⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⣀⣤⣶⣶⣶⠶⢶⢦⣤⣵⣦⡄⡀⡀⡀⡀⡀
⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⢠⣾⣿⠟⠋⠄⡀⡀⡀⡀⠁⠉⠋⠻⠢⡀⡀⡀⡀
⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⢠⣿⣿⣿⡃⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⠈⠄⡀⡀
⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⣸⣿⣿⣷⣿⣿⠤⡀⡀⡀⡀⡀⡀⡀⣐⡀⡀⢈⠄⡀
⡀⡀⡀⡀⡀⡀⡀⠠⡀⠠⠴⣿⣿⣿⣿⣿⣿⡿⠃⢠⢢⡴⠞⠟⠷⣄⡀⠐⢙⣀⣸⡀
⡀⡀⡀⡀⠠⠊⡀⡀⠈⢠⠈⢸⢋⠭⣙⢿⣿⠫⠌⣂⠫⣤⠶⣫⣍⣊⠛⠁⢻⣟⡢⡅
⡀⡀⡀⠠⠁⡀⡀⡀⡀⡀⡄⢰⠘⠎⡎⢾⣷⡂⠂⡀⡀⠈⠓⠂⡀⡀⡀⡀⡀⠈⠣⡀
⡀⡀⡀⡆⡀⡀⡀⡀⡀⡀⠠⢸⢄⠠⠁⣾⣿⣳⣠⡠⡀⡀⡀⡀⡀⡀⡀⢀⡀⡀⡀⠑
⡀⡀⡀⠐⡀⡀⡀⡀⡀⡀⡀⡼⠐⣄⢰⣿⣿⣿⣷⣽⣻⣶⣖⣠⡂⡏⣤⣀⠑⡀⡀⡀
⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⢠⡀⢠⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⡿⢶⠲⣦⡶⣄⡀
⡀⠰⡄⡀⢠⡀⡀⡀⡀⡀⡀⡀⡀⡀⣽⣿⣿⣿⣿⣿⡧⠻⣝⣳⢲⠤⡤⠴⠛⠁⡀⠉
⡀⡀⠈⡀⡀⡀⡀⡀⡀⡀⡀⡀⠁⢰⢿⣿⣿⣿⣿⣿⣧⣵⣌⠙⠺⠤⠏⣦⡀⡀⡀⡀
⠐⠃⡀⡀⡀⠌⡀⡀⡀⡀⡀⡀⡀⢁⠼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⢳⠐⢈⡀⡀
⠇⡀⡀⡀⡀⠠⠄⡀⡀⡀⡀⡀⡀⡀⢪⠈⠽⢿⣿⣿⣿⣿⣿⣿⣿⠟⠁⡀⠆⡁⡀⢀
⠁⡀⡀⡀⡀⡀⠂⡀⡀⡀⡀⡀⡀⡀⡀⣑⠋⣽⡟⢿⣿⠿⠻⡟⠁⡀⡀⠐⠐⠊⠖⢁
⡀⡀⡀⡀⡀⡀⠈⡀⡀⡀⡀⡀⡀⠠⠃⢠⠁⠈⠉⡀⡀⡀⡀⠈⠄⡀⠐⡀⠐⡀⢈⠁
⡀⡀⡀⡀⡀⡀⡀⡀⠄⡀⡀⡀⡀⡀⡀⠂⡀⡀⡀⡀⡀⡀⡀⠠⣄⣄⡑⡏⢚⡀⡄⠙
⡀⡀⡀⡀⡀⡀⡀⡀⡀⠢⡀⡀⡀⡀⡀⡀⡀⡀⠤⡀⢐⡀⡀⠉⡀⡀⠁⠁⠈⡀⡀⡀