⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⢀⠀⠀⠈⡁⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣬⣷⣤⡄⠁⠀⠀⢄⠀⠀⠈⠢⡀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡏⠛⠛⢻⣦⠁⠀⠀⢳⠀⠀⠠⠈⢆⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣷⡺⠿⠹⣿⡇⠀⠀⢈⣧⡀⠀⠀⠘⣆⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣥⣀⣴⣾⣿⢀⣠⡟⠁⡙⠀⠀⡴⠛⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠛⠛⣛⣿⢿⣿⣿⣿⡿⢃⠴⠃⢂⠎⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠀⠀⠀⠘⢩⠞⠁⠺⠋⠑⢴⣶⢎⡁⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡄⡟⠾⠀⠀⠘⢶⣿⣇⢠⡤⣠⣶⣷⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡻⢧⣀⣀⣠⡵⠾⠍⠻⣿⣿⣿⠟⠉⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠄⠉⢉⣁⣀⡠⠀⡴⣮⣏⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⢚⣫⠵⠚⠛⠁⠙⠟⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⡄⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠐⣶⣶⣤⣠⣴⣶⡾⢧⣿⣦⣤⣀⣸⡿⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡗⣮⠙⠀⠀⠀⠀⠤⠤⠒⠈⠀⢳⡄⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠸⣟⢊⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣙⠒⠶⡶⠀
⠀⢠⡶⠻⢿⠋⠙⣆⡀⠀⠀⠈⠊⣻⠟⢦⣀⠀⠀⠀⠀⠐⠀⠀⢀⣨⣷⠟⠀⠀
⠀⣸⠇⢠⡏⠛⢾⣭⣉⠳⢤⡀⢀⣿⠠⠀⠉⠻⢶⣤⣤⣀⣠⣴⡿⠟⠃⠀⠀⠀
⢰⣟⣲⣿⣇⣄⠀⠉⠛⠿⣦⣨⣾⡇⠀⠀⠀⠀⠈⢀⠉⠉⢂⡇⠀⠀⠀⠀⠀⠀
⠸⠇⠀⠫⠁⠪⣳⡀⠀⡴⢣⠟⢻⡇⠀⠀⠀⠀⢠⡏⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⠻⢾⡇⡏⠀⢸⡇⠀⠀⠀⠀⡾⠁⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⣀⠈⠁⠀⠀⢀⡼⠁⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣤⣄⣤⠿⢬⣶⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀