⠀⠀⠀⣀⣀⠀⠀⠀⣀⣀⠤⢄⠀⠀⣀⣀⠀⠀⢠⠒⠤⠄⠀⡔⠉⠑⠆⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠑⡄⠀⡇⠀⠀⢀⠆⠘⡀⠀⠀⠀⡇⠀⠀⢀⢸⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣀⡠⢱⠐⠚⢥⡀⠀⢧⠤⠒⠀⢇⡀⠀⢨⠟⡄⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡀⠀⠀⡇⠈⡆⠀⠀⠉⠂⠈⠦⠤⠤⠂⠈⠉⠁⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡠⢴⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⡄⠀⠀⠀⠀⠀⢢⠀⢆⠀⠀⠀⠀⠐⡞⠂⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣀⡠⡃⠀⠀⢣⠀⠀⡸⠀⢸⠀⠀⡀⠀⠀⠓⠒⠂⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡀⠈⠑⠄⠀⠑⠒⠁⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠑⢄⡀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢤⣀⠀⢸⠀⠀⣉⣢⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡦⠀⠀⠀⡠⣄⡀⢠⢀⠔⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠘⡄⠉⠑⡷⠉⠀⠀⠀⠀⠉⠓⠤⡀⠀⠀⣀⠴⠋⢉⡣⢄⠀⠠⡟⠁⢸⠘⡯⠤⠤⠤⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠘⢄⡸⠀⢀⠤⢲⣾⣿⡍⠲⡄⠈⠉⠉⠀⠀⢀⠾⢽⠉⠁⠀⠑⠒⠃⠀⠉⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠙⠦⣘⣿⣿⣃⠔⠃⠀⠠⠤⢶⡊⠁⠀⠀⠀⢰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⡀⠀⠀⠀⠀⠀⠀⣠⣶⣖⡒⠒⠻⠄⠀⠀⠀⢸⢸⠀⠀⠀⣠⠖⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣠⠤⠒⠀⠀⢀⣨⣷⣶⣖⣖⠊⣿⣿⣾⡇⣾⠀⠀⠀⠀⠀⠀⠀⣷⡆⠀⠮⢅⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠐⠮⢄⣀⡀⠀⠀⣷⣿⣿⣿⣿⡿⣿⣿⣿⣟⣿⣿⣷⣤⣀⠀⠀⢀⣼⢤⣧⡄⠀⠀⣉⠶⠂⠀⠀⠀⠀
⠀⠀⠀⠀⠀⡠⠃⠀⢰⣿⠙⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣏⠻⠿⣿⣿⣿⠏⠘⠓⠑⠶⣉⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢠⣊⣀⢤⠄⢸⣿⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣾⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢲⡄⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⠎⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠗⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠊⠁⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⡎⠀⢀⣀⠈⠉⠉⠉⠉⠻⣿⣿⣿⡿⣿⡿⠿⠿⠷⣶⠄⠀⠀⠀⠀⠀⠀⠑⠢⣀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠸⠔⠊⡹⠁⠀⠀⠀⠀⠀⠀⢠⣿⡟⠉⠉⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⢀⣀⣀⡠⠤⠵⠄⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⣀⠀⠀⠀⠀⣼⣿⠁⠀⠀⠀⠀⠀⣿⣇⡀⠀⠀⠀⠀⠈⠢⣀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣧⠔⠊⠁⢸⠀⠀⡀⠀⣿⡿⠀⠀⠀⢀⡀⠀⠈⠉⠉⠀⠀⠀⢠⠤⠤⠬⠵⡄⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⡠⠋⠘⠀⣿⣧⡀⠀⠀⡇⠈⠳⡄⠀⡏⠑⠢⢄⡀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀