⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣀⣀⣀⡀⠀⠀
⠀⠀⠀⢀⣠⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⡿⠿⠿⢿⣷⣄⠀⠀
⠀⠀⣴⣿⠿⠛⠛⠿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠟⠁⠀⠀⠀⠀⠀⠈⢿⣧⠀⠀
⢀⣾⡿⠁⠀⠀⠀⠀⠀⠙⣿⣿⣄⠀⠀⠀⠀⠀⠀⢠⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀
⢸⣿⠁⠀⠀⠀⠀⠀⠀⠀⣸⡿⠿⠒⠒⠤⠤⠒⠒⠛⠛⠓⠒⠒⠢⢤⣀⠀⠀⣼⡿
⢸⣿⡀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⠑⠚⢿⡁⠀⠀
⠈⢿⣧⡀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠙⣆
⠀⠀⡻⢿⣶⣤⣾⠀⠀⠀⠀⠀⠀⠀⠀ ⡄⠀ ⠀⠀⠀⠀⠀⠀ ⡄⠀⠀⠀⠀⠀⠀⠀⠸⡄
⠀⢠⠃⠀⠉⠛⢻⠀⠀⠀ ⢰⠀⠀⠀⡼⡇⠀⠀⠀⠀⠀⠀⠀ ⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⡇
⠀⢸⠀⠀⠀⠀⢸⠀⠀⠀ ⡞⡇⠀⢠⠃⢱⠀⠀⠀⠀⠀⠀⠀⢠⠃⡇⠀⠀⠀⠀⠀ ⢧⠀⡇
⠀⢸⠀⠀⠀⠀⢸⢀⠇⢠⠃⠸⡀⢸⠀⠀⢣⡘⣄⠀⠀ ⢀⡜⠀ ⢸⠀⢀⡴⠓⢤⣘⢦⢧
⠀⢸⠀⠀⠀⢀⣜⣜⡴⡇⠀⠀⠙⢌⡄⠀⠀⠙⢌⣆⡠⠊⠀⠀⠀⣜⠴⠋⡇⠀⢸⠀⠉⠓⠓
⠀⡼⠁⠀⠀⠀⠀⠀ ⠀⡇⠀ ⠀ ⠀⠀⠀⠀⠀⠀⠀ ⠀⠤⠀⠀ ⠀⠀⠀⠀ ⢇⡀⡼
⡼⠁⡔⠸⡀⢄⠀⠀⠀⢸⠀ ⠀⠀⠀ ⠀⢆⣀⠤⣀⡠⠀⠀⠀⠀⠀⠀⠀⠀⢀⣵⠃
⢇⠰⠣⣀⠑⠤⡵⣄⠀ ⢧⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠔⣫⠃
⠀⠉⠁⠀⠉⠉⠀⠀⣱⣦⣈⡻⡛⠒⠤⣀⣀⣀⣀⣀⣀⣀⣀⣴⠟⣏⡴⠁
⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⡿⠈⠛⢄⡀⠀⠀⠀⢠⡿⣆⢀⠎
⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⠃⠀⠀⠀⠙⣦⣠⣶⡿⠀⠹⠏
⠀⠀⠀⠀⠀⠘⠛⠛⠛⠃⠀⠀⠀⠀⠀⠛⠛⠛⠁