⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⣀⣤⣤⡶⣷⣿⣿⣿⣷⣶⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡇⠀⠀⣠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣷⣰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣯⣿⣿⣻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡗⣧⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣷⢿⣿⣿⣷⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣤⣤⣴⢶⣤⣀⠀⣠⣿⣷⣿⣿⣽⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢰⣟⣿⠓⢿⠿⣿⣿⣿⣷⣿⣿⡿⣿⣿⣿⣿⡿⣿⣿⡇⣿⣿⣿⣿⠘⣿⣿⣿⣿⡌⢻⣿⣿⣻⣿⣻⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢿⡟⣦⠤⠗⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⡇⣿⣿⣿⣿⠀⣿⣿⣿⢿⣷⢈⢻⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠻⣯⣿⣭⣻⣮⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⡇⣿⣿⣿⣿⠋⢹⣿⣿⡿⣿⠈⠻⣿⣿⣷⣿⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢻⣿⡇⠿⠿⠿⠏⠀⠸⠛⠛⠃⠉⠀⠀⠻⣿⢿⢋⣍⢝⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⣾⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣷⣼⣋⠁⠀⠀⠀⠀⣠⠴⢐⣒⣲⣄⢲⡄⠀⢹⡯⢿⢏⣽⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⣿⣿⣿⣿⣿⣿⣿⡘⠟⠋⠉⠁⠀⠈⠁⠀⠀⠀⠈⢵⣾⡿⠟⠛⠉⠉⠁⠀⣼⡃⣺⠭⠟⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣿⣿⣿⣧⣯⡿⡅⢀⡤⣂⣴⣭⣍⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢹⡁⣀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣿⣿⣿⣿⣿⣿⣿⡇⣹⣟⣾⣿⠛⠋⠉⠀⠀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣺⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⣿⣿⣿⣿⣿⣿⣿⢻⡥⣽⡄⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣟⣿⡿⠀⠳⡷⣿⡄⠀⠀⠀⠀⠀⠠⣤⣤⣶⡟⠁⠀⠀⠀⠀⢠⠜⠁⣫⡤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣿⣿⣿⣿⢻⣿⡇⠀⠀⠉⣿⣟⣦⡀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⣀⠴⢁⡠⣞⣵⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⣿⣷⡟⣾⡿⠀⠀⠀⠀⣿⠀⠀⠉⠳⢤⣀⠀⠀⠀⠀⠀⢀⡠⢞⡡⣴⢏⣫⣿⣷⣿⣿⡲⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣷⣿⡇⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠈⠉⠑⢲⣶⣾⡟⣾⣿⣽⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣟⣾⠽⣿⣿⣿⣿⣿⣿⣞⡉⠠⠉⠓⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⣧⣿⡟⠁⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⢀⣾⠉⠁⢿⣿⣿⣮⣇⣿⠟⣫⣟⠿⣗⡦⢹⡀⠀⠁⠀⠈⠻⣄⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⣠⠴⢋⡇⠀⠀⠀⠈⠙⠛⢚⣾⠒⣏⣹⣦⣷⣿⢯⡉⠙⠒⠒⠦⢤⣀⠙⢦⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣷⣿⡄⠀⠀⠀⠀⠀⠀⠀⢀⣼⣅⠀⠛⠂⠀⠀⠀⢀⡠⠖⠉⠀⣹⢶⣯⣟⣯⡞⡃⠙⢄⠀⠀⠀⠀⠀⠉⠘⢳⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣟⣷⡀⠀⠀⠀⠀⠀⢠⡏⠀⠈⠓⠤⢤⡤⠴⠚⠉⠀⣀⠴⠊⢠⠎⣼⢸⠀⡇⡧⠀⠈⢳⡀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⡌⠻⣦⣄⣀⡠⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠊⠁⠀⣠⠋⢰⢹⢸⠀⣳⢹⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⢳⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠉⠁⠀⡼⠁⠀⠀⠀⠀⢀⣀⠴⠋⠁⠀⠀⢀⡼⠁⢠⣿⣾⢸⡆⢼⢸⢦⡀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⢷⠀ ⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⢿⣶⣤⣀⡴⡃⠀⢠⣤⡤⠜⣉⡀⠀⠀⠀⢀⣠⠞⠀⣠⣿⣿⣿⢠⡇⠚⡾⠀⠱⢄⣀⣀⡘⠀⠀⠀⠀⠀⠀⠘⣧