⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡕⡷⡀⠀⠀⠀⠀⠀⠀⣀⣶⡿
⠀⠀⠀⡏⠉⠳⣤⠗⠛⢳⡀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠐⡀⠀⠀⠀⡠⣾⣯⣿⠇
⠀⠀⠀⠘⡆⠀⠀⠀⣠⠞⠀⠀⠀⠀⠀⢸⣿⢽⣿⣷⡅⢃⠘⡢⠊⢠⡻⢏⣾⠁
⠀⠀⠀⠀⠀⠉⢆⡜⠀⠀⠀⠀⠀⠀⠀⠈⢜⣿⣭⡿⠀⡸⠠⠁⠀⠆⣟⣿⠃⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣆⠊⠈⠑⠓⠒⠂⣤⣼⣯⡿⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⢀⣀⡀⡸⡇⠴⠒⠂⠀⠐⠒⠒⠦⠀⣿⠀⢀
⠀⠀⠀⠀⠀⠀⡠⠔⠊⠁⠀⠀⠀⠀⠀⠀⢩⠃⢳⡿⠃⠀⠀⠻⡿⠁⣰⡟⠀⠀
⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠘⢻⡟⠃⠀⠈⣿⠀⠀⠀
⠀⠀⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠀⠀⠀⠀⢀⠇⠀⠀⠀⡼⠇⠀⢀
⠀⠀⡘⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠑⠠⣀⠀⢁⡀⢀⢀⡔⠁⠀⠀⠐
⠀⠀⡇⠀⠀⠀⠀⠀⠀⢢⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠈⠉⠀⠉⡑⡬⠂⠀⢀⠀
⡰⣇⢱⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⣟⠂⠀⠀⠀⠀⠀⠀⠀⢀⠢⠛⠀⠀⠀⠂⠀
⢼⣷⠈⢆⠀⠀⠀⠀⠀⠀⢸⠀⠀⠘⢄⠀⠀⠀⠀⢀⢠⠖⠁⠀⠀⠀⠀⡀⠀⠀
⠈⠳⠤⣀⣢⡀⠀⠀⠀⢀⠜⢀⣀⣠⣴⣧⠀⠀⠀⡇⢈⠀⠀⠀⠀⠀⠀⠄⠀⠀
⠀⠀⠀⠀⠀⢁⠀⠀⠈⠉⠀⠉⠉⠙⢯⣯⣦⠀⠀⠱⣈⠆⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⠐⠒⠀⠤⠤⠤⠄⠵⠜⠀⠣⠤⠥⠜⠀⠀⠀⠀⠀⠀⠒⠀⠀