⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⣤⠤⠤⠤⠤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣀⡴⠞⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⢦⣀⠀⠀⠀⠀⠀
⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⣄⠀⢸⠀⠀⠀⢀⣄⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀
⠀⢠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠚⠉⡇⢸⡀⠀⠀⢻⡘⣆⠀⠀⠀⠀⠘⣆⠀⠀
⢠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠁⠀⠈⡇⠀⠀⠈⢹⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀
⣿⠀⠀⠀⠀⠀⠀⠀⣀⡴⠎⠀⠀⠀⠀⢿⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⣧⠀
⡇⠀⠀⠀⠀⠴⠖⠛⠁⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠱⢄⣀⠀⠀⠀⠀⠸⡄
⢣⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⣀⣀⣀⡀⠀⠀⠀⠉⠑⠀⠀⠀⢷
⢸⠀⠀⠀⠈⠁⠀⠀⠈⠉⠉⠉⠉⠉⣿⠉⠉⠉⠉⠙⣿⣿⠛⠛⠋⠀ ⠀⢸
⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀ ⢰⣿⣿⣧⠀⠀⠀⠀ ⢸
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⣿⠉⠙⢧⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⡟
⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⠀⠀⢿⠀⠀⠘⢷⣿⣿⣿⡿⠀⠀⠀⠀⣸⠁
⠘⣆⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⢸⡉⠉⠉⠀⠀⠀ ⣰⠁⠀
⠀⠀⠈⢷⡀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⢀⡼⠁⠀⠀
⠀⠀⠀⠀⠘⢦⡀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⢀⡠⠶⠋⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠉⢧⣀⣳⣆⣀⢀⣀⣀⣀⣠⣤⣤⣶⣶⣉⡾⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠈⠉ ⠀⣿⠛⠋⠉⠉⠀⠀⠀⢻⡄⠁⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⡴⠒⣦⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣶⠟⢧⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢸⡁⢆⢻⣴⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢀⠈⡆⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣇⠘⣯⣿⣁⣉⣠⣄⣀⣀⣀⣠⣤⣴⡾⠯⢾⢀⡇⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠘⠒⢋⣾⣿⣿⣿⣿⡟⢻⣿⣿⣿⣿⣿⣦⠘⠋⠁⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⡿⠁⠀⠻⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⠛⠋⠁⠀⠀⠀⠀⠈⠿⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀