⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣦⡀⠀⠀⠀⠀⠀⠀⢀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣩⢕⢦⡀⠀⠀⢀⡴⡏⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣻⣴⡿⠿⠿⢿⡷⣷⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⢋⡎⠀⠀⠑⠀⠹⡟⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢁⣾⠀⠀⢠⡌⡆⠀⢹⣇⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡇⣿⣽⣇⣼⣛⣛⡧⠀⢸⣷⠘⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⣿⣿⠉⠋⠇⠙⣻⡇⠀⣼⡇⣺⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⢻⣿⡆⠲⠦⠀⢉⡠⣣⣿⢃⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣻⣿⣷⣶⣶⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠰⣿⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣶⣭⠟⠋⠉⠉⠙⣦⠈⢿⣿⠟⢹⡆⠀⠀⠀⠀⠀⠈⠻⣷⡄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢠⠞⠋⠛⠉⣿⠁⠀⠀⠀⠀⠀⠀⠈⠣⣀⣠⢴⡞⢳⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠸⣄⣀⠀⣀⣻⣀⣠⣤⣤⠀⠀⠀⠀⠀⢰⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀⢠⣿⡿⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⡏⠙⣿⠁⠀⠀⢸⠟⡁⠀⠀⠀⠀⠁⠀⠀⠃⢸⠀⠀⠀⠀⢀⣰⣿⠟⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢣⠀⠇⡇⠀⢀⡟⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣠⣴⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⢰⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣀⣿⣠⣾⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠘⡌⠀⣿⡀⠀⢰⣀⣀⣀⣤⠤⠾⠻⣏⣱⣿⠿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡇⠀⠘⢮⣍⣭⣿⠀⠀⠀⠀⠀⠀⠈⠟⠿⣄⡀⠀⢉⡶⢤⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢡⠀⠀⠀⢩⠀⠀⢱⡀⠀⢀⣠⠤⠖⠒⠒⠒⠿⢿⣯⠀⠀⠙⢦⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⠀⠀⠀⢸⠀⠀⠀⢇⣴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠉⢣⠀⠀⠀⢣⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠸⣄⣀⣤⠤⢶⠶⠶⠼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⡇⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠖⠋⠁⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⡏⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⢀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠀⠀⡰⢁⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣎⣀⣠⠞⠁⠈⠉⢳⠀⠀
⠀⠀⠀⠀⠀⢹⠀⠠⠤⢤⣀⣀⣀⣤⣀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠔⠋⠉⠉⠉⠀⢀⣠⣴⡤⢨⡄⠀
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢻⠈⠁⠒⠠⠤⢈⡉⠉⠑⠒⠒⠈⠉⠉⠁⠀⢀⣀⠤⣤⣶⢾⠗⠊⡇⠀⢸⡇⠀
⠀⠀⠀⠀⠀⣸⢀⣀⣀⠀⠸⡟⠖⠢⢄⣀⠀⠈⠛⢲⡤⣀⠀⡠⢤⣒⡯⢵⠚⠩⢅⡞⡸⠀⠀⣧⠀⠈⡇⠀
⠀⠀⠀⠀⠀⢻⣨⣤⢬⡙⢺⡇⠀⠀⣄⠀⡹⢳⠢⢼⢃⠀⡇⠀⠁⢱⠀⠀⡟⠲⠌⡴⠁⡆⠀⢻⠀⠀⡇⠀