⣀⣀⣤⣤⣤⣤⣄⣀⣀⠀⠀⢀⣀⣀⣠⣤⣤⣤⣴⣤⣀⠀
⠘⠟⠋⢉⣠⣤⣭⣭⠭⡍⠀⠀⠀⢩⠭⣭⣭⣤⣄⡈⠙⠻⠂
⠀⠀⠴⠯⢽⣿⡿⣹⣍⠟⠀⠀⠀⠻⠸⠏⠿⠿⠧⡽⠂⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠆⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⢰⠃⠀⠀
⠀⠀⠀⠀⠀⢠⣀⣀⣀⣀⣀⣀⣀⣀⡤⠤⠞⠁⢀⡏⠀⠀⠀
⠀⠀⠀⠀⠀⠈⠋⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠸⠀⠀⠀


⠀⠀⠀⣀⠤⠤⠤⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⠤⠤⠤⠤⠤⠔⠒⠁⠀⠀⡀⠔⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⡠⠂⠁⠀⠀⡀⠀⢀⣀⠤⠤⠀⠒⡶⠿⢞⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⠣⠤⣤⠔⠒⠁⠀⣘⣡⠚⠒⢤⠶⠁⠀⠤⠧⡄⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣙⣤⣤⣶⣶⢁⣹⠔⠓⠤⣷⠔⠓⠓⠓⢳⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⡮⠀⢻⣿⣿⣿⢸⡁⢰⠀⠀⢾⢰⠀⠀⠀⢸⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠓⢤⠀⠹⠿⠟⠘⢤⠘⠀⠀⣻⡘⠀⠀⠀⢸⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠜⠀⠀⠀⠀⠀⠘⢄⣠⡔⠁⢇⣀⣀⡀⠜⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⢀⣀⠀⠀⢨⣽⡇⠀⠸⣟⡁⡏⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣀⣸⠀⠀⠀⠰⠮⢍⠀⠀⠘⠉⡇⠀⠀⢾⠃⡝⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢀⣤⣶⣿⣿⡀⠀⠀⠀⠀⠈⠒⠒⠒⠒⡇⠀⠀⢯⠀⢳⣤⡀⠀⠀⠀⠀
⠀⢀⣴⣿⣿⣿⣿⣿⣧⡄⠀⠀⠀⠀⠘⠚⠚⠚⠻⡀⠜⠀⠀⠀⣿⣿⡇⠀⠀⠀
⠀⢸⠀⠈⠛⠛⠿⣿⠟⠛⢄⡀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡠⠚⣿⣿⣿⡤⠀⠀
⢐⡍⠀⠀⠀⠀⡄⠋⠀⠀⠀⠉⠚⠢⠤⠤⣀⣀⡠⠤⠤⠒⠁⠀⠹⣁⠙⢯⠀⠀
⠀⠱⡀⠀⠀⠀⢎⠀⠀⠀⠀⠀⠀⠀⠤⠤⠛⠛⠓⠒⠒⠒⠂⠀⠀⠊⡄⠣⡄⠀
⠀⠀⠁⠢⡀⠀⠀⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢣⠠⡇⠀
⠀⠀⠀⠀⣐⢢⡀⠀⠆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣈⠇⠀
⠀⠀⠀⢐⣌⡨⢬⡦⡄⣸⡄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⡤⠪⠓⢣⠀
⠀⠀⠐⢎⠨⢃⠐⢡⠉⢈⣿⣷⣾⣶⣷⣾⣶⣷⣾⣶⣾⣶⣿⣿⡿⠫⠄⠔⠊⠀
⠀⠀⠀⠘⠤⠬⠶⠬⢶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠈⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠐⢻⣿⣿⣿⣿⠟⠛⢻⣿⣿⣿⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⣼⣿⣿⣿⣿⠀⠀⢸⣿⣿⣿⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣶⣤⣾⣿⣿⣿⣿⣿⣶⣶⣤⡀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠁⠁⠁⠁⠁⠁⠁⠉⠈⠈⠈⠈⠈⠈⠈⠈⠈⠈⠁⠀⠀⠀⠀