⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠱⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠛⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⢰⡏⠻⢦⡀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⢀⡴⠟⠉⢀⠃⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠀⣼⠁⠀⠀⣙⡶⠶⠚⠛⠉⠉⠉⠉⠉⠉⠛⠛⠶⣦⠴⠛⣄⠀⠀⠸⠀⢠⣿⠀⢀⣠⡄⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⢰⠃⣠⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢯⣥⠴⠋⣠⠶⢦⣄⣦⣼⣿⠋⠁⣰⠁⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠟⠁⠀⠀⠀⠀⣠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠲⡋⠀⠀⠀⠈⠙⠻⢾⣶⠶⠿⣦⡀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⡴⠛⣿⠟⠁⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣧⣀⢠⣿⣄⠀⡀⠀⠙⢷⡀⠈⢿⡄⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⡜⠀⡼⠁⠀⠀⠀⠀⠀⣴⠿⠛⢿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠉⠹⣿⢿⣿⣼⣿⣇⠀⠀⠀⢻⣄⠘⣧⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣇⡜⠀⠀⠀⠀⠀⠀⠘⠁⠀⢀⣼⡄⠀⡆⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⣼⠛⣆⠉⠠⠙⣿⠀⠀⠀⠀⢻⡄⣿⠀⠀⠀⠀⠀
⠀⠀⠀⣀⣠⠴⠋⠀⠀⠀⠀⠀⠀⡀⠀⢀⡴⠋⠀⢷⡀⣧⠀⠀⠀⠀⠀⢠⡾⢁⣤⣼⣷⣤⣼⣧⡀⠁⢛⠀⠀⠀⠀⠈⣿⣿⠀
⠀⠀⠙⢥⡀⠀⢀⡴⠋⠀⠀⢀⡜⢁⣴⣯⣤⣤⣄⡈⠻⢿⡄⠀⠀⠀⡴⢋⣠⣿⣋⣀⣀⣈⠉⠙⠻⣶⣿⠀⠀⠀⠀⠀⣿⡏⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠉⠂⡾⠁⢰⡇⠀⣾⣤⠟⠋⠀⣠⣤⣼⣿⣆⡀⠻⣄⡠⠾⠛⣫⡿⠛⠉⠉⠉⠛⢷⣆⠀⠈⣿⣷⡀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⠀⠀⢸⡇⢸⣿⡇⠀⠀⣼⠃⠀⠀⠀⠈⠻⣆⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⢹⡇⢠⠃⠙⠃⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢸⠀⠀⠈⣇⣾⢻⡇⠀⠀⣿⡀⠀⠀⠀⠀⣠⡟⠀⠀⠀⠈⢷⣄⡀⠀⠀⠀⠀⢀⡼⠃⡞⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠘⣿⡞⠀⠀⠀⠈⠻⠶⠶⠶⠟⠋⠀⠀⠀⠀⠀⠀⠈⠙⠛⠶⠾⠟⠋⢀⣼⣠⣶⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢸⠀⠀⢸⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⢩⡇⠀⣰⠃⠀⠀⣿⣇⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠘⣆⠀⢸⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⣴⠃⣀⠀⣸⢿⣿⠀⠀