⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣄⣤⣤⣠⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⠿⢿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⡿⠟⠛⠉⣿⡃⠀⠀⠈⠀⠀⠀⠀⠀⢹⡍⠛⠻⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠟⢻⠇⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠐⠈⡿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠁⠀⣿⠀⠀⠀⢰⣿⡔⣴⣶⣶⣶⣶⣶⣶⡖⣤⣿⡄⠀⠀⠀⢱⠀⠹⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⢠⣯⣤⣶⣿⣿⣿⡃⣿⣿⣿⣿⣿⣿⣿⡇⣻⣿⣿⣿⣶⣤⡸⡆⠀⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣾⡏⣰⣴⡾⣿⣿⢿⣿⣿⣿⣿⣯⡁⠈⠀⠀⠈⢈⣵⣿⣿⣿⡿⠿⣿⡏⣷⣄⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠇⠋⠀⠀⠙⢿⣿⣿⣿⣿⣶⡄⠀⣶⣿⣿⣿⣿⢟⢁⡀⠀⠱⢹⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⢀⠔⠉⣡⣭⣍⠻⣿⣿⡟⠂⠈⠿⣿⡿⣫⣴⣶⣤⠈⠑⠄⠘⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠇⠀⡆⠀⣾⣿⣿⣿⣷⢡⠈⠀⠀⠀⠀⠀⢣⣿⣿⣿⣿⡇⠀⢘⠀⢹⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⠀⠀⡆⠀⠹⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⢿⠿⠃⠀⢠⠀⢘⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠀⠀⠁⡀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠄⡀⠀⠀⠀⢀⠀⠄⠀⠀⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⠀⠀⠀⠀⠁⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢐⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡄⠀⠀⠀⠀⡆⠀⡁⠁⠁⠈⠈⠈⠀⠀⢀⠀⠀⠄⠇⠀⠀⠀⠠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⠀⠀⠀⠀⠂⠀⡀⠀⠀⠀⠀⠀⠀⣀⠠⠄⠈⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⡔⢠⠀⡀⠀⠈⠉⠉⠈⠉⠁⠀⠀⠀⢀⠠⠰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠘⠀⠇⠸⠀⠰⢆⢤⢄⣄⢠⠠⠤⡄⠲⡊⠁⠀⢀⠂⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠆⠀⡆⠀⠀⠘⠀⢀⠈⠨⣦⣦⣥⣭⣵⠀⠨⠀⠀⢀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⢰⠐⡁⠀⠀⠈⠀⠀⠀⣴⣿⣿⣿⣿⣿⣇⡀⡄⠔⠁⠀⠀⠀⢐⣵⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠒⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣾⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀