⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠊⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⠴⠋⠀⠀⡇⠀⠀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠤⠀⢒⠶⠂⠀⠀⠀⠀⠀⡔⠀⣀⠔⠁⠀⠀⠀⢀⠁⠀⡘⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠂⠒⠀⠠⠤⠀⢀ ⠀⠀⣀⠤⣠⠃⠉⠀⠀⠀⠀⢀⡴⠁⠀⠀⠀⠀⠀⠀⠜⣠⠞⠁⠀⠀⠀⠀⠀⢸⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⠛⠴⣢⣄⡀⣠⠎⠀⠀⠀⠀⠀⠀⢀⡼⠊⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⡏⠀⠀⠀⠉⡻⠷⢤⡀⠀⠀⢀⡠⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣎⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠀⠀⠀ ⠀⠀⠀⠸⠃⠀⠀⢀⡜⠁⠀⠀⠈⣱⠖⠭⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⣀⠔⠊⠀⠀⠀⠀⠈⠉⠒⠢⠤⣤⣀⣀⡀⠀⠀⠀⡇⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⡍⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⠏⣀⠴⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠚⠃⠀⠀⡇⠇⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⡸⠁⡇⠀⠰⣄⠀⣀ ⠀⠀⠀⠀⣠⠗⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⡰⡝⡇⡇⠀⠀⠈⠀⠀ ⠀⠀⠀⣰⠃⠀⢀⣀⣠⣤⣶⢞⣟⣛⣻⠿⠻⢿⣷⣶⣤⣄⡀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⣠⡳⠀⠘⡇⠀⠀⠀⠀⠀ ⠀⠀⢰⠃⣀⣴⣾⡿⠟⠛⠉⠁⠀⠀⢀⡤⠊⠁⠀⠀⣙⢻⣿⣶⣄⠀⠀⠀⠸⠀⡆⠀⠀⢸⠀⠀⠀⠀⠀⠀⡿⡃⠀⠀⡇⠀⠀⠀⠀⠀ ⠀⢠⣳⠟⣿⠟⠁⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠤⡙⢿⣷⡄⠀⠀⡇⡇⠀⠀⢸⡄⠀⠀⠀⢀⠀⡇⢣⠀⠀⢡⠀⠀⠀⠀⠀ ⢀⣿⢫⣾⠏⠀⠀⠀⠀⠀⠀⢠⠏⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡌⣷⡟⣦⠀⢹⢁⠀⠀⢸⢧⠀⠀⠀⢸⠀⢹⡈⢇⠀⠸⡀⠀⠀⠀⠀ ⢞⣿⣿⠯⠀⠀⠀⠀⠀⠀⣰⠃⠠⠴⠢⡄⠀⠀⠀⠀⠀⠀⠀⠀⠁⡇⢿⣮⣧⡈⡿⠀⠀⢸⢸⡀⠀⠀⠘⡇⠀⢇⠘⡆⠀⢳⠀⠀⠀⠀ ⢸⠋⡏⢀⠀⠀⠀⠀⠉⡱⠁⠀⠂⣓⠚⠀⠀⠀⠀⢠⢶⠦⡀⠀⠀⡇⢸⣿⣿⣧⡘⣆⠀⠸⡄⣧⠀⠀⠀⢰⠀⢸⡀⠘⡄⠈⢧⠀⠀⠀ ⠀⢀⠃⡆⠀⠀⠀⠀⡸⠁⠀⠀⠀⠈⠀⠀⠀⠀⠀⠘⠈⠇⢸⢴⡏⡇⢹⣿⣻⣿⡦⠘⡆⠀⡇⠸⣆⠀⠀⠘⣆⠀⣇⠀⠙⣄⠈⢧⠀⠀ ⠀⠘⠀⡇⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠬⣥⡄⢃⠇⣿⣿⡟⢻⡧⠱⡘⣆⢱⡀⠹⢆⠀⠀⠸⣆⠘⣆⠀⠘⢦⡀⢧⡀ ⠀⠀⠐⣥⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⡜⠀⡿⣸⠃⢸⡇⠀⠑⠜⣞⣧⠀⢫⢦⠀⠀⢻⢆⠘⡆⠀⠀⠓⢄⠙ ⠀⠀⠈⢰⠀⠀⠀⡇⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠯⠀⡜⠀⠀⡁⠋⠀⠘⠁⠀⠀⠈⢺⣷⢣⠀⠣⡳⡀⠈⣏⢦⡸⡀⠀⠀⠀⠓ ⠀⠀⠀⠸⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⡜⠀⠀⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⢂⠀⠑⢝⢄⢸⡑⡷⡹⡄⡤⡀⠀ ⠀⠀⠀⡤⡇⠀⠀⠘⣄⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⢀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡆⠀⠀⠑⢕⣿⡌⠻⣿⡅⠈⠒ ⠀⠀⠀⠘⡧⡀⠀⠀⠀⢇⢐⠃⠉⠈⠐⡄⠀⠀⢀⡠⠊⠀⡠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣢⠀⠀⠀⠀⠉⠀⠈⠛⠀⠀ ⠀⠀⠀⠀⠠⡷⡀⠀⠀⠀⠙⠳⠬⠤⣤⡦⠤⠒⠉⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⢢⡄⣀⡀⠀⠀⠀⣀⡀⠀⠀⣀⡊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠙⠉⠉⠛⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠤⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⠀⠀⣠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣎⣀⠠⠤⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀