⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣶⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣷⣶⣤⡀⠀⢀⣤⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡟⠙⠛⢿⣿⣷⡀⠀⠀⠀⠀⣤⣾⣿⠏⠉⠻⣿⣷⣾⣿⠿⠛⠛⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡏⠀⠀⠀⠀⠙⣿⣿⠿⠿⠿⠿⢿⣿⡏⠀⣿⣶⣾⣿⣿⣦⣄⠀⠀⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡀⠀⣿⣿⡿⠋⠙⢿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⣶⣶⣤⡀⠀
⠀⣼⡿⠛⠃⠘⢻⣷⡄⠀⠀⠀⢠⣾⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣶⣾⣿⣷⣄⣠⣾⣿⣿⡄⣿⣿⡇⠀⢠⣟⠁⠀⠈⠛⣿⡆
⢠⣿⣷⡆⠀⠀⠘⠻⣿⡄⠀⢠⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠙⠻⠿⣿⣿⠛⣻⣵⣿⣿⣷⠀⠘⠿⣷⣀⡀⢾⣿⡇
⢸⣿⣤⣤⠀⣀⣀⣶⡿⠃⢀⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣷⣾⣿⠟⠹⣿⣧⠀⠸⠿⠙⠿⠿⠟⠁
⠀⠙⠻⣿⣶⣿⠿⠿⠇⠀⣸⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⢹⣿⡆⠀⠀⣀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣶⣾⣿⡿⠿⢿⣿⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠰⣾⡿⠿⢿⣿⡿⠿⠿⠆⢰⣶⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣶⠈⠉⣭⣄⣼⣿⣇⣀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣀⣀⠀⢰⣿⣿⣿⣿⠀⠀⠀⠀⣠⣤⣤⣤⠀⠀⠀⠀⢰⣿⣿⣿⣍⠀⠀⠛⣻⣿⡿⠿⠿⠇⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡿⠿⣿⣿⣛⣣⣾⡉⠉⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢉⣽⣿⣤⣴⣾⣿⣿⣶⣦⣄⣀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⠿⠿⢿⣿⣧⡀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⢀⣠⣿⣿⡛⠛⠻⣿⣿⡄⠉⠙⠻⠟⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡀⠀⢠⣤⠙⢿⣿⣿⣶⣶⣶⣶⣦⣤⣤⣤⣤⣶⣶⣾⣿⡿⠋⢩⣤⠀⠀⣼⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣙⣿⣿⣿⣿⡿⠀⠀⢸⣿⡏⠉⢹⣿⡉⠉⠉⠉⣽⣿⠋⢻⣿⡆⠀⠘⢿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡟⣿⣿⣿⣷⣦⢀⣾⡿⠀⠀⠈⢿⣿⣦⣤⣾⣿⠟⠀⠀⢿⣿⣄⣴⣾⣿⣿⡏⢿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣷⣿⣇⣿⣍⣿⣿⣿⠿⠿⠿⠿⣶⠿⠟⠛⠛⠿⠿⠿⠿⠿⣿⣿⣿⣯⣿⣻⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢻⣿⣿⣿⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢻⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀