⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢀⠔⠓⣠⠋⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⡰⠋⠀⠀⢿⠀⠀⣄⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢰⠁⠀⣰⡇⠘⡀⠀⣟⠢⡘⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠠⡇⠀⢠⠏⢸⠀⣧⠀⠸⡀⠱⡌⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢰⡇⠀⣾⠀⢨⠀⡏⢆⠀⢳⡀⢣⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠸⡇⠀⣯⠀⡘⢠⡧⠔⠃⠉⠉⠉⠚⠢⢄⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢣⠀⢸⡾⠓⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢄⠀⠀⠀⣠⣶⣿⣿⣦⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠘⠄⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢾⡄⠘⣿⣻⣛⣭⣿⡟⠀⠀⠀⣠⡞
⠀⠀⠀⠀⠀⡇⠀⠀⠀⣰⠒⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⡽⣄⠹⣿⡓⢿⡿⠀⠀⠀⣴⠏⠀
⠀⠀⠀⠀⢰⠁⠀⠀⠀⠃⣀⣤⣤⡀⠀⠀⠀⠀⢿⣿⣿⠇⠀⠁⠻⢧⡀⠿⠠⢄⣾⠏⠀⠀
⠀⠀⠀⠀⡞⠀⠀⠀⠀⠰⣿⣿⣿⡿⠀⠀⢀⣠⡄⠉⠁⠀⣠⣀⠀⣼⣏⠀⠀⣸⠃⠀⠀⠀
⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠉⠛⠛⠁⠀⠀⠠⡼⠗⠀⠀⠀⠀⣨⠛⣿⣿⣷⣼⡏⠀⠀⠀⠀
⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢴⣥⣶⣾⣿⣿⡟⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣤⣚⣷⣿⣿⣻⡛⠛⢿⡦⣄⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢩⠖⠂⢠⣤⢤⡤⠐⠒⠈⠁⠀⠀⠀⠀⢹⡄⡏⠀⠀⠀⢳⣿⠇⠀⠀⠀
⠀⠀⠀⠀⠀⢀⡔⠁⠀⠀⠀⠀⠀⠈⠢⣀⠀⠢⣄⠀⠀⠀⢨⠇⢘⠁⠀⢀⡞⣿⠀⠀⠀⠀
⠀⠀⠀⠀⢠⠊⠀⠀⠀⠀⠀⠦⡀⠀⠀⠀⠉⠐⠚⢤⡀⠀⡜⠊⠉⣹⡟⠁⠀⠘⠃⠀⠀⠀
⢀⡴⠋⢉⠇⠀⠀⠀⠀⢀⡀⠤⠼⢦⡀⠀⠀⠀⠀⠀⠳⣄⣇⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀
⡏⠁⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣄⠀⠀⠀⡶⠃⡟⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣷⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠉⠉⠉⠀⢀⠇⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠈⠢⣀⠀⣣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⢀⣾⡜⣁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠉⢷⡤⢄⡀⠀⠀⠀⠀⠀⢀⡜⢁⡠⢤⡠⠚⠉⠁⠱⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠈⠣⠤⠀⠀⣄⣒⠒⠒⠛⠉⠁⠀⢪⣿⠁⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀