⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⣐⣒⣖⣿⣤⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⢯⣭⣞⡻⠭⢐⣪⡫⢣⢿⣯⢛⡶⣿⢶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⡵⠝⠪⣻⣭⡦⡼⣕⣺⣞⠕⠚⠽⣻⠶⣝⣕⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡌⠀⠀⠀⢍⠟⣪⣟⣚⢤⣲⣽⣶⣿⣿⠿⡜⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⢇⠀⢀⣱⣿⢫⣮⣷⣿⡿⣟⢛⠯⠒⠉⠀⢣⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⢷⡲⣾⣿⢿⣟⠯⠕⠊⠁⠑⢽⢾⣖⣤⣪⢏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢞⢾⣻⣭⣒⡢⠤⠤⠤⠤⠤⣒⣮⡷⣛⢮⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠪⠭⠭⠭⠭⠭⠒⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣖⡷⡫⡻⣷⣮⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢜⣿⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢪⣻⣮⢅⠀⢸⣿⣿⣯⣵⡤⠀⠀⠀⠀⠀⠀⠀⢜⣾⠕⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡅⣺⣕⣀⣀⣀⣸⣿⣿⡇⠀⢸⣿⣿⡟⡳⣍⣮⢄⠀⠀⠀⠀⠀⢸⣿⢤⣲⣀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡇⣿⣾⣟⣛⡛⣇⣯⣿⡇⠀⢸⣿⣿⢃⠀⢪⣧⢷⢆⠀⠀⠀⠀⣜⣿⣿⣿⡿⣿⣶⣛⣛⡾⣲⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠙⠊⠀⠀⠀⢸⣿⣿⡇⠀⢸⣿⡟⠀⠀⠀⢞⣆⣧⡀⠀⡄⣵⡿⣿⡿⣛⡵⢷⢷⣧⠚⡻⡌⣮⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⣒⡷⡯⠁⠀⠀⣀⠬⢹⡸⡸⠀⡇⣷⣿⣼⡟⠓⠁⡎⡟⣊⢄⣾⣿⣼⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠺⣻⡻⠚⠁⠀⠀⢔⡷⢟⣉⣻⣧⣷⡄⠡⡷⣷⣟⣿⣻⢾⠯⢼⣿⣿⣿⣸⣆⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣵⢕⡾⠝⠓⠪⣻⡸⡸⠀⠀⠑⢝⡫⠊⠀⠀⢸⣿⡇⡸⣿⣿⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⡾⢨⢏⠁⠀⠀⠀⠱⢷⢻⡣⠀⢠⣵⣾⣪⡆⡷⡯⠿⣛⡏⡟⣾⠎⠀⠀⠀⠀⠀⠀⠀⠀⠐⢲⢰⢲⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⡾⣢⡣⠀⠀⠀⠀⠀⠀⠑⡻⡙⣮⢤⣵⣥⢿⡿⠇⠀⡠⣪⡿⡼⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⢸⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢔⡟⣰⡣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠪⢷⡛⣯⠭⠈⠁⠀⢞⡟⡶⡫⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢸⢸⣲⡀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢜⣟⣵⡱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠪⡳⣝⠷⣗⢄⢸⢸⡱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣼⣿⣎⢶⣷⣿⣧⠶⣮⣕⢄⠀⠀⡀⣭⡄⣭⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢞⢟⣽⡕⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣑⠽⡶⣝⠾⣇⣧⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⡼⣨⢿⣼⣿⢿⣿⣿⣻⣟⢦⠝⡕⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡠⣀⢪⠏⣼⠕⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣪⢟⣭⣭⣭⣝⡿⢦⠷⣗⢄⠀⠀⠀⠀⠀⠀⠀⠀⢱⣽⡫⠊⢣⣿⢵⢿⣽⡣⠀⣀⣇⠇⡟⠃⠀⢲⣿⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⡄⠀⠀⢀⣒⡷⢿⣻⣿⣏⡾⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⢱⢫⠉⠉⠉⠑⠺⢟⢮⣳⣽⠾⣖⢄⠀⠀⠀⠀⠀⡸⡜⠀⠀⣀⣳⢿⣽⢭⣮⠶⢻⣧⣟⠊⢀⢔⡾⣿⣇⢤⠀⠀⠀⠀⠀⢀⠤⣀⡤⣀⣀⠤⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣿⣟⣧⣤⣼⣟⡻⣝⣊⣧⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⣀⠤⠤⢔⡾⣎⢮⡢⠀⠀⠀⠀⠀⠈⠺⣟⢯⡳⣝⢾⣒⣄⠀⠀⠈⢝⣽⣽⡻⣺⡷⢻⣿⠷⡻⠕⠉⢀⣺⠞⣕⡽⡿⣟⣽⠾⢶⣭⣢⢔⠞⣽⣵⣭⣻⣿⣟⡿⢷⣖⡄⠀⠀⠀⢰⣲⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢝⠕⠀⢜⣟⢷⣲⣽⣨⣿⡝⠀⠀⠀⠀⠀⠀⡤⣪⣾⢿⣾⣽⣞⣛⣭⣭⣥⣞⠒⡻⡝⣎⡀⠀⠀⠀⠀⠀⠀⠈⠺⣻⣯⡶⣟⢮⣲⣀⡤⣯⣞⣝⣼⣟⠽⠋⠀⠀⠀⣠⣪⣟⣿⣿⡏⣏⢯⣿⡟⣛⡳⣌⢿⡟⠊⠀⡇⣿⣰⣱⣫⢿⣻⣷⡶⠶⢾⣽⣿⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠯⡳⡿⣿⠒⠀⠀⠀⠀⠀⢠⣷⢿⡷⣷⣝⣕⢿⡏⠒⠉⠉⠉⠀⠀⠈⢹⢹⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠪⣻⣽⡾⣻⢭⣽⣻⠗⠁⠀⠀⠀⠀⠀⢸⣿⣞⠗⠀⢜⣿⡾⣻⢟⠂⢀⡤⣼⣸⢸⠀⠀⠀⢪⣿⣥⣯⣗⡾⣿⠃⠀⠀⠺⠝⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⡄⡷⡅⠤⠤⢤⣪⣟⠿⡟⣷⢢⣹⡿⡣⠀⢀⡤⣽⣭⣦⣯⢟⡾⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠯⡳⣽⠾⣻⣯⡦⡀⠀⠀⠀⠀⠘⢻⢣⠀⢀⢔⡵⣫⡪⣒⣽⡞⣏⡷⡷⠀⠀⠀⣀⠀⠓⢿⢿⢟⠽⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣎⡎⠭⠭⠭⢝⢿⣷⢿⣿⣟⡽⠘⡠⣯⣟⣯⡳⣍⣻⣾⡝⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠭⡷⣝⢮⣳⣽⡤⡀⠀⠀⠐⡻⣭⣞⢕⣭⢾⣏⣼⣞⠭⠒⠁⠀⠀⡤⣽⣛⣜⣕⣥⣝⣒⣂⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠁⠀⠀⠀⠀⠈⠙⢭⢋⠓⠁⠀⣜⣷⣿⣼⢸⡎⣆⣿⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢽⡶⣟⢯⡳⣵⢤⣀⣖⡵⡻⣳⠷⡫⠓⠉⠀⠀⠀⠀⠀⢱⡯⣮⣎⣾⢾⢿⣧⣶⣬⣹⢷⡢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢞⣿⡸⠶⠶⢷⣿⣷⣺⣾⣿⡷⡟⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢽⢾⣟⣯⣟⣳⢷⠯⠊⠀⠐⢲⢰⣶⠢⠤⢔⣷⣽⡫⢇⣿⣨⣶⢽⡟⠊⠉⡢⣧⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⣒⣭⣶⣶⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠺⠊⠀⠀⠀⠙⠽⣟⣿⢟⠯⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⢝⢮⣲⣽⡶⣗⢄⠀⢸⠸⣿⠩⠉⡏⡏⠁⠀⠀⣪⣳⢾⠽⡡⣒⣽⡟⣦⡣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣺⢶⣛⣿⠿⣛⠭⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⣟⢮⣳⣝⢾⣞⣄⠈⠀⠀⠘⡻⡱⢤⣯⣟⣗⣯⢾⣏⣼⣞⠯⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣲⡷⣏⡶⡫⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠺⣛⣯⡳⢝⢾⣭⢤⠀⠀⡪⣹⠷⢻⣧⢶⡯⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣖⡵⣋⡼⣻⠓⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣖⡀⡠⣽⣛⣏⡏⠉⢝⢮⡷⢯⣮⣞⠝⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣔⡵⢻⣽⣛⠗⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣽⣿⡇⠱⣷⣱⠉⢽⢮⢄⢡⣷⡽⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢔⣽⢻⣧⣟⠕⣡⣒⡷⡳⣽⣾⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣒⣒⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⡗⠀⣑⢷⣻⡱⠀⢡⣷⡄⢸⢸⠀⠀⠀⠀⠀⠀⠀⠀⢀⢴⣭⢟⣧⣞⠝⠉⢠⣽⣻⣞⡁⠀⡎⡎⣿⡾⠶⢾⡢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠪⠾⣿⣿⣿⣶⣭⣒⠤⡀⠀⠀⠀⠀⠀⡰⣷⣯⡶⡶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣗⣺⣿⣧⣇⢇⠀⠘⢿⠇⡇⡇⠀⠀⠀⠀⡤⣀⢤⣯⡞⣭⣞⠽⠉⠀⠀⠀⢸⣿⣿⣿⡎⠀⡇⡇⣿⡏⠹⢻⢻⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠩⢛⠷⣧⡩⡷⣕⢤⠀⠀⠀⠠⣵⣵⡟⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣪⣿⣧⡶⣝⣌⣿⡱⠀⠀⢸⢸⡇⡇⠀⢸⡶⢾⣿⣿⣹⢾⠭⠋⠀⠀⠀⠀⠀⠀⡸⣻⣿⣿⡇⠀⡇⡷⣟⠊⠀⢸⢸⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠪⣻⣯⡽⡷⣗⢄⠀⢹⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡱⣿⣯⢝⢹⡹⣿⢿⠜⠀⠀⢸⢸⢀⣧⠀⡜⣿⣿⣯⣾⠎⡎⣮⢄⠀⠀⠀⠀⠀⠀⢠⣷⢿⣿⡇⢤⣧⡃⠀⠀⠀⢸⢸⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠪⣳⣵⡽⢾⣾⣿⣿⣕⡦⠀⠀⠀⠀⠀⠀⠀⠀⠈⠯⣻⣟⣿⣿⣟⠊⠀⠀⠀⢸⢘⢸⣿⡇⠈⠯⢽⣿⡇⠀⠈⢻⢳⡢⠀⠀⠀⠀⠀⠀⠑⠽⠷⢟⢹⢸⠀⠀⠀⠀⢸⢸⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠯⡳⡯⣿⣿⣿⢽⢜⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣉⣒⡉⠀⠀⠤⠤⠤⢸⢸⠘⡿⠁⠀⠀⣸⣿⡧⠀⠀⢣⣧⡝⣕⡀⠀⠀⠀⠀⠀⠀⠀⠀⡸⢸⣲⠀⠀⠀⢸⢸⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣟⢟⢯⣰⣾⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⡋⠋⠻⠭⠭⠭⢸⢸⡆⡇⠀⠀⠃⢏⡇⣿⡣⠀⠀⡸⡘⢊⣮⠄⠀⠀⠀⠀⠀⠀⡇⡇⣫⣿⡇⠀⠀⢸⢸⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠭⠒⢽⡾⣞⢟⣯⡢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠸⡇⡇⠀⠀⠊⠿⣞⢾⠕⠀⠀⠸⢿⢇⠱⢷⣢⣀⣀⣀⠀⠀⠀⠅⠺⠗⠀⠀⠀⢸⢸⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢪⡿⡅⣷⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⣟⢘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢝⢾⣞⣻⣯⡦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⢰⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢞⣇⡀⢜⡿⡟⣛⣻⢾⣢⡀⠀⠀⠀⠀⠀⠀⣼⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⡇⡻⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⢠⠀⢊⣿⡞⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠾⠘⠀⡤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⢝⢮⣪⣳⣽⡤⡀⠀⠀⠀⠀⠀⠀⡌⡟⠁⣸⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣱⠫⢁⣺⣮⣗⢌⠪⢷⡢⠀⠀⠀⠀⠀⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⡀⠃⣃⢛⣛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣱⢽⢜⠀⠀⢹⣿⣇⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣯⣷⣿⣷⣭⣮⢶⣻⡶⣽⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠚⣟⢯⣫⡳⣵⣽⣯⡢⠀⠀⢣⢇⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⡏⢠⣼⡕⠣⢷⢿⣕⡈⡹⡱⠀⠀⠀⢰⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⢸⣻⠣⠀⢸⢸⣔⣢⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⡄⠀⣠⣞⣿⡻⢻⢾⡢⡀⠀⠀⠀⠀⠠⣯⣾⣫⠿⣽⡽⣫⣟⢿⣯⡒⠪⢷⣷⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠺⡟⡟⢿⢟⣻⠁⢀⣸⡘⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠸⡇⡇⠀⠀⠐⡻⡊⣎⡈⢻⠡⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣰⡣⠀⡠⡿⣯⣓⣪⣿⣕⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣻⣵⣟⢿⣾⡢⣸⣿⡯⢳⣕⡀⠀⠀⢸⢙⡿⡻⣟⡷⡯⠊⢊⣧⣟⠃⠀⢸⢸⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠯⡻⣻⠓⠀⡘⡿⠃⢸⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢿⠃⠸⡸⠀⠀⠀⠈⢝⡼⡜⢡⣷⡄⠀⡆⡇⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⡰⣿⡟⡶⣿⡿⠕⢸⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⣿⣾⢻⢆⣻⡊⣿⣛⣯⣃⣏⢟⣮⡦⠀⢸⣿⣿⣷⣷⢆⠀⣀⣞⡟⠃⠀⠀⢸⢸⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⢇⢰⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡸⢃⣧⡀⠀⠀⠀⠀⢱⣿⡆⢸⢸⡠⡾⣼⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⣖⣽⣿⡧⡼⠭⠭⡻⣝⣎⡠⣽⡱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⣾⣝⡷⢻⣮⣇⣿⡻⠒⠉⠚⠿⢝⢮⣽⣮⢕⣟⢾⣟⡟⣗⡽⣻⠓⠁⠀⠀⢀⣸⣼⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⣐⣢⣭⢶⣾⡌⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡇⢸⣿⡇⠀⠀⠀⠀⠀⢪⢳⣿⣟⣟⡾⠕⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣱⢋⣿⣋⡝⡟⠊⠀⠀⢪⣻⣿⢟⠊⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢟⣿⣞⣿⣿⣽⡫⠀⠀⢪⢶⠰⣽⢸⢝⣞⡻⣕⡈⠪⠛⠕⠁⠀⠀⠀⠀⠀⢪⢏⢏⠀⠀⠀⠀⠀⠀⢀⣀⠤⣂⣢⣭⠶⢟⣛⠭⠚⠊⠉⡇⡇⠀⢸⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⢣⡘⡿⠃⠀⠀⠀⠀⠀⢸⢸⢸⠊⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠯⣛⢿⣿⣶⡅⡤⡵⣿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣻⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠭⠈⢁⠀⠀⠀⢪⣯⠾⢾⠸⠀⠱⣷⡪⢿⣦⠀⠀⠀⠀⠀⠀⠀⡎⣏⡏⠁⣀⠤⢐⣢⣭⠶⢟⣛⠭⠓⠊⠉⠀⠀⠀⠀⠀⠀⠀⢸⢸⠸⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣮⢟⢁⣱⡱⠀⠀⠀⠀⠀⢀⣼⣾⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⢸⡸⠀⠀⠑⠽⡛⡯⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⢮⣲⣀⠈⡇⡇⣈⠀⠀⠀⠈⢝⣮⢝⣿⢄⠀⠀⣀⠤⣐⣸⣼⠾⢟⣛⠭⠑⠊⠉⠀⡤⢄⠀⣀⠤⣐⣒⣒⣒⠤⠤⣀⠀⣿⠀⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢔⣾⠕⡠⣵⡣⠀⠀⠀⠀⠀⠀⣸⣟⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⣧⢻⣢⠀⢰⣷⣏⡻⣕⣀⠀⠀⣀⣀⡀⡠⠤⡀⡀⡀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢙⣧⡟⢿⣯⣮⣿⣟⢯⡢⠀⠀⣀⠽⣟⣕⣿⣷⣾⣛⠭⡙⡟⡏⢀⢄⠀⠀⠀⡠⣪⢧⣟⢿⣾⣛⣭⠶⠶⠶⠶⠿⣭⣟⡶⣽⣰⠇⣇⣀⠀⠀⢀⣀⣀⡀⠀⠀⢔⡾⠕⣡⣪⣟⠊⠀⠀⠀⠀⠀⠀⢢⢏⡝⡟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠪⢷⠿⣝⣿⡡⣿⣷⣿⢿⢔⢾⣟⣟⣿⢟⣻⢷⡏⡳⣽⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⠀⠀⠀⠈⠂⠈⣿⣮⣳⣿⡿⣿⡱⢾⣛⠭⠑⠓⡻⣕⣻⣕⢄⡇⡇⡇⣞⣿⣕⣒⣣⣟⣾⢻⢆⢻⡊⣿⢩⡔⡷⡇⠀⠀⠉⠐⠪⢟⣶⣝⡞⣟⠶⠶⣞⣛⣛⣻⣿⣵⡱⢁⣪⢟⠊⠀⠀⠀⠀⠀⠀⢀⣪⢫⡑⡾⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡻⣜⡻⣿⣾⣷⣻⣝⡿⣾⣎⣿⣴⡫⡚⠀⠀⠀⡹⣫⣷⡇⠀⠀⠀⠀⠀⠀⠀⢀⢴⣷⣿⣿⢅⠀⠀⠀⠀⡄⣿⡷⣿⣿⡿⣿⣿⡦⡀⠀⠀⠀⠀⠑⣻⣕⢟⣧⣇⡇⢽⣻⠂⡆⣾⣝⣿⢻⣮⢇⣿⣟⠊⡔⣾⡕⠀⠀⠀⠀⠀⠀⠑⣟⢾⣭⣒⣒⣒⣭⣵⡀⡜⡎⢔⣞⠞⠀⠀⠀⠀⠀⠀⠀⡴⡵⠕⢜⢟⠿⢮⡢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣄⡠⣑⢿⣿⣿⢿⡛⡅⡇⡇⠀⢺⣿⢫⣷⣽⣖⣷⣿⣿⣿⡟⠃⠀⡀⣭⢀⠀⠰⢾⣷⣷⣶⣾⣻⢜⠀⠀⠀⢇⣯⡻⣷⣽⣇⣿⣟⡿⣷⣽⠤⡀⠀⠀⠀⠑⢝⢮⣻⡻⣳⣀⠀⠈⢝⢿⣟⣿⣿⡵⡫⠀⠀⠀⢸⢸⢴⣿⣲⡀⣀⣀⡀⠀⠀⠉⠒⠒⠒⢩⣾⡆⡇⡷⡕⠀⠀⠀⠀⠀⢀⠤⣲⡷⡯⡡⣵⡫⠭⠯⢷⡙⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡻⡿⡏⡿⠝⠉⠪⡳⣮⢷⣇⣷⡄⢸⣿⣸⣿⢻⢻⣿⣿⣾⡿⠜⠀⠀⢨⣻⢾⠶⢾⣿⡟⠿⡿⣺⢧⡇⠀⠀⠀⠀⢍⡏⡳⣿⡃⠝⠀⠀⠉⠯⡿⣷⡕⠀⠀⠀⠀⠈⠪⡻⣝⣻⣽⢄⠀⠀⠙⠭⠈⠁⠀⠀⠀⢤⣼⣾⣯⡻⣿⡾⡻⠛⣻⣿⢄⠀⠀⠀⠀⠸⣿⠃⢸⢱⠀⢀⡠⢔⣪⡵⢟⠯⣺⣗⡵⡫⢊⢤⡢⡀⡐⡿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣛⣛⣛⡛⠂⠀⠀⠀⠪⢷⡻⣾⡜⡀⠉⠫⡻⣾⣸⣽⣬⡿⠘⠀⠀⠀⠈⠒⠀⠀⠈⢝⣿⣯⣬⡽⣿⡸⠀⠀⠀⡐⡾⠎⠀⠉⠀⠀⢤⣦⡆⠀⢰⢶⠶⠶⣭⣭⣭⣭⣤⣒⣓⣟⣯⢝⢮⡢⡀⠀⠀⠀⠀⢸⣶⣿⣻⣳⡷⣯⣞⣽⣏⠽⡻⡡⣧⡄⠀⠀⠀⢇⡇⠀⢸⣼⠶⣟⠫⣑⠮⣓⣭⢾⡫⠓⡡⣪⣾⡿⣿⣷⣾⣰⡣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠪⢿⣫⡷⣗⢤⡀⠙⠯⠽⠕⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢿⣾⣾⣿⣻⠊⠀⠀⢠⣼⡜⠀⠀⢀⣖⣷⢿⠿⣧⡢⢣⣧⡄⠀⠈⠉⠉⠉⠀⠒⠒⠒⠋⢽⢾⡪⡷⣖⣀⠀⠸⢿⣾⣷⣜⣾⣽⡿⡻⠂⣿⠀⡇⡇⣿⡇⠀⢀⢼⣿⣧⣽⣿⣇⣪⣵⠾⣛⠭⠒⠉⢀⣖⣷⡫⣺⣛⡿⣻⣞⣾⢞⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⣟⢦⣍⢳⣭⣒⡄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢇⠇⡟⠃⠀⠀⠀⣱⡱⢐⣔⡀⡡⣿⣿⣇⣯⣿⢿⠇⡸⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠪⡳⣟⣻⣕⢄⠪⢯⣻⣿⣷⡇⣁⣖⡵⡣⠀⣱⡑⡟⠃⢔⢾⢽⣿⡗⠒⡇⣿⣿⣗⡢⣰⡀⠀⠀⡣⡇⣿⣯⣿⢷⣽⣿⣻⢹⣸⣒⣱⢻⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠽⡳⣦⣙⠻⢶⣭⣒⠤⠤⠀⠀⢀⣀⣀⡀⢆⠏⡞⠊⠀⠀⠀⢣⢣⠀⣈⢿⢾⡷⣿⢸⠭⡹⡿⣿⡄⠠⣿⠄⢀⣒⡢⠀⠀⠀⡠⣯⣶⣧⡄⠀⠀⠓⣻⣵⢝⣯⢬⠺⣟⣧⣷⣻⠗⠁⠀⢞⡏⣾⣌⣵⡱⢔⡷⣿⡇⠀⡇⣿⣿⣿⣿⣎⣮⡄⠀⠱⢷⡿⣷⣿⣿⡗⢁⢔⣼⡘⠒⣱⣯⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢒⠭⣛⠷⢦⣭⣉⣛⣛⣛⣛⣛⠻⡾⡄⣇⡢⡀⠀⢞⢏⠁⠀⠐⠕⠀⠀⢜⣿⡶⡟⣫⣿⡇⠀⡜⡎⢀⣫⣯⡷⡶⣷⣯⡟⣻⣿⣮⢄⠀⠀⠀⠑⢝⢮⡽⢮⡢⡉⠁⠀⠀⠀⢀⣼⢀⢇⢣⢇⢞⡏⢹⣿⡇⠀⡇⣿⣿⣿⣿⡇⠫⣧⢄⠀⠈⠯⡻⣽⣿⣯⣟⠕⠁⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⡖⣇⣀⣀⡤⣮⣰⣮⡶⣭⣾⣮⡄⠀⠈⠉⠒⠒⣒⢖⣦⢷⣛⣛⣟⡏⠪⣻⣽⡟⡃⠀⠀⠀⠀⠀⠀⠑⣻⢿⠿⡫⠊⠀⠀⠘⢻⢣⠺⠗⠀⡆⡿⣿⣷⣟⢿⢹⢸⠀⠀⠀⠀⠀⠈⠯⢾⡪⡷⣲⡀⠀⠀⢸⣿⢸⢸⢸⢸⢸⢸⢸⣿⠇⠀⢡⣿⡏⣭⣅⠀⠀⠁⢳⢀⠀⠀⠀⠑⠝⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⣽⠕⣛⢟⣿⣼⡛⣮⡀⡜⣿⣿⡇⠀⠀⠀⡠⣯⢟⣧⣞⠯⠓⠒⠚⠽⡷⣕⢬⠫⡳⣵⢤⡀⠀⠀⠀⠀⠀⡎⡇⡇⠀⠀⠀⠀⢇⣇⡀⠀⠀⠣⢧⣇⠮⢮⣯⣿⡎⠀⠀⠀⠀⠀⠀⠀⠈⠪⡷⣞⡳⣕⣀⢸⣿⢸⢀⡸⡜⡎⡎⠀⡇⠀⠀⢸⢻⣧⡾⡻⣕⢄⠀⠐⢻⡢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢸⣿⣿⢹⢸⡆⡇⣿⢏⠁⠀⡤⣵⢋⡾⠽⠉⠀⠀⠀⠀⠀⠀⠀⠑⢽⡾⣗⢝⠯⡷⣵⡤⣀⠀⠀⡇⡇⡇⠀⠀⠀⠀⠀⠸⡰⠀⠀⠀⡇⣿⣫⣩⣶⢿⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⡳⣕⣻⣝⢻⢚⣮⣡⣿⡝⣿⡇⡇⠀⠀⢸⢸⢞⣎⡀⠑⠟⢇⢤⠘⡻⡡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⣒⣭⣶⣼⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣯⣼⣿⣿⢸⢸⡇⣣⢣⠀⡠⣽⢋⡾⠕⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢝⢾⣒⠽⡫⢛⠶⣭⣃⣇⣇⣀⠀⠀⠀⠀⢡⣷⡄⠀⠀⠀⠚⢯⡏⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣻⣕⢟⣿⣯⣏⣵⡇⡇⡇⡇⠀⠀⢸⢸⠀⡜⡜⡠⡀⠘⢝⢮⡪⡹⡕⠀⠀⠀⠀⠀⠀⠀⣀⢔⣭⠶⣿⣿⡿⢟⡫⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣴⡕⡻⣿⣻⢿⡯⠊⠀⢜⠞⣴⡵⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠭⣻⢾⣵⣫⣞⡹⣜⣿⣶⢶⠶⠶⣶⣼⣼⣭⣥⣒⣂⣱⣱⣑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢝⣯⡫⠳⢾⣢⢣⡇⡇⠀⠀⢸⠘⠊⡿⡷⣯⡇⠀⠀⠈⠯⡷⡟⣕⡀⠀⠀⣀⢔⣽⡟⣳⢾⡯⠕⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⡹⣕⢤⠶⣊⣀⠤⣔⡵⣫⢟⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠝⣛⠾⣿⣾⣼⣤⣒⣒⣒⣛⣛⠭⠶⣺⣿⣯⣟⣳⣶⢶⣮⣥⣒⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠪⢝⣛⠗⠀⢰⢣⠀⢠⣾⡆⠊⠿⠷⡷⡣⠀⠀⠀⠀⠀⠪⡻⣎⢴⣭⡟⣳⠷⡯⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢝⠶⣭⣭⣛⣛⣭⣵⣞⠕⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣭⠤⠀⠄⠉⠉⠁⠐⠒⠒⣒⡒⣩⡭⢛⣛⠿⠿⣾⣿⡧⢈⡁⠒⠭⢛⡷⢾⣵⡢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢤⣯⣞⣹⡷⡫⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠒⠒⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⣮⣶⣕⢄⢴⣭⡶⣭⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢜⣟⢾⣹⢸⠀⠀⠀⠀⠀⢸⣿⢜⢾⢸⠀⠀⠀⠀⠉⠑⠭⢟⡻⠶⣭⣒⠤⣀⠁⠪⢟⡶⣕⢤⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⢀⢤⣯⡿⣟⠷⡫⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡂⢔⣲⡀⠀⡠⣭⣿⢿⣿⡾⣿⣟⣟⡫⡻⡙⡔⠀⠀⠀⡄⣗⢄⠀⠀⠀⠐⡇⡇⠚⠀⠀⠀⠀⠀⠀⠈⢩⣽⡻⠈⡤⢄⣀⠤⢄⣒⠤⠤⣀⠀⠉⠒⠭⣛⠶⣵⡦⡠⠽⢽⡷⣲⡀⠀⠀⠀⠀⢰⣿⡇⠀⡆⡇⠀⠀⡠⣪⣖⡤⣯⣞⣝⡷⢻⢸⠀⢡⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡇⡻⡾⠾⡾⡿⣞⣷⠟⣹⢾⢟⣆⣿⢸⠘⢻⢻⢡⠀⠀⡇⣇⣿⣾⣲⣄⢴⣧⣇⣀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢴⣾⣟⡭⣿⣩⣭⣤⣭⣍⣛⡶⣭⣖⣀⣒⣢⣽⡞⣋⣍⣙⢻⣮⣳⡢⠀⠀⠀⢇⢇⠀⠀⢱⢱⠀⢸⣿⣿⣿⢿⡵⡻⠒⢁⢸⢸⠀⠀⢹⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⠈⠊⠀⡇⣿⣿⣮⣯⡎⠀⡸⣿⡗⠀⠀⡇⡇⡇⠀⠀⠀⠚⣟⠓⢻⣟⣯⣿⣷⣿⢱⠀⠀⠀⠀⠀⠀⢜⢟⠽⣻⣯⣿⣽⡸⠉⠉⠉⠑⠪⢝⡷⣶⣤⣶⠶⣛⠭⠒⠐⠮⢯⡏⠊⢜⣎⡀⢜⢟⠃⠀⡘⡟⠃⠀⠀⠑⢟⠿⡯⠁⠀⠰⣾⣷⣾⡧⠄⠇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡳⣟⢿⣿⣸⡷⡯⠊⠀⠀⠀⢸⣿⣿⡆⠀⠀⠀⠀⠀⢸⣯⣿⣿⣿⣿⡸⢄⠀⠀⠀⠀⡘⡟⠃⠀⡔⣾⣽⣛⢮⣢⣀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⣀⠤⣒⣚⡹⡔⠀⡸⣼⡫⠁⠀⡰⡾⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠾⠷⢷⢟⠃⠘⢿⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠽⡻⠚⠀⠀⠀⠀⠀⠀⠸⣿⣿⡇⠀⠀⠀⠀⢸⣿⣿⣿⡏⣿⣿⡿⣿⣯⡦⡀⠀⢃⣷⣗⢤⣾⡿⡇⠀⡨⣴⣿⢱⣀⣠⣭⢐⣭⡢⠀⠀⡠⣯⣛⠭⢒⣒⢪⣿⣿⡻⠊⠀⠀⢔⣞⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⢹⠁⠀⠀⣀⡠⠤⣺⣻⣮⣻⣿⡿⠣⡛⠫⣻⣷⣽⡤⢜⣴⢽⣿⡇⡇⠀⢸⣿⣿⣟⣛⣛⢸⠸⣄⢇⢀⣞⣞⠊⡠⡽⣟⣟⡷⡫⠉⠀⢀⢔⡷⠕⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣷⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣪⡷⠶⠶⣯⣄⣸⣸⡬⠶⠾⣛⣫⣉⣒⣒⣛⠮⣗⠀⠠⢷⡢⠀⠉⠯⣿⠘⠙⠯⡿⣟⡇⠀⢸⣿⣿⢏⠀⠀⠐⠀⢒⢔⡾⠕⢀⣪⡫⠁⣻⢯⢁⠀⢀⣖⢾⡷⣕⢤⠀⠀⠀⠀⠀⠀⠠⢷⡢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⢈⠘⢛⡻⢭⣑⡻⣼⢸⠀⠀⣪⢟⡾⠶⠶⠶⣽⣛⢾⣒⣌⣮⢮⢄⠀⠀⠀⠀⠀⠀⠃⢧⣢⣸⣿⣿⢸⠀⠀⣀⣒⢾⠕⢁⣺⣞⠊⠀⣀⣺⢣⣧⣪⣞⠗⠀⠀⠑⢽⡶⣗⢄⠀⠀⠀⠀⠈⢪⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⢷⡢⣀⠪⢟⣛⠶⠾⠾⠶⠶⠯⠿⠷⠶⢿⣛⣛⠫⠭⠭⢛⣛⠾⣽⣑⢄⡀⠀⠀⠀⠀⠈⠺⣛⢾⢽⣡⣖⡽⣻⠒⡠⣪⣞⠗⠀⡠⣯⣟⠚⠀⠑⢟⣛⠂⠀⠀⠀⠀⠀⠑⢽⠾⠶⠶⠶⠶⢼⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⠣⠀⠀⠀⠀⠀⠀⠤⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠈⠪⣛⠷⣭⣔⣒⣒⣠⠤⠤⠤⣀⣒⣒⣒⣬⣭⣭⣭⣭⣭⣖⡤⣉⠚⠽⣻⠶⣯⣭⣭⣭⣭⣭⠶⢟⠫⠒⣡⣖⡵⡫⠊⠀⢔⡧⡯⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⡌⠀⠀⠀⠀⠀⢹⣿⡱⢿⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⣾⡿⡎⠀⠀⠀⠀⠉⡇⡇⢺⣿⡯⡹⡜⡜⠒⠒⠒⠉⠉⠉⠉⠉⠉⠐⠫⢛⠶⣭⣒⣂⠬⠍⣉⣉⡉⠭⠤⣒⣭⢶⢏⡟⠋⠀⠀⢇⣯⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠘⡛⣽⡻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⣫⡇⠀⠀⠀⠀⠀⢀⣧⣴⣿⡅⠸⢿⢿⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠊⠭⠭⢛⣛⡛⠭⠍⠒⢹⣿⣾⡎⠀⠀⠀⠀⢞⣎⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡸⠀⠀⡠⣪⣭⣂⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⢔⢷⢂⠀⠀⠀⠀⢸⣿⡇⡇⠀⢀⢸⢸⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡇⡇⠀⠀⠀⠀⠀⠀⢘⣮⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣭⡢⠀⢀⣪⣗⣪⣗⡬⢮⡢⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⢃⣇⡀⢞⢿⣾⣭⣺⡽⣳⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢻⢿⢾⢸⠀⠀⠀⠀⢣⢇⣸⡇⠀⢸⣯⣾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢱⢡⠀⠀⠀⠀⠀⠀⠀⢞⣎⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣵⡱⠰⢆⣪⣏⣿⣷⡦⣯⣫⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⢡⡣⡧⢯⢯⣿⣻⡆⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⣾⠈⠀⠀⠀⡜⡟⢏⢿⢱⠀⢸⢸⣻⢿⣳⣀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⣾⢸⣮⡄⠀⠀⠀⠀⠀⠀⠀⢞⣎⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠀⠀⠒⠒⠓⢻⣿⡎⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⡇⡇⡏⠝⠩⢹⡇⢁⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⢻⢠⠀⢀⢞⢟⣞⡿⣿⡆⢸⣿⡿⠒⢹⣿⡿⣿⣟⣮⡠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⢟⣛⢹⢁⠀⠀⠀⠀⠀⠀⠀⠀⢞⣎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⣧⣢⣄⢸⡇⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⣧⡕⡳⠶⣟⡵⣵⣿⢱⢣⠀⠈⢻⣳⣼⣿⠃⡟⢫⣵⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣮⣞⣮⣻⣽⢔⣲⡦⡀⠀⠀⠀⠀⢞⣎⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣾⣿⣿⣿⢻⢾⣷⡵⡫⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣷⣯⡷⣇⡀⠀⠀⠀⠑⣳⣯⣯⢾⣯⣵⢡⢏⠁⠀⠀⠀⢸⢙⢿⣾⢰⡿⣿⡞⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⠀⢸⡿⣢⢛⣟⣿⣧⡅⠀⠀⠀⠀⢞⣎⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣒⣒⣒⣺⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣵⢷⡻⡿⣟⠗⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣵⣥⣧⡟⠃⠀⠀⠀⠀⣀⣈⣉⣪⠞⣴⡣⠀⠀⠀⠀⣀⢸⢸⠈⠗⡳⣽⣟⣷⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡟⣯⣿⡇⡏⣺⣿⢿⣿⡿⠀⠀⠀⠀⠀⢜⣎⡀⠀⠀⠀⠀⠀⠀⠀⠀⡘⡿⠓⠒⠒⡺⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣪⣻⠊⢜⡿⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢸⢸⠀⣠⣲⣲⣽⣾⡿⣿⣿⣵⣻⠊⠀⠀⠀⠀⢢⣿⢗⣟⢇⠀⡇⡇⠑⠉⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡇⠪⣿⣇⢷⣼⣿⣾⣿⡇⠀⠀⠀⠀⠀⢞⣆⡀⠀⠀⠀⠀⠀⠀⠀⢰⠱⠀⢀⣪⣟⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢔⡾⠝⡴⡷⠕⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣘⡷⡫⠚⠓⢝⢿⢿⣥⣿⡇⠀⠀⠀⠀⠀⠀⠸⠿⢜⠾⠱⠀⢑⣕⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⢇⣇⡀⠀⠑⢽⣿⡫⣛⡯⠁⠀⠀⠀⠀⠀⠀⢜⣎⡀⠀⠀⠀⠀⠀⡜⡟⠃⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢪⢫⠁⣪⢏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣔⡵⡻⣧⣓⡀⢢⣾⢢⠘⢿⣿⣟⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⣻⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠘⡿⣮⡄⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢜⣎⡀⠀⠀⠀⢀⣸⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⡏⠁⣡⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢪⡿⢷⣵⢵⣳⡫⣻⣶⢿⣿⣯⣼⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠽⠗⠀⠀⢨⢿⡢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣎⡀⠀⠀⡎⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠸⡌⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⣧⡧⢧⡝⣶⡿⡫⠚⡨⣿⡿⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡪⡿⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⣎⡀⢠⣼⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⢱⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢝⣷⣝⢯⣿⢸⣖⡷⡫⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣽⡻⠊⠀⢆⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⢸⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠪⣻⣿⣻⠓⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢔⠾⠽⠉⠀⠀⢠⣾⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⡎⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣪⣞⠕⠀⠀⠀⠀⠀⢣⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⡤⣯⣟⠊⠀⠀⠀⠀⠀⠀⠰⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡇⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣞⡿⡕⢔⡵⡯⠉⠀⠀⠀⠀⠀⠀⠀⠀⢱⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢜⡟⠃⢸⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣪⣞⠗⠙⡻⣳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⡿⠃⠀⠀⠀⢀⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣯⣟⠝⢁⢜⢟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⡞⠊⠀⢀⢴⣽⣻⠯⠈⠀⠀⠀⠀⠀⠀⠀⠀⢸⠱⠀⠀⠀⡠⡼⣯⣧⣖⢤⣢⠤⠤⠤⠤⢜⣟⠊⡠⣽⣞⠕⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡌⠀⢠⣼⣽⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⡟⠃⠀⠀⠀⡰⣾⡿⣛⠫⡭⣊⣏⡭⢭⣿⡝⢁⣪⢏⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⢃⠀⠀⠺⣛⠷⣭⣖⠤⡀⠀⠀⠀⠀⠀⢀⣸⡸⠀⠀⠀⢀⣣⣷⢆⣺⣾⣿⣿⡻⡧⣭⣿⣽⣞⠕⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⣷⣖⡤⣀⠀⠀⠉⠐⠯⣻⣭⡢⣀⠀⠀⡎⡏⠁⠀⠀⢀⣱⡣⢝⢿⣏⣩⣤⣶⠾⡃⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠭⣛⠶⣗⡤⡀⠀⠀⠉⠪⣛⣯⣲⣼⡜⠀⠀⢀⣱⡱⠀⢪⢏⠑⠒⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠯⣻⣯⡦⡀⠀⠀⠈⠚⢟⠶⣭⣭⣞⠕⠀⢞⢏⠁⠀⣐⠻⠀⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠪⣻⣽⡦⣀⠀⠀⠀⠉⠁⠀⢀⣪⢏⠁⠀⠀⢸⠸⡾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠪⣛⠶⣭⣖⣒⣢⣽⣟⠗⠀⠀⠀⠀⠈⠈⠓⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠒⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
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