⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⣰⣄⣶⣴⣤⣶⣤⣶⣀⡄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⣠⣽⣾⣿⣿⡟⣏⣹⣭⣽⣿⡙⣿⣿⣿⣤⣄⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣶⣾⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⢿⣿⣿⣿⣿⣿⡹⣧⡀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣿⣿⢿⣿⣿⠿⡟⢿⢿⠸⢩⠏⣼⢋⠏⡿⣿⣿⣷⣿⣧⡄⠀⠀⠀⠀
⠀⠀⠀⢠⣿⣿⣳⣽⣿⣷⣴⣢⢣⣄⣎⣼⣿⣧⣾⣾⣿⣿⣗⢛⣿⡅⠀⠀⠀⠀
⠀⠀⠀⠐⣿⣷⣿⡟⣽⠟⡟⢹⢿⢻⡟⠛⡿⣿⣿⡇⢻⢹⣿⡊⣿⡇⠀⠀⠀⠀
⠀⠀⠀⠀⣺⣿⠟⠁⢻⠀⠅⢸⠈⠘⡃⢠⠁⡗⢁⠃⢸⠀⠙⣾⣿⡇⠀⠀⠀⠀
⠀⠀⠀⢸⡝⡿⢀⣤⣬⣄⣀⣸⠀⠀⠃⠀⠘⢀⣀⣀⣤⣤⡄⢻⣿⡂⠀⠀⠀⠀
⠀⠀⠀⢘⢻⡇⠀⠀⠰⠾⠿⠿⠟⠃⠀⠘⢿⠽⢷⠒⠶⡄⠀⢸⣾⡇⠀⠀⠀⠀
⠀⠀⠀⠘⠌⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠉⠁⠉⠀⣬⢿⠃⠀⠀⠀⠀
⠀⠀⠀⠀⠈⢜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⢁⣣⠁⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⠀⠀⠀⡘⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠸⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢸⠀⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⡇⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢸⠇⠀⠘⢦⡀⠀⠀⠀⠀⠀⡀⠔⡉⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀
⠀⠀⡠⠤⠤⢄⣸⠸⡀⠀⢡⠈⠐⠒⠒⠒⠈⠀⡸⠀⠀⢠⢠⣖⣂⡐⠐⠂⠄⠀
⣰⠁⠀⢼⣷⣿⠇⠀⠇⠀⠈⠇⠀⠀⠀⠀⠀⢠⠃⠀⠀⡄⢈⠿⠛⠋⢀⢀⣴⣶
⠹⡒⠒⠺⠿⠯⢀⡀⠰⠀⠀⢱⡀⠀⠀⠀⢀⡦⠀⡀⠔⠋⠁⣀⣠⣴⣿⡿⠛⠉
⢆⣻⣷⣶⣶⣄⠀⠈⠑⠂⠀⠀⠣⠤⠤⠰⠾⠦⠥⠶⠶⢴⣾⣿⣿⡿⠋⠀⠀⣠
⠹⣿⣷⡙⢿⣿⣷⣶⣤⣀⣀⣀⣀⣤⣤⣄⣤⣤⣾⣶⣿⠿⠿⠛⠁⢀⣤⣶⣿⣿