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