⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⠋⡆⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⢀⣤⢛⠛⣠⣿⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⠟⣡⠊⣠⣾⣿⠃⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣯⣿⠀⠊⣤⣿⣿⣿⠃⣴⣧⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⡟⣠⣶⣿⣿⣿⢋⣤⠿⠛⠉⢁⣭⣽⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀  ⠀⠀⠀⠀⠀⠀ ⠀⣠⠖⡭⢉⣿⣯⣿⣯⣿⣿⣿⣟⣧⠛⢉⣤⣶⣾⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣴⣫⠓⢱⣯⣿⢿⠋⠛⢛⠟⠯⠶⢟⣿⣯⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡮⢁⣴⣿⣿⣿⠖⣠⠐⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠛⠛⢿⣶⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣤⣷⣿⣿⠿⢛⣭⠒⠉⠀⠀⠀⣀⣀⣄⣤⣤⣴⣶⣶⣶⣿⣿⣿⣿⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣶⠏⠟⠝⠉⢀⣤⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢴⣯⣤⣶⣿⣿⣿⣿⣿⡿⣿⣯⠉⠉⠉⠉⠀⠀⠀⠈⣿⡀⣟⣿⣿⢿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠉⠛⣿⣧⠀⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⣿⣿⣯⣿⣦⡀⠀⠉⠻⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠉⢿⣮⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠀⣯⠉⠉⠛⢿⣿⣷⣄⠀⠈⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⠀⠀⠀⠀⠀⠀⠀⢀⢡⠃⣾⣿⣿⣦⠀⠀⠀⠙⢿⣿⣤⠀⠙⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢋⡟⢠⣿⣿⣿⠋⢿⣄⠀⠀⠀⠈⡄⠙⣶⣈⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⢲⣿⠀⣾⣿⣿⠁⠀⠀⠉⢷⡀⠀⠀⣇⠀⠀⠈⠻⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⣀⣿⡏⠀⣿⡿⠀⠀⠀⠀⠀⠀⠙⣦⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠿⣧⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣮⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀