⢀⠈⢀⠈⢀⠈⢀⠈⢀⠈⢀⠈⢀⠈⢀⠈⢀⠈⢀⠈⢰⣧⣼⣯⠄⣸⣠⣶⣶⣦⣾⠄⠄⠄⠄⡀⠄⢀⣿⣿⠄⠄⠄⢸⡇⢀⠈⢀⠈⢀⠈⢀⠈⢀⠈⢀⠈⢀⠈⢀⠈
⢀⠈⢀⠈⢀⠈⢀⠈⢀⠈⢀⠈⢀⠈⢀⠈⢀⠈⢀⠈⣾⣿⠿⠿⠶⠿⢿⣿⣿⣿⣿⣦⣤⣄⢀⡅⢠⣾⣛⡉⠄⠄⠄⠸⢀⣿⢀⠈⢀⠈⢀⠈⢀⠈⢀⠈⢀⠈⢀⠈⢀
⢀⠈⢀⠈⢀⠈⢀⠈⢀⠈⢀⠈⢀⠈⢀⠈⢀⠈⢀⡋⣡⣴⣶⣶⡀⠄⠄⠙⢿⣿⣿⣿⣿⣿⣴⣿⣿⣿⢃⣤⣄⣀⣥⣿⣿⢀⠈⢀⠈⢀⠈⢀⠈⢀⠈⢀⠈⢀⠈⢀⠈
⢀⠈⢀⠈⢀⠈⢀⠈⢀⠈⢀⠈⢀⠈⢀⠈⢀⠈⢸⣇⠻⣿⣿⣿⣧⣀⢀⣠⡌⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⣿⣿⣿⢀⠈⢀⠈⢀⠈⢀⠈⢀⠈⢀⠈⢀⠈⢀⠈
⢀⠈⢀⠈⢀⠈⢀⠈⢀⠈⢀⠈⢀⠈⢀⠈⢀⠈⢸⣿⣷⣤⣤⣤⣬⣙⣛⢿⣿⣿⣿⣿⣿⣿⡿⣿⣿⡍⠄⠄⢀⣤⣄⠉⠋⣰⢀⠈⢀⠈⢀⠈⢀⠈⢀⠈⢀⠈⢀⠈⢀
⢀⠈⢀⠈⢀⠈⢀⠈⢀⠈⢀⠈⢀⠈⢀⠈⢀⣼⣖⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⢇⣿⣿⡷⠶⠶⢿⣿⣿⠇⢀⣤⢀⠈⢀⠈⢀⠈⢀⠈⢀⠈⢀⠈⢀⠈⢀
⢀⠈⢀⠈⢀⠈⢀⠈⢀⠈⢀⠈⢀⠈⢀⠈⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣷⣶⣥⣴⣿⡗⢀⠈⢀⠈⢀⠈⢀⠈⢀⠈⢀⠈⢀⠈⢀
⢀⠈⢀⠈⢀⠈⢀⠈⢀⠈⢀⠈⢀⠈⢀⠈⢀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢀⠈⢀⠈⢀⠈⢀⠈⢀⠈⢀⠈⢀⠈⢀⠈⢀
⢀⠈⢀⠈⢀⠈⢀⠈⢀⠈⢀⠈⢀⠈⢀⠈⢸⣿⣦⣌⣛⣻⣿⣿⣧⠙⠛⠛⡭⠅⠒⠦⠭⣭⡻⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⢀⠈⢀⠈⢀⠈⢀⠈⢀⠈⢀⠈⢀⠈⢀⠈
⢀⠈⢀⠈⢀⠈⢀⠈⢀⠈⢀⠈⢀⠈⢀⠈⠘⣿⣿⣿⣿⣿⣿⣿⣿⡆⠄⠄⠄⠄⠄⠄⠄⠄⠹⠈⢋⣽⣿⣿⣿⣿⣵⣾⠃⢀⠈⢀⠈⢀⠈⢀⠈⢀⠈⢀⠈⢀⠈⢀⠈
⢀⠈⢀⠈⢀⠈⢀⠈⢀⠈⢀⠈⢀⠈⢀⠈⢀⠘⣿⣿⣿⣿⣿⣿⣿⣿⠄⣴⣿⣶⣄⠄⣴⣶⠄⢀⣾⣿⣿⣿⣿⣿⣿⠃⢀⠈⢀⠈⢀⠈⢀⠈⢀⠈⢀⠈⢀⠈⢀⠈⢀
⢀⠈⢀⠈⢀⠈⢀⠈⢀⠈⢀⠈⢀⠈⢀⠈⢀⠈⠈⠻⣿⣿⣿⣿⣿⣿⡄⢻⣿⣿⣿⠄⣿⣿⡀⣾⣿⣿⣿⣿⣛⠛⠁⢀⠈⢀⠈⢀⠈⢀⠈⢀⠈⢀⠈⢀⠈⢀⠈⢀⠈
⢀⠈⢀⠈⢀⠈⢀⠈⢀⠈⢀⠈⢀⠈⢀⠈⢀⠈⢀⠈⢀⠈⠛⢿⣿⣿⣿⠁⠞⢿⣿⣿⡄⢿⣿⡇⣸⣿⣿⠿⠛⠁⢀⠈⢀⠈⢀⠈⢀⠈⢀⠈⢀⠈⢀⠈⢀⠈⢀⠈⢀
⢀⠈⢀⠈⢀⠈⢀⠈⢀⠈⢀⠈⢀⠈⢀⠈⢀⠈⢀⠈⢀⠈⢀⠉⠻⣿⣿⣾⣦⡙⠻⣷⣾⣿⠃⠿⠋⠁⢀⠈⢀⠈⢀⠈⢀⠈⢀⠈⢀⠈⢀⠈⢀⠈⢀⠈⢀⠈⢀⠈⢀
⢀⠈⢀⠈⢀⠈⢀⠈⢀⠈⢀⠈⢀⠈⢀⠈⢀⠈⢀⠈⢀⠈⢀⠈⢀⠈⣝⡿⣿⣿⡆⣿⡿⠃⠄⢀⠈⢀⠈⢀⠈⢀⠈⢀⠈⢀⠈⢀⠈⢀⠈⢀⠈⢀⠈⢀⠈⢀⠈⢀⠈