⡠⠄
⢸⣀⠜⢄⡀⠀⠰⣶⣤⣀⠀⠀⣠⠔⠚⢛⣛⣦⡀⠀⠀⠀⠀⠀⠀⡐⠉⠉⢶⠄
⠈⢅⠀⡈⠱⣄⠀⠈⠛⠻⢷⡎⡡⣶⣿⣿⣿⢿⣿⡀⠀⠀⠀⠀⣴⣯⣝⣲⠊⠀
⠀⠀⠠⢅⢀⡎⣷⣄⠀⠀⠀⢿⡰⠊⠁⠀⠸⡼⡏⣇⠀⠀⢀⣾⣿⣿⣿⡏⠀⠀
⠀⠀⠀⠈⢻⣾⣿⣿⣷⣤⣀⣼⣧⡀⠀⣠⠴⣗⣳⣼⣄⣴⣿⣿⣿⣿⠟⠀
⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣶⠏⢹⠁⠀⡟⢹⢿⣿⣿⣿⡟⠀⠀
⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⠦⢅⣀⣨⣤⠴⡞⣿⣿⡟⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣿⣿⣿⣿⣿⠈⠲⢦⡾⣛⣾⣁⣸⠋⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡍⡿⠟⢻⡔⠚⠚⣷⣼⣾⠉⢹⠃⠀⣀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⣷⠀⠀⢧⠀⠸⠋⠸⠌⠃⢸⠀⢰⣿⠃⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⠀⣸⣤⣤⣶⣶⣶⣶⣾⣤⣿⠃⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣦⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⢸⠀⠀⠀⠀⠀⠀⠉⣿⠿⠏⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢹⠀⢸⠀⠀⠀⠂⠁⠀⠀⢿⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⢸⣤⣼⣀⣄⣀⡀⡀⢀⣀⡸⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠟⠉⠙⡿⠋⢹⠇⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣅⣀⣀⣤⡷⠶⡿⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢸⠃⣸⠃⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⣿⢠⡇⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⢰⣇⣸⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠛⠛⢯⡉⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠤⠤⠬⠏