⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡈⢿⣿⠿⠛⠉⠀⠀⣤⠀⠁⠐⠒⢲⡜⣿⣜
⣿⣿⠿⠟⣻⣽⣿⣿⣿⣿⣿⠿⠟⠃⠀⠀⠀⠀⠀⢀⠀⠘⣆⠂⢀⠀⠘⢿⡞⣿
⣉⣤⣶⣿⣿⣿⡿⠿⠋⠉⠀⠀⠀⠀⠀⠀⠀⣠⠾⠋⠒⡄⠙⣆⠀⢢⠀⠀⠱⢹
⣿⡿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠁⠀⠀⠀⠈⢆⠘⢦⠀⠁⠀⠀⡼
⢸⠀⠀⠀⠀⠀⠀⣀⡤⠂⠀⠀⡠⠞⠉⠀⠀⠀⠀⠀⠀⠀⠈⢂⠀⠣⡐⠀⠀⢸
⢸⠀⠀⠀⠀⢀⡾⠋⠀⢀⠄⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠑⡀⠄⢸
⢸⠀⠀⠀⡰⠋⠀⡀⠔⠁⠀⠀⠀⠀⠀⠀⠀⡠⢠⠢⠀⠀⠀⠀⠀⠘⢄⠈⠂⢸
⢸⠀⠀⠈⠀⣠⢖⣴⣷⠀⠀⠀⡠⢠⣄⠉⣦⠀⠸⣧⡄⠢⠀⠀⠀⠀⠀⠢⠀⢸
⢸⠀⠀⣀⠜⠁⢞⠛⠛⠃⢰⡈⠊⣄⢁⡀⠣⠀⠸⠛⠛⠢⠀⠢⡀⠀⠀⠀⠀⢸
⢸⢁⡴⠋⠀⣀⢦⣄⣛⣴⠦⠀⠨⡀⠁⠀⠟⢀⠞⣄⣛⣴⡤⣐⡀⢻⡄⢀⠀⢸
⡠⠋⠀⠀⠀⠀⣳⢮⣿⣿⣭⡆⠀⡀⠄⠑⠫⠂⠉⠈⢓⣛⣿⣵⣆⠃⢸⡆⠀⢸
⢸⠀⠀⠀⠀⠀⢻⣿⣿⣿⣷⣶⣄⢰⣄⠀⣀⠐⠤⡀⠀⢨⡻⢿⡿⠀⠘⣷⠀⢸
⢸⠀⠀⠀⠀⠀⠚⣿⣿⣿⣿⣿⣿⣾⣧⢸⣶⣅⣳⣬⣁⠀⣿⣶⠀⠀⢐⢿⠀⢸
⢸⠀⠈⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣧⣿⠃⠀⠀⡼⢸⠀⢸
⢸⣀⣀⠤⠒⠒⠒⠘⠛⠛⠛⠛⣷⢮⣭⣭⣭⣭⣿⣿⣿⡿⠃⠀⠀⠀⠁⠸⠀⢸
⢸⠀⠀⠀⠀⠀⠀⠀⠁⡭⠍⢀⠀⡿⣼⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸
⢸⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁⢸⠧⢿⡿⠟⡯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⣾⣷⣶⠿⠃⠀⠀⠀⠀⠀⠀⠐⡄⠤⠴⠾⢸
⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣿⠉⠁⠀⠒⠒⠒⠤⠤⠤⠤⣀⣧⠀⠀⠀⢸
⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⢸⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⢸⠀⠀⢀⣡⣄⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⠀⠀⠀⢸
⣤⣤⠁⣦⣴⡇⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⢨⣲⡐⢄⣀⣀