⠀⢀⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡷⠆⠀⠀⠀⠀⠀⣀⠄⡀⠀
⠀⠀⡤⡖⣾⡷⡦⣶⠖⣦⡦⡤⠤⠄⣀⣶⡒⠆⠀⠀⠀⠀⣀⡤⢄⠀⠀⣠⣴⡶⠞⠿⣧⠀⠀⠀⠀⢠⢟⠫⠁⢀⣄⢴⠞⡋⠋⠉⠁⠀
⠀⠀⠀⢀⣹⡇⠀⠑⠚⠚⠚⠊⠛⣼⣏⠋⠀⠀⠀⠀⠀⢠⣿⣃⢀⢧⣽⡟⡃⠄⠂⠁⠀⠀⠀⠀⠀⣼⣿⣦⣮⠗⠃⠂⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢠⣵⡅⡀⡀⡀⣀⠀⠀⠀⢯⡇⠀⠀⠀⠀⠀⢐⣣⡿⠜⠤⣟⡿⠂⠀⠀⠀⠀⠀⠀⠀⠠⠖⡛⡛⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⡟⢿⡗⠿⠿⠛⠉⠀⠀⢠⣿⡆⠀⠀⠀⠀⣠⣿⡻⠏⠁⢝⣻⣫⠀⠀⠀⠀⠀⠀⠀⠀⢀⠣⡟⠃⠑⠷⡡⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠊⢿⠁⠀⠀⠀⠀⠀⠀⠘⣺⣧⡀⡀⡔⣞⣵⠊⠁⠀⠀⠨⣗⣮⣣⣂⣤⣠⣄⣤⢄⡄⡎⢔⡗⠀⠀⠀⠳⣷⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠓⠋⠛⠛⠋⠃⠀⠀⠀⠀⠀⠀⠁⠉⠉⠙⠛⠛⠛⠛⠋⠁⠀⠛⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢠⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠸⡿⠣⠀⠀⠀⡀⣄⠾⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣫⠧⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠒⢫⣧⡁⡖⡡⣶⡝⠂⢀⡠⣦⣶⣸⣴⣡⣦⣠⡀⠀⢠⣟⠔⠉⠁⠀⠀⠀⣾⣣⣟⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠂⣛⡻⡋⡓⠆⠁⢠⡆⡷⠃⠃⠁⠐⠐⢡⢸⠆⠀⣚⡧⠊⠁⠀⠀⠀⠀⠱⣟⢟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠨⣢⡿⠋⠁⠀⠀⣝⠏⠀⠀⠀⠀⠀⠀⢸⢫⡇⠀⢓⣿⡄⠀⠀⠀⠀⠀⣨⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣀⣾⠋⠀⠀⠀⠀⠀⣷⣇⡀⠀⠀⠀⢀⣠⡥⣳⠂⠀⢨⣿⡧⣤⡀⣄⣄⣴⡟⣻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠱⠙⡴⣩⡀⣥⣃⡃⡖⠁⠀⠀⠘⡔⡱⣴⣭⢝⡓⡓⢁⣺⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠉⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠈⠈⠈⠀⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀