⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠶⠒⠒⠛⠉⠉⠉⣳⠀⠀⠀⣀⣠⣤⠤⠶⠶⠒⠒⠶⡄⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⢠⣇⣤⠶⠛⠉⠀⢀⣠⣤⣶⣶⡦⠀⡟⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠞⠋⠀⠀⣀⣴⣾⣿⣿⣿⣿⠟⢁⣼⠃⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠉⠀⠀⠀⣠⣾⣿⣿⣿⣿⡿⠋⠁⢀⡾⠁⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠋⠀⠀⠀⠀⣠⣾⣿⣿⣿⡿⠟⠉⠀⢀⣴⠏⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⠀⣀⣴⣿⣿⡿⠟⠋⠁⢀⣠⡴⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⡬⠓⠂⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠔⠛⣛⣋⣭⡤⠶⠶⠒⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣸⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢾⠀⡔⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣄⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⣷⣌⢻⠁⠀⣠⠔⠂⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠸⡆⢀⣴⣶⡦⡀⠀⠀⠀⠀⠀⢿⣶⡿⠛⠁⡴⢋⡤⠴⠒⠂⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠘⢳⣾⣟⣻⣧⡼⢒⣫⣭⠁⠀⡈⠁⠀⠀⠀⠐⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢀⡵⠙⠛⢻⠀⠛⠛⠋⠀⠀⢈⡵⠒⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣋⣤⣤⠤⠤⠤⠤⣤⣀⡀⠀⠀⠀⠀⠀⠀
⠀⠀⢀⣸⣁⠀⠀⠘⠦⣤⠼⢿⣶⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠾⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣙⣦⠀⠀⠀⠀⠀
⠀⠀⠉⠘⣧⣖⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣽⠀⠀⠀⠀⠀
⠀⠀⠀⠘⠀⠀⠙⠓⠲⠦⠤⠤⢤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡴⠶⠶⠶⠶⠶⠴⠏⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠻⣄⣀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀
⠀⢀⡤⠦⠤⠤⣤⣀⠀⠀⢀⣠⡴⢋⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠓⠶⠦⢤⣴⠋⠉⠙⠲⣄⠀
⢠⡟⠒⠂⠧⡀⠀⠉⠉⠉⠉⠁⠀⣸⠀⣄⠀⠀⠀⠠⣤⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠸⡆
⠸⣍⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠈⠑⠚⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⢀⡇
⠀⠈⠳⢤⣄⣀⣀⡀⠀⠀⠀⣀⣀⣠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⣠⠟⠀
⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠉⠁⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠛⢦⣀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡃⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠉⠛⠷⠶⢤⣦⣤⡴⣾⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⢹⢱⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⢷⣄⡀⠀⠀⠀⠀⠀⠀⣠⣾⡋⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃⢀⣮⡗⢱⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⢅⣀⠤⠛⠲⠦⠤⠤⠶⠛⠉⠀⡷⠈⠻⣤⣤⣄⣀⣀⣠⣔⡫⠁⢠⣮⠿⠦⠊⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠴⡃⠀⠀⠀⠀⠀⠀⢷⣀⠀⣀⢴⡕⡋⢃⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢗⢲⠀⡄⠠⢤⠀⡖⠲⣶⣏⠃⠈⢀⠇⠀⠀⠀⠀⠀⠀⠘⠦⠭⠴⠛⠤⠤⠃⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⠧⣌⣉⠴⠃⠀⠈⠉⠉⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀