⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣤⡤⢄⡀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡇⡇⠀⠀⠉⠓⠒⣏⠉⠉⠁⠉⠀⠈⠉⠁⠁⠓⢦⡶⣫⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢰⠃⢹⠉⠁⠈⠈⠛⠂⠒⠤⠤⢀⢀⡀⠀⠀⡴⠋⠉⢫⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡏⠀⣜⠀⠣⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠉⠓⠦⡽⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢰⠁⠀⡇⠀⠀⠈⣣⠀⠀⠀⠀⠀⠀⠀⠀⢠⠒⠒⠁⠉⠁⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣇⠀⡸⠀⡴⠋⠉⠀⠀⠀⢱⠀⣆⠀⡇⠀⠀⠑⠤⡀⠀⠀⠀⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⢆⡇⠀⠀⠀⠀⠀⠀⠀⠀⢣⠇⣇⡇⠀⠀⠀⠀⠀⠉⠂⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠘⠒⠒⠒⠒⠒⠒⢺⠒⠒⠒⡓⠒⠒⠒⠒⠒⠤⣀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣜⠀⠀⠀⣀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡤⠖⠋⢫⡉⠉⢰⠃⠈⠉⠙⢲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠤⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠈⠷⡎⠀⠀⠀⡇⠀⢸⠀⠀⢀⡤⠒⠉⠈⠀⠀⠀⠀⠀⠀⠀⠉⠣⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⠀⠀⣇⠀⠀⠀⡴⠹⣆⠀⢀⡇⠀⡠⡎⠕⡊⠉⢹⠀⠀⠀⠀⠀⠒⠉⡇⠀⠀⠀⠀⠑⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠹⡴⡞⠁⠀⠀⢯⣉⣡⠞⠁⠁⠸⠁⢣⠀⠀⠁⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢱⠀⠀⡇⡏⢀⠔⠒⠋⠉⡏⠁⠀⠀⠀⠀⠀⠀⠁⠀⠀⢀⠇⠀⠀⠀⠀⠚⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢧⠀⡇⣏⠏⠀⠀⠀⠀⣇⠀⠀⣄⠀⡰⠒⠀⠀⠀⠀⢨⠀⠀⠀⡀⠀⠀⠈⠈⠈⠉⠣⡀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⣧⡟⠈⠙⠢⡄⠀⠀⠈⡆⠀⡟⠂⢇⠀⠀⠀⠀⠀⠘⠂⠂⠉⠀⠀⠀⠀⠀⠀⠀⠀⣠⠇⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⡏⠑⠦⠬⣇⠈⠉⠓⠯⠉⠑⢢⠀⠀⠀⠠⠤⠔⡄⠀⠀⠀⠀⠀⠒⠃⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⢸⠀⠀⠀⠀⠀⢱⡄⠀⠀⠀⠀⠀⠈⠦⡀⠀⠀⠀⠀⢸⠀⠀⠀⢤⡀⢀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⣏⠀⠀⠀⠀⠀⢸⠀⠁⠢⣀⠀⠀⠀⠀⠀⠁⠄⢀⠀⠘⠀⠀⠀⢘⡄⠈⡇⠀⠾⠄⡎⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⣇⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠈⠉⠢⣄⠀⠀⠀⠀⠀⠂⠀⠄⠀⡇⠈⠑⠃⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢇⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠑⠢⠤⠄⢤⢈⡉⠀⠀⠀⠀⣀⠏⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢂⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠇⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀