⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣴⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠟⠋⣉⣉⠉⠙⠛⡿⠷⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢞⡭⠒⠓⠒⠉⠀⠀⠈⠋⠉⠙⠢⡍⠷⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠉⢉⠀⠀⢀⡤⡀⠀⢀⡠⢆⡀⠀⢀⣀⠀⠀⠙⠷⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⣠⠎⠒⠒⢉⠒⠨⠉⠁⠰⢆⣈⣉⠱⠌⠒⠤⠤⡄⠙⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠁⠀⡔⠉⠁⠈⠑⢢⢀⡔⠉⠀⠀⠉⢦⠀⠀⠀⠘⡼⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠐⡅⢾⣿⡆⠀⠀⣿⡀⠀⢰⣾⣶⢨⠃⠀⠀⣠⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠙⠦⢍⣀⠤⠚⠁⠙⠦⣈⣩⠥⠊⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⢧⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠒⢤⣀⠠⢄⡀⠀⢀⣀⣀⠀⢀⡀⠀⣀⢀⡤⠤⢤⠊⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⡀⠀⠁⠀⠀⠈⠋⠁⠀⠈⠑⠉⠀⠀⠀⠉⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡖⡓⠢⠤⡠⠴⣄⠀⠀⣠⣀⡀⠀⣀⠶⠤⠤⢺⠏⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠤⣁⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⡠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡷⢤⣤⠄⡀⣀⣀⣠⢤⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢰⣾⣖⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⡇⣿⡿⠿⡿⢿⣿⡟⣸⣿⣏⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢻⣿⡄⠀⠀⠀⠀⠀⢀⡠⠚⠉⢻⡿⣿⢧⠀⠀⠐⠃⠀⠀⢠⣿⣿⣿⡇⠈⠲⢄⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⢻⣿⡄⠀⠀⢠⠔⠉⠀⠀⠀⠘⢷⣼⣾⣆⠀⢠⡄⠀⢀⣾⣿⣿⡿⠀⠀⠀⠂⠈⠲⣄⠀⠀⠀⠀ ⠀⠀⠀⢿⣷⡀⠀⠸⡀⠀⠀⠀⢀⣀⠈⠻⣿⣿⣆⠈⠁⢠⣾⣿⡿⠋⠀⢀⣀⠀⠀⠀⣡⠃⠀⢄⠀⠀ ⠀⠀⠀⠈⢿⣿⡄⠀⠙⠢⢤⠚⠁⠈⢣⠀⠈⠻⢿⣦⣰⣿⠿⠋⠀⠀⠀⡎⠀⠑⢤⠔⠁⠀⠀⠀⠑⠄ ⠀⠀⠀⠀⠘⣿⣿⣄⡀⠀⢡⠀⠀⠀⠀⡇⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸⠂⡀⠀⠀⠀⠀⠸ ⠀⠀⠀⠀⠀⠘⢿⣧⠉⠣⠜⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠐⠤⠈⠈⠑⠂⠐⠁ ⠀⠀⠀⠀⠀⠀⠈⢿⣧⡀⠀⠀⠀⢀⠇⠀⣀⣤⣴⣶⣦⣀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⡀⠀⠀⡜⣠⣾⣿⣿⣿⣿⢿⣿⣿⣷⣦⣄⡀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⠄⢸⠉⢹⣿⣿⣿⣿⣿⡜⠀⣿⣿⣿⣿⣿⡷⡜⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠸⣿⣿⣿⣿⣿⠃⠀⣿⣿⣿⣿⣿⠃⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⡄⢸⣿⣿⣿⣿⣿⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⡆⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀