⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣠⣴⣶⣾⠿⠿⠛⠛⠛⠓⠒⠠⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀ ⠀⠀⣠⣶⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀ ⣠⣾⣿⣿⠏⠁⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣀⣠⣼⣿⣿⣿⡿⠁⠀⠀⢀⠠⠂⠁⠀⠀⠀⠀⠀⠐⠠⡀⠀⠀⠀⠀⠀⢲⣤⣅⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢀⣤⣶⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⢔⠀⠀⠐⣶⣤⣤⣀⡀⠀⠀⠈⢆⠀⠀⠀⠀⠈⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⢃⠉⠐⠘⠿⢿⣿⣿⣿⠋⠐⠠⡈⠀⠀⠀⠀⠀⠻⠿⠿⠿⣿⣿⣿⣦⣄⣤⣴⣶⣶⣶⣶⣶⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠢⡀⠀⠀⠀⠀⠈⠁⠒⠀⠠⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠛⠋⠉⠙⠛⠲⢄⠰⠀⠀⠀⠀⠀
⣿⣿⠿⠟⠋⠀⠀⠀⡠⠄⠠⢤⣀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠤⠔⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠟⠙⠛⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⠀⠀⠀⠀
⣿⡿⠀⠀⠀⠀⠀⡜⠁⠀⠀⠀⠀⠈⠒⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠡⠀⠀⠀
⠟⠁⠀⠀⠀⠀⠀⠃⠀⠀⠀⢀⡀⠀⠀⠀⠀⠑⠂⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠀⠀⠀⠀⠀⠈⠂⢀⠃⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠉⠚⠤⡀⠀⠀⠀⠈⠁⠂⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣇⠀⠀⠀⢠⠀⠀⠀⢰⢀⠉⢡⣶⣦⣄⣀⠀⠀⠀⢂⠀⠀
⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⡆⠀⠀⠀⠀⠀⠁⠂⠄⡀⠀⠀⠀⠈⠃⠆⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⣼⠀⠀⠀⠀⢆⠁⠚⠿⣿⣿⣿⡟⠂⢄⠈⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢱⡀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠓⠤⣀⡀⡀⠀⠈⠈⠒⠠⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠂⠠⠤⡔⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢆⠀⠀⠀⢐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠢⢄⡀⠀⠀⠀⠀⠁⠒⠠⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠒⡌⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡅⠓⠤⣀⠀⠀⠀⠀⠀⠉⠒⠢⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠈⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢃⠀⠀⠀⠊⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠈⠑⠲⢄⡀⠀⠀⠀⠈⠀⠈⠐⠂⠤⣀⠀⠀⠀⠀⠑⠅⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠀⠀⠀⠀⠑⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⠈⠻⣶⣤⣄⡀⡀⠀⠀⠀⠀⠈⠡⠒⠤⢄⡀⠢⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠉⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣶⣦⡤⣀⠀⠀⠀⠀⠀⠀⠉⠑⠢⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠺⡀⠀⠀⠀⠈⠓⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣷⡄⠈⠉⠲⠢⢴⣀⣀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢤⡀⠀⠀⠀⠀⠑⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⡄⠀⠀⢿⣄⠀⠀⣈⢩⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠑⠢⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⢏⠁⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢄⡀⠀⠀⠀⠀⠀⠈⠑⠂⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠂⠀⠀⠹⣀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠦⣀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠂⠤⠄⣀⡀⠀⠀⠀⣿⣿⣿⣿⣿⡿⡟⠄⠀⠀⢀⡯⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠦⢄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠛⠻⠋⠉⠉⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣦⠞⠁⡀⣀⡀⢀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠄⠀⠀⠒⠀⠀⠀⠤⠄⢀⣀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠒⠒⠂⠒⠒⡲⠖⠒⠂⠉⠑⠂⣤⣉⡺⣾⣿⣾⣤⣤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠐⠒⠀⠠⠤⠄⠀⣀⣀⡠⠐⠉⠀⠀⠀⠀⠀⣈⠀⠎⠃⠁⠀⠀⠂⢈⣉⣉