⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠀⠒⠀⠤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠤⠀⠀⠀⠂⠤⠄⢀⡀⠀⠀⠀⠈⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⢄⠀⠀⠈⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠈⠀⠀⡠⠀⠀⠀⡀⠔⡁⠀⠡⠀⠀⠀⠀⠀⠀⠀⠈⠢⠀⠀⠑⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠀⠀⠀⠄⡀⠤⠐⠈⠀⡐⠀⠌⠀⠑⠄⠀⠀⢂⠀⠠⠀⠀⠑⡀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⢀⠊⠁⠀⠁⠀⣠⡊⠤⠊⠀⠀⠀⠊⠢⡀⠈⡀⠀⠃⠀⠀⢠⠀⠀⠀⠈⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⢀⠂⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡈⡢⢁⠀⠘⠀⠀⢸⠀⠀⠀⠀⠀⠀⠁⠒⠠⠄⢀⠀⠤⢐⢲⣐⣒⠐⠒⠀⠄⡀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡀⠠⠴⠒⠊⠉⠁⠀⠀⠀⠀⠀⠈⠁⠒⠤⣄⡀⠘⠀⠀⢁⠠⡄⠑⠠⢀⡀⠀⠀⠀⠀⠀⣀⡠⠄⠂⠁⠀⠀⠀⠀⠁⢂⠐⡄⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢤⠰⢌⡄⠀⡇⠀⠀⠀⠀⠀⠤⠐⠂⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠄⢰⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠃⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠸⠱⢆⠆⠉⠒⠣⢄⠀⠀⠀⠀⠡⡀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠘⡊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⡈⠔⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⡠⣲⠒⡂⠂⠁⠀⠀⠀⠀⠀⣀⡀⢤⠀⠑⡀⠀⠀⠀⠀⢄⠀⢀⠁⠀⠀⠀⠀⠀⡠⠐⠉⢡⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⡗⢵⣏⠄⠀⠀⠀⡠⠄⢊⠀⠀⡠⠂⠀⠀⢰⣀⠀⠀⠀⠀⠑⢀⣀⠠⠤⠤⢴⡉⠀⠀⠀⠀⡄⢠⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢑⠀⠀⠀⠀⡀⠊⠀⢘⡀⠄⠊⠀⢀⠠⠒⡡⢏⢀⡩⠍⠛⠈⠁⠀⠀⠀⠀⠀⠣⠀⠀⠀⠀⠇⠘⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠉⠉⠉⠀⢀⠠⠔⠊⡁⠴⠪⠍⠉⢒⠦⠂⠀⠀⠀⠀⠀⠀⠀⠀⣸⠆⠀⠀⠀⢇⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠐⠈⢉⣉⣁⡒⡇⠀⣀⡀⠤⠔⠂⢉⠠⣐⠊⠁⠀⠀⠀⠛⠂⠑⠚⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠑⠄⢀⣀⡀⠄⠛⠤⠤⠀⡒⠬⠥⠀⡄⣀⣣⠀⠀⠀⠀⠀⠀⠀⡀⠠⡄⠒⠈⠁⢄⠀⢀⣼⢏⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠁⠀⠀⠀⠀⠊⠀⠀⢀⡀⠤⠐⠂⠁⠀⠀⠀⠇⠀⠀⠀⠀⠈⠉⠁⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⠀⢀⣀⠠⠄⠒⠈⠀⠀⠀⠐⠢⠀⠀⢀⠼⠀⠀⠀⠀⠀⠀⢀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠄⢂⠕⠁⠀⠀⢀⠀⠠⢂⣁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠔⢀⡂⢄⡀⢀⡀⠤⠐⣈⠠⣐⠈⠀⢁⠀⠐⠀⠀⠀⠀⠀⠀⠀⠁⠂⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠊⠒⡤⠀⡖⣀⡉⠀⢀⡢⢺⡘⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠂⠄⣀⠀⠀