⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠶⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⣠⣒⡘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⢰⠃⠀⠉⠻⠀⠀⠀⠀⢀⣀⡀⠀⢀⢀⠠⠐⠀⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢀⠤⠀⠀⠠⠤⠀⡀⠀⠀⠠⠄⠀⢣⠀⠀⢨⡀⠀⠀⠀⡀⠄⠒⠉⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠸⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⢈⣱⣄⡀⢧⠤⠒⠋⠉⠉⠉⠉⠉⠒⠲⠤⣀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠂⠀⠀⠀⠀⠀⠸⠀⢀⠠⠒⠉⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠦⣀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀
⠀⠀⠀⠘⠀⠀⠀⠀⠠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⣀⠀⠀⠀⡀⠀⡔⠁⠈⡄⠀⠀
⠀⠀⠀⠀⡆⠀⠀⠰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢮⠀⠈⠁⠢⡇⠘⠀⠀⢰⠀⠀⠀
⠀⠀⠀⠀⢡⠀⢠⠃⠀⣤⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢆⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠈⠣⡀⠀⠀⠈⠀⠀⢠⠃⠀⠀⠀
⠀⠀⠀⠀⢀⣂⣼⣀⡜⢸⣀⣠⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠱⣄⡄⠀⠀⠀⢧⠀⠀⠀⠀⠀⠈⠳⣄⡀⠀⡠⠃⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠑⣤⠀⠀⠀⠀⠪⣀⠀⠀⠘⢣⠀⠀⠀⠀⢀⠀⠀⠀⢸⢀⡠⠊⠑⠤⣀⡀⠸⡄⠀⠀⠀⠀⢣⠀⢱⡀⠙⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣿⢀⣠⢀⣴⠒⠚⠃⢀⠇⠈⢆⠀⠀⠀⠀⠑⢄⢀⠇⠁⠀⠀⠀⠀⠀⠉⠉⡇⠀⠀⠀⠀⠀⢣⠀⢧⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⡏⠉⠈⠋⠸⠀⠀⢈⠟⠙⠒⠊⢦⢰⠒⡤⢤⡤⠵⠀⠀⠀⠀⠀⣀⣤⡦⠀⡇⠀⠀⠀⠀⠀⠈⢧⠈⡆⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢸⡇⡀⠀⠀⠀⣆⡤⠋⠀⠀⠀⠀⠀⠉⠀⠉⠁⠀⠀⠀⠀⣨⣶⣿⣯⣥⠤⠄⡇⠀⠀⠀⠀⡀⠀⠘⡆⢸⡀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢸⢠⡇⠀⠀⠀⢩⠀⢠⣤⣤⣤⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢠⠃⣠⠂⠀⢀⡇⠀⠀⢳⠀⡇⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢸⢸⠀⠀⠀⠀⠀⢣⠀⣀⠤⠞⠋⠁⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⣀⣚⣉⡇⠀⢀⣾⠃⠀⣀⣸⡆⢸⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢸⠜⢄⠠⡀⣀⡀⠀⠳⣄⠀⠀⠀⠀⠀⠀⠐⠂⠁⠀⠀⠀⠀⠀⠔⠂⠀⠀⠀⠀⠉⠲⣿⡏⠀⣾⣿⣿⣧⣼⡇⠀⠀⠀⠀
⠀⠌⠁⠢⡀⠇⠀⢸⠀⠙⢤⡉⠓⢒⠖⠉⠉⠉⠉⠀⠂⠄⡀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠿⣿⣿⠏⠸⣇⠀⠀⠀⠀
⠀⠘⢄⠀⠈⠀⠀⣎⣀⡀⠀⠹⣶⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠖⢂⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⣅⣀⡹⠋⠀⠀⣿⠀⠀⠀⠀
⠀⠀⠀⠁⠢⢄⣼⣿⣿⣿⣷⣶⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠼⣾⠿⠳⡽⠀⠀⠀⣿⡇⠀⠀⠀
⠀⠀⠀⠀⠀⠸⣯⠻⣿⣿⣿⡀⢸⠄⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⠀⠀⠘⣦⣸⡏⠀⠀⠀⣿⣿⣄⠀⠀
⠀⠀⠀⠀⠀⠀⢿⣷⣄⠉⢹⣿⠃⠀⠀⠀⠑⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢀⡏⢻⣷⠀⢀⡞⠛⠛⠛⠋⠀
⠀⠀⠀⠀⠀⠀⠈⣿⣿⡆⠘⣿⡀⠀⠀⠀⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⢦⣤⣤⣶⣿⣇⡿⢻⣆⡜⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠘⣿⡟⢧⣽⣿⣶⣤⣤⣼⣿⠒⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁⠈⣿⣿⣿⠿⠋⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀