⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⣄⡀⠀⠀⠀⠀⣀⡤⠤⣄⡀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠉⠉⠉⠑⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠈⠑⠒⠒⠉⠁⠀⠀⠀⠹⡄⠀⠀⠀⠀⡔⠁⠀⣀⡀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡼⠹⡀⠀⠀⠀⠘⠦⣀⠤⠋⠀⠀⡞⠁⡇⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠛⠀⠀⠀⠀⠀⠀⡇⡄⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢸⢧⢳⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⡼⠁⡿⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡞⢸⠘⡆⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⡇⣸⠀⢹⡇⠀⣠⠤⠤⠤⠤⠤⠼⢱⠃⠘⡄⡇⠀⠀⠀⠑⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⣸⢁⡇⠀⠸⠱⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⢳⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠤⢤⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⡇⠀⠀⣠⠤⠤⣄⣀⡀⠀⠀⣀⡤⠤⠖⠒⡆⠀⣿⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⡇⠀⠀⠳⠦⠤⠤⠴⠃⠀⠀⠹⠤⠤⠤⠴⠃⢠⢻⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⡇⠀⠀⠀⠀⢠⣏⡋⠈⠓⠚⠹⠤⢤⠀⠀⠀⢸⡼⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠷⠲⣴⠦⣴⡖⠚⠀⠀⠀⢸⡇⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠛⠷⠶⠶⠶⠾⠷⠒⠚⠛⠛⠉⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⠊⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⢀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⠤⠤⠤⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⠉⠲⡄⢰⠒⠒⠒⢸⢆⠀⠀⠀⡖⠒⠦⣄⠀⠀⡆⣀⣀⡀⡄⠀⢀⠀⡄⠀⡄⠀⡆⠀⢸⠀⠧⡀⠀⣠⠇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⠀⠀⢹⢸⠀⠀⠀⢸⠀⠢⡀⠀⡗⠀⠀⣺⠀⠀⠍⠀⠀⡇⡇⠀⢸⠀⣿⠀⡇⠀⣇⠀⢸⠀⠀⠙⢾⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡜⠀⠀⣸⢸⠉⠀⠀⢼⠠⠤⠬⣆⡇⠀⠀⣿⠀⠀⡷⠶⠚⢆⡇⠀⢸⠀⡏⢳⢳⠀⡏⢦⢸⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣃⣀⡤⠃⠼⠤⠤⠄⠘⠀⠀⠀⠈⣧⣄⡴⠃⠀⠀⠇⠢⠤⠞⢳⣀⡞⠀⠇⢸⡏⠀⡇⠈⢻⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⢻⠈⡇⠀⡏⢸⠇⠀⡞⣀⢳⠞⠤⠢⠇⠀⠀⠃⡴⣄⣧⠈⠀⠀⠀⠘⠄⠤⠤⠼⠃⡤⣀⣃⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸⢦⡏⠀⢳⢳⡏⠀⢸⠀⡇⢆⠚⠶⡷⠀⠀⣿⠀⠀⡇⣆⠬⠤⠠⢼⠀⠀⠉⢸⣸⠀⠀⡜⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠁⢾⠙⠀⠀⢸⠀⣇⠀⡇⠀⣿⠀⢸⠀⡇⡇⠀⠀⠍⠀⠀⣺⠀⠀⡗⠀⡀⠢⠀⢸⠀⠀⠀⢸⢹⠀⠀⢸⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠇⣠⠀⡀⠧⠀⢸⠀⡆⠀⡄⠀⡄⠀⢀⠀⡄⡀⣀⣀⡆⠀⠀⣄⠦⠒⡖⠀⠀⠀⢆⢸⠒⠒⠒⢰⡄⠲⠉⢸⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠊⠤⠤⠤⠦⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡔⢀⠀⠀⠀⠀⠀⡄⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠉⠉⠊⠒⡤⢀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⡠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣀⣄⠦⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠉⠛⠛⠚⠒⠷⠾⠶⠶⠶⠷⠛⠛⠛⠛⠙⠈⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡇⢸⠀⠀⠀⠚⡖⣴⠦⣴⠲⠷⠀⠀⠀⠀⠀⡀⢳⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⡼⢸⠀⠀⠀⢤⠤⠹⠚⠓⠈⡋⣏⢠⠀⠀⠀⠀⡇⠀⠀⠀⠀⠇⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⢸⢸⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⡀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢻⢠⠃⠴⠤⠤⠤⠹⠀⠀⠃⠴⠤⠤⠦⠳⠀⠀⡇⠀⠀⠀⠇⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⢀⠀⣿⠀⡆⠒⠖⠤⡤⣀⠀⠀⡀⣀⣄⠤⠤⣠⠀⠀⡇⠀⠀⠀⡇⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢤⠤⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢀⠀⠀⠀⢳⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠏⠱⠸⠀⡇⢁⣸⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠑⠀⠀⠀⡇⡄⠘⠃⢱⠼⠤⠤⠤⠤⠤⣠⠀⡇⢹⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⡆⠘⢸⡞⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⡿⠁⡼⠀⠀⠀⠀⠀⠀⠁⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢳⢧⢸⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡄⡇⠀⠀⠀⠀⠀⠀⠛⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡇⠁⡞⠀⠀⠋⠤⣀⠦⠘⠀⠀⠀⡀⠹⡼⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡀⣀⠀⠁⡔⠀⠀⠀⠀⡄⠹⠀⠀⠀⠁⠉⠒⠒⠑⠈⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠑⠉⠉⠉⠉⠞⣠⠀⠀⠀⠀⠀⠀⡀⣄⠤⡤⣀⠀⠀⠀⠀⡀⣄⡤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀