⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡠⡠⠒⠒⠢⠢⠤⠤⣀⣀⡀⡀⢀⢀⡠⡠⠤⠤⠖⠖⠉⠉⠉⠉⢒⢒⣒⣒⣲⣲⠤⠤⣄⣄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡠⡠⠒⠒⠢⠢⠤⠤⣀⣀⡀⡀⢀⢀⡠⡠⠤⠤⠖⠖⠉⠉⠉⠉⢒⢒⣒⣒⣲⣲⠤⠤⣄⣄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⡠⡠⠃⠃⢠⢠⠊⠊⠉⠉⣉⣉⣁⣁⣛⣛⡳⡳⠤⠤⠤⠤⠔⠔⠒⠒⢈⢈⣩⣩⠖⠖⠒⠒⠦⠦⠤⠤⠽⠽⣄⣄⠀⠀
⠀⠀⠀⠀⠀⠀⡠⡠⠃⠃⢠⢠⠊⠊⠉⠉⣉⣉⣁⣁⣛⣛⡳⡳⠤⠤⠤⠤⠔⠔⠒⠒⢈⢈⣩⣩⠖⠖⠒⠒⠦⠦⠤⠤⠽⠽⣄⣄⠀⠀
⠀⠀⠀⠀⡰⡰⠃⠃⠀⠀⠀⠀⠀⠀⠼⠼⠁⠁⠀⠀⠀⠀⠈⠈⠑⠑⠢⠢⠤⠤⠋⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠘⡄⡄
⠀⠀⠀⠀⡰⡰⠃⠃⠀⠀⠀⠀⠀⠀⠼⠼⠁⠁⠀⠀⠀⠀⠈⠈⠑⠑⠢⠢⠤⠤⠋⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠘⡄⡄
⠀⠀⢰⢰⠃⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢠⣤⣤⢄⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⡤⢤⢤⣤⣤⠀⠀⠀⠀⠀⠀⡇⡇
⠀⠀⢰⢰⠃⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢠⣤⣤⢄⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⡤⢤⢤⣤⣤⠀⠀⠀⠀⠀⠀⡇⡇
⠀⠀⡎⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠉⠉⠛⠛⠛⠛⠂⠂⠀⠀⠀⠀⠀⠀⠈⠈⠛⠛⠛⠛⠃⠃⠀⠀⠀⠀⣠⣠⠃⠃
⠀⠀⡎⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠉⠉⠛⠛⠛⠛⠂⠂⠀⠀⠀⠀⠀⠀⠈⠈⠛⠛⠛⠛⠃⠃⠀⠀⠀⠀⣠⣠⠃⠃
⠀⠀⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢠⠃⠃⠀⠀
⠀⠀⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢠⠃⠃⠀⠀
⠀⠀⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡤⡤⠴⠴⠲⠲⠶⠶⢤⢤⣤⣤⠤⠤⣼⣼⣿⣿⣷⣷⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⣀⣀⠀⠀
⠀⠀⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡤⡤⠴⠴⠲⠲⠶⠶⢤⢤⣤⣤⠤⠤⣼⣼⣿⣿⣷⣷⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⣀⣀⠀⠀
⠀⠀⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣸⣸⡈⡈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⡆⡆
⠀⠀⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣸⣸⡈⡈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⡆⡆
⠀⠀⠸⠸⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢹⢹⠒⠒⠒⠒⠋⠋⠁⠁⢷⢷⣄⣄⣀⣀⣀⣀⣀⣀⡀⡀⢰⢰⠃⠃
⠀⠀⠸⠸⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢹⢹⠒⠒⠒⠒⠋⠋⠁⠁⢷⢷⣄⣄⣀⣀⣀⣀⣀⣀⡀⡀⢰⢰⠃⠃
⠀⠀⠀⠀⠱⠱⡄⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⡀⡀⠀⠀⠀⠀⢀⢀⡴⡴⠃⠃⣠⣠⠞⠞⠀⠀⠛⠛⠁⠁⠀⠀
⠀⠀⠀⠀⠱⠱⡄⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⡀⡀⠀⠀⠀⠀⢀⢀⡴⡴⠃⠃⣠⣠⠞⠞⠀⠀⠛⠛⠁⠁⠀⠀
⠀⠀⠀⠀⠀⠀⠈⠈⠑⠑⢄⢄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⢉⢉⣉⣉⠔⠔⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⠈⠑⠑⢄⢄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⢉⢉⣉⣉⠔⠔⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠑⠢⠢⠤⠤⠤⠤⠤⠤⠤⠤⠔⠔⠒⠒⠊⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠑⠢⠢⠤⠤⠤⠤⠤⠤⠤⠤⠔⠔⠒⠒⠊⠊⠀⠀⠀⠀⠀fuggg x---DDD