⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣾⣿⣷⡆⢀⣶⣢⣶⡚⠁⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄⡀⠀⠀⠈⢹⣿⣿⣿⢿⠿⢋⣼⠏⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠛⢻⣿⣿⣦⣄⣤⣼⢿⣷⡀⠈⠲⣿⡅⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠏⠀⠀⠠⣼⣿⣿⣿⡃⣶⣤⣾⡇⠀⠀⠘⣷⡄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⡇⠀⢀⣀⣴⣾⣿⡿⠋⠁⠀⢹⣧⠀⠀⠀⠘⣿⡆⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠟⠁⠀⠈⢹⣿⠿⠋⠀⠀⠀⠀⢾⣿⡀⠀⠀⠀⢙⣷⣄⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⠟⠋⠀⠀⠀⠀⠀⢸⣿⣆⡀⠀⠀⠀⠀⠀⠙⣿⣄⣀⣴⣿⣧⣿⣆⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣾⠛⢁⣀⣤⡾⠧⠀⣀⣀⠤⠜⠉⠛⠿⣦⣀⠀⠀⠀⠀⠈⠻⣿⡟⠣⠄⠴⠛⣇⠀⠀
⠀⠀⠀⠀⠀⠀⢀⣀⣴⠾⠋⣀⣴⢾⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⢸⣿⣴⣦⣶⣦⡟⠀⠀
⠀⠀⠀⣠⠶⠒⠻⣭⣿⣿⠞⠛⠱⣾⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠠⠈⠻⣦⣤⣤⣴⠟⠛⠙⠛⠻⣯⡀⠀⢀
⠀⢰⡾⢁⣤⠀⠀⠘⠃⠀⠀⠀⢀⣼⣷⣆⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣷⣦⣄⡀⠀⠈⠉⠙⣿⣄⣠⣤⠀⠀⠀⣿
⠀⠈⡻⠿⠿⣶⣠⣾⣿⡿⠾⠛⠉⠋⠈⣿⣦⡀⠀⠀⠀⠀⠀⠀⢿⣧⡀⠉⠙⢿⣿⣿⣿⡿⠿⠿⠉⠉
⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⢉⣿⠷⠀⠀⠀⠀⠀⠀⠀⠻⣧⡀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠉⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠟⠂⠁⠀⠀⠀⠀⠀⠀⠀⠹⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣲⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻⣶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣿⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀
⠀⠀⠀⠠⠀⠀⠀⡀⠀⠀⠸⢿⣷⣶⣶⣤⣀⣀⣀⣀⣀⣀⣤⣾⡟⠋⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠛⠛⠛⠛⠛⠛⢸⡇⠀⠀⢀⣤⣷⣄⣀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⣠⣼⣿⣿⠀
⠀⠀⠀⠀⠀⣀⣴⣦⡀⠀⠀⠀⠀⢀⣀⣿⡇⠀⠀⠀⠀⠀⠀⠈⠻⣦⣰⠟⠁⠀⠉⠙⠳⠶⠿⠿⣦⡀⠀⠀⣀⣾⠟⠁⢸⣿⠀
⠀⠀⣠⣶⠾⠛⠉⠙⢿⣦⣀⣤⣴⠞⠋⢹⣿⡄⠀⠀⠀⣀⠀⠀⠀⠈⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠉⠻⣦⡶⠋⠁⠀⠀⣸⣿⠀
⠀⣷⣼⡿⠋⠁⠀⠀⠀⠀⠀⠈⠛⠋⠀⠀⠀⠘⢿⣧⠀⠀⠀⣿⣧⡀⠀⠀⡀⠛⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⣰⣾⣷⣿⣿⠀
⠀⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡆⠀⠀⠿⣿⣿⣷⣦⡀⠀⠙⢿⣷⣤⡀⠀⠀⠀⠀⠀⢠⡾⠋⠉⠀⠀⠈⣿⠀
⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡀⠀⠀⣿⣧⠀⠙⢷⣄⠀⠈⠉⠹⢷⣄⠀⠀⠀⣠⣿⠁⠀⠀⠀⠀⠀⣿⠀
⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡄⠀⠻⣿⣄⠀⣸⣿⠟⠀⢀⣸⡿⠛⣿⡿⠻⠟⠃⠀⠀⠀⠀⠀⠀⣿⠀
⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⣴⡾⠟⠛⠃⠀⠀⣸⡇⢀⣿⠟⠀⢀⣼⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⣿⠀⠀⠀⠀⠀⠀⡀⠀⠂⠀⠀⠀⠀⠀⠀⣾⣏⣀⣀⣀⣠⣶⠾⠋⠀⠘⠳⠶⠶⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀