⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⣄⠀⠀⢀⣿⣿⡄⢠⣿⣿⡀⠀⠀⣠⣾⠏⠀⠀⠀⠀⠀⠀
⠀⠀⠈⠒⠤⣀⠀⠀⠀⠘⡟⠉⠛⢿⠀⠘⡇⢸⠃⢀⡿⠛⠉⣻⠃⠀⠀⠀⣀⠤⠒⠁
⠀⠀⠀⠀⠀⠈⠓⢦⣀⠀⠈⠂⠀⠈⢧⡀⠁⠈⢀⡞⠁⠀⠀⠁⠀⣀⡴⠚⠁⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⣤⡀⠀⣀⡼⢳⡄⣠⡞⣧⡀⠀⢀⣤⡾⠋⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣴⠟⠛⠻⣧⠀⢾⠁⠈⣿⣿⠀⠘⡇⠀⣿⠟⠛⢳⣆⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⢀⠸⣆⣏⡜⠀⣿⣧⠈⢆⣷⣸⠃⠀⠀⠀⢻⠄⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⡆⠀⣹⡟⠀⢰⡏⢻⡄⠈⢻⣏⠀⢡⠀⠀⡼⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣇⡼⠋⢷⡀⣿⡃⢸⣧⢠⡟⠙⣆⣼⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⠁⠀⢸⣿⠘⡇⢸⠉⣿⡇⠀⠈⢿⡇⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠠⢻⣿⡆⠈⠀⣸⣿⠱⠀⠆⠘⣇⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⠀⣸⡏⣿⡀⢠⡏⢻⡇⢠⠃⠀⢿⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠂⢀⡀⠀⠀⠀⡇⠀⢸⣣⡟⠀⢸⣇⣾⠃⠈⢷⣸⠆⠀⢸⠀⠀⠀⢀⠀⠀⠀
⠀⠀⠀⠀⠀⠈⠢⣄⠀⠃⠀⣼⡿⠀⠀⠨⣿⣿⠀⠀⠘⢿⡇⠀⠇⠀⡠⠒⠁⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⣼⠏⠀⠀⠀⣸⡟⣿⡄⠀⠀⠈⠻⣆⣠⠎⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠿⣧⡀⠀⠀⢀⡿⠁⠘⣷⠀⠀⠀⢀⡽⢧⡀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⡠⠀⠁⠀⠘⣷⡀⢀⡾⠁⢀⠀⠘⣧⠀⣠⡿⠁⠀⠀⠢⡀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡎⠀⢀⣼⣄⡀⠈⣳⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠐⢹⣷⡀⠉⢿⠏⠀⣰⣿⠓⢄⠀⠀⡠⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⢺⣿⣷⠀⠘⠀⢠⣿⣿⠂⠀⠑⡜⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⠀⣸⡟⣿⡇⠀⠀⣼⡏⣿⡀⢀⣴⠁⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⡿⠀⢸⣷⠀⢀⣿⠀⠹⣷⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠿⣷⠀⠀⣿⡀⣸⡏⠀⢠⡿⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠉⠀⠘⣧⡀⢹⣇⣿⠁⣠⡟⠀⠈⠙⢆⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠘⢿⠘⣿⡟⢠⠟⠀⠀⠀⠀⠀⠑⠄⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⢹⠃⣞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⢸⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀