⠀⠀⠀⠀⣀⡤⠴⠖⠒⠒⠒⠒⠲⠦⠤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠙⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣶⣦⣄⠀⠈⢷⡀⠀⠀⠀⠀⡠⢚⣭⡍⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣶⣄⢳⡀⠀⡠⣪⣾⣿⣿⣿⣆⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣿⣿⣷⠶⠶⠂⠀⠀⠉⠛⠷⣧⣪⣿⣿⣿⣿⣿⠿⢿⣇⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⠋⣁⡤⠀⠀⠀⠀⠀⠀⢰⠟⠉⠀⠀⠀⠀⠀⠉⠛⠿⣿⣆⠀⠀⠑⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣯⡶⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡰⣮⣿⡄⢢⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⠏⢀⡴⠁⣠⠀⡐⠀⡐⠀⠀⠀⢰⡀⠀⢢⠀⠀⢠⠀⠘⣿⣮⡻⣷⢘⣧⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢟⣿⠃⣠⠟⢠⣾⠃⡴⠀⣼⡇⡆⠀⠀⢸⣷⡀⠈⣷⡀⠈⣷⡀⠸⣿⣿⣿⣾⣿⡆⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⣰⡏⣠⣿⡏⢰⡇⢰⣿⢰⣇⠀⣇⠈⡿⣷⡀⠸⣷⡄⢹⣿⡄⢹⣿⣿⣿⣿⣿⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⢰⣿⢡⣿⣿⠁⣿⡇⣾⣃⢸⣿⡄⣿⡄⢷⠘⣷⣀⣯⢿⡼⣿⣷⡘⣿⣿⣿⣿⣿⡇⣴⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣧⣿⣿⣾⣿⣿⢨⣿⠁⡏⠀⣿⡇⢳⣸⣿⣸⡅⠈⢻⣿⡍⢻⣿⣿⣇⣿⣿⣿⣿⣿⣿⣿⡏⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣼⡟⣤⣤⣄⠹⡇⠀⠹⢿⣷⣇⢀⣀⣽⣧⣌⣿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⢻⣏⣄⣿⣆⠃⠀⠀⠈⠙⢿⠱⠟⡏⠉⣿⡿⢦⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠈⠏⣿⣿⣿⠀⠀⠀⠀⠀⠀⠁⠀⢿⣶⣿⣷⡾⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣇⠠⠷⠭⠼⠀⠀⠀⠀⠀⠀⠀⢀⣯⣛⣛⣋⢃⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⢧⡀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡳⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢛⣿⠟⢃⣿⣿⣿⣿⣿⣿⠸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠘⣿⢹⣿⣿⣿⣿⣿⣿⢠⡀⠀⠀⠀⠠⣀⣀⠄⠀ ⠀⠀⠒⣩⣿⣶⣿⣿⣿⣿⣿⣿⡇⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢣⠀⠉⠁⢻⠲⣿⣿⣿⣿⡏⣿⠈⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠄⠈⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠸⠀⠀⠀⢀⣀⡠⠤⠔⠒⠂⠉⠉⠁⡰⠁⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠸⠀⠸⣿⣿⣿⡧⣿⠀⠸⣿⣿⣿⣷⣤⠀⠤⠐⠈⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡁⠤⠔⠒⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⠀⠀⠆⠀⢿⣿⣿⡇⠘⡇⢄⠹⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⠀⠀⠀⠈⣿⣿⡇⠀⠀⠀⠑⢽⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⡿⠛⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⠜⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠐⠃⠒⠤⣀⠘⣿⣇⠀⠀⠀⠀⢀⡹⢃⢢⠀⠀⠀⠀⠀⠀⢀⠔⢱⣿⣿⡿⠁⠀⠀⠀⠀⠀⣀⠀⡀⠀⠀⠀ ⠁⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠑⣾⣿⠄⠒⠀⠁⠀⢀⡎⠄⠀⢀⣀⣀⡀⠐⠁⠀⣿⣿⠟⠑⢀⣀⠠⠒⠈⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⡠⠁⠀⠀⠀⠀⠀⠀⠀⠠⢪⡾⠛⠀⠀⠀⠀⢠⠞⠛⠛⠿⣶⠖⠈⠀⠀⠀⣸⡿⢃⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀⠀⠀⠀⢠⢡⣿⠁⠀⠀⠀⠀⠀⠏⠀⢀⠠⠊⠁⠀⠀⠀⠀⢠⢏⣴⠟⡩⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀