⠀⠀⠀⡰⡄⠔⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⡠⠁⡇⡄⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣄⣠⡇⠀⡇⢳⡀⠣⡀⠀⠀⠀⠀⢀⡤⡆⠀⠀⠀⠀⠀⢠⡆⠀⠀⠀⠀⠀⠀⢀⡟⡄⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⢳⡄⠀⠀
⠙⣽⠇⡜⠀⠀⠱⡄⠉⠉⠑⠒⠋⠁⡀⠓⣄⠀⠀⠀⢀⢾⡿⡄⠀⠀⠀⠀⠀⡬⣧⠘⢦⣀⣀⣀⠴⣿⠇⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀
⡞⢁⢦⠉⡇⠀⠀⣽⡦⣀⣀⣀⣴⠋⢧⠀⠈⠙⠒⠂⢠⠎⢣⡈⠑⠲⠤⠔⠋⡼⢩⡷⠄⠀⠀⣀⠔⣻⠀⠀⠀⠀⠀⠀⠀⣀⠇⡇⠀⠀
⡇⡼⠘⠦⠼⠄⠀⣿⠀⠀⠀⠀⣿⠀⠀⠉⠓⠒⣾⠚⠁⠀⠀⢩⢗⠤⠤⠴⠊⠁⠀⣿⠀⠀⠀⠀⠀⣿⠀⠀⠀⠈⠉⠉⠙⢆⣠⠜⠛⠒
⠿⠁⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠸⡃⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢘⠛⡄⠀⠀⠀⡿⠁⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢳⡇⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀
⠀⠀⠀⠀⠀⠀⡸⠀⡇⠀⠀⠀⢫⢸⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⡿⡀⠀⠀⠀⠀⠀⡇⡆⠀⠀⠀⠀⡞⠇⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀
⠀⠀⠀⠀⠀⠀⡇⠀⡇⠀⠀⠀⢸⠀⡇⠀⠀⠀⠍⡇⠀⠀⠀⠀⡇⡇⠀⠀⠀⠀⠀⡇⡇⠀⠀⠀⢸⠀⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⡇⡀⡇⠀⠀⠀⠐⠀⡇⠀⠀⠀⠂⡇⠀⠀⠀⠀⡇⡁⠀⠀⠀⠀⠀⡇⢱⠀⠀⠀⢸⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⡇⡇⡇⠀⠀⠀⢨⠀⢹⠀⠀⠀⡇⢣⠀⠀⠀⠀⠇⢧⠀⠀⠀⠀⠀⡇⢰⠀⠀⠀⢘⠀⡆⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⡅⡇⡇⠀⠀⠀⡇⢘⢸⠀⠀⠀⡇⢸⠀⠀⠀⢘⠀⢸⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⢘⠇⡇⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⡇⡇⡇⠀⠀⠀⡇⢨⢸⠀⠀⠀⡇⡌⠆⠀⠀⡇⢰⠸⡄⠀⠀⠀⠀⡇⢠⡇⠀⠀⢨⡆⡁⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⡇⡇⡇⠀⠀⠀⣇⢸⢸⠀⠀⠀⠇⠇⢱⠀⠀⢇⠸⠀⡇⠀⠀⠀⠀⡇⢨⠸⠀⠀⢸⢸⢨⠀⠀⠀⢀⡰⠃⣇⠀⣀⡀⠀
⠀⠀⠀⠀⠀⠀⠈⠛⠁⠀⠀⠀⠸⣸⢸⠀⠀⠀⠐⢇⢸⠀⠀⢸⢰⢠⠃⠀⠀⠀⠀⡇⢸⢸⠀⠀⢸⢸⠰⠀⠀⠒⠛⠲⡀⢠⠚⠉⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠛⠚⠀⠀⠀⢸⢸⢸⠀⠀⢸⢸⢸⠀⠀⢰⠀⠀⡇⠨⢸⠀⠀⠀⣿⣸⠀⠀⠀⠀⠀⢱⡇⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⡄⠀⠀⠀⠀⠀⠀⠀⢸⠀⣽⠀⠀⢸⡞⢨⠀⠀⢸⡀⠀⠳⠼⠼⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠴⢾⡁⠘⣦⠖⠀⠀⠀⠀⠀⠈⠓⠛⠀⠀⠈⠉⠙⠀⠀⣸⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠛⠻⡄⠈⣉⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀