⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠴⠒⠚⠋⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⠒⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠓⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠲⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢆⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢱⡀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⡾⠁⠀⠀⢯⡉⢠⣵⠦⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⡹⠟⠒⠢⠤⠤⠀⣄⣠⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢍⠉⠒⠤⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠠⡞⠁⠀⠀⢀⣴⣀⣠⣀⣀⡀⠀⠈⠉⠉⠉⠒⠢⠤⠤⣀⣀⣀⡀⠈⢳⡦⢀⠀⠈⠙⢢⣄⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢠⡁⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⢀⣿⠋⠉⢻⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⣶⡋⠉⢹⣿⣷⣿⣏⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⣟⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⣠⢰⠆⠀⠀⠀⠸⣿⣿⣶⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣶⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⡅⠀⠀⠀⠀⠈⠙⣆⠀⠀⠀⠀⠘⠻⠿⣿⣿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠿⣿⡿⠿⠛⠁⠀⠀⠀⢠⡜⠁⠀⠀⠀⠀⠀⠀⣾⠂⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠻⡄⠀⠀⠀⠀⢀⣈⣆⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⠠⠞⢀⡄⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⡀⠀⠀⠀⣏⠛⠀⠀⠈⠛⠲⣤⣤⣀⣀⣀⣀⣀⣀⣀⠀⠀⣀⣀⣀⣀⣀⣀⣠⣤⣤⠖⠋⠁⠀⠀⠟⢹⠃⠀⠀⠀⢀⡼⠃⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢂⣀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠉⠛⠛⠿⡿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠿⠛⠛⠋⠀⠀⠀⠀⠀⠀⡰⠋⠀⠀⢀⡰⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀
⠐⠚⠶⢄⣂⣐⠂⠐⠀⠒⠐⠂⠉⠂⠀⠀⠘⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠁⠀⠀⠀⠉⠑⠒⠒⠒⠒⣒⣒⡶⠲⠖⠚
⠀⠀⠀⠀⠀⠉⠉⠁⠓⠒⠒⠒⠒⠶⠤⢤⣀⣈⣳⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⡄⠤⠤⠤⠴⠖⠒⠒⠒⠓⠉⠉⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⢿⣶⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣴⠿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠻⢿⠿⠿⠿⠿⡿⠟⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀