = returnFalse; + } + return this.each( function() { + jQuery.event.remove( this, types, fn, selector ); + } ); + } +} ); + + +var + + // Support: IE <=10 - 11, Edge 12 - 13 only + // In IE/Edge using regex groups here causes severe slowdowns. + // See https://connect.microsoft.com/IE/feedback/details/1736512/ + rnoInnerhtml = /\s*$/g; + +// Prefer a tbody over its parent table for containing new rows +function manipulationTarget( elem, content ) { + if ( nodeName( elem, "table" ) && + nodeName( content.nodeType !== 11 ? content : content.firstChild, "tr" ) ) { + + return jQuery( elem ).children( "tbody" )[ 0 ] || elem; + } + + return elem; +} + +// Replace/restore the type attribute of script elements for safe DOM manipulation +function disableScript( elem ) { + elem.type = ( elem.getAttribute( "type" ) !== null ) + "/" + elem.type; + return elem; +} +function restoreScript( elem ) { + if ( ( elem.type || "" ).slice( 0, 5 ) === "true/" ) { + elem.type = elem.type.slice( 5 ); + } else { + elem.removeAttribute( "type" ); + } + + return elem; +} + +function cloneCopyEvent( src, dest ) { + var i, l, type, pdataOld, udataOld, udataCur, events; + + if ( dest.nodeType !== 1 ) { + return; + } + + // 1. Copy private data: events, handlers, etc. + if ( dataPriv.hasData( src ) ) { + pdataOld = dataPriv.get( src ); + events = pdataOld.events; + + if ( events ) { + dataPriv.remove( dest, "handle events" ); + + for ( type in events ) { + for ( i = 0, l = events[ type ].length; i < l; i++ ) { + jQuery.event.add( dest, type, events[ type ][ i ] ); + } + } + } + } + + // 2. Copy user data + if ( dataUser.hasData( src ) ) { + udataOld = dataUser.access( src ); + udataCur = jQuery.extend( {}, udataOld ); + + dataUser.set( dest, udataCur ); + } +} + +// Fix IE bugs, see support tests +function fixInput( src, dest ) { + var nodeName = dest.nodeName.toLowerCase(); + + // Fails to persist the checked state of a cloned checkbox or radio button. + if ( nodeName === "input" && rcheckableType.test( src.type ) ) { + dest.checked = src.checked; + + // Fails to return the selected option to the default selected state when cloning options + } else if ( nodeName === "input" || nodeName === "textarea" ) { + dest.defaultValue = src.defaultValue; + } +} + +function domManip( collection, args, callback, ignored ) { + + // Flatten any nested arrays + args = flat( args ); + + var fragment, first, scripts, hasScripts, node, doc, + i = 0, + l = collection.length, + iNoClone = l - 1, + value = args[ 0 ], + valueIsFunction = isFunction( value ); + + // We can't cloneNode fragments that contain checked, in WebKit + if ( valueIsFunction || + ( l > 1 && typeof value === "string" && + !support.checkClone && rchecked.test( value ) ) ) { + return collection.each( function( index ) { + var self = collection.eq( index ); + if ( valueIsFunction ) { + args[ 0 ] = value.call( this, index, self.html() ); + } + domManip( self, args, callback, ignored ); + } ); + } + + if ( l ) { + fragment = buildFragment( args, collection[ 0 ].ownerDocument, false, collection, ignored ); + first = fragment.firstChild; + + if ( fragment.childNodes.length === 1 ) { + fragment = first; + } + + // Require either new content or an interest in ignored elements to invoke the callback + if ( first || ignored ) { + scripts = jQuery.map( getAll( fragment, "script" ), disableScript ); + hasScripts = scripts.length; + + // Use the original fragment for the last item + // instead of the first because it can end up + // being emptied incorrectly in certain situations (#8070). + for ( ; i < l; i++ ) { + node = fragment; + + if ( i !== iNoClone ) { + node = jQuery.clone( node, true, true ); + + // Keep references to cloned scripts for later restoration + if ( hasScripts ) { + + // Support: Android <=4.0 only, PhantomJS 1 only + // push.apply(_, arraylike) throws on ancient WebKit + jQuery.merge( scripts, getAll( node, "script" ) ); + } + } + + callback.call( collection[ i ], node, i ); + } + + if ( hasScripts ) { + doc = scripts[ scripts.length - 1 ].ownerDocument; + + // Reenable scripts + jQuery.map( scripts, restoreScript ); + + // Evaluate executable scripts on first document insertion + for ( i = 0; i < hasScripts; i++ ) { + node = scripts[ i ]; + if ( rscriptType.test( node.type || "" ) && + !dataPriv.access( node, "globalEval" ) && + jQuery.contains( doc, node ) ) { + + if ( node.src && ( node.type || "" ).toLowerCase() !== "module" ) { + + // Optional AJAX dependency, but won't run scripts if not present + if ( jQuery._evalUrl && !node.noModule ) { + jQuery._evalUrl( node.src, { + nonce: node.nonce || node.getAttribute( "nonce" ) + }, doc ); + } + } else { + DOMEval( node.textContent.replace( rcleanScript, "" ), node, doc ); + } + } + } + } + } + } + + return collection; +} + +function remove( elem, selector, keepData ) { + var node, + nodes = selector ? jQuery.filter( selector, elem ) : elem, + i = 0; + + for ( ; ( node = nodes[ i ] ) != null; i++ ) { + if ( !keepData && node.nodeType === 1 ) { + jQuery.cleanData( getAll( node ) ); + } + + if ( node.parentNode ) { + if ( keepData && isAttached( node ) ) { + setGlobalEval( getAll( node, "script" ) ); + } + node.parentNode.removeChild( node ); + } + } + + return elem; +} + +jQuery.extend( { + htmlPrefilter: function( html ) { + return html; + }, + + clone: function( elem, dataAndEvents, deepDataAndEvents ) { + var i, l, srcElements, destElements, + clone = elem.cloneNode( true ), + inPage = isAttached( elem ); + + // Fix IE cloning issues + if ( !support.noCloneChecked && ( elem.nodeType === 1 || elem.nodeType === 11 ) && + !jQuery.isXMLDoc( elem ) ) { + + // We eschew Sizzle here for performance reasons: https://jsperf.com/getall-vs-sizzle/2 + destElements = getAll( clone ); + srcElements = getAll( elem ); + + for ( i = 0, l = srcElements.length; i < l; i++ ) { + fixInput( srcElements[ i ], destElements[ i ] ); + } + } + + // Copy the events from the original to the clone + if ( dataAndEvents ) { + if ( deepDataAndEvents ) { + srcElements = srcElements || getAll( elem ); + destElements = destElements || getAll( clone ); + + for ( i = 0, l = srcElements.length; i < l; i++ ) { + cloneCopyEvent( srcElements[ i ], destElements[ i ] ); + } + } else { + cloneCopyEvent( elem, clone ); + } + } + + // Preserve script evaluation history + destElements = getAll( clone, "script" ); + if ( destElements.length > 0 ) { + setGlobalEval( destElements, !inPage && getAll( elem, "script" ) ); + } + + // Return the cloned set + return clone; + }, + + cleanData: function( elems ) { + var data, elem, type, + special = jQuery.event.special, + i = 0; + + for ( ; ( elem = elems[ i ] ) !== undefined; i++ ) { + if ( acceptData( elem ) ) { + if ( ( data = elem[ dataPriv.expando ] ) ) { + if ( data.events ) { + for ( type in data.events ) { + if ( special[ type ] ) { + jQuery.event.remove( elem, type ); + + // This is a shortcut to avoid jQuery.event.remove's overhead + } else { + jQuery.removeEvent( elem, type, data.handle ); + } + } + } + + // Support: Chrome <=35 - 45+ + // Assign undefined instead of using delete, see Data#remove + elem[ dataPriv.expando ] = undefined; + } + if ( elem[ dataUser.expando ] ) { + + // Support: Chrome <=35 - 45+ + // Assign undefined instead of using delete, see Data#remove + elem[ dataUser.expando ] = undefined; + } + } + } + } +} ); + +jQuery.fn.extend( { + detach: function( selector ) { + return remove( this, selector, true ); + }, + + remove: function( selector ) { + return remove( this, selector ); + }, + + text: function( value ) { + return access( this, function( value ) { + return value === undefined ? + jQuery.text( this ) : + this.empty().each( function() { + if ( this.nodeType === 1 || this.nodeType === 11 || this.nodeType === 9 ) { + this.textContent = value; + } + } ); + }, null, value, arguments.length ); + }, + + append: function() { + return domManip( this, arguments, function( elem ) { + if ( this.nodeType === 1 || this.nodeType === 11 || this.nodeType === 9 ) { + var target = manipulationTarget( this, elem ); + target.appendChild( elem ); + } + } ); + }, + + prepend: function() { + return domManip( this, arguments, function( elem ) { + if ( this.nodeType === 1 || this.nodeType === 11 || this.nodeType === 9 ) { + var target = manipulationTarget( this, elem ); + target.insertBefore( elem, target.firstChild ); + } + } ); + }, + + before: function() { + return domManip( this, arguments, function( elem ) { + if ( this.parentNode ) { + this.parentNode.insertBefore( elem, this ); + } + } ); + }, + + after: function() { + return domManip( this, arguments, function( elem ) { + if ( this.parentNode ) { + this.parentNode.insertBefore( elem, this.nextSibling ); + } + } ); + }, + + empty: function() { + var elem, + i = 0; + + for ( ; ( elem = this[ i ] ) != null; i++ ) { + if ( elem.nodeType === 1 ) { + + // Prevent memory leaks + jQuery.cleanData( getAll( elem, false ) ); + + // Remove any remaining nodes + elem.textContent = ""; + } + } + + return this; + }, + + clone: function( dataAndEvents, deepDataAndEvents ) { + dataAndEvents = dataAndEvents == null ? false : dataAndEvents; + deepDataAndEvents = deepDataAndEvents == null ? dataAndEvents : deepDataAndEvents; + + return this.map( function() { + return jQuery.clone( this, dataAndEvents, deepDataAndEvents ); + } ); + }, + + html: function( value ) { + return access( this, function( value ) { + var elem = this[ 0 ] || {}, + i = 0, + l = this.length; + + if ( value === undefined && elem.nodeType === 1 ) { + return elem.innerHTML; + } + + // See if we can take a shortcut and just use innerHTML + if ( typeof value === "string" && !rnoInnerhtml.test( value ) && + !wrapMap[ ( rtagName.exec( value ) || [ "", "" ] )[ 1 ].toLowerCase() ] ) { + + value = jQuery.htmlPrefilter( value ); + + try { + for ( ; i < l; i++ ) { + elem = this[ i ] || {}; + + // Remove element nodes and prevent memory leaks + if ( elem.nodeType === 1 ) { + jQuery.cleanData( getAll( elem, false ) ); + elem.innerHTML = value; + } + } + + elem = 0; + + // If using innerHTML throws an exception, use the fallback method + } catch ( e ) {} + } + + if ( elem ) { + this.empty().append( value ); + } + }, null, value, arguments.length ); + }, + + replaceWith: function() { + var ignored = []; + + // Make the changes, replacing each non-ignored context element with the new content + return domManip( this, arguments, function( elem ) { + var parent = this.parentNode; + + if ( jQuery.inArray( this, ignored ) < 0 ) { + jQuery.cleanData( getAll( this ) ); + if ( parent ) { + parent.replaceChild( elem, this ); + } + } + + // Force callback invocation + }, ignored ); + } +} ); + +jQuery.each( { + appendTo: "append", + prependTo: "prepend", + insertBefore: "before", + insertAfter: "after", + replaceAll: "replaceWith" +}, function( name, original ) { + jQuery.fn[ name ] = function( selector ) { + var elems, + ret = [], + insert = jQuery( selector ), + last = insert.length - 1, + i = 0; + + for ( ; i <= last; i++ ) { + elems = i === last ? this : this.clone( true ); + jQuery( insert[ i ] )[ original ]( elems ); + + // Support: Android <=4.0 only, PhantomJS 1 only + // .get() because push.apply(_, arraylike) throws on ancient WebKit + push.apply( ret, elems.get() ); + } + + return this.pushStack( ret ); + }; +} ); +var rnumnonpx = new RegExp( "^(" + pnum + ")(?!px)[a-z%]+$", "i" ); + +var getStyles = function( elem ) { + + // Support: IE <=11 only, Firefox <=30 (#15098, #14150) + // IE throws on elements created in popups + // FF meanwhile throws on frame elements through "defaultView.getComputedStyle" + var view = elem.ownerDocument.defaultView; + + if ( !view || !view.opener ) { + view = window; + } + + return view.getComputedStyle( elem ); + }; + +var swap = function( elem, options, callback ) { + var ret, name, + old = {}; + + // Remember the old values, and insert the new ones + for ( name in options ) { + old[ name ] = elem.style[ name ]; + elem.style[ name ] = options[ name ]; + } + + ret = callback.call( elem ); + + // Revert the old values + for ( name in options ) { + elem.style[ name ] = old[ name ]; + } + + return ret; +}; + + +var rboxStyle = new RegExp( cssExpand.join( "|" ), "i" ); + + + +( function() { + + // Executing both pixelPosition & boxSizingReliable tests require only one layout + // so they're executed at the same time to save the second computation. + function computeStyleTests() { + + // This is a singleton, we need to execute it only once + if ( !div ) { + return; + } + + container.style.cssText = "position:absolute;left:-11111px;width:60px;" + + "margin-top:1px;padding:0;border:0"; + div.style.cssText = + "position:relative;display:block;box-sizing:border-box;overflow:scroll;" + + "margin:auto;border:1px;padding:1px;" + + "width:60%;top:1%"; + documentElement.appendChild( container ).appendChild( div ); + + var divStyle = window.getComputedStyle( div ); + pixelPositionVal = divStyle.top !== "1%"; + + // Support: Android 4.0 - 4.3 only, Firefox <=3 - 44 + reliableMarginLeftVal = roundPixelMeasures( divStyle.marginLeft ) === 12; + + // Support: Android 4.0 - 4.3 only, Safari <=9.1 - 10.1, iOS <=7.0 - 9.3 + // Some styles come back with percentage values, even though they shouldn't + div.style.right = "60%"; + pixelBoxStylesVal = roundPixelMeasures( divStyle.right ) === 36; + + // Support: IE 9 - 11 only + // Detect misreporting of content dimensions for box-sizing:border-box elements + boxSizingReliableVal = roundPixelMeasures( divStyle.width ) === 36; + + // Support: IE 9 only + // Detect overflow:scroll screwiness (gh-3699) + // Support: Chrome <=64 + // Don't get tricked when zoom affects offsetWidth (gh-4029) + div.style.position = "absolute"; + scrollboxSizeVal = roundPixelMeasures( div.offsetWidth / 3 ) === 12; + + documentElement.removeChild( container ); + + // Nullify the div so it wouldn't be stored in the memory and + // it will also be a sign that checks already performed + div = null; + } + + function roundPixelMeasures( measure ) { + return Math.round( parseFloat( measure ) ); + } + + var pixelPositionVal, boxSizingReliableVal, scrollboxSizeVal, pixelBoxStylesVal, + reliableTrDimensionsVal, reliableMarginLeftVal, + container = document.createElement( "div" ), + div = document.createElement( "div" ); + + // Finish early in limited (non-browser) environments + if ( !div.style ) { + return; + } + + // Support: IE <=9 - 11 only + // Style of cloned element affects source element cloned (#8908) + div.style.backgroundClip = "content-box"; + div.cloneNode( true ).style.backgroundClip = ""; + support.clearCloneStyle = div.style.backgroundClip === "content-box"; + + jQuery.extend( support, { + boxSizingReliable: function() { + computeStyleTests(); + return boxSizingReliableVal; + }, + pixelBoxStyles: function() { + computeStyleTests(); + return pixelBoxStylesVal; + }, + pixelPosition: function() { + computeStyleTests(); + return pixelPositionVal; + }, + reliableMarginLeft: function() { + computeStyleTests(); + return reliableMarginLeftVal; + }, + scrollboxSize: function() { + computeStyleTests(); + return scrollboxSizeVal; + }, + + // Support: IE 9 - 11+, Edge 15 - 18+ + // IE/Edge misreport `getComputedStyle` of table rows with width/height + // set in CSS while `offset*` properties report correct values. + // Behavior in IE 9 is more subtle than in newer versions & it passes + // some versions of this test; make sure not to make it pass there! + reliableTrDimensions: function() { + var table, tr, trChild, trStyle; + if ( reliableTrDimensionsVal == null ) { + table = document.createElement( "table" ); + tr = document.createElement( "tr" ); + trChild = document.createElement( "div" ); + + table.style.cssText = "position:absolute;left:-11111px"; + tr.style.height = "1px"; + trChild.style.height = "9px"; + + documentElement + .appendChild( table ) + .appendChild( tr ) + .appendChild( trChild ); + + trStyle = window.getComputedStyle( tr ); + reliableTrDimensionsVal = parseInt( trStyle.height ) > 3; + + documentElement.removeChild( table ); + } + return reliableTrDimensionsVal; + } + } ); +} )(); + + +function curCSS( elem, name, computed ) { + var width, minWidth, maxWidth, ret, + + // Support: Firefox 51+ + // Retrieving style before computed somehow + // fixes an issue with getting wrong values + // on detached elements + style = elem.style; + + computed = computed || getStyles( elem ); + + // getPropertyValue is needed for: + // .css('filter') (IE 9 only, #12537) + // .css('--customProperty) (#3144) + if ( computed ) { + ret = computed.getPropertyValue( name ) || computed[ name ]; + + if ( ret === "" && !isAttached( elem ) ) { + ret = jQuery.style( elem, name ); + } + + // A tribute to the "awesome hack by Dean Edwards" + // Android Browser returns percentage for some values, + // but width seems to be reliably pixels. + // This is against the CSSOM draft spec: + // https://drafts.csswg.org/cssom/#resolved-values + if ( !support.pixelBoxStyles() && rnumnonpx.test( ret ) && rboxStyle.test( name ) ) { + + // Remember the original values + width = style.width; + minWidth = style.minWidth; + maxWidth = style.maxWidth; + + // Put in the new values to get a computed value out + style.minWidth = style.maxWidth = style.width = ret; + ret = computed.width; + + // Revert the changed values + style.width = width; + style.minWidth = minWidth; + style.maxWidth = maxWidth; + } + } + + return ret !== undefined ? + + // Support: IE <=9 - 11 only + // IE returns zIndex value as an integer. + ret + "" : + ret; +} + + +function addGetHookIf( conditionFn, hookFn ) { + + // Define the hook, we'll check on the first run if it's really needed. + return { + get: function() { + if ( conditionFn() ) { + + // Hook not needed (or it's not possible to use it due + // to missing dependency), remove it. + delete this.get; + return; + } + + // Hook needed; redefine it so that the support test is not executed again. + return ( this.get = hookFn ).apply( this, arguments ); + } + }; +} + + +var cssPrefixes = [ "Webkit", "Moz", "ms" ], + emptyStyle = document.createElement( "div" ).style, + vendorProps = {}; + +// Return a vendor-prefixed property or undefined +function vendorPropName( name ) { + + // Check for vendor prefixed names + var capName = name[ 0 ].toUpperCase() + name.slice( 1 ), + i = cssPrefixes.length; + + while ( i-- ) { + name = cssPrefixes[ i ] + capName; + if ( name in emptyStyle ) { + return name; + } + } +} + +// Return a potentially-mapped jQuery.cssProps or vendor prefixed property +function finalPropName( name ) { + var final = jQuery.cssProps[ name ] || vendorProps[ name ]; + + if ( final ) { + return final; + } + if ( name in emptyStyle ) { + return name; + } + return vendorProps[ name ] = vendorPropName( name ) || name; +} + + +var + + // Swappable if display is none or starts with table + // except "table", "table-cell", or "table-caption" + // See here for display values: https://developer.mozilla.org/en-US/docs/CSS/display + rdisplayswap = /^(none|table(?!-c[ea]).+)/, + rcustomProp = /^--/, + cssShow = { position: "absolute", visibility: "hidden", display: "block" }, + cssNormalTransform = { + letterSpacing: "0", + fontWeight: "400" + }; + +function setPositiveNumber( _elem, value, subtract ) { + + // Any relative (+/-) values have already been + // normalized at this point + var matches = rcssNum.exec( value ); + return matches ? + + // Guard against undefined "subtract", e.g., when used as in cssHooks + Math.max( 0, matches[ 2 ] - ( subtract || 0 ) ) + ( matches[ 3 ] || "px" ) : + value; +} + +function boxModelAdjustment( elem, dimension, box, isBorderBox, styles, computedVal ) { + var i = dimension === "width" ? 1 : 0, + extra = 0, + delta = 0; + + // Adjustment may not be necessary + if ( box === ( isBorderBox ? "border" : "content" ) ) { + return 0; + } + + for ( ; i < 4; i += 2 ) { + + // Both box models exclude margin + if ( box === "margin" ) { + delta += jQuery.css( elem, box + cssExpand[ i ], true, styles ); + } + + // If we get here with a content-box, we're seeking "padding" or "border" or "margin" + if ( !isBorderBox ) { + + // Add padding + delta += jQuery.css( elem, "padding" + cssExpand[ i ], true, styles ); + + // For "border" or "margin", add border + if ( box !== "padding" ) { + delta += jQuery.css( elem, "border" + cssExpand[ i ] + "Width", true, styles ); + + // But still keep track of it otherwise + } else { + extra += jQuery.css( elem, "border" + cssExpand[ i ] + "Width", true, styles ); + } + + // If we get here with a border-box (content + padding + border), we're seeking "content" or + // "padding" or "margin" + } else { + + // For "content", subtract padding + if ( box === "content" ) { + delta -= jQuery.css( elem, "padding" + cssExpand[ i ], true, styles ); + } + + // For "content" or "padding", subtract border + if ( box !== "margin" ) { + delta -= jQuery.css( elem, "border" + cssExpand[ i ] + "Width", true, styles ); + } + } + } + + // Account for positive content-box scroll gutter when requested by providing computedVal + if ( !isBorderBox && computedVal >= 0 ) { + + // offsetWidth/offsetHeight is a rounded sum of content, padding, scroll gutter, and border + // Assuming integer scroll gutter, subtract the rest and round down + delta += Math.max( 0, Math.ceil( + elem[ "offset" + dimension[ 0 ].toUpperCase() + dimension.slice( 1 ) ] - + computedVal - + delta - + extra - + 0.5 + + // If offsetWidth/offsetHeight is unknown, then we can't determine content-box scroll gutter + // Use an explicit zero to avoid NaN (gh-3964) + ) ) || 0; + } + + return delta; +} + +function getWidthOrHeight( elem, dimension, extra ) { + + // Start with computed style + var styles = getStyles( elem ), + + // To avoid forcing a reflow, only fetch boxSizing if we need it (gh-4322). + // Fake content-box until we know it's needed to know the true value. + boxSizingNeeded = !support.boxSizingReliable() || extra, + isBorderBox = boxSizingNeeded && + jQuery.css( elem, "boxSizing", false, styles ) === "border-box", + valueIsBorderBox = isBorderBox, + + val = curCSS( elem, dimension, styles ), + offsetProp = "offset" + dimension[ 0 ].toUpperCase() + dimension.slice( 1 ); + + // Support: Firefox <=54 + // Return a confounding non-pixel value or feign ignorance, as appropriate. + if ( rnumnonpx.test( val ) ) { + if ( !extra ) { + return val; + } + val = "auto"; + } + + + // Support: IE 9 - 11 only + // Use offsetWidth/offsetHeight for when box sizing is unreliable. + // In those cases, the computed value can be trusted to be border-box. + if ( ( !support.boxSizingReliable() && isBorderBox || + + // Support: IE 10 - 11+, Edge 15 - 18+ + // IE/Edge misreport `getComputedStyle` of table rows with width/height + // set in CSS while `offset*` properties report correct values. + // Interestingly, in some cases IE 9 doesn't suffer from this issue. + !support.reliableTrDimensions() && nodeName( elem, "tr" ) || + + // Fall back to offsetWidth/offsetHeight when value is "auto" + // This happens for inline elements with no explicit setting (gh-3571) + val === "auto" || + + // Support: Android <=4.1 - 4.3 only + // Also use offsetWidth/offsetHeight for misreported inline dimensions (gh-3602) + !parseFloat( val ) && jQuery.css( elem, "display", false, styles ) === "inline" ) && + + // Make sure the element is visible & connected + elem.getClientRects().length ) { + + isBorderBox = jQuery.css( elem, "boxSizing", false, styles ) === "border-box"; + + // Where available, offsetWidth/offsetHeight approximate border box dimensions. + // Where not available (e.g., SVG), assume unreliable box-sizing and interpret the + // retrieved value as a content box dimension. + valueIsBorderBox = offsetProp in elem; + if ( valueIsBorderBox ) { + val = elem[ offsetProp ]; + } + } + + // Normalize "" and auto + val = parseFloat( val ) || 0; + + // Adjust for the element's box model + return ( val + + boxModelAdjustment( + elem, + dimension, + extra || ( isBorderBox ? "border" : "content" ), + valueIsBorderBox, + styles, + + // Provide the current computed size to request scroll gutter calculation (gh-3589) + val + ) + ) + "px"; +} + +jQuery.extend( { + + // Add in style property hooks for overriding the default + // behavior of getting and setting a style property + cssHooks: { + opacity: { + get: function( elem, computed ) { + if ( computed ) { + + // We should always get a number back from opacity + var ret = curCSS( elem, "opacity" ); + return ret === "" ? "1" : ret; + } + } + } + }, + + // Don't automatically add "px" to these possibly-unitless properties + cssNumber: { + "animationIterationCount": true, + "columnCount": true, + "fillOpacity": true, + "flexGrow": true, + "flexShrink": true, + "fontWeight": true, + "gridArea": true, + "gridColumn": true, + "gridColumnEnd": true, + "gridColumnStart": true, + "gridRow": true, + "gridRowEnd": true, + "gridRowStart": true, + "lineHeight": true, + "opacity": true, + "order": true, + "orphans": true, + "widows": true, + "zIndex": true, + "zoom": true + }, + + // Add in properties whose names you wish to fix before + // setting or getting the value + cssProps: {}, + + // Get and set the style property on a DOM Node + style: function( elem, name, value, extra ) { + + // Don't set styles on text and comment nodes + if ( !elem || elem.nodeType === 3 || elem.nodeType === 8 || !elem.style ) { + return; + } + + // Make sure that we're working with the right name + var ret, type, hooks, + origName = camelCase( name ), + isCustomProp = rcustomProp.test( name ), + style = elem.style; + + // Make sure that we're working with the right name. We don't + // want to query the value if it is a CSS custom property + // since they are user-defined. + if ( !isCustomProp ) { + name = finalPropName( origName ); + } + + // Gets hook for the prefixed version, then unprefixed version + hooks = jQuery.cssHooks[ name ] || jQuery.cssHooks[ origName ]; + + // Check if we're setting a value + if ( value !== undefined ) { + type = typeof value; + + // Convert "+=" or "-=" to relative numbers (#7345) + if ( type === "string" && ( ret = rcssNum.exec( value ) ) && ret[ 1 ] ) { + value = adjustCSS( elem, name, ret ); + + // Fixes bug #9237 + type = "number"; + } + + // Make sure that null and NaN values aren't set (#7116) + if ( value == null || value !== value ) { + return; + } + + // If a number was passed in, add the unit (except for certain CSS properties) + // The isCustomProp check can be removed in jQuery 4.0 when we only auto-append + // "px" to a few hardcoded values. + if ( type === "number" && !isCustomProp ) { + value += ret && ret[ 3 ] || ( jQuery.cssNumber[ origName ] ? "" : "px" ); + } + + // background-* props affect original clone's values + if ( !support.clearCloneStyle && value === "" && name.indexOf( "background" ) === 0 ) { + style[ name ] = "inherit"; + } + + // If a hook was provided, use that value, otherwise just set the specified value + if ( !hooks || !( "set" in hooks ) || + ( value = hooks.set( elem, value, extra ) ) !== undefined ) { + + if ( isCustomProp ) { + style.setProperty( name, value ); + } else { + style[ name ] = value; + } + } + + } else { + + // If a hook was provided get the non-computed value from there + if ( hooks && "get" in hooks && + ( ret = hooks.get( elem, false, extra ) ) !== undefined ) { + + return ret; + } + + // Otherwise just get the value from the style object + return style[ name ]; + } + }, + + css: function( elem, name, extra, styles ) { + var val, num, hooks, + origName = camelCase( name ), + isCustomProp = rcustomProp.test( name ); + + // Make sure that we're working with the right name. We don't + // want to modify the value if it is a CSS custom property + // since they are user-defined. + if ( !isCustomProp ) { + name = finalPropName( origName ); + } + + // Try prefixed name followed by the unprefixed name + hooks = jQuery.cssHooks[ name ] || jQuery.cssHooks[ origName ]; + + // If a hook was provided get the computed value from there + if ( hooks && "get" in hooks ) { + val = hooks.get( elem, true, extra ); + } + + // Otherwise, if a way to get the computed value exists, use that + if ( val === undefined ) { + val = curCSS( elem, name, styles ); + } + + // Convert "normal" to computed value + if ( val === "normal" && name in cssNormalTransform ) { + val = cssNormalTransform[ name ]; + } + + // Make numeric if forced or a qualifier was provided and val looks numeric + if ( extra === "" || extra ) { + num = parseFloat( val ); + return extra === true || isFinite( num ) ? num || 0 : val; + } + + return val; + } +} ); + +jQuery.each( [ "height", "width" ], function( _i, dimension ) { + jQuery.cssHooks[ dimension ] = { + get: function( elem, computed, extra ) { + if ( computed ) { + + // Certain elements can have dimension info if we invisibly show them + // but it must have a current display style that would benefit + return rdisplayswap.test( jQuery.css( elem, "display" ) ) && + + // Support: Safari 8+ + // Table columns in Safari have non-zero offsetWidth & zero + // getBoundingClientRect().width unless display is changed. + // Support: IE <=11 only + // Running getBoundingClientRect on a disconnected node + // in IE throws an error. + ( !elem.getClientRects().length || !elem.getBoundingClientRect().width ) ? + swap( elem, cssShow, function() { + return getWidthOrHeight( elem, dimension, extra ); + } ) : + getWidthOrHeight( elem, dimension, extra ); + } + }, + + set: function( elem, value, extra ) { + var matches, + styles = getStyles( elem ), + + // Only read styles.position if the test has a chance to fail + // to avoid forcing a reflow. + scrollboxSizeBuggy = !support.scrollboxSize() && + styles.position === "absolute", + + // To avoid forcing a reflow, only fetch boxSizing if we need it (gh-3991) + boxSizingNeeded = scrollboxSizeBuggy || extra, + isBorderBox = boxSizingNeeded && + jQuery.css( elem, "boxSizing", false, styles ) === "border-box", + subtract = extra ? + boxModelAdjustment( + elem, + dimension, + extra, + isBorderBox, + styles + ) : + 0; + + // Account for unreliable border-box dimensions by comparing offset* to computed and + // faking a content-box to get border and padding (gh-3699) + if ( isBorderBox && scrollboxSizeBuggy ) { + subtract -= Math.ceil( + elem[ "offset" + dimension[ 0 ].toUpperCase() + dimension.slice( 1 ) ] - + parseFloat( styles[ dimension ] ) - + boxModelAdjustment( elem, dimension, "border", false, styles ) - + 0.5 + ); + } + + // Convert to pixels if value adjustment is needed + if ( subtract && ( matches = rcssNum.exec( value ) ) && + ( matches[ 3 ] || "px" ) !== "px" ) { + + elem.style[ dimension ] = value; + value = jQuery.css( elem, dimension ); + } + + return setPositiveNumber( elem, value, subtract ); + } + }; +} ); + +jQuery.cssHooks.marginLeft = addGetHookIf( support.reliableMarginLeft, + function( elem, computed ) { + if ( computed ) { + return ( parseFloat( curCSS( elem, "marginLeft" ) ) || + elem.getBoundingClientRect().left - + swap( elem, { marginLeft: 0 }, function() { + return elem.getBoundingClientRect().left; + } ) + ) + "px"; + } + } +); + +// These hooks are used by animate to expand properties +jQuery.each( { + margin: "", + padding: "", + border: "Width" +}, function( prefix, suffix ) { + jQuery.cssHooks[ prefix + suffix ] = { + expand: function( value ) { + var i = 0, + expanded = {}, + + // Assumes a single number if not a string + parts = typeof value === "string" ? value.split( " " ) : [ value ]; + + for ( ; i < 4; i++ ) { + expanded[ prefix + cssExpand[ i ] + suffix ] = + parts[ i ] || parts[ i - 2 ] || parts[ 0 ]; + } + + return expanded; + } + }; + + if ( prefix !== "margin" ) { + jQuery.cssHooks[ prefix + suffix ].set = setPositiveNumber; + } +} ); + +jQuery.fn.extend( { + css: function( name, value ) { + return access( this, function( elem, name, value ) { + var styles, len, + map = {}, + i = 0; + + if ( Array.isArray( name ) ) { + styles = getStyles( elem ); + len = name.length; + + for ( ; i < len; i++ ) { + map[ name[ i ] ] = jQuery.css( elem, name[ i ], false, styles ); + } + + return map; + } + + return value !== undefined ? + jQuery.style( elem, name, value ) : + jQuery.css( elem, name ); + }, name, value, arguments.length > 1 ); + } +} ); + + +function Tween( elem, options, prop, end, easing ) { + return new Tween.prototype.init( elem, options, prop, end, easing ); +} +jQuery.Tween = Tween; + +Tween.prototype = { + constructor: Tween, + init: function( elem, options, prop, end, easing, unit ) { + this.elem = elem; + this.prop = prop; + this.easing = easing || jQuery.easing._default; + this.options = options; + this.start = this.now = this.cur(); + this.end = end; + this.unit = unit || ( jQuery.cssNumber[ prop ] ? "" : "px" ); + }, + cur: function() { + var hooks = Tween.propHooks[ this.prop ]; + + return hooks && hooks.get ? + hooks.get( this ) : + Tween.propHooks._default.get( this ); + }, + run: function( percent ) { + var eased, + hooks = Tween.propHooks[ this.prop ]; + + if ( this.options.duration ) { + this.pos = eased = jQuery.easing[ this.easing ]( + percent, this.options.duration * percent, 0, 1, this.options.duration + ); + } else { + this.pos = eased = percent; + } + this.now = ( this.end - this.start ) * eased + this.start; + + if ( this.options.step ) { + this.options.step.call( this.elem, this.now, this ); + } + + if ( hooks && hooks.set ) { + hooks.set( this ); + } else { + Tween.propHooks._default.set( this ); + } + return this; + } +}; + +Tween.prototype.init.prototype = Tween.prototype; + +Tween.propHooks = { + _default: { + get: function( tween ) { + var result; + + // Use a property on the element directly when it is not a DOM element, + // or when there is no matching style property that exists. + if ( tween.elem.nodeType !== 1 || + tween.elem[ tween.prop ] != null && tween.elem.style[ tween.prop ] == null ) { + return tween.elem[ tween.prop ]; + } + + // Passing an empty string as a 3rd parameter to .css will automatically + // attempt a parseFloat and fallback to a string if the parse fails. + // Simple values such as "10px" are parsed to Float; + // complex values such as "rotate(1rad)" are returned as-is. + result = jQuery.css( tween.elem, tween.prop, "" ); + + // Empty strings, null, undefined and "auto" are converted to 0. + return !result || result === "auto" ? 0 : result; + }, + set: function( tween ) { + + // Use step hook for back compat. + // Use cssHook if its there. + // Use .style if available and use plain properties where available. + if ( jQuery.fx.step[ tween.prop ] ) { + jQuery.fx.step[ tween.prop ]( tween ); + } else if ( tween.elem.nodeType === 1 && ( + jQuery.cssHooks[ tween.prop ] || + tween.elem.style[ finalPropName( tween.prop ) ] != null ) ) { + jQuery.style( tween.elem, tween.prop, tween.now + tween.unit ); + } else { + tween.elem[ tween.prop ] = tween.now; + } + } + } +}; + +// Support: IE <=9 only +// Panic based approach to setting things on disconnected nodes +Tween.propHooks.scrollTop = Tween.propHooks.scrollLeft = { + set: function( tween ) { + if ( tween.elem.nodeType && tween.elem.parentNode ) { + tween.elem[ tween.prop ] = tween.now; + } + } +}; + +jQuery.easing = { + linear: function( p ) { + return p; + }, + swing: function( p ) { + return 0.5 - Math.cos( p * Math.PI ) / 2; + }, + _default: "swing" +}; + +jQuery.fx = Tween.prototype.init; + +// Back compat <1.8 extension point +jQuery.fx.step = {}; + + + + +var + fxNow, inProgress, + rfxtypes = /^(?:toggle|show|hide)$/, + rrun = /queueHooks$/; + +function schedule() { + if ( inProgress ) { + if ( document.hidden === false && window.requestAnimationFrame ) { + window.requestAnimationFrame( schedule ); + } else { + window.setTimeout( schedule, jQuery.fx.interval ); + } + + jQuery.fx.tick(); + } +} + +// Animations created synchronously will run synchronously +function createFxNow() { + window.setTimeout( function() { + fxNow = undefined; + } ); + return ( fxNow = Date.now() ); +} + +// Generate parameters to create a standard animation +function genFx( type, includeWidth ) { + var which, + i = 0, + attrs = { height: type }; + + // If we include width, step value is 1 to do all cssExpand values, + // otherwise step value is 2 to skip over Left and Right + includeWidth = includeWidth ? 1 : 0; + for ( ; i < 4; i += 2 - includeWidth ) { + which = cssExpand[ i ]; + attrs[ "margin" + which ] = attrs[ "padding" + which ] = type; + } + + if ( includeWidth ) { + attrs.opacity = attrs.width = type; + } + + return attrs; +} + +function createTween( value, prop, animation ) { + var tween, + collection = ( Animation.tweeners[ prop ] || [] ).concat( Animation.tweeners[ "*" ] ), + index = 0, + length = collection.length; + for ( ; index < length; index++ ) { + if ( ( tween = collection[ index ].call( animation, prop, value ) ) ) { + + // We're done with this property + return tween; + } + } +} + +function defaultPrefilter( elem, props, opts ) { + var prop, value, toggle, hooks, oldfire, propTween, restoreDisplay, display, + isBox = "width" in props || "height" in props, + anim = this, + orig = {}, + style = elem.style, + hidden = elem.nodeType && isHiddenWithinTree( elem ), + dataShow = dataPriv.get( elem, "fxshow" ); + + // Queue-skipping animations hijack the fx hooks + if ( !opts.queue ) { + hooks = jQuery._queueHooks( elem, "fx" ); + if ( hooks.unqueued == null ) { + hooks.unqueued = 0; + oldfire = hooks.empty.fire; + hooks.empty.fire = function() { + if ( !hooks.unqueued ) { + oldfire(); + } + }; + } + hooks.unqueued++; + + anim.always( function() { + + // Ensure the complete handler is called before this completes + anim.always( function() { + hooks.unqueued--; + if ( !jQuery.queue( elem, "fx" ).length ) { + hooks.empty.fire(); + } + } ); + } ); + } + + // Detect show/hide animations + for ( prop in props ) { + value = props[ prop ]; + if ( rfxtypes.test( value ) ) { + delete props[ prop ]; + toggle = toggle || value === "toggle"; + if ( value === ( hidden ? "hide" : "show" ) ) { + + // Pretend to be hidden if this is a "show" and + // there is still data from a stopped show/hide + if ( value === "show" && dataShow && dataShow[ prop ] !== undefined ) { + hidden = true; + + // Ignore all other no-op show/hide data + } else { + continue; + } + } + orig[ prop ] = dataShow && dataShow[ prop ] || jQuery.style( elem, prop ); + } + } + + // Bail out if this is a no-op like .hide().hide() + propTween = !jQuery.isEmptyObject( props ); + if ( !propTween && jQuery.isEmptyObject( orig ) ) { + return; + } + + // Restrict "overflow" and "display" styles during box animations + if ( isBox && elem.nodeType === 1 ) { + + // Support: IE <=9 - 11, Edge 12 - 15 + // Record all 3 overflow attributes because IE does not infer the shorthand + // from identically-valued overflowX and overflowY and Edge just mirrors + // the overflowX value there. + opts.overflow = [ style.overflow, style.overflowX, style.overflowY ]; + + // Identify a display type, preferring old show/hide data over the CSS cascade + restoreDisplay = dataShow && dataShow.display; + if ( restoreDisplay == null ) { + restoreDisplay = dataPriv.get( elem, "display" ); + } + display = jQuery.css( elem, "display" ); + if ( display === "none" ) { + if ( restoreDisplay ) { + display = restoreDisplay; + } else { + + // Get nonempty value(s) by temporarily forcing visibility + showHide( [ elem ], true ); + restoreDisplay = elem.style.display || restoreDisplay; + display = jQuery.css( elem, "display" ); + showHide( [ elem ] ); + } + } + + // Animate inline elements as inline-block + if ( display === "inline" || display === "inline-block" && restoreDisplay != null ) { + if ( jQuery.css( elem, "float" ) === "none" ) { + + // Restore the original display value at the end of pure show/hide animations + if ( !propTween ) { + anim.done( function() { + style.display = restoreDisplay; + } ); + if ( restoreDisplay == null ) { + display = style.display; + restoreDisplay = display === "none" ? "" : display; + } + } + style.display = "inline-block"; + } + } + } + + if ( opts.overflow ) { + style.overflow = "hidden"; + anim.always( function() { + style.overflow = opts.overflow[ 0 ]; + style.overflowX = opts.overflow[ 1 ]; + style.overflowY = opts.overflow[ 2 ]; + } ); + } + + // Implement show/hide animations + propTween = false; + for ( prop in orig ) { + + // General show/hide setup for this element animation + if ( !propTween ) { + if ( dataShow ) { + if ( "hidden" in dataShow ) { + hidden = dataShow.hidden; + } + } else { + dataShow = dataPriv.access( elem, "fxshow", { display: restoreDisplay } ); + } + + // Store hidden/visible for toggle so `.stop().toggle()` "reverses" + if ( toggle ) { + dataShow.hidden = !hidden; + } + + // Show elements before animating them + if ( hidden ) { + showHide( [ elem ], true ); + } + + /* eslint-disable no-loop-func */ + + anim.done( function() { + + /* eslint-enable no-loop-func */ + + // The final step of a "hide" animation is actually hiding the element + if ( !hidden ) { + showHide( [ elem ] ); + } + dataPriv.remove( elem, "fxshow" ); + for ( prop in orig ) { + jQuery.style( elem, prop, orig[ prop ] ); + } + } ); + } + + // Per-property setup + propTween = createTween( hidden ? dataShow[ prop ] : 0, prop, anim ); + if ( !( prop in dataShow ) ) { + dataShow[ prop ] = propTween.start; + if ( hidden ) { + propTween.end = propTween.start; + propTween.start = 0; + } + } + } +} + +function propFilter( props, specialEasing ) { + var index, name, easing, value, hooks; + + // camelCase, specialEasing and expand cssHook pass + for ( index in props ) { + name = camelCase( index ); + easing = specialEasing[ name ]; + value = props[ index ]; + if ( Array.isArray( value ) ) { + easing = value[ 1 ]; + value = props[ index ] = value[ 0 ]; + } + + if ( index !== name ) { + props[ name ] = value; + delete props[ index ]; + } + + hooks = jQuery.cssHooks[ name ]; + if ( hooks && "expand" in hooks ) { + value = hooks.expand( value ); + delete props[ name ]; + + // Not quite $.extend, this won't overwrite existing keys. + // Reusing 'index' because we have the correct "name" + for ( index in value ) { + if ( !( index in props ) ) { + props[ index ] = value[ index ]; + specialEasing[ index ] = easing; + } + } + } else { + specialEasing[ name ] = easing; + } + } +} + +function Animation( elem, properties, options ) { + var result, + stopped, + index = 0, + length = Animation.prefilters.length, + deferred = jQuery.Deferred().always( function() { + + // Don't match elem in the :animated selector + delete tick.elem; + } ), + tick = function() { + if ( stopped ) { + return false; + } + var currentTime = fxNow || createFxNow(), + remaining = Math.max( 0, animation.startTime + animation.duration - currentTime ), + + // Support: Android 2.3 only + // Archaic crash bug won't allow us to use `1 - ( 0.5 || 0 )` (#12497) + temp = remaining / animation.duration || 0, + percent = 1 - temp, + index = 0, + length = animation.tweens.length; + + for ( ; index < length; index++ ) { + animation.tweens[ index ].run( percent ); + } + + deferred.notifyWith( elem, [ animation, percent, remaining ] ); + + // If there's more to do, yield + if ( percent < 1 && length ) { + return remaining; + } + + // If this was an empty animation, synthesize a final progress notification + if ( !length ) { + deferred.notifyWith( elem, [ animation, 1, 0 ] ); + } + + // Resolve the animation and report its conclusion + deferred.resolveWith( elem, [ animation ] ); + return false; + }, + animation = deferred.promise( { + elem: elem, + props: jQuery.extend( {}, properties ), + opts: jQuery.extend( true, { + specialEasing: {}, + easing: jQuery.easing._default + }, options ), + originalProperties: properties, + originalOptions: options, + startTime: fxNow || createFxNow(), + duration: options.duration, + tweens: [], + createTween: function( prop, end ) { + var tween = jQuery.Tween( elem, animation.opts, prop, end, + animation.opts.specialEasing[ prop ] || animation.opts.easing ); + animation.tweens.push( tween ); + return tween; + }, + stop: function( gotoEnd ) { + var index = 0, + + // If we are going to the end, we want to run all the tweens + // otherwise we skip this part + length = gotoEnd ? animation.tweens.length : 0; + if ( stopped ) { + return this; + } + stopped = true; + for ( ; index < length; index++ ) { + animation.tweens[ index ].run( 1 ); + } + + // Resolve when we played the last frame; otherwise, reject + if ( gotoEnd ) { + deferred.notifyWith( elem, [ animation, 1, 0 ] ); + deferred.resolveWith( elem, [ animation, gotoEnd ] ); + } else { + deferred.rejectWith( elem, [ animation, gotoEnd ] ); + } + return this; + } + } ), + props = animation.props; + + propFilter( props, animation.opts.specialEasing ); + + for ( ; index < length; index++ ) { + result = Animation.prefilters[ index ].call( animation, elem, props, animation.opts ); + if ( result ) { + if ( isFunction( result.stop ) ) { + jQuery._queueHooks( animation.elem, animation.opts.queue ).stop = + result.stop.bind( result ); + } + return result; + } + } + + jQuery.map( props, createTween, animation ); + + if ( isFunction( animation.opts.start ) ) { + animation.opts.start.call( elem, animation ); + } + + // Attach callbacks from options + animation + .progress( animation.opts.progress ) + .done( animation.opts.done, animation.opts.complete ) + .fail( animation.opts.fail ) + .always( animation.opts.always ); + + jQuery.fx.timer( + jQuery.extend( tick, { + elem: elem, + anim: animation, + queue: animation.opts.queue + } ) + ); + + return animation; +} + +jQuery.Animation = jQuery.extend( Animation, { + + tweeners: { + "*": [ function( prop, value ) { + var tween = this.createTween( prop, value ); + adjustCSS( tween.elem, prop, rcssNum.exec( value ), tween ); + return tween; + } ] + }, + + tweener: function( props, callback ) { + if ( isFunction( props ) ) { + callback = props; + props = [ "*" ]; + } else { + props = props.match( rnothtmlwhite ); + } + + var prop, + index = 0, + length = props.length; + + for ( ; index < length; index++ ) { + prop = props[ index ]; + Animation.tweeners[ prop ] = Animation.tweeners[ prop ] || []; + Animation.tweeners[ prop ].unshift( callback ); + } + }, + + prefilters: [ defaultPrefilter ], + + prefilter: function( callback, prepend ) { + if ( prepend ) { + Animation.prefilters.unshift( callback ); + } else { + Animation.prefilters.push( callback ); + } + } +} ); + +jQuery.speed = function( speed, easing, fn ) { + var opt = speed && typeof speed === "object" ? jQuery.extend( {}, speed ) : { + complete: fn || !fn && easing || + isFunction( speed ) && speed, + duration: speed, + easing: fn && easing || easing && !isFunction( easing ) && easing + }; + + // Go to the end state if fx are off + if ( jQuery.fx.off ) { + opt.duration = 0; + + } else { + if ( typeof opt.duration !== "number" ) { + if ( opt.duration in jQuery.fx.speeds ) { + opt.duration = jQuery.fx.speeds[ opt.duration ]; + + } else { + opt.duration = jQuery.fx.speeds._default; + } + } + } + + // Normalize opt.queue - true/undefined/null -> "fx" + if ( opt.queue == null || opt.queue === true ) { + opt.queue = "fx"; + } + + // Queueing + opt.old = opt.complete; + + opt.complete = function() { + if ( isFunction( opt.old ) ) { + opt.old.call( this ); + } + + if ( opt.queue ) { + jQuery.dequeue( this, opt.queue ); + } + }; + + return opt; +}; + +jQuery.fn.extend( { + fadeTo: function( speed, to, easing, callback ) { + + // Show any hidden elements after setting opacity to 0 + return this.filter( isHiddenWithinTree ).css( "opacity", 0 ).show() + + // Animate to the value specified + .end().animate( { opacity: to }, speed, easing, callback ); + }, + animate: function( prop, speed, easing, callback ) { + var empty = jQuery.isEmptyObject( prop ), + optall = jQuery.speed( speed, easing, callback ), + doAnimation = function() { + + // Operate on a copy of prop so per-property easing won't be lost + var anim = Animation( this, jQuery.extend( {}, prop ), optall ); + + // Empty animations, or finishing resolves immediately + if ( empty || dataPriv.get( this, "finish" ) ) { + anim.stop( true ); + } + }; + doAnimation.finish = doAnimation; + + return empty || optall.queue === false ? + this.each( doAnimation ) : + this.queue( optall.queue, doAnimation ); + }, + stop: function( type, clearQueue, gotoEnd ) { + var stopQueue = function( hooks ) { + var stop = hooks.stop; + delete hooks.stop; + stop( gotoEnd ); + }; + + if ( typeof type !== "string" ) { + gotoEnd = clearQueue; + clearQueue = type; + type = undefined; + } + if ( clearQueue ) { + this.queue( type || "fx", [] ); + } + + return this.each( function() { + var dequeue = true, + index = type != null && type + "queueHooks", + timers = jQuery.timers, + data = dataPriv.get( this ); + + if ( index ) { + if ( data[ index ] && data[ index ].stop ) { + stopQueue( data[ index ] ); + } + } else { + for ( index in data ) { + if ( data[ index ] && data[ index ].stop && rrun.test( index ) ) { + stopQueue( data[ index ] ); + } + } + } + + for ( index = timers.length; index--; ) { + if ( timers[ index ].elem === this && + ( type == null || timers[ index ].queue === type ) ) { + + timers[ index ].anim.stop( gotoEnd ); + dequeue = false; + timers.splice( index, 1 ); + } + } + + // Start the next in the queue if the last step wasn't forced. + // Timers currently will call their complete callbacks, which + // will dequeue but only if they were gotoEnd. + if ( dequeue || !gotoEnd ) { + jQuery.dequeue( this, type ); + } + } ); + }, + finish: function( type ) { + if ( type !== false ) { + type = type || "fx"; + } + return this.each( function() { + var index, + data = dataPriv.get( this ), + queue = data[ type + "queue" ], + hooks = data[ type + "queueHooks" ], + timers = jQuery.timers, + length = queue ? queue.length : 0; + + // Enable finishing flag on private data + data.finish = true; + + // Empty the queue first + jQuery.queue( this, type, [] ); + + if ( hooks && hooks.stop ) { + hooks.stop.call( this, true ); + } + + // Look for any active animations, and finish them + for ( index = timers.length; index--; ) { + if ( timers[ index ].elem === this && timers[ index ].queue === type ) { + timers[ index ].anim.stop( true ); + timers.splice( index, 1 ); + } + } + + // Look for any animations in the old queue and finish them + for ( index = 0; index < length; index++ ) { + if ( queue[ index ] && queue[ index ].finish ) { + queue[ index ].finish.call( this ); + } + } + + // Turn off finishing flag + delete data.finish; + } ); + } +} ); + +jQuery.each( [ "toggle", "show", "hide" ], function( _i, name ) { + var cssFn = jQuery.fn[ name ]; + jQuery.fn[ name ] = function( speed, easing, callback ) { + return speed == null || typeof speed === "boolean" ? + cssFn.apply( this, arguments ) : + this.animate( genFx( name, true ), speed, easing, callback ); + }; +} ); + +// Generate shortcuts for custom animations +jQuery.each( { + slideDown: genFx( "show" ), + slideUp: genFx( "hide" ), + slideToggle: genFx( "toggle" ), + fadeIn: { opacity: "show" }, + fadeOut: { opacity: "hide" }, + fadeToggle: { opacity: "toggle" } +}, function( name, props ) { + jQuery.fn[ name ] = function( speed, easing, callback ) { + return this.animate( props, speed, easing, callback ); + }; +} ); + +jQuery.timers = []; +jQuery.fx.tick = function() { + var timer, + i = 0, + timers = jQuery.timers; + + fxNow = Date.now(); + + for ( ; i < timers.length; i++ ) { + timer = timers[ i ]; + + // Run the timer and safely remove it when done (allowing for external removal) + if ( !timer() && timers[ i ] === timer ) { + timers.splice( i--, 1 ); + } + } + + if ( !timers.length ) { + jQuery.fx.stop(); + } + fxNow = undefined; +}; + +jQuery.fx.timer = function( timer ) { + jQuery.timers.push( timer ); + jQuery.fx.start(); +}; + +jQuery.fx.interval = 13; +jQuery.fx.start = function() { + if ( inProgress ) { + return; + } + + inProgress = true; + schedule(); +}; + +jQuery.fx.stop = function() { + inProgress = null; +}; + +jQuery.fx.speeds = { + slow: 600, + fast: 200, + + // Default speed + _default: 400 +}; + + +// Based off of the plugin by Clint Helfers, with permission. +// https://web.archive.org/web/20100324014747/http://blindsignals.com/index.php/2009/07/jquery-delay/ +jQuery.fn.delay = function( time, type ) { + time = jQuery.fx ? jQuery.fx.speeds[ time ] || time : time; + type = type || "fx"; + + return this.queue( type, function( next, hooks ) { + var timeout = window.setTimeout( next, time ); + hooks.stop = function() { + window.clearTimeout( timeout ); + }; + } ); +}; + + +( function() { + var input = document.createElement( "input" ), + select = document.createElement( "select" ), + opt = select.appendChild( document.createElement( "option" ) ); + + input.type = "checkbox"; + + // Support: Android <=4.3 only + // Default value for a checkbox should be "on" + support.checkOn = input.value !== ""; + + // Support: IE <=11 only + // Must access selectedIndex to make default options select + support.optSelected = opt.selected; + + // Support: IE <=11 only + // An input loses its value after becoming a radio + input = document.createElement( "input" ); + input.value = "t"; + input.type = "radio"; + support.radioValue = input.value === "t"; +} )(); + + +var boolHook, + attrHandle = jQuery.expr.attrHandle; + +jQuery.fn.extend( { + attr: function( name, value ) { + return access( this, jQuery.attr, name, value, arguments.length > 1 ); + }, + + removeAttr: function( name ) { + return this.each( function() { + jQuery.removeAttr( this, name ); + } ); + } +} ); + +jQuery.extend( { + attr: function( elem, name, value ) { + var ret, hooks, + nType = elem.nodeType; + + // Don't get/set attributes on text, comment and attribute nodes + if ( nType === 3 || nType === 8 || nType === 2 ) { + return; + } + + // Fallback to prop when attributes are not supported + if ( typeof elem.getAttribute === "undefined" ) { + return jQuery.prop( elem, name, value ); + } + + // Attribute hooks are determined by the lowercase version + // Grab necessary hook if one is defined + if ( nType !== 1 || !jQuery.isXMLDoc( elem ) ) { + hooks = jQuery.attrHooks[ name.toLowerCase() ] || + ( jQuery.expr.match.bool.test( name ) ? boolHook : undefined ); + } + + if ( value !== undefined ) { + if ( value === null ) { + jQuery.removeAttr( elem, name ); + return; + } + + if ( hooks && "set" in hooks && + ( ret = hooks.set( elem, value, name ) ) !== undefined ) { + return ret; + } + + elem.setAttribute( name, value + "" ); + return value; + } + + if ( hooks && "get" in hooks && ( ret = hooks.get( elem, name ) ) !== null ) { + return ret; + } + + ret = jQuery.find.attr( elem, name ); + + // Non-existent attributes return null, we normalize to undefined + return ret == null ? undefined : ret; + }, + + attrHooks: { + type: { + set: function( elem, value ) { + if ( !support.radioValue && value === "radio" && + nodeName( elem, "input" ) ) { + var val = elem.value; + elem.setAttribute( "type", value ); + if ( val ) { + elem.value = val; + } + return value; + } + } + } + }, + + removeAttr: function( elem, value ) { + var name, + i = 0, + + // Attribute names can contain non-HTML whitespace characters + // https://html.spec.whatwg.org/multipage/syntax.html#attributes-2 + attrNames = value && value.match( rnothtmlwhite ); + + if ( attrNames && elem.nodeType === 1 ) { + while ( ( name = attrNames[ i++ ] ) ) { + elem.removeAttribute( name ); + } + } + } +} ); + +// Hooks for boolean attributes +boolHook = { + set: function( elem, value, name ) { + if ( value === false ) { + + // Remove boolean attributes when set to false + jQuery.removeAttr( elem, name ); + } else { + elem.setAttribute( name, name ); + } + return name; + } +}; + +jQuery.each( jQuery.expr.match.bool.source.match( /\w+/g ), function( _i, name ) { + var getter = attrHandle[ name ] || jQuery.find.attr; + + attrHandle[ name ] = function( elem, name, isXML ) { + var ret, handle, + lowercaseName = name.toLowerCase(); + + if ( !isXML ) { + + // Avoid an infinite loop by temporarily removing this function from the getter + handle = attrHandle[ lowercaseName ]; + attrHandle[ lowercaseName ] = ret; + ret = getter( elem, name, isXML ) != null ? + lowercaseName : + null; + attrHandle[ lowercaseName ] = handle; + } + return ret; + }; +} ); + + + + +var rfocusable = /^(?:input|select|textarea|button)$/i, + rclickable = /^(?:a|area)$/i; + +jQuery.fn.extend( { + prop: function( name, value ) { + return access( this, jQuery.prop, name, value, arguments.length > 1 ); + }, + + removeProp: function( name ) { + return this.each( function() { + delete this[ jQuery.propFix[ name ] || name ]; + } ); + } +} ); + +jQuery.extend( { + prop: function( elem, name, value ) { + var ret, hooks, + nType = elem.nodeType; + + // Don't get/set properties on text, comment and attribute nodes + if ( nType === 3 || nType === 8 || nType === 2 ) { + return; + } + + if ( nType !== 1 || !jQuery.isXMLDoc( elem ) ) { + + // Fix name and attach hooks + name = jQuery.propFix[ name ] || name; + hooks = jQuery.propHooks[ name ]; + } + + if ( value !== undefined ) { + if ( hooks && "set" in hooks && + ( ret = hooks.set( elem, value, name ) ) !== undefined ) { + return ret; + } + + return ( elem[ name ] = value ); + } + + if ( hooks && "get" in hooks && ( ret = hooks.get( elem, name ) ) !== null ) { + return ret; + } + + return elem[ name ]; + }, + + propHooks: { + tabIndex: { + get: function( elem ) { + + // Support: IE <=9 - 11 only + // elem.tabIndex doesn't always return the + // correct value when it hasn't been explicitly set + // https://web.archive.org/web/20141116233347/http://fluidproject.org/blog/2008/01/09/getting-setting-and-removing-tabindex-values-with-javascript/ + // Use proper attribute retrieval(#12072) + var tabindex = jQuery.find.attr( elem, "tabindex" ); + + if ( tabindex ) { + return parseInt( tabindex, 10 ); + } + + if ( + rfocusable.test( elem.nodeName ) || + rclickable.test( elem.nodeName ) && + elem.href + ) { + return 0; + } + + return -1; + } + } + }, + + propFix: { + "for": "htmlFor", + "class": "className" + } +} ); + +// Support: IE <=11 only +// Accessing the selectedIndex property +// forces the browser to respect setting selected +// on the option +// The getter ensures a default option is selected +// when in an optgroup +// eslint rule "no-unused-expressions" is disabled for this code +// since it considers such accessions noop +if ( !support.optSelected ) { + jQuery.propHooks.selected = { + get: function( elem ) { + + /* eslint no-unused-expressions: "off" */ + + var parent = elem.parentNode; + if ( parent && parent.parentNode ) { + parent.parentNode.selectedIndex; + } + return null; + }, + set: function( elem ) { + + /* eslint no-unused-expressions: "off" */ + + var parent = elem.parentNode; + if ( parent ) { + parent.selectedIndex; + + if ( parent.parentNode ) { + parent.parentNode.selectedIndex; + } + } + } + }; +} + +jQuery.each( [ + "tabIndex", + "readOnly", + "maxLength", + "cellSpacing", + "cellPadding", + "rowSpan", + "colSpan", + "useMap", + "frameBorder", + "contentEditable" +], function() { + jQuery.propFix[ this.toLowerCase() ] = this; +} ); + + + + + // Strip and collapse whitespace according to HTML spec + // https://infra.spec.whatwg.org/#strip-and-collapse-ascii-whitespace + function stripAndCollapse( value ) { + var tokens = value.match( rnothtmlwhite ) || []; + return tokens.join( " " ); + } + + +function getClass( elem ) { + return elem.getAttribute && elem.getAttribute( "class" ) || ""; +} + +function classesToArray( value ) { + if ( Array.isArray( value ) ) { + return value; + } + if ( typeof value === "string" ) { + return value.match( rnothtmlwhite ) || []; + } + return []; +} + +jQuery.fn.extend( { + addClass: function( value ) { + var classes, elem, cur, curValue, clazz, j, finalValue, + i = 0; + + if ( isFunction( value ) ) { + return this.each( function( j ) { + jQuery( this ).addClass( value.call( this, j, getClass( this ) ) ); + } ); + } + + classes = classesToArray( value ); + + if ( classes.length ) { + while ( ( elem = this[ i++ ] ) ) { + curValue = getClass( elem ); + cur = elem.nodeType === 1 && ( " " + stripAndCollapse( curValue ) + " " ); + + if ( cur ) { + j = 0; + while ( ( clazz = classes[ j++ ] ) ) { + if ( cur.indexOf( " " + clazz + " " ) < 0 ) { + cur += clazz + " "; + } + } + + // Only assign if different to avoid unneeded rendering. + finalValue = stripAndCollapse( cur ); + if ( curValue !== finalValue ) { + elem.setAttribute( "class", finalValue ); + } + } + } + } + + return this; + }, + + removeClass: function( value ) { + var classes, elem, cur, curValue, clazz, j, finalValue, + i = 0; + + if ( isFunction( value ) ) { + return this.each( function( j ) { + jQuery( this ).removeClass( value.call( this, j, getClass( this ) ) ); + } ); + } + + if ( !arguments.length ) { + return this.attr( "class", "" ); + } + + classes = classesToArray( value ); + + if ( classes.length ) { + while ( ( elem = this[ i++ ] ) ) { + curValue = getClass( elem ); + + // This expression is here for better compressibility (see addClass) + cur = elem.nodeType === 1 && ( " " + stripAndCollapse( curValue ) + " " ); + + if ( cur ) { + j = 0; + while ( ( clazz = classes[ j++ ] ) ) { + + // Remove *all* instances + while ( cur.indexOf( " " + clazz + " " ) > -1 ) { + cur = cur.replace( " " + clazz + " ", " " ); + } + } + + // Only assign if different to avoid unneeded rendering. + finalValue = stripAndCollapse( cur ); + if ( curValue !== finalValue ) { + elem.setAttribute( "class", finalValue ); + } + } + } + } + + return this; + }, + + toggleClass: function( value, stateVal ) { + var type = typeof value, + isValidValue = type === "string" || Array.isArray( value ); + + if ( typeof stateVal === "boolean" && isValidValue ) { + return stateVal ? this.addClass( value ) : this.removeClass( value ); + } + + if ( isFunction( value ) ) { + return this.each( function( i ) { + jQuery( this ).toggleClass( + value.call( this, i, getClass( this ), stateVal ), + stateVal + ); + } ); + } + + return this.each( function() { + var className, i, self, classNames; + + if ( isValidValue ) { + + // Toggle individual class names + i = 0; + self = jQuery( this ); + classNames = classesToArray( value ); + + while ( ( className = classNames[ i++ ] ) ) { + + // Check each className given, space separated list + if ( self.hasClass( className ) ) { + self.removeClass( className ); + } else { + self.addClass( className ); + } + } + + // Toggle whole class name + } else if ( value === undefined || type === "boolean" ) { + className = getClass( this ); + if ( className ) { + + // Store className if set + dataPriv.set( this, "__className__", className ); + } + + // If the element has a class name or if we're passed `false`, + // then remove the whole classname (if there was one, the above saved it). + // Otherwise bring back whatever was previously saved (if anything), + // falling back to the empty string if nothing was stored. + if ( this.setAttribute ) { + this.setAttribute( "class", + className || value === false ? + "" : + dataPriv.get( this, "__className__" ) || "" + ); + } + } + } ); + }, + + hasClass: function( selector ) { + var className, elem, + i = 0; + + className = " " + selector + " "; + while ( ( elem = this[ i++ ] ) ) { + if ( elem.nodeType === 1 && + ( " " + stripAndCollapse( getClass( elem ) ) + " " ).indexOf( className ) > -1 ) { + return true; + } + } + + return false; + } +} ); + + + + +var rreturn = /\r/g; + +jQuery.fn.extend( { + val: function( value ) { + var hooks, ret, valueIsFunction, + elem = this[ 0 ]; + + if ( !arguments.length ) { + if ( elem ) { + hooks = jQuery.valHooks[ elem.type ] || + jQuery.valHooks[ elem.nodeName.toLowerCase() ]; + + if ( hooks && + "get" in hooks && + ( ret = hooks.get( elem, "value" ) ) !== undefined + ) { + return ret; + } + + ret = elem.value; + + // Handle most common string cases + if ( typeof ret === "string" ) { + return ret.replace( rreturn, "" ); + } + + // Handle cases where value is null/undef or number + return ret == null ? "" : ret; + } + + return; + } + + valueIsFunction = isFunction( value ); + + return this.each( function( i ) { + var val; + + if ( this.nodeType !== 1 ) { + return; + } + + if ( valueIsFunction ) { + val = value.call( this, i, jQuery( this ).val() ); + } else { + val = value; + } + + // Treat null/undefined as ""; convert numbers to string + if ( val == null ) { + val = ""; + + } else if ( typeof val === "number" ) { + val += ""; + + } else if ( Array.isArray( val ) ) { + val = jQuery.map( val, function( value ) { + return value == null ? "" : value + ""; + } ); + } + + hooks = jQuery.valHooks[ this.type ] || jQuery.valHooks[ this.nodeName.toLowerCase() ]; + + // If set returns undefined, fall back to normal setting + if ( !hooks || !( "set" in hooks ) || hooks.set( this, val, "value" ) === undefined ) { + this.value = val; + } + } ); + } +} ); + +jQuery.extend( { + valHooks: { + option: { + get: function( elem ) { + + var val = jQuery.find.attr( elem, "value" ); + return val != null ? + val : + + // Support: IE <=10 - 11 only + // option.text throws exceptions (#14686, #14858) + // Strip and collapse whitespace + // https://html.spec.whatwg.org/#strip-and-collapse-whitespace + stripAndCollapse( jQuery.text( elem ) ); + } + }, + select: { + get: function( elem ) { + var value, option, i, + options = elem.options, + index = elem.selectedIndex, + one = elem.type === "select-one", + values = one ? null : [], + max = one ? index + 1 : options.length; + + if ( index < 0 ) { + i = max; + + } else { + i = one ? index : 0; + } + + // Loop through all the selected options + for ( ; i < max; i++ ) { + option = options[ i ]; + + // Support: IE <=9 only + // IE8-9 doesn't update selected after form reset (#2551) + if ( ( option.selected || i === index ) && + + // Don't return options that are disabled or in a disabled optgroup + !option.disabled && + ( !option.parentNode.disabled || + !nodeName( option.parentNode, "optgroup" ) ) ) { + + // Get the specific value for the option + value = jQuery( option ).val(); + + // We don't need an array for one selects + if ( one ) { + return value; + } + + // Multi-Selects return an array + values.push( value ); + } + } + + return values; + }, + + set: function( elem, value ) { + var optionSet, option, + options = elem.options, + values = jQuery.makeArray( value ), + i = options.length; + + while ( i-- ) { + option = options[ i ]; + + /* eslint-disable no-cond-assign */ + + if ( option.selected = + jQuery.inArray( jQuery.valHooks.option.get( option ), values ) > -1 + ) { + optionSet = true; + } + + /* eslint-enable no-cond-assign */ + } + + // Force browsers to behave consistently when non-matching value is set + if ( !optionSet ) { + elem.selectedIndex = -1; + } + return values; + } + } + } +} ); + +// Radios and checkboxes getter/setter +jQuery.each( [ "radio", "checkbox" ], function() { + jQuery.valHooks[ this ] = { + set: function( elem, value ) { + if ( Array.isArray( value ) ) { + return ( elem.checked = jQuery.inArray( jQuery( elem ).val(), value ) > -1 ); + } + } + }; + if ( !support.checkOn ) { + jQuery.valHooks[ this ].get = function( elem ) { + return elem.getAttribute( "value" ) === null ? "on" : elem.value; + }; + } +} ); + + + + +// Return jQuery for attributes-only inclusion + + +support.focusin = "onfocusin" in window; + + +var rfocusMorph = /^(?:focusinfocus|focusoutblur)$/, + stopPropagationCallback = function( e ) { + e.stopPropagation(); + }; + +jQuery.extend( jQuery.event, { + + trigger: function( event, data, elem, onlyHandlers ) { + + var i, cur, tmp, bubbleType, ontype, handle, special, lastElement, + eventPath = [ elem || document ], + type = hasOwn.call( event, "type" ) ? event.type : event, + namespaces = hasOwn.call( event, "namespace" ) ? event.namespace.split( "." ) : []; + + cur = lastElement = tmp = elem = elem || document; + + // Don't do events on text and comment nodes + if ( elem.nodeType === 3 || elem.nodeType === 8 ) { + return; + } + + // focus/blur morphs to focusin/out; ensure we're not firing them right now + if ( rfocusMorph.test( type + jQuery.event.triggered ) ) { + return; + } + + if ( type.indexOf( "." ) > -1 ) { + + // Namespaced trigger; create a regexp to match event type in handle() + namespaces = type.split( "." ); + type = namespaces.shift(); + namespaces.sort(); + } + ontype = type.indexOf( ":" ) < 0 && "on" + type; + + // Caller can pass in a jQuery.Event object, Object, or just an event type string + event = event[ jQuery.expando ] ? + event : + new jQuery.Event( type, typeof event === "object" && event ); + + // Trigger bitmask: & 1 for native handlers; & 2 for jQuery (always true) + event.isTrigger = onlyHandlers ? 2 : 3; + event.namespace = namespaces.join( "." ); + event.rnamespace = event.namespace ? + new RegExp( "(^|\\.)" + namespaces.join( "\\.(?:.*\\.|)" ) + "(\\.|$)" ) : + null; + + // Clean up the event in case it is being reused + event.result = undefined; + if ( !event.target ) { + event.target = elem; + } + + // Clone any incoming data and prepend the event, creating the handler arg list + data = data == null ? + [ event ] : + jQuery.makeArray( data, [ event ] ); + + // Allow special events to draw outside the lines + special = jQuery.event.special[ type ] || {}; + if ( !onlyHandlers && special.trigger && special.trigger.apply( elem, data ) === false ) { + return; + } + + // Determine event propagation path in advance, per W3C events spec (#9951) + // Bubble up to document, then to window; watch for a global ownerDocument var (#9724) + if ( !onlyHandlers && !special.noBubble && !isWindow( elem ) ) { + + bubbleType = special.delegateType || type; + if ( !rfocusMorph.test( bubbleType + type ) ) { + cur = cur.parentNode; + } + for ( ; cur; cur = cur.parentNode ) { + eventPath.push( cur ); + tmp = cur; + } + + // Only add window if we got to document (e.g., not plain obj or detached DOM) + if ( tmp === ( elem.ownerDocument || document ) ) { + eventPath.push( tmp.defaultView || tmp.parentWindow || window ); + } + } + + // Fire handlers on the event path + i = 0; + while ( ( cur = eventPath[ i++ ] ) && !event.isPropagationStopped() ) { + lastElement = cur; + event.type = i > 1 ? + bubbleType : + special.bindType || type; + + // jQuery handler + handle = ( + dataPriv.get( cur, "events" ) || Object.create( null ) + )[ event.type ] && + dataPriv.get( cur, "handle" ); + if ( handle ) { + handle.apply( cur, data ); + } + + // Native handler + handle = ontype && cur[ ontype ]; + if ( handle && handle.apply && acceptData( cur ) ) { + event.result = handle.apply( cur, data ); + if ( event.result === false ) { + event.preventDefault(); + } + } + } + event.type = type; + + // If nobody prevented the default action, do it now + if ( !onlyHandlers && !event.isDefaultPrevented() ) { + + if ( ( !special._default || + special._default.apply( eventPath.pop(), data ) === false ) && + acceptData( elem ) ) { + + // Call a native DOM method on the target with the same name as the event. + // Don't do default actions on window, that's where global variables be (#6170) + if ( ontype && isFunction( elem[ type ] ) && !isWindow( elem ) ) { + + // Don't re-trigger an onFOO event when we call its FOO() method + tmp = elem[ ontype ]; + + if ( tmp ) { + elem[ ontype ] = null; + } + + // Prevent re-triggering of the same event, since we already bubbled it above + jQuery.event.triggered = type; + + if ( event.isPropagationStopped() ) { + lastElement.addEventListener( type, stopPropagationCallback ); + } + + elem[ type ](); + + if ( event.isPropagationStopped() ) { + lastElement.removeEventListener( type, stopPropagationCallback ); + } + + jQuery.event.triggered = undefined; + + if ( tmp ) { + elem[ ontype ] = tmp; + } + } + } + } + + return event.result; + }, + + // Piggyback on a donor event to simulate a different one + // Used only for `focus(in | out)` events + simulate: function( type, elem, event ) { + var e = jQuery.extend( + new jQuery.Event(), + event, + { + type: type, + isSimulated: true + } + ); + + jQuery.event.trigger( e, null, elem ); + } + +} ); + +jQuery.fn.extend( { + + trigger: function( type, data ) { + return this.each( function() { + jQuery.event.trigger( type, data, this ); + } ); + }, + triggerHandler: function( type, data ) { + var elem = this[ 0 ]; + if ( elem ) { + return jQuery.event.trigger( type, data, elem, true ); + } + } +} ); + + +// Support: Firefox <=44 +// Firefox doesn't have focus(in | out) events +// Related ticket - https://bugzilla.mozilla.org/show_bug.cgi?id=687787 +// +// Support: Chrome <=48 - 49, Safari <=9.0 - 9.1 +// focus(in | out) events fire after focus & blur events, +// which is spec violation - http://www.w3.org/TR/DOM-Level-3-Events/#events-focusevent-event-order +// Related ticket - https://bugs.chromium.org/p/chromium/issues/detail?id=449857 +if ( !support.focusin ) { + jQuery.each( { focus: "focusin", blur: "focusout" }, function( orig, fix ) { + + // Attach a single capturing handler on the document while someone wants focusin/focusout + var handler = function( event ) { + jQuery.event.simulate( fix, event.target, jQuery.event.fix( event ) ); + }; + + jQuery.event.special[ fix ] = { + setup: function() { + + // Handle: regular nodes (via `this.ownerDocument`), window + // (via `this.document`) & document (via `this`). + var doc = this.ownerDocument || this.document || this, + attaches = dataPriv.access( doc, fix ); + + if ( !attaches ) { + doc.addEventListener( orig, handler, true ); + } + dataPriv.access( doc, fix, ( attaches || 0 ) + 1 ); + }, + teardown: function() { + var doc = this.ownerDocument || this.document || this, + attaches = dataPriv.access( doc, fix ) - 1; + + if ( !attaches ) { + doc.removeEventListener( orig, handler, true ); + dataPriv.remove( doc, fix ); + + } else { + dataPriv.access( doc, fix, attaches ); + } + } + }; + } ); +} +var location = window.location; + +var nonce = { guid: Date.now() }; + +var rquery = ( /\?/ ); + + + +// Cross-browser xml parsing +jQuery.parseXML = function( data ) { + var xml; + if ( !data || typeof data !== "string" ) { + return null; + } + + // Support: IE 9 - 11 only + // IE throws on parseFromString with invalid input. + try { + xml = ( new window.DOMParser() ).parseFromString( data, "text/xml" ); + } catch ( e ) { + xml = undefined; + } + + if ( !xml || xml.getElementsByTagName( "parsererror" ).length ) { + jQuery.error( "Invalid XML: " + data ); + } + return xml; +}; + + +var + rbracket = /\[\]$/, + rCRLF = /\r?\n/g, + rsubmitterTypes = /^(?:submit|button|image|reset|file)$/i, + rsubmittable = /^(?:input|select|textarea|keygen)/i; + +function buildParams( prefix, obj, traditional, add ) { + var name; + + if ( Array.isArray( obj ) ) { + + // Serialize array item. + jQuery.each( obj, function( i, v ) { + if ( traditional || rbracket.test( prefix ) ) { + + // Treat each array item as a scalar. + add( prefix, v ); + + } else { + + // Item is non-scalar (array or object), encode its numeric index. + buildParams( + prefix + "[" + ( typeof v === "object" && v != null ? i : "" ) + "]", + v, + traditional, + add + ); + } + } ); + + } else if ( !traditional && toType( obj ) === "object" ) { + + // Serialize object item. + for ( name in obj ) { + buildParams( prefix + "[" + name + "]", obj[ name ], traditional, add ); + } + + } else { + + // Serialize scalar item. + add( prefix, obj ); + } +} + +// Serialize an array of form elements or a set of +// key/values into a query string +jQuery.param = function( a, traditional ) { + var prefix, + s = [], + add = function( key, valueOrFunction ) { + + // If value is a function, invoke it and use its return value + var value = isFunction( valueOrFunction ) ? + valueOrFunction() : + valueOrFunction; + + s[ s.length ] = encodeURIComponent( key ) + "=" + + encodeURIComponent( value == null ? "" : value ); + }; + + if ( a == null ) { + return ""; + } + + // If an array was passed in, assume that it is an array of form elements. + if ( Array.isArray( a ) || ( a.jquery && !jQuery.isPlainObject( a ) ) ) { + + // Serialize the form elements + jQuery.each( a, function() { + add( this.name, this.value ); + } ); + + } else { + + // If traditional, encode the "old" way (the way 1.3.2 or older + // did it), otherwise encode params recursively. + for ( prefix in a ) { + buildParams( prefix, a[ prefix ], traditional, add ); + } + } + + // Return the resulting serialization + return s.join( "&" ); +}; + +jQuery.fn.extend( { + serialize: function() { + return jQuery.param( this.serializeArray() ); + }, + serializeArray: function() { + return this.map( function() { + + // Can add propHook for "elements" to filter or add form elements + var elements = jQuery.prop( this, "elements" ); + return elements ? jQuery.makeArray( elements ) : this; + } ) + .filter( function() { + var type = this.type; + + // Use .is( ":disabled" ) so that fieldset[disabled] works + return this.name && !jQuery( this ).is( ":disabled" ) && + rsubmittable.test( this.nodeName ) && !rsubmitterTypes.test( type ) && + ( this.checked || !rcheckableType.test( type ) ); + } ) + .map( function( _i, elem ) { + var val = jQuery( this ).val(); + + if ( val == null ) { + return null; + } + + if ( Array.isArray( val ) ) { + return jQuery.map( val, function( val ) { + return { name: elem.name, value: val.replace( rCRLF, "\r\n" ) }; + } ); + } + + return { name: elem.name, value: val.replace( rCRLF, "\r\n" ) }; + } ).get(); + } +} ); + + +var + r20 = /%20/g, + rhash = /#.*$/, + rantiCache = /([?&])_=[^&]*/, + rheaders = /^(.*?):[ \t]*([^\r\n]*)$/mg, + + // #7653, #8125, #8152: local protocol detection + rlocalProtocol = /^(?:about|app|app-storage|.+-extension|file|res|widget):$/, + rnoContent = /^(?:GET|HEAD)$/, + rprotocol = /^\/\//, + + /* Prefilters + * 1) They are useful to introduce custom dataTypes (see ajax/jsonp.js for an example) + * 2) These are called: + * - BEFORE asking for a transport + * - AFTER param serialization (s.data is a string if s.processData is true) + * 3) key is the dataType + * 4) the catchall symbol "*" can be used + * 5) execution will start with transport dataType and THEN continue down to "*" if needed + */ + prefilters = {}, + + /* Transports bindings + * 1) key is the dataType + * 2) the catchall symbol "*" can be used + * 3) selection will start with transport dataType and THEN go to "*" if needed + */ + transports = {}, + + // Avoid comment-prolog char sequence (#10098); must appease lint and evade compression + allTypes = "*/".concat( "*" ), + + // Anchor tag for parsing the document origin + originAnchor = document.createElement( "a" ); + originAnchor.href = location.href; + +// Base "constructor" for jQuery.ajaxPrefilter and jQuery.ajaxTransport +function addToPrefiltersOrTransports( structure ) { + + // dataTypeExpression is optional and defaults to "*" + return function( dataTypeExpression, func ) { + + if ( typeof dataTypeExpression !== "string" ) { + func = dataTypeExpression; + dataTypeExpression = "*"; + } + + var dataType, + i = 0, + dataTypes = dataTypeExpression.toLowerCase().match( rnothtmlwhite ) || []; + + if ( isFunction( func ) ) { + + // For each dataType in the dataTypeExpression + while ( ( dataType = dataTypes[ i++ ] ) ) { + + // Prepend if requested + if ( dataType[ 0 ] === "+" ) { + dataType = dataType.slice( 1 ) || "*"; + ( structure[ dataType ] = structure[ dataType ] || [] ).unshift( func ); + + // Otherwise append + } else { + ( structure[ dataType ] = structure[ dataType ] || [] ).push( func ); + } + } + } + }; +} + +// Base inspection function for prefilters and transports +function inspectPrefiltersOrTransports( structure, options, originalOptions, jqXHR ) { + + var inspected = {}, + seekingTransport = ( structure === transports ); + + function inspect( dataType ) { + var selected; + inspected[ dataType ] = true; + jQuery.each( structure[ dataType ] || [], function( _, prefilterOrFactory ) { + var dataTypeOrTransport = prefilterOrFactory( options, originalOptions, jqXHR ); + if ( typeof dataTypeOrTransport === "string" && + !seekingTransport && !inspected[ dataTypeOrTransport ] ) { + + options.dataTypes.unshift( dataTypeOrTransport ); + inspect( dataTypeOrTransport ); + return false; + } else if ( seekingTransport ) { + return !( selected = dataTypeOrTransport ); + } + } ); + return selected; + } + + return inspect( options.dataTypes[ 0 ] ) || !inspected[ "*" ] && inspect( "*" ); +} + +// A special extend for ajax options +// that takes "flat" options (not to be deep extended) +// Fixes #9887 +function ajaxExtend( target, src ) { + var key, deep, + flatOptions = jQuery.ajaxSettings.flatOptions || {}; + + for ( key in src ) { + if ( src[ key ] !== undefined ) { + ( flatOptions[ key ] ? target : ( deep || ( deep = {} ) ) )[ key ] = src[ key ]; + } + } + if ( deep ) { + jQuery.extend( true, target, deep ); + } + + return target; +} + +/* Handles responses to an ajax request: + * - finds the right dataType (mediates between content-type and expected dataType) + * - returns the corresponding response + */ +function ajaxHandleResponses( s, jqXHR, responses ) { + + var ct, type, finalDataType, firstDataType, + contents = s.contents, + dataTypes = s.dataTypes; + + // Remove auto dataType and get content-type in the process + while ( dataTypes[ 0 ] === "*" ) { + dataTypes.shift(); + if ( ct === undefined ) { + ct = s.mimeType || jqXHR.getResponseHeader( "Content-Type" ); + } + } + + // Check if we're dealing with a known content-type + if ( ct ) { + for ( type in contents ) { + if ( contents[ type ] && contents[ type ].test( ct ) ) { + dataTypes.unshift( type ); + break; + } + } + } + + // Check to see if we have a response for the expected dataType + if ( dataTypes[ 0 ] in responses ) { + finalDataType = dataTypes[ 0 ]; + } else { + + // Try convertible dataTypes + for ( type in responses ) { + if ( !dataTypes[ 0 ] || s.converters[ type + " " + dataTypes[ 0 ] ] ) { + finalDataType = type; + break; + } + if ( !firstDataType ) { + firstDataType = type; + } + } + + // Or just use first one + finalDataType = finalDataType || firstDataType; + } + + // If we found a dataType + // We add the dataType to the list if needed + // and return the corresponding response + if ( finalDataType ) { + if ( finalDataType !== dataTypes[ 0 ] ) { + dataTypes.unshift( finalDataType ); + } + return responses[ finalDataType ]; + } +} + +/* Chain conversions given the request and the original response + * Also sets the responseXXX fields on the jqXHR instance + */ +function ajaxConvert( s, response, jqXHR, isSuccess ) { + var conv2, current, conv, tmp, prev, + converters = {}, + + // Work with a copy of dataTypes in case we need to modify it for conversion + dataTypes = s.dataTypes.slice(); + + // Create converters map with lowercased keys + if ( dataTypes[ 1 ] ) { + for ( conv in s.converters ) { + converters[ conv.toLowerCase() ] = s.converters[ conv ]; + } + } + + current = dataTypes.shift(); + + // Convert to each sequential dataType + while ( current ) { + + if ( s.responseFields[ current ] ) { + jqXHR[ s.responseFields[ current ] ] = response; + } + + // Apply the dataFilter if provided + if ( !prev && isSuccess && s.dataFilter ) { + response = s.dataFilter( response, s.dataType ); + } + + prev = current; + current = dataTypes.shift(); + + if ( current ) { + + // There's only work to do if current dataType is non-auto + if ( current === "*" ) { + + current = prev; + + // Convert response if prev dataType is non-auto and differs from current + } else if ( prev !== "*" && prev !== current ) { + + // Seek a direct converter + conv = converters[ prev + " " + current ] || converters[ "* " + current ]; + + // If none found, seek a pair + if ( !conv ) { + for ( conv2 in converters ) { + + // If conv2 outputs current + tmp = conv2.split( " " ); + if ( tmp[ 1 ] === current ) { + + // If prev can be converted to accepted input + conv = converters[ prev + " " + tmp[ 0 ] ] || + converters[ "* " + tmp[ 0 ] ]; + if ( conv ) { + + // Condense equivalence converters + if ( conv === true ) { + conv = converters[ conv2 ]; + + // Otherwise, insert the intermediate dataType + } else if ( converters[ conv2 ] !== true ) { + current = tmp[ 0 ]; + dataTypes.unshift( tmp[ 1 ] ); + } + break; + } + } + } + } + + // Apply converter (if not an equivalence) + if ( conv !== true ) { + + // Unless errors are allowed to bubble, catch and return them + if ( conv && s.throws ) { + response = conv( response ); + } else { + try { + response = conv( response ); + } catch ( e ) { + return { + state: "parsererror", + error: conv ? e : "No conversion from " + prev + " to " + current + }; + } + } + } + } + } + } + + return { state: "success", data: response }; +} + +jQuery.extend( { + + // Counter for holding the number of active queries + active: 0, + + // Last-Modified header cache for next request + lastModified: {}, + etag: {}, + + ajaxSettings: { + url: location.href, + type: "GET", + isLocal: rlocalProtocol.test( location.protocol ), + global: true, + processData: true, + async: true, + contentType: "application/x-www-form-urlencoded; charset=UTF-8", + + /* + timeout: 0, + data: null, + dataType: null, + username: null, + password: null, + cache: null, + throws: false, + traditional: false, + headers: {}, + */ + + accepts: { + "*": allTypes, + text: "text/plain", + html: "text/html", + xml: "application/xml, text/xml", + json: "application/json, text/javascript" + }, + + contents: { + xml: /\bxml\b/, + html: /\bhtml/, + json: /\bjson\b/ + }, + + responseFields: { + xml: "responseXML", + text: "responseText", + json: "responseJSON" + }, + + // Data converters + // Keys separate source (or catchall "*") and destination types with a single space + converters: { + + // Convert anything to text + "* text": String, + + // Text to html (true = no transformation) + "text html": true, + + // Evaluate text as a json expression + "text json": JSON.parse, + + // Parse text as xml + "text xml": jQuery.parseXML + }, + + // For options that shouldn't be deep extended: + // you can add your own custom options here if + // and when you create one that shouldn't be + // deep extended (see ajaxExtend) + flatOptions: { + url: true, + context: true + } + }, + + // Creates a full fledged settings object into target + // with both ajaxSettings and settings fields. + // If target is omitted, writes into ajaxSettings. + ajaxSetup: function( target, settings ) { + return settings ? + + // Building a settings object + ajaxExtend( ajaxExtend( target, jQuery.ajaxSettings ), settings ) : + + // Extending ajaxSettings + ajaxExtend( jQuery.ajaxSettings, target ); + }, + + ajaxPrefilter: addToPrefiltersOrTransports( prefilters ), + ajaxTransport: addToPrefiltersOrTransports( transports ), + + // Main method + ajax: function( url, options ) { + + // If url is an object, simulate pre-1.5 signature + if ( typeof url === "object" ) { + options = url; + url = undefined; + } + + // Force options to be an object + options = options || {}; + + var transport, + + // URL without anti-cache param + cacheURL, + + // Response headers + responseHeadersString, + responseHeaders, + + // timeout handle + timeoutTimer, + + // Url cleanup var + urlAnchor, + + // Request state (becomes false upon send and true upon completion) + completed, + + // To know if global events are to be dispatched + fireGlobals, + + // Loop variable + i, + + // uncached part of the url + uncached, + + // Create the final options object + s = jQuery.ajaxSetup( {}, options ), + + // Callbacks context + callbackContext = s.context || s, + + // Context for global events is callbackContext if it is a DOM node or jQuery collection + globalEventContext = s.context && + ( callbackContext.nodeType || callbackContext.jquery ) ? + jQuery( callbackContext ) : + jQuery.event, + + // Deferreds + deferred = jQuery.Deferred(), + completeDeferred = jQuery.Callbacks( "once memory" ), + + // Status-dependent callbacks + statusCode = s.statusCode || {}, + + // Headers (they are sent all at once) + requestHeaders = {}, + requestHeadersNames = {}, + + // Default abort message + strAbort = "canceled", + + // Fake xhr + jqXHR = { + readyState: 0, + + // Builds headers hashtable if needed + getResponseHeader: function( key ) { + var match; + if ( completed ) { + if ( !responseHeaders ) { + responseHeaders = {}; + while ( ( match = rheaders.exec( responseHeadersString ) ) ) { + responseHeaders[ match[ 1 ].toLowerCase() + " " ] = + ( responseHeaders[ match[ 1 ].toLowerCase() + " " ] || [] ) + .concat( match[ 2 ] ); + } + } + match = responseHeaders[ key.toLowerCase() + " " ]; + } + return match == null ? null : match.join( ", " ); + }, + + // Raw string + getAllResponseHeaders: function() { + return completed ? responseHeadersString : null; + }, + + // Caches the header + setRequestHeader: function( name, value ) { + if ( completed == null ) { + name = requestHeadersNames[ name.toLowerCase() ] = + requestHeadersNames[ name.toLowerCase() ] || name; + requestHeaders[ name ] = value; + } + return this; + }, + + // Overrides response content-type header + overrideMimeType: function( type ) { + if ( completed == null ) { + s.mimeType = type; + } + return this; + }, + + // Status-dependent callbacks + statusCode: function( map ) { + var code; + if ( map ) { + if ( completed ) { + + // Execute the appropriate callbacks + jqXHR.always( map[ jqXHR.status ] ); + } else { + + // Lazy-add the new callbacks in a way that preserves old ones + for ( code in map ) { + statusCode[ code ] = [ statusCode[ code ], map[ code ] ]; + } + } + } + return this; + }, + + // Cancel the request + abort: function( statusText ) { + var finalText = statusText || strAbort; + if ( transport ) { + transport.abort( finalText ); + } + done( 0, finalText ); + return this; + } + }; + + // Attach deferreds + deferred.promise( jqXHR ); + + // Add protocol if not provided (prefilters might expect it) + // Handle falsy url in the settings object (#10093: consistency with old signature) + // We also use the url parameter if available + s.url = ( ( url || s.url || location.href ) + "" ) + .replace( rprotocol, location.protocol + "//" ); + + // Alias method option to type as per ticket #12004 + s.type = options.method || options.type || s.method || s.type; + + // Extract dataTypes list + s.dataTypes = ( s.dataType || "*" ).toLowerCase().match( rnothtmlwhite ) || [ "" ]; + + // A cross-domain request is in order when the origin doesn't match the current origin. + if ( s.crossDomain == null ) { + urlAnchor = document.createElement( "a" ); + + // Support: IE <=8 - 11, Edge 12 - 15 + // IE throws exception on accessing the href property if url is malformed, + // e.g. http://example.com:80x/ + try { + urlAnchor.href = s.url; + + // Support: IE <=8 - 11 only + // Anchor's host property isn't correctly set when s.url is relative + urlAnchor.href = urlAnchor.href; + s.crossDomain = originAnchor.protocol + "//" + originAnchor.host !== + urlAnchor.protocol + "//" + urlAnchor.host; + } catch ( e ) { + + // If there is an error parsing the URL, assume it is crossDomain, + // it can be rejected by the transport if it is invalid + s.crossDomain = true; + } + } + + // Convert data if not already a string + if ( s.data && s.processData && typeof s.data !== "string" ) { + s.data = jQuery.param( s.data, s.traditional ); + } + + // Apply prefilters + inspectPrefiltersOrTransports( prefilters, s, options, jqXHR ); + + // If request was aborted inside a prefilter, stop there + if ( completed ) { + return jqXHR; + } + + // We can fire global events as of now if asked to + // Don't fire events if jQuery.event is undefined in an AMD-usage scenario (#15118) + fireGlobals = jQuery.event && s.global; + + // Watch for a new set of requests + if ( fireGlobals && jQuery.active++ === 0 ) { + jQuery.event.trigger( "ajaxStart" ); + } + + // Uppercase the type + s.type = s.type.toUpperCase(); + + // Determine if request has content + s.hasContent = !rnoContent.test( s.type ); + + // Save the URL in case we're toying with the If-Modified-Since + // and/or If-None-Match header later on + // Remove hash to simplify url manipulation + cacheURL = s.url.replace( rhash, "" ); + + // More options handling for requests with no content + if ( !s.hasContent ) { + + // Remember the hash so we can put it back + uncached = s.url.slice( cacheURL.length ); + + // If data is available and should be processed, append data to url + if ( s.data && ( s.processData || typeof s.data === "string" ) ) { + cacheURL += ( rquery.test( cacheURL ) ? "&" : "?" ) + s.data; + + // #9682: remove data so that it's not used in an eventual retry + delete s.data; + } + + // Add or update anti-cache param if needed + if ( s.cache === false ) { + cacheURL = cacheURL.replace( rantiCache, "$1" ); + uncached = ( rquery.test( cacheURL ) ? "&" : "?" ) + "_=" + ( nonce.guid++ ) + + uncached; + } + + // Put hash and anti-cache on the URL that will be requested (gh-1732) + s.url = cacheURL + uncached; + + // Change '%20' to '+' if this is encoded form body content (gh-2658) + } else if ( s.data && s.processData && + ( s.contentType || "" ).indexOf( "application/x-www-form-urlencoded" ) === 0 ) { + s.data = s.data.replace( r20, "+" ); + } + + // Set the If-Modified-Since and/or If-None-Match header, if in ifModified mode. + if ( s.ifModified ) { + if ( jQuery.lastModified[ cacheURL ] ) { + jqXHR.setRequestHeader( "If-Modified-Since", jQuery.lastModified[ cacheURL ] ); + } + if ( jQuery.etag[ cacheURL ] ) { + jqXHR.setRequestHeader( "If-None-Match", jQuery.etag[ cacheURL ] ); + } + } + + // Set the correct header, if data is being sent + if ( s.data && s.hasContent && s.contentType !== false || options.contentType ) { + jqXHR.setRequestHeader( "Content-Type", s.contentType ); + } + + // Set the Accepts header for the server, depending on the dataType + jqXHR.setRequestHeader( + "Accept", + s.dataTypes[ 0 ] && s.accepts[ s.dataTypes[ 0 ] ] ? + s.accepts[ s.dataTypes[ 0 ] ] + + ( s.dataTypes[ 0 ] !== "*" ? ", " + allTypes + "; q=0.01" : "" ) : + s.accepts[ "*" ] + ); + + // Check for headers option + for ( i in s.headers ) { + jqXHR.setRequestHeader( i, s.headers[ i ] ); + } + + // Allow custom headers/mimetypes and early abort + if ( s.beforeSend && + ( s.beforeSend.call( callbackContext, jqXHR, s ) === false || completed ) ) { + + // Abort if not done already and return + return jqXHR.abort(); + } + + // Aborting is no longer a cancellation + strAbort = "abort"; + + // Install callbacks on deferreds + completeDeferred.add( s.complete ); + jqXHR.done( s.success ); + jqXHR.fail( s.error ); + + // Get transport + transport = inspectPrefiltersOrTransports( transports, s, options, jqXHR ); + + // If no transport, we auto-abort + if ( !transport ) { + done( -1, "No Transport" ); + } else { + jqXHR.readyState = 1; + + // Send global event + if ( fireGlobals ) { + globalEventContext.trigger( "ajaxSend", [ jqXHR, s ] ); + } + + // If request was aborted inside ajaxSend, stop there + if ( completed ) { + return jqXHR; + } + + // Timeout + if ( s.async && s.timeout > 0 ) { + timeoutTimer = window.setTimeout( function() { + jqXHR.abort( "timeout" ); + }, s.timeout ); + } + + try { + completed = false; + transport.send( requestHeaders, done ); + } catch ( e ) { + + // Rethrow post-completion exceptions + if ( completed ) { + throw e; + } + + // Propagate others as results + done( -1, e ); + } + } + + // Callback for when everything is done + function done( status, nativeStatusText, responses, headers ) { + var isSuccess, success, error, response, modified, + statusText = nativeStatusText; + + // Ignore repeat invocations + if ( completed ) { + return; + } + + completed = true; + + // Clear timeout if it exists + if ( timeoutTimer ) { + window.clearTimeout( timeoutTimer ); + } + + // Dereference transport for early garbage collection + // (no matter how long the jqXHR object will be used) + transport = undefined; + + // Cache response headers + responseHeadersString = headers || ""; + + // Set readyState + jqXHR.readyState = status > 0 ? 4 : 0; + + // Determine if successful + isSuccess = status >= 200 && status < 300 || status === 304; + + // Get response data + if ( responses ) { + response = ajaxHandleResponses( s, jqXHR, responses ); + } + + // Use a noop converter for missing script + if ( !isSuccess && jQuery.inArray( "script", s.dataTypes ) > -1 ) { + s.converters[ "text script" ] = function() {}; + } + + // Convert no matter what (that way responseXXX fields are always set) + response = ajaxConvert( s, response, jqXHR, isSuccess ); + + // If successful, handle type chaining + if ( isSuccess ) { + + // Set the If-Modified-Since and/or If-None-Match header, if in ifModified mode. + if ( s.ifModified ) { + modified = jqXHR.getResponseHeader( "Last-Modified" ); + if ( modified ) { + jQuery.lastModified[ cacheURL ] = modified; + } + modified = jqXHR.getResponseHeader( "etag" ); + if ( modified ) { + jQuery.etag[ cacheURL ] = modified; + } + } + + // if no content + if ( status === 204 || s.type === "HEAD" ) { + statusText = "nocontent"; + + // if not modified + } else if ( status === 304 ) { + statusText = "notmodified"; + + // If we have data, let's convert it + } else { + statusText = response.state; + success = response.data; + error = response.error; + isSuccess = !error; + } + } else { + + // Extract error from statusText and normalize for non-aborts + error = statusText; + if ( status || !statusText ) { + statusText = "error"; + if ( status < 0 ) { + status = 0; + } + } + } + + // Set data for the fake xhr object + jqXHR.status = status; + jqXHR.statusText = ( nativeStatusText || statusText ) + ""; + + // Success/Error + if ( isSuccess ) { + deferred.resolveWith( callbackContext, [ success, statusText, jqXHR ] ); + } else { + deferred.rejectWith( callbackContext, [ jqXHR, statusText, error ] ); + } + + // Status-dependent callbacks + jqXHR.statusCode( statusCode ); + statusCode = undefined; + + if ( fireGlobals ) { + globalEventContext.trigger( isSuccess ? "ajaxSuccess" : "ajaxError", + [ jqXHR, s, isSuccess ? success : error ] ); + } + + // Complete + completeDeferred.fireWith( callbackContext, [ jqXHR, statusText ] ); + + if ( fireGlobals ) { + globalEventContext.trigger( "ajaxComplete", [ jqXHR, s ] ); + + // Handle the global AJAX counter + if ( !( --jQuery.active ) ) { + jQuery.event.trigger( "ajaxStop" ); + } + } + } + + return jqXHR; + }, + + getJSON: function( url, data, callback ) { + return jQuery.get( url, data, callback, "json" ); + }, + + getScript: function( url, callback ) { + return jQuery.get( url, undefined, callback, "script" ); + } +} ); + +jQuery.each( [ "get", "post" ], function( _i, method ) { + jQuery[ method ] = function( url, data, callback, type ) { + + // Shift arguments if data argument was omitted + if ( isFunction( data ) ) { + type = type || callback; + callback = data; + data = undefined; + } + + // The url can be an options object (which then must have .url) + return jQuery.ajax( jQuery.extend( { + url: url, + type: method, + dataType: type, + data: data, + success: callback + }, jQuery.isPlainObject( url ) && url ) ); + }; +} ); + +jQuery.ajaxPrefilter( function( s ) { + var i; + for ( i in s.headers ) { + if ( i.toLowerCase() === "content-type" ) { + s.contentType = s.headers[ i ] || ""; + } + } +} ); + + +jQuery._evalUrl = function( url, options, doc ) { + return jQuery.ajax( { + url: url, + + // Make this explicit, since user can override this through ajaxSetup (#11264) + type: "GET", + dataType: "script", + cache: true, + async: false, + global: false, + + // Only evaluate the response if it is successful (gh-4126) + // dataFilter is not invoked for failure responses, so using it instead + // of the default converter is kludgy but it works. + converters: { + "text script": function() {} + }, + dataFilter: function( response ) { + jQuery.globalEval( response, options, doc ); + } + } ); +}; + + +jQuery.fn.extend( { + wrapAll: function( html ) { + var wrap; + + if ( this[ 0 ] ) { + if ( isFunction( html ) ) { + html = html.call( this[ 0 ] ); + } + + // The elements to wrap the target around + wrap = jQuery( html, this[ 0 ].ownerDocument ).eq( 0 ).clone( true ); + + if ( this[ 0 ].parentNode ) { + wrap.insertBefore( this[ 0 ] ); + } + + wrap.map( function() { + var elem = this; + + while ( elem.firstElementChild ) { + elem = elem.firstElementChild; + } + + return elem; + } ).append( this ); + } + + return this; + }, + + wrapInner: function( html ) { + if ( isFunction( html ) ) { + return this.each( function( i ) { + jQuery( this ).wrapInner( html.call( this, i ) ); + } ); + } + + return this.each( function() { + var self = jQuery( this ), + contents = self.contents(); + + if ( contents.length ) { + contents.wrapAll( html ); + + } else { + self.append( html ); + } + } ); + }, + + wrap: function( html ) { + var htmlIsFunction = isFunction( html ); + + return this.each( function( i ) { + jQuery( this ).wrapAll( htmlIsFunction ? html.call( this, i ) : html ); + } ); + }, + + unwrap: function( selector ) { + this.parent( selector ).not( "body" ).each( function() { + jQuery( this ).replaceWith( this.childNodes ); + } ); + return this; + } +} ); + + +jQuery.expr.pseudos.hidden = function( elem ) { + return !jQuery.expr.pseudos.visible( elem ); +}; +jQuery.expr.pseudos.visible = function( elem ) { + return !!( elem.offsetWidth || elem.offsetHeight || elem.getClientRects().length ); +}; + + + + +jQuery.ajaxSettings.xhr = function() { + try { + return new window.XMLHttpRequest(); + } catch ( e ) {} +}; + +var xhrSuccessStatus = { + + // File protocol always yields status code 0, assume 200 + 0: 200, + + // Support: IE <=9 only + // #1450: sometimes IE returns 1223 when it should be 204 + 1223: 204 + }, + xhrSupported = jQuery.ajaxSettings.xhr(); + +support.cors = !!xhrSupported && ( "withCredentials" in xhrSupported ); +support.ajax = xhrSupported = !!xhrSupported; + +jQuery.ajaxTransport( function( options ) { + var callback, errorCallback; + + // Cross domain only allowed if supported through XMLHttpRequest + if ( support.cors || xhrSupported && !options.crossDomain ) { + return { + send: function( headers, complete ) { + var i, + xhr = options.xhr(); + + xhr.open( + options.type, + options.url, + options.async, + options.username, + options.password + ); + + // Apply custom fields if provided + if ( options.xhrFields ) { + for ( i in options.xhrFields ) { + xhr[ i ] = options.xhrFields[ i ]; + } + } + + // Override mime type if needed + if ( options.mimeType && xhr.overrideMimeType ) { + xhr.overrideMimeType( options.mimeType ); + } + + // X-Requested-With header + // For cross-domain requests, seeing as conditions for a preflight are + // akin to a jigsaw puzzle, we simply never set it to be sure. + // (it can always be set on a per-request basis or even using ajaxSetup) + // For same-domain requests, won't change header if already provided. + if ( !options.crossDomain && !headers[ "X-Requested-With" ] ) { + headers[ "X-Requested-With" ] = "XMLHttpRequest"; + } + + // Set headers + for ( i in headers ) { + xhr.setRequestHeader( i, headers[ i ] ); + } + + // Callback + callback = function( type ) { + return function() { + if ( callback ) { + callback = errorCallback = xhr.onload = + xhr.onerror = xhr.onabort = xhr.ontimeout = + xhr.onreadystatechange = null; + + if ( type === "abort" ) { + xhr.abort(); + } else if ( type === "error" ) { + + // Support: IE <=9 only + // On a manual native abort, IE9 throws + // errors on any property access that is not readyState + if ( typeof xhr.status !== "number" ) { + complete( 0, "error" ); + } else { + complete( + + // File: protocol always yields status 0; see #8605, #14207 + xhr.status, + xhr.statusText + ); + } + } else { + complete( + xhrSuccessStatus[ xhr.status ] || xhr.status, + xhr.statusText, + + // Support: IE <=9 only + // IE9 has no XHR2 but throws on binary (trac-11426) + // For XHR2 non-text, let the caller handle it (gh-2498) + ( xhr.responseType || "text" ) !== "text" || + typeof xhr.responseText !== "string" ? 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ve{constructor(t,e){super(t,e),this._interval=null,this._activeElement=null,this._isSliding=!1,this.touchTimeout=null,this._swipeHelper=null,this._indicatorsElement=we.findOne(".carousel-indicators",this._element),this._addEventListeners(),this._config.ride===ti&&this.cycle()}static get Default(){return ri}static get DefaultType(){return ai}static get NAME(){return"carousel"}next(){this._slide(ze)}nextWhenVisible(){!document.hidden&&Bt(this._element)&&this.next()}prev(){this._slide(Re)}pause(){this._isSliding&&jt(this._element),this._clearInterval()}cycle(){this._clearInterval(),this._updateInterval(),this._interval=setInterval((()=>this.nextWhenVisible()),this._config.interval)}_maybeEnableCycle(){this._config.ride&&(this._isSliding?fe.one(this._element,Ke,(()=>this.cycle())):this.cycle())}to(t){const e=this._getItems();if(t>e.length-1||t<0)return;if(this._isSliding)return void fe.one(this._element,Ke,(()=>this.to(t)));const i=this._getItemIndex(this._getActive());if(i===t)return;const n=t>i?ze:Re;this._slide(n,e[t])}dispose(){this._swipeHelper&&this._swipeHelper.dispose(),super.dispose()}_configAfterMerge(t){return t.defaultInterval=t.interval,t}_addEventListeners(){this._config.keyboard&&fe.on(this._element,Qe,(t=>this._keydown(t))),"hover"===this._config.pause&&(fe.on(this._element,Xe,(()=>this.pause())),fe.on(this._element,Ue,(()=>this._maybeEnableCycle()))),this._config.touch&&je.isSupported()&&this._addTouchEventListeners()}_addTouchEventListeners(){for(const t of we.find(".carousel-item img",this._element))fe.on(t,Ge,(t=>t.preventDefault()));const t={leftCallback:()=>this._slide(this._directionToOrder(qe)),rightCallback:()=>this._slide(this._directionToOrder(Ve)),endCallback:()=>{"hover"===this._config.pause&&(this.pause(),this.touchTimeout&&clearTimeout(this.touchTimeout),this.touchTimeout=setTimeout((()=>this._maybeEnableCycle()),500+this._config.interval))}};this._swipeHelper=new je(this._element,t)}_keydown(t){if(/input|textarea/i.test(t.target.tagName))return;const e=oi[t.key];e&&(t.preventDefault(),this._slide(this._directionToOrder(e)))}_getItemIndex(t){return this._getItems().indexOf(t)}_setActiveIndicatorElement(t){if(!this._indicatorsElement)return;const e=we.findOne(ii,this._indicatorsElement);e.classList.remove(ei),e.removeAttribute("aria-current");const i=we.findOne(`[data-bs-slide-to="${t}"]`,this._indicatorsElement);i&&(i.classList.add(ei),i.setAttribute("aria-current","true"))}_updateInterval(){const t=this._activeElement||this._getActive();if(!t)return;const e=Number.parseInt(t.getAttribute("data-bs-interval"),10);this._config.interval=e||this._config.defaultInterval}_slide(t,e=null){if(this._isSliding)return;const i=this._getActive(),n=t===ze,s=e||Gt(this._getItems(),i,n,this._config.wrap);if(s===i)return;const 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.collapse.collapsing").filter((t=>t!==this._element)).map((t=>Ei.getOrCreateInstance(t,{toggle:!1})))),t.length&&t[0]._isTransitioning)return;if(fe.trigger(this._element,hi).defaultPrevented)return;for(const e of t)e.hide();const e=this._getDimension();this._element.classList.remove(gi),this._element.classList.add(_i),this._element.style[e]=0,this._addAriaAndCollapsedClass(this._triggerArray,!0),this._isTransitioning=!0;const i=`scroll${e[0].toUpperCase()+e.slice(1)}`;this._queueCallback((()=>{this._isTransitioning=!1,this._element.classList.remove(_i),this._element.classList.add(gi,mi),this._element.style[e]="",fe.trigger(this._element,di)}),this._element,!0),this._element.style[e]=`${this._element[i]}px`}hide(){if(this._isTransitioning||!this._isShown())return;if(fe.trigger(this._element,ui).defaultPrevented)return;const t=this._getDimension();this._element.style[t]=`${this._element.getBoundingClientRect()[t]}px`,qt(this._element),this._element.classList.add(_i),this._element.classList.remove(gi,mi);for(const t of this._triggerArray){const e=we.getElementFromSelector(t);e&&!this._isShown(e)&&this._addAriaAndCollapsedClass([t],!1)}this._isTransitioning=!0,this._element.style[t]="",this._queueCallback((()=>{this._isTransitioning=!1,this._element.classList.remove(_i),this._element.classList.add(gi),fe.trigger(this._element,fi)}),this._element,!0)}_isShown(t=this._element){return t.classList.contains(mi)}_configAfterMerge(t){return t.toggle=Boolean(t.toggle),t.parent=Ht(t.parent),t}_getDimension(){return this._element.classList.contains("collapse-horizontal")?"width":"height"}_initializeChildren(){if(!this._config.parent)return;const t=this._getFirstLevelChildren(vi);for(const e of t){const t=we.getElementFromSelector(e);t&&this._addAriaAndCollapsedClass([e],this._isShown(t))}}_getFirstLevelChildren(t){const e=we.find(bi,this._config.parent);return we.find(t,this._config.parent).filter((t=>!e.includes(t)))}_addAriaAndCollapsedClass(t,e){if(t.length)for(const i of t)i.classList.toggle("collapsed",!e),i.setAttribute("aria-expanded",e)}static jQueryInterface(t){const e={};return"string"==typeof t&&/show|hide/.test(t)&&(e.toggle=!1),this.each((function(){const i=Ei.getOrCreateInstance(this,e);if("string"==typeof t){if(void 0===i[t])throw new TypeError(`No method named "${t}"`);i[t]()}}))}}fe.on(document,pi,vi,(function(t){("A"===t.target.tagName||t.delegateTarget&&"A"===t.delegateTarget.tagName)&&t.preventDefault();for(const t of we.getMultipleElementsFromSelector(this))Ei.getOrCreateInstance(t,{toggle:!1}).toggle()})),Qt(Ei);const Ai="dropdown",Ti=".bs.dropdown",Ci=".data-api",Oi="ArrowUp",xi="ArrowDown",ki=`hide${Ti}`,Li=`hidden${Ti}`,Si=`show${Ti}`,Di=`shown${Ti}`,$i=`click${Ti}${Ci}`,Ii=`keydown${Ti}${Ci}`,Ni=`keyup${Ti}${Ci}`,Pi="show",Mi='[data-bs-toggle="dropdown"]:not(.disabled):not(:disabled)',ji=`${Mi}.${Pi}`,Fi=".dropdown-menu",Hi=Kt()?"top-end":"top-start",Bi=Kt()?"top-start":"top-end",Wi=Kt()?"bottom-end":"bottom-start",zi=Kt()?"bottom-start":"bottom-end",Ri=Kt()?"left-start":"right-start",qi=Kt()?"right-start":"left-start",Vi={autoClose:!0,boundary:"clippingParents",display:"dynamic",offset:[0,2],popperConfig:null,reference:"toggle"},Yi={autoClose:"(boolean|string)",boundary:"(string|element)",display:"string",offset:"(array|string|function)",popperConfig:"(null|object|function)",reference:"(string|element|object)"};class Ki extends ve{constructor(t,e){super(t,e),this._popper=null,this._parent=this._element.parentNode,this._menu=we.next(this._element,Fi)[0]||we.prev(this._element,Fi)[0]||we.findOne(Fi,this._parent),this._inNavbar=this._detectNavbar()}static get Default(){return Vi}static get DefaultType(){return Yi}static get NAME(){return Ai}toggle(){return this._isShown()?this.hide():this.show()}show(){if(Wt(this._element)||this._isShown())return;const t={relatedTarget:this._element};if(!fe.trigger(this._element,Si,t).defaultPrevented){if(this._createPopper(),"ontouchstart"in document.documentElement&&!this._parent.closest(".navbar-nav"))for(const t of[].concat(...document.body.children))fe.on(t,"mouseover",Rt);this._element.focus(),this._element.setAttribute("aria-expanded",!0),this._menu.classList.add(Pi),this._element.classList.add(Pi),fe.trigger(this._element,Di,t)}}hide(){if(Wt(this._element)||!this._isShown())return;const t={relatedTarget:this._element};this._completeHide(t)}dispose(){this._popper&&this._popper.destroy(),super.dispose()}update(){this._inNavbar=this._detectNavbar(),this._popper&&this._popper.update()}_completeHide(t){if(!fe.trigger(this._element,ki,t).defaultPrevented){if("ontouchstart"in document.documentElement)for(const t of[].concat(...document.body.children))fe.off(t,"mouseover",Rt);this._popper&&this._popper.destroy(),this._menu.classList.remove(Pi),this._element.classList.remove(Pi),this._element.setAttribute("aria-expanded","false"),_e.removeDataAttribute(this._menu,"popper"),fe.trigger(this._element,Li,t)}}_getConfig(t){if("object"==typeof(t=super._getConfig(t)).reference&&!Ft(t.reference)&&"function"!=typeof t.reference.getBoundingClientRect)throw new TypeError(`${Ai.toUpperCase()}: Option "reference" provided type "object" without a required "getBoundingClientRect" method.`);return t}_createPopper(){if(void 0===e)throw new TypeError("Bootstrap's dropdowns require Popper (https://popper.js.org)");let t=this._element;"parent"===this._config.reference?t=this._parent:Ft(this._config.reference)?t=Ht(this._config.reference):"object"==typeof this._config.reference&&(t=this._config.reference);const i=this._getPopperConfig();this._popper=Dt(t,this._menu,i)}_isShown(){return this._menu.classList.contains(Pi)}_getPlacement(){const t=this._parent;if(t.classList.contains("dropend"))return Ri;if(t.classList.contains("dropstart"))return qi;if(t.classList.contains("dropup-center"))return"top";if(t.classList.contains("dropdown-center"))return"bottom";const e="end"===getComputedStyle(this._menu).getPropertyValue("--bs-position").trim();return t.classList.contains("dropup")?e?Bi:Hi:e?zi:Wi}_detectNavbar(){return null!==this._element.closest(".navbar")}_getOffset(){const{offset:t}=this._config;return"string"==typeof t?t.split(",").map((t=>Number.parseInt(t,10))):"function"==typeof t?e=>t(e,this._element):t}_getPopperConfig(){const t={placement:this._getPlacement(),modifiers:[{name:"preventOverflow",options:{boundary:this._config.boundary}},{name:"offset",options:{offset:this._getOffset()}}]};return(this._inNavbar||"static"===this._config.display)&&(_e.setDataAttribute(this._menu,"popper","static"),t.modifiers=[{name:"applyStyles",enabled:!1}]),{...t,...Xt(this._config.popperConfig,[t])}}_selectMenuItem({key:t,target:e}){const i=we.find(".dropdown-menu .dropdown-item:not(.disabled):not(:disabled)",this._menu).filter((t=>Bt(t)));i.length&&Gt(i,e,t===xi,!i.includes(e)).focus()}static jQueryInterface(t){return this.each((function(){const e=Ki.getOrCreateInstance(this,t);if("string"==typeof t){if(void 0===e[t])throw new TypeError(`No method named "${t}"`);e[t]()}}))}static clearMenus(t){if(2===t.button||"keyup"===t.type&&"Tab"!==t.key)return;const e=we.find(ji);for(const i of e){const e=Ki.getInstance(i);if(!e||!1===e._config.autoClose)continue;const n=t.composedPath(),s=n.includes(e._menu);if(n.includes(e._element)||"inside"===e._config.autoClose&&!s||"outside"===e._config.autoClose&&s)continue;if(e._menu.contains(t.target)&&("keyup"===t.type&&"Tab"===t.key||/input|select|option|textarea|form/i.test(t.target.tagName)))continue;const o={relatedTarget:e._element};"click"===t.type&&(o.clickEvent=t),e._completeHide(o)}}static dataApiKeydownHandler(t){const e=/input|textarea/i.test(t.target.tagName),i="Escape"===t.key,n=[Oi,xi].includes(t.key);if(!n&&!i)return;if(e&&!i)return;t.preventDefault();const s=this.matches(Mi)?this:we.prev(this,Mi)[0]||we.next(this,Mi)[0]||we.findOne(Mi,t.delegateTarget.parentNode),o=Ki.getOrCreateInstance(s);if(n)return t.stopPropagation(),o.show(),void o._selectMenuItem(t);o._isShown()&&(t.stopPropagation(),o.hide(),s.focus())}}fe.on(document,Ii,Mi,Ki.dataApiKeydownHandler),fe.on(document,Ii,Fi,Ki.dataApiKeydownHandler),fe.on(document,$i,Ki.clearMenus),fe.on(document,Ni,Ki.clearMenus),fe.on(document,$i,Mi,(function(t){t.preventDefault(),Ki.getOrCreateInstance(this).toggle()})),Qt(Ki);const Qi="backdrop",Xi="show",Ui=`mousedown.bs.${Qi}`,Gi={className:"modal-backdrop",clickCallback:null,isAnimated:!1,isVisible:!0,rootElement:"body"},Ji={className:"string",clickCallback:"(function|null)",isAnimated:"boolean",isVisible:"boolean",rootElement:"(element|string)"};class Zi extends be{constructor(t){super(),this._config=this._getConfig(t),this._isAppended=!1,this._element=null}static get Default(){return Gi}static get DefaultType(){return Ji}static get NAME(){return Qi}show(t){if(!this._config.isVisible)return void Xt(t);this._append();const e=this._getElement();this._config.isAnimated&&qt(e),e.classList.add(Xi),this._emulateAnimation((()=>{Xt(t)}))}hide(t){this._config.isVisible?(this._getElement().classList.remove(Xi),this._emulateAnimation((()=>{this.dispose(),Xt(t)}))):Xt(t)}dispose(){this._isAppended&&(fe.off(this._element,Ui),this._element.remove(),this._isAppended=!1)}_getElement(){if(!this._element){const t=document.createElement("div");t.className=this._config.className,this._config.isAnimated&&t.classList.add("fade"),this._element=t}return this._element}_configAfterMerge(t){return t.rootElement=Ht(t.rootElement),t}_append(){if(this._isAppended)return;const t=this._getElement();this._config.rootElement.append(t),fe.on(t,Ui,(()=>{Xt(this._config.clickCallback)})),this._isAppended=!0}_emulateAnimation(t){Ut(t,this._getElement(),this._config.isAnimated)}}const tn=".bs.focustrap",en=`focusin${tn}`,nn=`keydown.tab${tn}`,sn="backward",on={autofocus:!0,trapElement:null},rn={autofocus:"boolean",trapElement:"element"};class an extends be{constructor(t){super(),this._config=this._getConfig(t),this._isActive=!1,this._lastTabNavDirection=null}static get Default(){return on}static get DefaultType(){return rn}static get NAME(){return"focustrap"}activate(){this._isActive||(this._config.autofocus&&this._config.trapElement.focus(),fe.off(document,tn),fe.on(document,en,(t=>this._handleFocusin(t))),fe.on(document,nn,(t=>this._handleKeydown(t))),this._isActive=!0)}deactivate(){this._isActive&&(this._isActive=!1,fe.off(document,tn))}_handleFocusin(t){const{trapElement:e}=this._config;if(t.target===document||t.target===e||e.contains(t.target))return;const i=we.focusableChildren(e);0===i.length?e.focus():this._lastTabNavDirection===sn?i[i.length-1].focus():i[0].focus()}_handleKeydown(t){"Tab"===t.key&&(this._lastTabNavDirection=t.shiftKey?sn:"forward")}}const ln=".fixed-top, .fixed-bottom, .is-fixed, .sticky-top",cn=".sticky-top",hn="padding-right",dn="margin-right";class un{constructor(){this._element=document.body}getWidth(){const t=document.documentElement.clientWidth;return Math.abs(window.innerWidth-t)}hide(){const t=this.getWidth();this._disableOverFlow(),this._setElementAttributes(this._element,hn,(e=>e+t)),this._setElementAttributes(ln,hn,(e=>e+t)),this._setElementAttributes(cn,dn,(e=>e-t))}reset(){this._resetElementAttributes(this._element,"overflow"),this._resetElementAttributes(this._element,hn),this._resetElementAttributes(ln,hn),this._resetElementAttributes(cn,dn)}isOverflowing(){return this.getWidth()>0}_disableOverFlow(){this._saveInitialAttribute(this._element,"overflow"),this._element.style.overflow="hidden"}_setElementAttributes(t,e,i){const n=this.getWidth();this._applyManipulationCallback(t,(t=>{if(t!==this._element&&window.innerWidth>t.clientWidth+n)return;this._saveInitialAttribute(t,e);const s=window.getComputedStyle(t).getPropertyValue(e);t.style.setProperty(e,`${i(Number.parseFloat(s))}px`)}))}_saveInitialAttribute(t,e){const i=t.style.getPropertyValue(e);i&&_e.setDataAttribute(t,e,i)}_resetElementAttributes(t,e){this._applyManipulationCallback(t,(t=>{const i=_e.getDataAttribute(t,e);null!==i?(_e.removeDataAttribute(t,e),t.style.setProperty(e,i)):t.style.removeProperty(e)}))}_applyManipulationCallback(t,e){if(Ft(t))e(t);else for(const i of we.find(t,this._element))e(i)}}const fn=".bs.modal",pn=`hide${fn}`,mn=`hidePrevented${fn}`,gn=`hidden${fn}`,_n=`show${fn}`,bn=`shown${fn}`,vn=`resize${fn}`,yn=`click.dismiss${fn}`,wn=`mousedown.dismiss${fn}`,En=`keydown.dismiss${fn}`,An=`click${fn}.data-api`,Tn="modal-open",Cn="show",On="modal-static",xn={backdrop:!0,focus:!0,keyboard:!0},kn={backdrop:"(boolean|string)",focus:"boolean",keyboard:"boolean"};class Ln extends ve{constructor(t,e){super(t,e),this._dialog=we.findOne(".modal-dialog",this._element),this._backdrop=this._initializeBackDrop(),this._focustrap=this._initializeFocusTrap(),this._isShown=!1,this._isTransitioning=!1,this._scrollBar=new un,this._addEventListeners()}static get Default(){return xn}static get DefaultType(){return kn}static get NAME(){return"modal"}toggle(t){return this._isShown?this.hide():this.show(t)}show(t){this._isShown||this._isTransitioning||fe.trigger(this._element,_n,{relatedTarget:t}).defaultPrevented||(this._isShown=!0,this._isTransitioning=!0,this._scrollBar.hide(),document.body.classList.add(Tn),this._adjustDialog(),this._backdrop.show((()=>this._showElement(t))))}hide(){this._isShown&&!this._isTransitioning&&(fe.trigger(this._element,pn).defaultPrevented||(this._isShown=!1,this._isTransitioning=!0,this._focustrap.deactivate(),this._element.classList.remove(Cn),this._queueCallback((()=>this._hideModal()),this._element,this._isAnimated())))}dispose(){fe.off(window,fn),fe.off(this._dialog,fn),this._backdrop.dispose(),this._focustrap.deactivate(),super.dispose()}handleUpdate(){this._adjustDialog()}_initializeBackDrop(){return new Zi({isVisible:Boolean(this._config.backdrop),isAnimated:this._isAnimated()})}_initializeFocusTrap(){return new an({trapElement:this._element})}_showElement(t){document.body.contains(this._element)||document.body.append(this._element),this._element.style.display="block",this._element.removeAttribute("aria-hidden"),this._element.setAttribute("aria-modal",!0),this._element.setAttribute("role","dialog"),this._element.scrollTop=0;const e=we.findOne(".modal-body",this._dialog);e&&(e.scrollTop=0),qt(this._element),this._element.classList.add(Cn),this._queueCallback((()=>{this._config.focus&&this._focustrap.activate(),this._isTransitioning=!1,fe.trigger(this._element,bn,{relatedTarget:t})}),this._dialog,this._isAnimated())}_addEventListeners(){fe.on(this._element,En,(t=>{"Escape"===t.key&&(this._config.keyboard?this.hide():this._triggerBackdropTransition())})),fe.on(window,vn,(()=>{this._isShown&&!this._isTransitioning&&this._adjustDialog()})),fe.on(this._element,wn,(t=>{fe.one(this._element,yn,(e=>{this._element===t.target&&this._element===e.target&&("static"!==this._config.backdrop?this._config.backdrop&&this.hide():this._triggerBackdropTransition())}))}))}_hideModal(){this._element.style.display="none",this._element.setAttribute("aria-hidden",!0),this._element.removeAttribute("aria-modal"),this._element.removeAttribute("role"),this._isTransitioning=!1,this._backdrop.hide((()=>{document.body.classList.remove(Tn),this._resetAdjustments(),this._scrollBar.reset(),fe.trigger(this._element,gn)}))}_isAnimated(){return this._element.classList.contains("fade")}_triggerBackdropTransition(){if(fe.trigger(this._element,mn).defaultPrevented)return;const t=this._element.scrollHeight>document.documentElement.clientHeight,e=this._element.style.overflowY;"hidden"===e||this._element.classList.contains(On)||(t||(this._element.style.overflowY="hidden"),this._element.classList.add(On),this._queueCallback((()=>{this._element.classList.remove(On),this._queueCallback((()=>{this._element.style.overflowY=e}),this._dialog)}),this._dialog),this._element.focus())}_adjustDialog(){const t=this._element.scrollHeight>document.documentElement.clientHeight,e=this._scrollBar.getWidth(),i=e>0;if(i&&!t){const t=Kt()?"paddingLeft":"paddingRight";this._element.style[t]=`${e}px`}if(!i&&t){const t=Kt()?"paddingRight":"paddingLeft";this._element.style[t]=`${e}px`}}_resetAdjustments(){this._element.style.paddingLeft="",this._element.style.paddingRight=""}static jQueryInterface(t,e){return this.each((function(){const i=Ln.getOrCreateInstance(this,t);if("string"==typeof t){if(void 0===i[t])throw new TypeError(`No method named "${t}"`);i[t](e)}}))}}fe.on(document,An,'[data-bs-toggle="modal"]',(function(t){const e=we.getElementFromSelector(this);["A","AREA"].includes(this.tagName)&&t.preventDefault(),fe.one(e,_n,(t=>{t.defaultPrevented||fe.one(e,gn,(()=>{Bt(this)&&this.focus()}))}));const i=we.findOne(".modal.show");i&&Ln.getInstance(i).hide(),Ln.getOrCreateInstance(e).toggle(this)})),Ee(Ln),Qt(Ln);const Sn=".bs.offcanvas",Dn=".data-api",$n=`load${Sn}${Dn}`,In="show",Nn="showing",Pn="hiding",Mn=".offcanvas.show",jn=`show${Sn}`,Fn=`shown${Sn}`,Hn=`hide${Sn}`,Bn=`hidePrevented${Sn}`,Wn=`hidden${Sn}`,zn=`resize${Sn}`,Rn=`click${Sn}${Dn}`,qn=`keydown.dismiss${Sn}`,Vn={backdrop:!0,keyboard:!0,scroll:!1},Yn={backdrop:"(boolean|string)",keyboard:"boolean",scroll:"boolean"};class Kn extends ve{constructor(t,e){super(t,e),this._isShown=!1,this._backdrop=this._initializeBackDrop(),this._focustrap=this._initializeFocusTrap(),this._addEventListeners()}static get Default(){return Vn}static get DefaultType(){return Yn}static get NAME(){return"offcanvas"}toggle(t){return this._isShown?this.hide():this.show(t)}show(t){this._isShown||fe.trigger(this._element,jn,{relatedTarget:t}).defaultPrevented||(this._isShown=!0,this._backdrop.show(),this._config.scroll||(new un).hide(),this._element.setAttribute("aria-modal",!0),this._element.setAttribute("role","dialog"),this._element.classList.add(Nn),this._queueCallback((()=>{this._config.scroll&&!this._config.backdrop||this._focustrap.activate(),this._element.classList.add(In),this._element.classList.remove(Nn),fe.trigger(this._element,Fn,{relatedTarget:t})}),this._element,!0))}hide(){this._isShown&&(fe.trigger(this._element,Hn).defaultPrevented||(this._focustrap.deactivate(),this._element.blur(),this._isShown=!1,this._element.classList.add(Pn),this._backdrop.hide(),this._queueCallback((()=>{this._element.classList.remove(In,Pn),this._element.removeAttribute("aria-modal"),this._element.removeAttribute("role"),this._config.scroll||(new un).reset(),fe.trigger(this._element,Wn)}),this._element,!0)))}dispose(){this._backdrop.dispose(),this._focustrap.deactivate(),super.dispose()}_initializeBackDrop(){const t=Boolean(this._config.backdrop);return new Zi({className:"offcanvas-backdrop",isVisible:t,isAnimated:!0,rootElement:this._element.parentNode,clickCallback:t?()=>{"static"!==this._config.backdrop?this.hide():fe.trigger(this._element,Bn)}:null})}_initializeFocusTrap(){return new an({trapElement:this._element})}_addEventListeners(){fe.on(this._element,qn,(t=>{"Escape"===t.key&&(this._config.keyboard?this.hide():fe.trigger(this._element,Bn))}))}static jQueryInterface(t){return this.each((function(){const e=Kn.getOrCreateInstance(this,t);if("string"==typeof t){if(void 0===e[t]||t.startsWith("_")||"constructor"===t)throw new TypeError(`No method named "${t}"`);e[t](this)}}))}}fe.on(document,Rn,'[data-bs-toggle="offcanvas"]',(function(t){const e=we.getElementFromSelector(this);if(["A","AREA"].includes(this.tagName)&&t.preventDefault(),Wt(this))return;fe.one(e,Wn,(()=>{Bt(this)&&this.focus()}));const i=we.findOne(Mn);i&&i!==e&&Kn.getInstance(i).hide(),Kn.getOrCreateInstance(e).toggle(this)})),fe.on(window,$n,(()=>{for(const t of we.find(Mn))Kn.getOrCreateInstance(t).show()})),fe.on(window,zn,(()=>{for(const t of we.find("[aria-modal][class*=show][class*=offcanvas-]"))"fixed"!==getComputedStyle(t).position&&Kn.getOrCreateInstance(t).hide()})),Ee(Kn),Qt(Kn);const Qn={"*":["class","dir","id","lang","role",/^aria-[\w-]*$/i],a:["target","href","title","rel"],area:[],b:[],br:[],col:[],code:[],dd:[],div:[],dl:[],dt:[],em:[],hr:[],h1:[],h2:[],h3:[],h4:[],h5:[],h6:[],i:[],img:["src","srcset","alt","title","width","height"],li:[],ol:[],p:[],pre:[],s:[],small:[],span:[],sub:[],sup:[],strong:[],u:[],ul:[]},Xn=new Set(["background","cite","href","itemtype","longdesc","poster","src","xlink:href"]),Un=/^(?!javascript:)(?:[a-z0-9+.-]+:|[^&:/?#]*(?:[/?#]|$))/i,Gn=(t,e)=>{const i=t.nodeName.toLowerCase();return e.includes(i)?!Xn.has(i)||Boolean(Un.test(t.nodeValue)):e.filter((t=>t instanceof RegExp)).some((t=>t.test(i)))},Jn={allowList:Qn,content:{},extraClass:"",html:!1,sanitize:!0,sanitizeFn:null,template:"
"},Zn={allowList:"object",content:"object",extraClass:"(string|function)",html:"boolean",sanitize:"boolean",sanitizeFn:"(null|function)",template:"string"},ts={entry:"(string|element|function|null)",selector:"(string|element)"};class es extends be{constructor(t){super(),this._config=this._getConfig(t)}static get Default(){return Jn}static get DefaultType(){return Zn}static get NAME(){return"TemplateFactory"}getContent(){return Object.values(this._config.content).map((t=>this._resolvePossibleFunction(t))).filter(Boolean)}hasContent(){return this.getContent().length>0}changeContent(t){return this._checkContent(t),this._config.content={...this._config.content,...t},this}toHtml(){const t=document.createElement("div");t.innerHTML=this._maybeSanitize(this._config.template);for(const[e,i]of Object.entries(this._config.content))this._setContent(t,i,e);const e=t.children[0],i=this._resolvePossibleFunction(this._config.extraClass);return i&&e.classList.add(...i.split(" ")),e}_typeCheckConfig(t){super._typeCheckConfig(t),this._checkContent(t.content)}_checkContent(t){for(const[e,i]of Object.entries(t))super._typeCheckConfig({selector:e,entry:i},ts)}_setContent(t,e,i){const n=we.findOne(i,t);n&&((e=this._resolvePossibleFunction(e))?Ft(e)?this._putElementInTemplate(Ht(e),n):this._config.html?n.innerHTML=this._maybeSanitize(e):n.textContent=e:n.remove())}_maybeSanitize(t){return this._config.sanitize?function(t,e,i){if(!t.length)return t;if(i&&"function"==typeof i)return i(t);const n=(new window.DOMParser).parseFromString(t,"text/html"),s=[].concat(...n.body.querySelectorAll("*"));for(const t of s){const i=t.nodeName.toLowerCase();if(!Object.keys(e).includes(i)){t.remove();continue}const n=[].concat(...t.attributes),s=[].concat(e["*"]||[],e[i]||[]);for(const e of n)Gn(e,s)||t.removeAttribute(e.nodeName)}return n.body.innerHTML}(t,this._config.allowList,this._config.sanitizeFn):t}_resolvePossibleFunction(t){return Xt(t,[this])}_putElementInTemplate(t,e){if(this._config.html)return e.innerHTML="",void e.append(t);e.textContent=t.textContent}}const is=new Set(["sanitize","allowList","sanitizeFn"]),ns="fade",ss="show",os=".tooltip-inner",rs=".modal",as="hide.bs.modal",ls="hover",cs="focus",hs={AUTO:"auto",TOP:"top",RIGHT:Kt()?"left":"right",BOTTOM:"bottom",LEFT:Kt()?"right":"left"},ds={allowList:Qn,animation:!0,boundary:"clippingParents",container:!1,customClass:"",delay:0,fallbackPlacements:["top","right","bottom","left"],html:!1,offset:[0,6],placement:"top",popperConfig:null,sanitize:!0,sanitizeFn:null,selector:!1,template:'',title:"",trigger:"hover focus"},us={allowList:"object",animation:"boolean",boundary:"(string|element)",container:"(string|element|boolean)",customClass:"(string|function)",delay:"(number|object)",fallbackPlacements:"array",html:"boolean",offset:"(array|string|function)",placement:"(string|function)",popperConfig:"(null|object|function)",sanitize:"boolean",sanitizeFn:"(null|function)",selector:"(string|boolean)",template:"string",title:"(string|element|function)",trigger:"string"};class fs extends ve{constructor(t,i){if(void 0===e)throw new TypeError("Bootstrap's tooltips require Popper (https://popper.js.org)");super(t,i),this._isEnabled=!0,this._timeout=0,this._isHovered=null,this._activeTrigger={},this._popper=null,this._templateFactory=null,this._newContent=null,this.tip=null,this._setListeners(),this._config.selector||this._fixTitle()}static get Default(){return ds}static get DefaultType(){return us}static get NAME(){return"tooltip"}enable(){this._isEnabled=!0}disable(){this._isEnabled=!1}toggleEnabled(){this._isEnabled=!this._isEnabled}toggle(){this._isEnabled&&(this._activeTrigger.click=!this._activeTrigger.click,this._isShown()?this._leave():this._enter())}dispose(){clearTimeout(this._timeout),fe.off(this._element.closest(rs),as,this._hideModalHandler),this._element.getAttribute("data-bs-original-title")&&this._element.setAttribute("title",this._element.getAttribute("data-bs-original-title")),this._disposePopper(),super.dispose()}show(){if("none"===this._element.style.display)throw new Error("Please use show on visible elements");if(!this._isWithContent()||!this._isEnabled)return;const t=fe.trigger(this._element,this.constructor.eventName("show")),e=(zt(this._element)||this._element.ownerDocument.documentElement).contains(this._element);if(t.defaultPrevented||!e)return;this._disposePopper();const i=this._getTipElement();this._element.setAttribute("aria-describedby",i.getAttribute("id"));const{container:n}=this._config;if(this._element.ownerDocument.documentElement.contains(this.tip)||(n.append(i),fe.trigger(this._element,this.constructor.eventName("inserted"))),this._popper=this._createPopper(i),i.classList.add(ss),"ontouchstart"in document.documentElement)for(const t of[].concat(...document.body.children))fe.on(t,"mouseover",Rt);this._queueCallback((()=>{fe.trigger(this._element,this.constructor.eventName("shown")),!1===this._isHovered&&this._leave(),this._isHovered=!1}),this.tip,this._isAnimated())}hide(){if(this._isShown()&&!fe.trigger(this._element,this.constructor.eventName("hide")).defaultPrevented){if(this._getTipElement().classList.remove(ss),"ontouchstart"in document.documentElement)for(const t of[].concat(...document.body.children))fe.off(t,"mouseover",Rt);this._activeTrigger.click=!1,this._activeTrigger[cs]=!1,this._activeTrigger[ls]=!1,this._isHovered=null,this._queueCallback((()=>{this._isWithActiveTrigger()||(this._isHovered||this._disposePopper(),this._element.removeAttribute("aria-describedby"),fe.trigger(this._element,this.constructor.eventName("hidden")))}),this.tip,this._isAnimated())}}update(){this._popper&&this._popper.update()}_isWithContent(){return Boolean(this._getTitle())}_getTipElement(){return this.tip||(this.tip=this._createTipElement(this._newContent||this._getContentForTemplate())),this.tip}_createTipElement(t){const e=this._getTemplateFactory(t).toHtml();if(!e)return null;e.classList.remove(ns,ss),e.classList.add(`bs-${this.constructor.NAME}-auto`);const i=(t=>{do{t+=Math.floor(1e6*Math.random())}while(document.getElementById(t));return t})(this.constructor.NAME).toString();return e.setAttribute("id",i),this._isAnimated()&&e.classList.add(ns),e}setContent(t){this._newContent=t,this._isShown()&&(this._disposePopper(),this.show())}_getTemplateFactory(t){return this._templateFactory?this._templateFactory.changeContent(t):this._templateFactory=new es({...this._config,content:t,extraClass:this._resolvePossibleFunction(this._config.customClass)}),this._templateFactory}_getContentForTemplate(){return{[os]:this._getTitle()}}_getTitle(){return this._resolvePossibleFunction(this._config.title)||this._element.getAttribute("data-bs-original-title")}_initializeOnDelegatedTarget(t){return this.constructor.getOrCreateInstance(t.delegateTarget,this._getDelegateConfig())}_isAnimated(){return this._config.animation||this.tip&&this.tip.classList.contains(ns)}_isShown(){return this.tip&&this.tip.classList.contains(ss)}_createPopper(t){const e=Xt(this._config.placement,[this,t,this._element]),i=hs[e.toUpperCase()];return Dt(this._element,t,this._getPopperConfig(i))}_getOffset(){const{offset:t}=this._config;return"string"==typeof t?t.split(",").map((t=>Number.parseInt(t,10))):"function"==typeof t?e=>t(e,this._element):t}_resolvePossibleFunction(t){return Xt(t,[this._element])}_getPopperConfig(t){const e={placement:t,modifiers:[{name:"flip",options:{fallbackPlacements:this._config.fallbackPlacements}},{name:"offset",options:{offset:this._getOffset()}},{name:"preventOverflow",options:{boundary:this._config.boundary}},{name:"arrow",options:{element:`.${this.constructor.NAME}-arrow`}},{name:"preSetPlacement",enabled:!0,phase:"beforeMain",fn:t=>{this._getTipElement().setAttribute("data-popper-placement",t.state.placement)}}]};return{...e,...Xt(this._config.popperConfig,[e])}}_setListeners(){const t=this._config.trigger.split(" ");for(const e of t)if("click"===e)fe.on(this._element,this.constructor.eventName("click"),this._config.selector,(t=>{this._initializeOnDelegatedTarget(t).toggle()}));else if("manual"!==e){const t=e===ls?this.constructor.eventName("mouseenter"):this.constructor.eventName("focusin"),i=e===ls?this.constructor.eventName("mouseleave"):this.constructor.eventName("focusout");fe.on(this._element,t,this._config.selector,(t=>{const e=this._initializeOnDelegatedTarget(t);e._activeTrigger["focusin"===t.type?cs:ls]=!0,e._enter()})),fe.on(this._element,i,this._config.selector,(t=>{const e=this._initializeOnDelegatedTarget(t);e._activeTrigger["focusout"===t.type?cs:ls]=e._element.contains(t.relatedTarget),e._leave()}))}this._hideModalHandler=()=>{this._element&&this.hide()},fe.on(this._element.closest(rs),as,this._hideModalHandler)}_fixTitle(){const t=this._element.getAttribute("title");t&&(this._element.getAttribute("aria-label")||this._element.textContent.trim()||this._element.setAttribute("aria-label",t),this._element.setAttribute("data-bs-original-title",t),this._element.removeAttribute("title"))}_enter(){this._isShown()||this._isHovered?this._isHovered=!0:(this._isHovered=!0,this._setTimeout((()=>{this._isHovered&&this.show()}),this._config.delay.show))}_leave(){this._isWithActiveTrigger()||(this._isHovered=!1,this._setTimeout((()=>{this._isHovered||this.hide()}),this._config.delay.hide))}_setTimeout(t,e){clearTimeout(this._timeout),this._timeout=setTimeout(t,e)}_isWithActiveTrigger(){return Object.values(this._activeTrigger).includes(!0)}_getConfig(t){const e=_e.getDataAttributes(this._element);for(const t of Object.keys(e))is.has(t)&&delete e[t];return t={...e,..."object"==typeof t&&t?t:{}},t=this._mergeConfigObj(t),t=this._configAfterMerge(t),this._typeCheckConfig(t),t}_configAfterMerge(t){return t.container=!1===t.container?document.body:Ht(t.container),"number"==typeof t.delay&&(t.delay={show:t.delay,hide:t.delay}),"number"==typeof t.title&&(t.title=t.title.toString()),"number"==typeof t.content&&(t.content=t.content.toString()),t}_getDelegateConfig(){const t={};for(const[e,i]of Object.entries(this._config))this.constructor.Default[e]!==i&&(t[e]=i);return t.selector=!1,t.trigger="manual",t}_disposePopper(){this._popper&&(this._popper.destroy(),this._popper=null),this.tip&&(this.tip.remove(),this.tip=null)}static jQueryInterface(t){return this.each((function(){const e=fs.getOrCreateInstance(this,t);if("string"==typeof t){if(void 0===e[t])throw new TypeError(`No method named "${t}"`);e[t]()}}))}}Qt(fs);const ps=".popover-header",ms=".popover-body",gs={...fs.Default,content:"",offset:[0,8],placement:"right",template:'',trigger:"click"},_s={...fs.DefaultType,content:"(null|string|element|function)"};class bs extends fs{static get Default(){return gs}static get DefaultType(){return _s}static get NAME(){return"popover"}_isWithContent(){return this._getTitle()||this._getContent()}_getContentForTemplate(){return{[ps]:this._getTitle(),[ms]:this._getContent()}}_getContent(){return this._resolvePossibleFunction(this._config.content)}static jQueryInterface(t){return this.each((function(){const e=bs.getOrCreateInstance(this,t);if("string"==typeof t){if(void 0===e[t])throw new TypeError(`No method named "${t}"`);e[t]()}}))}}Qt(bs);const vs=".bs.scrollspy",ys=`activate${vs}`,ws=`click${vs}`,Es=`load${vs}.data-api`,As="active",Ts="[href]",Cs=".nav-link",Os=`${Cs}, .nav-item > ${Cs}, .list-group-item`,xs={offset:null,rootMargin:"0px 0px -25%",smoothScroll:!1,target:null,threshold:[.1,.5,1]},ks={offset:"(number|null)",rootMargin:"string",smoothScroll:"boolean",target:"element",threshold:"array"};class Ls extends ve{constructor(t,e){super(t,e),this._targetLinks=new Map,this._observableSections=new Map,this._rootElement="visible"===getComputedStyle(this._element).overflowY?null:this._element,this._activeTarget=null,this._observer=null,this._previousScrollData={visibleEntryTop:0,parentScrollTop:0},this.refresh()}static get Default(){return xs}static get DefaultType(){return ks}static get NAME(){return"scrollspy"}refresh(){this._initializeTargetsAndObservables(),this._maybeEnableSmoothScroll(),this._observer?this._observer.disconnect():this._observer=this._getNewObserver();for(const t of this._observableSections.values())this._observer.observe(t)}dispose(){this._observer.disconnect(),super.dispose()}_configAfterMerge(t){return t.target=Ht(t.target)||document.body,t.rootMargin=t.offset?`${t.offset}px 0px -30%`:t.rootMargin,"string"==typeof t.threshold&&(t.threshold=t.threshold.split(",").map((t=>Number.parseFloat(t)))),t}_maybeEnableSmoothScroll(){this._config.smoothScroll&&(fe.off(this._config.target,ws),fe.on(this._config.target,ws,Ts,(t=>{const e=this._observableSections.get(t.target.hash);if(e){t.preventDefault();const i=this._rootElement||window,n=e.offsetTop-this._element.offsetTop;if(i.scrollTo)return void i.scrollTo({top:n,behavior:"smooth"});i.scrollTop=n}})))}_getNewObserver(){const t={root:this._rootElement,threshold:this._config.threshold,rootMargin:this._config.rootMargin};return new IntersectionObserver((t=>this._observerCallback(t)),t)}_observerCallback(t){const e=t=>this._targetLinks.get(`#${t.target.id}`),i=t=>{this._previousScrollData.visibleEntryTop=t.target.offsetTop,this._process(e(t))},n=(this._rootElement||document.documentElement).scrollTop,s=n>=this._previousScrollData.parentScrollTop;this._previousScrollData.parentScrollTop=n;for(const o of t){if(!o.isIntersecting){this._activeTarget=null,this._clearActiveClass(e(o));continue}const t=o.target.offsetTop>=this._previousScrollData.visibleEntryTop;if(s&&t){if(i(o),!n)return}else s||t||i(o)}}_initializeTargetsAndObservables(){this._targetLinks=new Map,this._observableSections=new Map;const t=we.find(Ts,this._config.target);for(const e of t){if(!e.hash||Wt(e))continue;const t=we.findOne(decodeURI(e.hash),this._element);Bt(t)&&(this._targetLinks.set(decodeURI(e.hash),e),this._observableSections.set(e.hash,t))}}_process(t){this._activeTarget!==t&&(this._clearActiveClass(this._config.target),this._activeTarget=t,t.classList.add(As),this._activateParents(t),fe.trigger(this._element,ys,{relatedTarget:t}))}_activateParents(t){if(t.classList.contains("dropdown-item"))we.findOne(".dropdown-toggle",t.closest(".dropdown")).classList.add(As);else for(const e of we.parents(t,".nav, .list-group"))for(const t of we.prev(e,Os))t.classList.add(As)}_clearActiveClass(t){t.classList.remove(As);const e=we.find(`${Ts}.${As}`,t);for(const t of e)t.classList.remove(As)}static jQueryInterface(t){return this.each((function(){const e=Ls.getOrCreateInstance(this,t);if("string"==typeof t){if(void 0===e[t]||t.startsWith("_")||"constructor"===t)throw new TypeError(`No method named "${t}"`);e[t]()}}))}}fe.on(window,Es,(()=>{for(const t of we.find('[data-bs-spy="scroll"]'))Ls.getOrCreateInstance(t)})),Qt(Ls);const Ss=".bs.tab",Ds=`hide${Ss}`,$s=`hidden${Ss}`,Is=`show${Ss}`,Ns=`shown${Ss}`,Ps=`click${Ss}`,Ms=`keydown${Ss}`,js=`load${Ss}`,Fs="ArrowLeft",Hs="ArrowRight",Bs="ArrowUp",Ws="ArrowDown",zs="Home",Rs="End",qs="active",Vs="fade",Ys="show",Ks=".dropdown-toggle",Qs=`:not(${Ks})`,Xs='[data-bs-toggle="tab"], [data-bs-toggle="pill"], [data-bs-toggle="list"]',Us=`.nav-link${Qs}, .list-group-item${Qs}, [role="tab"]${Qs}, ${Xs}`,Gs=`.${qs}[data-bs-toggle="tab"], .${qs}[data-bs-toggle="pill"], .${qs}[data-bs-toggle="list"]`;class Js extends ve{constructor(t){super(t),this._parent=this._element.closest('.list-group, .nav, [role="tablist"]'),this._parent&&(this._setInitialAttributes(this._parent,this._getChildren()),fe.on(this._element,Ms,(t=>this._keydown(t))))}static get NAME(){return"tab"}show(){const t=this._element;if(this._elemIsActive(t))return;const e=this._getActiveElem(),i=e?fe.trigger(e,Ds,{relatedTarget:t}):null;fe.trigger(t,Is,{relatedTarget:e}).defaultPrevented||i&&i.defaultPrevented||(this._deactivate(e,t),this._activate(t,e))}_activate(t,e){t&&(t.classList.add(qs),this._activate(we.getElementFromSelector(t)),this._queueCallback((()=>{"tab"===t.getAttribute("role")?(t.removeAttribute("tabindex"),t.setAttribute("aria-selected",!0),this._toggleDropDown(t,!0),fe.trigger(t,Ns,{relatedTarget:e})):t.classList.add(Ys)}),t,t.classList.contains(Vs)))}_deactivate(t,e){t&&(t.classList.remove(qs),t.blur(),this._deactivate(we.getElementFromSelector(t)),this._queueCallback((()=>{"tab"===t.getAttribute("role")?(t.setAttribute("aria-selected",!1),t.setAttribute("tabindex","-1"),this._toggleDropDown(t,!1),fe.trigger(t,$s,{relatedTarget:e})):t.classList.remove(Ys)}),t,t.classList.contains(Vs)))}_keydown(t){if(![Fs,Hs,Bs,Ws,zs,Rs].includes(t.key))return;t.stopPropagation(),t.preventDefault();const e=this._getChildren().filter((t=>!Wt(t)));let i;if([zs,Rs].includes(t.key))i=e[t.key===zs?0:e.length-1];else{const n=[Hs,Ws].includes(t.key);i=Gt(e,t.target,n,!0)}i&&(i.focus({preventScroll:!0}),Js.getOrCreateInstance(i).show())}_getChildren(){return we.find(Us,this._parent)}_getActiveElem(){return this._getChildren().find((t=>this._elemIsActive(t)))||null}_setInitialAttributes(t,e){this._setAttributeIfNotExists(t,"role","tablist");for(const t of e)this._setInitialAttributesOnChild(t)}_setInitialAttributesOnChild(t){t=this._getInnerElement(t);const e=this._elemIsActive(t),i=this._getOuterElement(t);t.setAttribute("aria-selected",e),i!==t&&this._setAttributeIfNotExists(i,"role","presentation"),e||t.setAttribute("tabindex","-1"),this._setAttributeIfNotExists(t,"role","tab"),this._setInitialAttributesOnTargetPanel(t)}_setInitialAttributesOnTargetPanel(t){const e=we.getElementFromSelector(t);e&&(this._setAttributeIfNotExists(e,"role","tabpanel"),t.id&&this._setAttributeIfNotExists(e,"aria-labelledby",`${t.id}`))}_toggleDropDown(t,e){const i=this._getOuterElement(t);if(!i.classList.contains("dropdown"))return;const n=(t,n)=>{const s=we.findOne(t,i);s&&s.classList.toggle(n,e)};n(Ks,qs),n(".dropdown-menu",Ys),i.setAttribute("aria-expanded",e)}_setAttributeIfNotExists(t,e,i){t.hasAttribute(e)||t.setAttribute(e,i)}_elemIsActive(t){return t.classList.contains(qs)}_getInnerElement(t){return t.matches(Us)?t:we.findOne(Us,t)}_getOuterElement(t){return t.closest(".nav-item, .list-group-item")||t}static jQueryInterface(t){return this.each((function(){const e=Js.getOrCreateInstance(this);if("string"==typeof t){if(void 0===e[t]||t.startsWith("_")||"constructor"===t)throw new TypeError(`No method named "${t}"`);e[t]()}}))}}fe.on(document,Ps,Xs,(function(t){["A","AREA"].includes(this.tagName)&&t.preventDefault(),Wt(this)||Js.getOrCreateInstance(this).show()})),fe.on(window,js,(()=>{for(const t of we.find(Gs))Js.getOrCreateInstance(t)})),Qt(Js);const Zs=".bs.toast",to=`mouseover${Zs}`,eo=`mouseout${Zs}`,io=`focusin${Zs}`,no=`focusout${Zs}`,so=`hide${Zs}`,oo=`hidden${Zs}`,ro=`show${Zs}`,ao=`shown${Zs}`,lo="hide",co="show",ho="showing",uo={animation:"boolean",autohide:"boolean",delay:"number"},fo={animation:!0,autohide:!0,delay:5e3};class po extends ve{constructor(t,e){super(t,e),this._timeout=null,this._hasMouseInteraction=!1,this._hasKeyboardInteraction=!1,this._setListeners()}static get Default(){return fo}static get DefaultType(){return uo}static get NAME(){return"toast"}show(){fe.trigger(this._element,ro).defaultPrevented||(this._clearTimeout(),this._config.animation&&this._element.classList.add("fade"),this._element.classList.remove(lo),qt(this._element),this._element.classList.add(co,ho),this._queueCallback((()=>{this._element.classList.remove(ho),fe.trigger(this._element,ao),this._maybeScheduleHide()}),this._element,this._config.animation))}hide(){this.isShown()&&(fe.trigger(this._element,so).defaultPrevented||(this._element.classList.add(ho),this._queueCallback((()=>{this._element.classList.add(lo),this._element.classList.remove(ho,co),fe.trigger(this._element,oo)}),this._element,this._config.animation)))}dispose(){this._clearTimeout(),this.isShown()&&this._element.classList.remove(co),super.dispose()}isShown(){return this._element.classList.contains(co)}_maybeScheduleHide(){this._config.autohide&&(this._hasMouseInteraction||this._hasKeyboardInteraction||(this._timeout=setTimeout((()=>{this.hide()}),this._config.delay)))}_onInteraction(t,e){switch(t.type){case"mouseover":case"mouseout":this._hasMouseInteraction=e;break;case"focusin":case"focusout":this._hasKeyboardInteraction=e}if(e)return void this._clearTimeout();const i=t.relatedTarget;this._element===i||this._element.contains(i)||this._maybeScheduleHide()}_setListeners(){fe.on(this._element,to,(t=>this._onInteraction(t,!0))),fe.on(this._element,eo,(t=>this._onInteraction(t,!1))),fe.on(this._element,io,(t=>this._onInteraction(t,!0))),fe.on(this._element,no,(t=>this._onInteraction(t,!1)))}_clearTimeout(){clearTimeout(this._timeout),this._timeout=null}static jQueryInterface(t){return this.each((function(){const e=po.getOrCreateInstance(this,t);if("string"==typeof t){if(void 0===e[t])throw new TypeError(`No method named 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(element.nodeName || '').toLowerCase() : null;\n}","export default function getWindow(node) {\n if (node == null) {\n return window;\n }\n\n if (node.toString() !== '[object Window]') {\n var ownerDocument = node.ownerDocument;\n return ownerDocument ? ownerDocument.defaultView || window : window;\n }\n\n return node;\n}","import getWindow from \"./getWindow.js\";\n\nfunction isElement(node) {\n var OwnElement = getWindow(node).Element;\n return node instanceof OwnElement || node instanceof Element;\n}\n\nfunction isHTMLElement(node) {\n var OwnElement = getWindow(node).HTMLElement;\n return node instanceof OwnElement || node instanceof HTMLElement;\n}\n\nfunction isShadowRoot(node) {\n // IE 11 has no ShadowRoot\n if (typeof ShadowRoot === 'undefined') {\n return false;\n }\n\n var OwnElement = getWindow(node).ShadowRoot;\n return node instanceof OwnElement || node instanceof ShadowRoot;\n}\n\nexport { isElement, isHTMLElement, isShadowRoot };","import getNodeName from \"../dom-utils/getNodeName.js\";\nimport { isHTMLElement } from \"../dom-utils/instanceOf.js\"; // This modifier takes the styles prepared by the `computeStyles` modifier\n// and applies them to the HTMLElements such as popper and arrow\n\nfunction applyStyles(_ref) {\n var state = _ref.state;\n Object.keys(state.elements).forEach(function (name) {\n var style = state.styles[name] || {};\n var attributes = state.attributes[name] || {};\n var element = state.elements[name]; // arrow is optional + virtual elements\n\n if (!isHTMLElement(element) || !getNodeName(element)) {\n return;\n } // Flow doesn't support to extend this property, but it's the most\n // effective way to apply styles to an HTMLElement\n // $FlowFixMe[cannot-write]\n\n\n Object.assign(element.style, style);\n Object.keys(attributes).forEach(function (name) {\n var value = attributes[name];\n\n if (value === false) {\n element.removeAttribute(name);\n } else {\n element.setAttribute(name, value === true ? '' : value);\n }\n });\n });\n}\n\nfunction effect(_ref2) {\n var state = _ref2.state;\n var initialStyles = {\n popper: {\n position: state.options.strategy,\n left: '0',\n top: '0',\n margin: '0'\n },\n arrow: {\n position: 'absolute'\n },\n reference: {}\n };\n Object.assign(state.elements.popper.style, initialStyles.popper);\n state.styles = initialStyles;\n\n if (state.elements.arrow) {\n Object.assign(state.elements.arrow.style, initialStyles.arrow);\n }\n\n return function () {\n Object.keys(state.elements).forEach(function (name) {\n var element = state.elements[name];\n var attributes = state.attributes[name] || {};\n var styleProperties = Object.keys(state.styles.hasOwnProperty(name) ? state.styles[name] : initialStyles[name]); // Set all values to an empty string to unset them\n\n var style = styleProperties.reduce(function (style, property) {\n style[property] = '';\n return style;\n }, {}); // arrow is optional + virtual elements\n\n if (!isHTMLElement(element) || !getNodeName(element)) {\n return;\n }\n\n Object.assign(element.style, style);\n Object.keys(attributes).forEach(function (attribute) {\n element.removeAttribute(attribute);\n });\n });\n };\n} // eslint-disable-next-line import/no-unused-modules\n\n\nexport default {\n name: 'applyStyles',\n enabled: true,\n phase: 'write',\n fn: applyStyles,\n effect: effect,\n requires: ['computeStyles']\n};","import { auto } from \"../enums.js\";\nexport default function getBasePlacement(placement) {\n return placement.split('-')[0];\n}","export var max = Math.max;\nexport var min = Math.min;\nexport var round = Math.round;","export default function getUAString() {\n var uaData = navigator.userAgentData;\n\n if (uaData != null && uaData.brands && Array.isArray(uaData.brands)) {\n return uaData.brands.map(function (item) {\n return item.brand + \"/\" + item.version;\n }).join(' ');\n }\n\n return navigator.userAgent;\n}","import getUAString from \"../utils/userAgent.js\";\nexport default function isLayoutViewport() {\n return !/^((?!chrome|android).)*safari/i.test(getUAString());\n}","import { isElement, isHTMLElement } from \"./instanceOf.js\";\nimport { round } from \"../utils/math.js\";\nimport getWindow from \"./getWindow.js\";\nimport isLayoutViewport from \"./isLayoutViewport.js\";\nexport default function getBoundingClientRect(element, includeScale, isFixedStrategy) {\n if (includeScale === void 0) {\n includeScale = false;\n }\n\n if (isFixedStrategy === void 0) {\n isFixedStrategy = false;\n }\n\n var clientRect = element.getBoundingClientRect();\n var scaleX = 1;\n var scaleY = 1;\n\n if (includeScale && isHTMLElement(element)) {\n scaleX = element.offsetWidth > 0 ? round(clientRect.width) / element.offsetWidth || 1 : 1;\n scaleY = element.offsetHeight > 0 ? round(clientRect.height) / element.offsetHeight || 1 : 1;\n }\n\n var _ref = isElement(element) ? getWindow(element) : window,\n visualViewport = _ref.visualViewport;\n\n var addVisualOffsets = !isLayoutViewport() && isFixedStrategy;\n var x = (clientRect.left + (addVisualOffsets && visualViewport ? visualViewport.offsetLeft : 0)) / scaleX;\n var y = (clientRect.top + (addVisualOffsets && visualViewport ? visualViewport.offsetTop : 0)) / scaleY;\n var width = clientRect.width / scaleX;\n var height = clientRect.height / scaleY;\n return {\n width: width,\n height: height,\n top: y,\n right: x + width,\n bottom: y + height,\n left: x,\n x: x,\n y: y\n };\n}","import getBoundingClientRect from \"./getBoundingClientRect.js\"; // Returns the layout rect of an element relative to its offsetParent. Layout\n// means it doesn't take into account transforms.\n\nexport default function getLayoutRect(element) {\n var clientRect = getBoundingClientRect(element); // Use the clientRect sizes if it's not been transformed.\n // Fixes https://github.com/popperjs/popper-core/issues/1223\n\n var width = element.offsetWidth;\n var height = element.offsetHeight;\n\n if (Math.abs(clientRect.width - width) <= 1) {\n width = clientRect.width;\n }\n\n if (Math.abs(clientRect.height - height) <= 1) {\n height = clientRect.height;\n }\n\n return {\n x: element.offsetLeft,\n y: element.offsetTop,\n width: width,\n height: height\n };\n}","import { isShadowRoot } from \"./instanceOf.js\";\nexport default function contains(parent, child) {\n var rootNode = child.getRootNode && child.getRootNode(); // First, attempt with faster native method\n\n if (parent.contains(child)) {\n return true;\n } // then fallback to custom implementation with Shadow DOM support\n else if (rootNode && isShadowRoot(rootNode)) {\n var next = child;\n\n do {\n if (next && parent.isSameNode(next)) {\n return true;\n } // $FlowFixMe[prop-missing]: need a better way to handle this...\n\n\n next = next.parentNode || next.host;\n } while (next);\n } // Give up, the result is false\n\n\n return false;\n}","import getWindow from \"./getWindow.js\";\nexport default function getComputedStyle(element) {\n return getWindow(element).getComputedStyle(element);\n}","import getNodeName from \"./getNodeName.js\";\nexport default function isTableElement(element) {\n return ['table', 'td', 'th'].indexOf(getNodeName(element)) >= 0;\n}","import { isElement } from \"./instanceOf.js\";\nexport default function getDocumentElement(element) {\n // $FlowFixMe[incompatible-return]: assume body is always available\n return ((isElement(element) ? element.ownerDocument : // $FlowFixMe[prop-missing]\n element.document) || window.document).documentElement;\n}","import getNodeName from \"./getNodeName.js\";\nimport getDocumentElement from \"./getDocumentElement.js\";\nimport { isShadowRoot } from \"./instanceOf.js\";\nexport default function getParentNode(element) {\n if (getNodeName(element) === 'html') {\n return element;\n }\n\n return (// this is a quicker (but less type safe) way to save quite some bytes from the bundle\n // $FlowFixMe[incompatible-return]\n // $FlowFixMe[prop-missing]\n element.assignedSlot || // step into the shadow DOM of the parent of a slotted node\n element.parentNode || ( // DOM Element detected\n isShadowRoot(element) ? element.host : null) || // ShadowRoot detected\n // $FlowFixMe[incompatible-call]: HTMLElement is a Node\n getDocumentElement(element) // fallback\n\n );\n}","import getWindow from \"./getWindow.js\";\nimport getNodeName from \"./getNodeName.js\";\nimport getComputedStyle from \"./getComputedStyle.js\";\nimport { isHTMLElement, isShadowRoot } from \"./instanceOf.js\";\nimport isTableElement from \"./isTableElement.js\";\nimport getParentNode from \"./getParentNode.js\";\nimport getUAString from \"../utils/userAgent.js\";\n\nfunction getTrueOffsetParent(element) {\n if (!isHTMLElement(element) || // https://github.com/popperjs/popper-core/issues/837\n getComputedStyle(element).position === 'fixed') {\n return null;\n }\n\n return element.offsetParent;\n} // `.offsetParent` reports `null` for fixed elements, while absolute elements\n// return the containing block\n\n\nfunction getContainingBlock(element) {\n var isFirefox = /firefox/i.test(getUAString());\n var isIE = /Trident/i.test(getUAString());\n\n if (isIE && isHTMLElement(element)) {\n // In IE 9, 10 and 11 fixed elements containing block is always established by the viewport\n var elementCss = getComputedStyle(element);\n\n if (elementCss.position === 'fixed') {\n return null;\n }\n }\n\n var currentNode = getParentNode(element);\n\n if (isShadowRoot(currentNode)) {\n currentNode = currentNode.host;\n }\n\n while (isHTMLElement(currentNode) && ['html', 'body'].indexOf(getNodeName(currentNode)) < 0) {\n var css = getComputedStyle(currentNode); // This is non-exhaustive but covers the most common CSS properties that\n // create a containing block.\n // https://developer.mozilla.org/en-US/docs/Web/CSS/Containing_block#identifying_the_containing_block\n\n if (css.transform !== 'none' || css.perspective !== 'none' || css.contain === 'paint' || ['transform', 'perspective'].indexOf(css.willChange) !== -1 || isFirefox && css.willChange === 'filter' || isFirefox && css.filter && css.filter !== 'none') {\n return currentNode;\n } else {\n currentNode = currentNode.parentNode;\n }\n }\n\n return null;\n} // Gets the closest ancestor positioned element. Handles some edge cases,\n// such as table ancestors and cross browser bugs.\n\n\nexport default function getOffsetParent(element) {\n var window = getWindow(element);\n var offsetParent = getTrueOffsetParent(element);\n\n while (offsetParent && isTableElement(offsetParent) && getComputedStyle(offsetParent).position === 'static') {\n offsetParent = getTrueOffsetParent(offsetParent);\n }\n\n if (offsetParent && (getNodeName(offsetParent) === 'html' || getNodeName(offsetParent) === 'body' && getComputedStyle(offsetParent).position === 'static')) {\n return window;\n }\n\n return offsetParent || getContainingBlock(element) || window;\n}","export default function getMainAxisFromPlacement(placement) {\n return ['top', 'bottom'].indexOf(placement) >= 0 ? 'x' : 'y';\n}","import { max as mathMax, min as mathMin } from \"./math.js\";\nexport function within(min, value, max) {\n return mathMax(min, mathMin(value, max));\n}\nexport function withinMaxClamp(min, value, max) {\n var v = within(min, value, max);\n return v > max ? max : v;\n}","import getFreshSideObject from \"./getFreshSideObject.js\";\nexport default function mergePaddingObject(paddingObject) {\n return Object.assign({}, getFreshSideObject(), paddingObject);\n}","export default function getFreshSideObject() {\n return {\n top: 0,\n right: 0,\n bottom: 0,\n left: 0\n };\n}","export default function expandToHashMap(value, keys) {\n return keys.reduce(function (hashMap, key) {\n hashMap[key] = value;\n return hashMap;\n }, {});\n}","import getBasePlacement from \"../utils/getBasePlacement.js\";\nimport getLayoutRect from \"../dom-utils/getLayoutRect.js\";\nimport contains from \"../dom-utils/contains.js\";\nimport getOffsetParent from \"../dom-utils/getOffsetParent.js\";\nimport getMainAxisFromPlacement from \"../utils/getMainAxisFromPlacement.js\";\nimport { within } from \"../utils/within.js\";\nimport mergePaddingObject from \"../utils/mergePaddingObject.js\";\nimport expandToHashMap from \"../utils/expandToHashMap.js\";\nimport { left, right, basePlacements, top, bottom } from \"../enums.js\"; // eslint-disable-next-line import/no-unused-modules\n\nvar toPaddingObject = function toPaddingObject(padding, state) {\n padding = typeof padding === 'function' ? padding(Object.assign({}, state.rects, {\n placement: state.placement\n })) : padding;\n return mergePaddingObject(typeof padding !== 'number' ? padding : expandToHashMap(padding, basePlacements));\n};\n\nfunction arrow(_ref) {\n var _state$modifiersData$;\n\n var state = _ref.state,\n name = _ref.name,\n options = _ref.options;\n var arrowElement = state.elements.arrow;\n var popperOffsets = state.modifiersData.popperOffsets;\n var basePlacement = getBasePlacement(state.placement);\n var axis = getMainAxisFromPlacement(basePlacement);\n var isVertical = [left, right].indexOf(basePlacement) >= 0;\n var len = isVertical ? 'height' : 'width';\n\n if (!arrowElement || !popperOffsets) {\n return;\n }\n\n var paddingObject = toPaddingObject(options.padding, state);\n var arrowRect = getLayoutRect(arrowElement);\n var minProp = axis === 'y' ? top : left;\n var maxProp = axis === 'y' ? bottom : right;\n var endDiff = state.rects.reference[len] + state.rects.reference[axis] - popperOffsets[axis] - state.rects.popper[len];\n var startDiff = popperOffsets[axis] - state.rects.reference[axis];\n var arrowOffsetParent = getOffsetParent(arrowElement);\n var clientSize = arrowOffsetParent ? axis === 'y' ? arrowOffsetParent.clientHeight || 0 : arrowOffsetParent.clientWidth || 0 : 0;\n var centerToReference = endDiff / 2 - startDiff / 2; // Make sure the arrow doesn't overflow the popper if the center point is\n // outside of the popper bounds\n\n var min = paddingObject[minProp];\n var max = clientSize - arrowRect[len] - paddingObject[maxProp];\n var center = clientSize / 2 - arrowRect[len] / 2 + centerToReference;\n var offset = within(min, center, max); // Prevents breaking syntax highlighting...\n\n var axisProp = axis;\n state.modifiersData[name] = (_state$modifiersData$ = {}, _state$modifiersData$[axisProp] = offset, _state$modifiersData$.centerOffset = offset - center, _state$modifiersData$);\n}\n\nfunction effect(_ref2) {\n var state = _ref2.state,\n options = _ref2.options;\n var _options$element = options.element,\n arrowElement = _options$element === void 0 ? '[data-popper-arrow]' : _options$element;\n\n if (arrowElement == null) {\n return;\n } // CSS selector\n\n\n if (typeof arrowElement === 'string') {\n arrowElement = state.elements.popper.querySelector(arrowElement);\n\n if (!arrowElement) {\n return;\n }\n }\n\n if (!contains(state.elements.popper, arrowElement)) {\n return;\n }\n\n state.elements.arrow = arrowElement;\n} // eslint-disable-next-line import/no-unused-modules\n\n\nexport default {\n name: 'arrow',\n enabled: true,\n phase: 'main',\n fn: arrow,\n effect: effect,\n requires: ['popperOffsets'],\n requiresIfExists: ['preventOverflow']\n};","export default function getVariation(placement) {\n return placement.split('-')[1];\n}","import { top, left, right, bottom, end } from \"../enums.js\";\nimport getOffsetParent from \"../dom-utils/getOffsetParent.js\";\nimport getWindow from \"../dom-utils/getWindow.js\";\nimport getDocumentElement from \"../dom-utils/getDocumentElement.js\";\nimport getComputedStyle from \"../dom-utils/getComputedStyle.js\";\nimport getBasePlacement from \"../utils/getBasePlacement.js\";\nimport getVariation from \"../utils/getVariation.js\";\nimport { round } from \"../utils/math.js\"; // eslint-disable-next-line import/no-unused-modules\n\nvar unsetSides = {\n top: 'auto',\n right: 'auto',\n bottom: 'auto',\n left: 'auto'\n}; // Round the offsets to the nearest suitable subpixel based on the DPR.\n// Zooming can change the DPR, but it seems to report a value that will\n// cleanly divide the values into the appropriate subpixels.\n\nfunction roundOffsetsByDPR(_ref, win) {\n var x = _ref.x,\n y = _ref.y;\n var dpr = win.devicePixelRatio || 1;\n return {\n x: round(x * dpr) / dpr || 0,\n y: round(y * dpr) / dpr || 0\n };\n}\n\nexport function mapToStyles(_ref2) {\n var _Object$assign2;\n\n var popper = _ref2.popper,\n popperRect = _ref2.popperRect,\n placement = _ref2.placement,\n variation = _ref2.variation,\n offsets = _ref2.offsets,\n position = _ref2.position,\n gpuAcceleration = _ref2.gpuAcceleration,\n adaptive = _ref2.adaptive,\n roundOffsets = _ref2.roundOffsets,\n isFixed = _ref2.isFixed;\n var _offsets$x = offsets.x,\n x = _offsets$x === void 0 ? 0 : _offsets$x,\n _offsets$y = offsets.y,\n y = _offsets$y === void 0 ? 0 : _offsets$y;\n\n var _ref3 = typeof roundOffsets === 'function' ? roundOffsets({\n x: x,\n y: y\n }) : {\n x: x,\n y: y\n };\n\n x = _ref3.x;\n y = _ref3.y;\n var hasX = offsets.hasOwnProperty('x');\n var hasY = offsets.hasOwnProperty('y');\n var sideX = left;\n var sideY = top;\n var win = window;\n\n if (adaptive) {\n var offsetParent = getOffsetParent(popper);\n var heightProp = 'clientHeight';\n var widthProp = 'clientWidth';\n\n if (offsetParent === getWindow(popper)) {\n offsetParent = getDocumentElement(popper);\n\n if (getComputedStyle(offsetParent).position !== 'static' && position === 'absolute') {\n heightProp = 'scrollHeight';\n widthProp = 'scrollWidth';\n }\n } // $FlowFixMe[incompatible-cast]: force type refinement, we compare offsetParent with window above, but Flow doesn't detect it\n\n\n offsetParent = offsetParent;\n\n if (placement === top || (placement === left || placement === right) && variation === end) {\n sideY = bottom;\n var offsetY = isFixed && offsetParent === win && win.visualViewport ? win.visualViewport.height : // $FlowFixMe[prop-missing]\n offsetParent[heightProp];\n y -= offsetY - popperRect.height;\n y *= gpuAcceleration ? 1 : -1;\n }\n\n if (placement === left || (placement === top || placement === bottom) && variation === end) {\n sideX = right;\n var offsetX = isFixed && offsetParent === win && win.visualViewport ? win.visualViewport.width : // $FlowFixMe[prop-missing]\n offsetParent[widthProp];\n x -= offsetX - popperRect.width;\n x *= gpuAcceleration ? 1 : -1;\n }\n }\n\n var commonStyles = Object.assign({\n position: position\n }, adaptive && unsetSides);\n\n var _ref4 = roundOffsets === true ? roundOffsetsByDPR({\n x: x,\n y: y\n }, getWindow(popper)) : {\n x: x,\n y: y\n };\n\n x = _ref4.x;\n y = _ref4.y;\n\n if (gpuAcceleration) {\n var _Object$assign;\n\n return Object.assign({}, commonStyles, (_Object$assign = {}, _Object$assign[sideY] = hasY ? '0' : '', _Object$assign[sideX] = hasX ? '0' : '', _Object$assign.transform = (win.devicePixelRatio || 1) <= 1 ? \"translate(\" + x + \"px, \" + y + \"px)\" : \"translate3d(\" + x + \"px, \" + y + \"px, 0)\", _Object$assign));\n }\n\n return Object.assign({}, commonStyles, (_Object$assign2 = {}, _Object$assign2[sideY] = hasY ? y + \"px\" : '', _Object$assign2[sideX] = hasX ? x + \"px\" : '', _Object$assign2.transform = '', _Object$assign2));\n}\n\nfunction computeStyles(_ref5) {\n var state = _ref5.state,\n options = _ref5.options;\n var _options$gpuAccelerat = options.gpuAcceleration,\n gpuAcceleration = _options$gpuAccelerat === void 0 ? true : _options$gpuAccelerat,\n _options$adaptive = options.adaptive,\n adaptive = _options$adaptive === void 0 ? true : _options$adaptive,\n _options$roundOffsets = options.roundOffsets,\n roundOffsets = _options$roundOffsets === void 0 ? true : _options$roundOffsets;\n var commonStyles = {\n placement: getBasePlacement(state.placement),\n variation: getVariation(state.placement),\n popper: state.elements.popper,\n popperRect: state.rects.popper,\n gpuAcceleration: gpuAcceleration,\n isFixed: state.options.strategy === 'fixed'\n };\n\n if (state.modifiersData.popperOffsets != null) {\n state.styles.popper = Object.assign({}, state.styles.popper, mapToStyles(Object.assign({}, commonStyles, {\n offsets: state.modifiersData.popperOffsets,\n position: state.options.strategy,\n adaptive: adaptive,\n roundOffsets: roundOffsets\n })));\n }\n\n if (state.modifiersData.arrow != null) {\n state.styles.arrow = Object.assign({}, state.styles.arrow, mapToStyles(Object.assign({}, commonStyles, {\n offsets: state.modifiersData.arrow,\n position: 'absolute',\n adaptive: false,\n roundOffsets: roundOffsets\n })));\n }\n\n state.attributes.popper = Object.assign({}, state.attributes.popper, {\n 'data-popper-placement': state.placement\n });\n} // eslint-disable-next-line import/no-unused-modules\n\n\nexport default {\n name: 'computeStyles',\n enabled: true,\n phase: 'beforeWrite',\n fn: computeStyles,\n data: {}\n};","import getWindow from \"../dom-utils/getWindow.js\"; // eslint-disable-next-line import/no-unused-modules\n\nvar passive = {\n passive: true\n};\n\nfunction effect(_ref) {\n var state = _ref.state,\n instance = _ref.instance,\n options = _ref.options;\n var _options$scroll = options.scroll,\n scroll = _options$scroll === void 0 ? true : _options$scroll,\n _options$resize = options.resize,\n resize = _options$resize === void 0 ? true : _options$resize;\n var window = getWindow(state.elements.popper);\n var scrollParents = [].concat(state.scrollParents.reference, state.scrollParents.popper);\n\n if (scroll) {\n scrollParents.forEach(function (scrollParent) {\n scrollParent.addEventListener('scroll', instance.update, passive);\n });\n }\n\n if (resize) {\n window.addEventListener('resize', instance.update, passive);\n }\n\n return function () {\n if (scroll) {\n scrollParents.forEach(function (scrollParent) {\n scrollParent.removeEventListener('scroll', instance.update, passive);\n });\n }\n\n if (resize) {\n window.removeEventListener('resize', instance.update, passive);\n }\n };\n} // eslint-disable-next-line import/no-unused-modules\n\n\nexport default {\n name: 'eventListeners',\n enabled: true,\n phase: 'write',\n fn: function fn() {},\n effect: effect,\n data: {}\n};","var hash = {\n left: 'right',\n right: 'left',\n bottom: 'top',\n top: 'bottom'\n};\nexport default function getOppositePlacement(placement) {\n return placement.replace(/left|right|bottom|top/g, function (matched) {\n return hash[matched];\n });\n}","var hash = {\n start: 'end',\n end: 'start'\n};\nexport default function getOppositeVariationPlacement(placement) {\n return placement.replace(/start|end/g, function (matched) {\n return hash[matched];\n });\n}","import getWindow from \"./getWindow.js\";\nexport default function getWindowScroll(node) {\n var win = getWindow(node);\n var scrollLeft = win.pageXOffset;\n var scrollTop = win.pageYOffset;\n return {\n scrollLeft: scrollLeft,\n scrollTop: scrollTop\n };\n}","import getBoundingClientRect from \"./getBoundingClientRect.js\";\nimport getDocumentElement from \"./getDocumentElement.js\";\nimport getWindowScroll from \"./getWindowScroll.js\";\nexport default function getWindowScrollBarX(element) {\n // If has a CSS width greater than the viewport, then this will be\n // incorrect for RTL.\n // Popper 1 is broken in this case and never had a bug report so let's assume\n // it's not an issue. I don't think anyone ever specifies width on \n // anyway.\n // Browsers where the left scrollbar doesn't cause an issue report `0` for\n // this (e.g. Edge 2019, IE11, Safari)\n return getBoundingClientRect(getDocumentElement(element)).left + getWindowScroll(element).scrollLeft;\n}","import getComputedStyle from \"./getComputedStyle.js\";\nexport default function isScrollParent(element) {\n // Firefox wants us to check `-x` and `-y` variations as well\n var _getComputedStyle = getComputedStyle(element),\n overflow = _getComputedStyle.overflow,\n overflowX = _getComputedStyle.overflowX,\n overflowY = _getComputedStyle.overflowY;\n\n return /auto|scroll|overlay|hidden/.test(overflow + overflowY + overflowX);\n}","import getParentNode from \"./getParentNode.js\";\nimport isScrollParent from \"./isScrollParent.js\";\nimport getNodeName from \"./getNodeName.js\";\nimport { isHTMLElement } from \"./instanceOf.js\";\nexport default function getScrollParent(node) {\n if (['html', 'body', '#document'].indexOf(getNodeName(node)) >= 0) {\n // $FlowFixMe[incompatible-return]: assume body is always available\n return node.ownerDocument.body;\n }\n\n if (isHTMLElement(node) && isScrollParent(node)) {\n return node;\n }\n\n return getScrollParent(getParentNode(node));\n}","import getScrollParent from \"./getScrollParent.js\";\nimport getParentNode from \"./getParentNode.js\";\nimport getWindow from \"./getWindow.js\";\nimport isScrollParent from \"./isScrollParent.js\";\n/*\ngiven a DOM element, return the list of all scroll parents, up the list of ancesors\nuntil we get to the top window object. This list is what we attach scroll listeners\nto, because if any of these parent elements scroll, we'll need to re-calculate the\nreference element's position.\n*/\n\nexport default function listScrollParents(element, list) {\n var _element$ownerDocumen;\n\n if (list === void 0) {\n list = [];\n }\n\n var scrollParent = getScrollParent(element);\n var isBody = scrollParent === ((_element$ownerDocumen = element.ownerDocument) == null ? void 0 : _element$ownerDocumen.body);\n var win = getWindow(scrollParent);\n var target = isBody ? [win].concat(win.visualViewport || [], isScrollParent(scrollParent) ? scrollParent : []) : scrollParent;\n var updatedList = list.concat(target);\n return isBody ? updatedList : // $FlowFixMe[incompatible-call]: isBody tells us target will be an HTMLElement here\n updatedList.concat(listScrollParents(getParentNode(target)));\n}","export default function rectToClientRect(rect) {\n return Object.assign({}, rect, {\n left: rect.x,\n top: rect.y,\n right: rect.x + rect.width,\n bottom: rect.y + rect.height\n });\n}","import { viewport } from \"../enums.js\";\nimport getViewportRect from \"./getViewportRect.js\";\nimport getDocumentRect from \"./getDocumentRect.js\";\nimport listScrollParents from \"./listScrollParents.js\";\nimport getOffsetParent from \"./getOffsetParent.js\";\nimport getDocumentElement from \"./getDocumentElement.js\";\nimport getComputedStyle from \"./getComputedStyle.js\";\nimport { isElement, isHTMLElement } from \"./instanceOf.js\";\nimport getBoundingClientRect from \"./getBoundingClientRect.js\";\nimport getParentNode from \"./getParentNode.js\";\nimport contains from \"./contains.js\";\nimport getNodeName from \"./getNodeName.js\";\nimport rectToClientRect from \"../utils/rectToClientRect.js\";\nimport { max, min } from \"../utils/math.js\";\n\nfunction getInnerBoundingClientRect(element, strategy) {\n var rect = getBoundingClientRect(element, false, strategy === 'fixed');\n rect.top = rect.top + element.clientTop;\n rect.left = rect.left + element.clientLeft;\n rect.bottom = rect.top + element.clientHeight;\n rect.right = rect.left + element.clientWidth;\n rect.width = element.clientWidth;\n rect.height = element.clientHeight;\n rect.x = rect.left;\n rect.y = rect.top;\n return rect;\n}\n\nfunction getClientRectFromMixedType(element, clippingParent, strategy) {\n return clippingParent === viewport ? rectToClientRect(getViewportRect(element, strategy)) : isElement(clippingParent) ? getInnerBoundingClientRect(clippingParent, strategy) : rectToClientRect(getDocumentRect(getDocumentElement(element)));\n} // A \"clipping parent\" is an overflowable container with the characteristic of\n// clipping (or hiding) overflowing elements with a position different from\n// `initial`\n\n\nfunction getClippingParents(element) {\n var clippingParents = listScrollParents(getParentNode(element));\n var canEscapeClipping = ['absolute', 'fixed'].indexOf(getComputedStyle(element).position) >= 0;\n var clipperElement = canEscapeClipping && isHTMLElement(element) ? getOffsetParent(element) : element;\n\n if (!isElement(clipperElement)) {\n return [];\n } // $FlowFixMe[incompatible-return]: https://github.com/facebook/flow/issues/1414\n\n\n return clippingParents.filter(function (clippingParent) {\n return isElement(clippingParent) && contains(clippingParent, clipperElement) && getNodeName(clippingParent) !== 'body';\n });\n} // Gets the maximum area that the element is visible in due to any number of\n// clipping parents\n\n\nexport default function getClippingRect(element, boundary, rootBoundary, strategy) {\n var mainClippingParents = boundary === 'clippingParents' ? getClippingParents(element) : [].concat(boundary);\n var clippingParents = [].concat(mainClippingParents, [rootBoundary]);\n var firstClippingParent = clippingParents[0];\n var clippingRect = clippingParents.reduce(function (accRect, clippingParent) {\n var rect = getClientRectFromMixedType(element, clippingParent, strategy);\n accRect.top = max(rect.top, accRect.top);\n accRect.right = min(rect.right, accRect.right);\n accRect.bottom = min(rect.bottom, accRect.bottom);\n accRect.left = max(rect.left, accRect.left);\n return accRect;\n }, getClientRectFromMixedType(element, firstClippingParent, strategy));\n clippingRect.width = clippingRect.right - clippingRect.left;\n clippingRect.height = clippingRect.bottom - clippingRect.top;\n clippingRect.x = clippingRect.left;\n clippingRect.y = clippingRect.top;\n return clippingRect;\n}","import getWindow from \"./getWindow.js\";\nimport getDocumentElement from \"./getDocumentElement.js\";\nimport getWindowScrollBarX from \"./getWindowScrollBarX.js\";\nimport isLayoutViewport from \"./isLayoutViewport.js\";\nexport default function getViewportRect(element, strategy) {\n var win = getWindow(element);\n var html = getDocumentElement(element);\n var visualViewport = win.visualViewport;\n var width = html.clientWidth;\n var height = html.clientHeight;\n var x = 0;\n var y = 0;\n\n if (visualViewport) {\n width = visualViewport.width;\n height = visualViewport.height;\n var layoutViewport = isLayoutViewport();\n\n if (layoutViewport || !layoutViewport && strategy === 'fixed') {\n x = visualViewport.offsetLeft;\n y = visualViewport.offsetTop;\n }\n }\n\n return {\n width: width,\n height: height,\n x: x + getWindowScrollBarX(element),\n y: y\n };\n}","import getDocumentElement from \"./getDocumentElement.js\";\nimport getComputedStyle from \"./getComputedStyle.js\";\nimport getWindowScrollBarX from \"./getWindowScrollBarX.js\";\nimport getWindowScroll from \"./getWindowScroll.js\";\nimport { max } from \"../utils/math.js\"; // Gets the entire size of the scrollable document area, even extending outside\n// of the `` and `` rect bounds if horizontally scrollable\n\nexport default function getDocumentRect(element) {\n var _element$ownerDocumen;\n\n var html = getDocumentElement(element);\n var winScroll = getWindowScroll(element);\n var body = (_element$ownerDocumen = element.ownerDocument) == null ? void 0 : _element$ownerDocumen.body;\n var width = max(html.scrollWidth, html.clientWidth, body ? body.scrollWidth : 0, body ? body.clientWidth : 0);\n var height = max(html.scrollHeight, html.clientHeight, body ? body.scrollHeight : 0, body ? body.clientHeight : 0);\n var x = -winScroll.scrollLeft + getWindowScrollBarX(element);\n var y = -winScroll.scrollTop;\n\n if (getComputedStyle(body || html).direction === 'rtl') {\n x += max(html.clientWidth, body ? body.clientWidth : 0) - width;\n }\n\n return {\n width: width,\n height: height,\n x: x,\n y: y\n };\n}","import getBasePlacement from \"./getBasePlacement.js\";\nimport getVariation from \"./getVariation.js\";\nimport getMainAxisFromPlacement from \"./getMainAxisFromPlacement.js\";\nimport { top, right, bottom, left, start, end } from \"../enums.js\";\nexport default function computeOffsets(_ref) {\n var reference = _ref.reference,\n element = _ref.element,\n placement = _ref.placement;\n var basePlacement = placement ? getBasePlacement(placement) : null;\n var variation = placement ? getVariation(placement) : null;\n var commonX = reference.x + reference.width / 2 - element.width / 2;\n var commonY = reference.y + reference.height / 2 - element.height / 2;\n var offsets;\n\n switch (basePlacement) {\n case top:\n offsets = {\n x: commonX,\n y: reference.y - element.height\n };\n break;\n\n case bottom:\n offsets = {\n x: commonX,\n y: reference.y + reference.height\n };\n break;\n\n case right:\n offsets = {\n x: reference.x + reference.width,\n y: commonY\n };\n break;\n\n case left:\n offsets = {\n x: reference.x - element.width,\n y: commonY\n };\n break;\n\n default:\n offsets = {\n x: reference.x,\n y: reference.y\n };\n }\n\n var mainAxis = basePlacement ? getMainAxisFromPlacement(basePlacement) : null;\n\n if (mainAxis != null) {\n var len = mainAxis === 'y' ? 'height' : 'width';\n\n switch (variation) {\n case start:\n offsets[mainAxis] = offsets[mainAxis] - (reference[len] / 2 - element[len] / 2);\n break;\n\n case end:\n offsets[mainAxis] = offsets[mainAxis] + (reference[len] / 2 - element[len] / 2);\n break;\n\n default:\n }\n }\n\n return offsets;\n}","import getClippingRect from \"../dom-utils/getClippingRect.js\";\nimport getDocumentElement from \"../dom-utils/getDocumentElement.js\";\nimport getBoundingClientRect from \"../dom-utils/getBoundingClientRect.js\";\nimport computeOffsets from \"./computeOffsets.js\";\nimport rectToClientRect from \"./rectToClientRect.js\";\nimport { clippingParents, reference, popper, bottom, top, right, basePlacements, viewport } from \"../enums.js\";\nimport { isElement } from \"../dom-utils/instanceOf.js\";\nimport mergePaddingObject from \"./mergePaddingObject.js\";\nimport expandToHashMap from \"./expandToHashMap.js\"; // eslint-disable-next-line import/no-unused-modules\n\nexport default function detectOverflow(state, options) {\n if (options === void 0) {\n options = {};\n }\n\n var _options = options,\n _options$placement = _options.placement,\n placement = _options$placement === void 0 ? state.placement : _options$placement,\n _options$strategy = _options.strategy,\n strategy = _options$strategy === void 0 ? state.strategy : _options$strategy,\n _options$boundary = _options.boundary,\n boundary = _options$boundary === void 0 ? clippingParents : _options$boundary,\n _options$rootBoundary = _options.rootBoundary,\n rootBoundary = _options$rootBoundary === void 0 ? viewport : _options$rootBoundary,\n _options$elementConte = _options.elementContext,\n elementContext = _options$elementConte === void 0 ? popper : _options$elementConte,\n _options$altBoundary = _options.altBoundary,\n altBoundary = _options$altBoundary === void 0 ? false : _options$altBoundary,\n _options$padding = _options.padding,\n padding = _options$padding === void 0 ? 0 : _options$padding;\n var paddingObject = mergePaddingObject(typeof padding !== 'number' ? padding : expandToHashMap(padding, basePlacements));\n var altContext = elementContext === popper ? reference : popper;\n var popperRect = state.rects.popper;\n var element = state.elements[altBoundary ? altContext : elementContext];\n var clippingClientRect = getClippingRect(isElement(element) ? element : element.contextElement || getDocumentElement(state.elements.popper), boundary, rootBoundary, strategy);\n var referenceClientRect = getBoundingClientRect(state.elements.reference);\n var popperOffsets = computeOffsets({\n reference: referenceClientRect,\n element: popperRect,\n strategy: 'absolute',\n placement: placement\n });\n var popperClientRect = rectToClientRect(Object.assign({}, popperRect, popperOffsets));\n var elementClientRect = elementContext === popper ? popperClientRect : referenceClientRect; // positive = overflowing the clipping rect\n // 0 or negative = within the clipping rect\n\n var overflowOffsets = {\n top: clippingClientRect.top - elementClientRect.top + paddingObject.top,\n bottom: elementClientRect.bottom - clippingClientRect.bottom + paddingObject.bottom,\n left: clippingClientRect.left - elementClientRect.left + paddingObject.left,\n right: elementClientRect.right - clippingClientRect.right + paddingObject.right\n };\n var offsetData = state.modifiersData.offset; // Offsets can be applied only to the popper element\n\n if (elementContext === popper && offsetData) {\n var offset = offsetData[placement];\n Object.keys(overflowOffsets).forEach(function (key) {\n var multiply = [right, bottom].indexOf(key) >= 0 ? 1 : -1;\n var axis = [top, bottom].indexOf(key) >= 0 ? 'y' : 'x';\n overflowOffsets[key] += offset[axis] * multiply;\n });\n }\n\n return overflowOffsets;\n}","import getOppositePlacement from \"../utils/getOppositePlacement.js\";\nimport getBasePlacement from \"../utils/getBasePlacement.js\";\nimport getOppositeVariationPlacement from \"../utils/getOppositeVariationPlacement.js\";\nimport detectOverflow from \"../utils/detectOverflow.js\";\nimport computeAutoPlacement from \"../utils/computeAutoPlacement.js\";\nimport { bottom, top, start, right, left, auto } from \"../enums.js\";\nimport getVariation from \"../utils/getVariation.js\"; // eslint-disable-next-line import/no-unused-modules\n\nfunction getExpandedFallbackPlacements(placement) {\n if (getBasePlacement(placement) === auto) {\n return [];\n }\n\n var oppositePlacement = getOppositePlacement(placement);\n return [getOppositeVariationPlacement(placement), oppositePlacement, getOppositeVariationPlacement(oppositePlacement)];\n}\n\nfunction flip(_ref) {\n var state = _ref.state,\n options = _ref.options,\n name = _ref.name;\n\n if (state.modifiersData[name]._skip) {\n return;\n }\n\n var _options$mainAxis = options.mainAxis,\n checkMainAxis = _options$mainAxis === void 0 ? true : _options$mainAxis,\n _options$altAxis = options.altAxis,\n checkAltAxis = _options$altAxis === void 0 ? true : _options$altAxis,\n specifiedFallbackPlacements = options.fallbackPlacements,\n padding = options.padding,\n boundary = options.boundary,\n rootBoundary = options.rootBoundary,\n altBoundary = options.altBoundary,\n _options$flipVariatio = options.flipVariations,\n flipVariations = _options$flipVariatio === void 0 ? true : _options$flipVariatio,\n allowedAutoPlacements = options.allowedAutoPlacements;\n var preferredPlacement = state.options.placement;\n var basePlacement = getBasePlacement(preferredPlacement);\n var isBasePlacement = basePlacement === preferredPlacement;\n var fallbackPlacements = specifiedFallbackPlacements || (isBasePlacement || !flipVariations ? [getOppositePlacement(preferredPlacement)] : getExpandedFallbackPlacements(preferredPlacement));\n var placements = [preferredPlacement].concat(fallbackPlacements).reduce(function (acc, placement) {\n return acc.concat(getBasePlacement(placement) === auto ? computeAutoPlacement(state, {\n placement: placement,\n boundary: boundary,\n rootBoundary: rootBoundary,\n padding: padding,\n flipVariations: flipVariations,\n allowedAutoPlacements: allowedAutoPlacements\n }) : placement);\n }, []);\n var referenceRect = state.rects.reference;\n var popperRect = state.rects.popper;\n var checksMap = new Map();\n var makeFallbackChecks = true;\n var firstFittingPlacement = placements[0];\n\n for (var i = 0; i < placements.length; i++) {\n var placement = placements[i];\n\n var _basePlacement = getBasePlacement(placement);\n\n var isStartVariation = getVariation(placement) === start;\n var isVertical = [top, bottom].indexOf(_basePlacement) >= 0;\n var len = isVertical ? 'width' : 'height';\n var overflow = detectOverflow(state, {\n placement: placement,\n boundary: boundary,\n rootBoundary: rootBoundary,\n altBoundary: altBoundary,\n padding: padding\n });\n var mainVariationSide = isVertical ? isStartVariation ? right : left : isStartVariation ? bottom : top;\n\n if (referenceRect[len] > popperRect[len]) {\n mainVariationSide = getOppositePlacement(mainVariationSide);\n }\n\n var altVariationSide = getOppositePlacement(mainVariationSide);\n var checks = [];\n\n if (checkMainAxis) {\n checks.push(overflow[_basePlacement] <= 0);\n }\n\n if (checkAltAxis) {\n checks.push(overflow[mainVariationSide] <= 0, overflow[altVariationSide] <= 0);\n }\n\n if (checks.every(function (check) {\n return check;\n })) {\n firstFittingPlacement = placement;\n makeFallbackChecks = false;\n break;\n }\n\n checksMap.set(placement, checks);\n }\n\n if (makeFallbackChecks) {\n // `2` may be desired in some cases – research later\n var numberOfChecks = flipVariations ? 3 : 1;\n\n var _loop = function _loop(_i) {\n var fittingPlacement = placements.find(function (placement) {\n var checks = checksMap.get(placement);\n\n if (checks) {\n return checks.slice(0, _i).every(function (check) {\n return check;\n });\n }\n });\n\n if (fittingPlacement) {\n firstFittingPlacement = fittingPlacement;\n return \"break\";\n }\n };\n\n for (var _i = numberOfChecks; _i > 0; _i--) {\n var _ret = _loop(_i);\n\n if (_ret === \"break\") break;\n }\n }\n\n if (state.placement !== firstFittingPlacement) {\n state.modifiersData[name]._skip = true;\n state.placement = firstFittingPlacement;\n state.reset = true;\n }\n} // eslint-disable-next-line import/no-unused-modules\n\n\nexport default {\n name: 'flip',\n enabled: true,\n phase: 'main',\n fn: flip,\n requiresIfExists: ['offset'],\n data: {\n _skip: false\n }\n};","import getVariation from \"./getVariation.js\";\nimport { variationPlacements, basePlacements, placements as allPlacements } from \"../enums.js\";\nimport detectOverflow from \"./detectOverflow.js\";\nimport getBasePlacement from \"./getBasePlacement.js\";\nexport default function computeAutoPlacement(state, options) {\n if (options === void 0) {\n options = {};\n }\n\n var _options = options,\n placement = _options.placement,\n boundary = _options.boundary,\n rootBoundary = _options.rootBoundary,\n padding = _options.padding,\n flipVariations = _options.flipVariations,\n _options$allowedAutoP = _options.allowedAutoPlacements,\n allowedAutoPlacements = _options$allowedAutoP === void 0 ? allPlacements : _options$allowedAutoP;\n var variation = getVariation(placement);\n var placements = variation ? flipVariations ? variationPlacements : variationPlacements.filter(function (placement) {\n return getVariation(placement) === variation;\n }) : basePlacements;\n var allowedPlacements = placements.filter(function (placement) {\n return allowedAutoPlacements.indexOf(placement) >= 0;\n });\n\n if (allowedPlacements.length === 0) {\n allowedPlacements = placements;\n } // $FlowFixMe[incompatible-type]: Flow seems to have problems with two array unions...\n\n\n var overflows = allowedPlacements.reduce(function (acc, placement) {\n acc[placement] = detectOverflow(state, {\n placement: placement,\n boundary: boundary,\n rootBoundary: rootBoundary,\n padding: padding\n })[getBasePlacement(placement)];\n return acc;\n }, {});\n return Object.keys(overflows).sort(function (a, b) {\n return overflows[a] - overflows[b];\n });\n}","import { top, bottom, left, right } from \"../enums.js\";\nimport detectOverflow from \"../utils/detectOverflow.js\";\n\nfunction getSideOffsets(overflow, rect, preventedOffsets) {\n if (preventedOffsets === void 0) {\n preventedOffsets = {\n x: 0,\n y: 0\n };\n }\n\n return {\n top: overflow.top - rect.height - preventedOffsets.y,\n right: overflow.right - rect.width + preventedOffsets.x,\n bottom: overflow.bottom - rect.height + preventedOffsets.y,\n left: overflow.left - rect.width - preventedOffsets.x\n };\n}\n\nfunction isAnySideFullyClipped(overflow) {\n return [top, right, bottom, left].some(function (side) {\n return overflow[side] >= 0;\n });\n}\n\nfunction hide(_ref) {\n var state = _ref.state,\n name = _ref.name;\n var referenceRect = state.rects.reference;\n var popperRect = state.rects.popper;\n var preventedOffsets = state.modifiersData.preventOverflow;\n var referenceOverflow = detectOverflow(state, {\n elementContext: 'reference'\n });\n var popperAltOverflow = detectOverflow(state, {\n altBoundary: true\n });\n var referenceClippingOffsets = getSideOffsets(referenceOverflow, referenceRect);\n var popperEscapeOffsets = getSideOffsets(popperAltOverflow, popperRect, preventedOffsets);\n var isReferenceHidden = isAnySideFullyClipped(referenceClippingOffsets);\n var hasPopperEscaped = isAnySideFullyClipped(popperEscapeOffsets);\n state.modifiersData[name] = {\n referenceClippingOffsets: referenceClippingOffsets,\n popperEscapeOffsets: popperEscapeOffsets,\n isReferenceHidden: isReferenceHidden,\n hasPopperEscaped: hasPopperEscaped\n };\n state.attributes.popper = Object.assign({}, state.attributes.popper, {\n 'data-popper-reference-hidden': isReferenceHidden,\n 'data-popper-escaped': hasPopperEscaped\n });\n} // eslint-disable-next-line import/no-unused-modules\n\n\nexport default {\n name: 'hide',\n enabled: true,\n phase: 'main',\n requiresIfExists: ['preventOverflow'],\n fn: hide\n};","import getBasePlacement from \"../utils/getBasePlacement.js\";\nimport { top, left, right, placements } from \"../enums.js\"; // eslint-disable-next-line import/no-unused-modules\n\nexport function distanceAndSkiddingToXY(placement, rects, offset) {\n var basePlacement = getBasePlacement(placement);\n var invertDistance = [left, top].indexOf(basePlacement) >= 0 ? -1 : 1;\n\n var _ref = typeof offset === 'function' ? offset(Object.assign({}, rects, {\n placement: placement\n })) : offset,\n skidding = _ref[0],\n distance = _ref[1];\n\n skidding = skidding || 0;\n distance = (distance || 0) * invertDistance;\n return [left, right].indexOf(basePlacement) >= 0 ? {\n x: distance,\n y: skidding\n } : {\n x: skidding,\n y: distance\n };\n}\n\nfunction offset(_ref2) {\n var state = _ref2.state,\n options = _ref2.options,\n name = _ref2.name;\n var _options$offset = options.offset,\n offset = _options$offset === void 0 ? [0, 0] : _options$offset;\n var data = placements.reduce(function (acc, placement) {\n acc[placement] = distanceAndSkiddingToXY(placement, state.rects, offset);\n return acc;\n }, {});\n var _data$state$placement = data[state.placement],\n x = _data$state$placement.x,\n y = _data$state$placement.y;\n\n if (state.modifiersData.popperOffsets != null) {\n state.modifiersData.popperOffsets.x += x;\n state.modifiersData.popperOffsets.y += y;\n }\n\n state.modifiersData[name] = data;\n} // eslint-disable-next-line import/no-unused-modules\n\n\nexport default {\n name: 'offset',\n enabled: true,\n phase: 'main',\n requires: ['popperOffsets'],\n fn: offset\n};","import computeOffsets from \"../utils/computeOffsets.js\";\n\nfunction popperOffsets(_ref) {\n var state = _ref.state,\n name = _ref.name;\n // Offsets are the actual position the popper needs to have to be\n // properly positioned near its reference element\n // This is the most basic placement, and will be adjusted by\n // the modifiers in the next step\n state.modifiersData[name] = computeOffsets({\n reference: state.rects.reference,\n element: state.rects.popper,\n strategy: 'absolute',\n placement: state.placement\n });\n} // eslint-disable-next-line import/no-unused-modules\n\n\nexport default {\n name: 'popperOffsets',\n enabled: true,\n phase: 'read',\n fn: popperOffsets,\n data: {}\n};","import { top, left, right, bottom, start } from \"../enums.js\";\nimport getBasePlacement from \"../utils/getBasePlacement.js\";\nimport getMainAxisFromPlacement from \"../utils/getMainAxisFromPlacement.js\";\nimport getAltAxis from \"../utils/getAltAxis.js\";\nimport { within, withinMaxClamp } from \"../utils/within.js\";\nimport getLayoutRect from \"../dom-utils/getLayoutRect.js\";\nimport getOffsetParent from \"../dom-utils/getOffsetParent.js\";\nimport detectOverflow from \"../utils/detectOverflow.js\";\nimport getVariation from \"../utils/getVariation.js\";\nimport getFreshSideObject from \"../utils/getFreshSideObject.js\";\nimport { min as mathMin, max as mathMax } from \"../utils/math.js\";\n\nfunction preventOverflow(_ref) {\n var state = _ref.state,\n options = _ref.options,\n name = _ref.name;\n var _options$mainAxis = options.mainAxis,\n checkMainAxis = _options$mainAxis === void 0 ? true : _options$mainAxis,\n _options$altAxis = options.altAxis,\n checkAltAxis = _options$altAxis === void 0 ? false : _options$altAxis,\n boundary = options.boundary,\n rootBoundary = options.rootBoundary,\n altBoundary = options.altBoundary,\n padding = options.padding,\n _options$tether = options.tether,\n tether = _options$tether === void 0 ? true : _options$tether,\n _options$tetherOffset = options.tetherOffset,\n tetherOffset = _options$tetherOffset === void 0 ? 0 : _options$tetherOffset;\n var overflow = detectOverflow(state, {\n boundary: boundary,\n rootBoundary: rootBoundary,\n padding: padding,\n altBoundary: altBoundary\n });\n var basePlacement = getBasePlacement(state.placement);\n var variation = getVariation(state.placement);\n var isBasePlacement = !variation;\n var mainAxis = getMainAxisFromPlacement(basePlacement);\n var altAxis = getAltAxis(mainAxis);\n var popperOffsets = state.modifiersData.popperOffsets;\n var referenceRect = state.rects.reference;\n var popperRect = state.rects.popper;\n var tetherOffsetValue = typeof tetherOffset === 'function' ? tetherOffset(Object.assign({}, state.rects, {\n placement: state.placement\n })) : tetherOffset;\n var normalizedTetherOffsetValue = typeof tetherOffsetValue === 'number' ? {\n mainAxis: tetherOffsetValue,\n altAxis: tetherOffsetValue\n } : Object.assign({\n mainAxis: 0,\n altAxis: 0\n }, tetherOffsetValue);\n var offsetModifierState = state.modifiersData.offset ? state.modifiersData.offset[state.placement] : null;\n var data = {\n x: 0,\n y: 0\n };\n\n if (!popperOffsets) {\n return;\n }\n\n if (checkMainAxis) {\n var _offsetModifierState$;\n\n var mainSide = mainAxis === 'y' ? top : left;\n var altSide = mainAxis === 'y' ? bottom : right;\n var len = mainAxis === 'y' ? 'height' : 'width';\n var offset = popperOffsets[mainAxis];\n var min = offset + overflow[mainSide];\n var max = offset - overflow[altSide];\n var additive = tether ? -popperRect[len] / 2 : 0;\n var minLen = variation === start ? referenceRect[len] : popperRect[len];\n var maxLen = variation === start ? -popperRect[len] : -referenceRect[len]; // We need to include the arrow in the calculation so the arrow doesn't go\n // outside the reference bounds\n\n var arrowElement = state.elements.arrow;\n var arrowRect = tether && arrowElement ? getLayoutRect(arrowElement) : {\n width: 0,\n height: 0\n };\n var arrowPaddingObject = state.modifiersData['arrow#persistent'] ? state.modifiersData['arrow#persistent'].padding : getFreshSideObject();\n var arrowPaddingMin = arrowPaddingObject[mainSide];\n var arrowPaddingMax = arrowPaddingObject[altSide]; // If the reference length is smaller than the arrow length, we don't want\n // to include its full size in the calculation. If the reference is small\n // and near the edge of a boundary, the popper can overflow even if the\n // reference is not overflowing as well (e.g. virtual elements with no\n // width or height)\n\n var arrowLen = within(0, referenceRect[len], arrowRect[len]);\n var minOffset = isBasePlacement ? referenceRect[len] / 2 - additive - arrowLen - arrowPaddingMin - normalizedTetherOffsetValue.mainAxis : minLen - arrowLen - arrowPaddingMin - normalizedTetherOffsetValue.mainAxis;\n var maxOffset = isBasePlacement ? -referenceRect[len] / 2 + additive + arrowLen + arrowPaddingMax + normalizedTetherOffsetValue.mainAxis : maxLen + arrowLen + arrowPaddingMax + normalizedTetherOffsetValue.mainAxis;\n var arrowOffsetParent = state.elements.arrow && getOffsetParent(state.elements.arrow);\n var clientOffset = arrowOffsetParent ? mainAxis === 'y' ? arrowOffsetParent.clientTop || 0 : arrowOffsetParent.clientLeft || 0 : 0;\n var offsetModifierValue = (_offsetModifierState$ = offsetModifierState == null ? void 0 : offsetModifierState[mainAxis]) != null ? _offsetModifierState$ : 0;\n var tetherMin = offset + minOffset - offsetModifierValue - clientOffset;\n var tetherMax = offset + maxOffset - offsetModifierValue;\n var preventedOffset = within(tether ? mathMin(min, tetherMin) : min, offset, tether ? mathMax(max, tetherMax) : max);\n popperOffsets[mainAxis] = preventedOffset;\n data[mainAxis] = preventedOffset - offset;\n }\n\n if (checkAltAxis) {\n var _offsetModifierState$2;\n\n var _mainSide = mainAxis === 'x' ? top : left;\n\n var _altSide = mainAxis === 'x' ? bottom : right;\n\n var _offset = popperOffsets[altAxis];\n\n var _len = altAxis === 'y' ? 'height' : 'width';\n\n var _min = _offset + overflow[_mainSide];\n\n var _max = _offset - overflow[_altSide];\n\n var isOriginSide = [top, left].indexOf(basePlacement) !== -1;\n\n var _offsetModifierValue = (_offsetModifierState$2 = offsetModifierState == null ? void 0 : offsetModifierState[altAxis]) != null ? _offsetModifierState$2 : 0;\n\n var _tetherMin = isOriginSide ? _min : _offset - referenceRect[_len] - popperRect[_len] - _offsetModifierValue + normalizedTetherOffsetValue.altAxis;\n\n var _tetherMax = isOriginSide ? _offset + referenceRect[_len] + popperRect[_len] - _offsetModifierValue - normalizedTetherOffsetValue.altAxis : _max;\n\n var _preventedOffset = tether && isOriginSide ? withinMaxClamp(_tetherMin, _offset, _tetherMax) : within(tether ? _tetherMin : _min, _offset, tether ? _tetherMax : _max);\n\n popperOffsets[altAxis] = _preventedOffset;\n data[altAxis] = _preventedOffset - _offset;\n }\n\n state.modifiersData[name] = data;\n} // eslint-disable-next-line import/no-unused-modules\n\n\nexport default {\n name: 'preventOverflow',\n enabled: true,\n phase: 'main',\n fn: preventOverflow,\n requiresIfExists: ['offset']\n};","export default function getAltAxis(axis) {\n return axis === 'x' ? 'y' : 'x';\n}","import getBoundingClientRect from \"./getBoundingClientRect.js\";\nimport getNodeScroll from \"./getNodeScroll.js\";\nimport getNodeName from \"./getNodeName.js\";\nimport { isHTMLElement } from \"./instanceOf.js\";\nimport getWindowScrollBarX from \"./getWindowScrollBarX.js\";\nimport getDocumentElement from \"./getDocumentElement.js\";\nimport isScrollParent from \"./isScrollParent.js\";\nimport { round } from \"../utils/math.js\";\n\nfunction isElementScaled(element) {\n var rect = element.getBoundingClientRect();\n var scaleX = round(rect.width) / element.offsetWidth || 1;\n var scaleY = round(rect.height) / element.offsetHeight || 1;\n return scaleX !== 1 || scaleY !== 1;\n} // Returns the composite rect of an element relative to its offsetParent.\n// Composite means it takes into account transforms as well as layout.\n\n\nexport default function getCompositeRect(elementOrVirtualElement, offsetParent, isFixed) {\n if (isFixed === void 0) {\n isFixed = false;\n }\n\n var isOffsetParentAnElement = isHTMLElement(offsetParent);\n var offsetParentIsScaled = isHTMLElement(offsetParent) && isElementScaled(offsetParent);\n var documentElement = getDocumentElement(offsetParent);\n var rect = getBoundingClientRect(elementOrVirtualElement, offsetParentIsScaled, isFixed);\n var scroll = {\n scrollLeft: 0,\n scrollTop: 0\n };\n var offsets = {\n x: 0,\n y: 0\n };\n\n if (isOffsetParentAnElement || !isOffsetParentAnElement && !isFixed) {\n if (getNodeName(offsetParent) !== 'body' || // https://github.com/popperjs/popper-core/issues/1078\n isScrollParent(documentElement)) {\n scroll = getNodeScroll(offsetParent);\n }\n\n if (isHTMLElement(offsetParent)) {\n offsets = getBoundingClientRect(offsetParent, true);\n offsets.x += offsetParent.clientLeft;\n offsets.y += offsetParent.clientTop;\n } else if (documentElement) {\n offsets.x = getWindowScrollBarX(documentElement);\n }\n }\n\n return {\n x: rect.left + scroll.scrollLeft - offsets.x,\n y: rect.top + scroll.scrollTop - offsets.y,\n width: rect.width,\n height: rect.height\n };\n}","import getWindowScroll from \"./getWindowScroll.js\";\nimport getWindow from \"./getWindow.js\";\nimport { isHTMLElement } from \"./instanceOf.js\";\nimport getHTMLElementScroll from \"./getHTMLElementScroll.js\";\nexport default function getNodeScroll(node) {\n if (node === getWindow(node) || !isHTMLElement(node)) {\n return getWindowScroll(node);\n } else {\n return getHTMLElementScroll(node);\n }\n}","export default function getHTMLElementScroll(element) {\n return {\n scrollLeft: element.scrollLeft,\n scrollTop: element.scrollTop\n };\n}","import { modifierPhases } from \"../enums.js\"; // source: https://stackoverflow.com/questions/49875255\n\nfunction order(modifiers) {\n var map = new Map();\n var visited = new Set();\n var result = [];\n modifiers.forEach(function (modifier) {\n map.set(modifier.name, modifier);\n }); // On visiting object, check for its dependencies and visit them recursively\n\n function sort(modifier) {\n visited.add(modifier.name);\n var requires = [].concat(modifier.requires || [], modifier.requiresIfExists || []);\n requires.forEach(function (dep) {\n if (!visited.has(dep)) {\n var depModifier = map.get(dep);\n\n if (depModifier) {\n sort(depModifier);\n }\n }\n });\n result.push(modifier);\n }\n\n modifiers.forEach(function (modifier) {\n if (!visited.has(modifier.name)) {\n // check for visited object\n sort(modifier);\n }\n });\n return result;\n}\n\nexport default function orderModifiers(modifiers) {\n // order based on dependencies\n var orderedModifiers = order(modifiers); // order based on phase\n\n return modifierPhases.reduce(function (acc, phase) {\n return acc.concat(orderedModifiers.filter(function (modifier) {\n return modifier.phase === phase;\n }));\n }, []);\n}","import getCompositeRect from \"./dom-utils/getCompositeRect.js\";\nimport getLayoutRect from \"./dom-utils/getLayoutRect.js\";\nimport listScrollParents from \"./dom-utils/listScrollParents.js\";\nimport getOffsetParent from \"./dom-utils/getOffsetParent.js\";\nimport orderModifiers from \"./utils/orderModifiers.js\";\nimport debounce from \"./utils/debounce.js\";\nimport mergeByName from \"./utils/mergeByName.js\";\nimport detectOverflow from \"./utils/detectOverflow.js\";\nimport { isElement } from \"./dom-utils/instanceOf.js\";\nvar DEFAULT_OPTIONS = {\n placement: 'bottom',\n modifiers: [],\n strategy: 'absolute'\n};\n\nfunction areValidElements() {\n for (var _len = arguments.length, args = new Array(_len), _key = 0; _key < _len; _key++) {\n args[_key] = arguments[_key];\n }\n\n return !args.some(function (element) {\n return !(element && typeof element.getBoundingClientRect === 'function');\n });\n}\n\nexport function popperGenerator(generatorOptions) {\n if (generatorOptions === void 0) {\n generatorOptions = {};\n }\n\n var _generatorOptions = generatorOptions,\n _generatorOptions$def = _generatorOptions.defaultModifiers,\n defaultModifiers = _generatorOptions$def === void 0 ? [] : _generatorOptions$def,\n _generatorOptions$def2 = _generatorOptions.defaultOptions,\n defaultOptions = _generatorOptions$def2 === void 0 ? DEFAULT_OPTIONS : _generatorOptions$def2;\n return function createPopper(reference, popper, options) {\n if (options === void 0) {\n options = defaultOptions;\n }\n\n var state = {\n placement: 'bottom',\n orderedModifiers: [],\n options: Object.assign({}, DEFAULT_OPTIONS, defaultOptions),\n modifiersData: {},\n elements: {\n reference: reference,\n popper: popper\n },\n attributes: {},\n styles: {}\n };\n var effectCleanupFns = [];\n var isDestroyed = false;\n var instance = {\n state: state,\n setOptions: function setOptions(setOptionsAction) {\n var options = typeof setOptionsAction === 'function' ? setOptionsAction(state.options) : setOptionsAction;\n cleanupModifierEffects();\n state.options = Object.assign({}, defaultOptions, state.options, options);\n state.scrollParents = {\n reference: isElement(reference) ? listScrollParents(reference) : reference.contextElement ? listScrollParents(reference.contextElement) : [],\n popper: listScrollParents(popper)\n }; // Orders the modifiers based on their dependencies and `phase`\n // properties\n\n var orderedModifiers = orderModifiers(mergeByName([].concat(defaultModifiers, state.options.modifiers))); // Strip out disabled modifiers\n\n state.orderedModifiers = orderedModifiers.filter(function (m) {\n return m.enabled;\n });\n runModifierEffects();\n return instance.update();\n },\n // Sync update – it will always be executed, even if not necessary. This\n // is useful for low frequency updates where sync behavior simplifies the\n // logic.\n // For high frequency updates (e.g. `resize` and `scroll` events), always\n // prefer the async Popper#update method\n forceUpdate: function forceUpdate() {\n if (isDestroyed) {\n return;\n }\n\n var _state$elements = state.elements,\n reference = _state$elements.reference,\n popper = _state$elements.popper; // Don't proceed if `reference` or `popper` are not valid elements\n // anymore\n\n if (!areValidElements(reference, popper)) {\n return;\n } // Store the reference and popper rects to be read by modifiers\n\n\n state.rects = {\n reference: getCompositeRect(reference, getOffsetParent(popper), state.options.strategy === 'fixed'),\n popper: getLayoutRect(popper)\n }; // Modifiers have the ability to reset the current update cycle. The\n // most common use case for this is the `flip` modifier changing the\n // placement, which then needs to re-run all the modifiers, because the\n // logic was previously ran for the previous placement and is therefore\n // stale/incorrect\n\n state.reset = false;\n state.placement = state.options.placement; // On each update cycle, the `modifiersData` property for each modifier\n // is filled with the initial data specified by the modifier. This means\n // it doesn't persist and is fresh on each update.\n // To ensure persistent data, use `${name}#persistent`\n\n state.orderedModifiers.forEach(function (modifier) {\n return state.modifiersData[modifier.name] = Object.assign({}, modifier.data);\n });\n\n for (var index = 0; index < state.orderedModifiers.length; index++) {\n if (state.reset === true) {\n state.reset = false;\n index = -1;\n continue;\n }\n\n var _state$orderedModifie = state.orderedModifiers[index],\n fn = _state$orderedModifie.fn,\n _state$orderedModifie2 = _state$orderedModifie.options,\n _options = _state$orderedModifie2 === void 0 ? {} : _state$orderedModifie2,\n name = _state$orderedModifie.name;\n\n if (typeof fn === 'function') {\n state = fn({\n state: state,\n options: _options,\n name: name,\n instance: instance\n }) || state;\n }\n }\n },\n // Async and optimistically optimized update – it will not be executed if\n // not necessary (debounced to run at most once-per-tick)\n update: debounce(function () {\n return new Promise(function (resolve) {\n instance.forceUpdate();\n resolve(state);\n });\n }),\n destroy: function destroy() {\n cleanupModifierEffects();\n isDestroyed = true;\n }\n };\n\n if (!areValidElements(reference, popper)) {\n return instance;\n }\n\n instance.setOptions(options).then(function (state) {\n if (!isDestroyed && options.onFirstUpdate) {\n options.onFirstUpdate(state);\n }\n }); // Modifiers have the ability to execute arbitrary code before the first\n // update cycle runs. They will be executed in the same order as the update\n // cycle. This is useful when a modifier adds some persistent data that\n // other modifiers need to use, but the modifier is run after the dependent\n // one.\n\n function runModifierEffects() {\n state.orderedModifiers.forEach(function (_ref) {\n var name = _ref.name,\n _ref$options = _ref.options,\n options = _ref$options === void 0 ? {} : _ref$options,\n effect = _ref.effect;\n\n if (typeof effect === 'function') {\n var cleanupFn = effect({\n state: state,\n name: name,\n instance: instance,\n options: options\n });\n\n var noopFn = function noopFn() {};\n\n effectCleanupFns.push(cleanupFn || noopFn);\n }\n });\n }\n\n function cleanupModifierEffects() {\n effectCleanupFns.forEach(function (fn) {\n return fn();\n });\n effectCleanupFns = [];\n }\n\n return instance;\n };\n}\nexport var createPopper = /*#__PURE__*/popperGenerator(); // eslint-disable-next-line import/no-unused-modules\n\nexport { detectOverflow };","export default function debounce(fn) {\n var pending;\n return function () {\n if (!pending) {\n pending = new Promise(function (resolve) {\n Promise.resolve().then(function () {\n pending = undefined;\n resolve(fn());\n });\n });\n }\n\n return pending;\n };\n}","export default function mergeByName(modifiers) {\n var merged = modifiers.reduce(function (merged, current) {\n var existing = merged[current.name];\n merged[current.name] = existing ? Object.assign({}, existing, current, {\n options: Object.assign({}, existing.options, current.options),\n data: Object.assign({}, existing.data, current.data)\n }) : current;\n return merged;\n }, {}); // IE11 does not support Object.values\n\n return Object.keys(merged).map(function (key) {\n return merged[key];\n });\n}","import { popperGenerator, detectOverflow } from \"./createPopper.js\";\nimport eventListeners from \"./modifiers/eventListeners.js\";\nimport popperOffsets from \"./modifiers/popperOffsets.js\";\nimport computeStyles from \"./modifiers/computeStyles.js\";\nimport applyStyles from \"./modifiers/applyStyles.js\";\nimport offset from \"./modifiers/offset.js\";\nimport flip from \"./modifiers/flip.js\";\nimport preventOverflow from \"./modifiers/preventOverflow.js\";\nimport arrow from \"./modifiers/arrow.js\";\nimport hide from \"./modifiers/hide.js\";\nvar defaultModifiers = [eventListeners, popperOffsets, computeStyles, applyStyles, offset, flip, preventOverflow, arrow, hide];\nvar createPopper = /*#__PURE__*/popperGenerator({\n defaultModifiers: defaultModifiers\n}); // eslint-disable-next-line import/no-unused-modules\n\nexport { createPopper, popperGenerator, defaultModifiers, detectOverflow }; // eslint-disable-next-line import/no-unused-modules\n\nexport { createPopper as createPopperLite } from \"./popper-lite.js\"; // eslint-disable-next-line import/no-unused-modules\n\nexport * from \"./modifiers/index.js\";","import { popperGenerator, detectOverflow } from \"./createPopper.js\";\nimport eventListeners from \"./modifiers/eventListeners.js\";\nimport popperOffsets from \"./modifiers/popperOffsets.js\";\nimport computeStyles from \"./modifiers/computeStyles.js\";\nimport applyStyles from \"./modifiers/applyStyles.js\";\nvar defaultModifiers = [eventListeners, popperOffsets, computeStyles, applyStyles];\nvar createPopper = /*#__PURE__*/popperGenerator({\n defaultModifiers: defaultModifiers\n}); // eslint-disable-next-line import/no-unused-modules\n\nexport { createPopper, popperGenerator, defaultModifiers, detectOverflow };","/*!\n * Bootstrap v5.3.3 (https://getbootstrap.com/)\n * Copyright 2011-2024 The Bootstrap Authors (https://github.com/twbs/bootstrap/graphs/contributors)\n * Licensed under MIT (https://github.com/twbs/bootstrap/blob/main/LICENSE)\n */\nimport * as Popper from '@popperjs/core';\n\n/**\n * --------------------------------------------------------------------------\n * Bootstrap dom/data.js\n * Licensed under MIT (https://github.com/twbs/bootstrap/blob/main/LICENSE)\n * --------------------------------------------------------------------------\n */\n\n/**\n * Constants\n */\n\nconst elementMap = new Map();\nconst Data = {\n set(element, key, instance) {\n if (!elementMap.has(element)) {\n elementMap.set(element, new Map());\n }\n const instanceMap = elementMap.get(element);\n\n // make it clear we only want one instance per element\n // can be removed later when multiple key/instances are fine to be used\n if (!instanceMap.has(key) && instanceMap.size !== 0) {\n // eslint-disable-next-line no-console\n console.error(`Bootstrap doesn't allow more than one instance per element. Bound instance: ${Array.from(instanceMap.keys())[0]}.`);\n return;\n }\n instanceMap.set(key, instance);\n },\n get(element, key) {\n if (elementMap.has(element)) {\n return elementMap.get(element).get(key) || null;\n }\n return null;\n },\n remove(element, key) {\n if (!elementMap.has(element)) {\n return;\n }\n const instanceMap = elementMap.get(element);\n instanceMap.delete(key);\n\n // free up element references if there are no instances left for an element\n if (instanceMap.size === 0) {\n elementMap.delete(element);\n }\n }\n};\n\n/**\n * --------------------------------------------------------------------------\n * Bootstrap util/index.js\n * Licensed under MIT (https://github.com/twbs/bootstrap/blob/main/LICENSE)\n * --------------------------------------------------------------------------\n */\n\nconst MAX_UID = 1000000;\nconst MILLISECONDS_MULTIPLIER = 1000;\nconst TRANSITION_END = 'transitionend';\n\n/**\n * Properly escape IDs selectors to handle weird IDs\n * @param {string} selector\n * @returns {string}\n */\nconst parseSelector = selector => {\n if (selector && window.CSS && window.CSS.escape) {\n // document.querySelector needs escaping to handle IDs (html5+) containing for instance /\n selector = selector.replace(/#([^\\s\"#']+)/g, (match, id) => `#${CSS.escape(id)}`);\n }\n return selector;\n};\n\n// Shout-out Angus Croll (https://goo.gl/pxwQGp)\nconst toType = object => {\n if (object === null || object === undefined) {\n return `${object}`;\n }\n return Object.prototype.toString.call(object).match(/\\s([a-z]+)/i)[1].toLowerCase();\n};\n\n/**\n * Public Util API\n */\n\nconst getUID = prefix => {\n do {\n prefix += Math.floor(Math.random() * MAX_UID);\n } while (document.getElementById(prefix));\n return prefix;\n};\nconst getTransitionDurationFromElement = element => {\n if (!element) {\n return 0;\n }\n\n // Get transition-duration of the element\n let {\n transitionDuration,\n transitionDelay\n } = window.getComputedStyle(element);\n const floatTransitionDuration = Number.parseFloat(transitionDuration);\n const floatTransitionDelay = Number.parseFloat(transitionDelay);\n\n // Return 0 if element or transition duration is not found\n if (!floatTransitionDuration && !floatTransitionDelay) {\n return 0;\n }\n\n // If multiple durations are defined, take the first\n transitionDuration = transitionDuration.split(',')[0];\n transitionDelay = transitionDelay.split(',')[0];\n return (Number.parseFloat(transitionDuration) + Number.parseFloat(transitionDelay)) * MILLISECONDS_MULTIPLIER;\n};\nconst triggerTransitionEnd = element => {\n element.dispatchEvent(new Event(TRANSITION_END));\n};\nconst isElement = object => {\n if (!object || typeof object !== 'object') {\n return false;\n }\n if (typeof object.jquery !== 'undefined') {\n object = object[0];\n }\n return typeof object.nodeType !== 'undefined';\n};\nconst getElement = object => {\n // it's a jQuery object or a node element\n if (isElement(object)) {\n return object.jquery ? object[0] : object;\n }\n if (typeof object === 'string' && object.length > 0) {\n return document.querySelector(parseSelector(object));\n }\n return null;\n};\nconst isVisible = element => {\n if (!isElement(element) || element.getClientRects().length === 0) {\n return false;\n }\n const elementIsVisible = getComputedStyle(element).getPropertyValue('visibility') === 'visible';\n // Handle `details` element as its content may falsie appear visible when it is closed\n const closedDetails = element.closest('details:not([open])');\n if (!closedDetails) {\n return elementIsVisible;\n }\n if (closedDetails !== element) {\n const summary = element.closest('summary');\n if (summary && summary.parentNode !== closedDetails) {\n return false;\n }\n if (summary === null) {\n return false;\n }\n }\n return elementIsVisible;\n};\nconst isDisabled = element => {\n if (!element || element.nodeType !== Node.ELEMENT_NODE) {\n return true;\n }\n if (element.classList.contains('disabled')) {\n return true;\n }\n if (typeof element.disabled !== 'undefined') {\n return element.disabled;\n }\n return element.hasAttribute('disabled') && element.getAttribute('disabled') !== 'false';\n};\nconst findShadowRoot = element => {\n if (!document.documentElement.attachShadow) {\n return null;\n }\n\n // Can find the shadow root otherwise it'll return the document\n if (typeof element.getRootNode === 'function') {\n const root = element.getRootNode();\n return root instanceof ShadowRoot ? root : null;\n }\n if (element instanceof ShadowRoot) {\n return element;\n }\n\n // when we don't find a shadow root\n if (!element.parentNode) {\n return null;\n }\n return findShadowRoot(element.parentNode);\n};\nconst noop = () => {};\n\n/**\n * Trick to restart an element's animation\n *\n * @param {HTMLElement} element\n * @return void\n *\n * @see https://www.charistheo.io/blog/2021/02/restart-a-css-animation-with-javascript/#restarting-a-css-animation\n */\nconst reflow = element => {\n element.offsetHeight; // eslint-disable-line no-unused-expressions\n};\nconst getjQuery = () => {\n if (window.jQuery && !document.body.hasAttribute('data-bs-no-jquery')) {\n return window.jQuery;\n }\n return null;\n};\nconst DOMContentLoadedCallbacks = [];\nconst onDOMContentLoaded = callback => {\n if (document.readyState === 'loading') {\n // add listener on the first call when the document is in loading state\n if (!DOMContentLoadedCallbacks.length) {\n document.addEventListener('DOMContentLoaded', () => {\n for (const callback of DOMContentLoadedCallbacks) {\n callback();\n }\n });\n }\n DOMContentLoadedCallbacks.push(callback);\n } else {\n callback();\n }\n};\nconst isRTL = () => document.documentElement.dir === 'rtl';\nconst defineJQueryPlugin = plugin => {\n onDOMContentLoaded(() => {\n const $ = getjQuery();\n /* istanbul ignore if */\n if ($) {\n const name = plugin.NAME;\n const JQUERY_NO_CONFLICT = $.fn[name];\n $.fn[name] = plugin.jQueryInterface;\n $.fn[name].Constructor = plugin;\n $.fn[name].noConflict = () => {\n $.fn[name] = JQUERY_NO_CONFLICT;\n return plugin.jQueryInterface;\n };\n }\n });\n};\nconst execute = (possibleCallback, args = [], defaultValue = possibleCallback) => {\n return typeof possibleCallback === 'function' ? possibleCallback(...args) : defaultValue;\n};\nconst executeAfterTransition = (callback, transitionElement, waitForTransition = true) => {\n if (!waitForTransition) {\n execute(callback);\n return;\n }\n const durationPadding = 5;\n const emulatedDuration = getTransitionDurationFromElement(transitionElement) + durationPadding;\n let called = false;\n const handler = ({\n target\n }) => {\n if (target !== transitionElement) {\n return;\n }\n called = true;\n transitionElement.removeEventListener(TRANSITION_END, handler);\n execute(callback);\n };\n transitionElement.addEventListener(TRANSITION_END, handler);\n setTimeout(() => {\n if (!called) {\n triggerTransitionEnd(transitionElement);\n }\n }, emulatedDuration);\n};\n\n/**\n * Return the previous/next element of a list.\n *\n * @param {array} list The list of elements\n * @param activeElement The active element\n * @param shouldGetNext Choose to get next or previous element\n * @param isCycleAllowed\n * @return {Element|elem} The proper element\n */\nconst getNextActiveElement = (list, activeElement, shouldGetNext, isCycleAllowed) => {\n const listLength = list.length;\n let index = list.indexOf(activeElement);\n\n // if the element does not exist in the list return an element\n // depending on the direction and if cycle is allowed\n if (index === -1) {\n return !shouldGetNext && isCycleAllowed ? list[listLength - 1] : list[0];\n }\n index += shouldGetNext ? 1 : -1;\n if (isCycleAllowed) {\n index = (index + listLength) % listLength;\n }\n return list[Math.max(0, Math.min(index, listLength - 1))];\n};\n\n/**\n * --------------------------------------------------------------------------\n * Bootstrap dom/event-handler.js\n * Licensed under MIT (https://github.com/twbs/bootstrap/blob/main/LICENSE)\n * --------------------------------------------------------------------------\n */\n\n\n/**\n * Constants\n */\n\nconst namespaceRegex = /[^.]*(?=\\..*)\\.|.*/;\nconst stripNameRegex = /\\..*/;\nconst stripUidRegex = /::\\d+$/;\nconst eventRegistry = {}; // Events storage\nlet uidEvent = 1;\nconst customEvents = {\n mouseenter: 'mouseover',\n mouseleave: 'mouseout'\n};\nconst nativeEvents = new Set(['click', 'dblclick', 'mouseup', 'mousedown', 'contextmenu', 'mousewheel', 'DOMMouseScroll', 'mouseover', 'mouseout', 'mousemove', 'selectstart', 'selectend', 'keydown', 'keypress', 'keyup', 'orientationchange', 'touchstart', 'touchmove', 'touchend', 'touchcancel', 'pointerdown', 'pointermove', 'pointerup', 'pointerleave', 'pointercancel', 'gesturestart', 'gesturechange', 'gestureend', 'focus', 'blur', 'change', 'reset', 'select', 'submit', 'focusin', 'focusout', 'load', 'unload', 'beforeunload', 'resize', 'move', 'DOMContentLoaded', 'readystatechange', 'error', 'abort', 'scroll']);\n\n/**\n * Private methods\n */\n\nfunction makeEventUid(element, uid) {\n return uid && `${uid}::${uidEvent++}` || element.uidEvent || uidEvent++;\n}\nfunction getElementEvents(element) {\n const uid = makeEventUid(element);\n element.uidEvent = uid;\n eventRegistry[uid] = eventRegistry[uid] || {};\n return eventRegistry[uid];\n}\nfunction bootstrapHandler(element, fn) {\n return function handler(event) {\n hydrateObj(event, {\n delegateTarget: element\n });\n if (handler.oneOff) {\n EventHandler.off(element, event.type, fn);\n }\n return fn.apply(element, [event]);\n };\n}\nfunction bootstrapDelegationHandler(element, selector, fn) {\n return function handler(event) {\n const domElements = element.querySelectorAll(selector);\n for (let {\n target\n } = event; target && target !== this; target = target.parentNode) {\n for (const domElement of domElements) {\n if (domElement !== target) {\n continue;\n }\n hydrateObj(event, {\n delegateTarget: target\n });\n if (handler.oneOff) {\n EventHandler.off(element, event.type, selector, fn);\n }\n return fn.apply(target, [event]);\n }\n }\n };\n}\nfunction findHandler(events, callable, delegationSelector = null) {\n return Object.values(events).find(event => event.callable === callable && event.delegationSelector === delegationSelector);\n}\nfunction normalizeParameters(originalTypeEvent, handler, delegationFunction) {\n const isDelegated = typeof handler === 'string';\n // TODO: tooltip passes `false` instead of selector, so we need to check\n const callable = isDelegated ? delegationFunction : handler || delegationFunction;\n let typeEvent = getTypeEvent(originalTypeEvent);\n if (!nativeEvents.has(typeEvent)) {\n typeEvent = originalTypeEvent;\n }\n return [isDelegated, callable, typeEvent];\n}\nfunction addHandler(element, originalTypeEvent, handler, delegationFunction, oneOff) {\n if (typeof originalTypeEvent !== 'string' || !element) {\n return;\n }\n let [isDelegated, callable, typeEvent] = normalizeParameters(originalTypeEvent, handler, delegationFunction);\n\n // in case of mouseenter or mouseleave wrap the handler within a function that checks for its DOM position\n // this prevents the handler from being dispatched the same way as mouseover or mouseout does\n if (originalTypeEvent in customEvents) {\n const wrapFunction = fn => {\n return function (event) {\n if (!event.relatedTarget || event.relatedTarget !== event.delegateTarget && !event.delegateTarget.contains(event.relatedTarget)) {\n return fn.call(this, event);\n }\n };\n };\n callable = wrapFunction(callable);\n }\n const events = getElementEvents(element);\n const handlers = events[typeEvent] || (events[typeEvent] = {});\n const previousFunction = findHandler(handlers, callable, isDelegated ? handler : null);\n if (previousFunction) {\n previousFunction.oneOff = previousFunction.oneOff && oneOff;\n return;\n }\n const uid = makeEventUid(callable, originalTypeEvent.replace(namespaceRegex, ''));\n const fn = isDelegated ? bootstrapDelegationHandler(element, handler, callable) : bootstrapHandler(element, callable);\n fn.delegationSelector = isDelegated ? handler : null;\n fn.callable = callable;\n fn.oneOff = oneOff;\n fn.uidEvent = uid;\n handlers[uid] = fn;\n element.addEventListener(typeEvent, fn, isDelegated);\n}\nfunction removeHandler(element, events, typeEvent, handler, delegationSelector) {\n const fn = findHandler(events[typeEvent], handler, delegationSelector);\n if (!fn) {\n return;\n }\n element.removeEventListener(typeEvent, fn, Boolean(delegationSelector));\n delete events[typeEvent][fn.uidEvent];\n}\nfunction removeNamespacedHandlers(element, events, typeEvent, namespace) {\n const storeElementEvent = events[typeEvent] || {};\n for (const [handlerKey, event] of Object.entries(storeElementEvent)) {\n if (handlerKey.includes(namespace)) {\n removeHandler(element, events, typeEvent, event.callable, event.delegationSelector);\n }\n }\n}\nfunction getTypeEvent(event) {\n // allow to get the native events from namespaced events ('click.bs.button' --> 'click')\n event = event.replace(stripNameRegex, '');\n return customEvents[event] || event;\n}\nconst EventHandler = {\n on(element, event, handler, delegationFunction) {\n addHandler(element, event, handler, delegationFunction, false);\n },\n one(element, event, handler, delegationFunction) {\n addHandler(element, event, handler, delegationFunction, true);\n },\n off(element, originalTypeEvent, handler, delegationFunction) {\n if (typeof originalTypeEvent !== 'string' || !element) {\n return;\n }\n const [isDelegated, callable, typeEvent] = normalizeParameters(originalTypeEvent, handler, delegationFunction);\n const inNamespace = typeEvent !== originalTypeEvent;\n const events = getElementEvents(element);\n const storeElementEvent = events[typeEvent] || {};\n const isNamespace = originalTypeEvent.startsWith('.');\n if (typeof callable !== 'undefined') {\n // Simplest case: handler is passed, remove that listener ONLY.\n if (!Object.keys(storeElementEvent).length) {\n return;\n }\n removeHandler(element, events, typeEvent, callable, isDelegated ? handler : null);\n return;\n }\n if (isNamespace) {\n for (const elementEvent of Object.keys(events)) {\n removeNamespacedHandlers(element, events, elementEvent, originalTypeEvent.slice(1));\n }\n }\n for (const [keyHandlers, event] of Object.entries(storeElementEvent)) {\n const handlerKey = keyHandlers.replace(stripUidRegex, '');\n if (!inNamespace || originalTypeEvent.includes(handlerKey)) {\n removeHandler(element, events, typeEvent, event.callable, event.delegationSelector);\n }\n }\n },\n trigger(element, event, args) {\n if (typeof event !== 'string' || !element) {\n return null;\n }\n const $ = getjQuery();\n const typeEvent = getTypeEvent(event);\n const inNamespace = event !== typeEvent;\n let jQueryEvent = null;\n let bubbles = true;\n let nativeDispatch = true;\n let defaultPrevented = false;\n if (inNamespace && $) {\n jQueryEvent = $.Event(event, args);\n $(element).trigger(jQueryEvent);\n bubbles = !jQueryEvent.isPropagationStopped();\n nativeDispatch = !jQueryEvent.isImmediatePropagationStopped();\n defaultPrevented = jQueryEvent.isDefaultPrevented();\n }\n const evt = hydrateObj(new Event(event, {\n bubbles,\n cancelable: true\n }), args);\n if (defaultPrevented) {\n evt.preventDefault();\n }\n if (nativeDispatch) {\n element.dispatchEvent(evt);\n }\n if (evt.defaultPrevented && jQueryEvent) {\n jQueryEvent.preventDefault();\n }\n return evt;\n }\n};\nfunction hydrateObj(obj, meta = {}) {\n for (const [key, value] of Object.entries(meta)) {\n try {\n obj[key] = value;\n } catch (_unused) {\n Object.defineProperty(obj, key, {\n configurable: true,\n get() {\n return value;\n }\n });\n }\n }\n return obj;\n}\n\n/**\n * --------------------------------------------------------------------------\n * Bootstrap dom/manipulator.js\n * Licensed under MIT (https://github.com/twbs/bootstrap/blob/main/LICENSE)\n * --------------------------------------------------------------------------\n */\n\nfunction normalizeData(value) {\n if (value === 'true') {\n return true;\n }\n if (value === 'false') {\n return false;\n }\n if (value === Number(value).toString()) {\n return Number(value);\n }\n if (value === '' || value === 'null') {\n return null;\n }\n if (typeof value !== 'string') {\n return value;\n }\n try {\n return JSON.parse(decodeURIComponent(value));\n } catch (_unused) {\n return value;\n }\n}\nfunction normalizeDataKey(key) {\n return key.replace(/[A-Z]/g, chr => `-${chr.toLowerCase()}`);\n}\nconst Manipulator = {\n setDataAttribute(element, key, value) {\n element.setAttribute(`data-bs-${normalizeDataKey(key)}`, value);\n },\n removeDataAttribute(element, key) {\n element.removeAttribute(`data-bs-${normalizeDataKey(key)}`);\n },\n getDataAttributes(element) {\n if (!element) {\n return {};\n }\n const attributes = {};\n const bsKeys = Object.keys(element.dataset).filter(key => key.startsWith('bs') && !key.startsWith('bsConfig'));\n for (const key of bsKeys) {\n let pureKey = key.replace(/^bs/, '');\n pureKey = pureKey.charAt(0).toLowerCase() + pureKey.slice(1, pureKey.length);\n attributes[pureKey] = normalizeData(element.dataset[key]);\n }\n return attributes;\n },\n getDataAttribute(element, key) {\n return normalizeData(element.getAttribute(`data-bs-${normalizeDataKey(key)}`));\n }\n};\n\n/**\n * --------------------------------------------------------------------------\n * Bootstrap util/config.js\n * Licensed under MIT (https://github.com/twbs/bootstrap/blob/main/LICENSE)\n * --------------------------------------------------------------------------\n */\n\n\n/**\n * Class definition\n */\n\nclass Config {\n // Getters\n static get Default() {\n return {};\n }\n static get DefaultType() {\n return {};\n }\n static get NAME() {\n throw new Error('You have to implement the static method \"NAME\", for each component!');\n }\n _getConfig(config) {\n config = this._mergeConfigObj(config);\n config = this._configAfterMerge(config);\n this._typeCheckConfig(config);\n return config;\n }\n _configAfterMerge(config) {\n return config;\n }\n _mergeConfigObj(config, element) {\n const jsonConfig = isElement(element) ? Manipulator.getDataAttribute(element, 'config') : {}; // try to parse\n\n return {\n ...this.constructor.Default,\n ...(typeof jsonConfig === 'object' ? jsonConfig : {}),\n ...(isElement(element) ? Manipulator.getDataAttributes(element) : {}),\n ...(typeof config === 'object' ? config : {})\n };\n }\n _typeCheckConfig(config, configTypes = this.constructor.DefaultType) {\n for (const [property, expectedTypes] of Object.entries(configTypes)) {\n const value = config[property];\n const valueType = isElement(value) ? 'element' : toType(value);\n if (!new RegExp(expectedTypes).test(valueType)) {\n throw new TypeError(`${this.constructor.NAME.toUpperCase()}: Option \"${property}\" provided type \"${valueType}\" but expected type \"${expectedTypes}\".`);\n }\n }\n }\n}\n\n/**\n * --------------------------------------------------------------------------\n * Bootstrap base-component.js\n * Licensed under MIT (https://github.com/twbs/bootstrap/blob/main/LICENSE)\n * --------------------------------------------------------------------------\n */\n\n\n/**\n * Constants\n */\n\nconst VERSION = '5.3.3';\n\n/**\n * Class definition\n */\n\nclass BaseComponent extends Config {\n constructor(element, config) {\n super();\n element = getElement(element);\n if (!element) {\n return;\n }\n this._element = element;\n this._config = this._getConfig(config);\n Data.set(this._element, this.constructor.DATA_KEY, this);\n }\n\n // Public\n dispose() {\n Data.remove(this._element, this.constructor.DATA_KEY);\n EventHandler.off(this._element, this.constructor.EVENT_KEY);\n for (const propertyName of Object.getOwnPropertyNames(this)) {\n this[propertyName] = null;\n }\n }\n _queueCallback(callback, element, isAnimated = true) {\n executeAfterTransition(callback, element, isAnimated);\n }\n _getConfig(config) {\n config = this._mergeConfigObj(config, this._element);\n config = this._configAfterMerge(config);\n this._typeCheckConfig(config);\n return config;\n }\n\n // Static\n static getInstance(element) {\n return Data.get(getElement(element), this.DATA_KEY);\n }\n static getOrCreateInstance(element, config = {}) {\n return this.getInstance(element) || new this(element, typeof config === 'object' ? config : null);\n }\n static get VERSION() {\n return VERSION;\n }\n static get DATA_KEY() {\n return `bs.${this.NAME}`;\n }\n static get EVENT_KEY() {\n return `.${this.DATA_KEY}`;\n }\n static eventName(name) {\n return `${name}${this.EVENT_KEY}`;\n }\n}\n\n/**\n * --------------------------------------------------------------------------\n * Bootstrap dom/selector-engine.js\n * Licensed under MIT (https://github.com/twbs/bootstrap/blob/main/LICENSE)\n * --------------------------------------------------------------------------\n */\n\nconst getSelector = element => {\n let selector = element.getAttribute('data-bs-target');\n if (!selector || selector === '#') {\n let hrefAttribute = element.getAttribute('href');\n\n // The only valid content that could double as a selector are IDs or classes,\n // so everything starting with `#` or `.`. If a \"real\" URL is used as the selector,\n // `document.querySelector` will rightfully complain it is invalid.\n // See https://github.com/twbs/bootstrap/issues/32273\n if (!hrefAttribute || !hrefAttribute.includes('#') && !hrefAttribute.startsWith('.')) {\n return null;\n }\n\n // Just in case some CMS puts out a full URL with the anchor appended\n if (hrefAttribute.includes('#') && !hrefAttribute.startsWith('#')) {\n hrefAttribute = `#${hrefAttribute.split('#')[1]}`;\n }\n selector = hrefAttribute && hrefAttribute !== '#' ? hrefAttribute.trim() : null;\n }\n return selector ? selector.split(',').map(sel => parseSelector(sel)).join(',') : null;\n};\nconst SelectorEngine = {\n find(selector, element = document.documentElement) {\n return [].concat(...Element.prototype.querySelectorAll.call(element, selector));\n },\n findOne(selector, element = document.documentElement) {\n return Element.prototype.querySelector.call(element, selector);\n },\n children(element, selector) {\n return [].concat(...element.children).filter(child => child.matches(selector));\n },\n parents(element, selector) {\n const parents = [];\n let ancestor = element.parentNode.closest(selector);\n while (ancestor) {\n parents.push(ancestor);\n ancestor = ancestor.parentNode.closest(selector);\n }\n return parents;\n },\n prev(element, selector) {\n let previous = element.previousElementSibling;\n while (previous) {\n if (previous.matches(selector)) {\n return [previous];\n }\n previous = previous.previousElementSibling;\n }\n return [];\n },\n // TODO: this is now unused; remove later along with prev()\n next(element, selector) {\n let next = element.nextElementSibling;\n while (next) {\n if (next.matches(selector)) {\n return [next];\n }\n next = next.nextElementSibling;\n }\n return [];\n },\n focusableChildren(element) {\n const focusables = ['a', 'button', 'input', 'textarea', 'select', 'details', '[tabindex]', '[contenteditable=\"true\"]'].map(selector => `${selector}:not([tabindex^=\"-\"])`).join(',');\n return this.find(focusables, element).filter(el => !isDisabled(el) && isVisible(el));\n },\n getSelectorFromElement(element) {\n const selector = getSelector(element);\n if (selector) {\n return SelectorEngine.findOne(selector) ? selector : null;\n }\n return null;\n },\n getElementFromSelector(element) {\n const selector = getSelector(element);\n return selector ? SelectorEngine.findOne(selector) : null;\n },\n getMultipleElementsFromSelector(element) {\n const selector = getSelector(element);\n return selector ? SelectorEngine.find(selector) : [];\n }\n};\n\n/**\n * --------------------------------------------------------------------------\n * Bootstrap util/component-functions.js\n * Licensed under MIT (https://github.com/twbs/bootstrap/blob/main/LICENSE)\n * --------------------------------------------------------------------------\n */\n\nconst enableDismissTrigger = (component, method = 'hide') => {\n const clickEvent = `click.dismiss${component.EVENT_KEY}`;\n const name = component.NAME;\n EventHandler.on(document, clickEvent, `[data-bs-dismiss=\"${name}\"]`, function (event) {\n if (['A', 'AREA'].includes(this.tagName)) {\n event.preventDefault();\n }\n if (isDisabled(this)) {\n return;\n }\n const target = SelectorEngine.getElementFromSelector(this) || this.closest(`.${name}`);\n const instance = component.getOrCreateInstance(target);\n\n // Method argument is left, for Alert and only, as it doesn't implement the 'hide' method\n instance[method]();\n });\n};\n\n/**\n * --------------------------------------------------------------------------\n * Bootstrap alert.js\n * Licensed under MIT (https://github.com/twbs/bootstrap/blob/main/LICENSE)\n * --------------------------------------------------------------------------\n */\n\n\n/**\n * Constants\n */\n\nconst NAME$f = 'alert';\nconst DATA_KEY$a = 'bs.alert';\nconst EVENT_KEY$b = `.${DATA_KEY$a}`;\nconst EVENT_CLOSE = `close${EVENT_KEY$b}`;\nconst EVENT_CLOSED = `closed${EVENT_KEY$b}`;\nconst CLASS_NAME_FADE$5 = 'fade';\nconst CLASS_NAME_SHOW$8 = 'show';\n\n/**\n * Class definition\n */\n\nclass Alert extends BaseComponent {\n // Getters\n static get NAME() {\n return NAME$f;\n }\n\n // Public\n close() {\n const closeEvent = EventHandler.trigger(this._element, EVENT_CLOSE);\n if (closeEvent.defaultPrevented) {\n return;\n }\n this._element.classList.remove(CLASS_NAME_SHOW$8);\n const isAnimated = this._element.classList.contains(CLASS_NAME_FADE$5);\n this._queueCallback(() => this._destroyElement(), this._element, isAnimated);\n }\n\n // Private\n _destroyElement() {\n this._element.remove();\n EventHandler.trigger(this._element, EVENT_CLOSED);\n this.dispose();\n }\n\n // Static\n static jQueryInterface(config) {\n return this.each(function () {\n const data = Alert.getOrCreateInstance(this);\n if (typeof config !== 'string') {\n return;\n }\n if (data[config] === undefined || config.startsWith('_') || config === 'constructor') {\n throw new TypeError(`No method named \"${config}\"`);\n }\n data[config](this);\n });\n }\n}\n\n/**\n * Data API implementation\n */\n\nenableDismissTrigger(Alert, 'close');\n\n/**\n * jQuery\n */\n\ndefineJQueryPlugin(Alert);\n\n/**\n * --------------------------------------------------------------------------\n * Bootstrap button.js\n * Licensed under MIT (https://github.com/twbs/bootstrap/blob/main/LICENSE)\n * --------------------------------------------------------------------------\n */\n\n\n/**\n * Constants\n */\n\nconst NAME$e = 'button';\nconst DATA_KEY$9 = 'bs.button';\nconst EVENT_KEY$a = `.${DATA_KEY$9}`;\nconst DATA_API_KEY$6 = '.data-api';\nconst CLASS_NAME_ACTIVE$3 = 'active';\nconst SELECTOR_DATA_TOGGLE$5 = '[data-bs-toggle=\"button\"]';\nconst EVENT_CLICK_DATA_API$6 = `click${EVENT_KEY$a}${DATA_API_KEY$6}`;\n\n/**\n * Class definition\n */\n\nclass Button extends BaseComponent {\n // Getters\n static get NAME() {\n return NAME$e;\n }\n\n // Public\n toggle() {\n // Toggle class and sync the `aria-pressed` attribute with the return value of the `.toggle()` method\n this._element.setAttribute('aria-pressed', this._element.classList.toggle(CLASS_NAME_ACTIVE$3));\n }\n\n // Static\n static jQueryInterface(config) {\n return this.each(function () {\n const data = Button.getOrCreateInstance(this);\n if (config === 'toggle') {\n data[config]();\n }\n });\n }\n}\n\n/**\n * Data API implementation\n */\n\nEventHandler.on(document, EVENT_CLICK_DATA_API$6, SELECTOR_DATA_TOGGLE$5, event => {\n event.preventDefault();\n const button = event.target.closest(SELECTOR_DATA_TOGGLE$5);\n const data = Button.getOrCreateInstance(button);\n data.toggle();\n});\n\n/**\n * jQuery\n */\n\ndefineJQueryPlugin(Button);\n\n/**\n * --------------------------------------------------------------------------\n * Bootstrap util/swipe.js\n * Licensed under MIT (https://github.com/twbs/bootstrap/blob/main/LICENSE)\n * --------------------------------------------------------------------------\n */\n\n\n/**\n * Constants\n */\n\nconst NAME$d = 'swipe';\nconst EVENT_KEY$9 = '.bs.swipe';\nconst EVENT_TOUCHSTART = `touchstart${EVENT_KEY$9}`;\nconst EVENT_TOUCHMOVE = `touchmove${EVENT_KEY$9}`;\nconst EVENT_TOUCHEND = `touchend${EVENT_KEY$9}`;\nconst EVENT_POINTERDOWN = `pointerdown${EVENT_KEY$9}`;\nconst EVENT_POINTERUP = `pointerup${EVENT_KEY$9}`;\nconst POINTER_TYPE_TOUCH = 'touch';\nconst POINTER_TYPE_PEN = 'pen';\nconst CLASS_NAME_POINTER_EVENT = 'pointer-event';\nconst SWIPE_THRESHOLD = 40;\nconst Default$c = {\n endCallback: null,\n leftCallback: null,\n rightCallback: null\n};\nconst DefaultType$c = {\n endCallback: '(function|null)',\n leftCallback: '(function|null)',\n rightCallback: '(function|null)'\n};\n\n/**\n * Class definition\n */\n\nclass Swipe extends Config {\n constructor(element, config) {\n super();\n this._element = element;\n if (!element || !Swipe.isSupported()) {\n return;\n }\n this._config = this._getConfig(config);\n this._deltaX = 0;\n this._supportPointerEvents = Boolean(window.PointerEvent);\n this._initEvents();\n }\n\n // Getters\n static get Default() {\n return Default$c;\n }\n static get DefaultType() {\n return DefaultType$c;\n }\n static get NAME() {\n return NAME$d;\n }\n\n // Public\n dispose() {\n EventHandler.off(this._element, EVENT_KEY$9);\n }\n\n // Private\n _start(event) {\n if (!this._supportPointerEvents) {\n this._deltaX = event.touches[0].clientX;\n return;\n }\n if (this._eventIsPointerPenTouch(event)) {\n this._deltaX = event.clientX;\n }\n }\n _end(event) {\n if (this._eventIsPointerPenTouch(event)) {\n this._deltaX = event.clientX - this._deltaX;\n }\n this._handleSwipe();\n execute(this._config.endCallback);\n }\n _move(event) {\n this._deltaX = event.touches && event.touches.length > 1 ? 0 : event.touches[0].clientX - this._deltaX;\n }\n _handleSwipe() {\n const absDeltaX = Math.abs(this._deltaX);\n if (absDeltaX <= SWIPE_THRESHOLD) {\n return;\n }\n const direction = absDeltaX / this._deltaX;\n this._deltaX = 0;\n if (!direction) {\n return;\n }\n execute(direction > 0 ? this._config.rightCallback : this._config.leftCallback);\n }\n _initEvents() {\n if (this._supportPointerEvents) {\n EventHandler.on(this._element, EVENT_POINTERDOWN, event => this._start(event));\n EventHandler.on(this._element, EVENT_POINTERUP, event => this._end(event));\n this._element.classList.add(CLASS_NAME_POINTER_EVENT);\n } else {\n EventHandler.on(this._element, EVENT_TOUCHSTART, event => this._start(event));\n EventHandler.on(this._element, EVENT_TOUCHMOVE, event => this._move(event));\n EventHandler.on(this._element, EVENT_TOUCHEND, event => this._end(event));\n }\n }\n _eventIsPointerPenTouch(event) {\n return this._supportPointerEvents && (event.pointerType === POINTER_TYPE_PEN || event.pointerType === POINTER_TYPE_TOUCH);\n }\n\n // Static\n static isSupported() {\n return 'ontouchstart' in document.documentElement || navigator.maxTouchPoints > 0;\n }\n}\n\n/**\n * --------------------------------------------------------------------------\n * Bootstrap carousel.js\n * Licensed under MIT (https://github.com/twbs/bootstrap/blob/main/LICENSE)\n * --------------------------------------------------------------------------\n */\n\n\n/**\n * Constants\n */\n\nconst NAME$c = 'carousel';\nconst DATA_KEY$8 = 'bs.carousel';\nconst EVENT_KEY$8 = `.${DATA_KEY$8}`;\nconst DATA_API_KEY$5 = '.data-api';\nconst ARROW_LEFT_KEY$1 = 'ArrowLeft';\nconst ARROW_RIGHT_KEY$1 = 'ArrowRight';\nconst TOUCHEVENT_COMPAT_WAIT = 500; // Time for mouse compat events to fire after touch\n\nconst ORDER_NEXT = 'next';\nconst ORDER_PREV = 'prev';\nconst DIRECTION_LEFT = 'left';\nconst DIRECTION_RIGHT = 'right';\nconst EVENT_SLIDE = `slide${EVENT_KEY$8}`;\nconst EVENT_SLID = `slid${EVENT_KEY$8}`;\nconst EVENT_KEYDOWN$1 = `keydown${EVENT_KEY$8}`;\nconst EVENT_MOUSEENTER$1 = `mouseenter${EVENT_KEY$8}`;\nconst EVENT_MOUSELEAVE$1 = `mouseleave${EVENT_KEY$8}`;\nconst EVENT_DRAG_START = `dragstart${EVENT_KEY$8}`;\nconst EVENT_LOAD_DATA_API$3 = `load${EVENT_KEY$8}${DATA_API_KEY$5}`;\nconst EVENT_CLICK_DATA_API$5 = `click${EVENT_KEY$8}${DATA_API_KEY$5}`;\nconst CLASS_NAME_CAROUSEL = 'carousel';\nconst CLASS_NAME_ACTIVE$2 = 'active';\nconst CLASS_NAME_SLIDE = 'slide';\nconst CLASS_NAME_END = 'carousel-item-end';\nconst CLASS_NAME_START = 'carousel-item-start';\nconst CLASS_NAME_NEXT = 'carousel-item-next';\nconst CLASS_NAME_PREV = 'carousel-item-prev';\nconst SELECTOR_ACTIVE = '.active';\nconst SELECTOR_ITEM = '.carousel-item';\nconst SELECTOR_ACTIVE_ITEM = SELECTOR_ACTIVE + SELECTOR_ITEM;\nconst SELECTOR_ITEM_IMG = '.carousel-item img';\nconst SELECTOR_INDICATORS = '.carousel-indicators';\nconst SELECTOR_DATA_SLIDE = '[data-bs-slide], [data-bs-slide-to]';\nconst SELECTOR_DATA_RIDE = '[data-bs-ride=\"carousel\"]';\nconst KEY_TO_DIRECTION = {\n [ARROW_LEFT_KEY$1]: DIRECTION_RIGHT,\n [ARROW_RIGHT_KEY$1]: DIRECTION_LEFT\n};\nconst Default$b = {\n interval: 5000,\n keyboard: true,\n pause: 'hover',\n ride: false,\n touch: true,\n wrap: true\n};\nconst DefaultType$b = {\n interval: '(number|boolean)',\n // TODO:v6 remove boolean support\n keyboard: 'boolean',\n pause: '(string|boolean)',\n ride: '(boolean|string)',\n touch: 'boolean',\n wrap: 'boolean'\n};\n\n/**\n * Class definition\n */\n\nclass Carousel extends BaseComponent {\n constructor(element, config) {\n super(element, config);\n this._interval = null;\n this._activeElement = null;\n this._isSliding = false;\n this.touchTimeout = null;\n this._swipeHelper = null;\n this._indicatorsElement = SelectorEngine.findOne(SELECTOR_INDICATORS, this._element);\n this._addEventListeners();\n if (this._config.ride === CLASS_NAME_CAROUSEL) {\n this.cycle();\n }\n }\n\n // Getters\n static get Default() {\n return Default$b;\n }\n static get DefaultType() {\n return DefaultType$b;\n }\n static get NAME() {\n return NAME$c;\n }\n\n // Public\n next() {\n this._slide(ORDER_NEXT);\n }\n nextWhenVisible() {\n // FIXME TODO use `document.visibilityState`\n // Don't call next when the page isn't visible\n // or the carousel or its parent isn't visible\n if (!document.hidden && isVisible(this._element)) {\n this.next();\n }\n }\n prev() {\n this._slide(ORDER_PREV);\n }\n pause() {\n if (this._isSliding) {\n triggerTransitionEnd(this._element);\n }\n this._clearInterval();\n }\n cycle() {\n this._clearInterval();\n this._updateInterval();\n this._interval = setInterval(() => this.nextWhenVisible(), this._config.interval);\n }\n _maybeEnableCycle() {\n if (!this._config.ride) {\n return;\n }\n if (this._isSliding) {\n EventHandler.one(this._element, EVENT_SLID, () => this.cycle());\n return;\n }\n this.cycle();\n }\n to(index) {\n const items = this._getItems();\n if (index > items.length - 1 || index < 0) {\n return;\n }\n if (this._isSliding) {\n EventHandler.one(this._element, EVENT_SLID, () => this.to(index));\n return;\n }\n const activeIndex = this._getItemIndex(this._getActive());\n if (activeIndex === index) {\n return;\n }\n const order = index > activeIndex ? ORDER_NEXT : ORDER_PREV;\n this._slide(order, items[index]);\n }\n dispose() {\n if (this._swipeHelper) {\n this._swipeHelper.dispose();\n }\n super.dispose();\n }\n\n // Private\n _configAfterMerge(config) {\n config.defaultInterval = config.interval;\n return config;\n }\n _addEventListeners() {\n if (this._config.keyboard) {\n EventHandler.on(this._element, EVENT_KEYDOWN$1, event => this._keydown(event));\n }\n if (this._config.pause === 'hover') {\n EventHandler.on(this._element, EVENT_MOUSEENTER$1, () => this.pause());\n EventHandler.on(this._element, EVENT_MOUSELEAVE$1, () => this._maybeEnableCycle());\n }\n if (this._config.touch && Swipe.isSupported()) {\n this._addTouchEventListeners();\n }\n }\n _addTouchEventListeners() {\n for (const img of SelectorEngine.find(SELECTOR_ITEM_IMG, this._element)) {\n EventHandler.on(img, EVENT_DRAG_START, event => event.preventDefault());\n }\n const endCallBack = () => {\n if (this._config.pause !== 'hover') {\n return;\n }\n\n // If it's a touch-enabled device, mouseenter/leave are fired as\n // part of the mouse compatibility events on first tap - the carousel\n // would stop cycling until user tapped out of it;\n // here, we listen for touchend, explicitly pause the carousel\n // (as if it's the second time we tap on it, mouseenter compat event\n // is NOT fired) and after a timeout (to allow for mouse compatibility\n // events to fire) we explicitly restart cycling\n\n this.pause();\n if (this.touchTimeout) {\n clearTimeout(this.touchTimeout);\n }\n this.touchTimeout = setTimeout(() => this._maybeEnableCycle(), TOUCHEVENT_COMPAT_WAIT + this._config.interval);\n };\n const swipeConfig = {\n leftCallback: () => this._slide(this._directionToOrder(DIRECTION_LEFT)),\n rightCallback: () => this._slide(this._directionToOrder(DIRECTION_RIGHT)),\n endCallback: endCallBack\n };\n this._swipeHelper = new Swipe(this._element, swipeConfig);\n }\n _keydown(event) {\n if (/input|textarea/i.test(event.target.tagName)) {\n return;\n }\n const direction = KEY_TO_DIRECTION[event.key];\n if (direction) {\n event.preventDefault();\n this._slide(this._directionToOrder(direction));\n }\n }\n _getItemIndex(element) {\n return this._getItems().indexOf(element);\n }\n _setActiveIndicatorElement(index) {\n if (!this._indicatorsElement) {\n return;\n }\n const activeIndicator = SelectorEngine.findOne(SELECTOR_ACTIVE, this._indicatorsElement);\n activeIndicator.classList.remove(CLASS_NAME_ACTIVE$2);\n activeIndicator.removeAttribute('aria-current');\n const newActiveIndicator = SelectorEngine.findOne(`[data-bs-slide-to=\"${index}\"]`, this._indicatorsElement);\n if (newActiveIndicator) {\n newActiveIndicator.classList.add(CLASS_NAME_ACTIVE$2);\n newActiveIndicator.setAttribute('aria-current', 'true');\n }\n }\n _updateInterval() {\n const element = this._activeElement || this._getActive();\n if (!element) {\n return;\n }\n const elementInterval = Number.parseInt(element.getAttribute('data-bs-interval'), 10);\n this._config.interval = elementInterval || this._config.defaultInterval;\n }\n _slide(order, element = null) {\n if (this._isSliding) {\n return;\n }\n const activeElement = this._getActive();\n const isNext = order === ORDER_NEXT;\n const nextElement = element || getNextActiveElement(this._getItems(), activeElement, isNext, this._config.wrap);\n if (nextElement === activeElement) {\n return;\n }\n const nextElementIndex = this._getItemIndex(nextElement);\n const triggerEvent = eventName => {\n return EventHandler.trigger(this._element, eventName, {\n relatedTarget: nextElement,\n direction: this._orderToDirection(order),\n from: this._getItemIndex(activeElement),\n to: nextElementIndex\n });\n };\n const slideEvent = triggerEvent(EVENT_SLIDE);\n if (slideEvent.defaultPrevented) {\n return;\n }\n if (!activeElement || !nextElement) {\n // Some weirdness is happening, so we bail\n // TODO: change tests that use empty divs to avoid this check\n return;\n }\n const isCycling = Boolean(this._interval);\n this.pause();\n this._isSliding = true;\n this._setActiveIndicatorElement(nextElementIndex);\n this._activeElement = nextElement;\n const directionalClassName = isNext ? CLASS_NAME_START : CLASS_NAME_END;\n const orderClassName = isNext ? CLASS_NAME_NEXT : CLASS_NAME_PREV;\n nextElement.classList.add(orderClassName);\n reflow(nextElement);\n activeElement.classList.add(directionalClassName);\n nextElement.classList.add(directionalClassName);\n const completeCallBack = () => {\n nextElement.classList.remove(directionalClassName, orderClassName);\n nextElement.classList.add(CLASS_NAME_ACTIVE$2);\n activeElement.classList.remove(CLASS_NAME_ACTIVE$2, orderClassName, directionalClassName);\n this._isSliding = false;\n triggerEvent(EVENT_SLID);\n };\n this._queueCallback(completeCallBack, activeElement, this._isAnimated());\n if (isCycling) {\n this.cycle();\n }\n }\n _isAnimated() {\n return this._element.classList.contains(CLASS_NAME_SLIDE);\n }\n _getActive() {\n return SelectorEngine.findOne(SELECTOR_ACTIVE_ITEM, this._element);\n }\n _getItems() {\n return SelectorEngine.find(SELECTOR_ITEM, this._element);\n }\n _clearInterval() {\n if (this._interval) {\n clearInterval(this._interval);\n this._interval = null;\n }\n }\n _directionToOrder(direction) {\n if (isRTL()) {\n return direction === DIRECTION_LEFT ? ORDER_PREV : ORDER_NEXT;\n }\n return direction === DIRECTION_LEFT ? ORDER_NEXT : ORDER_PREV;\n }\n _orderToDirection(order) {\n if (isRTL()) {\n return order === ORDER_PREV ? DIRECTION_LEFT : DIRECTION_RIGHT;\n }\n return order === ORDER_PREV ? DIRECTION_RIGHT : DIRECTION_LEFT;\n }\n\n // Static\n static jQueryInterface(config) {\n return this.each(function () {\n const data = Carousel.getOrCreateInstance(this, config);\n if (typeof config === 'number') {\n data.to(config);\n return;\n }\n if (typeof config === 'string') {\n if (data[config] === undefined || config.startsWith('_') || config === 'constructor') {\n throw new TypeError(`No method named \"${config}\"`);\n }\n data[config]();\n }\n });\n }\n}\n\n/**\n * Data API implementation\n */\n\nEventHandler.on(document, EVENT_CLICK_DATA_API$5, SELECTOR_DATA_SLIDE, function (event) {\n const target = SelectorEngine.getElementFromSelector(this);\n if (!target || !target.classList.contains(CLASS_NAME_CAROUSEL)) {\n return;\n }\n event.preventDefault();\n const carousel = Carousel.getOrCreateInstance(target);\n const slideIndex = this.getAttribute('data-bs-slide-to');\n if (slideIndex) {\n carousel.to(slideIndex);\n carousel._maybeEnableCycle();\n return;\n }\n if (Manipulator.getDataAttribute(this, 'slide') === 'next') {\n carousel.next();\n carousel._maybeEnableCycle();\n return;\n }\n carousel.prev();\n carousel._maybeEnableCycle();\n});\nEventHandler.on(window, EVENT_LOAD_DATA_API$3, () => {\n const carousels = SelectorEngine.find(SELECTOR_DATA_RIDE);\n for (const carousel of carousels) {\n Carousel.getOrCreateInstance(carousel);\n }\n});\n\n/**\n * jQuery\n */\n\ndefineJQueryPlugin(Carousel);\n\n/**\n * --------------------------------------------------------------------------\n * Bootstrap collapse.js\n * Licensed under MIT (https://github.com/twbs/bootstrap/blob/main/LICENSE)\n * --------------------------------------------------------------------------\n */\n\n\n/**\n * Constants\n */\n\nconst NAME$b = 'collapse';\nconst DATA_KEY$7 = 'bs.collapse';\nconst EVENT_KEY$7 = `.${DATA_KEY$7}`;\nconst DATA_API_KEY$4 = '.data-api';\nconst EVENT_SHOW$6 = `show${EVENT_KEY$7}`;\nconst EVENT_SHOWN$6 = `shown${EVENT_KEY$7}`;\nconst EVENT_HIDE$6 = `hide${EVENT_KEY$7}`;\nconst EVENT_HIDDEN$6 = `hidden${EVENT_KEY$7}`;\nconst EVENT_CLICK_DATA_API$4 = `click${EVENT_KEY$7}${DATA_API_KEY$4}`;\nconst CLASS_NAME_SHOW$7 = 'show';\nconst CLASS_NAME_COLLAPSE = 'collapse';\nconst CLASS_NAME_COLLAPSING = 'collapsing';\nconst CLASS_NAME_COLLAPSED = 'collapsed';\nconst CLASS_NAME_DEEPER_CHILDREN = `:scope .${CLASS_NAME_COLLAPSE} .${CLASS_NAME_COLLAPSE}`;\nconst CLASS_NAME_HORIZONTAL = 'collapse-horizontal';\nconst WIDTH = 'width';\nconst HEIGHT = 'height';\nconst SELECTOR_ACTIVES = '.collapse.show, .collapse.collapsing';\nconst SELECTOR_DATA_TOGGLE$4 = '[data-bs-toggle=\"collapse\"]';\nconst Default$a = {\n parent: null,\n toggle: true\n};\nconst DefaultType$a = {\n parent: '(null|element)',\n toggle: 'boolean'\n};\n\n/**\n * Class definition\n */\n\nclass Collapse extends BaseComponent {\n constructor(element, config) {\n super(element, config);\n this._isTransitioning = false;\n this._triggerArray = [];\n const toggleList = SelectorEngine.find(SELECTOR_DATA_TOGGLE$4);\n for (const elem of toggleList) {\n const selector = SelectorEngine.getSelectorFromElement(elem);\n const filterElement = SelectorEngine.find(selector).filter(foundElement => foundElement === this._element);\n if (selector !== null && filterElement.length) {\n this._triggerArray.push(elem);\n }\n }\n this._initializeChildren();\n if (!this._config.parent) {\n this._addAriaAndCollapsedClass(this._triggerArray, this._isShown());\n }\n if (this._config.toggle) {\n this.toggle();\n }\n }\n\n // Getters\n static get Default() {\n return Default$a;\n }\n static get DefaultType() {\n return DefaultType$a;\n }\n static get NAME() {\n return NAME$b;\n }\n\n // Public\n toggle() {\n if (this._isShown()) {\n this.hide();\n } else {\n this.show();\n }\n }\n show() {\n if (this._isTransitioning || this._isShown()) {\n return;\n }\n let activeChildren = [];\n\n // find active children\n if (this._config.parent) {\n activeChildren = this._getFirstLevelChildren(SELECTOR_ACTIVES).filter(element => element !== this._element).map(element => Collapse.getOrCreateInstance(element, {\n toggle: false\n }));\n }\n if (activeChildren.length && activeChildren[0]._isTransitioning) {\n return;\n }\n const startEvent = EventHandler.trigger(this._element, EVENT_SHOW$6);\n if (startEvent.defaultPrevented) {\n return;\n }\n for (const activeInstance of activeChildren) {\n activeInstance.hide();\n }\n const dimension = this._getDimension();\n this._element.classList.remove(CLASS_NAME_COLLAPSE);\n this._element.classList.add(CLASS_NAME_COLLAPSING);\n this._element.style[dimension] = 0;\n this._addAriaAndCollapsedClass(this._triggerArray, true);\n this._isTransitioning = true;\n const complete = () => {\n this._isTransitioning = false;\n this._element.classList.remove(CLASS_NAME_COLLAPSING);\n this._element.classList.add(CLASS_NAME_COLLAPSE, CLASS_NAME_SHOW$7);\n this._element.style[dimension] = '';\n EventHandler.trigger(this._element, EVENT_SHOWN$6);\n };\n const capitalizedDimension = dimension[0].toUpperCase() + dimension.slice(1);\n const scrollSize = `scroll${capitalizedDimension}`;\n this._queueCallback(complete, this._element, true);\n this._element.style[dimension] = `${this._element[scrollSize]}px`;\n }\n hide() {\n if (this._isTransitioning || !this._isShown()) {\n return;\n }\n const startEvent = EventHandler.trigger(this._element, EVENT_HIDE$6);\n if (startEvent.defaultPrevented) {\n return;\n }\n const dimension = this._getDimension();\n this._element.style[dimension] = `${this._element.getBoundingClientRect()[dimension]}px`;\n reflow(this._element);\n this._element.classList.add(CLASS_NAME_COLLAPSING);\n this._element.classList.remove(CLASS_NAME_COLLAPSE, CLASS_NAME_SHOW$7);\n for (const trigger of this._triggerArray) {\n const element = SelectorEngine.getElementFromSelector(trigger);\n if (element && !this._isShown(element)) {\n this._addAriaAndCollapsedClass([trigger], false);\n }\n }\n this._isTransitioning = true;\n const complete = () => {\n this._isTransitioning = false;\n this._element.classList.remove(CLASS_NAME_COLLAPSING);\n this._element.classList.add(CLASS_NAME_COLLAPSE);\n EventHandler.trigger(this._element, EVENT_HIDDEN$6);\n };\n this._element.style[dimension] = '';\n this._queueCallback(complete, this._element, true);\n }\n _isShown(element = this._element) {\n return element.classList.contains(CLASS_NAME_SHOW$7);\n }\n\n // Private\n _configAfterMerge(config) {\n config.toggle = Boolean(config.toggle); // Coerce string values\n config.parent = getElement(config.parent);\n return config;\n }\n _getDimension() {\n return this._element.classList.contains(CLASS_NAME_HORIZONTAL) ? WIDTH : HEIGHT;\n }\n _initializeChildren() {\n if (!this._config.parent) {\n return;\n }\n const children = this._getFirstLevelChildren(SELECTOR_DATA_TOGGLE$4);\n for (const element of children) {\n const selected = SelectorEngine.getElementFromSelector(element);\n if (selected) {\n this._addAriaAndCollapsedClass([element], this._isShown(selected));\n }\n }\n }\n _getFirstLevelChildren(selector) {\n const children = SelectorEngine.find(CLASS_NAME_DEEPER_CHILDREN, this._config.parent);\n // remove children if greater depth\n return SelectorEngine.find(selector, this._config.parent).filter(element => !children.includes(element));\n }\n _addAriaAndCollapsedClass(triggerArray, isOpen) {\n if (!triggerArray.length) {\n return;\n }\n for (const element of triggerArray) {\n element.classList.toggle(CLASS_NAME_COLLAPSED, !isOpen);\n element.setAttribute('aria-expanded', isOpen);\n }\n }\n\n // Static\n static jQueryInterface(config) {\n const _config = {};\n if (typeof config === 'string' && /show|hide/.test(config)) {\n _config.toggle = false;\n }\n return this.each(function () {\n const data = Collapse.getOrCreateInstance(this, _config);\n if (typeof config === 'string') {\n if (typeof data[config] === 'undefined') {\n throw new TypeError(`No method named \"${config}\"`);\n }\n data[config]();\n }\n });\n }\n}\n\n/**\n * Data API implementation\n */\n\nEventHandler.on(document, EVENT_CLICK_DATA_API$4, SELECTOR_DATA_TOGGLE$4, function (event) {\n // preventDefault only for elements (which change the URL) not inside the collapsible element\n if (event.target.tagName === 'A' || event.delegateTarget && event.delegateTarget.tagName === 'A') {\n event.preventDefault();\n }\n for (const element of SelectorEngine.getMultipleElementsFromSelector(this)) {\n Collapse.getOrCreateInstance(element, {\n toggle: false\n }).toggle();\n }\n});\n\n/**\n * jQuery\n */\n\ndefineJQueryPlugin(Collapse);\n\n/**\n * --------------------------------------------------------------------------\n * Bootstrap dropdown.js\n * Licensed under MIT (https://github.com/twbs/bootstrap/blob/main/LICENSE)\n * --------------------------------------------------------------------------\n */\n\n\n/**\n * Constants\n */\n\nconst NAME$a = 'dropdown';\nconst DATA_KEY$6 = 'bs.dropdown';\nconst EVENT_KEY$6 = `.${DATA_KEY$6}`;\nconst DATA_API_KEY$3 = '.data-api';\nconst ESCAPE_KEY$2 = 'Escape';\nconst TAB_KEY$1 = 'Tab';\nconst ARROW_UP_KEY$1 = 'ArrowUp';\nconst ARROW_DOWN_KEY$1 = 'ArrowDown';\nconst RIGHT_MOUSE_BUTTON = 2; // MouseEvent.button value for the secondary button, usually the right button\n\nconst EVENT_HIDE$5 = `hide${EVENT_KEY$6}`;\nconst EVENT_HIDDEN$5 = `hidden${EVENT_KEY$6}`;\nconst EVENT_SHOW$5 = `show${EVENT_KEY$6}`;\nconst EVENT_SHOWN$5 = `shown${EVENT_KEY$6}`;\nconst EVENT_CLICK_DATA_API$3 = `click${EVENT_KEY$6}${DATA_API_KEY$3}`;\nconst EVENT_KEYDOWN_DATA_API = `keydown${EVENT_KEY$6}${DATA_API_KEY$3}`;\nconst EVENT_KEYUP_DATA_API = `keyup${EVENT_KEY$6}${DATA_API_KEY$3}`;\nconst CLASS_NAME_SHOW$6 = 'show';\nconst CLASS_NAME_DROPUP = 'dropup';\nconst CLASS_NAME_DROPEND = 'dropend';\nconst CLASS_NAME_DROPSTART = 'dropstart';\nconst CLASS_NAME_DROPUP_CENTER = 'dropup-center';\nconst CLASS_NAME_DROPDOWN_CENTER = 'dropdown-center';\nconst SELECTOR_DATA_TOGGLE$3 = '[data-bs-toggle=\"dropdown\"]:not(.disabled):not(:disabled)';\nconst SELECTOR_DATA_TOGGLE_SHOWN = `${SELECTOR_DATA_TOGGLE$3}.${CLASS_NAME_SHOW$6}`;\nconst SELECTOR_MENU = '.dropdown-menu';\nconst SELECTOR_NAVBAR = '.navbar';\nconst SELECTOR_NAVBAR_NAV = '.navbar-nav';\nconst SELECTOR_VISIBLE_ITEMS = '.dropdown-menu .dropdown-item:not(.disabled):not(:disabled)';\nconst PLACEMENT_TOP = isRTL() ? 'top-end' : 'top-start';\nconst PLACEMENT_TOPEND = isRTL() ? 'top-start' : 'top-end';\nconst PLACEMENT_BOTTOM = isRTL() ? 'bottom-end' : 'bottom-start';\nconst PLACEMENT_BOTTOMEND = isRTL() ? 'bottom-start' : 'bottom-end';\nconst PLACEMENT_RIGHT = isRTL() ? 'left-start' : 'right-start';\nconst PLACEMENT_LEFT = isRTL() ? 'right-start' : 'left-start';\nconst PLACEMENT_TOPCENTER = 'top';\nconst PLACEMENT_BOTTOMCENTER = 'bottom';\nconst Default$9 = {\n autoClose: true,\n boundary: 'clippingParents',\n display: 'dynamic',\n offset: [0, 2],\n popperConfig: null,\n reference: 'toggle'\n};\nconst DefaultType$9 = {\n autoClose: '(boolean|string)',\n boundary: '(string|element)',\n display: 'string',\n offset: '(array|string|function)',\n popperConfig: '(null|object|function)',\n reference: '(string|element|object)'\n};\n\n/**\n * Class definition\n */\n\nclass Dropdown extends BaseComponent {\n constructor(element, config) {\n super(element, config);\n this._popper = null;\n this._parent = this._element.parentNode; // dropdown wrapper\n // TODO: v6 revert #37011 & change markup https://getbootstrap.com/docs/5.3/forms/input-group/\n this._menu = SelectorEngine.next(this._element, SELECTOR_MENU)[0] || SelectorEngine.prev(this._element, SELECTOR_MENU)[0] || SelectorEngine.findOne(SELECTOR_MENU, this._parent);\n this._inNavbar = this._detectNavbar();\n }\n\n // Getters\n static get Default() {\n return Default$9;\n }\n static get DefaultType() {\n return DefaultType$9;\n }\n static get NAME() {\n return NAME$a;\n }\n\n // Public\n toggle() {\n return this._isShown() ? this.hide() : this.show();\n }\n show() {\n if (isDisabled(this._element) || this._isShown()) {\n return;\n }\n const relatedTarget = {\n relatedTarget: this._element\n };\n const showEvent = EventHandler.trigger(this._element, EVENT_SHOW$5, relatedTarget);\n if (showEvent.defaultPrevented) {\n return;\n }\n this._createPopper();\n\n // If this is a touch-enabled device we add extra\n // empty mouseover listeners to the body's immediate children;\n // only needed because of broken event delegation on iOS\n // https://www.quirksmode.org/blog/archives/2014/02/mouse_event_bub.html\n if ('ontouchstart' in document.documentElement && !this._parent.closest(SELECTOR_NAVBAR_NAV)) {\n for (const element of [].concat(...document.body.children)) {\n EventHandler.on(element, 'mouseover', noop);\n }\n }\n this._element.focus();\n this._element.setAttribute('aria-expanded', true);\n this._menu.classList.add(CLASS_NAME_SHOW$6);\n this._element.classList.add(CLASS_NAME_SHOW$6);\n EventHandler.trigger(this._element, EVENT_SHOWN$5, relatedTarget);\n }\n hide() {\n if (isDisabled(this._element) || !this._isShown()) {\n return;\n }\n const relatedTarget = {\n relatedTarget: this._element\n };\n this._completeHide(relatedTarget);\n }\n dispose() {\n if (this._popper) {\n this._popper.destroy();\n }\n super.dispose();\n }\n update() {\n this._inNavbar = this._detectNavbar();\n if (this._popper) {\n this._popper.update();\n }\n }\n\n // Private\n _completeHide(relatedTarget) {\n const hideEvent = EventHandler.trigger(this._element, EVENT_HIDE$5, relatedTarget);\n if (hideEvent.defaultPrevented) {\n return;\n }\n\n // If this is a touch-enabled device we remove the extra\n // empty mouseover listeners we added for iOS support\n if ('ontouchstart' in document.documentElement) {\n for (const element of [].concat(...document.body.children)) {\n EventHandler.off(element, 'mouseover', noop);\n }\n }\n if (this._popper) {\n this._popper.destroy();\n }\n this._menu.classList.remove(CLASS_NAME_SHOW$6);\n this._element.classList.remove(CLASS_NAME_SHOW$6);\n this._element.setAttribute('aria-expanded', 'false');\n Manipulator.removeDataAttribute(this._menu, 'popper');\n EventHandler.trigger(this._element, EVENT_HIDDEN$5, relatedTarget);\n }\n _getConfig(config) {\n config = super._getConfig(config);\n if (typeof config.reference === 'object' && !isElement(config.reference) && typeof config.reference.getBoundingClientRect !== 'function') {\n // Popper virtual elements require a getBoundingClientRect method\n throw new TypeError(`${NAME$a.toUpperCase()}: Option \"reference\" provided type \"object\" without a required \"getBoundingClientRect\" method.`);\n }\n return config;\n }\n _createPopper() {\n if (typeof Popper === 'undefined') {\n throw new TypeError('Bootstrap\\'s dropdowns require Popper (https://popper.js.org)');\n }\n let referenceElement = this._element;\n if (this._config.reference === 'parent') {\n referenceElement = this._parent;\n } else if (isElement(this._config.reference)) {\n referenceElement = getElement(this._config.reference);\n } else if (typeof this._config.reference === 'object') {\n referenceElement = this._config.reference;\n }\n const popperConfig = this._getPopperConfig();\n this._popper = Popper.createPopper(referenceElement, this._menu, popperConfig);\n }\n _isShown() {\n return this._menu.classList.contains(CLASS_NAME_SHOW$6);\n }\n _getPlacement() {\n const parentDropdown = this._parent;\n if (parentDropdown.classList.contains(CLASS_NAME_DROPEND)) {\n return PLACEMENT_RIGHT;\n }\n if (parentDropdown.classList.contains(CLASS_NAME_DROPSTART)) {\n return PLACEMENT_LEFT;\n }\n if (parentDropdown.classList.contains(CLASS_NAME_DROPUP_CENTER)) {\n return PLACEMENT_TOPCENTER;\n }\n if (parentDropdown.classList.contains(CLASS_NAME_DROPDOWN_CENTER)) {\n return PLACEMENT_BOTTOMCENTER;\n }\n\n // We need to trim the value because custom properties can also include spaces\n const isEnd = getComputedStyle(this._menu).getPropertyValue('--bs-position').trim() === 'end';\n if (parentDropdown.classList.contains(CLASS_NAME_DROPUP)) {\n return isEnd ? PLACEMENT_TOPEND : PLACEMENT_TOP;\n }\n return isEnd ? PLACEMENT_BOTTOMEND : PLACEMENT_BOTTOM;\n }\n _detectNavbar() {\n return this._element.closest(SELECTOR_NAVBAR) !== null;\n }\n _getOffset() {\n const {\n offset\n } = this._config;\n if (typeof offset === 'string') {\n return offset.split(',').map(value => Number.parseInt(value, 10));\n }\n if (typeof offset === 'function') {\n return popperData => offset(popperData, this._element);\n }\n return offset;\n }\n _getPopperConfig() {\n const defaultBsPopperConfig = {\n placement: this._getPlacement(),\n modifiers: [{\n name: 'preventOverflow',\n options: {\n boundary: this._config.boundary\n }\n }, {\n name: 'offset',\n options: {\n offset: this._getOffset()\n }\n }]\n };\n\n // Disable Popper if we have a static display or Dropdown is in Navbar\n if (this._inNavbar || this._config.display === 'static') {\n Manipulator.setDataAttribute(this._menu, 'popper', 'static'); // TODO: v6 remove\n defaultBsPopperConfig.modifiers = [{\n name: 'applyStyles',\n enabled: false\n }];\n }\n return {\n ...defaultBsPopperConfig,\n ...execute(this._config.popperConfig, [defaultBsPopperConfig])\n };\n }\n _selectMenuItem({\n key,\n target\n }) {\n const items = SelectorEngine.find(SELECTOR_VISIBLE_ITEMS, this._menu).filter(element => isVisible(element));\n if (!items.length) {\n return;\n }\n\n // if target isn't included in items (e.g. when expanding the dropdown)\n // allow cycling to get the last item in case key equals ARROW_UP_KEY\n getNextActiveElement(items, target, key === ARROW_DOWN_KEY$1, !items.includes(target)).focus();\n }\n\n // Static\n static jQueryInterface(config) {\n return this.each(function () {\n const data = Dropdown.getOrCreateInstance(this, config);\n if (typeof config !== 'string') {\n return;\n }\n if (typeof data[config] === 'undefined') {\n throw new TypeError(`No method named \"${config}\"`);\n }\n data[config]();\n });\n }\n static clearMenus(event) {\n if (event.button === RIGHT_MOUSE_BUTTON || event.type === 'keyup' && event.key !== TAB_KEY$1) {\n return;\n }\n const openToggles = SelectorEngine.find(SELECTOR_DATA_TOGGLE_SHOWN);\n for (const toggle of openToggles) {\n const context = Dropdown.getInstance(toggle);\n if (!context || context._config.autoClose === false) {\n continue;\n }\n const composedPath = event.composedPath();\n const isMenuTarget = composedPath.includes(context._menu);\n if (composedPath.includes(context._element) || context._config.autoClose === 'inside' && !isMenuTarget || context._config.autoClose === 'outside' && isMenuTarget) {\n continue;\n }\n\n // Tab navigation through the dropdown menu or events from contained inputs shouldn't close the menu\n if (context._menu.contains(event.target) && (event.type === 'keyup' && event.key === TAB_KEY$1 || /input|select|option|textarea|form/i.test(event.target.tagName))) {\n continue;\n }\n const relatedTarget = {\n relatedTarget: context._element\n };\n if (event.type === 'click') {\n relatedTarget.clickEvent = event;\n }\n context._completeHide(relatedTarget);\n }\n }\n static dataApiKeydownHandler(event) {\n // If not an UP | DOWN | ESCAPE key => not a dropdown command\n // If input/textarea && if key is other than ESCAPE => not a dropdown command\n\n const isInput = /input|textarea/i.test(event.target.tagName);\n const isEscapeEvent = event.key === ESCAPE_KEY$2;\n const isUpOrDownEvent = [ARROW_UP_KEY$1, ARROW_DOWN_KEY$1].includes(event.key);\n if (!isUpOrDownEvent && !isEscapeEvent) {\n return;\n }\n if (isInput && !isEscapeEvent) {\n return;\n }\n event.preventDefault();\n\n // TODO: v6 revert #37011 & change markup https://getbootstrap.com/docs/5.3/forms/input-group/\n const getToggleButton = this.matches(SELECTOR_DATA_TOGGLE$3) ? this : SelectorEngine.prev(this, SELECTOR_DATA_TOGGLE$3)[0] || SelectorEngine.next(this, SELECTOR_DATA_TOGGLE$3)[0] || SelectorEngine.findOne(SELECTOR_DATA_TOGGLE$3, event.delegateTarget.parentNode);\n const instance = Dropdown.getOrCreateInstance(getToggleButton);\n if (isUpOrDownEvent) {\n event.stopPropagation();\n instance.show();\n instance._selectMenuItem(event);\n return;\n }\n if (instance._isShown()) {\n // else is escape and we check if it is shown\n event.stopPropagation();\n instance.hide();\n getToggleButton.focus();\n }\n }\n}\n\n/**\n * Data API implementation\n */\n\nEventHandler.on(document, EVENT_KEYDOWN_DATA_API, SELECTOR_DATA_TOGGLE$3, Dropdown.dataApiKeydownHandler);\nEventHandler.on(document, EVENT_KEYDOWN_DATA_API, SELECTOR_MENU, Dropdown.dataApiKeydownHandler);\nEventHandler.on(document, EVENT_CLICK_DATA_API$3, Dropdown.clearMenus);\nEventHandler.on(document, EVENT_KEYUP_DATA_API, Dropdown.clearMenus);\nEventHandler.on(document, EVENT_CLICK_DATA_API$3, SELECTOR_DATA_TOGGLE$3, function (event) {\n event.preventDefault();\n Dropdown.getOrCreateInstance(this).toggle();\n});\n\n/**\n * jQuery\n */\n\ndefineJQueryPlugin(Dropdown);\n\n/**\n * --------------------------------------------------------------------------\n * Bootstrap util/backdrop.js\n * Licensed under MIT (https://github.com/twbs/bootstrap/blob/main/LICENSE)\n * --------------------------------------------------------------------------\n */\n\n\n/**\n * Constants\n */\n\nconst NAME$9 = 'backdrop';\nconst CLASS_NAME_FADE$4 = 'fade';\nconst CLASS_NAME_SHOW$5 = 'show';\nconst EVENT_MOUSEDOWN = `mousedown.bs.${NAME$9}`;\nconst Default$8 = {\n className: 'modal-backdrop',\n clickCallback: null,\n isAnimated: false,\n isVisible: true,\n // if false, we use the backdrop helper without adding any element to the dom\n rootElement: 'body' // give the choice to place backdrop under different elements\n};\nconst DefaultType$8 = {\n className: 'string',\n clickCallback: '(function|null)',\n isAnimated: 'boolean',\n isVisible: 'boolean',\n rootElement: '(element|string)'\n};\n\n/**\n * Class definition\n */\n\nclass Backdrop extends Config {\n constructor(config) {\n super();\n this._config = this._getConfig(config);\n this._isAppended = false;\n this._element = null;\n }\n\n // Getters\n static get Default() {\n return Default$8;\n }\n static get DefaultType() {\n return DefaultType$8;\n }\n static get NAME() {\n return NAME$9;\n }\n\n // Public\n show(callback) {\n if (!this._config.isVisible) {\n execute(callback);\n return;\n }\n this._append();\n const element = this._getElement();\n if (this._config.isAnimated) {\n reflow(element);\n }\n element.classList.add(CLASS_NAME_SHOW$5);\n this._emulateAnimation(() => {\n execute(callback);\n });\n }\n hide(callback) {\n if (!this._config.isVisible) {\n execute(callback);\n return;\n }\n this._getElement().classList.remove(CLASS_NAME_SHOW$5);\n this._emulateAnimation(() => {\n this.dispose();\n execute(callback);\n });\n }\n dispose() {\n if (!this._isAppended) {\n return;\n }\n EventHandler.off(this._element, EVENT_MOUSEDOWN);\n this._element.remove();\n this._isAppended = false;\n }\n\n // Private\n _getElement() {\n if (!this._element) {\n const backdrop = document.createElement('div');\n backdrop.className = this._config.className;\n if (this._config.isAnimated) {\n backdrop.classList.add(CLASS_NAME_FADE$4);\n }\n this._element = backdrop;\n }\n return this._element;\n }\n _configAfterMerge(config) {\n // use getElement() with the default \"body\" to get a fresh Element on each instantiation\n config.rootElement = getElement(config.rootElement);\n return config;\n }\n _append() {\n if (this._isAppended) {\n return;\n }\n const element = this._getElement();\n this._config.rootElement.append(element);\n EventHandler.on(element, EVENT_MOUSEDOWN, () => {\n execute(this._config.clickCallback);\n });\n this._isAppended = true;\n }\n _emulateAnimation(callback) {\n executeAfterTransition(callback, this._getElement(), this._config.isAnimated);\n }\n}\n\n/**\n * --------------------------------------------------------------------------\n * Bootstrap util/focustrap.js\n * Licensed under MIT (https://github.com/twbs/bootstrap/blob/main/LICENSE)\n * --------------------------------------------------------------------------\n */\n\n\n/**\n * Constants\n */\n\nconst NAME$8 = 'focustrap';\nconst DATA_KEY$5 = 'bs.focustrap';\nconst EVENT_KEY$5 = `.${DATA_KEY$5}`;\nconst EVENT_FOCUSIN$2 = `focusin${EVENT_KEY$5}`;\nconst EVENT_KEYDOWN_TAB = `keydown.tab${EVENT_KEY$5}`;\nconst TAB_KEY = 'Tab';\nconst TAB_NAV_FORWARD = 'forward';\nconst TAB_NAV_BACKWARD = 'backward';\nconst Default$7 = {\n autofocus: true,\n trapElement: null // The element to trap focus inside of\n};\nconst DefaultType$7 = {\n autofocus: 'boolean',\n trapElement: 'element'\n};\n\n/**\n * Class definition\n */\n\nclass FocusTrap extends Config {\n constructor(config) {\n super();\n this._config = this._getConfig(config);\n this._isActive = false;\n this._lastTabNavDirection = null;\n }\n\n // Getters\n static get Default() {\n return Default$7;\n }\n static get DefaultType() {\n return DefaultType$7;\n }\n static get NAME() {\n return NAME$8;\n }\n\n // Public\n activate() {\n if (this._isActive) {\n return;\n }\n if (this._config.autofocus) {\n this._config.trapElement.focus();\n }\n EventHandler.off(document, EVENT_KEY$5); // guard against infinite focus loop\n EventHandler.on(document, EVENT_FOCUSIN$2, event => this._handleFocusin(event));\n EventHandler.on(document, EVENT_KEYDOWN_TAB, event => this._handleKeydown(event));\n this._isActive = true;\n }\n deactivate() {\n if (!this._isActive) {\n return;\n }\n this._isActive = false;\n EventHandler.off(document, EVENT_KEY$5);\n }\n\n // Private\n _handleFocusin(event) {\n const {\n trapElement\n } = this._config;\n if (event.target === document || event.target === trapElement || trapElement.contains(event.target)) {\n return;\n }\n const elements = SelectorEngine.focusableChildren(trapElement);\n if (elements.length === 0) {\n trapElement.focus();\n } else if (this._lastTabNavDirection === TAB_NAV_BACKWARD) {\n elements[elements.length - 1].focus();\n } else {\n elements[0].focus();\n }\n }\n _handleKeydown(event) {\n if (event.key !== TAB_KEY) {\n return;\n }\n this._lastTabNavDirection = event.shiftKey ? TAB_NAV_BACKWARD : TAB_NAV_FORWARD;\n }\n}\n\n/**\n * --------------------------------------------------------------------------\n * Bootstrap util/scrollBar.js\n * Licensed under MIT (https://github.com/twbs/bootstrap/blob/main/LICENSE)\n * --------------------------------------------------------------------------\n */\n\n\n/**\n * Constants\n */\n\nconst SELECTOR_FIXED_CONTENT = '.fixed-top, .fixed-bottom, .is-fixed, .sticky-top';\nconst SELECTOR_STICKY_CONTENT = '.sticky-top';\nconst PROPERTY_PADDING = 'padding-right';\nconst PROPERTY_MARGIN = 'margin-right';\n\n/**\n * Class definition\n */\n\nclass ScrollBarHelper {\n constructor() {\n this._element = document.body;\n }\n\n // Public\n getWidth() {\n // https://developer.mozilla.org/en-US/docs/Web/API/Window/innerWidth#usage_notes\n const documentWidth = document.documentElement.clientWidth;\n return Math.abs(window.innerWidth - documentWidth);\n }\n hide() {\n const width = this.getWidth();\n this._disableOverFlow();\n // give padding to element to balance the hidden scrollbar width\n this._setElementAttributes(this._element, PROPERTY_PADDING, calculatedValue => calculatedValue + width);\n // trick: We adjust positive paddingRight and negative marginRight to sticky-top elements to keep showing fullwidth\n this._setElementAttributes(SELECTOR_FIXED_CONTENT, PROPERTY_PADDING, calculatedValue => calculatedValue + width);\n this._setElementAttributes(SELECTOR_STICKY_CONTENT, PROPERTY_MARGIN, calculatedValue => calculatedValue - width);\n }\n reset() {\n this._resetElementAttributes(this._element, 'overflow');\n this._resetElementAttributes(this._element, PROPERTY_PADDING);\n this._resetElementAttributes(SELECTOR_FIXED_CONTENT, PROPERTY_PADDING);\n this._resetElementAttributes(SELECTOR_STICKY_CONTENT, PROPERTY_MARGIN);\n }\n isOverflowing() {\n return this.getWidth() > 0;\n }\n\n // Private\n _disableOverFlow() {\n this._saveInitialAttribute(this._element, 'overflow');\n this._element.style.overflow = 'hidden';\n }\n _setElementAttributes(selector, styleProperty, callback) {\n const scrollbarWidth = this.getWidth();\n const manipulationCallBack = element => {\n if (element !== this._element && window.innerWidth > element.clientWidth + scrollbarWidth) {\n return;\n }\n this._saveInitialAttribute(element, styleProperty);\n const calculatedValue = window.getComputedStyle(element).getPropertyValue(styleProperty);\n element.style.setProperty(styleProperty, `${callback(Number.parseFloat(calculatedValue))}px`);\n };\n this._applyManipulationCallback(selector, manipulationCallBack);\n }\n _saveInitialAttribute(element, styleProperty) {\n const actualValue = element.style.getPropertyValue(styleProperty);\n if (actualValue) {\n Manipulator.setDataAttribute(element, styleProperty, actualValue);\n }\n }\n _resetElementAttributes(selector, styleProperty) {\n const manipulationCallBack = element => {\n const value = Manipulator.getDataAttribute(element, styleProperty);\n // We only want to remove the property if the value is `null`; the value can also be zero\n if (value === null) {\n element.style.removeProperty(styleProperty);\n return;\n }\n Manipulator.removeDataAttribute(element, styleProperty);\n element.style.setProperty(styleProperty, value);\n };\n this._applyManipulationCallback(selector, manipulationCallBack);\n }\n _applyManipulationCallback(selector, callBack) {\n if (isElement(selector)) {\n callBack(selector);\n return;\n }\n for (const sel of SelectorEngine.find(selector, this._element)) {\n callBack(sel);\n }\n }\n}\n\n/**\n * --------------------------------------------------------------------------\n * Bootstrap modal.js\n * Licensed under MIT (https://github.com/twbs/bootstrap/blob/main/LICENSE)\n * --------------------------------------------------------------------------\n */\n\n\n/**\n * Constants\n */\n\nconst NAME$7 = 'modal';\nconst DATA_KEY$4 = 'bs.modal';\nconst EVENT_KEY$4 = `.${DATA_KEY$4}`;\nconst DATA_API_KEY$2 = '.data-api';\nconst ESCAPE_KEY$1 = 'Escape';\nconst EVENT_HIDE$4 = `hide${EVENT_KEY$4}`;\nconst EVENT_HIDE_PREVENTED$1 = `hidePrevented${EVENT_KEY$4}`;\nconst EVENT_HIDDEN$4 = `hidden${EVENT_KEY$4}`;\nconst EVENT_SHOW$4 = `show${EVENT_KEY$4}`;\nconst EVENT_SHOWN$4 = `shown${EVENT_KEY$4}`;\nconst EVENT_RESIZE$1 = `resize${EVENT_KEY$4}`;\nconst EVENT_CLICK_DISMISS = `click.dismiss${EVENT_KEY$4}`;\nconst EVENT_MOUSEDOWN_DISMISS = `mousedown.dismiss${EVENT_KEY$4}`;\nconst EVENT_KEYDOWN_DISMISS$1 = `keydown.dismiss${EVENT_KEY$4}`;\nconst EVENT_CLICK_DATA_API$2 = `click${EVENT_KEY$4}${DATA_API_KEY$2}`;\nconst CLASS_NAME_OPEN = 'modal-open';\nconst CLASS_NAME_FADE$3 = 'fade';\nconst CLASS_NAME_SHOW$4 = 'show';\nconst CLASS_NAME_STATIC = 'modal-static';\nconst OPEN_SELECTOR$1 = '.modal.show';\nconst SELECTOR_DIALOG = '.modal-dialog';\nconst SELECTOR_MODAL_BODY = '.modal-body';\nconst SELECTOR_DATA_TOGGLE$2 = '[data-bs-toggle=\"modal\"]';\nconst Default$6 = {\n backdrop: true,\n focus: true,\n keyboard: true\n};\nconst DefaultType$6 = {\n backdrop: '(boolean|string)',\n focus: 'boolean',\n keyboard: 'boolean'\n};\n\n/**\n * Class definition\n */\n\nclass Modal extends BaseComponent {\n constructor(element, config) {\n super(element, config);\n this._dialog = SelectorEngine.findOne(SELECTOR_DIALOG, this._element);\n this._backdrop = this._initializeBackDrop();\n this._focustrap = this._initializeFocusTrap();\n this._isShown = false;\n this._isTransitioning = false;\n this._scrollBar = new ScrollBarHelper();\n this._addEventListeners();\n }\n\n // Getters\n static get Default() {\n return Default$6;\n }\n static get DefaultType() {\n return DefaultType$6;\n }\n static get NAME() {\n return NAME$7;\n }\n\n // Public\n toggle(relatedTarget) {\n return this._isShown ? this.hide() : this.show(relatedTarget);\n }\n show(relatedTarget) {\n if (this._isShown || this._isTransitioning) {\n return;\n }\n const showEvent = EventHandler.trigger(this._element, EVENT_SHOW$4, {\n relatedTarget\n });\n if (showEvent.defaultPrevented) {\n return;\n }\n this._isShown = true;\n this._isTransitioning = true;\n this._scrollBar.hide();\n document.body.classList.add(CLASS_NAME_OPEN);\n this._adjustDialog();\n this._backdrop.show(() => this._showElement(relatedTarget));\n }\n hide() {\n if (!this._isShown || this._isTransitioning) {\n return;\n }\n const hideEvent = EventHandler.trigger(this._element, EVENT_HIDE$4);\n if (hideEvent.defaultPrevented) {\n return;\n }\n this._isShown = false;\n this._isTransitioning = true;\n this._focustrap.deactivate();\n this._element.classList.remove(CLASS_NAME_SHOW$4);\n this._queueCallback(() => this._hideModal(), this._element, this._isAnimated());\n }\n dispose() {\n EventHandler.off(window, EVENT_KEY$4);\n EventHandler.off(this._dialog, EVENT_KEY$4);\n this._backdrop.dispose();\n this._focustrap.deactivate();\n super.dispose();\n }\n handleUpdate() {\n this._adjustDialog();\n }\n\n // Private\n _initializeBackDrop() {\n return new Backdrop({\n isVisible: Boolean(this._config.backdrop),\n // 'static' option will be translated to true, and booleans will keep their value,\n isAnimated: this._isAnimated()\n });\n }\n _initializeFocusTrap() {\n return new FocusTrap({\n trapElement: this._element\n });\n }\n _showElement(relatedTarget) {\n // try to append dynamic modal\n if (!document.body.contains(this._element)) {\n document.body.append(this._element);\n }\n this._element.style.display = 'block';\n this._element.removeAttribute('aria-hidden');\n this._element.setAttribute('aria-modal', true);\n this._element.setAttribute('role', 'dialog');\n this._element.scrollTop = 0;\n const modalBody = SelectorEngine.findOne(SELECTOR_MODAL_BODY, this._dialog);\n if (modalBody) {\n modalBody.scrollTop = 0;\n }\n reflow(this._element);\n this._element.classList.add(CLASS_NAME_SHOW$4);\n const transitionComplete = () => {\n if (this._config.focus) {\n this._focustrap.activate();\n }\n this._isTransitioning = false;\n EventHandler.trigger(this._element, EVENT_SHOWN$4, {\n relatedTarget\n });\n };\n this._queueCallback(transitionComplete, this._dialog, this._isAnimated());\n }\n _addEventListeners() {\n EventHandler.on(this._element, EVENT_KEYDOWN_DISMISS$1, event => {\n if (event.key !== ESCAPE_KEY$1) {\n return;\n }\n if (this._config.keyboard) {\n this.hide();\n return;\n }\n this._triggerBackdropTransition();\n });\n EventHandler.on(window, EVENT_RESIZE$1, () => {\n if (this._isShown && !this._isTransitioning) {\n this._adjustDialog();\n }\n });\n EventHandler.on(this._element, EVENT_MOUSEDOWN_DISMISS, event => {\n // a bad trick to segregate clicks that may start inside dialog but end outside, and avoid listen to scrollbar clicks\n EventHandler.one(this._element, EVENT_CLICK_DISMISS, event2 => {\n if (this._element !== event.target || this._element !== event2.target) {\n return;\n }\n if (this._config.backdrop === 'static') {\n this._triggerBackdropTransition();\n return;\n }\n if (this._config.backdrop) {\n this.hide();\n }\n });\n });\n }\n _hideModal() {\n this._element.style.display = 'none';\n this._element.setAttribute('aria-hidden', true);\n this._element.removeAttribute('aria-modal');\n this._element.removeAttribute('role');\n this._isTransitioning = false;\n this._backdrop.hide(() => {\n document.body.classList.remove(CLASS_NAME_OPEN);\n this._resetAdjustments();\n this._scrollBar.reset();\n EventHandler.trigger(this._element, EVENT_HIDDEN$4);\n });\n }\n _isAnimated() {\n return this._element.classList.contains(CLASS_NAME_FADE$3);\n }\n _triggerBackdropTransition() {\n const hideEvent = EventHandler.trigger(this._element, EVENT_HIDE_PREVENTED$1);\n if (hideEvent.defaultPrevented) {\n return;\n }\n const isModalOverflowing = this._element.scrollHeight > document.documentElement.clientHeight;\n const initialOverflowY = this._element.style.overflowY;\n // return if the following background transition hasn't yet completed\n if (initialOverflowY === 'hidden' || this._element.classList.contains(CLASS_NAME_STATIC)) {\n return;\n }\n if (!isModalOverflowing) {\n this._element.style.overflowY = 'hidden';\n }\n this._element.classList.add(CLASS_NAME_STATIC);\n this._queueCallback(() => {\n this._element.classList.remove(CLASS_NAME_STATIC);\n this._queueCallback(() => {\n this._element.style.overflowY = initialOverflowY;\n }, this._dialog);\n }, this._dialog);\n this._element.focus();\n }\n\n /**\n * The following methods are used to handle overflowing modals\n */\n\n _adjustDialog() {\n const isModalOverflowing = this._element.scrollHeight > document.documentElement.clientHeight;\n const scrollbarWidth = this._scrollBar.getWidth();\n const isBodyOverflowing = scrollbarWidth > 0;\n if (isBodyOverflowing && !isModalOverflowing) {\n const property = isRTL() ? 'paddingLeft' : 'paddingRight';\n this._element.style[property] = `${scrollbarWidth}px`;\n }\n if (!isBodyOverflowing && isModalOverflowing) {\n const property = isRTL() ? 'paddingRight' : 'paddingLeft';\n this._element.style[property] = `${scrollbarWidth}px`;\n }\n }\n _resetAdjustments() {\n this._element.style.paddingLeft = '';\n this._element.style.paddingRight = '';\n }\n\n // Static\n static jQueryInterface(config, relatedTarget) {\n return this.each(function () {\n const data = Modal.getOrCreateInstance(this, config);\n if (typeof config !== 'string') {\n return;\n }\n if (typeof data[config] === 'undefined') {\n throw new TypeError(`No method named \"${config}\"`);\n }\n data[config](relatedTarget);\n });\n }\n}\n\n/**\n * Data API implementation\n */\n\nEventHandler.on(document, EVENT_CLICK_DATA_API$2, SELECTOR_DATA_TOGGLE$2, function (event) {\n const target = SelectorEngine.getElementFromSelector(this);\n if (['A', 'AREA'].includes(this.tagName)) {\n event.preventDefault();\n }\n EventHandler.one(target, EVENT_SHOW$4, showEvent => {\n if (showEvent.defaultPrevented) {\n // only register focus restorer if modal will actually get shown\n return;\n }\n EventHandler.one(target, EVENT_HIDDEN$4, () => {\n if (isVisible(this)) {\n this.focus();\n }\n });\n });\n\n // avoid conflict when clicking modal toggler while another one is open\n const alreadyOpen = SelectorEngine.findOne(OPEN_SELECTOR$1);\n if (alreadyOpen) {\n Modal.getInstance(alreadyOpen).hide();\n }\n const data = Modal.getOrCreateInstance(target);\n data.toggle(this);\n});\nenableDismissTrigger(Modal);\n\n/**\n * jQuery\n */\n\ndefineJQueryPlugin(Modal);\n\n/**\n * --------------------------------------------------------------------------\n * Bootstrap offcanvas.js\n * Licensed under MIT (https://github.com/twbs/bootstrap/blob/main/LICENSE)\n * --------------------------------------------------------------------------\n */\n\n\n/**\n * Constants\n */\n\nconst NAME$6 = 'offcanvas';\nconst DATA_KEY$3 = 'bs.offcanvas';\nconst EVENT_KEY$3 = `.${DATA_KEY$3}`;\nconst DATA_API_KEY$1 = '.data-api';\nconst EVENT_LOAD_DATA_API$2 = `load${EVENT_KEY$3}${DATA_API_KEY$1}`;\nconst ESCAPE_KEY = 'Escape';\nconst CLASS_NAME_SHOW$3 = 'show';\nconst CLASS_NAME_SHOWING$1 = 'showing';\nconst CLASS_NAME_HIDING = 'hiding';\nconst CLASS_NAME_BACKDROP = 'offcanvas-backdrop';\nconst OPEN_SELECTOR = '.offcanvas.show';\nconst EVENT_SHOW$3 = `show${EVENT_KEY$3}`;\nconst EVENT_SHOWN$3 = `shown${EVENT_KEY$3}`;\nconst EVENT_HIDE$3 = `hide${EVENT_KEY$3}`;\nconst EVENT_HIDE_PREVENTED = `hidePrevented${EVENT_KEY$3}`;\nconst EVENT_HIDDEN$3 = `hidden${EVENT_KEY$3}`;\nconst EVENT_RESIZE = `resize${EVENT_KEY$3}`;\nconst EVENT_CLICK_DATA_API$1 = `click${EVENT_KEY$3}${DATA_API_KEY$1}`;\nconst EVENT_KEYDOWN_DISMISS = `keydown.dismiss${EVENT_KEY$3}`;\nconst SELECTOR_DATA_TOGGLE$1 = '[data-bs-toggle=\"offcanvas\"]';\nconst Default$5 = {\n backdrop: true,\n keyboard: true,\n scroll: false\n};\nconst DefaultType$5 = {\n backdrop: '(boolean|string)',\n keyboard: 'boolean',\n scroll: 'boolean'\n};\n\n/**\n * Class definition\n */\n\nclass Offcanvas extends BaseComponent {\n constructor(element, config) {\n super(element, config);\n this._isShown = false;\n this._backdrop = this._initializeBackDrop();\n this._focustrap = this._initializeFocusTrap();\n this._addEventListeners();\n }\n\n // Getters\n static get Default() {\n return Default$5;\n }\n static get DefaultType() {\n return DefaultType$5;\n }\n static get NAME() {\n return NAME$6;\n }\n\n // Public\n toggle(relatedTarget) {\n return this._isShown ? this.hide() : this.show(relatedTarget);\n }\n show(relatedTarget) {\n if (this._isShown) {\n return;\n }\n const showEvent = EventHandler.trigger(this._element, EVENT_SHOW$3, {\n relatedTarget\n });\n if (showEvent.defaultPrevented) {\n return;\n }\n this._isShown = true;\n this._backdrop.show();\n if (!this._config.scroll) {\n new ScrollBarHelper().hide();\n }\n this._element.setAttribute('aria-modal', true);\n this._element.setAttribute('role', 'dialog');\n this._element.classList.add(CLASS_NAME_SHOWING$1);\n const completeCallBack = () => {\n if (!this._config.scroll || this._config.backdrop) {\n this._focustrap.activate();\n }\n this._element.classList.add(CLASS_NAME_SHOW$3);\n this._element.classList.remove(CLASS_NAME_SHOWING$1);\n EventHandler.trigger(this._element, EVENT_SHOWN$3, {\n relatedTarget\n });\n };\n this._queueCallback(completeCallBack, this._element, true);\n }\n hide() {\n if (!this._isShown) {\n return;\n }\n const hideEvent = EventHandler.trigger(this._element, EVENT_HIDE$3);\n if (hideEvent.defaultPrevented) {\n return;\n }\n this._focustrap.deactivate();\n this._element.blur();\n this._isShown = false;\n this._element.classList.add(CLASS_NAME_HIDING);\n this._backdrop.hide();\n const completeCallback = () => {\n this._element.classList.remove(CLASS_NAME_SHOW$3, CLASS_NAME_HIDING);\n this._element.removeAttribute('aria-modal');\n this._element.removeAttribute('role');\n if (!this._config.scroll) {\n new ScrollBarHelper().reset();\n }\n EventHandler.trigger(this._element, EVENT_HIDDEN$3);\n };\n this._queueCallback(completeCallback, this._element, true);\n }\n dispose() {\n this._backdrop.dispose();\n this._focustrap.deactivate();\n super.dispose();\n }\n\n // Private\n _initializeBackDrop() {\n const clickCallback = () => {\n if (this._config.backdrop === 'static') {\n EventHandler.trigger(this._element, EVENT_HIDE_PREVENTED);\n return;\n }\n this.hide();\n };\n\n // 'static' option will be translated to true, and booleans will keep their value\n const isVisible = Boolean(this._config.backdrop);\n return new Backdrop({\n className: CLASS_NAME_BACKDROP,\n isVisible,\n isAnimated: true,\n rootElement: this._element.parentNode,\n clickCallback: isVisible ? clickCallback : null\n });\n }\n _initializeFocusTrap() {\n return new FocusTrap({\n trapElement: this._element\n });\n }\n _addEventListeners() {\n EventHandler.on(this._element, EVENT_KEYDOWN_DISMISS, event => {\n if (event.key !== ESCAPE_KEY) {\n return;\n }\n if (this._config.keyboard) {\n this.hide();\n return;\n }\n EventHandler.trigger(this._element, EVENT_HIDE_PREVENTED);\n });\n }\n\n // Static\n static jQueryInterface(config) {\n return this.each(function () {\n const data = Offcanvas.getOrCreateInstance(this, config);\n if (typeof config !== 'string') {\n return;\n }\n if (data[config] === undefined || config.startsWith('_') || config === 'constructor') {\n throw new TypeError(`No method named \"${config}\"`);\n }\n data[config](this);\n });\n }\n}\n\n/**\n * Data API implementation\n */\n\nEventHandler.on(document, EVENT_CLICK_DATA_API$1, SELECTOR_DATA_TOGGLE$1, function (event) {\n const target = SelectorEngine.getElementFromSelector(this);\n if (['A', 'AREA'].includes(this.tagName)) {\n event.preventDefault();\n }\n if (isDisabled(this)) {\n return;\n }\n EventHandler.one(target, EVENT_HIDDEN$3, () => {\n // focus on trigger when it is closed\n if (isVisible(this)) {\n this.focus();\n }\n });\n\n // avoid conflict when clicking a toggler of an offcanvas, while another is open\n const alreadyOpen = SelectorEngine.findOne(OPEN_SELECTOR);\n if (alreadyOpen && alreadyOpen !== target) {\n Offcanvas.getInstance(alreadyOpen).hide();\n }\n const data = Offcanvas.getOrCreateInstance(target);\n data.toggle(this);\n});\nEventHandler.on(window, EVENT_LOAD_DATA_API$2, () => {\n for (const selector of SelectorEngine.find(OPEN_SELECTOR)) {\n Offcanvas.getOrCreateInstance(selector).show();\n }\n});\nEventHandler.on(window, EVENT_RESIZE, () => {\n for (const element of SelectorEngine.find('[aria-modal][class*=show][class*=offcanvas-]')) {\n if (getComputedStyle(element).position !== 'fixed') {\n Offcanvas.getOrCreateInstance(element).hide();\n }\n }\n});\nenableDismissTrigger(Offcanvas);\n\n/**\n * jQuery\n */\n\ndefineJQueryPlugin(Offcanvas);\n\n/**\n * --------------------------------------------------------------------------\n * Bootstrap util/sanitizer.js\n * Licensed under MIT (https://github.com/twbs/bootstrap/blob/main/LICENSE)\n * --------------------------------------------------------------------------\n */\n\n// js-docs-start allow-list\nconst ARIA_ATTRIBUTE_PATTERN = /^aria-[\\w-]*$/i;\nconst DefaultAllowlist = {\n // Global attributes allowed on any supplied element below.\n '*': ['class', 'dir', 'id', 'lang', 'role', ARIA_ATTRIBUTE_PATTERN],\n a: ['target', 'href', 'title', 'rel'],\n area: [],\n b: [],\n br: [],\n col: [],\n code: [],\n dd: [],\n div: [],\n dl: [],\n dt: [],\n em: [],\n hr: [],\n h1: [],\n h2: [],\n h3: [],\n h4: [],\n h5: [],\n h6: [],\n i: [],\n img: ['src', 'srcset', 'alt', 'title', 'width', 'height'],\n li: [],\n ol: [],\n p: [],\n pre: [],\n s: [],\n small: [],\n span: [],\n sub: [],\n sup: [],\n strong: [],\n u: [],\n ul: []\n};\n// js-docs-end allow-list\n\nconst uriAttributes = new Set(['background', 'cite', 'href', 'itemtype', 'longdesc', 'poster', 'src', 'xlink:href']);\n\n/**\n * A pattern that recognizes URLs that are safe wrt. XSS in URL navigation\n * contexts.\n *\n * Shout-out to Angular https://github.com/angular/angular/blob/15.2.8/packages/core/src/sanitization/url_sanitizer.ts#L38\n */\n// eslint-disable-next-line unicorn/better-regex\nconst SAFE_URL_PATTERN = /^(?!javascript:)(?:[a-z0-9+.-]+:|[^&:/?#]*(?:[/?#]|$))/i;\nconst allowedAttribute = (attribute, allowedAttributeList) => {\n const attributeName = attribute.nodeName.toLowerCase();\n if (allowedAttributeList.includes(attributeName)) {\n if (uriAttributes.has(attributeName)) {\n return Boolean(SAFE_URL_PATTERN.test(attribute.nodeValue));\n }\n return true;\n }\n\n // Check if a regular expression validates the attribute.\n return allowedAttributeList.filter(attributeRegex => attributeRegex instanceof RegExp).some(regex => regex.test(attributeName));\n};\nfunction sanitizeHtml(unsafeHtml, allowList, sanitizeFunction) {\n if (!unsafeHtml.length) {\n return unsafeHtml;\n }\n if (sanitizeFunction && typeof sanitizeFunction === 'function') {\n return sanitizeFunction(unsafeHtml);\n }\n const domParser = new window.DOMParser();\n const createdDocument = domParser.parseFromString(unsafeHtml, 'text/html');\n const elements = [].concat(...createdDocument.body.querySelectorAll('*'));\n for (const element of elements) {\n const elementName = element.nodeName.toLowerCase();\n if (!Object.keys(allowList).includes(elementName)) {\n element.remove();\n continue;\n }\n const attributeList = [].concat(...element.attributes);\n const allowedAttributes = [].concat(allowList['*'] || [], allowList[elementName] || []);\n for (const attribute of attributeList) {\n if (!allowedAttribute(attribute, allowedAttributes)) {\n element.removeAttribute(attribute.nodeName);\n }\n }\n }\n return createdDocument.body.innerHTML;\n}\n\n/**\n * --------------------------------------------------------------------------\n * Bootstrap util/template-factory.js\n * Licensed under MIT (https://github.com/twbs/bootstrap/blob/main/LICENSE)\n * --------------------------------------------------------------------------\n */\n\n\n/**\n * Constants\n */\n\nconst NAME$5 = 'TemplateFactory';\nconst Default$4 = {\n allowList: DefaultAllowlist,\n content: {},\n // { selector : text , selector2 : text2 , }\n extraClass: '',\n html: false,\n sanitize: true,\n sanitizeFn: null,\n template: '
'\n};\nconst DefaultType$4 = {\n allowList: 'object',\n content: 'object',\n extraClass: '(string|function)',\n html: 'boolean',\n sanitize: 'boolean',\n sanitizeFn: '(null|function)',\n template: 'string'\n};\nconst DefaultContentType = {\n entry: '(string|element|function|null)',\n selector: '(string|element)'\n};\n\n/**\n * Class definition\n */\n\nclass TemplateFactory extends Config {\n constructor(config) {\n super();\n this._config = this._getConfig(config);\n }\n\n // Getters\n static get Default() {\n return Default$4;\n }\n static get DefaultType() {\n return DefaultType$4;\n }\n static get NAME() {\n return NAME$5;\n }\n\n // Public\n getContent() {\n return Object.values(this._config.content).map(config => this._resolvePossibleFunction(config)).filter(Boolean);\n }\n hasContent() {\n return this.getContent().length > 0;\n }\n changeContent(content) {\n this._checkContent(content);\n this._config.content = {\n ...this._config.content,\n ...content\n };\n return this;\n }\n toHtml() {\n const templateWrapper = document.createElement('div');\n templateWrapper.innerHTML = this._maybeSanitize(this._config.template);\n for (const [selector, text] of Object.entries(this._config.content)) {\n this._setContent(templateWrapper, text, selector);\n }\n const template = templateWrapper.children[0];\n const extraClass = this._resolvePossibleFunction(this._config.extraClass);\n if (extraClass) {\n template.classList.add(...extraClass.split(' '));\n }\n return template;\n }\n\n // Private\n _typeCheckConfig(config) {\n super._typeCheckConfig(config);\n this._checkContent(config.content);\n }\n _checkContent(arg) {\n for (const [selector, content] of Object.entries(arg)) {\n super._typeCheckConfig({\n selector,\n entry: content\n }, DefaultContentType);\n }\n }\n _setContent(template, content, selector) {\n const templateElement = SelectorEngine.findOne(selector, template);\n if (!templateElement) {\n return;\n }\n content = this._resolvePossibleFunction(content);\n if (!content) {\n templateElement.remove();\n return;\n }\n if (isElement(content)) {\n this._putElementInTemplate(getElement(content), templateElement);\n return;\n }\n if (this._config.html) {\n templateElement.innerHTML = this._maybeSanitize(content);\n return;\n }\n templateElement.textContent = content;\n }\n _maybeSanitize(arg) {\n return this._config.sanitize ? sanitizeHtml(arg, this._config.allowList, this._config.sanitizeFn) : arg;\n }\n _resolvePossibleFunction(arg) {\n return execute(arg, [this]);\n }\n _putElementInTemplate(element, templateElement) {\n if (this._config.html) {\n templateElement.innerHTML = '';\n templateElement.append(element);\n return;\n }\n templateElement.textContent = element.textContent;\n }\n}\n\n/**\n * --------------------------------------------------------------------------\n * Bootstrap tooltip.js\n * Licensed under MIT (https://github.com/twbs/bootstrap/blob/main/LICENSE)\n * --------------------------------------------------------------------------\n */\n\n\n/**\n * Constants\n */\n\nconst NAME$4 = 'tooltip';\nconst DISALLOWED_ATTRIBUTES = new Set(['sanitize', 'allowList', 'sanitizeFn']);\nconst CLASS_NAME_FADE$2 = 'fade';\nconst CLASS_NAME_MODAL = 'modal';\nconst CLASS_NAME_SHOW$2 = 'show';\nconst SELECTOR_TOOLTIP_INNER = '.tooltip-inner';\nconst SELECTOR_MODAL = `.${CLASS_NAME_MODAL}`;\nconst EVENT_MODAL_HIDE = 'hide.bs.modal';\nconst TRIGGER_HOVER = 'hover';\nconst TRIGGER_FOCUS = 'focus';\nconst TRIGGER_CLICK = 'click';\nconst TRIGGER_MANUAL = 'manual';\nconst EVENT_HIDE$2 = 'hide';\nconst EVENT_HIDDEN$2 = 'hidden';\nconst EVENT_SHOW$2 = 'show';\nconst EVENT_SHOWN$2 = 'shown';\nconst EVENT_INSERTED = 'inserted';\nconst EVENT_CLICK$1 = 'click';\nconst EVENT_FOCUSIN$1 = 'focusin';\nconst EVENT_FOCUSOUT$1 = 'focusout';\nconst EVENT_MOUSEENTER = 'mouseenter';\nconst EVENT_MOUSELEAVE = 'mouseleave';\nconst AttachmentMap = {\n AUTO: 'auto',\n TOP: 'top',\n RIGHT: isRTL() ? 'left' : 'right',\n BOTTOM: 'bottom',\n LEFT: isRTL() ? 'right' : 'left'\n};\nconst Default$3 = {\n allowList: DefaultAllowlist,\n animation: true,\n boundary: 'clippingParents',\n container: false,\n customClass: '',\n delay: 0,\n fallbackPlacements: ['top', 'right', 'bottom', 'left'],\n html: false,\n offset: [0, 6],\n placement: 'top',\n popperConfig: null,\n sanitize: true,\n sanitizeFn: null,\n selector: false,\n template: '
' + '
' + '
' + '
',\n title: '',\n trigger: 'hover focus'\n};\nconst DefaultType$3 = {\n allowList: 'object',\n animation: 'boolean',\n boundary: '(string|element)',\n container: '(string|element|boolean)',\n customClass: '(string|function)',\n delay: '(number|object)',\n fallbackPlacements: 'array',\n html: 'boolean',\n offset: '(array|string|function)',\n placement: '(string|function)',\n popperConfig: '(null|object|function)',\n sanitize: 'boolean',\n sanitizeFn: '(null|function)',\n selector: '(string|boolean)',\n template: 'string',\n title: '(string|element|function)',\n trigger: 'string'\n};\n\n/**\n * Class definition\n */\n\nclass Tooltip extends BaseComponent {\n constructor(element, config) {\n if (typeof Popper === 'undefined') {\n throw new TypeError('Bootstrap\\'s tooltips require Popper (https://popper.js.org)');\n }\n super(element, config);\n\n // Private\n this._isEnabled = true;\n this._timeout = 0;\n this._isHovered = null;\n this._activeTrigger = {};\n this._popper = null;\n this._templateFactory = null;\n this._newContent = null;\n\n // Protected\n this.tip = null;\n this._setListeners();\n if (!this._config.selector) {\n this._fixTitle();\n }\n }\n\n // Getters\n static get Default() {\n return Default$3;\n }\n static get DefaultType() {\n return DefaultType$3;\n }\n static get NAME() {\n return NAME$4;\n }\n\n // Public\n enable() {\n this._isEnabled = true;\n }\n disable() {\n this._isEnabled = false;\n }\n toggleEnabled() {\n this._isEnabled = !this._isEnabled;\n }\n toggle() {\n if (!this._isEnabled) {\n return;\n }\n this._activeTrigger.click = !this._activeTrigger.click;\n if (this._isShown()) {\n this._leave();\n return;\n }\n this._enter();\n }\n dispose() {\n clearTimeout(this._timeout);\n EventHandler.off(this._element.closest(SELECTOR_MODAL), EVENT_MODAL_HIDE, this._hideModalHandler);\n if (this._element.getAttribute('data-bs-original-title')) {\n this._element.setAttribute('title', this._element.getAttribute('data-bs-original-title'));\n }\n this._disposePopper();\n super.dispose();\n }\n show() {\n if (this._element.style.display === 'none') {\n throw new Error('Please use show on visible elements');\n }\n if (!(this._isWithContent() && this._isEnabled)) {\n return;\n }\n const showEvent = EventHandler.trigger(this._element, this.constructor.eventName(EVENT_SHOW$2));\n const shadowRoot = findShadowRoot(this._element);\n const isInTheDom = (shadowRoot || this._element.ownerDocument.documentElement).contains(this._element);\n if (showEvent.defaultPrevented || !isInTheDom) {\n return;\n }\n\n // TODO: v6 remove this or make it optional\n this._disposePopper();\n const tip = this._getTipElement();\n this._element.setAttribute('aria-describedby', tip.getAttribute('id'));\n const {\n container\n } = this._config;\n if (!this._element.ownerDocument.documentElement.contains(this.tip)) {\n container.append(tip);\n EventHandler.trigger(this._element, this.constructor.eventName(EVENT_INSERTED));\n }\n this._popper = this._createPopper(tip);\n tip.classList.add(CLASS_NAME_SHOW$2);\n\n // If this is a touch-enabled device we add extra\n // empty mouseover listeners to the body's immediate children;\n // only needed because of broken event delegation on iOS\n // https://www.quirksmode.org/blog/archives/2014/02/mouse_event_bub.html\n if ('ontouchstart' in document.documentElement) {\n for (const element of [].concat(...document.body.children)) {\n EventHandler.on(element, 'mouseover', noop);\n }\n }\n const complete = () => {\n EventHandler.trigger(this._element, this.constructor.eventName(EVENT_SHOWN$2));\n if (this._isHovered === false) {\n this._leave();\n }\n this._isHovered = false;\n };\n this._queueCallback(complete, this.tip, this._isAnimated());\n }\n hide() {\n if (!this._isShown()) {\n return;\n }\n const hideEvent = EventHandler.trigger(this._element, this.constructor.eventName(EVENT_HIDE$2));\n if (hideEvent.defaultPrevented) {\n return;\n }\n const tip = this._getTipElement();\n tip.classList.remove(CLASS_NAME_SHOW$2);\n\n // If this is a touch-enabled device we remove the extra\n // empty mouseover listeners we added for iOS support\n if ('ontouchstart' in document.documentElement) {\n for (const element of [].concat(...document.body.children)) {\n EventHandler.off(element, 'mouseover', noop);\n }\n }\n this._activeTrigger[TRIGGER_CLICK] = false;\n this._activeTrigger[TRIGGER_FOCUS] = false;\n this._activeTrigger[TRIGGER_HOVER] = false;\n this._isHovered = null; // it is a trick to support manual triggering\n\n const complete = () => {\n if (this._isWithActiveTrigger()) {\n return;\n }\n if (!this._isHovered) {\n this._disposePopper();\n }\n this._element.removeAttribute('aria-describedby');\n EventHandler.trigger(this._element, this.constructor.eventName(EVENT_HIDDEN$2));\n };\n this._queueCallback(complete, this.tip, this._isAnimated());\n }\n update() {\n if (this._popper) {\n this._popper.update();\n }\n }\n\n // Protected\n _isWithContent() {\n return Boolean(this._getTitle());\n }\n _getTipElement() {\n if (!this.tip) {\n this.tip = this._createTipElement(this._newContent || this._getContentForTemplate());\n }\n return this.tip;\n }\n _createTipElement(content) {\n const tip = this._getTemplateFactory(content).toHtml();\n\n // TODO: remove this check in v6\n if (!tip) {\n return null;\n }\n tip.classList.remove(CLASS_NAME_FADE$2, CLASS_NAME_SHOW$2);\n // TODO: v6 the following can be achieved with CSS only\n tip.classList.add(`bs-${this.constructor.NAME}-auto`);\n const tipId = getUID(this.constructor.NAME).toString();\n tip.setAttribute('id', tipId);\n if (this._isAnimated()) {\n tip.classList.add(CLASS_NAME_FADE$2);\n }\n return tip;\n }\n setContent(content) {\n this._newContent = content;\n if (this._isShown()) {\n this._disposePopper();\n this.show();\n }\n }\n _getTemplateFactory(content) {\n if (this._templateFactory) {\n this._templateFactory.changeContent(content);\n } else {\n this._templateFactory = new TemplateFactory({\n ...this._config,\n // the `content` var has to be after `this._config`\n // to override config.content in case of popover\n content,\n extraClass: this._resolvePossibleFunction(this._config.customClass)\n });\n }\n return this._templateFactory;\n }\n _getContentForTemplate() {\n return {\n [SELECTOR_TOOLTIP_INNER]: this._getTitle()\n };\n }\n _getTitle() {\n return this._resolvePossibleFunction(this._config.title) || this._element.getAttribute('data-bs-original-title');\n }\n\n // Private\n _initializeOnDelegatedTarget(event) {\n return this.constructor.getOrCreateInstance(event.delegateTarget, this._getDelegateConfig());\n }\n _isAnimated() {\n return this._config.animation || this.tip && this.tip.classList.contains(CLASS_NAME_FADE$2);\n }\n _isShown() {\n return this.tip && this.tip.classList.contains(CLASS_NAME_SHOW$2);\n }\n _createPopper(tip) {\n const placement = execute(this._config.placement, [this, tip, this._element]);\n const attachment = AttachmentMap[placement.toUpperCase()];\n return Popper.createPopper(this._element, tip, this._getPopperConfig(attachment));\n }\n _getOffset() {\n const {\n offset\n } = this._config;\n if (typeof offset === 'string') {\n return offset.split(',').map(value => Number.parseInt(value, 10));\n }\n if (typeof offset === 'function') {\n return popperData => offset(popperData, this._element);\n }\n return offset;\n }\n _resolvePossibleFunction(arg) {\n return execute(arg, [this._element]);\n }\n _getPopperConfig(attachment) {\n const defaultBsPopperConfig = {\n placement: attachment,\n modifiers: [{\n name: 'flip',\n options: {\n fallbackPlacements: this._config.fallbackPlacements\n }\n }, {\n name: 'offset',\n options: {\n offset: this._getOffset()\n }\n }, {\n name: 'preventOverflow',\n options: {\n boundary: this._config.boundary\n }\n }, {\n name: 'arrow',\n options: {\n element: `.${this.constructor.NAME}-arrow`\n }\n }, {\n name: 'preSetPlacement',\n enabled: true,\n phase: 'beforeMain',\n fn: data => {\n // Pre-set Popper's placement attribute in order to read the arrow sizes properly.\n // Otherwise, Popper mixes up the width and height dimensions since the initial arrow style is for top placement\n this._getTipElement().setAttribute('data-popper-placement', data.state.placement);\n }\n }]\n };\n return {\n ...defaultBsPopperConfig,\n ...execute(this._config.popperConfig, [defaultBsPopperConfig])\n };\n }\n _setListeners() {\n const triggers = this._config.trigger.split(' ');\n for (const trigger of triggers) {\n if (trigger === 'click') {\n EventHandler.on(this._element, this.constructor.eventName(EVENT_CLICK$1), this._config.selector, event => {\n const context = this._initializeOnDelegatedTarget(event);\n context.toggle();\n });\n } else if (trigger !== TRIGGER_MANUAL) {\n const eventIn = trigger === TRIGGER_HOVER ? this.constructor.eventName(EVENT_MOUSEENTER) : this.constructor.eventName(EVENT_FOCUSIN$1);\n const eventOut = trigger === TRIGGER_HOVER ? this.constructor.eventName(EVENT_MOUSELEAVE) : this.constructor.eventName(EVENT_FOCUSOUT$1);\n EventHandler.on(this._element, eventIn, this._config.selector, event => {\n const context = this._initializeOnDelegatedTarget(event);\n context._activeTrigger[event.type === 'focusin' ? TRIGGER_FOCUS : TRIGGER_HOVER] = true;\n context._enter();\n });\n EventHandler.on(this._element, eventOut, this._config.selector, event => {\n const context = this._initializeOnDelegatedTarget(event);\n context._activeTrigger[event.type === 'focusout' ? TRIGGER_FOCUS : TRIGGER_HOVER] = context._element.contains(event.relatedTarget);\n context._leave();\n });\n }\n }\n this._hideModalHandler = () => {\n if (this._element) {\n this.hide();\n }\n };\n EventHandler.on(this._element.closest(SELECTOR_MODAL), EVENT_MODAL_HIDE, this._hideModalHandler);\n }\n _fixTitle() {\n const title = this._element.getAttribute('title');\n if (!title) {\n return;\n }\n if (!this._element.getAttribute('aria-label') && !this._element.textContent.trim()) {\n this._element.setAttribute('aria-label', title);\n }\n this._element.setAttribute('data-bs-original-title', title); // DO NOT USE IT. Is only for backwards compatibility\n this._element.removeAttribute('title');\n }\n _enter() {\n if (this._isShown() || this._isHovered) {\n this._isHovered = true;\n return;\n }\n this._isHovered = true;\n this._setTimeout(() => {\n if (this._isHovered) {\n this.show();\n }\n }, this._config.delay.show);\n }\n _leave() {\n if (this._isWithActiveTrigger()) {\n return;\n }\n this._isHovered = false;\n this._setTimeout(() => {\n if (!this._isHovered) {\n this.hide();\n }\n }, this._config.delay.hide);\n }\n _setTimeout(handler, timeout) {\n clearTimeout(this._timeout);\n this._timeout = setTimeout(handler, timeout);\n }\n _isWithActiveTrigger() {\n return Object.values(this._activeTrigger).includes(true);\n }\n _getConfig(config) {\n const dataAttributes = Manipulator.getDataAttributes(this._element);\n for (const dataAttribute of Object.keys(dataAttributes)) {\n if (DISALLOWED_ATTRIBUTES.has(dataAttribute)) {\n delete dataAttributes[dataAttribute];\n }\n }\n config = {\n ...dataAttributes,\n ...(typeof config === 'object' && config ? config : {})\n };\n config = this._mergeConfigObj(config);\n config = this._configAfterMerge(config);\n this._typeCheckConfig(config);\n return config;\n }\n _configAfterMerge(config) {\n config.container = config.container === false ? document.body : getElement(config.container);\n if (typeof config.delay === 'number') {\n config.delay = {\n show: config.delay,\n hide: config.delay\n };\n }\n if (typeof config.title === 'number') {\n config.title = config.title.toString();\n }\n if (typeof config.content === 'number') {\n config.content = config.content.toString();\n }\n return config;\n }\n _getDelegateConfig() {\n const config = {};\n for (const [key, value] of Object.entries(this._config)) {\n if (this.constructor.Default[key] !== value) {\n config[key] = value;\n }\n }\n config.selector = false;\n config.trigger = 'manual';\n\n // In the future can be replaced with:\n // const keysWithDifferentValues = Object.entries(this._config).filter(entry => this.constructor.Default[entry[0]] !== this._config[entry[0]])\n // `Object.fromEntries(keysWithDifferentValues)`\n return config;\n }\n _disposePopper() {\n if (this._popper) {\n this._popper.destroy();\n this._popper = null;\n }\n if (this.tip) {\n this.tip.remove();\n this.tip = null;\n }\n }\n\n // Static\n static jQueryInterface(config) {\n return this.each(function () {\n const data = Tooltip.getOrCreateInstance(this, config);\n if (typeof config !== 'string') {\n return;\n }\n if (typeof data[config] === 'undefined') {\n throw new TypeError(`No method named \"${config}\"`);\n }\n data[config]();\n });\n }\n}\n\n/**\n * jQuery\n */\n\ndefineJQueryPlugin(Tooltip);\n\n/**\n * --------------------------------------------------------------------------\n * Bootstrap popover.js\n * Licensed under MIT (https://github.com/twbs/bootstrap/blob/main/LICENSE)\n * --------------------------------------------------------------------------\n */\n\n\n/**\n * Constants\n */\n\nconst NAME$3 = 'popover';\nconst SELECTOR_TITLE = '.popover-header';\nconst SELECTOR_CONTENT = '.popover-body';\nconst Default$2 = {\n ...Tooltip.Default,\n content: '',\n offset: [0, 8],\n placement: 'right',\n template: '
' + '
' + '

' + '
' + '
',\n trigger: 'click'\n};\nconst DefaultType$2 = {\n ...Tooltip.DefaultType,\n content: '(null|string|element|function)'\n};\n\n/**\n * Class definition\n */\n\nclass Popover extends Tooltip {\n // Getters\n static get Default() {\n return Default$2;\n }\n static get DefaultType() {\n return DefaultType$2;\n }\n static get NAME() {\n return NAME$3;\n }\n\n // Overrides\n _isWithContent() {\n return this._getTitle() || this._getContent();\n }\n\n // Private\n _getContentForTemplate() {\n return {\n [SELECTOR_TITLE]: this._getTitle(),\n [SELECTOR_CONTENT]: this._getContent()\n };\n }\n _getContent() {\n return this._resolvePossibleFunction(this._config.content);\n }\n\n // Static\n static jQueryInterface(config) {\n return this.each(function () {\n const data = Popover.getOrCreateInstance(this, config);\n if (typeof config !== 'string') {\n return;\n }\n if (typeof data[config] === 'undefined') {\n throw new TypeError(`No method named \"${config}\"`);\n }\n data[config]();\n });\n }\n}\n\n/**\n * jQuery\n */\n\ndefineJQueryPlugin(Popover);\n\n/**\n * --------------------------------------------------------------------------\n * Bootstrap scrollspy.js\n * Licensed under MIT (https://github.com/twbs/bootstrap/blob/main/LICENSE)\n * --------------------------------------------------------------------------\n */\n\n\n/**\n * Constants\n */\n\nconst NAME$2 = 'scrollspy';\nconst DATA_KEY$2 = 'bs.scrollspy';\nconst EVENT_KEY$2 = `.${DATA_KEY$2}`;\nconst DATA_API_KEY = '.data-api';\nconst EVENT_ACTIVATE = `activate${EVENT_KEY$2}`;\nconst EVENT_CLICK = `click${EVENT_KEY$2}`;\nconst EVENT_LOAD_DATA_API$1 = `load${EVENT_KEY$2}${DATA_API_KEY}`;\nconst CLASS_NAME_DROPDOWN_ITEM = 'dropdown-item';\nconst CLASS_NAME_ACTIVE$1 = 'active';\nconst SELECTOR_DATA_SPY = '[data-bs-spy=\"scroll\"]';\nconst SELECTOR_TARGET_LINKS = '[href]';\nconst SELECTOR_NAV_LIST_GROUP = '.nav, .list-group';\nconst SELECTOR_NAV_LINKS = '.nav-link';\nconst SELECTOR_NAV_ITEMS = '.nav-item';\nconst SELECTOR_LIST_ITEMS = '.list-group-item';\nconst SELECTOR_LINK_ITEMS = `${SELECTOR_NAV_LINKS}, ${SELECTOR_NAV_ITEMS} > ${SELECTOR_NAV_LINKS}, ${SELECTOR_LIST_ITEMS}`;\nconst SELECTOR_DROPDOWN = '.dropdown';\nconst SELECTOR_DROPDOWN_TOGGLE$1 = '.dropdown-toggle';\nconst Default$1 = {\n offset: null,\n // TODO: v6 @deprecated, keep it for backwards compatibility reasons\n rootMargin: '0px 0px -25%',\n smoothScroll: false,\n target: null,\n threshold: [0.1, 0.5, 1]\n};\nconst DefaultType$1 = {\n offset: '(number|null)',\n // TODO v6 @deprecated, keep it for backwards compatibility reasons\n rootMargin: 'string',\n smoothScroll: 'boolean',\n target: 'element',\n threshold: 'array'\n};\n\n/**\n * Class definition\n */\n\nclass ScrollSpy extends BaseComponent {\n constructor(element, config) {\n super(element, config);\n\n // this._element is the observablesContainer and config.target the menu links wrapper\n this._targetLinks = new Map();\n this._observableSections = new Map();\n this._rootElement = getComputedStyle(this._element).overflowY === 'visible' ? null : this._element;\n this._activeTarget = null;\n this._observer = null;\n this._previousScrollData = {\n visibleEntryTop: 0,\n parentScrollTop: 0\n };\n this.refresh(); // initialize\n }\n\n // Getters\n static get Default() {\n return Default$1;\n }\n static get DefaultType() {\n return DefaultType$1;\n }\n static get NAME() {\n return NAME$2;\n }\n\n // Public\n refresh() {\n this._initializeTargetsAndObservables();\n this._maybeEnableSmoothScroll();\n if (this._observer) {\n this._observer.disconnect();\n } else {\n this._observer = this._getNewObserver();\n }\n for (const section of this._observableSections.values()) {\n this._observer.observe(section);\n }\n }\n dispose() {\n this._observer.disconnect();\n super.dispose();\n }\n\n // Private\n _configAfterMerge(config) {\n // TODO: on v6 target should be given explicitly & remove the {target: 'ss-target'} case\n config.target = getElement(config.target) || document.body;\n\n // TODO: v6 Only for backwards compatibility reasons. Use rootMargin only\n config.rootMargin = config.offset ? `${config.offset}px 0px -30%` : config.rootMargin;\n if (typeof config.threshold === 'string') {\n config.threshold = config.threshold.split(',').map(value => Number.parseFloat(value));\n }\n return config;\n }\n _maybeEnableSmoothScroll() {\n if (!this._config.smoothScroll) {\n return;\n }\n\n // unregister any previous listeners\n EventHandler.off(this._config.target, EVENT_CLICK);\n EventHandler.on(this._config.target, EVENT_CLICK, SELECTOR_TARGET_LINKS, event => {\n const observableSection = this._observableSections.get(event.target.hash);\n if (observableSection) {\n event.preventDefault();\n const root = this._rootElement || window;\n const height = observableSection.offsetTop - this._element.offsetTop;\n if (root.scrollTo) {\n root.scrollTo({\n top: height,\n behavior: 'smooth'\n });\n return;\n }\n\n // Chrome 60 doesn't support `scrollTo`\n root.scrollTop = height;\n }\n });\n }\n _getNewObserver() {\n const options = {\n root: this._rootElement,\n threshold: this._config.threshold,\n rootMargin: this._config.rootMargin\n };\n return new IntersectionObserver(entries => this._observerCallback(entries), options);\n }\n\n // The logic of selection\n _observerCallback(entries) {\n const targetElement = entry => this._targetLinks.get(`#${entry.target.id}`);\n const activate = entry => {\n this._previousScrollData.visibleEntryTop = entry.target.offsetTop;\n this._process(targetElement(entry));\n };\n const parentScrollTop = (this._rootElement || document.documentElement).scrollTop;\n const userScrollsDown = parentScrollTop >= this._previousScrollData.parentScrollTop;\n this._previousScrollData.parentScrollTop = parentScrollTop;\n for (const entry of entries) {\n if (!entry.isIntersecting) {\n this._activeTarget = null;\n this._clearActiveClass(targetElement(entry));\n continue;\n }\n const entryIsLowerThanPrevious = entry.target.offsetTop >= this._previousScrollData.visibleEntryTop;\n // if we are scrolling down, pick the bigger offsetTop\n if (userScrollsDown && entryIsLowerThanPrevious) {\n activate(entry);\n // if parent isn't scrolled, let's keep the first visible item, breaking the iteration\n if (!parentScrollTop) {\n return;\n }\n continue;\n }\n\n // if we are scrolling up, pick the smallest offsetTop\n if (!userScrollsDown && !entryIsLowerThanPrevious) {\n activate(entry);\n }\n }\n }\n _initializeTargetsAndObservables() {\n this._targetLinks = new Map();\n this._observableSections = new Map();\n const targetLinks = SelectorEngine.find(SELECTOR_TARGET_LINKS, this._config.target);\n for (const anchor of targetLinks) {\n // ensure that the anchor has an id and is not disabled\n if (!anchor.hash || isDisabled(anchor)) {\n continue;\n }\n const observableSection = SelectorEngine.findOne(decodeURI(anchor.hash), this._element);\n\n // ensure that the observableSection exists & is visible\n if (isVisible(observableSection)) {\n this._targetLinks.set(decodeURI(anchor.hash), anchor);\n this._observableSections.set(anchor.hash, observableSection);\n }\n }\n }\n _process(target) {\n if (this._activeTarget === target) {\n return;\n }\n this._clearActiveClass(this._config.target);\n this._activeTarget = target;\n target.classList.add(CLASS_NAME_ACTIVE$1);\n this._activateParents(target);\n EventHandler.trigger(this._element, EVENT_ACTIVATE, {\n relatedTarget: target\n });\n }\n _activateParents(target) {\n // Activate dropdown parents\n if (target.classList.contains(CLASS_NAME_DROPDOWN_ITEM)) {\n SelectorEngine.findOne(SELECTOR_DROPDOWN_TOGGLE$1, target.closest(SELECTOR_DROPDOWN)).classList.add(CLASS_NAME_ACTIVE$1);\n return;\n }\n for (const listGroup of SelectorEngine.parents(target, SELECTOR_NAV_LIST_GROUP)) {\n // Set triggered links parents as active\n // With both