⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢀⣤⣶⡿⠟⠛⠛⠉⠉⠉⠛⠛⠛⠿⣶⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢠⣾⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢰⣿⠋⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣤⣶⡿⣿⣛⣛⣛⣛⡛⠛⠛⠻⠿⠿⣶⣤⣀⠀⠀⠀⠀⢀⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣿⣿⠿⠟⠛⠛⠛⠛⠻⠿⣷⣦⣄⣀⠈⠙⠻⣷⣦⡀⢠⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣷⣄⠀⠈⠛⣷⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢿⣇⢀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠘⢿⣆⠀⣼⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣠⣾⡿⠿⠛⠛⠛⠛⠛⠛⠛⠛⠻⠿⢷⣶⣤⣬⣋⣾⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠿⠟⠿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢿⣧⠀⠀⢀⣴⡿⠿⠿⣿⡆⣀⣀⣀⣀⣀⠀⠀⠀⠀⣼⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣀⣴⡿⠃⠀⠀⠀⢸⣿⠟⠛⠉⠙⢿⣷⡀⠀⣼⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠘⠿⣿⡿⠀⠀⠀⠀⢰⣿⠟⣴⡄⠀⠀⠀⠹⣿⣼⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢠⣿⠃⠀⠀⠀⠀⢸⣿⢠⣿⠇⠀⠀⠀⠀⢻⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢸⣿⠀⠀⠀⠀⠀⢸⣿⠘⣿⡄⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢸⣿⠀⠀⠀⠀⠀⠸⣿⠀⣿⡇⠀⠀⠀⠀⢠⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣿⡄⠀⠀⠀⠀⠀⣿⡆⠹⣿⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢻⣷⡀⢀⡀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣸⣿⡏⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢰⣿⠁⠀⢿⣧⠀⠀⠀⠀⠀⣠⣾⠟⠀⠛⠁⢻⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢸⣿⠀⠀⠘⠿⣷⣤⣤⣴⣾⠟⠁⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢿⣧⡀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⣠⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢿⣷⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠉⠛⠻⠿⣶⣶⣤⣤⣶⣶⣶⡾⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
