⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠊⠀⠀⠀⠀⠀⠀⠙⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢰⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡂⠀⠀⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⠀⠀⠹⡄⠀⠀⠐⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⣸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⠀⠀⠀⣿⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⣿⠀⠀⢻⡇⠀⠀⠀⠲⡄⠀⠀⠀⡴⠁⠀⠀⢸⡏⠀⠀⣿⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⢸⣿⠀⠀⠸⣿⠀⠀⠀⠀⣽⡀⠀⢔⡇⠀⠀⠀⢸⡇⠀⠀⢸⣧⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢰⣇⠀⠀⠀⢿⣿⠀⠀⢸⣿⣦⣄⠀⢼⣧⡇⢸⣽⠆⢀⣴⡟⡟⠀⢀⣼⠋⠀⠀⢀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠘⣿⡀⠀⠀⠀⠹⣷⡀⠀⠑⠍⠙⢷⣤⣿⣿⣿⣿⣤⡟⠁⠞⠁⠀⣾⠃⠀⠀⢀⣾⠇⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⠀⠙⢷⣄⠀⠀⠀⠈⣷⣤⣤⣤⣤⣼⣿⣿⣿⣿⣿⣿⣶⠶⠶⠶⠾⠏⠀⣀⣤⡾⠏⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣰⠁⠀⠀⠈⠛⠷⣶⣤⣄⠀⣀⣤⣴⠶⠾⣿⣿⣿⣿⣿⣿⡿⠿⠿⣶⣤⣤⡾⠟⠉⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀
⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠉⠙⣿⠟⠁⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣦⣀⠀⠹⢯⣀⠀⠀⠀⠀⠀⠀⠀⠀⣻⠇⠀⠀⠀⠀⠀
⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠒⠊⠉⢀⣴⣿⣿⣿⣿⠿⣥⣀⠉⢻⣿⣿⣿⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠸⣷⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠿⣿⣿⣿⣿⡇⠀⣿⣿⠀⢸⣿⣿⣿⣿⡛⠻⣷⣄⠀⠀⠀⠀⢀⣠⣿⠃⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠹⣧⣀⣀⣀⣀⣀⣠⣾⠋⠁⣼⣿⣿⣿⣿⣧⣀⠉⠛⠰⢾⣿⣿⣿⣿⣷⡀⠻⣷⣶⠶⠟⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠛⠛⠛⠛⠻⢿⡿⠁⠀⣴⡿⣿⣿⣿⣿⡏⠁⣾⣷⠀⢸⣿⣿⣿⣿⡿⣷⣄⠀⠙⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢀⣤⡾⠋⠠⣿⣿⣿⣿⣧⠀⢿⣿⡆⢸⣿⣿⣿⣿⠃⠈⠻⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠏⠀⠀⠀⢸⣿⣿⣿⣯⣀⣀⣩⣶⣿⣿⣿⣿⣿⠀⠀⠀⠀⠙⢿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠁⠀⠀⠀⢠⣿⡟⠛⢿⣿⣿⣿⣿⣿⣿⡿⠋⠙⣿⣇⠀⠀⠀⠀⠀⠙⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢴⣾⡟⠁⠀⠀⠀⠀⠀⣼⡏⠀⠀⠈⠉⠛⣿⣿⠛⠉⠁⠀⠀⠈⣿⡄⡆⠀⠀⠀⠀⠈⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢻⣿⠀⠀⠀⠀⠀⠀⡴⣿⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⣿⣷⠃⠀⠀⠀⠀⢀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⣿⡆⠀⠀⠀⠀⠀⠙⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠁⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢿⣇⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠰⣿⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡟⠃⠀⠀⠀⠀⣰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠈⢿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠃⠀⠀⠀⢀⡴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⢄⠀⠀⠀⠘⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⠐⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣆⠀⠀⠀⠀⠀⠀⠀⢀⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠄⠀⠀⠀⠀⠰⠋