⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠶⣄⠘⡆⠀⠀⢰⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠉⠑⢄⠀⣇⡞⣠⡴⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⣯⣓⡲⢯⠀⣇⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡷⣿⢭⡁⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠤⠤⠤⠤⠖⢋⠁⠠⠨⣻⣬⣱⠀⠀⠈⠱⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⠁⠀⡿⡄⠈⠱⣄⠀⠀⠀⠀⠀⠀⠀⠉⠢⢄⡀⠀⢀⣀⡤⠴⠊⠇⠀⠈⢧⡀⠀⠀⠩⠄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠂⢠⠇⢧⡀⠂⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠀⠀⠀⠀⣷⡀⠐⠀⠱⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⠤⠴⠋⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠀⠀⠄⠀⢸⡵⡆⠄⡀⠑⠄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⢸⠱⢱⠀⠈⠑⠤⢕⣄⠀ ⠀⠀⠀⠈⠣⡀⢀⣴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⠀⠀⠀⠀⠀⠀⠀⠘⠄⠀⠀⠀⠘⠀⢅⢇⠀⠀⠀⠀⠹⠇ ⠀⠀⠐⢶⣲⡽⢘⠍⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡍⠙⡆⠀⢠⠆⠀⠀⠀⠀⡃⠀⠀⠀⡊⠀⠈⣏⡆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠠⢆⢁⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠂⡇⡰⠁⠀⠀⠀⠀⠀⠐⡀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⠾⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣴⣷⠤⠤⠄⠀⠀⠀⠀⠀⠆⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⡀⣀⣷⡤⢅⣁⡑⠦⠤⡀⠀⠀⠀⢃⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠁⠀⠀⡤⡟⠡⠉⠷⡄⠀⠈⠉⠉⠁⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⠀⠁⢠⡮⢳⡗⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⢶⣒⡮⠋⠀⡏⡇⢀⠀⠀⢨⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠰⡦⡀⠀⠀⠀⢦⡀⢠⠀⡠⠇⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⢳⢇⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠘⣌⠢⢀⡀⠀⠑⣼⣷⠁⠀⠀⢀⠔⡻⠀⠀⠀⠀⠀⠀⠈⠓⠛⠓⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠘⢆⠂⠈⠐⠀⢜⣿⠤⠤⠎⠁⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣱⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠑⠤⡀⠀⠀⣇⠀⠀⠐⢠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢋⠉⢹⠀⢺⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⢀⡨⠕⠶⢾⠀⢖⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠏⠉⠁⣀⣀⠀⠀⢺⡎⠁⠀⢘⠄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠜⠁⠀⠀⠀⢀⣿⠀⠈⠑⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⡇⠀⠀⣿⢸⣄⠀⢐⠈⠣⢤⠇⢨⢀⡀⡠⠰⠄⠀⠀⠀ ⠀⠀⠀⡰⠁⠀⢀⠀⠀⣸⢿⡀⠀⠀⠀⠁⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣆⠑⢄⠀⢿⣾⠄⠙⠃⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡇⠀⠀⠀⢀⠔⠁⡿⠈⠂⡀⠀⠀⠀⠀⠈⠐⠠⢄⡀⠀⠀⠀⠀⠀⠈⠓⠒⠛⠋⠁⠀⠀⠀⠀⠀⠀⢰⠀⠀⡾⠒⢲⠀⠀⠀⠀ ⠀⠀⡸⢀⠠⠂⠉⠀⠀⠀⠀⠀⠀⠀⠁⠢⠄⡌⡀⡀⢀⠀⡈⡉⢒⠲⠖⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢹⠉⠓⠙⠒⠚⠀⠀⠀⠀ ⠐⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⡰⡄⠔⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡠⠁⡇⡄⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣄⣠⡇⠀⡇⢳⡀⠣⡀⠀⠀⠀⠀⢀⡤⡆⠀⠀⠀⠀⠀⢠⡆⠀⠀⠀⠀⠀⠀⢀⡟⡄⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⢳⡄⠀⠀ ⠙⣽⠇⡜⠀⠀⠱⡄⠉⠉⠑⠒⠋⠁⡀⠓⣄⠀⠀⠀⢀⢾⡿⡄⠀⠀⠀⠀⠀⡬⣧⠘⢦⣀⣀⣀⠴⣿⠇⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀ ⡞⢁⢦⠉⡇⠀⠀⣽⡦⣀⣀⣀⣴⠋⢧⠀⠈⠙⠒⠂⢠⠎⢣⡈⠑⠲⠤⠔⠋⡼⢩⡷⠄⠀⠀⣀⠔⣻⠀⠀⠀⠀⠀⠀⠀⣀⠇⡇⠀⠀ ⡇⡼⠘⠦⠼⠄⠀⣿⠀⠀⠀⠀⣿⠀⠀⠉⠓⠒⣾⠚⠁⠀⠀⢩⢗⠤⠤⠴⠊⠁⠀⣿⠀⠀⠀⠀⠀⣿⠀⠀⠀⠈⠉⠉⠙⢆⣠⠜⠛⠒ ⠿⠁⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠸⡃⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢘⠛⡄⠀⠀⠀⡿⠁⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢳⡇⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡸⠀⡇⠀⠀⠀⢫⢸⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⡿⡀⠀⠀⠀⠀⠀⡇⡆⠀⠀⠀⠀⡞⠇⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡇⠀⡇⠀⠀⠀⢸⠀⡇⠀⠀⠀⠍⡇⠀⠀⠀⠀⡇⡇⠀⠀⠀⠀⠀⡇⡇⠀⠀⠀⢸⠀⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡇⡀⡇⠀⠀⠀⠐⠀⡇⠀⠀⠀⠂⡇⠀⠀⠀⠀⡇⡁⠀⠀⠀⠀⠀⡇⢱⠀⠀⠀⢸⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡇⡇⡇⠀⠀⠀⢨⠀⢹⠀⠀⠀⡇⢣⠀⠀⠀⠀⠇⢧⠀⠀⠀⠀⠀⡇⢰⠀⠀⠀⢘⠀⡆⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡅⡇⡇⠀⠀⠀⡇⢘⢸⠀⠀⠀⡇⢸⠀⠀⠀⢘⠀⢸⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⢘⠇⡇⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡇⡇⡇⠀⠀⠀⡇⢨⢸⠀⠀⠀⡇⡌⠆⠀⠀⡇⢰⠸⡄⠀⠀⠀⠀⡇⢠⡇⠀⠀⢨⡆⡁⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡇⡇⡇⠀⠀⠀⣇⢸⢸⠀⠀⠀⠇⠇⢱⠀⠀⢇⠸⠀⡇⠀⠀⠀⠀⡇⢨⠸⠀⠀⢸⢸⢨⠀⠀⠀⢀⡰⠃⣇⠀⣀⡀⠀ ⠀⠀⠀⠀⠀⠀⠈⠛⠁⠀⠀⠀⠸⣸⢸⠀⠀⠀⠐⢇⢸⠀⠀⢸⢰⢠⠃⠀⠀⠀⠀⡇⢸⢸⠀⠀⢸⢸⠰⠀⠀⠒⠛⠲⡀⢠⠚⠉⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠛⠚⠀⠀⠀⢸⢸⢸⠀⠀⢸⢸⢸⠀⠀⢰⠀⠀⡇⠨⢸⠀⠀⠀⣿⣸⠀⠀⠀⠀⠀⢱⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⡄⠀⠀⠀⠀⠀⠀⠀⢸⠀⣽⠀⠀⢸⡞⢨⠀⠀⢸⡀⠀⠳⠼⠼⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠴⢾⡁⠘⣦⠖⠀⠀⠀⠀⠀⠈⠓⠛⠀⠀⠈⠉⠙⠀⠀⣸⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠛⠻⡄⠈⣉⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀