⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣶⣿⣿⣿⣿⣷⣶⣶⣦⣄⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⠿⠛⠋⠉⠉⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣤⣤⣤⣄⣀⣀⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣀⣤⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣀⡤⠴⠖⠛⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣻⣿⣿⣿⣿⣿⣿⠉⠙⠛⢿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⡿⠃⠀⢠⣶⣾⡟⢻⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⠿⣿⣿⣿⠟⠀⠀⠀⠀⢈⣠⣤⣾⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠁⣼⣿⡿⠁⠀⠀⠀⠀⠀⠈⠛⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡀⢿⣿⡇⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⡏⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠹⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⣾⡷⠄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⡿⣋⣜⠀⠀⠀⠀⠀⠀⠀⠀ ⠉⠉⠛⠶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⡃⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⠻⣷⣦⣄⡀⠀⠀⠀⣿⣿⣮⡙⠯⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡈⠻⣿⣿⣷⣄⣤⣾⣿⣿⣯⠓⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⠙⣾⡞⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⣸⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⢠⣤⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⢿⣿⣿⣿⣿⠿⢿⣧⣤⡶⠞⠿⣷⢲⣄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠉⣽⣿⡟⠀⠀⠉⠁⠀⠀⠀⡸⠃⠃ ⠀⠀⠀⠀⠀⠀⠀⢀⣰⡇⠀⠀⣠⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣿⣿⠇⠀⢠⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⠟⡟⠀⢸⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠁⠁⣰⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⣷⡤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⣀⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢰⣶⣿⣿⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠛⠛⠛⠛⢿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⡿⠛⢻⣿⣿⠀⠉⠛⠛⠿⠿⠿⣿⣿⣿⣿⣿⣿⡟⠉⠉⠁⠀⠈⠉⠉⠛⠛⠿⠿⢿⣿⣷⣶⣶⣶⣤⣤⣤⡴⠶⠂ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⠀⠀⢈⣿⣿⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⢻⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⠀⠀⣸⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠘⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠀⢀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡆⠈⠻⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣷⠀⠀⣸⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡠⠊⠻⣀⣠⣤⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠰⠁⠈⠁⠀⢀⡠⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⢐⠒⢂⣄⡀⠀⠀ ⠀⠀⠀⡞⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⡡⠊⠀⠀⠀⠀⠉⠓⠄ ⢰⠀⠀⠑⢄⣀⣀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠘⣄⠀⠀⠀⠀⠀⠀⠈⠑⠠⠄⣀⡀⠀⠤⠐⠊⠀⡜⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠱⡀⠠⡀⠀⠑⠀⠀⢠⠀⠀⠄⠀⠀⠀⢀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡙⢢⠨⢙⣉⠄⠃⢠⠀⠀⢈⡤⠐⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢿⣿⡄⠹⢾⡲⢠⢸⡀⠀⠐⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠐⠝⢞⠁⠈⡀⠈⢆⠀⠀⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠑⡄⢑⠄⠀⠁⠒⠀⠌⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣀⣀⡠⡪⣵⠁⠀⠀⠀⠀⠀⡸⢈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣓⠧⠭⡝⠁⠀⠀⠀⠀⠀⠘⢳⡷⢌⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⢀⣤⠀⣠⣾⡆⢀⣴⣶⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⡀⣸⣿⡇⠻⠿⠇⠻⠿⠷⢠⣶⣿⡟⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣷⠀⣠⣴⣶⣿⣿⣿⣷⣶⣦⣉⡛⡀⠿⡿⢀⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡘⢗⣤⣾⣿⢻⢹⡅⡇⡏⢺⣿⣿⣿⠿⢾⢶⢤⣬⣡⣀⣀⠀⣆⢔⣄⡴ ⣀⣴⣶⠾⠿⢁⡾⡝⡸⠀⡇⡇⠇⣸⠛⡟⠂⠀⠀⠀⠈⠀⠉⠙⠛⠛⠛⠛⠉⠀ ⠈⠉⠁⠀⠀⢸⠇⢱⠀⠀⠁⠁⢠⡧⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠜⠀⠼⠀⠀⠀⠀⠰⠇⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⣰⣶⣄⠀⠀⠀⠀⣠⣤⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⠀⠀⣠⣾⣿⣿⣿⠀⢀⣴⣿⣿⣿⡟⠀⠀⠀⠀⠀⢀⣀⣴⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣧⠀⣿⣿⣿⣿⣿⠀⢾⣿⣿⣿⣿⡇⠀⢀⣴⣶⣶⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⡄⠀⢰⣿⣿⣿⣿⠀⠈⠉⠛⠛⠉⠀⠀⠙⠛⠛⠛⠃⠰⣿⣿⣿⣿⣿⡟⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣆⡀⠉⠉⠉⠀⣀⣴⣤⣷⣾⣷⣿⣾⣶⣿⣴⣦⣦⡄⢈⠙⠿⠿⣿⠇⢠⣾⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣀⠀⢿⣿⠿⠁⢀⣀⣾⣾⣿⣿⣿⣿⣿⣿⢿⣿⡿⢿⣿⣿⣿⣿⣿⣶⣤⡄⢀⡄⠈⠛⠻⠿⠃⢠⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢿⣷⡄⠀⠀⣤⣼⣿⣿⢿⣿⠻⣿⡏⠈⣿⠀⣿⡇⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣾⣠⣶⠀⣀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⣴⠀⠀⣴⢀⠀⠀⣠ ⠀⠀⠀⠀⠀⠀⢶⡌⠋⣡⣼⣿⠿⣿⣿⣿⠀⣿⠀⢹⡇⠀⣿⠀⣿⠃⠘⢿⣿⣿⣿⣿⠿⠿⠟⢻⠿⣿⠻⡿⠻⣿⢷⣷⣶⣶⣴⣦⣤⣀⠀⠀⣿⣶⠟⣡⣧⣤⣾⠋ ⠀⠀⢀⣀⣀⣀⣠⣿⣿⣿⠻⠃⣴⣿⡟⢻⡇⢿⠀⢸⡇⠀⣿⠀⣿⠀⠀⣾⡿⢿⣿⣿⣆⠀⠀⠀⠀⠈⠀⠁⠀⠘⠀⠉⠙⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠁⠀ ⣠⣴⣿⣶⣿⡿⠛⠋⠻⠙⠀⢸⡟⠹⣧⠸⡇⢸⡇⢸⡟⠀⡏⠀⠟⠀⣰⡿⠁⢸⣿⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠚⠛⠛⠉⠁⠀⠀⠀⠀⠀⢸⣇⠀⠸⣧⠁⠈⠇⠸⠇⠀⠇⠀⠀⢠⣿⠁⠀⠈⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠀⠀⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠃⠀⠀⠻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣧⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠘⠛⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠀⠀⠀⠴⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡼⡿⠙⣿⡿⡀⠀⠀⠀⠀⠀ ⣀⡀⠀⠠⢇⣀⠆⠀⠀⢳⣄⠀⠀⠀⠀ ⠛⠁⣤⣐⣤⠥⠤⠀⠀⠈⢫⣀⠀⠀⠀ ⠀⠀⠉⢂⡇⠀⠀⠈⢄⠳⡌⡇⡀⠀⠀ ⠀⠀⠀⠀⢣⠀⢀⠀⢀⠉⠀⠈⢢⣆⡀ ⠀⠀⠀⠀⠒⠥⠺⠤⠼⠀⠠⠤⠜⠚⠉

⠀⠀⠀⠀⢀⣴⣿⣿⣿⣷⣄⠠⣤⣤⣤⣤⣤⣤⣄⣀⡀⠀⠀⠀ ⠀⠀⠀⣀⣼⣿⡟⠉⡉⠻⣿⣷⣮⣿⣿⣿⣿⣿⣿⡿⠿⢷⣦⠀ ⠀⢠⣾⣿⣿⣿⣷⡀⣿⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⣸⣿⣧ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢰⣿⣿⣿⣿⣿⣿⣍⠉⠿⠋⠹⠟⠛⢿⡿⢿⣿⠿⢿⡿⠻⠟⠀ ⢸⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠘⠁⠀⡿⠀⠘⠁⠀⠀⠀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣴⣶⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣤⣀⣠⡄⠀⠀⠀ ⠀⣿⣿⣿⣟⡿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣿⣿⠿⠃⠀⠀ ⠀⠘⣿⣿⣿⣿⣶⣶⣦⣤⣶⣶⣶⣆⠈⠉⠉⠉⠉⠁⠀⠀⠀⠀ ⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠙⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠄⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣿⣿⣿⣿⣿⠟⠛⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⣂⣿⣿⡿⠟⣡⡞⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⢋⣴⣼⣿⣥⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⡠⠔⠂⠈⠁⠀⠀⠈⠉⠉⠛⠻⢿⣶⣶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠿⣿⣿⣿⣎⢃⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣷⣌⠉⠻⣿⡟⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣶⣤⣀⡀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣦⡁⠙⢈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣷⣄⠀⢀⣠⣼⣿⣿⣿⣿⣿⣿⡏⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣦⡄⠀⣸⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡏⠉⢹⣿⣿⣶⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠸⣿⣿⠇⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣏⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⢀⣤⣀⣀⣴⠏⠉⡉⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⢿⣿⣿⣆⣤⣶⣾⣿⠿⠿⠿⣿⣿⡖⠛⣿⣦⣀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠟⠁⠙⢿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠙⢿⡿⠿⠟⠋⠁⠀⠀⠀⠀⠉⣻⣦⠸⣿⠏ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡟⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡾⠟⠀⠋⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡏⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⡇⠀⠀⠀⠀⢠⣶⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⡇⠀⠀⠀⠀⣾⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⡿⠿⠁⠀⠀⢀⣼⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣧⠀⠀⠀⣴⣾⣿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⡟⠉⣿⠋⠀⠀⢀⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠇⠀⠹⠄⠀⢠⣾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣧⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⡿⢿⡿⠻⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣀⣀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠿⠿⠟ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣤⣴⣶⣶⣶⣤⣿⡿⠁⠀⠀⠀ ⣀⠤⠴⠒⠒⠛⠛⠛⠛⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⣿⣿⣿⡟⠻⢿⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⢿⣿⠟⠀⠸⣊⡽⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⡁⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣿⣷⣶⣿⣷⣶⣤⣄⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆ ⠀⢠⣴⠾⠛⠛⠛⠛⠲⠦⠤⠴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡛⠛⠛⠿⠿⠃ ⢠⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣴⣶⣾⣿⣿⣿⣿⣷⣶⣤⣀⣀⣠⣾⣿⣿⣿⣿⣿⡿⠿⠿⣿⣿⣿⣷⣦⣄⠀⠀ ⠈⣿⣿⣶⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠙⠛⠋⠀⠀ ⠀⠘⢿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠉⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠻⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠙⣷⣆⠘⢿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⡟⠛⠛⠛⠛⠋⠀⣿⣿⣿⣿⠀⢤⡇⣽⠇⠀⠈⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⠀⠀⠉⠁⠀⠐⢰⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠿⣿⣿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠙⠻⠟⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⢻⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠈⠿⠿⢇⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣿⣷⣶⣤⠀ ⢰⡎⠉⠉⠑⠂⠁⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⣤⣄⡀⢀⣼⣿⣿⣿⣿⣯⣍⡉⠁ ⠘⣿⣶⣤⣤⣄⣀⣀⣠⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠉⠁⠀ ⠀⠀⠙⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⠫⣅⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠟⠉⠉⠁⢿⣿⠐⠝⠀⣸⠆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠋⠁⠀⠀⠀⠀⢸⣿⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠷⠦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⠘⠿⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣴⣶⣶⣶⣶⣶⣦⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⡿⠿⠛⠛⠋⠉⠉⠉⠉⠉⠙⠛⠻⠿⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⣾⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⣀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣾⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣴⣾⣿⣿⣿⡿⣶⣦⡀⠀⠀⠀⠀⠀⠈⠻⣿⣦⡀⠀⠀⠀ ⠀⠀⢠⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣤⣿⣿⣿⣿⣿⣿⣿⣆⠘⣿⠟⣷⣦⣄⡀⠀⠀⠀⠘⣿⣷⡀⠀⠀ ⠀⢠⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣤⣽⣿⣿⣿⣿⣿⣿⣿⡋⢠⣿⡧⠈⠙⣿⣿⣿⣶⣦⡄⠘⣿⣷⡀⠀ ⠀⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣴⣯⣩⣿⣿⣿⣿⣦⠘⣿⣧⠀ ⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠉⠉⠉⠛⢻⣿⢿⡿⡿⡿⢿⡟⠀⢻⣿⡄ ⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣳⠀⠀⠀⠹⠋⠛⠽⠟⠋⠋⠀⠀⢸⣿⡇ ⣿⣿⠀⠀⠀⠀⠀⠀⠀⢀⡀⣦⣪⣿⣿⣿⣿⣿⡿⠹⠹⣿⣿⣿⣿⣷⣓⣴⢀⡀⡀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇ ⣿⣿⠀⠀⠀⠀⠀⣤⣳⣶⣿⣿⣿⣿⣿⣿⡏⡿⠃⢀⡀⠈⠉⠛⠻⠿⣿⣷⣽⣟⠷⠶⡄⠀⠀⠀⠀⠀⢸⣿⡇ ⢸⣿⡆⣤⣄⣻⣷⣿⣿⣿⣿⣿⣿⡿⣿⡁⠇⠁⠀⢻⡞⠉⠀⠀⠀⠀⠀⠙⠻⠿⠟⠛⠀⠀⠀⠀⠀⠀⣸⣿⠇ ⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣄⣠⣠⡴⠿⣣⣿⡵⠧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡿⠀ ⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⠿⣿⣿⣿⣿⣴⡞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠃⠀ ⠀⠀⠹⣿⣿⣿⣿⣿⣿⢻⠿⣆⠘⠢⡘⠘⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⠃⠀⠀ ⠀⠀⠀⠙⣿⣿⣿⡏⠙⢦⣣⠈⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣀⢀⣦⣀⠀⢀⣠⣾⡿⠃⠀⠀⠀ ⠀⠀⠀⠀⠈⠻⣿⣧⡀⠀⠉⠣⡀⠀⠀⣠⣤⣀⣠⣤⣐⣴⣷⣅⣤⣦⣟⣿⢿⣸⣿⣿⣾⣿⣿⠟⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠉⠻⣿⣷⣄⣀⣴⣦⣤⣽⣟⣙⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⣠⣶⣶⠶⠖⠒⠒⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⠞⠁⠙⠏⢀⣀⣠⣤⣤⢬⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡰⠃⠀⠐⠒⠉⠉⠉⠉⠉⠉⣩⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀ ⢀⠃⠀⠀⠀⠀⠀⠀⣀⣀⠤⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⣉⠥⠄⠀⠩⠽⢶⣤⣀⠀⠀⠀ ⢸⠀⠀⠀⠀⣼⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢋⡴⠋⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⢦⡀ ⠘⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⢠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡇⠀⠀⠀⠀⠑⢤⣀⣀⣀⣠⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠒⠁⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠘⣷⠀⠀⠀⠀⠀⠀⠠⣀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠒⠒⠒⠒⠂⠉⠁⠀⠀⠀⢀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠹⣆⠀⠀⣄⠀⠀⠀⠈⠑⢄⠀⠀⠀⡴⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠙⢦⡀⠈⠑⠢⢤⡤⠄⠀⢱⠀⢰⠁⠀⠀⠀⠈⢆⠀⠀⣀⡠⠔⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢰⠏⢹⣶⠒⣋⡥⣤⡄⠊⠁⠀⢸⡆⠀⠀⠀⠀⣸⠶⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢿⣿⣿⣿⡀⠘⣿⣶⡷⢤⢄⣀⠀⡇⠀⠀⠀⠀⢼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠙⠻⠿⢧⠱⣤⡼⣧⡞⠀⢾⡉⠻⢦⡀⠀⠀⠈⠓⠲⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠒⠛⢿⡁⠀⠀⠠⡇⠀⠀⠙⣄⠀⠀⠀⠀⠈⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣄⠀⠑⢄⠀⠀⠈⠓⠤⢄⣀⣀⡀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠃⢀⠼⠀⠀⠀⠀⠀⠀⠀⠀⠹⡀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡤⢋⣍⣴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢰⣟⢻⠋⢿⠭⠋⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣿⣰⠀⡎⠣⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⣉⡙⠒⢚⣒⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⡧⠻⠤⠿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣤⠶⠛⠉⠉⠁⠀⠉⠉⠛⠳⣦⣀⠀⠀⠀⠀ ⠀⠀⣴⠟⠁⠀⠀⠀⠀⢀⣤⣶⣤⡀⠀⠀⠙⢷⡀⠀⠀ ⠀⣾⠃⠀⠀⠀⠀⣐⣾⣿⣿⣿⢆⣯⠳⣦⣤⣈⢻⡄⠀ ⣸⠇⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⡟⠛⠶⣷⣿⣿⡇⣿⠀ ⣿⠀⠀⠀⠀⢀⣸⣿⣿⡿⢿⣿⣿⣄⠈⡉⠉⠉⠀⢸⡆ ⢿⣀⣠⣴⣷⣿⣿⡟⠉⢠⠆⠉⠉⠻⠿⠿⠀⠀⠀⣼⠃ ⠸⣿⣿⣿⣿⡿⣿⣷⣶⡺⠞⠃⠀⠀⠀⠀⠀⠀⢠⡟⠀ ⠀⠹⣿⣿⢟⠗⠀⠈⠉⠁⠀⠀⠀⢀⠀⣀⠀⣠⡟⠁⠀ ⠀⠀⠈⠳⣤⡀⣀⣰⣶⣶⣴⣷⣶⣿⣷⣿⡿⠋⠀⠀⠀ ⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⡿⠿⠛⠉⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣶⣶⣶⣿⣿⣿⣿⣿⣿⣷⣶⣶⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⡿⠿⠛⠋⠉⠁⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠈⠉⠛⠻⠿⣿⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣶⣿⣷⣶⣦⡀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⢶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠘⢿⣶⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠀⠘⣿⣿⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣰⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠰⣶⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⣸⣿⡀⠙⢿⣿⣷⣦⣄⡀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣦⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣴⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⣠⣀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⣴⣿⣿⡇⠀⠀⠙⢿⣿⣿⣿⣷⣶⣤⣀⠀⠀⠻⣿⣿⣿⣷⡀⠀⠀⠀ ⠀⠀⠀⣼⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⢀⣼⠟⠛⢿⣿⣿⣿⣿⣷⣦⡀⠹⣿⣿⣿⣷⡀⠀⠀ ⠀⠀⣼⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠠⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠻⠿⢿⣿⣿⣿⣿⣶⣶⣾⣿⣿⣿⣿⣿⣿⣷⣄⠹⣿⣿⣿⣷⠀⠀ ⠀⢰⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⢰⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠉⢹⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⢹⣿⣿⣿⣇⠀ ⠀⣾⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⢠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠄⠀⠀⠀⠀⠀⠙⠙⠱⠃⢿⣿⣿⣿⡿⣭⠙⠋⠀⠀⠀⢿⣿⣿⣿⡀ ⢠⣿⣿⣿⡇⠀⠀⣴⣄⢠⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡇⢹⠙⣿⣿⣿⣿⣿⣿⣿⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠈⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇ ⢸⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠁⡇⠈⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣧⣁⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿ ⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢻⣿⢁⠏⠘⠀⡇⠀⠀⠀⠀⠀⠈⠙⠛⠿⣿⣿⣿⣿⣾⣼⣧⣦⣴⢃⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿ ⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⣿⣿⠀⢸⠇⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣠⡄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠄⠸⡟⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⡟ ⠘⣿⣿⣿⣿⣿⣿⣿⠋⠛⣿⣿⣶⣄⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⡇ ⠀⢿⣿⣿⣿⣿⣿⣿⣷⣤⣿⣿⡉⠙⣿⣦⣴⡶⢰⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠁ ⠀⠘⣿⣿⣿⣿⡟⠉⢻⣿⡿⢿⣷⣶⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⢀⣠⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⠇⠀ ⠀⠀⠹⣿⣿⣿⣇⠀⠀⢻⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⢸⣧⣴⠖⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡟⠀⠀ ⠀⠀⠀⠹⣿⣿⣿⣆⠀⢸⢇⠀⠀⢿⣿⣿⣿⣿⡿⣿⡛⠀⠀⠀⠀⠀⣠⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⡿⠁⠀⠀ ⠀⠀⠀⠀⠹⣿⣿⣿⣧⡀⠀⠣⡀⠘⣿⠃⣿⣿⠇⣿⣧⣀⣀⣀⣤⠾⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⡟⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣆⠀⠱⣤⡿⠆⠉⠉⠀⠈⠙⠻⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⠏⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣷⣄⣹⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣄⣀⣀⣴⣿⣋⣉⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣛⠛⠋⠉⠙⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣾⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣿⣿⣷⣶⣤⣤⣀⣀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣤⣶⣶⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠻⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⡠⢤⠖⠒⠢⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣰⠕⠁⣞⣯⡆⢁⠚⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⡠⠞⠊⠀⠀⠹⠋⠁⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢰⠙⠸⠀⠀⠀⠀⢀⣼⡇⢀⡀⠇⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠘⡄⠀⠀⡀⣀⢴⣿⡟⢁⠜⠀⠘⢖⣇⣤⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠘⢖⣩⣾⣿⡻⡯⢺⠈⠀⠀⠀⠀⠈⠘⠚⠼⢜⡇⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠛⠭⣾⠤⢼⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢾⢤⠀⠀⠀⢀⡠⣾⠿⠷ ⠀⠀⠀⠀⠀⣜⡻⢓⣤⡠⠒⡡⠀⠀⠀⠀⠀⠀⠀⠀⠈⢪⣲⣠⡐⡜⣽⠃⠀⠀ ⠀⠀⠀⠀⠀⠀⠡⣿⡟⢧⡀⠐⢄⠀⠀⢠⠏⠀⠀⠀⠀⠀⠉⠓⢉⢜⠆⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⢳⡀⠀⠑⠠⠃⠀⠀⠀⣠⣂⣀⠠⠔⡡⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⠄⣀⣑⣦⣄⠀⠈⡦⠐⠒⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡏⠀⠎⢀⣼⠙⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠅⠹⠤⠜⢰⣏⣣⠤⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⣶⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠿⣿⣿⣿⣿⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢈⣻⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣤⣤⣴⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠙⠛⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠠⠐⠤⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠉⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣄⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠿⠟⠻⢿⣿⣿⣟⠛⠛⠛⠛⠛⠛⠻⠶⣤⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣷⠀⠀⠀⠙⠿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠉⠓ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣿⡇⠀⠀⠀⠀⢸⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣶⣿⣿⠀⠀⠀⢀⣠⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠉⠉⠋⠉⠀⠀⠀⠐⠺⠿⠿⠟⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣤⣤⣀⡀⠀⠀⠀⣀⣄⣄⡀⢀⠂⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣽⣿⣿⣿⣷⣇⣀⠔⠁ ⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡜⠀ ⠀⠀⠀⠀⠀⣠⣾⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠻⠿⠿⠋⠀ ⠀⠀⠀⣠⣾⡿⠟⠋⠁⠀⠙⢿⣿⣿⣿⡿⠿⠟⣿⣿⣿⡉⠀⠀⠀⠀⠀⠀⠀⠀ ⠐⠒⠛⠉⠁⠀⠀⠀⠀⠀⠀⢸⣿⣿⡟⠀⠀⠀⢻⣿⢻⣧⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⠟⠛⠂⠀⠀⠸⢿⠄⠙⠿⠦⠀⠀⠀⠀⠀⠀

⠀⠀⠀⢀⣠⣶⣿⣿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠊⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠹⢿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣀⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣼⣶⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⣸⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠙⠟⠀⣘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠟⠉⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣶⣤⣀⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣟⡛⠛⠛⠉⠉⠉⠻⣿⣿⣿⣿⣿⣯⣉⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠻⢿⣷⣤⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠷⣄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠈⠛⠻⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠟⠛⠛⣹⠿⠿⠛⠋⠉⠉⠀⠀⠀⠀⠀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠛⠛⠋⠟⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⣴⣀⣤⣦⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢠⣴⠿⠛⣿⣿⠋⠻⣿⣟⠻⠿⠿⢿⣿⣿⣶⣶⡦⣤⣀⡀⠀ ⢰⣿⣧⣴⣦⢿⣿⣷⡦⠘⣿⠀⠀⠀⠀⣹⠉⣿⣿⣿⣶⣬⣷⠀ ⠘⠟⢻⣿⠋⠀⢿⣿⣷⣼⣿⣷⣤⣤⣴⣿⣿⣿⣿⣿⣿⣿⢿⠃ ⠀⠀⢠⣿⣶⣶⣿⣿⣿⣿⠟⠉⠉⠙⠻⠟⡿⢻⢿⢻⡏⠏⠀⠀ ⠀⣾⣿⣿⣿⣿⣿⣿⣿⣧⣤⣀⡀⠀⠀⠀⠁⠈⠘⠈⠀⠀⠀⠀ ⠀⠈⠉⠳⣾⣿⣿⣿⣿⣿⣿⣿⣿⣦⣶⣄⢠⢰⣴⢠⠀⣄⠀⠀ ⠀⠀⠀⠀⠈⠙⠿⣿⣝⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣷⡟⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠛⠛⠛⠛⠛⠻⠿⠟⠋⠀⠀⠀

⢀⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⠉⠙⢿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢻⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⢿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣷⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢰⣿⠋⢻⡇⠈⠉⠙⣿⣿⣿⡏⠀⠀⠈⠉⠉⠛⠛⠓⠒⠒ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣾⠁⠀⠀⠀⣿⡇⠻⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠟⠀⠀⠀⠀⠚⠛⠀⠚⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⢾⣿⣷⣤⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⡟⠻⠿⠂⠼⢿⣿⡿⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⣤⠀⠀⠀⠈⠻⢴⠃⠀⠀⠀⠀⠀⠀⠀ ⢰⣤⡆⠀⠀⠠⡏⠙⠧⣤⠉⠀⠀⠀⠀⠀⢸⣷⡤⠀⠀⠀⠀⠀⠀ ⠈⠛⠁⢠⣤⣄⡙⢢⣤⠤⠤⠤⠄⠀⠀⠀⠀⢹⣄⣀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠻⣍⠉⣽⠁⠀⠀⠀⠀⣄⠀⢳⡀⠘⢿⡋⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢹⣯⠀⠀⠀⠀⠀⠘⢦⡈⠻⡏⠀⡷⢤⠄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⡀⠀⠀⠀⡉⠉⠁⠀⠙⢣⣀⣤⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⢧⣀⠀⢧⠀⠀⢀⡇⠀⠀⠀⠀⠀⣿⡷⣦⣤ ⠀⠀⠀⠀⠀⠀⠀⠺⠧⠬⠟⠿⠦⣀⡼⠦⠤⠤⠤⠤⠤⠾⠛⠋⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣄⣀⡀⠀⠀⠀⠀⠀⣦⣴⣿⣦⣶⣆⣀⠀⢀⣼⠃⠀⠀⠀⢠ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⢸⣿⣿⣿⣿⣿⣿⣿⢏⣠⡾⠁⠀⠀⢀⣴⠏ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣀⣤⡶⠟⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣅⠀⢀⡶⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⠿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⠿⠟⠃⠈⠉⠙⠻⠿⠛⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⡿⠟⠉⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣀⣤⣾⣿⣿⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠈⠹⣿⣿⣿⣿⣿⣿⣿⡏⠉⠉⠉⠉⠉⢿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣤⣤⣶⣿⠿⠿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣹⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠈⢿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡟⢿⣿⣿⢦⠀⠀⠀⠀⠀⠀⢹⣿⣷⡀⠀⠻⢿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠟⠂⠀⠁⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⠟⠂⠀⠀⠙⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣶⣾⣿⣿⣿⣿⣷⣶⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣴⣾⠿⠛⠉⠁⠀⢀⣠⣤⣄⠀⠉⠙⠛⠿⣿⣦⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣾⡿⠛⠁⠀⢠⣘⣷⣿⣿⣿⣿⡟⢳⣦⣀⠀⠀⠈⠛⣿⣷⣄⠀⠀⠀ ⠀⠀⣰⣿⠟⠀⠀⢀⣰⣶⣿⣿⣿⣿⣿⣿⣃⣰⡧⠙⢿⣶⣤⣀⡈⠻⣿⣦⠀⠀ ⠀⣰⣿⠋⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣦⣼⣉⣿⣿⣿⣦⡹⣿⣧⠀ ⢠⣿⡏⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⡦⠀⠀⠘⠿⠻⣿⣿⣿⠿⠁⢹⣿⡆ ⣼⣿⣤⣰⣦⣷⣿⣿⣿⣿⡟⠙⠙⢿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣷ ⣿⣿⣿⣿⣿⣿⢿⡟⠹⠈⡄⠀⠀⠀⠈⠙⠻⢿⣷⣶⣦⣄⢀⠀⠀⠀⠀⠀⣿⣿ ⢹⣿⣿⣿⠿⣿⣈⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠀⠀⠀⠀⢠⣿⡿ ⠘⣿⣿⡟⣷⣿⣌⣷⣶⣾⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠇ ⠀⠹⣿⣆⠘⡀⢹⣿⣿⣿⠇⠀⠀⣹⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡟⠀ ⠀⠀⠹⣿⣧⡀⢄⡇⠛⠙⠦⠖⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⠀⠀ ⠀⠀⠀⠈⠻⣿⣾⣧⡀⢀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣭⣈⣀⠀⠀⠀⠀⣀⣀⣤⣴⣾⡿⠟⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⠿⢿⣿⣿⡿⠿⠿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⣠⡮⠷⠴⠾⢭⣦⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡴⠋⠁⠀⠀⢐⣩⢕⠈⠙⢦⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⣿⣷⣾⡇⠀⠀⢹⡙⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣸⠁⢠⣤⡀⠀⠀⠀⠙⠻⠟⠁⠀⠀⠀⢷⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣿⠀⠿⠶⣇⡤⢴⢒⣛⣝⣏⠉⢸⣧⠀⠸⣖⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠸⡄⠐⣎⣹⣷⣿⣾⣿⣿⠿⢧⠞⢻⡄⠀⣧⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣖⠒⠢⣧⠀⢸⣿⣿⣿⣿⠏⠀⠀⢀⢤⢸⡇⠀⣻⣠⠶⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠘⢦⡀⢸⠀⠀⣿⣿⣿⣿⣀⢦⣤⣼⡠⠿⠁⠀⡿⠁⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠙⢾⡆⠀⠓⠛⠚⠓⠊⠉⠉⠀⠀⠀⠀⠞⠁⣠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡇⠀⠀⡠⢊⣉⡉⠗⢄⠀⠀⠀⠀⠀⠀⢳⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⡔⡇⠀⢰⢁⠀⠤⠤⠤⠘⡄⢠⠞⠋⠀⠐⠛⠿⠧⣤⣠⣀⢄⠀⠀⠀⠀ ⠀⠀⢸⢀⡇⠀⠘⡄⠀⠀⢒⣒⠀⣇⡏⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠓⠶⣷⣄ ⢀⣴⣚⣸⣁⣀⣀⣧⣴⣶⣤⣤⢴⣿⣁⣀⣀⣹⡤⣄⣀⣤⠤⠤⠶⠒⠚⠉⠉⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠒⣆⣰⠛⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣯⡷⠚⠉⠉⠉⠉⢷⣦⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⠤⣴⠋⠀⠀⠀⠀⢠⣤⠀⠱⣳⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⣾⠃⠀⠀⠐⠿⠇⣈⣉⣤⣄⣿⠆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⠤⡟⠀⠀⠀⠀⣤⢞⣯⠧⠇⠳⠋⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⠶⡇⠀⠀⠀⣼⠃⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⢀⣧⣖⡮⠭⢭⣄⣈⢻⡆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⢇⠀⠀⠀⣯⢤⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⢸⠀⠀⠀⠘⢾⣋⣇⢶⣤⢤⢠⢲⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⣤⣠⣬⣿⣀⠀⠀⠀⠀⠉⡛⠾⠿⠾⠿⢾⣦⣤⣤⠀ ⠀⠀⠀⢰⢽⡋⠄⠀⠉⠛⡀⠀⠀⠀⠀⣀⠀⠀⠀⢸⢸⣃⣨⣿⠃ ⣧⡀⠀⠈⠚⢛⣶⣤⣤⣤⡶⠀⠀⠀⠀⠀⠀⡨⢄⢸⣿⠀⠀⠀⠀ ⠙⢿⡛⠿⠍⠛⠉⢡⡏⠁⠀⠀⢠⣀⣀⣠⡄⠓⠀⢸⣿⠀⠀⠀⠀ ⠀⠀⠙⠶⢤⣤⣤⡾⣿⢤⡤⡤⢼⡏⠉⣿⠥⡤⢦⠼⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁⠀⠈⠉⠉⠉⠉⠉⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⠀⣀⣤⣆⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠸⣿⣿⠷⠸⡄⠀⠀⠀⢀⣀⣤⣼⠥⢤⣤⣄⣷⡀⠀⠀⠀⣠⠶⠛⣧⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠙⠁⠀⠀⢀⣠⡶⠛⠉⠁⠀⠀⠀⠀⠀⠀⠉⠙⠓⢶⣏⠁⠀⠀⡏⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣆⣐⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣾⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⠆⠀⠀⠀⠀⠀⠀⠈⢻⡅⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⡞⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡖⠚⠉⠉⣻⠂ ⠀⠀⠀⢸⣧⣤⣤⡤⠶⠶⣶⠒⠒⣻⣿⠛⢛⣿⡛⠛⢻⡗⠒⢶⡄⠀⠀⠀⢿⠀⠀⣰⠏⠀ ⣤⣴⣾⣻⠿⣦⡟⠻⢦⡾⠉⠳⠞⠉⠙⢷⠋⠀⠛⠶⠋⢳⡶⠛⣇⠀⠀⠀⠘⣇⢠⠏⠀⠀ ⠙⠻⢿⡏⠀⢰⣶⡄⠀⢠⠀⡀⢠⡀⢴⣶⡆⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀⠀⣿⠏⠀⠀⠀ ⠀⠀⢸⠁⢰⠨⡍⠁⠀⢿⡼⠿⠾⠃⠈⠉⠠⠰⠀⠀⠀⠀⠀⢘⣿⠀⠀⠀⠀⢸⣀⣠⣤⡄ ⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢸⡅⠀⣼⠀ ⠀⠀⠀⠙⣦⣀⣄⢀⡀⠀⢀⠀⠀⣀⠀⢠⣄⠀⢠⣄⣠⢶⣀⣼⠁⠀⠀⠀⠀⣀⣇⢠⡇⠀ ⠀⠀⠀⠀⢸⣿⣽⣏⣹⣴⣋⣳⣞⣉⣷⣏⣈⣻⡿⠬⠿⠖⠛⠁⠀⠀⠀⠀⠀⢹⣹⣾⠁⠀ ⠀⠀⠀⠀⠈⢿⣆⠈⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⠀⠘⡇⢿⡀⠀ ⠀⠀⠀⠀⠀⠀⠻⣷⠶⠤⠤⣤⣄⣀⡤⠤⠤⠤⠤⠶⠶⠂⠀⠀⠀⠀⠈⢳⣄⣠⣷⠀⠻⣄ ⠀⠀⠀⠀⠀⠀⠀⢸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣙⣁⣀⣈⣹

⠀⠀⠀⠀⢀⡤⢤⣀⣀⡤⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣠⠚⣩⣽⣷⡾⢮⢜⣶⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣰⠏⣀⠛⣗⣯⡺⣥⣽⣞⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢰⠃⢀⣽⢢⡙⠻⣿⡻⡻⢿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⠀⡞⡽⣦⣭⣂⠻⣿⣿⣯⠠⠌⠋⣒⡒⢦⠤⢤⣄⣀⣀⣠⣴⠏ ⠘⣄⡇⡴⠡⣾⠛⢧⠈⠷⡿⠺⠉⣆⠠⠄⠀⠈⠀⢁⣨⣬⠾⠋⠀ ⠀⠘⢿⣴⣀⢿⠀⠤⠉⠋⡆⠀⡄⠉⣦⠴⠚⣛⡭⠝⠊⠁⠀⠀⠀ ⢰⣿⣺⢵⣕⢄⢡⣘⣄⣸⠁⠀⡇⠀⣷⡴⠊⠀⠀⠀⠀⠀⠀⠀⠀ ⠘⠋⠀⢹⣹⣗⣧⣷⠀⣘⣆⡆⠃⢰⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠙⠫⡈⠻⠭⠁⠈⠳⣓⢄⠃⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⣔⠡⢰⡇⠀⠀⠀⠀⢹⣧⣌⣰⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣠⢮⠉⣾⡚⢁⣿⠃⠀⠀⠀⣠⠲⣟⠃⡝⢵⢤⡀⠀⠀⠀⠀⠀ ⠀⠓⠚⢺⡋⠼⠛⠉⠀⠀⠀⢰⣋⣹⣏⢺⢻⣣⠱⣇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠁⠀⠉⠉⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠠⠤⠤⠤⠤⠤⠠⠤⠤⠀⠂⠢⠖⠰⠀⠀⠠⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣀⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⡞⠋⠛⠋⣽⢻⢧⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⣿⠉⠀⠀⠀⠀⠈⠟⠀⢷⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣸⡞⠋⠁⠀⠀⠀⣲⡄⠀⢰⣾⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢶⣻⠀⠀⠀⠀⠀⠘⠀⢾⡖⠂⣈⡷⠀⠀⠀⢴⣶⣦ ⠀⠀⠀⠀⠀⢀⣀⡟⠀⠀⠀⠀⠀⠐⠢⠤⠤⢵⣶⣛⣁⣦⣴⠤⠈⠋⠁ ⠀⠀⠀⠀⠀⠈⣷⠏⠀⢀⡇⠀⣸⠀⠀⠀⠀⠀⢹⡀⢀⣹⠟⠀⠀⠀⠀ ⠀⠀⠀⠀⢤⣼⡏⠀⣿⠟⢠⡼⠃⠀⠀⠀⠀⠀⠈⣿⡉⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⡀⣸⠟⠁⠀⠙⠒⠋⠀⠀⠀⢀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀ ⣀⣀⡼⣿⠃⠀⠀⠀⠀⠀⢳⠀⠀⠀⢸⠀⠀⣠⣾⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⠒⠤⣄⣀⣀⣀⣀⣀⣀⣸⡄⠀⢀⣿⣴⣞⣃⣼⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀