⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢰⣶⡆⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣠⣶⣿⡿⠿⣿⣷⣄⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀
⠀⠀⠀⢠⣿⣿⠁⠀⠀⠈⢻⣿⡇⠀⢸⣿⣧⣤⣤⠀⠀⠀
⠀⠀⠀⠈⣿⣿⣄⠀⠀⢀⣾⣿⠇⠀⢸⣿⡟⠛⠛⠀⠀⠀
⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⠿⠋⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢸⣿⣿⣤⣤⣤⣤⣤⣤⣤⣤⣤⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⡆⠀⠀⠀⠀
⠀⠀⠀⠀⣾⣾⣾⣾⣾⣾⣾⣾⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡏⣤⣤⣤⣿⣿⡇⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠁⠛⠛⠛⣿⣿⡇⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣠⣿⡿⠃⠀⣀⣀⣀⣿⣿⡇⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣠⣾⣿⠟⠁⠀⠨⠿⠿⠿⣿⣿⡇⠀⠀⠀⠀
⠀⠀⠀⠲⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠇⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⣶⣶⡆⠀⠀⠀⠀
⠀⠀⠀⠀⢀⣴⣿⠿⠿⠿⣿⣦⡀⠀⠀⣿⣿⡇⠀⠀⠀⠀
⠀⠀⠀⠀⣾⣿⠃⠀⠀⠀⠘⣿⣷⠀⠀⣿⣿⡇⠀⠀⠀⠀
⠀⠀⠀⠀⢻⣿⣦⡀⠀⢀⣼⣿⡟⠀⠀⣿⣿⡇⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠙⠻⠿⠿⠿⠟⠋⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣻⣿⡟⠛⠛⠛⠛⠛⠛⣿⣿⡇⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣽⣿⣇⣀⣀⣀⣀⣀⣀⣿⣿⡇⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠾⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠇⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡄⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣶⣶⣶⣶⣶⣶⣶⣶⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣿⣿⠀⠀⠀⢸⣿⣿⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣿⣿⠀⠀⠀⢸⣿⣿⠀⠀⢸⣿⣇⣀⣀⠀⠀⠀
⠀⠀⠀⠀⣿⣿⠀⠀⠀⢸⣿⣿⠀⠀⢸⣿⡟⠛⠛⠀⠀⠀
⠀⠀⠀⠀⣿⣿⣀⣀⣀⣸⣿⣿⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠿⠿⠿⠿⠿⠿⠿⠿⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⠇⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀