⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠤⠒⠒⠚⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠑⠒⠲⠤⣀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⡠⠖⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠦⣀⠀⠀⠀ ⠀⠀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀ ⠀⡼⠁⠀⢠⣀⡀⠀⢀⡤⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠈⢧⠀ ⠀⢧⠀⠀⠀⡇⠀⠀⢺⠃⢰⠽⡂⡮⢇⢸⠀⠀⠾⡅⣜⢳⠀⠀⠾⡅⢰⢰⢛⠆⡟⡞⡆⡞⣳⢸⠀⠀⠀⢸⡆ ⠀⠈⢦⡀⠈⠉⠁⠀⠈⠀⠀⠉⠀⠈⠁⠈⠀⠀⠉⠁⠈⠁⠀⠀⠉⠀⠈⠠⠝⠀⠁⠁⠁⠈⠉⠈⠀⠀⠀⢸⠃ ⠀⠀⠀⠉⠲⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⠀ ⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠤⠤⠤⠤⢤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠊⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⣤⣄⣀⣀⡀⠀⠀⠀⢸⡇⠀⢀⡤⠋⠉⠓⠒⠉⠉⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣼⣃⡠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢄⠀⠀⠀⠹⣿⣿⣿⠿⠿⠛⠛⠛⠛⠛⠻⠿⣿⠿⠿⠋⣀⣻⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⠰⠀⣀⠐⠙⠫⣭⣤⣤⣄⣀⣀⡀⠀⠀⠐⣏⠠⠀⣀⠉⠻⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣷⣶⣬⣆⠀⠀⠀⢀⣸⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣀⣴⣿⣭⣙⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢙⠻⢿⣿⣿⣿⣿⣿⣿⣿⡯⡽⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⡃⠀⠀⠑⠈⢛⠛⠿⢿⣿⣿⣷⣝⣯⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡚⡀⠀⠀⠐⠀⢠⠤⢤⣔⢄⠀⠀⠀⠉⠍⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠤⠀⠀⠀⢂⠀⠀⠀⡴⡫⠠⣠⠀⢀⠄⡐⡋⠙⠢⠑⡦⠂⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⡁⠈⠀⠠⠌⢄⡁⢃⠀⠖⢐⠀⠀⡀⠠⡀⢀⠈⢠⡇⠀⠀⢀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⠔⠀⠀⠐⠀⠢⠀⡸⠀⠐⠒⠁⠀⠈⠁⠀⠀⠀⢀⢚⣠⣥⣬⣌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⡀⠀⠀⡀⠀⠀⠀⠠⡄⡀⣀⣀⣤⣤⠜⢤⣤⣜⣿⣿⣿⣿⣿⣿⣧⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠘⠂⠀⠀⠀⠀⢠⠔⠲⡿⢟⣿⣿⣿⡆⢰⣿⡿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠑⢤⠖⠐⢒⡉⢀⣼⣧⣬⣿⣿⣿⣄⡠⢟⣽⡿⢿⣿⣿⣿⣿⣿⢿⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⠂⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⢿⣿⣿⡿⣿⣆⠹⣯⡻⢿⣿⡿⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠂⣀⣀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⢿⣿⠀⠀⠉⠛⢻⠛⠓⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀