⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠤⠤⠤⠤⣤⡦⠤⠤⢤⣤⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠶⠚⠋⠉⠀⠀⠀⠀⠀⠀⢀⣠⠖⠚⠻⢿⣿⡻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠀⠀⠀⠀⠀⠹⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡇⠀⣀⣀⣀⣠⣤⣄⣀⣻⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠶⠟⠋⠉⠉⠉⠀⠀⠉⠉⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣴⠀⣧⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡏⠀⠟⣆⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣼⣆⢹⡀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠈⠛⢦⢣⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⢤⡀⠈⢻⣇⠀⠀⠀⢸⡟⠷⠦⢤⣤⣀⣀⣀⣠⣤⣾⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠈⢶⣎⣻⣆⠀⠀⣿⠛⠒⠲⠤⢼⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣧⣤⡖⠒⢯⣽⣿⣷⣴⡃⠀⠀⠀⠀⠸⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠚⠉⠉⠉⠉⠩⠯⠭⠽⠽⠿⠶⣤⣄⣀⣀⣀⣀⠉⢙⣻⣿⣿⣿⣿⣿⡿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠿⣿⣿⣿⡿⣿⣿⣿⣍⡛⣿⣿⣶⣝⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡆⠀⠀⠀⠀⠀⣀⣄⣉⣽⣿⣿⣿⣿⣿⣿⣷⣾⣩⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⣰⠂⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⢀⣼⣡⢸⡟⠀⢠⡿⠀⣠⡾⠛⠉⠀⠀⠀⠀⠉⠙⠛⠻⢿⡉⠀⠉⠉⠛⠻⢷⣤⣀⠤⣀⣀⣼⡾⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⠄⠀⠀⠀⠀⠀⡀⢼⡷⠃⢸⣿⠀⢸⠃⣸⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠉⠛⠦⣌⠻⣇⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢰⡟⠓⠀⠐⠲⢿⠉⠀⠈⡇⠀⢸⣻⠀⡇⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠈⠙⢶⣝⠠⡀⠀ ⠀⠀⠀⠀⠀⢠⣿⠀⣠⠶⡀⠰⠀⢧⡀⠀⡏⠀⢸⣿⣾⡇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢮⡂ ⠀⠀⠀⠀⢀⡼⣣⠚⠀⢠⠹⡀⠀⠘⣷⠀⡇⠀⠈⣯⣿⢱⡇⠀⠀⠀⠀⠀⠀⢰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⣿ ⠀⠀⠀⢀⣾⣿⣷⣤⣤⣾⠶⠿⠿⠦⢿⣧⡇⠀⠀⣯⣿⢸⢧⠀⠀⠀⠀⠀⠀⠀⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏ ⠀⠀⢀⣾⣿⠿⠛⠉⠁⠀⠀⠀⠀⠀⠀⣀⡬⠽⣶⣾⡏⣾⠻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀ ⠀⢀⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⣴⡞⢉⣴⣞⣁⣹⣷⣿⣧⣬⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠀⠀ ⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠋⣴⠋⠀⠀⠀⢸⡃⡀⠀⠀⣿⠙⠲⢄⣀⠀⠀⠀⠀⠀⢀⣀⠤⠖⠋⠁⠀⢹⡹⣲⣦⣄⣀⣀⣠⣶⣿⣅⠀⠀⠀ ⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⣸⠃⠀⠀⠀⠀⢠⡏⠉⠉⢹⡟⢆⠀⠀⠈⠉⠉⣱⠋⠉⠉⠁⠀⠀⠀⠀⠁⢸⠀⠀⣿⡿⠟⠛⠛⠻⣿⡟⣆⠀⠀ ⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠆⢻⠀⠀⠀⠀⠀⢀⡷⠒⠒⢸⣧⠈⠓⢦⡤⠴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⢰⣿⡷⠦⠤⠤⣴⣿⡇⢻⠀⠀ ⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠈⢷⣄⡀⠀⠀⠘⡦⠖⠊⣹⠿⣷⡶⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⠀⣾⣿⡷⠶⠶⣾⢣⣿⠃⡞⠀⠀ ⠈⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⣀⠉⠉⣙⣻⣶⣷⠖⠛⠋⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⢸⣿⣿⣛⠒⢒⣿⣿⠃⢠⠃⠀⠀ ⠀⠈⢻⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠉⣉⣭⠟⠉⠸⣿⣷⣦⣄⠀⢀⡿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⢸⣿⣿⣯⣽⣿⣿⠇⣠⠟⠀⠀⠀ ⠀⠀⠀⠙⠻⢿⣯⣉⣽⣿⣿⠿⠛⠋⠉⠁⠀⠀⠀⠀⠘⣿⣿⣿⣽⡿⠛⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡷⠀⢸⡿⡟⠛⠛⠛⠛⠉⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⠛⠁⠀⠀⠀⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⡇⢱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⢸⠃⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢀⡟⠀⠀⡾⡆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⡀⠀⠀⠀⠀⠀⠘⠀⢀⣾⠇⢀⡜⠁⢹⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⠄⠀⠀⠀⠀⠀⠀⣈⠈⢀⠞⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⢸⣠⠎⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⢰⠇⢠⠟⠁⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⠀⣠⠇⠀⣠⣎⡴⠃⠀⢀⣀⣤⣤⣤⣾⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣀⣠⣤⣴⣶⣾⣿⣿⣿⣿⣿⢿⣯⡶⣿⣿⢿⣶⣾⣿⣯⣶⣺⣻⣿⣽⡛⡟⣿⡯⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣤⣤⣾⣿⣿⣿⡟⣧⣮⣿⣿⣿⣿⣿⣿⣿⣿⣽⢿⣧⣷⣷⣿⣿⣿⡚⣏⡯⡗⣟⣯⡯⡧⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⣷⣿⢳⣿⣿⡵⢿⣾⡿⣿⣿⣿⡿⣽⣷⣿⣝⣽⢾⢻⣧⡟⣏⡧⢷⣫⠵⢶⣟⣉⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢯⣿⣿⡿⡷⣯⢿⡽⢯⠿⡼⢯⡿⣻⣿⣾⢻⡿⣯⣳⡿⣿⣿⣿⣵⣾⢽⣼⣿⢽⠕⢚⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣯⣿⣟⣾⡽⡽⢯⣿⡽⢏⡿⡽⢧⣱⣞⣽⣽⣿⣽⣿⣷⡿⣝⣿⣽⣿⢿⣹⣽⢼⣺⡽⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣯⣿⡽⣭⢯⡹⣝⣎⣿⡙⣶⠳⣬⢾⣿⢾⣿⣞⣿⢿⣿⣿⣽⣾⢽⢿⣿⣽⢼⣾⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⢿⡟⣽⢏⣻⡳⣼⢻⣧⡿⣌⣶⢙⣾⣷⣿⣷⢿⣾⣯⢿⣿⣻⢿⣺⢽⢿⢋⣹⣿⣽⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⣽⣿⣹⢋⢿⢽⣺⢿⣻⣿⢿⣯⣾⢿⣷⣿⣷⣾⢙⣶⣌⡿⣧⢻⣼⡳⣻⢏⣽⡟⢿⣿⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣾⢼⣽⣿⢿⢽⣾⣽⣿⣿⢿⣿⣞⣿⢾⣿⢾⣬⠳⣶⡙⣿⣎⣝⡹⢯⣭⡽⣿⣯⣿⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠇⣿⣿⡽⣺⢼⣽⣹⢿⣿⣽⣿⣝⡿⣷⣿⣽⣿⣽⣽⣞⣱⢧⡽⡿⢏⡽⣿⢯⡽⡽⣾⣟⣿⣯⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⢚⠕⢽⣿⣼⢽⣾⣵⣿⣿⣿⡿⣳⣯⡿⢻⣾⣿⣻⡿⢯⡼⠿⢯⡽⢿⣯⡷⡿⣿⣿⢯⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡏⣿⣉⣟⢶⠵⣫⢷⡧⣏⡟⣧⢻⢾⣽⣝⣿⣷⣽⡿⣿⣿⣿⡿⣾⢿⡵⣿⣿⢳⣿⣷⡿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣧⣿⡧⡯⣯⣟⡗⡯⣏⡚⣿⣿⣿⣷⣷⣧⢿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣮⣧⡟⣿⣿⣿⣾⣤⣤⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡯⣿⡟⡛⣽⣿⣻⣺⣶⣯⣿⣾⣶⢿⣿⣿⡶⣯⢿⣿⣿⣿⣿⣿⣾⣶⣴⣤⣠⣀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣾⣤⣤⣤⣀⢀⠀⠃⡴⣎⣠⠀⠇⣠⠀⣀⣀⣀⣀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠇⢰⠀⠀⠀⠀⠁⠟⢠⠇⢰⠀⠀⡆⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠎⣠⢸⠀⠀⠀⠀⠀⠀⢧⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡇⠘⠀⠀⠞⢀⠈⣈⠀⠀⠀⠀⠀⠀⠄⣷⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡀⢹⠁⡜⢀⠇⣾⢀⠀⠘⠀⠀⠀⠀⠀⡀⣧⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⡼⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡆⡾⠀⠀⡟⢀⠀⡇⢸⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⡾⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠈⠃⢸⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⡀⠳⠀⠀⠀⠀⠀⠀⠀⠋⡾⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢱⡇⢸⠀⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠳⠀⠀⠀⠁⠛⡿⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⡟⡿⢸⠀⡷⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢿⠛⡿⣽⣿⣿⣿⠘⠀⠀⠀⠀⠁⠉⠋⠛⠿⣿⣿⣽⣉⣯⢿⠻⠙⠀⠀⠀ ⠀⠀⠀⠟⣠⠇⣿⣿⣽⣯⣿⣿⢸⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⡿⢀⠀⣄⣦⣷⣿⠸⠉⠟⣭⣉⠉⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⢻⠈⠀ ⠀⠀⠃⢠⠃⣿⣿⢒⠒⣛⣿⣿⢸⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠈⠀⠋⠛⠖⣷⣶⣻⣙⠉⠉⣀⣦⠹⠀⠀⠀⠀⠀⠀⠀⠀⡀⣦⢿⠈ ⠀⠀⡞⠃⣿⢣⣾⠶⠶⡷⣿⣾⠀⠏⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠚⡶⣷⠿⣹⠊⠖⡦⠘⠀⠀⡀⣄⢷⠈⡆⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⢻ ⠀⠀⢻⡇⣿⣴⠤⠤⠦⡷⣿⢰⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠚⠴⡤⢦⠓⠈⣧⢸⠒⠒⡷⢀⠀⠀⠀⠀⠀⢻⠆⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿ ⠀⠀⣆⡟⣿⠻⠛⠛⠟⡿⣿⠀⠀⢸⠁⠀⠀⠀⠀⠁⠉⠉⠋⣱⠉⠉⠈⠀⠀⢆⡟⢹⠉⠉⡏⢠⠀⠀⠀⠀⠃⣸⠇⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢰ ⠀⠀⠀⣅⣿⣶⣠⣀⣀⣄⣦⣲⡹⢹⠀⠁⠋⠖⠤⣀⢀⠀⠀⠀⠀⠀⣀⢄⠲⠙⣿⠀⠀⡀⡃⢸⠀⠀⠀⠋⣴⠋⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣸⠀ ⠀⠀⠞⣠⠀⠀⠀⠀⠀⠀⠀⠀⡀⣧⠿⣼⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣧⣬⣧⣿⣷⣹⣁⣞⣴⢉⡞⣴⠀⠀⠀⠀⠀⠀⠀⠀⠁⠟⣾⢀⠀ ⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠻⣾⡏⣾⣶⠽⡬⣀⠀⠀⠀⠀⠀⠀⠁⠉⠛⠿⣿⣾⢀⠀⠀ ⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢠⠀⠀⠀⠀⠀⠀⠀⠀⠃⠙⠀⠀⠀⠀⠀⠀⠀⢧⢸⣿⣯⠀⠀⡇⣧⢿⠦⠿⠿⠶⣾⣤⣤⣷⣿⣾⢀⠀⠀⠀ ⣿⣆⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢰⠀⠀⠀⠀⠀⠀⡇⢱⣿⣯⠈⠀⡇⠀⣷⠘⠀⡀⠹⢠⠀⠚⣣⡼⢀⠀⠀⠀⠀ ⡂⢮⠛⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣾⣿⢸⠀⡏⠀⡀⢧⠀⠰⡀⠶⣠⠀⣿⢠⠀⠀⠀⠀⠀ ⠀⡀⠠⣝⢶⠙⠈⠀⠀⠀⠀⠀⠀⠀⣆⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢰⡇⠀⣻⢸⠀⡇⠈⠀⠉⢿⠲⠐⠀⠓⡟⢰⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡀⣇⠻⣌⠦⠛⠉⠀⠀⠀⠀⠀⡀⢦⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡟⣸⠃⢸⠀⣿⢸⠃⡷⢼⡀⠀⠀⠀⠀⠀⠄⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠁⡾⣼⣀⣀⠤⣀⣤⢷⠻⠛⠉⠉⠀⡉⢿⠻⠛⠙⠉⠀⠀⠀⠀⠉⠛⡾⣠⠀⡿⢠⠀⡟⢸⣡⣼⢀⠀⠀⠀⠀⠀⠀⠁⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠂⣰⠀⠀⠀⠀⠀⠀⠀⠀⣄⣷⣿⣿⣩⣾⣷⣿⣿⣿⣿⣿⣿⣽⣉⣄⣀⠀⠀⠀⠀⠀⡆⣴⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⢰⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣷⣝⣶⣿⣿⡛⣍⣿⣿⣿⡿⣿⣿⣿⠿⠙⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⣴⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣶⡿⣿⣿⣿⣿⣿⣻⢙⠉⣀⣀⣀⣀⣄⣤⠶⠿⠽⠽⠭⠯⠩⠉⠉⠉⠉⠚⡴⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠸⠀⠀⠀⠀⡃⣴⣷⣿⣽⢯⠒⡖⣤⣧⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⢼⠤⠲⠒⠛⣿⠀⠀⣆⣻⣎⢶⠈⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣿⣿⣿⣾⣤⣠⣀⣀⣀⣤⢤⠦⠷⡟⢸⠀⠀⠀⣇⢻⠈⡀⢤⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⣿⣾⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢀⠀⠀⠀⠀⢣⢦⠛⠈⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⡀⢹⣆⣼⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀⣆⠟⠀⡏⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢰⠀⠀⠀⠀⠀⠀⠀⣧⠀⣴⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⢿⠉⠉⠀⠀⠉⠉⠉⠋⠟⠶⣿⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⣿⣻⣀⣄⣤⣠⣀⣀⣀⠀⡇⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣿⣿⣿⠹⠀⠀⠀⠀⠀⠉⠞⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡞⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡻⣿⢿⠻⠚⠖⣠⢀⠀⠀⠀⠀⠀⠀⠉⠋⠚⠶⣴⣠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣤⣤⣤⣤⢤⠤⠤⡦⣤⠤⠤⠤⠤⣤⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀