⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠏⢀⣀⣤⣤⣤⣤⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⡿⣿⣴⢶⣶⣿⣟⣶⣿⣭⠿⠦⠤⠽⣷⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⡿⢫⣿⢋⣠⣿⣿⡶⢻⡏⠀⠀⠀⠀⠀⠀⠀⠉⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⡿⠋⠈⣸⣿⣿⣿⡿⠿⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢯⠋⠈⠀⣴⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠒⠀⠀⢰⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢼⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢀⡀⠤⠤⠤⣀⠀⢀⡀⠤⠤⠤⣀⣱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⠀⢀⡖⠁⠀⠀⠀⠀⠀⠱⡏⠀⠀⠀⠀⠈⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀
⠀⠀⠀⠈⣿⣿⣿⣿⣿⡆⠀⠀⢸⠀⠀⠴⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢀⡴⠋⠉⢹⡶⠶⢤
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣸⢻⡜⡄⠀⠀⠀⠀⠀⠀⢀⠶⠒⠒⠀⠐⣄⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠟⠛⠓⠶⣏⠀⠀⣀
⠀⠀⠀⢸⢧⣿⣿⣿⣿⣿⡿⠀⠷⠙⠲⠄⠀⡀⠠⠔⠁⠀⠀⠀⢀⣠⡇⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⡇⠀⡀⠀⠀⠈⢦⠞⠁
⠀⠀⠀⢸⡈⢻⣿⣿⣿⡿⠧⣄⠀⠀⠀⢀⡴⠖⠒⠚⠛⠛⠛⠛⠉⠀⠈⠙⠦⣀⣠⣀⠀⠀⠀⠀⢰⣿⣿⣿⣿⠄⠀⠈⢢⡀⠠⢾⠀⠀
⠀⠀⠀⠀⣴⣾⣿⣿⣿⢲⡶⡄⠀⢀⡶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⢸⠀⠀⠀⠀⣸⣿⣿⠟⠋⠀⠀⠀⡎⠀⠀⠈⠉⠀
⡀⠀⠀⠘⣿⣿⣿⣿⣿⣦⣤⡴⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡷⢰⠃⠀⠀⣠⣾⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠
⠙⢦⡀⠀⠈⠛⢻⣿⣿⣿⣿⡇⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⣀⣠⠎⢀⣤⣾⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀
⠀⠀⠈⠳⢄⠀⢸⣿⣿⣿⣿⡇⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⠀⣠⣴⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡰⠁⠀⠀
⠀⠀⠀⠀⠈⠙⢾⣿⣿⣿⣿⡇⠀⠀⠈⠳⠤⣀⡀⠀⠀⢀⣀⠤⡖⠋⢀⡤⠾⠿⣏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢨⠇⠙⢿⠷⠖⠒⠛⠓⠒⠚⠛⠯⡉⠉⠀⠀⡷⠶⠯⡁⠀⠀⠀⠙⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠁⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢀⡌⠀⠀⠀⠳⡀⠀⠀⠀⠀⠀⡌⠀⠙⢆⠀⠀⡧⠂⠀⢡⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⢀⡔⠁⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⠌⠀⠀⠀⠀⠀⠰⡀⠀⠀⠀⢰⠃⠀⠀⠈⠣⡴⠉⠡⡀⠈⡆⠀⠀⠀⠀⠀⠀⠘⠄⠀⢀⡴⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⢩⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠁⠀⠀⠀⠀⠀⠀⠀⠈⣶⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣷⣄⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣎⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⢀⡠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣶⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⡤⠴⠒⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠻⠿⢿⣿⣿⣿⣿⠏⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀