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