⠠⡀⢤⠒⠉⡀⣤⣶⢻⠋⣿⣿⣿⣿⣿⢸⠀⣄⠳⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡀⢍⠻⠉⡀⣧⣿⣿⣿⣿⣿⢺⠀⠀⣀⣅⠻⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠻⠀⠀⠀⠀⣗⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠞⠤⣂⣯⠻⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⠻⠙⠀⠂⠀⠀⣷⣾⡇⣾⣿⣿⣿⣿⣿⠸⠀⢀⠀⠀⡀⣿⣿⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣀⣄⣤⢶⢿⠛⠈⠀⠈⡇⢻⣿⣿⣟⣿⡿⠀⠀⠀⠀⠀⠀⣧⣸⢱⣞⠳⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣀⠤⠲⠙⡈⣄⣦⢳⡿⣿⣼⡟⣿⣿⣿⠀⠀⠀⠀⠀⠀⡃⢸⡟⢀⠀⡀⢢⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣀⠄⠠⠒⠑⡉⢀⠤⠂⣿⣾⢿⢻⣿⣿⣀⠀⠀⠀⠀⠀⠀⡇⢹⢀⠀⠀⠀⠀⣥⢻⠈⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣀⢥⠸⣿⣷⣿⣿⣿⢰⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀⣀⣽⢤⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡄⢸⢿⠻⡏⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⡿⢸⠀⠀⠀⠀⠀⠀⠀⢇⢖⠲⠑⠀⠈⠀⠀⠀⢀⠀⠀⠀⠀⢐⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠉⢸⣿⣯⡿⣯⣸⠀⠀⠀⠀⠀⠀⠀⠀⡿⢸⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠁⢄⠁⠀⠀⠀⠄⠀⠁⠀⠈⠄⠨⠀⠓⠊ ⣤⣤⢤⠤⠤⠠⠂⡗⢳⣿⣿⣿⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡄⣷⠿⠿⠿⠿⠽⠷⠳⡶⣲⣾⢗⢰ ⠀⠀⠀⠄⠤⠤⠤⠠⠖⣿⣿⣿⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⡇⠾⠘⠀⠀⠀⠀⠀⣀⣤⣴⡶⣿⣵⣷⣞⢍⡾⠑ ⠀⠀⠀⠀⠀⡀⢀⡧⠃⣿⣿⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⢸⠀⠀⠀⠀⠀⠀⠀⠀⡂⣿⣞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⠀⢠⣳ ⠀⠀⠀⠀⠀⠀⠀⡇⡇⣿⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠋⣿⢻⠈⠀⠀⠀⠀⠀⠀⠀⡇⣷⢸⠻⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠐⠀⠀⡍ ⠀⠀⠀⠀⠀⠀⠀⡇⡇⣴⢟⢀⠀⠀⠀⠀⠀⠉⠒⡴⣤⣧⣮⢷⠈⠀⠀⠀⠀⠀⠀⡇⡸⢧⣸⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠊⣾ ⠉⠉⠋⠚⠒⠒⠤⡧⣹⡿⣱⠸⠀⠀⠀⠄⣀⠀⠀⠀⠀⡀⠀⡀⣄⠳⠈⠀⠀⠀⠀⡇⢠⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠁⠀⣾ ⣉⣂⣓⠝⠯⠻⠾⣿⡟⣠⡿⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⡟⢼⠈⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀ ⡶⣶⣤⣶⣒⢿⣶⣸⠀⠃⣷⠀⠉⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣼⠀⠁⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠁ ⠀⠀⠀⠀⠀⠀⡏⢰⠇⣼⡆⡜⢀⠀⠀⠀⠀⠀⠁⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⡀ ⠀⠀⠀⠀⠀⠃⣸⠀⠅⢸⠀⢸⠀⠀⠀⠀⠀⠀⡿⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⢠⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠛⢀⠀⡅⢸⠁⢸⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠁⠁⡟⣴⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣼⠀⠀⡆⢸⠁⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠞⣧⣸⠀⠀⠀⠁⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡿⢠⠀⠁⡎⢸⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢂⡏⢀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣸⠀⠀⠂⢿⡜⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⡄⠀⣼⠀⠀⠠⠃⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣹⠉⠛⠟⣿⢰⠄⣦⢿⠙⠈⠀⠀⠀⠀⠋⠿⣿⢶⠼⠪⠖⢿⢸⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣽⡆⣮⣯⣻⡸⠐⠀⡀⣦⢿⠈⠀⠀⡟⣾⣠⠀⠄⡠⣣⢻⣦⢾⠀⠀⠀⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⠀⣧⣿⢸⠀⠈⠀⠐⠀⡀⢷⠀⡇⣸⠀⠀⠃⠈⡄⣶⣿⠀⣿⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⠀⣸⣦⢻⢶⢀⠀⠀⠀⠀⡄⠀⡴⠀⠀⠀⠀⢆⠐⠤⠀⠀⣼⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠁⢸⠀⣇⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡅⠀⠀⡇⢺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡇⠀⠀⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⢠⠀⠀⡇⠋⠛⠑⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡇⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠈⠀⣀⢄⡤⣣⢶⠽⠻⠛⠉⠉⠉⠀⠀⠀⠀⠀ ⠀⠀⠀⡄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠁⠈⠀⠀⠉⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠞⢤⠲⡒⣉⢍⠤⡷⠒⠑⠉⠀⠀⡄⣂⣤⣤⢶⠴⠠ ⠀⠀⠀⠀⢦⠙⠉⠀⠀⠀⠀⠀⠁⠉⠻⢌⢻⡀⠀⠀⡂⣟⣿⣾⠶⠷⠻⠞⠼⡠⢀⠀⠀⠀⠀⠀⣀⣀⠄⠤⠢⡒⣐⠉⠠⠤⠀⠀⠀⠀