⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣷⣶⣿⣿⣟⡗⢀⣀⣤⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣷⣤⣤⣤⣤⣄⣤⣤⣀⣀⡀⠀⠀⠸⣿⠈⠉⠀⠻⠿⢿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⡇⠀⠀⠀⠀⠁⠁⠁⠙⠛⠛⠋⠛⠳⠟⠷⣦⡤⣄⣀⣼⠋⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠿⢶⣴⡦⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⣠⣿⣟⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⢀⠞⠁⢸⡹⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⣠⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⡔⠁⠀⠀⣾⡆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣾⡏⠀⢰⣿⣿⡇⠀⠀⠀⠀⠀⠀⣰⣿⣷⠀⠀⠀⡜⠀⠀⠀⢸⠀⠀⠀⢀⣿⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⠅⠀⠀⠹⠿⠃⣆⣀⣀⠀⠀⢸⣻⣿⣿⠀⠀⠀⠃⠀⠀⠀⡎⠀⠀⠀⣸⡟⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⡹⠀⠀⠀⠀⠀⠀⠸⣤⠏⠀⠀⠀⠹⠿⠛⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⣠⣟⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠃⠀⠀⣼⡟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡇⠀⠀⠀⠀⠀⠀⠸⡟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡻⠶⠒⠋⡳⣄⠀⣀⡤⢶⣄⠀⠀⠀⢀⡀⠀⠀⠀⠏⠀⠀⠀⠀⠀⠀⢠⡞⠑⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠎⣿⣿⢅⠀⠻⣷⣤⣶⡫⢿⣶⣄⣤⣖⡶⣶⣤⣄⣀⣤⣬⣇⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣟⣿⡑⠮⣥⣾⣁⣀⣄⣼⣿⠿⠋⠁⠀⠈⢻⣿⣷⣝⡻⢏⡥⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢜⣾⣧⣴⣾⣿⡏⢻⣦⣞⠋⠁⠀⠀⠀⠀⠀⠀⢿⣿⣿⣯⡙⠛⠺⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣵⣿⣿⠉⠉⢹⠉⣷⣿⠛⠛⠓⢦⣄⡀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣮⣢⢀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⢪⣾⣿⣿⣿⠀⢔⡼⢄⡟⢻⡠⢄⣠⢮⣀⠉⠳⣦⣄⣀⠀⠈⢿⣮⡻⢿⣿⣷⣕⢄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⢾⡟⢱⣿⢿⠀⠉⠀⠲⣿⣿⠃⠀⠾⠈⠾⠀⣠⣿⣾⣾⣷⣦⣌⣿⣿⣦⡉⠛⢿⣷⡵⡀ ⠀⡠⣐⣆⣢⢄⠀⠀⢪⢧⣟⠍⠏⣧⣤⣤⢠⣿⣿⣄⣀⡀⠀⢀⣼⡞⠛⠛⠛⡿⣿⣿⣿⣿⡛⠿⢦⣄⠈⢿⣵ ⢸⣾⠃⠀⠈⢳⣣⠀⠀⣉⣀⠘⣷⣾⠟⠻⢿⣽⣟⣻⣉⣽⢿⠺⢿⣦⣤⣀⡀⠘⢿⣿⢿⣿⢿⣦⡢⡪⣳⡀⡇ ⠸⢻⣆⠀⠀⠈⢗⠛⠒⣖⠉⠉⠁⣿⠀⠀⠀⠹⡟⢶⡚⠛⠛⢿⣾⣿⣿⣿⣿⣷⣾⣇⡀⠀⣈⣿⣿⣮⣅⠿⡣ ⠀⢫⢻⡆⠀⠀⠈⠀⠀⢸⡀⠀⠀⠹⣆⠀⠀⠀⢣⠀⢳⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣛⠛⠛⠛⠛⠛⠋⠂ ⠀⠀⢣⢿⡄⠀⠀⠀⣀⡠⣧⣄⣀⣀⣻⡄⠀⠀⠀⠀⢸⡇⠀⠀⢸⣿⣿⣿⣿⣿⢟⣛⣛⡻⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠙⠛⠓⠒⠒⠉⠉⠁⠀⠀⠀⠘⠿⡤⠤⠤⠌⠛⠓⠒⠒⠛⠛⠛⠛⠋⠉⠉⠉⠓⠒⠂⠀⠀⠀⠀⠈⠁