⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣿⣷⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣿⣿⣿⣿⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⢃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⠇⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣠⣼⣿⠀⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⠈⠹⢻⡿⣿⣿⣿⣿⡘⢿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⣻⣿⡟⢲⣶⣮⡷⠌⠛⠛⠛⠳⣬⣿⣿⢿⣿⡿⠿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠧⣿⣎⠊⠭⠑⠁⠀⠀⠀⠀⠀⠻⠬⠟⢸⣿⢯⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣳⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⠀⠀⠀⠐⠀⠐⠐⠀⠀⢠⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⣿⣿⣿⣿⣿⣿⣦⡄⢀⠀⠀⣀⢠⣴⣾⣿⣿⣿⣿⣿⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⣼⣿⣿⣿⣿⣿⣿⣿⡇⠀⠈⠁⠀⣼⣿⣿⣿⣿⣿⣿⣿⡆⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡿⣿⣿⣿⣿⠿⠿⢿⣟⡦⣀⠀⠀⡀⣼⣻⣿⣿⣿⣿⣿⣿⣿⣄⡱⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⡿⣻⠋⠀⠀⠀⠀⠉⠑⠯⠿⠽⠟⠚⠉⠀⠀⠉⠙⣿⣿⣯⣿⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⢫⠼⡱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢚⡿⣿⣿⣻⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⣿⣿⢥⠋⡔⢡⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠜⡼⣹⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠡⠘⢻⡌⠂⢌⡼⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣆⠃⡐⢧⣻⠿⣛⣆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣼⢳⠈⠁⠁⠀⡟⣤⠞⡐⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣮⠸⡄⢐⣲⠏⠡⣀⠻⣇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡼⠋⠁⠀⠀⠀⠀⡏⠀⡿⠑⡞⢀⡞⠉⢱⠤⣒⠮⣍⠲⠤⢤⠚⠳⡄⢠⡧⠤⡽⢋⠇⠀⠀⠀⠱⣫⢧⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢺⠁⠀⠀⠀⠀⠀⢰⠀⢠⡇⠀⠟⠀⢳⣚⡵⣉⣧⢚⠴⣩⣃⡺⡦⡤⠟⢸⠇⠠⢡⠀⠃⠀⠀⠀⠀⠈⠎⢇⠀⠀⠀ ⠀⠀⠀⠀⠀⢩⠀⠀⠀⠀⠀⠀⢠⠀⢸⠁⢰⠋⠀⢸⣧⠛⣭⡗⢹⡏⢲⡝⢫⣷⣿⠀⠀⡇⠐⢸⠀⠘⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀ ⠀⠀⠀⠀⠀⢣⣥⣄⡀⠀⠀⠀⡀⠀⡜⠠⢠⠁⡄⠘⣯⢷⠊⠀⠀⠀⠀⠱⣷⢺⡍⠀⡇⢱⠀⡘⠄⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⣟⣯⡏⠑⠢⢄⠇⢸⠃⢀⡃⠀⢣⠀⠈⠙⠢⢀⣀⡀⣀⠠⠛⠉⠀⠘⠀⢰⠀⡘⡀⢰⠀⠀⣀⢤⣦⣶⣎⠀⠀⠀ ⠀⠀⠀⠀⣸⣟⡾⣹⡇⠀⠀⠸⣰⠏⢀⡼⠀⠀⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠈⢇⠢⣑⡸⠐⠁⠀⢺⣿⣳⢿⠀⠀⠀ ⠀⠀⠀⢠⣿⣽⢳⣻⠅⠠⠀⣾⠏⢀⡼⠁⠀⣠⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠸⡄⠘⣖⡄⠀⠠⣹⢳⣯⢿⡆⠀⠀ ⠀⠀⠀⣼⣿⡞⣯⣽⢊⢄⣵⠏⠀⡞⠁⠀⢸⡥⣧⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣟⢦⠀⠀⢹⡀⠻⣇⠀⢒⣹⢗⡾⣟⣿⠀⠀ ⠀⠀⣼⣿⣷⣻⢷⣻⡦⣿⠏⠀⡾⠡⠀⠀⠠⣹⣿⣷⣿⣿⣿⢧⡙⣮⣿⣶⣿⣿⣟⣯⠒⠀⠀⠀⢷⠀⠻⣦⠒⣼⢯⡿⣽⣿⣆⠀ ⠀⣴⣿⣿⣳⢯⣟⡷⣿⠃⢀⡲⠍⠀⢡⠀⠀⣼⡿⣱⢎⠶⣩⢫⡝⡭⣭⠭⣍⠿⣽⡟⠀⠀⠠⠈⠸⣆⠀⢻⣳⣯⣟⣾⣳⣿⣿⠀ ⢰⣿⣿⢿⣽⣻⣞⡿⠁⠠⣠⣿⣷⢦⣀⠁⠀⣿⣓⠧⣎⢻⢧⡳⢎⡵⣺⠳⣬⢛⡼⣷⠀⠀⠀⢁⣠⣽⠄⠂⢽⣷⣻⣞⣷⣻⣿⣷