⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣰⡾⠿⡟⢿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠸⣱⣧⣬⣤⡈⣻⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⣿⣟⡑⠁⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢈⣿⣾⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢹⣽⣿⣿⣿⣿⡿⠏⡧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣯⣀⠀⣈⣼⣷⣶⣤⣤⣤⠤⣀⣀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣀⣤⣴⣶⣶⣿⣿⣶⣿⣿⣿⣿⡿⣏⣵⡈⠋⠛⢷⣝⣂⠱⠱⡀⠀⠀⠀⠀⠀ ⠀⠀⡐⠃⣮⣿⣿⡷⣛⣏⣿⣿⡿⣽⣿⣿⣿⣾⣿⣗⠁⠀⢸⣿⣟⣗⢳⡕⢆⠀⠀⠀⠀ ⠀⠀⢛⣄⣷⣿⣿⣠⢭⡟⢿⣿⣿⣿⣿⣿⡿⠿⣿⠿⠧⠂⢸⡟⢿⣿⣟⣯⣮⣧⣄⠀⠀ ⠀⠐⣹⣧⣿⣿⡿⠻⢿⣿⣯⣿⣿⢿⣿⣏⣯⣎⣵⣧⡀⢀⠜⠁⠀⠙⠻⣿⣿⣿⣯⢃⠀ ⢠⣾⣿⣿⣿⡿⠃⠀⠘⢿⣷⢻⣿⣿⣿⡷⠧⣬⣿⡟⠀⡂⠀⠀⠀⠀⠀⢸⣿⣿⣿⣦⠇ ⢸⣻⣿⣿⣿⠀⠀⠀⠀⣾⣿⣷⣿⣿⣿⣷⣦⣼⣿⣧⢴⠃⠀⠀⠀⠀⠀⠀⠉⢿⣿⣆⡂ ⢀⣿⣿⢳⡟⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣾⣷⣆⠀⠀⠀⠀⠀⢀⣴⣿⡷⠙ ⢀⣹⣿⣾⡀⠀⠀⠠⣬⡟⣽⡿⢿⣿⣿⣿⣿⣿⡿⡏⣿⣿⣿⣦⡀⠀⠀⢠⣿⢿⣿⣿⣀ ⠀⣸⣿⣿⣽⡆⠀⠐⡿⣿⣿⡀⣎⢻⣿⣿⣭⣿⣯⡹⣿⣼⣿⣸⡍⢂⠠⡼⠏⣸⣿⣿⡿ ⠠⢿⣿⣿⠙⣷⠀⡄⢸⡿⣿⣿⣟⡩⢿⡿⠏⠻⣯⣿⠻⣿⣽⡼⣽⣎⢃⠐⠻⠿⠿⠟⠁ ⠀⠸⠿⠿⠿⠋⠀⠱⣎⢰⣿⣿⣿⣿⢿⠇⠀⠀⠈⠹⣇⣽⣿⣷⣿⣷⡮⠆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣾⣿⣷⣻⡾⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⢖⢄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⢿⢉⣿⣧⡀⠀⠀⠀⠀⠀⠀⠈⣿⡛⢿⣿⡇⠱⡄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⣿⣽⢻⣿⢿⡇⠀⠀⠀⠀⠀⠀⠀⢻⣿⡶⣿⣿⠅⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣷⣿⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣺⣻⣦⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⢿⣾⡆⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡾⡷⢩⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣼⣦⣰⡄⠀⠀