⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⠿⠛⠉⠉⢻⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠟⠁⠀⠀⠀⠀⠀⢿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠋⠁⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⡿⠟⠉⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣤⣀⣀⣀⠀⠀⠀⠀⠀⣠⣴⣿⣿⠟⠉⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣾⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣿⣿⣿⠿⢿⣿⣿⣿⣷⣶⣾⣿⡿⠋⠀⠀⠀⠀⠀⣰⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠟⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠁⢀⡴⠋⠀⠀⠀⡠⠊⠉⠉⣻⠿⠋⠀⠀⠀⠀⠀⠀⣼⠃⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⢠⠎⠀⠀⠀⢀⠞⠀⠀⢀⡜⠁⠀⠀⠀⠀⠀⠀⠀⣸⣃⣀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⢀⠎⠀⠀⠀⣠⠃⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⢉⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣴⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⡠⠊⠀⠀⠀⠀⡇⠀⠀⢠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣇⠀
⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⣼⣿⠿⢿⣿⠏⠀⠀⠀⠀⠀⢀⣤⣶⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠂⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦
⠀⠀⠀⠀⠀⢀⣾⡿⠛⠻⣿⣿⣶⣿⣿⠀⠀⠁⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣠⣿⣿⣿⣿⠁⠀⠀⢿⣿⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀
⣠⣾⣿⠏⠀⠀⠀⠀⠀⠀⠀⠘⢦⡉⠻⢿⣿⣷⣦⣀⠀⠀⠈⢿⣿⣿⣿⣿⠋⢀⡴⠊⠁⠀⠀⠀⠀⠈⠉⠒⠠⡀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀
⣿⡟⠁⠀⠀⣀⡤⠤⣄⠀⠀⠀⠀⢉⠳⢄⠈⠛⠿⣿⣷⣦⣀⠀⠉⠉⠉⠀⢀⠎⢿⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠈⢢⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀
⣿⡇⠀⠀⣼⠋⣴⣿⣿⣷⠀⠀⠀⢸⠉⠒⠭⣒⢄⡈⠙⠻⣿⣷⣦⣀⠀⠀⡌⠀⠘⠷⣤⣤⠾⢻⣄⠀⠀⢀⡼⠀⠀⡇⠀⠀⠙⢿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀
⣿⡇⠀⠀⢿⡄⣿⣿⣿⣿⠀⠀⠀⠸⠀⠀⠀⠈⠙⠪⢗⣤⡀⠙⠻⢿⣷⣦⣃⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠉⠀⠀⠀⡀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀
⣿⡇⠀⠀⠈⠻⠾⠿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠄⠀⢹⡟⢿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⡇⠀⠀⡀⠀⢀⣀⠀⠀⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⢻⣿⣷⣦⣄⣠⣤⣤⣤⣀⣀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⡇⠀⡀⡇⠀⢇⣠⠇⢀⢇⠀⠀⢀⠉⠓⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⢸⣿⠈⣿⠻⣿⣿⠛⠻⢿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⡇⠀⠘⢼⡢⣀⣀⢴⡺⠃⠀⠀⢸⠀⠀⢸⠀⣿⠓⡦⣄⡀⠀⠀⠀⢸⡇⠀⣿⢸⣿⠀⡟⠀⣿⠙⣷⢦⣀⠙⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⡏⠢⣀⠀⠀⠉⠉⠁⠀⣠⢾⣿⣿⣦⣄⣸⠀⣿⠀⡇⢸⠉⠓⠦⣄⡸⢿⣶⣿⣼⣿⠀⡇⠀⣿⠀⣿⠢⢌⠉⠻⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣦⣄⡉⠳⢶⣶⣶⣿⣿⣦⣌⡙⠻⢿⣿⣷⣿⣄⡇⢸⠀⠀⠀⠀⠉⠓⠮⣝⡻⢿⣷⣷⣄⣿⠀⣿⠀⠀⠉⠒⢼⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠉⠻⢿⣿⣷⣶⣬⣙⡻⣿⣿⣿⣿⣷⣦⣌⡙⠿⣿⣿⣾⣤⣀⠀⠀⠀⠀⠀⠀⠉⠓⠮⣝⡿⣿⣷⣿⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⢠⣀⣠⣴
⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣷⣦⣍⡛⠿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠉⠓⠯⣟⡀⠀⠀⠀⠀⢸⣿⠤⠤⡀⠀⠀⠀⡟⢶⣄⠀⠀⣸⡏⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣉⠛⣿⣿⣷⣦⣤⣄⣀⣀⠀⠀⠀⠀⠉⠓⠦⣄⡀⣸⣿⠀⠀⠈⠢⠤⠔⠁⠀⠉⠛⠛⠋⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠋⠀⠀⠀⠉⠉⠛⣿⣿⡿⠛⠋⠉⠉⠉⠉⣉⠍⠙⠻⢿⣷⣦⣀⠀⠀⠀⢸⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡏⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠤⠊⠀⠀⠀⠀⠀⠈⠙⢿⣷⣄⠀⣸⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡿⣷⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡀⠀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠈⠻⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀