⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠿⡄⠀⠀⠀⠀⠀⠀⠀⠰⡿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⡇⠹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠈⢧⢀⣀⣀⣀⡀⠀⢸⠃⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⠀⠀⢸⣿⣿⣿⣿⣿⣶⣼⠃⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢠⣤⣿⣿⣿⣿⠀⠀⢸⣿⣿⣿⣿⣿⣿⡟⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣆⠀⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⡟⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⣹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀⠒⠚⠉⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣶⣀⣠⣿⣿⣿⣿⣿⣿⡿⠀⣀⣀⣠⣤⠄⠀⠈⠙⠛⣹⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⡇⠙⠋⠁⠿⠃⠀⠀⠀⠀⠈⠁⠈⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣅⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣼⣿⣿⣿⣿⣿⡟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⠿⣿⣿⡷⢄⡀⠀⠀⠀⠀⠀⠠⢾⣿⣿⣿⣿⠿⠛⠓⢶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣴⠟⠉⠙⠛⠂⠈⡿⢣⠀⠙⠳⣦⣤⣀⠴⡇⠀⠈⠉⠉⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢲⠁⠘⠂⠀⠀⠈⠉⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⡟⠈⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀⠀⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⣧⠀⠀⠀⢡⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⢀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⢀⣤⠏⠈⠳⠤⣤⣤⡴⠋⣧⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠈⡟⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⢸⡠⠀⠀⠀⠀⠀⠀⠀⣾⡏⠀⣴⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠹⣇⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠘⣿⡄⠀⣿⠁⠚⢀⠀⡀⠀⠄⠀⠀⠐⠻⣦⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⣾⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⢀⣠⣿⡇⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⠁⠀⢠⣀⡀⢀⣀⣀⣀⡀⠀⡠⢻⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢿⣇⠀⢸⣿⣦⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⠬⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠺⣧⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣿⡀⢸⣿⣿⣦⡀⠀⠀⢀⠀⣴⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣄⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠻⢿⣿⣿⣶⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣆⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠈⢿⡿⢿⣍⡉⠙⠛⠛⠛⠛⠁⡼⠀⠀⠀⠀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢸⡇⠀⠙⠛⣦⣤⣤⣄⡀⢠⠃⠀⠀⠀⠀⠁⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠈⠛⣿⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⣾⠇⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢸⠶⠤⡀⠀⣀⣀⣀⣀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠉⠉⠉⢹⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠇⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠋⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⡿⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⣾⣿⣿⣷⣶⣦⣄⠀⣰⣿⣿⣿⣿⣿⣶⣤⡀⠀⣠⣿⠁⠀⠀⠀⠀⠀