⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤⣶⣦⣦⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣽⣿⣿⣿⣿⣿⣿⣿⣷⣿⣯⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠛⠋⠉⢉⠉⠉⠉⡉⠙⠿⣿⣿⣿⣿⣿⣽⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡟⢠⣀⣖⣠⠏⠀⠀⠀⢐⢠⡄⣀⢻⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠤⠐⠐⠒⠛⠛⠃⠀⠀⠊⠁⡠⢠⡀⠀⠱⠥⠒⠈⠀⠿⠿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢴⣭⣤⣤⣤⣤⣀⣀⠀⠀⠀⠂⣖⢒⣉⣀⣸⠈⠢⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⠀⠀⠀⠸⣿⡿⠋⠈⠙⢿⡿⠃⠁⠀⠀⠀⠀⣀⣤⣤⣤⣤⣤⣤⣤⣾⠶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠃⠀⠀⠀⠀⢹⠅⠀⠀⣤⠜⠀⠀⠀⠀⠀⣠⣾⣿⣿⡿⠿⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠁⠀⠀⠀⠀⠀⠀⠆⢀⡠⠃⠀⠀⠀⠀⠀⣼⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⠀⠀⠀⠀⠀⠀⠑⠤⠤⠊⠁⠀⠀⠀⠀⠀⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⢀⣠⣤⣶⣶⣶⣶⣦⣄⡀⠀⠀⠀⠀⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠀⢿⣦⣤⣴⣾⡿⠋⠉⠉⠉⠉⠙⠛⠿⢿⣦⣀⠀⠀⠀⣿⡆⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀
⠀⢀⣀⣀⣀⡤⠐⠀⠀⠀⡀⢨⠋⠀⠀⢺⣿⣿⣿⡏⠀⠀⠀⠀⠀⢀⡤⠀⠀⠀⠈⠻⣿⣶⣶⣿⣇⠀⠀⠤⠋⠁⠀⠀⠀⠀⠀⣀⣀⢠⠄⠀⢀⡨⠍⠂⠁⠀⠀⠀
⠀⠀⠀⠉⠁⠀⠤⠤⠖⢊⠁⠀⠀⠀⠀⠾⠿⠿⠿⠃⠀⠀⠐⢂⠮⠋⠀⠀⢀⣠⠔⠂⠀⠙⠻⢿⣿⣷⠀⠀⠀⠀⠀⠀⠒⠈⠈⠐⠉⠁⠀⠀⠀⢀⣀⠤⣰⠖⠀⠀
⠀⠠⡤⠖⠂⠀⠠⠔⠊⠁⠀⠀⠀⠀⣠⠤⠂⠀⠀⠀⢀⣀⠀⠀⢀⠤⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⢤⡤⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠉⡀⠀⠀⠀
⠀⠀⠀⠀⢤⠄⠀⠘⠉⠀⠀⠒⢂⡁⢀⠤⠀⠀⠀⠀⠐⠒⠒⠈⠀⠀⠀⠀⠀⠀⣒⠆⠊⠀⠀⠀⠁⠀⢄⡲⠁⠀⠀⡀⠀⠀⠐⠒⠈⠁⠀⠀⠀⠀⡰⠋⠀⠀⠀⠀
⠀⠀⠒⠊⠁⠀⠀⠀⠀⠀⣀⠤⠔⠊⠁⠀⠀⠀⠀⠄⣒⠮⠋⠀⠀⠀⠀⠠⠔⠉⠀⠀⠀⠀⠀⣀⡤⠒⠁⠀⠀⠀⠒⠚⠛⠉⠉⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀