⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣸⣿⡶⢦⣤⡀⠀⠀⠀⠀⠀⠀⣇⠀⣾⠛⢁⣠⣴⠴⢾⣧⠀⠀⠀
⠀⠀⠀⠀⣿⣿⡎⣿⣿⣾⣻⣾⣿⣿⣿⣯⣷⢚⣞⣛⣙⣛⠿⣿⣬⣹⠀⠀⠀
⠀⠀⠀⠀⣿⣿⢮⣿⣿⣿⡿⣵⣿⣿⣿⣿⣿⣿⣿⣭⣝⢿⣿⣷⣘⣿⡀⠀⠀
⠀⠀⠀⠀⢻⣿⣶⣿⢿⣵⣿⣿⣿⣿⡟⣿⣿⣿⣿⡜⣿⣿⣤⠛⢿⣮⠀⠀⠀
⠀⠀⠀⠀⣿⣭⣶⢣⣿⡿⣿⣿⣿⡿⡄⣿⣿⣿⣿⣿⢹⣿⣿⣿⡜⣿⡀⠀⠀
⠀⠀⠀⣿⣿⣿⢡⣿⢛⡆⣿⣿⢟⣼⢤⣿⣿⡿⢻⣿⣷⢻⣿⣶⣥⣿⣿⠀⠀
⠀⠀⣾⣿⣿⡏⣿⣿⣿⣫⣶⡊⠀⣿⣶⣮⣙⣾⢛⠁⠀⣾⣶⣤⢻⣿⡸⣧⠀
⠀⣸⣿⣿⣿⡘⣿⣿⡅⣿⣿⠀⠀⣿⣿⣿⣿⡀⣯⠀⠀⣿⣿⣿⣸⣿⡇⣿⡄
⠀⠀⠀⣿⣿⣧⢿⣿⣿⣰⣭⣛⣰⢟⢛⣭⣾⣿⣶⢤⣛⣭⣭⢢⣿⣿⣿⠀⠙
⠀⠀⠀⠹⠋⢻⣦⢻⢣⣶⣙⢿⣿⣿⣬⣭⣵⣷⣭⣼⡿⢛⣴⡿⠙⣿⡇⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠛⠀⣿⣴⠀⣼⣬⠀⣐⢿⡏⠀⠻⠀⠀⠀⠀⠀⠀
⠀⣶⣶⡄⠀⠀⠀⠀⠀⠀⣠⣿⣯⣿⣿⣿⣿⣿⣿⣱⡀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⠁⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣦⠀⠀⠀⠀⠀⠀⠀
⢿⣿⣿⠀⠀⠀⠀⠀⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣸⣿⢋⣤⣀⠀⠀⠀⠀
⠀⢿⣿⣿⣦⣰⣿⣿⣿⣾⣝⣀⣿⣿⣿⣿⣿⣿⣿⣿⡇⣾⣿⣿⣿⣿⠀⠀⠀
⠀⠀⠀⠙⢣⣿⣿⣿⣿⣿⣿⢡⣶⣾⣭⣭⣭⣭⣵⣶⣿⣸⣿⣿⣿⠟⠀⠀⠀
⠀⠀⠀⠀⠀⠙⠻⣿⣿⠿⠑⢻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⡀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣠⣠⡄⠀⠀⣸⣠⣠⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣀⣀⣀⠀⠀⠀⣸⣀⣀⣀⣶⣀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣀⣀⣀⠀⠀⠀⠀⠀⠙⠿⠀⠟⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀