⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣶⡶⡶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠈⠳⠶⣤⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣗⠯⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢀⣀⠀⠈⣄⠀⠀⣀⠀⣯⡭⢿⣱⣶⣾⣧⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣾⣯⠀⠀⡘⠱⠿⡧⠄⠻⡿⢟⡿⣺⠿⠡⡈⠌⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢰⡿⡅⠀⠀⠀⠰⠤⠀⠀⠂⠀⠳⡧⠤⠦⡑⠁⠌⠀⠐⡄⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠃⢁⡀⡀⣠⢎⡀⠄⡁⠀⠁⡀⠄⠀⠄⣀⢀⣠⣶⡌⠐⠆⠀⠀⠀⠀⠀⠀⠀
⠀⠀⡾⣝⢒⡇⢾⣿⡦⠀⠁⠀⠀⠀⢱⡟⣿⣿⣿⣿⡵⠡⡄⠀⠀⠀⠀⠀⠀⠀
⠀⠸⣿⣣⣾⣽⣿⣿⡗⠀⠀⠀⠀⠀⠀⡝⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢿⣿⣿⡿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠸⣻⣿⣿⣿⡗⠀⠰⡀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠸⢻⣿⣿⣿⡧⠀⣿⣿⡆⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠄⣀⠀⠀⣺⣿⣧⣿⡷⣀⣿⣿⣿⡄⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⠠⢀⢹⢠⢽⣿⣿⣿⡗⠘⢰⢎⡿⣷⡀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⢾⣿⣿⣿⡟⠀⠈⢙⠾⠉⠉⢣⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⡐⠁⠀⠀⠀⠀⠀⣘⣼⣿⣿⣿⣏⠀⠀⠀⠁⠀⠀⠈⠣⠀
⠀⠀⠀⠀⠀⠀⢀⡜⠀⠀⠀⠀⠀⠀⡠⣱⣿⣿⠹⣿⣯⢂⠀⠀⠀⠀⠀⠀⢀⣇
⠀⠀⠀⠀⣠⣾⣿⠁⠀⠀⠀⠀⠀⢠⢾⣿⣿⡏⠀⢿⣿⡧⠀⠀⠀⠀⠍⠘⢲⠩
⠀⠀⢀⣾⢿⠎⡅⠀⠀⠀⠀⠀⠠⢡⣿⣿⡿⠀⠀⢘⣿⣷⠩⠀⠀⡐⡄⠀⠀⠀
⠀⠀⣛⢾⠉⣔⡀⠀⠀⠀⠀⢀⢜⣿⣿⣿⢣⡆⠀⠀⢿⣿⡤⠀⠒⠑⠀⠀⠀⠀
⠀⠐⠡⢋⠀⠐⠈⠓⠠⢀⢄⢈⣾⣿⣿⡏⠞⠷⠀⠀⢸⣿⣷⠈⠀