⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⠋⠀⠀⠀⡠⠔⠀⠀⠀⠀⠀⠐⢄⡀⠀⠀⠈⢶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⡟⠁⠀⢀⣴⠞⠀⠀⠀⠀⣠⠀⠀⠀⠀⠹⣦⡀⠀⠀⢻⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⠁⠀⢠⣾⠏⠀⠀⠀⠀⢠⣿⡆⠀⠀⠀⠀⠸⣿⣆⠀⠀⢿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⡇⠀⢠⣿⡟⠀⠀⠀⠀⠀⣾⣿⣿⡄⠀⠀⠀⠀⢹⣿⡆⠀⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣇⠀⣾⣿⡇⠀⠀⠀⠀⣸⣿⣿⣿⣷⠀⠀⠀⠀⢸⣿⣿⠀⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⠀⣿⣿⡇⠀⠀⠀⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⠀⣼⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀
⢆⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣧⢹⣿⣿⡀⠀⠀⠀⢿⣿⣿⣿⣿⠀⠀⠀⠀⣼⣿⡿⣰⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⣠⠃
⠈⢦⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣯⣿⣿⣷⡀⠀⠀⠸⣿⣿⣿⡏⠀⠀⠀⣼⣿⣿⣷⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀
⠀⠘⣷⡀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣷⡀⠀⠀⣿⣿⣿⡇⠀⢀⣼⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⢀⣼⠃⠀⠀
⠀⠀⠘⣿⣄⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣷⠀⢀⣿⣿⣿⡇⠀⣼⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⢠⣾⠏⠀⠀⠀
⠀⢀⠠⠘⣿⣦⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⡿⠀⣸⣿⣿⣿⣧⠀⢻⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⣰⣿⠃⡐⠀⠀⠀
⠀⠈⣆⠱⡈⢿⣷⡀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠃⢠⣿⣿⣿⣿⣿⡆⠘⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⢀⣼⣿⢃⠜⣠⠇⠀⠀
⠀⠀⢻⣷⡘⣎⢻⣿⣆⠀⠀⠀⠀⠀⣿⣿⣿⠏⠀⣾⣿⣿⣿⣿⣿⣿⡀⠘⣿⣿⣿⠀⠀⠀⠀⠀⣠⣾⡿⣡⢎⣼⣿⠀⠀⠀
⠀⠀⠸⣿⣿⣮⢷⣿⣿⣷⡀⠀⠀⠀⣿⣿⡏⠀⢸⣿⣿⣿⣿⣿⣿⣿⣇⠀⠸⣿⣿⠀⠀⠀⢀⣴⣿⣟⣵⣣⣿⣿⡇⠀⠀⠀
⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⣿⣿⠀⠀⢼⣿⡙⣿⣿⣿⠏⣹⣿⠀⠀⢿⣿⡀⠀⣠⣾⣿⣿⣿⣽⣿⣿⣿⠁⠀⠀⠀
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⠀⠀⢸⣿⢻⣾⣿⡟⡾⢻⡟⠀⠀⣼⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀
⠀⠀⠀⠘⣿⡿⠟⠿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠈⢿⣦⢻⣿⣿⣰⣿⠃⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⢿⣿⠇⠀⠀⠀⠀
⠀⠀⠀⠀⣟⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⡹⣦⠀⠘⣿⣿⣿⣧⣿⠃⠀⣠⠟⣾⣿⣿⣿⣿⡿⠋⠁⠀⠀⠀⢹⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣧⠈⠓⢄⠈⢿⣿⣿⠃⡠⠞⠁⣸⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣆⠀⠀⠀⠈⠻⠁⠀⠀⠀⢠⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣷⡄⠀⠀⠀⠀⣼⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡀⠉⠁⠂⠀⠀⠊⠉⠀⣾⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣃⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀