⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣠⡤⣤⡀⠀⣤⣄⣀⠀⡄⠀⠀⡢⠀⡤⡄⢠⣤⣤⡄⠀⠀⡆⠀⠀⢠⠀⠀⠀⠀⠀⢀⣦⢤⣀⠀⠀⠀⡂⠀⠀⢀⡤⣄⢰⣠⣄⡄⡠⠀⠀⢠⣤⣤⠀⢀⣤⡀⠀
⠀⢀⡝⠁⠀⠀⠉⠀⡇⠀⢸⠀⢱⡀⡜⠁⠸⡀⠈⠀⢸⠀⠀⠀⡸⢣⠀⠀⡾⠀⠀⠀⠀⣰⠃⠀⠀⠈⠀⠀⢰⢻⠀⠀⠸⡀⠈⠀⢸⠀⠀⡇⠀⠀⣸⠀⠀⠀⢩⠀⠁⠀
⠀⠀⡇⠀⠀⠀⠀⢀⡟⣏⠁⠀⠀⡟⠀⠀⠀⠙⡄⠀⢸⠀⠀⣰⠥⠼⡄⠀⡇⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢠⠧⠤⡆⠀⠀⠙⡆⠀⢸⠀⢀⡇⠀⠀⡏⠉⠉⠀⠀⠳⡀⠀
⠀⠀⢳⣄⣀⡤⠄⢸⣀⡈⣆⡀⡇⢀⠀⣧⣠⢇⣀⣎⡀⢰⠃⠀⠀⢣⢀⣇ ⠀⠀⠘⣤⣀⣠⠄⢠⠏⢀⠀⢹⠀⣧⣠⢇⣀⣜⣀⢸⣠⣀⢄⣧⣠ ⡄⠰⠀
⠀⣰⠋⠀⠀⠙⠀⡜⠀⢉⠆⠸⡀⣰⠃⠰⡁⠘⠀⢀⡇⠀⠀⢠⢣⠀⠀⢸⠀⠀⠀⠀⢠⠎⠁⠀⠉⠀⠀⢀⢾⠀⠐⡇⠘⠀⠀⡇⠀⡜⠀⠀⢸⠀⠀⠀⢸⠀⠑⠀⠀
⠀⡇⠀⠀⠀⠀⠀⡗⢖⠋⠀⠀⢳⠁⠀⠀⠙⡄⠀⢸⠀⠀⢠⣋⣘⡆⠀⡜⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢀⣞⣀⣇⠀⠀⠙⡄⠀⢰⠁⠀⡇⠀⠀⢸⠒⠒⠀⠈⠳⡀⠀⠀
⠀⠱⣄⡀⣀⡄⠀⡇⠈⣆⠀⠀⡆⠀⠀⢆⣀⡜⠀⢸⠀⢀⠎⠀⠀⢱⠀⣇⣀⡀⠀⠀⠘⣄⣀⢀⠀⡜⠀⠀⢸⠀⢆⣀⡜⠀⢸⠀⠀⣇⣀⡀⣇⣀⣀⠀⣄⣀⠇⠀⠀
⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⢄⠀⣤⠀⠠⠤⢄⢠⢤⠤⡤⡄⢠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠜⣐⣸⠀⢸⢤⠜⠀⢸⠀⠁⢃⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠬⠀⠴⠁⠨⠄⠮⠈⠦⠀⠦⠀⠀⠼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀