⠀⠀⠀⠀⠀⠀⣀⣤⣶⡶⢛⠟⡿⠻⢻⢿⢶⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢀⣠⡾⡫⢊⠌⡐⢡⠊⢰⠁⡎⠘⡄⢢⠙⡛⡷⢤⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢠⢪⢋⡞⢠⠃⡜⠀⠎⠀⠉⠀⠃⠀⠃⠀⠃⠙⠘⠊⢻⠦⠀⠀⠀⠀⠀⠀
⠀⠀⢇⡇⡜⠀⠜⠀⠁⠀⢀⠔⠉⠉⠑⠄⠀⠀⡰⠊⠉⠑⡄⡇⠀⠀⠀⠀⠀⠀
⠀⠀⡸⠧⠄⠀⠀⠀⠀⠀⠘⡀⠾⠀⠀⣸⠀⠀⢧⠀⠛⠀⠌⡇⠀⠀⠀⠀⠀⠀
⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠒⠚⠁⠈⠉⠲⡍⠒⠈⠀⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠈⠲⣆⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠉⡹⠤⠶⠁⠀⠀⠀⠈⢦⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠈⣦⡀⠀⠀⠀⠀⠧⣴⠁⠀⠘⠓⢲⣄⣀⣀⣀⡤⠔⠃⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣜⠀⠈⠓⠦⢄⣀⣀⣸⠀⠀⠀⠀⠁⢈⢇⣼⡁⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢠⠒⠛⠲⣄⠀⠀⠀⣠⠏⠀⠉⠲⣤⠀⢸⠋⢻⣤⡛⣄⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢡⠀⠀⠀⠀⠉⢲⠾⠁⠀⠀⠀⠀⠈⢳⡾⣤⠟⠁⠹⣿⢆⠀⠀⠀⠀⠀⠀
⠀⢀⠼⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀
⠀⡏⠀⠘⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀
⢰⣄⠀⠀⠀⠉⠳⠦⣤⣤⡤⠴⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢯⣆⠀⠀⠀
⢸⣉⠉⠓⠲⢦⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣠⣼⢹⡄⠀⠀
⠘⡍⠙⠒⠶⢤⣄⣈⣉⡉⠉⠙⠛⠛⠛⠛⠛⠛⢻⠉⠉⠉⢙⣏⣁⣸⠇⡇⠀⠀
⠀⢣⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⠛⠛⠛⠛⠛⠛⠛⠒⠒⠒⠋⠉⠀⠸⠚⢇⠀⠀
⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⢤⣨⠇⠀
⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢻⡀⣸⠀⠀⠀
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠛⠉⠁⠀⠀⠀
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢠⢄⣀⣤⠤⠴⠒⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀
⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀
⠀⠀⢀⡷⢤⣤⣀⣀⣀⣀⣠⠤⠾⣤⣀⡘⠛⠶⠶⠶⠶⠖⠒⠋⠙⠓⠲⢤⣀⠀
⠀⠀⠘⠧⣀⡀⠈⠉⠉⠁⠀⠀⠀⠀⠈⠙⠳⣤⣄⣀⣀⣀⠀⠀⠀⠀⠀⢀⣈⡇
⠀⠀⠀⠀⠀⠉⠛⠲⠤⠤⢤⣤⣄⣀⣀⣀⣀⡸⠇⠀⠀⠀⠉⠉⠉⠉⠉⠉⠁⠀