⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣶⣿⣿⣿⣿⣿⣿⠿⠿⢿⣿⣿⣿⣷⣿⣯⣴⣢⡤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣟⠻⠋⠙⠉⠈⠁⠀⠀⠀⠀⠀⠀⠁⠉⠛⠻⢿⣿⣿⣶⣯⣶⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢟⡿⣿⣷⡦⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⣿⣿⢟⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⢀⣄⡀⠀⠀⠈⠚⢿⣿⣮⡢⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣴⣿⡿⡵⠋⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣝⣢⣼⣿⢧⠇⠀⠀⠀⠀⠀⠙⢿⣿⣮⣢⡀⠀⠀⠀⠀ ⠀⠀⠀⣼⣽⣿⡿⠁⠀⠀⢰⣶⡢⣄⣼⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢽⣿⣿⣷⡁⠀⠀⠀⠀⠀⠀⠀⠀⠳⣿⣷⡱⡄⠀⠀⠀ ⠀⠀⢰⣿⣿⢷⠃⠀⠀⠀⠈⢿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡽⣿⢮⣗⡄⠀⠀⠀⠀⠀⠀⠀⢻⣿⣷⣽⡄⠀⠀ ⠀⠀⣿⣿⣿⡎⠀⠀⠀⠀⢀⣜⣿⢟⣿⡳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣟⠟⠁⠈⠙⠓⠛⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⡿⡀⠀ ⠀⣸⣿⣿⢳⠃⠀⠀⠀⠀⢸⣿⣯⠋⠻⣿⣾⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠤⢀⡀⠀⠘⡟⣿⣿⣷⡀ ⠀⣿⣿⣏⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢯⣿⣷⣮⡆⠀⠘⣞⣿⡟⣷ ⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⢻⠃⠀⠀⠀⢸⣿⣿⣘ ⣿⣿⣿⡟⠀⠀⣀⣤⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⡟⠀⠀⠀⠀⠈⣿⣿⠩ ⢿⣿⣿⠃⢠⣾⣿⢿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⣿⣿⠃ ⣸⣿⣿⡇⠀⠉⠹⣿⣷⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠀⠀⠀⠀⠀⢀⣿⣿⣶ ⣿⣿⣿⡇⠀⠀⠀⠸⡞⣷⣣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣬⣵⣦⡀⠀⠀⡼⣿⣿⠏ ⠻⣿⣿⣧⠀⠀⠀⠀⠙⢟⣷⣯⣷⣶⣶⣖⡢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡟⣿⣾⣻⣿⣿⣷⠀⢰⣿⣿⡾⠀ ⠀⣿⣿⡝⡆⠀⠀⠀⠀⠀⠙⠛⠿⠿⠿⣿⢿⣾⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣷⣍⣿⣿⣿⣿⡇⣴⣿⣿⣿⠃⠀ ⠀⠹⣿⣿⡜⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣽⣷⣌⠢⣀⠀⠀⠀⠀⠀⢀⣤⣲⣶⣖⣰⣿⣿⣯⠟⠙⢿⣿⣯⣽⣿⣿⣷⣿⢯⠏⠀⠀ ⠀⠀⠹⣿⣿⣬⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣾⣵⣶⣤⣴⣶⣿⣿⡿⠿⠿⠿⠿⠛⠁⠀⠀⠀⠉⠛⢓⣿⣿⣿⡣⠋⠀⠀⠀ ⠀⠀⠀⠈⢮⣿⣿⣕⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⠟⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⠻⣿⣿⣾⣷⣢⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⠝⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⢿⣻⢿⣿⣿⣭⣴⣢⡤⠤⣀⢀⣀⠀⠀⠀⠀⢀⣀⢀⣀⣠⠤⣴⣶⣿⣿⡿⢟⡿⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠻⠿⢻⣿⣿⣿⣿⣷⣾⣿⣿⣷⣿⣿⣶⣿⣿⣿⣿⣿⡿⠯⠟⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠈⠉⠉⠉⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀