⠀⠀⠀⢳⠀⠈⢇⠀⢣⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⢸⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠈⣇⠀⠈⢧⡀⠳⡀⠀⠀⠀⠀⠀⠀⠈⢧⣠⣼⣇⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠘⢦⡀⠀⢳⣤⣉⠲⣤⣀⣀⡀⠤⠤⠼⠿⣅⣹⣮⣷⠒⠦⠤⢄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠙⠓⢻⣦⠬⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠈⠉⠛⠧⣀⠀⠀⠀⠉⠓⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⡀⠀⠈⠑⢦⡀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⡇⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠈⢦⠀⠀⠀⠀⠀⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⡇⠀⠀⢹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀⠀⢱⡄⠀⠀⠀⠀⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⡼⠀⠀⠀⠀⠀⢠⣇⠀⠀⠈⣯⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡄⠀⡼⢿⡄⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢸⣷⠀⠀⠀⢸⠀⣸⢻⡀⠀⠀⢹⠀⢙⢾⣹⡆⠀⠀⢳⣄⢀⣠⣤⠀⢻⡄⡆⢸⢿⡀⠀⠀⠀⠀⢷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣿⡟⠀⡀⠀⣿⢠⣯⢈⣇⠀⠀⠈⡇⠧⠤⠽⠓⢤⣠⣴⣿⣿⣿⣿⣇⠀⢻⠀⠘⡿⣇⠀⠰⣄⠀⢸⡇⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣿⡇⢀⡇⠀⡟⣼⠳⠤⠽⣧⡀⠀⢧⠀⢀⣤⣶⣿⣿⣿⣿⣿⣿⣿⡿⠔⠋⠀⠀⠙⢿⣀⡀⠘⢿⣷⡇⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀
⠀⠠⣿⠁⢸⣧⣤⣿⣧⣤⣤⣤⣽⣷⣄⢸⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣀⠀⠀⢀⣀⡤⠭⠓⠀⢻⡇⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀
⠀⠀⣿⡆⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢹⡏⡇⠀⡏⢹⣷⣶⣶⣾⣿⣧⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀
⠀⠀⣿⣇⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⢸⣧⡇⢠⡇⢸⣿⣿⣿⣿⣿⣿⣤⣶⣿⢦⡀⠀⠀⠀⠀⠀
⠀⢸⣿⣿⡄⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠈⠙⠛⠿⠿⠿⠛⠋⠁⠀⠀⠘⠉⣿⣸⣇⣿⣿⣿⣿⡿⠻⣿⣿⣿⠃⠀⣷⠀⠀⠀⠀⠀
⠀⢸⡟⣿⣿⣆⢻⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⡿⠛⣦⣼⣿⣟⠀⠀⣿⠀⠀⠀⠀⠀
⠀⠘⣧⣿⣿⣿⣷⣿⣿⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣿⣿⣿⣿⣦⣴⡟⠀⠀⠀⠀⠀
⠀⠀⠘⢿⣿⡟⠻⣿⣿⣷⣄⣀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣴⡾⠛⠛⠻⠟⢻⣿⣿⣿⣿⣿⣿⣿⠀⠀⠹⣿⣿⣿⠋⢷⠀⠀⠀⠀⠀
⠀⠀⠀⣾⣿⣿⠀⠸⢿⣿⣿⣏⡭⠭⠿⠛⠟⢿⣿⠿⠟⠛⠉⠁⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠘⣿⣇⠀⢸⠀⠀⠀⠀⠀
⠀⠀⠀⣿⠈⠹⣇⠀⠸⣟⣿⠁⠀⠀⠀⢀⡤⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⢸⣿⣿⡟⠀⠀⠀⠀⠀
⠀⠀⠀⢹⣶⣶⣿⡆⢀⣿⠁⠀⠀⠀⢰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⣿⣿⣿⣿⡟⠁⠀⠀⠀⠰⡏⠙⢿⣄⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠛⠛⠛⠛⠛⠑⠂⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠛⠛⠒⠒⠒⠒⠒⠛⠀⠀⠙⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀