⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢤⣄⠀⠀⢰⠏⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⢶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⡀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠈⠳⣤⠏⠀⣸⠀⠀⠀⣀⣀⡤⠴⠚⠋⠁⠀⠙⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢤⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠑⣆⠀⠀⠀⠀⠸⡅⠀⠀⠀⠀⠮⠷⠴⠓⠊⢙⣭⠁⠀⠀⠀⠀⠀⠀⠀⢰⢿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⠛⢸⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠸⢆⠀⠀⠀⠀⠹⣄⠀⠀⠀⡀⠀⠀⠀⢀⡿⢻⡆⠀⠀⠀⠀⠀⢀⣠⠎⢸⣀⠀⠀⠀⠀⠀⢀⣰⠛⠀⢀⠉⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠸⣆⠀⠀⠀⠀⢈⡷⡶⠦⢷⡄⠀⠀⣾⠋⠉⠙⢦⡀⠲⡖⠚⠉⠁⠀⠀⠈⠑⠒⠒⠒⠚⠈⠀⠀⠀⠼⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠈⠓⣆⣠⠐⠊⢀⡇⠀⠈⣿⡀⢰⡟⠀⠀⠀⠀⢻⡄⢡⠀⢀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⠈⠘⢷⣼⣄⣠⣼⠉⣿⡿⠁⠀⠀⠀⠀⠈⣷⣾⣿⣿⣿⣇⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠠⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠤⠄⠊⠉⠁⠀⠀⠀⠀⠀⠀⠀⠐⣾⣿⣿⣿⠃⠀⠈⡇⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠈⠩⠍⡉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢻⣿⣿⡟⠀⠀⠐⡇⠀⢀⠀⠀⠀⠀⢸⣿⣿⣿⠟⣛⡆⠀⠀⠀⠀⠀⠀⠀⠀⠸⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠉⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢻⢀⣿⢿⠇⠀⢰⡆⡇⠀⣿⠀⠀⠀⠀⢸⠻⣿⣿⣾⠋⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠂⠒⠦⢤⡄⠀⠀
⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⢸⡸⣆⡀⢸⠀⠀⠸⡇⡇⠀⣿⠀⠀⠀⠀⢸⡆⢸⣷⣿⢠⡇⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡖⠒⠈⠁⠀⠀
⠀⠀⠀⠀⠀⠙⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣷⣾⡁⢸⠀⠀⠀⠁⡇⠀⣿⠁⠀⠀⠀⣸⠀⠈⠹⠇⢸⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⣠⠚⠁⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⣠⠞⠋⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠄⠘⣧⠀⠀⠀⡇⠀⠀⠀⠀⠀⢠⡇⠀⠀⣷⣴⣿⣿⣿⣿⣿⡟⠉⠳⣄⠀⠼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⣟⠀⠀⠀⠘⣿⣿⣿⣿⠋⠀⠈⢻⣟⠀⠀⠈⠳⣤⣾⢧⠀⠀⠀⠀⣠⡾⠀⠀⠀⢸⣿⣿⣿⣿⣿⠋⠀⠀⠀⠈⠻⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⢹⣿⣿⡇⠀⠀⠀⣸⠏⠙⠲⠤⢴⣿⡇⠈⢳⣶⣖⣚⣉⠠⠤⠖⠂⠉⢻⣿⣿⣿⡿⢄⣀⠀⠀⠀⠀⠈⠳⣀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⡀⠤⠟⠁⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠸⣿⣿⠃⠀⠀⢰⡿⠂⠀⠀⠀⢿⢿⠇⠀⢸⠻⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⠋⠀⠀⠈⠛⢦⣀⠀⠀⠀⠨⡖⠒⢒⣲⠄⠀⠀⠀
⠀⠀⠘⠣⡄⢀⣤⡤⠤⣤⣄⡀⠀⠈⣷⣠⠖⠛⠛⠃⠀⠀⣰⡏⠀⠀⠀⠀⠀⠀⢸⠀⠀⠘⡆⠉⠀⠀⠀⠀⠀⠀⠀⢸⣿⠁⣀⣠⣤⣤⣤⣤⣬⣇⠀⠀⢀⣧⠖⠛⠁⠀⠀⠀⠀
⠀⠀⠀⠀⠉⣏⠀⠀⠀⠀⠀⠉⠛⠒⠟⠁⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⢸⣠⡀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠟⠋⠀⠀⠀⠀⠀⠀⠈⠀⠲⡏⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠙⣄⣀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⢸⠀⠀⠀⠀⠀⠘⣿⡽⢠⠇⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⢀⣴⣿⣷⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣇⠉⠉⠉⠉⠉⢳⠀⠀⠀⠀⢠⠀⠀⠀⠀⠘⠶⠬⣦⡀⠀⠀⠀⠀⠘⠦⠾⠀⠀⠀⠀⠀⠀⠀⠀⡞⠂⢹⣿⠟⠁⣠⡴⣦⠀⠀⢀⣤⣶⠋⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠈⢧⣀⣀⣀⡼⣤⣀⣄⣀⠀⠀⠀⠈⠙⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠛⢠⡞⠁⠀⣰⠟⣰⠃⠀⢀⡏⠀⠙⢤⣀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠉⠳⣆⣀⣠⡴⠛⢷⣄⣀⡀⠐⠂⣀⠀⠀⠀⣀⣠⠞⠁⠀⠈⢳⣄⣼⠇⠀⡇⠀⠀⣼⠀⠀⠀⠀⠈⠒⠒⢦⣀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣤⡄⠉⠁⠀⠀⠀⠀⠉⠉⠓⠒⠒⠒⠒⠋⠉⠀⠀⠀⠀⣀⣸⣧⡀⠀⠀⠙⠒⠚⠁⠀⠀⠀⠀⠀⣀⣀⣀⡤⠤⠬⠇
⠀⠀⠀⠀⠀⣯⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣶⣦⣤⣀⣄⣀⡀⠀⠀⢀⣀⣀⣠⣀⣠⣤⣴⣾⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⢠⠤⠒⠋⠉⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢀⡼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⢀⣠⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⡿⠟⠉⠉⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠻⠛⠛⠉⠉⠉⢉⣻⣿⣿⣿⣿⣿⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢀⣰⠁⠀⢀⣀⣀⠀⢀⣀⡀⠀⠀⠀⢀⣴⣿⣿⣿⠿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣴⣶⣾⣿⣿⣿⡿⡟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠦⠴⠂⠋⠉⠀⠀⠀⠀⠀⠉⣣⣤⣾⣿⣿⣿⣿⣿⣦⣀⠀⢀⣀⣠⠤⠤⠤⢤⡀⠀⠀⠀⠀⣀⡴⠋⠁⠀⠈⠛⠻⣿⣿⣿⣿⣿⣶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⠉⠀⠀⠀⠀⠀⠀⠹⡄⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢯⡛⢻⠛⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠛⠛⡟⠉⢉⠤⠼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢬⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠓⡴⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢤⣄⠀⠀⢰⠏⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⢶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⡀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠈⠳⣤⠏⠀⣸⠀⠀⠀⣀⣀⡤⠴⠚⠋⠁⠀⠙⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢤⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠑⣆⠀⠀⠀⠀⠸⡅⠀⠀⠀⠀⠮⠷⠴⠓⠊⢙⣭⠁⠀⠀⠀⠀⠀⠀⠀⢰⢿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⠛⢸⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠸⢆⠀⠀⠀⠀⠹⣄⠀⠀⠀⡀⠀⠀⠀⢀⡿⢻⡆⠀⠀⠀⠀⠀⢀⣠⠎⢸⣀⠀⠀⠀⠀⠀⢀⣰⠛⠀⢀⠉⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠸⣆⠀⠀⠀⠀⢈⡷⡶⠦⢷⡄⠀⠀⣾⠋⠉⠙⢦⡀⠲⡖⠚⠉⠁⠀⠀⠈⠑⠒⠒⠒⠚⠈⠀⠀⠀⠼⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠈⠓⣆⣠⠐⠊⢀⡇⠀⠈⣿⡀⢰⡟⠀⠀⠀⠀⢻⡄⢡⠀⢀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⠈⠘⢷⣼⣄⣠⣼⠉⣿⡿⠁⠀⠀⠀⠀⠈⣷⣾⣿⣿⣿⣇⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠠⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠤⠄⠊⠉⠁⠀⠀⠀⠀⠀⠀⠀⠐⣾⣿⣿⣿⠃⠀⠈⡇⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠈⠩⠍⡉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢻⣿⣿⡟⠀⠀⠐⡇⠀⢀⠀⠀⠀⠀⢸⣿⣿⣿⠟⣛⡆⠀⠀⠀⠀⠀⠀⠀⠀⠸⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠉⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢻⢀⣿⢿⠇⠀⢰⡆⡇⠀⣿⠀⠀⠀⠀⢸⠻⣿⣿⣾⠋⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠂⠒⠦⢤⡄⠀⠀
⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⢸⡸⣆⡀⢸⠀⠀⠸⡇⡇⠀⣿⠀⠀⠀⠀⢸⡆⢸⣷⣿⢠⡇⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡖⠒⠈⠁⠀⠀
⠀⠀⠀⠀⠀⠙⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣷⣾⡁⢸⠀⠀⠀⠁⡇⠀⣿⠁⠀⠀⠀⣸⠀⠈⠹⠇⢸⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⣠⠚⠁⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⣠⠞⠋⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠄⠘⣧⠀⠀⠀⡇⠀⠀⠀⠀⠀⢠⡇⠀⠀⣷⣴⣿⣿⣿⣿⣿⡟⠉⠳⣄⠀⠼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⣟⠀⠀⠀⠘⣿⣿⣿⣿⠋⠀⠈⢻⣟⠀⠀⠈⠳⣤⣾⢧⠀⠀⠀⠀⣠⡾⠀⠀⠀⢸⣿⣿⣿⣿⣿⠋⠀⠀⠀⠈⠻⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⢹⣿⣿⡇⠀⠀⠀⣸⠏⠙⠲⠤⢴⣿⡇⠈⢳⣶⣖⣚⣉⠠⠤⠖⠂⠉⢻⣿⣿⣿⡿⢄⣀⠀⠀⠀⠀⠈⠳⣀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⡀⠤⠟⠁⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠸⣿⣿⠃⠀⠀⢰⡿⠂⠀⠀⠀⢿⢿⠇⠀⢸⠻⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⠋⠀⠀⠈⠛⢦⣀⠀⠀⠀⠨⡖⠒⢒⣲⠄⠀⠀⠀
⠀⠀⠘⠣⡄⢀⣤⡤⠤⣤⣄⡀⠀⠈⣷⣠⠖⠛⠛⠃⠀⠀⣰⡏⠀⠀⠀⠀⠀⠀⢸⠀⠀⠘⡆⠉⠀⠀⠀⠀⠀⠀⠀⢸⣿⠁⣀⣠⣤⣤⣤⣤⣬⣇⠀⠀⢀⣧⠖⠛⠁⠀⠀⠀⠀
⠀⠀⠀⠀⠉⣏⠀⠀⠀⠀⠀⠉⠛⠒⠟⠁⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⢸⣠⡀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠟⠋⠀⠀⠀⠀⠀⠀⠈⠀⠲⡏⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠙⣄⣀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⢸⠀⠀⠀⠀⠀⠘⣿⡽⢠⠇⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⢀⣴⣿⣷⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣇⠉⠉⠉⠉⠉⢳⠀⠀⠀⠀⢠⠀⠀⠀⠀⠘⠶⠬⣦⡀⠀⠀⠀⠀⠘⠦⠾⠀⠀⠀⠀⠀⠀⠀⠀⡞⠂⢹⣿⠟⠁⣠⡴⣦⠀⠀⢀⣤⣶⠋⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠈⢧⣀⣀⣀⡼⣤⣀⣄⣀⠀⠀⠀⠈⠙⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠛⢠⡞⠁⠀⣰⠟⣰⠃⠀⢀⡏⠀⠙⢤⣀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠉⠳⣆⣀⣠⡴⠛⢷⣄⣀⡀⠐⠂⣀⠀⠀⠀⣀⣠⠞⠁⠀⠈⢳⣄⣼⠇⠀⡇⠀⠀⣼⠀⠀⠀⠀⠈⠒⠒⢦⣀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣤⡄⠉⠁⠀⠀⠀⠀⠉⠉⠓⠒⠒⠒⠒⠋⠉⠀⠀⠀⠀⣀⣸⣧⡀⠀⠀⠙⠒⠚⠁⠀⠀⠀⠀⠀⣀⣀⣀⡤⠤⠬⠇
⠀⠀⠀⠀⠀⣯⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣶⣦⣤⣀⣄⣀⡀⠀⠀⢀⣀⣀⣠⣀⣠⣤⣴⣾⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⢠⠤⠒⠋⠉⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢀⡼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⢀⣠⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⡿⠟⠉⠉⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠻⠛⠛⠉⠉⠉⢉⣻⣿⣿⣿⣿⣿⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢀⣰⠁⠀⢀⣀⣀⠀⢀⣀⡀⠀⠀⠀⢀⣴⣿⣿⣿⠿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣴⣶⣾⣿⣿⣿⡿⡟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠦⠴⠂⠋⠉⠀⠀⠀⠀⠀⠉⣣⣤⣾⣿⣿⣿⣿⣿⣦⣀⠀⢀⣀⣠⠤⠤⠤⢤⡀⠀⠀⠀⠀⣀⡴⠋⠁⠀⠈⠛⠻⣿⣿⣿⣿⣿⣶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⠉⠀⠀⠀⠀⠀⠀⠹⡄⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢯⡛⢻⠛⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠛⠛⡟⠉⢉⠤⠼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢬⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠓⡴⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀