⣿⣿⡿⠁⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⣜⡔⠊⠁⠀⠀⠀⠉⠢⠴⠚⠒⠂⢄⠀⠀⠀⠑⢮⠐⢤⣄⠀⠀⠀⠀ ⣿⡟⠁⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢏⠀⠀⠀⠀⠀⠀⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠑⢄⠉⢧⡀⠀⠀ ⠏⠀⠀⢀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⢸⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠑⢄⢻⡄⠀ ⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⡜⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠰⡙⣆ ⠀⠀⠐⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⡇⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⢱⠈ ⠀⠀⡰⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⢀⡃⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠃⠀⠀⠀⠀⠂ ⠀⠀⠁⠀⣹⡄⠀⠀⠀⠀⠀⠀⠀⡇⠀⠸⡇⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣿⠿⠿⠛⠛⠛⠛⠛⠛⢳⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⠃⢳⡀⠀⠀⠀⠀⠀⠀⠃⠀⡄⣧⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀ ⠀⠀⠀⡜⠀⠈⢷⡀⠀⠀⠀⠀⢀⠀⢰⡧⢼⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠤⢄⣀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀ ⠀⠀⠀⡇⠀⠀⣀⣙⣦⡀⠀⠀⠘⠀⢸⠀⠹⡄⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠮⠒⠉⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣧⣾⣿⣿⣿⣿⣿⣦⡀⠀⡆⣮⣤⣀⢻⡄⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣶⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀ ⠀⠀⠀⣿⣿⡿⠛⠉⣏⡙⠻⣿⣦⣱⣿⣿⣿⣧⢻⡀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⡻⢿⣏⠉⠛⡇⠀⠀⠀⠀ ⠀⠀⠀⢿⣿⡇⠀⢰⡻⠿⣷⣿⣿⡟⡿⠛⠚⢿⣧⣡⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟⠻⢿⣾⣿⡟⠿⠷⠽⠀⠀⡇⠀⠀⠀⠀ ⠀⠀⠀⠈⢿⡇⠀⠘⠁⡠⠊⣿⣿⠃⠘⢥⣸⠁⡙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡏⡇⢀⠖⢹⣿⡇⠙⢶⣶⠀⢠⡇⠀⠀⡜⠀ ⠀⠀⠀⠀⢸⠁⠀⠀⣾⠀⠀⠘⠛⠀⠀⢈⡿⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢱⡇⠀⠀⠛⠃⠀⢀⡇⠀⣸⠀⠀⡰⠀⠀ ⠀⠀⠀⠀⡼⠀⠀⠀⠈⢇⠀⠀⠀⠀⢠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⠀⠀⠀⣀⠞⠀⢀⡇⠀⣠⠁⠀⠀ ⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠉⠑⠊⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠉⠉⠀⠀⣼⠁⢠⠃⠀⠀⣠ ⣆⡀⢆⠠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢠⠃⠀⢀⡼⣻ ⣿⣿⠮⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢀⠆⠀⣠⡟⢰⣿ ⣿⣿⣧⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⠋⢀⣜⣿⡇⣿⣿ ⣿⣿⣿⣆⠘⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣋⠴⣫⣾⣿⣿⣿⣿ ⣿⣿⣿⣿⣧⠈⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠦⠤⠦⠶⠦⠖⠚⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⢡⣾⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣷⡌⢽⠙⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⣿⣿⠿ ⣿⣿⣿⣿⣿⣿⣿⣮⣷⣿⣿⡟⢦⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣶⣿⣿⣿⠿⠿⠭⠉⠉⠁⠀⠀