⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠁⠀⠀⢰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠉⠙⣇⠀⠀⠈⠉⠙⣎⠉⠙⠳⣄⢀⣀⣀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣇⣶⠤⠤⢄⣀⣀⠤⠤⠬⠧⠒⠒⠉⠁⠀⠀⠀⠀⠀⠉⠑⠢⣄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢀⣀⡠⠤⠴⠧⠤⠒⣲⠇⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢻⢷⡈⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀
⠀⠀⠀⣠⠔⠋⠁⠀⠀⠀⠀⢀⡤⠞⠃⢠⠇⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢀⠻⡄⠀⠉⠲⢤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀
⠀⢀⠞⠁⠀⠀⠀⠀⠀⣤⠖⠋⠀⠀⢀⣿⡄⡟⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠑⢝⢦⠀⠀⠀⠈⠙⠒⠦⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀
⠀⡎⠀⠀⠀⠀⠀⢀⡾⠁⠀⢀⠀⠀⡸⡟⢁⡇⣧⡀⠀⠀⠀⠀⠀⠀⠦⢄⣀⣸⡀⠀⠀⠈⠷⣄⠀⠀⠀⠀⠀⠀⠀⠹⡏⠙⠒⠦⣄⡀⠀⠀⠀⠀⡀⠀⢸⠀⠀⠀
⠀⡇⠀⠀⠀⠀⠀⡞⠀⠀⠀⡞⠀⢀⡇⣇⠸⣄⢻⡣⠆⠀⠀⠀⠀⠀⠀⠀⢐⢹⠈⢭⡉⠑⠒⠻⣦⣄⡀⠀⠀⠀⠀⠀⢹⡀⠀⠀⡇⠙⠀⠀⠀⠀⠐⠀⢸⠃⠀⠀
⢠⡇⠀⠀⠀⠀⣸⠁⠀⠀⢀⡗⠰⣼⣸⡼⢶⡚⠻⣷⡀⢠⡀⠀⠀⠀⠀⠀⠈⣸⣠⣊⣁⣀⠀⠀⠙⣿⣍⠓⠄⠀⠀⠀⠀⢧⠀⠀⢧⠀⠀⠀⠀⠀⢀⢀⡏⠀⠀⠀
⠀⢹⡀⠀⠀⢀⡿⠀⠀⠀⢸⠃⠀⡏⠁⠀⣀⡹⣦⣯⣿⠄⢳⠀⠀⠀⠀⠀⠀⢻⣿⣻⢶⠾⠯⣵⣦⣘⣯⣧⡀⠀⠀⠀⠀⠸⡄⠀⢾⠀⠀⠀⠀⠀⣼⡟⠀⠀⠀⠀
⠀⠀⠳⡄⠀⡼⠇⠀⠀⠀⣿⡀⢰⣧⣾⣿⠿⢛⠛⣿⠻⣄⠘⠃⠀⠀⠀⠀⠀⢈⣇⣿⠂⣿⠀⢸⡋⢻⣿⣿⣷⡀⠀⠀⠀⠀⣷⠀⠈⣇⠀⢀⡠⠖⠉⡆⠀⠀⠀⠀
⠀⠀⠀⠙⢦⡏⠀⠀⠀⢰⣿⡇⣻⣾⡋⣯⡢⠿⠴⡿⠀⠈⠓⢤⡀⠀⠀⠀⠀⠀⠸⡏⠋⠉⠉⠙⠛⠋⠉⠸⣿⣧⠀⠀⠀⠀⢸⡀⠀⢸⡏⠉⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢸⠀⠀⠀⠀⣾⣿⡇⣽⡋⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⢄⠀⠀⠀⠸⡵⡀⠀⠀⠀⠀⠀⠀⠀⢹⡾⡆⠀⠀⠀⠀⡇⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⡟⠀⠀⠀⠀⣿⣿⣧⠙⡇⠀⠀⠀⠀⠀⠀⠀⠀⣰⡀⠀⠀⠀⠙⢦⠀⠀⠘⠹⡄⠀⠀⠀⠀⠀⠀⠀⣧⢻⠀⠀⠀⠀⡇⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⡇⠀⠀⠀⠀⣿⡟⣺⣤⣧⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⡀⠐⠂⠀⠀⠱⣄⠀⠘⠽⡄⠀⠀⠀⠀⠀⠀⢸⣾⠀⠀⠀⠀⣷⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢳⠀⠀⠀⠀⣿⣷⣸⣿⡸⡆⠀⠀⠀⠀⠀⠀⠀⠈⠺⠇⠀⠀⠀⠀⠀⠈⢧⠀⠰⢵⡀⠀⠀⠀⠀⠀⡀⣧⡇⠀⠀⠀⡇⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢸⡄⠀⠀⠀⣿⣿⡀⢫⢧⣹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡀⠤⣣⠀⠀⠀⠀⢠⣻⣿⡇⠀⠀⠀⡇⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⡇⠀⠀⠀⣿⡏⡇⠟⡎⠳⣳⡀⠀⠀⢀⣀⡠⠄⠐⠀⠀⠀⠀⠂⠂⠒⠒⠒⢻⡄⡟⡆⠀⠀⢠⣳⣿⣿⣧⠀⠀⢰⠃⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢹⠀⠀⠀⣿⡇⡇⠸⡽⡄⠙⢷⡄⠀⠀⠀⠀⠀⠀⠤⠤⢄⠀⠀⠀⠀⠀⠀⠘⣷⠰⣵⠀⡰⣵⣿⣿⣿⡇⠀⠀⣼⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠈⣇⠀⠀⠸⡇⣿⠀⠸⢹⢦⠀⠙⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡄⠘⣞⡟⣹⣿⣿⣿⡇⠀⢠⡇⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⣇⢸⠀⠀⠸⡗⢵⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⡏⠀⣿⣿⣿⣿⡇⠀⣼⣷⠀⠀⠀⠀⣿⣧⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⢹⢸⠀⠀⠀⡇⠈⠋⢿⢷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣊⡴⡇⡀⢹⠀⣿⣿⣿⣿⠇⢠⣿⣿⡄⠀⠀⠀⢹⣿⡆⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠸⣼⠀⠀⠀⡇⠀⠀⢸⣧⠉⠪⣖⢤⡀⠀⠀⠀⡠⠀⣀⡤⠞⠁⠀⢹⠀⢸⢸⣿⣿⣿⣿⢀⣾⣿⣿⣧⠀⠀⠀⢸⣿⣽⡄⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⣧⠀⠀⠀⡇⠀⠀⣸⡟⡆⠀⠈⠓⢬⣁⣀⠤⡖⠋⠁⠀⠀⠀⠀⢸⠀⡎⢸⣿⣿⣿⡿⣼⣿⣿⣿⣿⡄⠀⠀⠀⠇⢷⡹⡄⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⢸⡄⠀⠀⡇⠀⠀⣿⣿⣽⠀⠀⠀⠀⠘⡆⠀⡇⠀⠀⠀⠀⠀⠀⢸⠀⡇⢸⣿⣿⣿⣷⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠈⣷⠹⣄⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣆⣇⠀⢰⠇⠀⢸⣿⣿⣿⡀⠀⠀⠀⠀⣇⠀⡇⠀⠀⠀⠀⠀⠀⡞⢰⠁⡜⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠈⣧⠙⣆⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣟⠹⣾⡄⣾⠀⠀⣾⣿⣿⡏⡟⡄⠀⠀⠀⢸⠀⣇⠀⠀⠀⠀⠀⢀⡇⡾⠊⠀⡇⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠘⣦⠈⢧⠀