⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣠⠀⠀⠀⠀⠀⢰⡄⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣲⣄⣀⠀⠀⠀⠀⠀⠀⣀⣠⣿⡏⣾⣿⣿⡇⣸⣿⢳⣾⠻⢧⣾⣿⡿⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⣠⣤⣤⣤⣿⣿⣿⣟⣶⡀⠀⠀⠀⠀⠀⠻⠿⠟⠀⠻⠟⠿⠗⠿⠗⠘⠿⠟⠉⠻⠿⠃⠀⠀
⠀⡠⠔⠒⢲⡦⡀⠀⡠⠖⠒⢲⢤⡀⠀⠀⠀⠀⠀⡿⠛⢁⣼⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣷⣀⠀⠀⠀⢠⣤⡄⣤⣤⢠⣤⣤⣤⣤⣄⠀⣤⡤⠀⢠⣤⣤⣤⡀
⠘⡀⠀⠀⠀⠀⢜⠞⠀⠀⠀⠀⠀⠹⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⢽⣿⠛⢻⡏⠈⠻⣿⣿⣾⡌⠉⠀⠀⠀⠘⣿⡿⢿⣿⠏⠉⣿⣷⣿⡏⢰⣿⢃⣄⢸⣿⢰⣿⠇
⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡘⡇⠀⠀⢻⡀⢀⣈⣻⡿⣻⡄⠀⠀⠀⠀⠛⠁⠘⠋⠀⠘⠛⠋⠛⠓⠛⠛⠛⠃⠛⠛⠛⠋⠀
⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⢿⣧⣴⣄⠈⡇⡍⣈⣀⣻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⢀⡴⠁⠀⠀⠀⠀⠀⠀⠘⢿⣧⡏⣿⣿⣿⣶⠭⢷⠀⠉⠛⠛⠃⠛⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠈⠳⡀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⣿⠉⠙⠉⠁⣞⣀⣨⡆⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠈⠢⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⠀⠘⢦⡀⠀⠀⢙⡷⠘⢒⣤⡀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠂⠀⠀⢳⠀⠠⢿⡗⠛⠏⠏⠁⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⣠⠤⡼⣷⣄⠈⠁⠀⠉⠀⢠⠟⢗⠒⠠⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⠒⠈⠁⠀⠀⠀⡏⠻⣷⣶⣶⣶⣿⠏⠀⡼⠆⠀⠀⠀⠉⠐⠢⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠉⠀⠀⠀⠀⠀⠀⠀⢰⠙⠦⣀⡙⠛⢛⣁⡤⠚⠁⠀⠠⠀⠀⠀⠀⠀⠀⠉⠒⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⠐⠃⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠟⡾⢻⡟⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠃⢀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠸⠀⣀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀