⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⠀⠀⡆
⠀⠑⢄⠈⠐⡄⠀⠀⠀⢀⠀⠀⠀⠀⢻⣧⡀⠀⢷⡀
⠀⠀⠀⢆⠀⢠⠀⠀⠀⠀⢀⠀⠀⠀⠀⠻⣷⣄⡈⢷⡄
⠀⠀⠀⢈⣢⠈⢢⡄⠀⠀⠸⣆⡀⠀⣀⣀⣽⣿⣿⣿⣿⣿⣿⣦⣄
⠀⢀⠎⡩⠝⠋⠐⣚⣠⣤⠰⣍⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠈⠁⣠⣴⡾⠿⠿⠿⣿⣿⣧⡹⢿⣿⡿⣿⣿⢿⣿⣿⣿⣿⣿⡎⠻⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⠀
⢠⠞⡉⠄⣒⣚⣋⣴⠟⣉⣥⣶⣦⡙⢷⣶⣶⣿⣿⣿⣿⡏⠉⠻⢿⣿⣿⣧⣄⣀⡀⠉⠀⠀⡐⠀⠀⠀
⠃⠈⠀⢈⣤⣾⣿⢃⣾⣿⡏⠀⠬⣉⡥⠾⢻⣿⣿⣿⣿⣷⣀⠀⠀⠻⣿⣿⣿⣿⣿⠵⠒⠂⠀⠀⠀⠀
⠀⢀⣴⡿⢿⣿⡏⣼⠏⢹⠀⠀⠀⠀⢄⣠⣾⡿⠁⠢⠿⠿⢿⣷⡄⠠⠿⠛⡿⣿⠃⠀⠀
⠀⣾⠏⡴⢀⣿⡇⣿⠀⠀⠀⠀⠀⠀⠀⠄⠊⠀⠀⠀⡀⠂⠈⢻⣿⠀⠀⠀⠀⠃⠀⠀
⢸⡿⢸⢣⢾⣿⡇⢿⣰⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣯⡤⠂⠀⠀
⢸⡇⡏⠂⣸⣿⣷⠸⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠊⠉⠉⠁⠀⠀
⠸⠁⠇⠀⣿⣿⣿⣇⢻⣿⣷⡀⠀
⠀⠀⠀⠀⣿⣧⣄⢻⣦⠙⢷⣌⠢⡀
⠀⠀⠀⠀⢻⣿⢸⠘⣿⣷⣦⣙⠳⠄⣀⣀⣀⡀⠠⣀⣤⣴⣶⣶⣶⣶⠒⠒⠠⠀⡀
⠀⠀⠀⠀⠀⢻⡆⠄⠍⢿⣿⣿⣿⣶⣶⣶⣶⣶⠟⠛⠉⠉⠉⠉⠉⠙⠻⢦⡁⠲⣤⣁
⠀⠀⠀⠀⠀⠀⠙⠄⠀⠈⠻⣿⣿⣔⠪⡛⠬⡀⠀⠀⠀⠀⠀⠘⠈⡆⠀⠀⠙⢦⠢⠻⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠷⣬⣐⣀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣀⣀⣶⡄⢣⡱⡘⠛⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢸⣻⠀⡇⣷⡘⣶⣕
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡞⢁⠝⠀⣠⣿⣷⠘⣿⣆⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢇⢀⠔⣰⠟⡀⣽⡇⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣁⠜⢋⠔⣰⣿⡇⢠⠹⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡇⣾⣧⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⡳⣤⡀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠈⠛⢛⡉⣽⡟⣰⣿⣿⠀
⠀⠠⡈⠓⢶⣶⣿⣿⠿⣿⣶⣌⡈⢳⣄⠀⢄⡉⠓⠦⣄⠀⠀⡈⠉⠳⣦⣀⡉⣉⣡⣴⠟⢰⣿⣿⡿
⠀⠀⠈⠛⣿⣿⠋⠀⠤⠦⠤⣙⠻⣾⣿⣷⣄⡈⠢⠄⠘⣷⣄⠀⠑⠤⠙⢻⣿⣿⠿⢋⣴⠈⣿⡿⠁
⠀⠀⠒⠊⣿⣿⡄⠀⠤⠤⢤⣤⣤⣼⣿⣿⣿⣿⣷⣶⣶⣿⣿⣷⣶⣶⣾⡿⢛⣡⣴⣿⣿⠃⠋
⠀⠀⠀⠊⠸⣿⣇⠀⠀⠀⠀⠀⠈⠉⠉⠉⣉⣉⠉⠉⣉⣉⣙⣛⣛⣉⡥⢰⣿⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠉⠻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⡿⠟⠡⠾⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠙⢷⣦⣄⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣛⠛⠓⠢⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⣿⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠐⣄⠂⠤⠌⣻⣿⡙⢆⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⣀⠀⠀⠁⢒⣾⡿⠿⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠟⠛⠉⠀⠀⠈⠇