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