⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣼⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠻⠟⣒⣀⠀⠉⠛⠋⠍⡍⡀⠐⠒⠀⠤⠀⡀⣰⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠀⠀⠀⠦⠀⡀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠑⠠⢀⠀⠀⠸⠿⠟⠙⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣾⡄⠀⠀⢻⠒⠲⢤⡁⠂⠜⡐⠀⠀⠀⠸⡄⠀⠀⠁⠦⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠿⢿⠁⠀⠐⠠⠀⣁⣀⠀⠈⠓⢦⡀⠁⠄⡀⠀⠈⠀⠀⢀⠔⢀⠄⠀⠀⠢⡰⠃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠃⡰⠀⢈⠒⡒⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⢀⠈⠀⢀⢀⡔⠋⠀⠎⢀⣤⡀⠀⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣇⡀⢠⠀⠁⡀⠀⣠⠁⠀⠀⠀⠀⠀⠀⠀⡇⠀⠑⢄⠀⠉⠀⠀⠀⠀⠈⠛⠁⢀⠀⠀⠀⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠇⠙⢰⠄⠐⣀⣾⣿⠀⠀⠀⠀⠀⠀⠀⣰⡇⠀⠀⠘⠧⡀⠀⠀⠀⠀⠃⠀⡇⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡏⠀⠀⣾⡩⠋⠁⠀⢀⡄⠀⠀⠀⠀⡠⠊⠥⣻⡀⠀⠀⡄⠙⢄⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠇⠀⢰⣿⠀⠙⣟⣿⣶⠫⡄⠀⠈⠁⢀⡀⠀⠀⠑⢄⠸⠇⠀⠀⢳⡀⠀⠀⠀⠗⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⠸⡏⠀⠀⣿⡿⡏⠀⠀⠂⠀⠀⠙⣿⣿⣶⣤⡀⡿⠀⠀⠀⠀⢱⡄⠀⠀⠘⡄⢃⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⡀⡀⠀⢀⠱⠀⠀⠘⠛⠀⠀⠀⠀⠀⠀⠸⣿⣿⢿⠇⢠⠁⠀⠀⠀⠀⡄⠱⡄⠀⠀⢰⠀⡀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⠀⠀⢑⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⢂⠄⢀⠀⠀⡀⠀⠀⢳⣦⣿⠀⠀⠈⠁⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⡆⠀⠀⠁⣄⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠁⡖⠁⠀⠀⢰⠤⣀⠈⢿⣿⡆⡀⠀⠀⠀⠂⠀⠀⠀⠁⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢿⣿⢀⠢⠄⠀⣀⣀⣀⣀⣤⡴⠜⠀⠀⠀⣴⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠠⠀⣄⠐⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠠⠁⠤⠌⠁⠄⠀⢨⣿⡟⠋⠁⠀⡏⠀⢀⣴⠾⠿⠿⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠑⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠠⠁⡈⠀⠀⠀⡀⠀⠘⠁⠀⠀⠀⡜⠀⡴⡫⠈⠀⠑⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⡐⠄⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢣⠀⢣⡀⢣⠀⠀⠁⠀⠐⠀⣃⠊⡐⠀⠀⠀⠀⠐⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠐⢤⠊⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⠀⠀⠑⠤⠘⠈⠑⠄⣠⠜⣀⣀⠋⠞⠐⡀⠠⠀⡀⡤⢤⣤⠄⠀⠀⠀⠀⠀⠀⠀⠘⣀⣀⣠⠚⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠐⠀⣤⠀⠑⠀⠀⠀⠀⠀⣤⠀⠶⠈⣤⣎⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⢀⢔⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢄⠀⠀⠡⣿⠀⢀⠀⠀⠀⠀⠀⠀⠀⠐⣄⠰⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⡠⠐⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢃⢀⡤⢥⣀⠈⠀⠀⠀⠀⠀⠐⠀⠀⠌⠇⠁⠀⠀⠀⢀⠜⢃⢀⠀⠂⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠰⢻⣾⡁⠀⣾⣿⣶⣔⠈⢩⡶⠶⢸⣇⠀⠷⡴⣤⣶⣿⣦⣄⠀⠆⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠃⠘⠻⢥⠤⡾⠿⣿⣍⠀⢸⣷⣤⣿⣿⡀⠈⣘⣼⣿⣿⣿⣿⠚⠇⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠘⠀⠀⠀⡠⠊⠀⠀⢐⠿⠟⠛⣿⣿⠿⣿⣿⡏⠀⠉⠻⣿⡝⠃⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⢀⣴⠋⠀⠀⠀⢠⠏⠀⠀⠀⡏⠀⠀⠀⠹⡀⠀⠀⠀⠈⠻⣤⣀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠛⠁⠀⠀⠀⢠⡏⠀⠀⠀⢰⣷⠀⠀⠀⠀⢷⡀⠀⠀⠀⠀⡨⠥⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢢⠀⠀⠀⣾⠃⠀⠀⠀⢸⣏⠀⠀⠀⠀⠸⣷⡄⢀⠠⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⢚⠃⠄⢀⣀⠀⠀⡿⠀⢀⣀⠀⠄⠋⠁⠄⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⡉⠑⡐⠠⠤⠄⠀⢤⠔⠒⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⡌⠀⠀⠀⠀⡀⠀⠀⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠠⠀⠀⠉⠍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⡐⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡀⠀⢀⣠⣄⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠀⠀⢿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀