⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣲⣾⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡇⠀⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡇⠀⣻⣿⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⢀⡼⠿⠇⠀⠀⠀⠀⠀⠿⠿⣀⢀⡀⣀⢀⡀⣀⡸⠿⠇⠀⠀⠀⠀⠀⠿⢿⡀⡀⠀⠀⠀⠀ ⠀⠀⠀⣀⡸⠿⠇⠀⠀⠀⣀⣀⠀⠀⠀⠀⠿⠿⠿⠿⠿⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⣀⣀⠿⠿⣀⡀⠀⠀ ⠀⠀⢸⣿⡇⠀⠀⠀⢠⣀⡿⠿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⣀⣀⣿⡷⠀⠀ ⠀⠀⢸⣿⡇⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣤⣿⣿⣿⡟⠀⠀ ⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⣿⡟⠀⠀ ⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠿⢿⡿⢿⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠻⡿⢿⡿⠀⠀⣿⣟⠀⠀ ⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣯⠀⠀ ⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣰⠿⠷⠀⢀⣀⣸⠿⠇⠀⢀⣀⡀⠀⠀⠀⠀⠀⣿⡷⠀⠀ ⠀⠀⠸⠿⢇⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⢸⣿⡇⠀⠀⠀⢸⣿⡇⠀⠀⠀⣀⣀⡿⠟⠀⠀ ⠀⠀⠀⠀⠸⠿⢇⣠⡄⠀⠀⠀⠀⠀⠀⠀⠿⠿⣄⣤⣤⣼⠿⢧⣀⣤⣤⡼⠿⠇⠀⣄⣠⡿⠟⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⣤⡞⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠀⠘⠛⠛⠛⠃⠀⠀⠀⠟⠛⣦⣄⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀ ⠀⠀⢠⣤⡞⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⣦⡤⠀⠀ ⠠⣤⣜⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⣤⡄ ⢘⣿⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇ ⢨⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⡇ ⠰⣿⡇⠀⠀⠀⠀⠀⠀⠀⢶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⠀⠀⠀⠀⠀⠀⣿⡇ ⢘⣿⡇⠀⠀⠀⠀⠀⢰⣶⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠀⠀⠀⠀⠀⠠⣿⡇ ⢈⣿⡟⠀⠀⠀⢰⣶⡞⠉⢽⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⣷⣶⣶⣶⣶⣞⠉⠁ ⠀⠈⢹⣿⣿⣿⣿⣿⡇⠀⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠁⠉⠈⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⡍⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⣷⣶⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⣷⣾⣿⣿⣿⣿⣶⡇⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⣷⣾⠋⠁⠉⠈⠀⠉⠈⢱⣾⡆⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⣿⡷⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⣿⣟⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡃⠀⠀⠀⠀⠀⣿⡯⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠽⢿⠿⡿⢿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⠿⡿⢿⠿⠁⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠁⠿⢿⡿⠿⢿⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠿⢿⡿⠿⢿⠽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⡇⣿⢸⠀⠀⠀⠀⠀⠀⠀⡯⣿⠀⠀⠀⠀⠀⡃⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⡇⣿⢸⠀⠀⠀⠀⠀⠀⠀⣟⣿⠀⠀⠀⠀⠀⡇⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⡇⣿⢸⠀⠀⠀⠀⠀⠀⠀⡷⣿⠀⠀⠀⠀⠀⡇⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⡆⣾⢱⠈⠉⠀⠈⠉⠁⠋⣾⣷⠀⠀⠀⠀⠀⡇⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⡇⣶⣿⣿⣿⣿⣾⣷⠀⠀⠀⠀⠀⠀⠀⡇⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣶⣷⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⡍⣶⢰⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠉⠁⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢻⠀⡇⣿⣿⣿⣿⣿⢹⠈⠀ ⠁⠉⣞⣶⣶⣶⣶⣷⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢽⠉⡞⣶⢰⠀⠀⠀⡟⣿⢈ ⡇⣿⠠⠀⠀⠀⠀⠀⣿⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣶⢰⠀⠀⠀⠀⠀⡇⣿⢘ ⡇⣿⠀⠀⠀⠀⠀⠀⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⢶⠀⠀⠀⠀⠀⠀⠀⡇⣿⠰ ⡇⣿⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣿⢨ ⡇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⣿⢘ ⡄⣤⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠛⣜⣤⠠ ⠀⠀⡤⣦⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠛⡞⣤⢠⠀⠀ ⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⢸⠀⠀⠀⠀ ⠀⠀⠀⠀⣄⣦⠛⠟⠀⠀⠀⠃⠛⠛⠛⠘⠀⠛⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠛⡞⣤⢠⠀⠀⠀⠀ ⠀⠀⠀⠀⠟⡿⣠⣄⠀⠇⠿⡼⣤⣤⣀⢧⠿⣼⣤⣤⣄⠿⠿⠀⠀⠀⠀⠀⠀⠀⡄⣠⢇⠿⠸⠀⠀⠀⠀ ⠀⠀⠟⡿⣀⣀⠀⠀⠀⡇⣿⢸⠀⠀⠀⡇⣿⢸⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⢇⠿⠸⠀⠀ ⠀⠀⡷⣿⠀⠀⠀⠀⠀⡀⣀⢀⠀⠇⠿⣸⣀⢀⠀⠷⠿⣰⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⢸⠀⠀ ⠀⠀⣯⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⢸⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⢸⠀⠀ ⠀⠀⣟⣿⠀⠀⡿⢿⡿⠻⠀⠀⠀⡀⣀⢀⠀⠀⠀⠀⠀⠀⠀⢿⡿⢿⠿⠀⠀⠀⠀⠀⠀⠀⡇⣿⢸⠀⠀ ⠀⠀⡟⣿⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⡇⣿⢸⠀⠀ ⠀⠀⡟⣿⣿⣿⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⢸⠀⠀⠀⡇⣿⢸⠀⠀ ⠀⠀⡷⣿⣀⣀⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠿⡿⣀⢠⠀⠀⠀⡇⣿⢸⠀⠀ ⠀⠀⡀⣀⠿⠿⣀⣀⠀⠀⠀⠀⠀⠀⠀⠇⠿⠿⠿⠿⠿⠿⠿⠀⠀⠀⠀⣀⣀⠀⠀⠀⠇⠿⡸⣀⠀⠀⠀ ⠀⠀⠀⠀⡀⡀⢿⠿⠀⠀⠀⠀⠀⠇⠿⡸⣀⡀⢀⣀⡀⢀⣀⠿⠿⠀⠀⠀⠀⠀⠇⠿⡼⢀⢀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⡇⣿⢸⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⡇⣿⢸⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡀⣿⣻⠀⡇⣿⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣿⣿⠀⡇⣿⣸⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⢿⠀⡇⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⡇⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣾⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣾⣲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀