⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣶⣾⣾⣿⡿⣷⣿⣶⣶⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⣴⣿⣿⣿⣿⣿⣻⣽⣞⣿⣽⣾⢯⣿⡽⣟⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠐⠻⠋⠉⠀⠀⠀⠀⠉⠛⠻⣿⣾⣽⣻⢷⣿⢿⣳⣯⣿⣻⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣯⣿⢾⣟⣿⣻⣽⡷⣯⣟⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣿⣾⢯⣟⡷⣿⣻⣽⣾⣻⣿⣆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣯⡿⣽⡷⣟⣷⢯⣷⣟⣿⣦⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⢯⣟⣿⢾⣻⡷⣯⣟⣿⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣿⢻⡟⣾⡟⣯⣿⣽⣾⣿⣷⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⢿⣻⣽⣿⣽⢯⣟⣯⡿⣽⡾⣿⣿⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⢿⣻⡾⣟⣯⣿⣿⣯⡿⣯⣷⢿⣯⣟⣿⣿⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣀⣿⠁⠀⠀⠀⠀⣠⣶⣿⣿⢿⣻⡾⣟⣯⣟⣯⣷⣿⠟⢿⣿⣳⣯⡿⣾⣽⣻⣿⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⣾⠏⠀⢀⣠⣶⣿⣿⣿⢿⣽⣻⢯⣟⡿⣽⣾⠟⠋⠁⠀⣸⣿⡷⣯⢿⣳⣯⣿⣿⡇⠀⠀⠀⠀ ⠀⠀⠀⢀⣾⣿⠀⢠⣿⣿⢿⣯⢿⣿⣻⢾⣻⣯⣿⠿⠋⠀⠀⠀⠀⠀⡄⣿⣟⣿⣻⢯⣷⢿⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⣼⣿⡇⠀⢸⣿⣿⣻⢾⣟⣷⣻⣿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠆⣿⣯⣿⣻⢯⣿⣿⡏⠀⠀⠀⠀⠀ ⠀⠀⣸⣿⣿⡇⠀⠈⣿⣿⡽⣿⡾⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡆⢠⣿⣷⢯⣟⣿⣳⣿⠀⠀⠀⠀⠀⠀ ⠀⢀⣿⣿⣿⡇⠀⠀⢹⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⣀⢀⣤⣶⣿⣿⠇⢸⣿⣯⢿⣻⣞⣿⡏⠀⠀⠀⠀⠀⠀ ⠠⣸⣿⣿⣿⣷⠀⠀⠈⠻⠃⠀⠀⠀⠀⠀⠀⢀⣼⣷⣿⣿⣿⣿⡿⠀⣼⣿⢯⣟⣯⣿⡟⠀⠀⠀⠀⠀⠀⠀ ⠰⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣟⣯⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⡿⣽⡾⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀ ⠠⢻⣿⣿⣿⣿⣿⣿⣷⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉⠀⣾⣿⣽⡷⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉⠀⠀⠀⣸⣿⣟⡾⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣀⠀⠀⠀⠀⢀⣿⡿⣞⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣶⣤⣼⣿⣻⣟⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣷⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣾⣽⣿⣿⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠿⢿⣿⣟⣷⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⢯⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⣿⡇⠀⠀⠀⠛⠻⢿⣿⣿⣿⣿⣧⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣟⣿⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⣿⣿⣷⡆⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣷⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣯⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣷⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⢿⣿⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠙⠿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⡀⠙⠛⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀