⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠇
⠀⠈⢿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠏⠀
⠀⠀⠈⢻⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣶⣶⣶⣾⣿⣿⣿⣿⣿⣶⣶⣶⣦⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠏⠀⠀
⠀⠀⠀⠀⢻⣿⣄⠀⠀⠀⠀⣀⣤⣶⣿⡿⢟⣿⣿⡿⠛⠋⠉⠀⠀⠀⠀⠈⠉⠛⠻⣿⣿⣿⠿⣿⣷⣦⣄⡀⠀⠀⠀⠀⣼⣿⠃⠀⠀⠀
⠀⠀⠀⠀⠀⠛⠋⠀⣠⣶⣿⠿⠛⠉⢀⣴⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣄⠈⠙⠻⢿⣷⣦⡀⠈⠛⠃⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⣴⣿⠿⠋⠁⠀⠀⢠⣿⡟⠁⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣧⠀⠀⠀⠉⠻⢿⣷⣄⠀⠀⠀⠀⠀
⠀⠀⠀⣠⣾⣿⠟⠁⠀⠀⠀⠀⢠⣿⡟⠀⠀⠀⠀⠀⢀⣴⣿⠿⠿⠿⠿⢿⣷⣄⠀⠀⠀⠀⠀⠘⣿⣧⠀⠀⠀⠀⠀⠙⢿⣿⣦⡀⠀⠀
⠀⢀⣴⣿⠟⠁⠀⠀⠀⠀⠀⠀⣾⣿⠀⠀⠀⠀⠀⣰⣿⠟⠁⠀⠀⠀⠀⠀⠙⢿⣷⡀⠀⠀⠀⠀⢸⣿⡆⠀⠀⠀⠀⠀⠀⠘⢿⣿⣄⠀
⣠⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡇⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣧
⠻⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿
⠀⠘⢿⣷⣄⠀⠀⠀⠀⠀⠀⠀⢿⣿⠀⠀⠀⠀⠀⠹⣿⣆⠀⠀⠀⠀⠀⠀⢀⣾⡿⠁⠀⠀⠀⠀⢸⣿⠇⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⠀
⠀⠀⠀⠙⢿⣷⣄⡀⠀⠀⠀⠀⠘⣿⣇⠀⠀⠀⠀⠀⠙⠿⣿⣶⣤⣤⣴⣾⣿⠟⠁⠀⠀⠀⠀⢀⣿⡟⠀⠀⠀⠀⠀⢀⣴⣿⠟⠁⠀⠀
⠀⠀⠀⠀⠀⠙⠿⣿⣦⣀⠀⠀⠀⠙⣿⣧⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⣠⣾⡟⠁⠀⠀⢀⣠⣾⡿⠟⠁⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣦⣄⡀⠘⢿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⠀⣀⣤⣾⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣶⣽⣿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣾⣿⣿⣵⣾⣿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀