⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣤⣺⣿⣿⡾⠿⠛⠛⠛⠛⠛⠛⠛⠻⠿⠷⣮⣽⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⣴⣿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠷⣿⣿⡒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀ ⠀⠀⠀⠀⠀⢴⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡉⠻⢷⣯⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣴⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠸⠿⣷⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⠟⠁⠀⠀⠉⠻⣿⣿⣆⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢰⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣦⣤⡀⠀⠀⣾⣿⠟⠁⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⣄⠀⠀⠀⠀⠀⠀
⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣷⣦⠀⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⢿⣿⣷⡀⠀⠀⠀⠀
⠀⠀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣦⣤⣄⡀⠀⠀⠀⠀⠉⠀⠉⢿⣄⡁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣷⠆⠀⠀⠹⣿⣷⡀⠀⠀⠀
⠀⢰⠇⠀⠀⠀⠀⠀⠀⢀⣤⡾⠿⠛⠛⠛⠻⢿⣿⣦⡀⠀⠀⠀⠀⣴⡟⠙⢿⣦⣀⣀⣀⣀⣀⣤⣶⣿⡟⠀⠀ ⠹⣿⣿⠀⠀⠀
⣤⣾⠀⠀⠀⠀⠀⢀⣴⠿⠋⠀⠀⠀⠀⠀⠀⠀⠹⣿⣷⠀⠀⢀⣼⣿⠇⠀⠀⠹⢿⣿⣿⣿⣿⣿⣿⣿⠄⠀⠀⠀⠀⠀⠹⣿⣧⠀⠀
⣿⣿⠀⠀⠀⠀⣠⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣀⣴⣿⣿⡿⠀⠀⠀⠀⠀⠙⢿⣿⣿⠟⡁⠟⠀⠀⠀⠀⠀⠀⠀⢹⣿⡆⠀
⣿⣿⠀⠀⢠⡾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣷⠀
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠿⠿⠟⠋⠀⠀⠀⠀⠀⠀⣀⣠⣤⣴⣶⣶⣦⣤⣄⡀⠀⢀⣤⡀⠀⠀⣿⢿⠀
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠇ ⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⠿⠟⠛⠛⠛⠙⠛⠛⠻⢿⣿⣽⢿⣦⣿⢸⠀
⢿⣾⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠏⠀⠀⠀⠀⢀⣴⣾⡿⠿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣬⣿⣿⣿⠇⣿⣾⠀
⠈⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡟⠁⠀⠀⠀⢀⣴⡿⡛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⢰⣿⡟⠀
⠀⢹⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⢸⡇⢠⣶⡟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡇⠀
⠀⠘⣿⣧⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁⠀⠀⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡇
⠀⠀⢹⣿⣧⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠙⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡟⣻⣿⠇⠀
⠀⠀⠀⠻⣿⣷⣄⠀⠘⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⠟⢠⣿⡿⠀⠀
⠀⠀⠀⠀⠙⢿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⠟⠁⣠⣿⣧⠁⠀⠀
⠀⠀⠀⠀⠀⠈⠻⢿⣿⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣡⣤⣾⡟⠀⠀
⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣶⣿⣿⣿⡷⠏⠛⠛⠉⠀⠀⠀
⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠹⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣾⣿⣿⣿⠿⠟⠛⣽⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣦⣄⡀⠀⠀⠀⢀⣸⣿⢿⣿⣅⠀⠀⣀⣤⣾⣿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⡻⢿⣿⣿⣿⣿⣿⡿⣯⣿⣿⣟⣿⣿⣿⢻⣿⢟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀