⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣴⣿⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣷⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠈⠉⠉⠙⠻⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡿⠹⠉⠀⠉⢸⣿⣿⣿⢹⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⡀⠎⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣫⠖⠀⠀⠀⠀⣾⣿⣿⣿⠈⠿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣷⡄⠀⢀⣀⣠⣶⣗⡤⠀⠀
⠀⠀⠀⠀⠀⠀⢠⣾⣿⡷⠃⠀⠀⠀⠀⠀⢹⣿⣿⡏⠀⠀⠹⣿⣿⣷⣀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣶⣿⡿⠟⠛⠉⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣼⣻⣿⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⠀⠀⠀⠀⢻⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣼⢇⣿⠟⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣄⢀⣠⣴⣾⣿⡿⠛⠋⢹⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠐⣾⢸⡿⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣷⠄⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢠⣿⣸⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠁⠀⠀⣠⣴⣶⣾⣿⣿⣿⣿⣿⡏⠁⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢀⣿⣿⡇⠀⡄⠀⠀⠀⠀⠀⢸⣿⣿⠏⣀⣰⣿⣿⣿⣿⡿⠟⠋⠻⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢸⣿⢹⡇⢀⣷⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠿⠛⠁⠀⠀⠀⠀⠹⣿⣿⣿⣆⠄⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠠⣿⡸⣿⠘⣾⡇⢀⣠⣴⣿⣿⣿⡿⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣶⣧⡆⠀⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢻⣷⢻⣬⣾⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡿⣿⣿⣿⣾⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢀⡀⢠⣤⣿⣿⣿⣿⣿⣿⡟⠉⣹⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠠⣽⣿⣿⣿⣿⣿⣿⡻⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀
⠸⠿⡿⢹⢿⡿⠏⠀⠈⣿⣏⢿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢪⠶⠋⠀⠀⠀⠀⠈⠻⣷⣝⣿⣿⣿⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣾⣿⣿⣿⠿⠃⠈⠻⢿⣿⣿⣷⣀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⡛⠿⢿⣿⣿⣿⣷⣶⣶⣶⣿⣿⣿⣿⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠘⢿⣿⣿⣦⡀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⡟⠻⠷⢶⣤⣬⣭⣭⣭⣭⣽⣿⣿⠿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠯⠁⠉⠢⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡟⠇⠀⠀⠀⠀⠀⠈⠉⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⣿⢁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀