⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠉⠑⢢⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁⠀⠀⠀⠘⠁⠀⠀⠘⣆⡤⠤⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⢀⡀⠀⠀⠀⠰⣿⠀⠀⠀⢧⣠⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢀⠜⠉⢻⡀⠀⠀⢸⠀⠀⠀⡖⣄⡇⠀⠀⠀⣆⡇⠀⠀⢠⡾⠁⠀⠈⢧⠀⠀⠀⠀⠀⠀⣀⡠⠤⠤⠒⠊⠉⠒⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣠⠋⠠⠤⢤⡧⠀⠀⢸⡗⢀⣘⣯⢸⠆⠀⠀⣠⢿⠀⠀⠀⣸⣇⠀⢐⣼⡿⠤⠒⠋⠉⠁⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢀⠔⠁⡀⠐⠒⢠⡇⠀⠀⢸⡳⡏⠁⢉⣿⠀⠈⠋⠁⣿⠀⠀⠐⢿⣯⡠⠊⢁⠀⠀⠀⠀⠀⠀⣰⢰⡃⠀⣟⠀⠀⠀⠀⠀⠀⠱⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡇⠐⠒⠒⠛⢻⡞⠁⠀⢀⠜⠋⠑⢶⣾⣿⠞⠒⠠⣶⣿⡄⢀⡀⣼⠋⠀⠀⢸⣧⡐⠀⠀⠠⢠⡏⢃⡇⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⡀⠀⠀⠤⠲⣿⠦⠴⠁⠀⠀⠀⠈⠉⠉⠓⠤⠶⣿⣿⣁⡠⠋⡀⠀⠀⠀⠈⣿⣹⡤⢤⣴⣾⡄⠘⣧⠏⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡆⠈⡽⠁⠀⠈⢢⡀⢀⡴⠛⣿⣧⡼⠿⢿⣿⣶⢏⣼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠋⡼⠁⣒⢤⣄⣀⣿⣏⢀⣼⠟⣿⣿⣄⣤⣿⠧⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠈⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣽⣷⣶⡖⠉⠉⢢⠀⠀⠈⠙⠻⠾⢧⣴⣋⣹⣤⠤⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣤⣤⣤⠤⠄⠀⠀⠀
⠀⠀⠀⠀⠈⢶⣄⡀⠀⠀⠀⠀⡰⠂⡆⣾⣿⠿⢿⣧⡀⠀⠈⠀⠀⠀⠀⡀⡀⡄⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢯⣽⡁⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠘⣛⣟⣦⣀⠴⣨⢖⣣⠜⣻⠟⠛⠛⠛⠻⣶⣤⠀⠀⠀⢰⡃⢸⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣆⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠠⢾⣿⣿⣷⠊⠑⠒⠀⠈⠉⠒⠒⠠⠤⢴⣛⣷⣄⢀⣼⣷⣞⡄⣠⠞⢀⣤⢇⢠⡼⣂⣴⡷⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⣄⠀
⠀⠀⠀⠀⠀⠀⠀⠈⢉⢹⣿⡄⠀⠀⠀⠀⠀⠀⠀⠈⠀⡶⠇⠉⠹⣿⡟⢳⣾⣷⣦⣶⣿⣿⣟⣭⡾⠟⣫⣴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⡗⠂⠀⠀⣉⡇⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣭⠒⠊⠁⠀⢀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣞⠉⠀⢀⣀⣠⣤⠀⣀⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠿⡿⠛⠛⠛⠛⠛⠛⠛⢛⢻⡿⢻⠻⣶⣶⣾⡛⡉⠳⡶⣃⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠨⠲⠷⢿⣿⣿⣷⣶⣿⣷⣕⣦⡄⠀⠀⠀⠀⠀⠀⠀