⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠄⠀⠀⡀⠈⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢴⡀⠐⠀⠀⠀⠀⠀⠀⠄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠈⠁⠁⠐⠄⠏⢣⠁⠀⠀⠀⠀⡀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢅⠀⠀⠀⠞⠂⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⢀⡤⣄⡞⠁⢹⠀⠀⡀⡀⠐⠀⠁⠂⠒⠊⠁⠂⠐ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣀⣀⣀⠀⠀⣀⣀⣀⠀⢸⠀⠀⠀⠀⠀⠀⡤⢌⠽⣄⠀⠂⡘⠀⠀⠀⠀⠈⡀⠁⠀⠀⠀⠂⠄⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡃⠀⠀⣿⠀⠀⠀⠀⣿⠀⠀⢸⠀⠀⠀⠈⣏⡈⠀⡸⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠈⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⢤⣀⣠⠄⠀⠀⠀⡎⠀⠈⠀⠀⠀⠉⠙⠃⠀⣀⡪⠴⠒⡶⠒⠒⣖⠄⡄⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⡀⠀⠀⠀⠀⠀⠀⣀⠜⠀⠀⠀⠀⠀⠀⠀⢀⡖⠁⠀⢀⡴⠋⠀⠀⠄⠀⠑⠤⠈⢳⡀⠁⠀⠀⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠆⠈⣩⠙⠒⠊⠉⢐⠑⠢⣀⣀⣀⣀⣀⣀⣎⢀⠀⠀⠀⠀⣷⠀⠀⠀⠀⣿⠀⠀⢀⢣⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⠠⡀⠁⠀⢀⠀⠀⢀⣅⡀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠿⠀⠀⠀⢘⠆⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠉⠢⠄⡐⠩⡢⣀⢠⠀⠈⠑⠢⠄⠤⠤⣇⠀⠀⠀⠀⠀⠀⡤⠒⠒⢆⠀⠠⠀⠀⢸⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⣸⠁⠀⡔⠀⠉⠕⠁⠉⠐⠢⠄⡀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⣿⢲⡖⠋⠀⠀⠡⠀⡞⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠋⢺⣤⣀⡜⠀⠀⠀⠀⠀⠀⠀⠉⠒⠠⢄⣈⢧⡀⠀⠀⠀⣿⠘⠃⠀⠀⠀⣀⣜⡠⠤⠖⠒⠒ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠉⠉⠉⡃⠒⢄⣀⡀⠀⠀⢀⣀⣀⡤⠞⠋⠉⠉⠒⠛⠒⠒⠒⢉⡟⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠤⣀⠀⠀⠀⠃⠀⡁⠒⣤⣤⠝⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⠀⢀⠀⡀⠠⠔⠒⠊ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠀⠀⠀⠉⢹⠓⠤⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠋⠚⠀⠈⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠀⠀⠀⠀⡎⡁⠀⡰⡇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⢐⠀⠇⠀⡇⠱⡀⠀⠀⠀⡀⠀⠈⠷⣆⣀⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⠇⠀⡇⢸⠂⠀⠙⠶⡖⣄⣷⡄⠀⢜⠝⠛⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡨⠀⠀⠀⠀⠠⠀⠀⡗⠏⠀⠀⠀⣠⠏⢇⠈⠻⣦⡓⠂⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⢀⠁⠀⡸⢠⠁⠀⠠⠎⡝⠀⠈⢇⠀⠐⡟⠛⠲⢾⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⡅⠀⢠⠁⠀⠀⠀⠀⢐⠁⠀⠀⢇⣂⠀⣧⢠⠀⢸⢼⠤⣀⡀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠓⠋⠀⠀⠈⠺⠤⠤⣀⣀⡅⠀⠀⠀⢸⠀⠁⡏⢀⣴⠘⣾⠀⠀⠀⠈⠑⢤⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠉⠂⠒⠒⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀