⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣄⣂⡀⠁⠄⠀⠀⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣶⠔⣄⠉⠈⠡⢴⣆⣀⢀⡀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⡠⠝⠋⠀⠀⢀⡉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⣡⠄⠊⢀⠔⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠂⠌⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡱⠜⠁⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣡⡴⠔⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠴⣉⠀⠤⠔⠒⠒⠋⠉⠉⠉⠉⠁⠀⠀⠀⢠⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠠⠠⠮⠟⠋⠀⠀⠀⢄⠀⠀⠐⠄⠀⠁⠰⣾⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀
⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⡤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠄⠂⠂⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠙⢶⡤⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡄⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣀⢠⠠⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⢀⠌⢴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂
⠀⠀⠀⠌⠀⠀⢸⣿⣾⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣠⠎⠋⠁⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⠰⡁
⠠⠂⠈⠀⡀⠀⠨⣻⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣡⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠉⠀⡸⠀⠀⣴⡶
⠁⠀⠀⠀⡀⠀⢱⣿⣿⣦⣤⠀⠀⠀⠐⠀⢀⠀⠀⠀⠀⠀⠶⠁⠀⠀⠀⠀⠀⠀⢄⢳⣆⠀⠀⠀⡀⠠⠂⢀⠄⠠⠀⠀⠀⠐⡢⠊⠀⠀⡠⠋⠀
⠀⠌⣆⠀⣲⣄⣸⣿⣿⣿⡿⢀⣀⢠⠄⠀⠀⠀⠀⠀⠀⢄⠉⠀⠀⡀⠀⠀⠀⠀⢀⠈⠳⠀⣀⡘⡐⠂⡈⢀⠀⡊⠌⠀⠀⠊⠀⣀⡴⠋⠀⠀⠀
⠀⢃⠇⢰⡟⢻⣿⣿⣿⣿⣿⡷⣟⠱⠉⣄⠀⠀⠀⠀⠈⠋⠀⠀⠈⠀⠀⠀⠀⠀⣡⢒⣄⠀⣿⣼⣿⢀⣿⠏⡸⠉⠀⠀⢠⣨⠞⠋⠀⠀⠀⠀⠀
⠀⠠⡀⠲⢃⢺⠹⡻⢿⣿⣿⢯⡟⢰⡀⠿⠆⣦⣀⡄⠀⠀⠀⠀⠀⠀⠁⡀⠀⠀⠱⡽⠿⡀⣷⣿⠃⣼⠏⠀⠜⠄⣀⡤⠊⠀⠀⠀⠀⠀⠀⠀⠀