⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣀⣤⣄⡀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠸⠀⠀⣀⣠⣴⣿⣿⣿⡿⣿⣦⣶⣶⠾⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣶⣾⣿⣷⣶⡦⢠⣤⠤⣤⡿⠛⠉⡝⠻⣷⣆⣱⣽⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠰⣿⡏⠰⢩⣶⣿⣢⡜⠀⠀⠀⢡⠀⠀⠙⠃⠐⠒⣊⣈⠇⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⡇⡇⢸⣚⣉⣩⡴⠁⠀⠀⠀⠈⠒⠒⠒⠈⠉⠁⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠈⠉⠀⠇⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⣆⡀⠀⠀⢠⣶⣶⠄⠀⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⣁⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⡼⣽⠀⠀⠈⠉⠁⠀⠀⠀⠙⣄⠀⠀⠀⠀⠀⠀⢈⣿⡆⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢠⣷⡄⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⣿⣇⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠸⣿⣧⡀⠀⠀⠃⣠⠖⢀⣀⣀⣀⣀⡀⠀⠀⠀⠈⢣⠀⠀⠀⠀⢠⣿⣿⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣆⠀⢀⠀⢠⣎⢹⠀⣏⣀⣧⣼⣦⣄⠀⠀⠀⢣⠀⠀⠀⣬⣿⡇⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣄⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠈⡄⠀⢠⣿⣿⠤⢄⡀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⡀⠄⠒⠹⣿⣿⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠳⠀⣺⣿⡇⠀⠀⠈⠉⠒⠄⠀⢀
⠀⣀⠤⠐⠊⠁⠀⠀⠀⠀⠩⣿⣿⣆⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠘⢠⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀
⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣯⠀⠀⠘⣿⣿⣿⣿⣿⡿⣯⠏⢀⠀⠀⠀⣽⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣦⢀⣆⡈⠛⠼⠷⠗⠛⠁⣠⣿⠆⠀⣸⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⡿⢿⣶⣶⡶⣶⣶⠿⠟⠉⢠⣴⣿⠏⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⢿⣤⣀⠈⠁⠀⠀⠀⠀⢠⡾⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣀⣤⣄⡀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠸⠀⠀⣀⣠⣴⣿⣿⣿⡿⣿⣦⣶⣶⠾⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣶⣾⣿⣷⣶⡦⢠⣤⠤⣤⡿⠛⠉⡝⠻⣷⣆⣱⣽⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠰⣿⡏⠰⢩⣶⣿⣢⡜⠀⠀⠀⢡⠀⠀⠙⠃⠐⠒⣊⣈⠇⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⡇⡇⢸⣚⣉⣩⡴⠁⠀⠀⠀⠈⠒⠒⠒⠈⠉⠁⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠈⠉⠀⠇⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⣆⡀⠀⠀⢠⣶⣶⠄⠀⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⣁⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⡼⣽⠀⠀⠈⠉⠁⠀⠀⠀⠙⣄⠀⠀⠀⠀⠀⠀⢈⣿⡆⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢠⣷⡄⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⣿⣇⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠸⣿⣧⡀⠀⠀⠃⣠⠖⢀⣀⣀⣀⣀⡀⠀⠀⠀⠈⢣⠀⠀⠀⠀⢠⣿⣿⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣆⠀⢀⠀⢠⣎⢹⠀⣏⣀⣧⣼⣦⣄⠀⠀⠀⢣⠀⠀⠀⣬⣿⡇⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣄⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠈⡄⠀⢠⣿⣿⠤⢄⡀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⡀⠄⠒⠹⣿⣿⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠳⠀⣺⣿⡇⠀⠀⠈⠉⠒⠄⠀⢀
⠀⣀⠤⠐⠊⠁⠀⠀⠀⠀⠩⣿⣿⣆⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠘⢠⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀
⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣯⠀⠀⠘⣿⣿⣿⣿⣿⡿⣯⠏⢀⠀⠀⠀⣽⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣦⢀⣆⡈⠛⠼⠷⠗⠛⠁⣠⣿⠆⠀⣸⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⡿⢿⣶⣶⡶⣶⣶⠿⠟⠉⢠⣴⣿⠏⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⢿⣤⣀⠈⠁⠀⠀⠀⠀⢠⡾⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
