⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⢻⠿⢿⣿⣿⣿⣿⣿⣿⣶ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣾⣿⣿⣿⡿⠿⠟⠛⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠠⠾⠀⠀⠀⠉⠛⡿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡿⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⡿⠯⠙⠛ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⡇⠂⡀⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡋⡿⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣟⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⡇⢃⣀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⡿⣸⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠁⣼ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⠁⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⢀⣾⣿ ⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⠋⢷⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⣾⣿⣿ ⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⠇⠀⣼⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⡏⠀⠀⣿⣿⠹⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿ ⠀⠀⠀⠀⢰⣿⣿⣿⣿⡟⠀⠀⢠⣿⡏⠀⠈⢿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⡇ ⠀⠀⠀⣰⣿⣿⣿⣿⣿⠠⣀⠀⣸⣿⡇⠀⠀⠀⠹⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⡿⠐ ⠀⠀⣴⣿⣿⣿⣿⣿⠁⠀⠀⠉⣿⣿⣄⣀⡀⠀⠀⠈⠻⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⡄ ⠀⣼⣿⣿⣿⣿⣿⠏⠀⠀⠀⢸⣿⣿⠀⠉⠛⠷⣶⣦⣄⣙⣿⣿⣦⡀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⡟⠬⢆ ⠈⠙⠛⠛⠻⠿⡏⠀⠀⠀⠀⢸⣿⣿⠀⠀⣀⣀⣄⡉⠛⠿⣿⣿⣿⣷⣄⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⣉⣿⣿⣿⣿⣿⣿⠿ ⠀⠀⠀⠀⠀⢠⣴⣶⣷⣶⣄⣼⣿⣿⣾⣿⣿⣿⣿⣿⡇⠀⠀⠉⠙⠛⠛⠃⠀⠀⠈⠀⠀⠀⠀⣠⣤⣶⣶⣿⣿⣿⣿⠿⠟⢻⡿⠉⠠⠄ ⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠐⢦⣤⣇⡀⠀⠀⠀⠙⣿⣿⣿⣿⣋⠉⠀⠀⠀⢸⡧⢤⠀⠀ ⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⣠⠚⠀⠀⠀⠀⠈⠻⠿⠛⠛⠉⠀⠀⠀⠙⠛⠿⣿⣿⣦⣄⡀⢸⢷⠈⠀⠀ ⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⣼⡇⠀⠀⠀⠀⣀⣀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⢻⣿⣾⣮⣤⡀⡂ ⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣢⣄⡈⠛⠛⠛⠛⠛⠛⠛⣿⠛⠷⣦⣤⣤⣤⡾⠃⠀⠀⣀⢤⣾⠓⠉⡉⢙⠻⡛⡷ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⡿⠟⠁⠈⠻⢿⣷⣮⣓⠦⣀⡀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣦⡖⠿⢺⡿⣿⠤⠴⠶⠿⠞⠒⠆ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠀⣾⣿⣷⣦⡀⠉⠻⣿⣷⣶⣙⠷⣲⢼⣇⣤⣿⣿⣿⣿⣿⣿⣿⣿⣦⡢⢀⣀⣀⣀⣠⣤⣼⣾⣷ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣦⡀⢀⣽⣿⡿⡷⡿⠸⣃⣭⡭⠹⣿⣿⠿⠿⠿⠿⠿⠿⠛⠛⠛⠛⠛⠛⠛⠉⠉ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣷⣾⣿⠛⠒⠖⠏⢠⠋⠥⠥⠀⠘⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀