⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⡇⠀⠀⡆⠀⠀⠀⢀⣿⠀⢸⠀⠀⠀⠀⢸⡇⠀⠀⠈⠇⠸⣿⣿⣿⠀⡆⠀⠀⠀⠀⠀⢿⢧⡀⠀⡧⡄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⢀⠀⠀⠀⠁⠀⠀⠀⣸⡇⠀⡾⡆⠀⠀⠀⠈⣷⠀⠀⠀⠠⠀⢿⣿⣿⠀⡇⠀⠀⠀⠀⠀⢸⡀⠈⠛⢠⠘⢆⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⡸⢀⠀⠀⢠⡄⠀⢸⠀⠀⢸⠀⠀⠀⢠⡏⡇⢀⠁⢡⠀⠀⠀⠀⣿⡆⠀⠀⠀⣀⠼⣿⣿⡄⢁⠀⠀⠀⠀⠀⠈⡇⠀⠀⢸⣶⡀⢣⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⢃⡾⠀⠀⠸⠁⠀⢸⠀⠀⣼⠀⠁⠢⣼⡀⠀⠘⠀⠈⡄⠀⣀⣀⢽⢿⡖⠈⠉⠀⠄⢿⣿⡇⢸⠀⠀⠀⠀⠀⢀⡇⠀⠀⢸⣿⣿⡾⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⡼⣸⡇⠀⠀⡄⠀⠀⣼⠀⠀⢿⠀⠀⠀⠇⠀⠉⡇⠀⠀⠱⠀⠀⠀⠘⠀⢳⡀⠀⠀⠐⢸⢻⡇⢸⡄⠀⠀⠀⠀⢸⡇⢀⠠⢺⣿⠟⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢀⡇⣿⡇⠀⠀⡇⠀⠀⢸⡆⢰⢸⠀⠀⠼⢀⠀⢀⠀⠀⠀⠀⢣⠀⠀⣀⡇⠀⠱⡤⠀⠀⢱⡆⠇⢸⡇⠀⠀⠀⠀⢸⠋⢁⣴⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢸⢀⣿⡇⠀⠀⡇⠀⢐⣺⣧⣽⠼⣤⣀⣆⡀⠀⠹⠀⠀⠀⠀⠀⢆⠀⣀⣸⣐⣤⣰⢤⣤⣤⣷⣲⣾⡷⢿⣿⠀⠀⢸⣴⣿⣿⡿⣇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⡾⢸⣿⣇⠀⠀⡇⠀⠀⠀⡗⠈⠉⢹⣿⣿⣿⣶⠿⠛⠀⠀⠀⠀⠀⠊⢛⢛⠟⢻⣿⣿⣿⣿⣿⡇⢈⡅⠈⠃⠀⠀⣿⣿⣿⣿⠡⣿⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⡇⢸⡿⢹⠀⠀⢱⠀⠀⠀⡇⠁⠀⠈⢿⠛⠛⠛⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⢛⠋⠉⠉⠁⢸⣷⠀⠀⠀⢠⣿⣿⡟⣼⢸⠋⡇⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⡇⢸⠁⠈⡇⠀⡎⡆⠀⠀⣇⠀⠀⠀⠈⢈⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠃⠀⠀⣠⡟⢸⠸⠀⠀⡘⠛⢏⠀⣿⣸⠀⢳⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠠⡇⡌⠀⠀⠸⡀⣿⣹⣄⣴⠉⢧⢀⠀⠀⠈⠆⠄⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠙⠃⠊⡆⠃⢸⢂⣀⠔⠃⠀⢸⢠⣿⣿⠀⢸⡀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⡇⠃⠀⠀⠀⡷⣿⣷⣿⣿⣦⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⣈⣌⠄⠀⢀⣠⠊⣼⣿⣿⠀⢸⡇⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⡇⢁⠈⠉⠛⠛⢲⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⢤⡐⣿⡿⠙⠛⠛⢱⠇⢠⣿⣿⣿⠔⠒⠃⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⡇⠸⠀⠀⠀⢀⣼⣿⣿⣯⣛⠲⠶⠶⠤⣤⣤⣤⣤⣤⡤⠤⠶⠒⡖⠿⣿⡉⠀⣈⣡⣿⠃⠀⠀⢀⣟⣀⣼⣿⡟⠈⡄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠸⠄⠀⠀⠀⢰⡇⣇⠤⡾⣿⣿⣿⣿⣿⣿⣷⣦⣇⣀⠈⢻⠟⠋⠀⠈⠑⠤⡀⠀⠀⠀⠈⢑⣿⣿⢇⣀⣤⣶⣿⣿⣿⣿⠋⠀⠀⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠑⢄⡀⠀⠈⠃⠀⢸⠁⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⡟⡁⠀⠀⠀⠀⠀⠀⠈⠃⢄⢀⠤⡎⠘⣿⣿⣿⣿⣿⣿⡿⡿⠁⠀⠀⠀⢡⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⢀⣿⠛⠿⢿⣿⣿⣿⣿⣿⠀⠀⠀⢉⠗⠀⠀⢒⠂⠀⠀⢡⠀⢡⠀⢹⣿⣿⡿⠟⠋⢀⡇⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣸⣿⠀⠀⢸⡇⠀⢹⣿⣿⡄⠀⠀⠀⠡⡀⠀⠂⠀⠀⠀⠃⠀⠈⠀⠘⣿⣿⠇⠀⠀⣼⡇⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀