⠀⢹⣿⣿⣿⣿⡿⠀⡞⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣖⣶⣶⣶⣤⣴⡦⠃⠀⠀⠁⠀⠀⠀
⡀⠘⣿⣿⣿⣿⠃⢰⠃⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⡟⢸⠋⡀⢀⣀⣀⣀⣀⣤⡀⠀⠀⠀⠀⠀
⣧⠀⢻⣿⣿⡏⠀⡞⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣾⡇⣾⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠸⡄⢸⣿⡿⠀⢰⢃⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⣿⣇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢧⠸⣿⠃⣰⠏⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠸⣿⣿⣿⣶⣦⣤⣤⣤⣤⣤⣤⣴⣶⣶⠖⠒⠋
⠀⠘⡖⢏⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠈⠙⠛⠻⠷⠾⣿⣶⣶⡶⠶⠶⠾⡟⠀⠈⠁
⠀⠀⢻⡞⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠤⠴⠶⠒⠒⠒⠶⠿⢴⣆⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀
⠀⠀⢸⠁⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠋⠁⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠈⣙⡶⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀
⠀⠀⡜⢰⠇⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠀⠀⠈⢣⡀⠀⣰⣿⡀⠀⠈⢳⡄⠀⠀⠀⠀⠀⠀⡇⢿⠀⠀⠀
⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣄⠀⠀⢠⡗⠋⣉⣉⡛⢦⣤⡾⠽⣄⠀⠀⠀⠀⠀⢹⢸⡀⠀⠀
⠀⠀⢀⡇⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⡜⠀⣠⠀⠀⠀⠀⠀⠀⠀⠘⠻⠿⢿⠿⡏⠀⠀⣿⣿⡇⠈⢯⠀⠀⠹⣦⣠⠀⠀⠀⠈⣏⡇⠀⠀
⠀⠀⢸⠁⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠻⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡏⠉⠱⣀⣸⠂⠀⠀⠀⠙⢧⠀⠀⠀⢹⡄⠀⠀
⠀⠀⢸⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠤⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⢳⠀⠀
⠀⠀⡞⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀
⠀⠀⠃⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢰⠀⡇⠀⠀⠀⠀⠀
⠀⠀⠂⠀⠀⣇⠀⠀⢦⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⡶⠶⠶⣶⣤⠀⠀⠀⠀⠀⠀⢀⡜⠁⡎⢀⡇⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢹⡀⠀⠀⠑⢄⡈⠓⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣔⡩⠦⠀⣈⣉⣉⣉⢸⣀⣀⣀⡠⠤⠖⠉⣠⠎⢀⣾⣀⣀⣀⣀⡀⠀
⠀⠀⠀⠀⠀⣈⣧⠀⠀⠀⠀⠉⠒⠤⣀⡉⠁⠀⠐⠀⠒⠀⣉⣩⡿⣇⣀⣀⣿⣽⣿⣿⢿⠧⠤⠀⠐⠒⠂⠉⠀⣠⠞⠢⣌⠑⠢⣀⠀⠀
⠉⠉⠉⠉⠉⠀⠈⠣⡀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠁⠀⠀⠙⠚⢿⣤⡏⠉⠉⠁⡸⠀⠀⠀⠀⠀⠀⡠⠔⠁⠀⠀⠀⠙⠢⣈⠂⠀
⠄⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⣀⡠⠖⠛⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⢶⡒⠒⠦⠤⠤⠤⣀⡈⠑⠢⣤⡄⠠⠶⡶⢶⡂⠐⠢⣌⠙⠢⢄⠀⢀⢬⠑⢤⡀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠑⢤⡀⠀⠀⠐⢄⡀⠀⠀⠀⠀⠉⠢⣄⠀⠀⠀⠀⠉⠒⠤⣈⠙⢷⠎⢸⠂⠉⠢⢄⠀⠉⠢⢄⠉⠃⢸⠀⠀⠈⠒⢄⡀⠀⠀⠀
⠀⠀⠀⠀⠀⠙⠢⡀⠀⠀⠉⠢⣄⠀⠀⠀⠀⠀⠑⠦⡀⠀⠀⠀⠀⠈⠓⢬⠤⠛⠢⠄⠀⠀⠑⠦⡀⠀⠉⠒⠃⠀⠀⠢⢄⠀⠈⠂⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢈⠑⢤⡀⠀⠀⠑⠦⡀⠀⠀⠀⠀⠈⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢤⡀⠀⠀⠀⠀⠀⠉⠂⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠑⠦⡈⠲⢄⡀⠀⠈⠒⢄⡀⠀⠀⠀⠀⠑⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⢄⡀⠀⠀⠀⠀⠀⠀⠀