⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣿⣿⣧⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣿⡟⢻⣷⡀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣿⡇⠀⢻⣷⡄⠀⠀⢸⣿⡇⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣿⣿⠀⠀⠹⣿⡄⠀⢸⣿⡇⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠙⣿⣆⠘⣿⡇⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠘⣿⣶⣿⡇⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠈⢿⣿⡇⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣠⣾⡿⠛⠛⠛⠻⢿⣷⣄⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣸⣿⠋⠀⠀⠀⠀⠀⠀⠹⣿⣆⠀⠀⠀⠀
⠀⠀⠀⢀⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀
⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠀⠀⠀⠀
⠀⠀⠀⠀⣿⣷⠀⠀⠀⠀⠀⠀⠀⢀⣿⡿⠀⠀⠀⠀
⠀⠀⠀⠀⠸⣿⣧⡀⠀⠀⠀⠀⢀⣾⡿⠃⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠈⠻⢿⣶⣶⣶⣾⡿⠛⠁⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣿⣿⠛⠛⠛⠛⠿⣿⣦⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠘⣿⡇⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⢰⣿⡇⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣿⣿⣤⣤⣤⣤⣶⡿⠟⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣿⣿⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣿⣿⠛⠛⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣿⣿⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣿⣿⠛⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣿⣿⣶⣶⣶⣶⣶⣶⡆⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀