⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⣱⣶⣶⡜⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⢻⣿⣿⣷⠟⢀⠄⠀⠀⠃⣠⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠙⠷⣮⣭⣥⡶⠏⠀⠀⠀⠀⢯⣠⡄⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⣀⠀⣀⣀⣀⣀⠀⠀⢰⡄⠀⠀⠀⠀⠀⡀⠀⠀⠀
⠀⣀⠀⠀⠀⠀⠀⣀⢳⡀⠀⠀⠀⣀⠀⠀⢀⡀⢀⣿⡇⠙⢦⢻⣶⣿⠁⠀⠀⠀
⠀⠈⠀⣾⠇⠀⠀⠉⣸⣿⣤⣄⠀⠙⠦⠄⠀⠁⢸⣿⣇⣠⡤⠚⢿⡿⠀⠀⠀⠀
⠀⠀⠸⠋⠀⢀⣴⣿⣿⣿⣿⣿⣷⡄⠀⠀⣾⠾⣿⣶⣿⣿⣿⠀⠀⠛⠁⠀⠀⠀
⠀⠀⠀⠀⢀⣿⠻⣿⣿⣿⣿⣿⣿⠛⠀⠀⢸⣿⣿⣿⡟⢸⣿⡄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢌⠃⠀⠹⣿⣿⠛⠛⠁⠀⠀⠀⠀⠙⠿⠛⢀⣾⠏⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢸⣦⡀⠀⠈⢋⢓⠀⠀⠀⠤⠄⠀⠀⢀⣤⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⡼⠹⣿⣦⣀⠈⠛⣿⣿⣷⣶⣷⣷⣾⣿⠟⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠈⠀⠐⠒⠻⡄⢀⠀⣾⣿⡟⠻⣿⣿⡟⢡⣤⣴⢀⠿⠟⠃⠀⠀⡄⠀⠀
⠀⠇⠀⠀⠀⠀⠀⢠⡿⢊⣾⣭⣭⣽⣷⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⣰⠁⠀⠀
⠀⠸⡄⠀⠀⣀⣴⡟⠐⠛⠋⠃⠀⠹⣿⡿⠋⠻⠿⠛⠓⢿⣿⡆⠀⣠⠃⠀⠀⠀
⠀⠀⠸⣄⠀⡿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠴⠃⠀⠀⠀⠀
⠀⠀⠀⠘⡦⢀⣀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣶⡀⠀⠀⠀⠀
⠀⠀⠀⢋⢾⣿⣿⣿⣶⣿⠑⠒⠀⠀⠀⠀⠀⠀⠀⢶⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀
⠀⠀⠀⠀⠘⢿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠿⠿⠋⠀⠀⠀⠀