⠀⠀⢠⠋⠀⠀⠈⠱⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠉⣆⠀⠀⠀⠀⠀⠀⠀⠀⡞⠁⠀⠀⠙⡄⠀⠀⠀⠀⠀⠀⠀⢠⠋⠀⠀⠈⢱⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⠀⠈⡆⠀⠀ ⠀⠀⠘⣄⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠡⡀⠀⠀⢀⠏⠀⠀⠀⠀⠀⠀⠀⢀⠗⠒⠀⠐⠲⣇⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⢀⠇⠀⠀ ⠀⠀⠀⠈⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠊⠉⠲⡄⠀⠀⠀⠀⠀⠀⠀⠀⢠⠒⠋⠑⠢⣼⠃⠀⠀⠀⠀⠀⠀⣝⡤⠚⠉⠒⢄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠊⠉⠲⡄⠀⠀⠀⠀⠀⠀⠀⠀⢠ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡏⢧⡀⠀⠀⠀⢀⡴⢻⡁⠀⠀⠀⢸⠆⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⣠⠴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⠢⢀⡠⠜⠁⠀⠈⡗⠒⢻⠉⠀⠀⠑⠤⣀⠤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⢄⣠⠴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘ ⠀⠀⠀⢀⡠⠤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠤⣀⠀⠀⠀ ⠀⠀⢠⠋⠀⠀⠀⠱⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁⠀⠀⠈⣆⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠟⡆⠀⠀⠀⠀⠀⠀⠀⢠⠋⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁⠀⠀⠈⡆⠀⠀ ⠀⠀⠘⣄⠀⠀⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⢀⠏⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⠀⢀⠇⠀⠀ ⠀⠀⠀⠈⠁⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠁⠀⠀⠀ ⢆⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠋⠉⠒⣄⠀⠀⠀⠀⠀⠀⠀⠀⠠⠚⠉⠉⠢⡀⠀⡇⠀⠀⠀⠀⡇⠀⡴⠊⠉⠑⢢⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⠉⠒⣄⠀⠀⠀⠀⠀⠀⠀⠀⠠ ⢨⠀⠀⣀⣠⠤⠤⠤⠤⠜⠒⠒⠂⢠⠼⠤⠤⠤⢤⠤⠤⠤⠤⠓⠒⠒⠒⠒⠣⠤⠧⠤⠄⠀⠠⠡⠼⠀⠀⠀⠀⠘⠦⠤⠤⠤⡤⠤⠤⠤⠼⡖⠒⠒⠒⠺⠤⠤⠤⠤⢀⣀⠀⠀⡇ ⣪⡶⠛⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢸⠀⢠⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⡆⠀⡇⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠶⣌ ⠁⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢸⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡇⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈ ⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢸⠀⢸⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⡇⠀⡇⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢸⠀⢸⠀⠀⠀⠈⠻⣿⣦⠀⠀⠀⠀⣴⠀⠀⠀⠀⣴⣿⡟⠁⠀⠀⠀⡇⠀⡇⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢸⠀⢸⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⢰⢝⢇⠀⠀⠀⠉⠁⢀⣀⡀⠀⠀⡇⠀⡇⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢸⠀⢸⠀⡔⠉⠀⠀⠉⢲⠀⠀⠀⠓⠒⠚⠂⠀⠀⢠⠊⠁⠀⠈⠙⣆⡇⠀⡇⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢸⠀⢸⠀⠙⠢⠤⠠⠔⠊⠀⠀⢠⠤⠤⠤⣤⠀⠀⠀⠓⠤⠄⠤⠖⠁⡇⠀⡇⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢸⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⠤⠤⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡇⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢸⠀⠘⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠠⠇⠀⡇⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠸⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠇⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢳⢤⣀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⡾ ⢨⠀⠀⠉⠒⠲⠤⠴⠤⢤⡤⠤⠤⠼⣤⠤⠤⠤⠤⠤⢤⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡤⠤⠤⠤⠤⠤⢤⡧⠤⠤⠤⡤⠤⠤⠤⠔⠒⠉⠁⠀⢇ ⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⠤⠒⠁⠀⠀⠀⠀⠀⡞⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢱⠀⠀⠀⠀⠀⠀⠑⠢⠴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈ ⠀⠀⠀⣠⠄⠒⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⡾⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⢣⠂⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠐⠢⢄⠀⠀⠀ ⠀⠀⢰⠁⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⢰⠁⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠈⠆⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⡇⠀⠀ ⠀⠀⠈⢦⡀⠀⣀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠹⢤⠇⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠘⣄⠜⠀⠀⠀⠀⠀⠀⠀⠀⠙⢄⠀⢀⣠⠃⠀⠀ ⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⡌⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⢱⡀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀ ⠃⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠁⠀⠙⢦⠀⡸⠁⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⢣⠀⢠⠊⠁⠀⠉⢆⠀⠀⠀⠀⠀⠀⠀⠀⡐ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⡸⣰⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠈⢆⢸⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠇