⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣶⣶⣶⣤⣄⣀⠤⠲⢾⣍⡙⠻⢿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢷⣶⣤⠙⢿⣷⣄⠙⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣷⣼⣿⣿⣧⠀⢟⠉⢆⢹⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣾⣿⣿⣿⣿⣿⣧⠀⣷⠆⢘⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠻⢤⣾⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣸⣿⣿⣿⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢀⣿⣿⣿⣿⠀⠀⠀⠈⠻⣿⡻⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀
⠤⣄⣤⣾⣿⣿⣿⣿⠀⠀⣀⣠⣤⡞⣿⣽⣿⣿⣿⣿⣿⣿⢿⣿⣿⠛⠳⠶⣿⣿⣿⣿⣿⣿⣯⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⡿⣿⣿⡿⣄⠉⠁⠛⠛⠛⠛⠚⠻⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢸⠇⣿⣿⡍⠉⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⡋⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢹⡏⣷⣾⡄⠀⠀⠀⠀⠀⠀⠀⣠⡾⣿⠻⡙⠙⠆⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⡇⠸⡇⠻⣗⠒⠂⠀⠀⣠⣾⣿⣠⣷⣴⣿⡃⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠓⠀⢳⠀⠈⠢⠤⠒⢻⣿⣿⣿⣿⡿⠿⠛⠓⠆⠀⠀⠀⢸⣿⣿⣿⣿⣿⡿⣿⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠈⡿⠟⠋⠁⠀⣀⣀⣀⣢⠀⠀⠀⢸⣿⣿⣿⣿⣿⣷⢻⡇⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⣀⠤⠒⠈⠁⠀⠀⠀⠈⡆⠀⠀⠸⡟⣿⣿⣿⣿⣿⡄⢿⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡡⠔⠉⠀⠀⢀⣀⡀⠀⠀⠀⠀⠘⣄⠀⠀⣿⠘⣿⣿⣿⣿⣧⠈⢇⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠀⢀⠤⢒⠈⢁⣀⠈⠑⠢⡀⠀⠀⡜⡆⠀⢹⡄⠘⣿⣿⣿⣿⡄⠈⢆⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠁⠀⠀⢰⠗⠂⠀⠀⠀⠀⠉⠳⢄⠑⠠⣤⢿⣽⠀⠈⣇⠀⠘⣿⣿⣿⣷⠀⠈⢦⠀⠀
⠀⠀⠀⠀⠀⠀⢀⠴⠋⠀⠀⠀⣠⢃⡤⠔⠚⠉⠉⠁⠲⢄⡀⢳⢠⠛⢸⠇⠀⠀⠘⡄⠀⠈⢿⣿⣿⣇⠀⠀⠣⠀
⠀⠀⠀⠀⠀⢠⠋⠀⠀⠀⠀⢠⡷⠋⠀⠀⠀⠀⠀⠀⠀⠀⠹⡀⡜⢀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣆⠀⠀⠀
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠠⡁⠉⡐⠠⣀⡀⠀⠀⠀⠀⠀⡷⠃⠞⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣆⠀⠀
⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⡇⢠⠀⠒⢔⠻⢵⣤⣀⠀⡴⢁⣼⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣆⠀
⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠇⠀⠣⠀⠀⠑⠤⠤⠼⣏⠀⣿⡏⢈⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⢦
⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⡀⠀⠀⠀⡀⠀⠀⠀⡐⢁⢼⠏⠀⠈⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆