⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣾⡟⣯⣽⣻⣿⣿⣿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣀⣴⣿⢻⣿⣿⢻⣿⣷⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣀⣴⣿⣿⣏⣿⣿⣿⡈⢻⣽⣿⣿⣾⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣴⣿⣿⣿⣿⢾⣿⣿⣿⣇⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣴⠿⠿⠿⢿⣿⣿⣿⣿⣿⢻⢻⣄⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠷⠄⠀⠀⠀⠀⠀⠀⠀⠀ ⠉⠀⠀⠀⠀⢸⣿⣿⣿⣿⢹⣒⠢⣿⣄⠀⠀⠚⢻⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⡏⣿⣿⡟⣿⣿⡮⠈⠀⠀⠰⣿⣿⠻⣿⣿⣧⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⣿⣼⣿⣇⠉⠋⠀⠀⡀⠀⠀⠉⠉⢀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣄⠀⠀⢀⣉⡀⠀⠀⣠⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣷⡦⣀⣀⣀⢴⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣸⠿⢿⣿⣿⠛⠉⠀⠀⠀⠀⠀⠙⠛⢿⣿⡿⠿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⠎⠀⠀⣎⣿⣿⡂⠒⠒⢢⣤⣖⣛⣉⣁⣼⣿⡇⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣼⢀⠀⠀⠇⢹⣿⡍⡉⣹⣿⣧⠀⠀⠀⠀⣾⣿⣇⢀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢿⠀⢧⣀⡇⠘⣿⡇⠀⠉⢹⣧⡀⠀⠁⠈⣿⡿⢹⠎⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⠀⠀⢻⢆⠀⢿⡇⠀⠀⢸⡇⠻⣆⠀⢰⣿⠃⣺⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡄⠀⢸⡄⠃⡈⣿⡀⠀⢨⢸⡦⢻⣧⣽⠿⢰⢿⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡅⠀⠸⡛⡄⠈⠹⠁⠀⢸⠈⣧⠀⠹⣏⢠⠇⢸⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢁⠀⠀⡇⠹⣥⠀⢡⠀⢸⠀⢸⡆⠀⢹⡟⠀⢸⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢰⠀⠀⣿⠀⠈⠄⠀⢡⠀⠀⠀⣧⠀⠀⢻⠀⢸⠀⠀⢸⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⡄⠀⣿⠀⠀⢠⠀⠀⢣⡄⠀⢽⠀⠀⢉⣧⣿⠀⠀⣼⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢇⠀⣿⠀⠀⠀⠄⠀⠀⠃⠂⢸⡇⠠⠃⢛⣿⠀⠀⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⢠⣿⠀⠀⠀⠀⠀⠀⠈⢢⡘⠃⠀⢰⠈⣿⠶⠒⠿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠿⠘⠀⠀⠀⠀⡄⠀⠀⠈⠋⠢⠄⠈⢆⢻⠀⠀⠐⢌⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠈⠁⠈⢻⣦⡭⣍⠢⣽⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢻⠹⣦⣷⣽⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡄⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡆⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⠁⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⢣⠀⠀⠀⢿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⠀⠀⠘⣼⠀⠀⠀⡄⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢃⠀⠀⢸⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⠀⠀⠀⠘⡆⠀⠀⠰⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠈⡆⠀⠀⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡟⠀⠀⠀⠀⢡⠀⠀⠀⢃⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠘⡄⠀⢸⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠃⠀⠀⠀⠀⠈⡄⠀⠀⠀⢆⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⢹⠀⠀⢿⣿⣿⣿⣿⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠈⢂⠀⠀⠀⢃⠀⠀⠀⠀⠀⠀⣇⢸⠘⣿⣿⣿⣿⣇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣤⠀⠀⠀⠀⠀⠘⡆⡆⢹⣿⣿⣿⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠠⢱⢧⠘⣿⣿⣿⣿⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠈⡆⠀⢹⣿⣿⣿⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⡄⠀⠀⠀⠀⠀⠀⠹⢰⠈⣿⣿⣿⣿⡆⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠐⠀⠇⢇⢹⣿⣿⣿⡇⠀⠀ ⠀⠀⠀⠀⠣⠀⡀⠀⡀⠀⠀⠀⠀⣀⡀⣀⣀⣀⣀⣀⣀⣀⣆⣀⣠⣤⣤⣤⣤⣴⣾⣾⣿⣿⣿⡧⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢿⠉⠉⠉⠉⠁⠉⡍⠀⠈⡇⠀⠀⠀⠀⠀⠀⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠸⡙⠶⢄⣀⠀⠀⢣⠀⠀⡇⠀⠀⠀⠀⠀⢸⠃⣿⣿⣿⣾⣿⣿⣿⣿⣿⣏⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠈⠉⢹⠀⠀⡇⠒⠂⠐⠒⠉⢸⢹⣿⣿⣿⣾⢿⣿⣿⣿⣿⣿⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠈⡆⠀⡇⠀⠀⠀⠀⠀⢸⢸⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⡄⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⡇⠀⠃⠀⠀⠀⠀⠀⡞⠈⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⣷⠀⢠⠀⠀⠀⠀⠀⡇⠀⢸⣿⣿⣯⣷⣿⣿⣿⣿⣿⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢸⠀⠀⠀⢠⢿⠀⢸⢠⠀⠀⠀⡖⡇⠀⠀⢿⣿⣿⣿⣿⣿⣿⡟⢻⣿⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠞⠀⡖⠀⡎⣸⠀⠸⠀⠇⠀⢀⠁⢃⠀⠀⠘⣿⣿⣿⣿⣿⣿⡧⢸⣿⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⡇⠀⡇⢸⠀⠀⡃⠀⡇⢸⠀⢸⠀⠀⠀⢹⣿⣿⣿⣿⣿⡗⠨⣿⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠀⠀⢸⠀⠀⢸⠀⠀⠀⠀⡇⠈⠀⠀⡇⠀⠀⠀⢿⣿⣿⣿⣿⡏⠀⣿⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠘⠀⠀⡇⠀⠀⢰⠀⢡⠀⠀⠀⢃⠀⠀⠀⠘⣿⣿⣿⣿⠇⠀⢿⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡄⠀⡇⠀⠀⢰⠀⠈⠀⠀⠀⢸⠀⠀⠀⠀⢸⣿⣿⡟⠀⠀⢸⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡇⠀⡇⠀⠀⠸⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⢸⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢃⢠⠃⠀⠀⠀⡇⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⣿⣿⠁⠀⠀⢸⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⠀⠀⠀⢈⢰⠀⠀⠀⠀⢱⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⣿⡏⠀⠀⠀⢸⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢸⠀⠀⠀⠀⠘⡄⠀⠀⠀⢸⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⢸⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡇⢀⠀⠀⢸⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⣿⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⢸⠀⠀⠀⠀⠀⠸⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⢸⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⡆⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠰⡆⠀⠀⠀⠀⠀⡇⠀⠀⢠⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⡇⠀⠀⠀⠀⢀⠇⣀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⢳⠀⠀⠀⠀⢸⡇⢁⣀⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠰⢸⠀⠀⠀⠀⢠⣷⠿⠛⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢀⣤⣤⣄⡇⠀⠀⠀⢠⠏⠀⠀⠈⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠉⠀⠛⡏⠀⠀⠀⣘⣀⡤⡤⠤⢄⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⢣⡀⠀⠀⣿⠓⠛⠉⠉⠉⠚⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣶⠾⠿⠿⠿⢧⡀⠀⣿⣄⢼⣰⡴⣦⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣏⠠⡐⢄⢢⡰⣆⣴⠀⠀⠉⠛⠛⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠙⠛⠛⠒⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀