⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣀⣀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⠿⠟⠛⠉⠉⠉⠁⠀⠉⠉⠉⠉⠛⠻⠷ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣴⣾⠟⠁⠀⠀⠀⢀⣠⠴⠒⠋⠉⠉⠉⠻⣿⣿⣿⣿⣶⣦⣄ ⠀⠀⠀⠀⣠⣾⠟⣿⣿⣦⣄⡴⠞⠉⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⣴⡿⠃⠀⠙⣿⡿⠋⠀⠀⠀⣠⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⣼⡟⠁⠀⠀⣰⠟⠀⠀⢀⣴⣿⣿⣿⠿⠛⠋⠙⡽⡿⡉⠉⠙⠻⢿⣿⣿ ⠀⢸⡟⠀⠀⠀⣼⠏⠀⠀⣰⣿⣿⡿⠋⠁⠀⠀⠀⢀⠇⡇⣇⠀⠀⠀⠀⠉⠻ ⢀⣿⠃⠀⠀⢸⠛⠀⠀⣰⣿⣿⡟⠁⠀⠀⣄⡀⠀⡸⠙⡇⢸⡄⠀⢀⡀⠀⠀ ⢸⡟⠀⠄⠀⡏⠂⠀⢠⣿⣿⡟⠀⠀⠀⠀⠸⡿⣷⣏⠀⡇⢀⡷⣾⡟⠁⠀⠀ ⣾⡇⠀⠀⢰⡧⠀⠀⢸⣿⣿⢁⣀⡠⠤⠴⠒⠛⠮⣻⣦⣧⣾⡾⠛⠢⠤⠤⣀ ⣿⡇⠀⠀⢸⣿⣿⣶⣾⣿⣿⠿⢷⣒⣒⠒⠒⠒⠒⣲⣿⣿⣟⡒⠒⠒⠒⢒⣒ ⢸⣧⠀⠀⠈⣟⣿⣿⣿⣿⣿⡆⠀⠀⠀⠉⠉⣶⣿⣿⠃⣇⣻⡿⣷⡖⠉⠉⠀ ⠘⣿⡀⠀⠀⢿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⢸⠿⠛⢇⠀⡇⢁⡏⠚⠿⡆⠀⠀ ⠀⢹⣧⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⢸⠀⡇⣸⠀⠀⠀⠀⠀⢀ ⠀⠀⢻⣇⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀⡇⣇⡇⠀⠀⠀⣀⣴⣿ ⠀⠀⠀⢻⣧⡀⠀⠈⠻⣿⣿⣿⡽⣿⣿⣿⣿⣷⣶⣦⣼⣿⣤⣶⣶⣿⣿⣿⣿ ⠀⠀⠀⠀⠹⣷⣄⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿ ⠀⠀⠀⠀⠀⠈⠻⣷⣄⠀⠀⣈⣙⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣯⣁⣤ ⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣋⣉⡉⠉⠉⠍⠛⠛⠻⠿⠿⠾⠛⠛⠛⠏⠉⣉ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠉⠉⠛⠛⠛⠛⠿⠿⠶⠶⠶⠿⠿⠟⠛⠛⠛⠛⠛ ⠀⠀⠀⠀⠀⣀⣠⡴⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣠⣤⠤ ⠀⠀⠀⠀⠀⠿⣭⣍⣛⣛⣛⣛⣛⣛⣛⣛⣋⣉⣉⣩⣭⠭⠭⠭⠶⠶⠖⠒⠛ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⢰ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⣰⠟⠁⠀⠉⢳⡄⠀⠀⠀. ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⣧⠀⠀⠀⠀⢸⠧⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠈⠳⠤⡤⠴⠋⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠉⠙⠓⠒⠒⠒⠒⠒⠒⠚⠋⠉⢰⠇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀. ⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀. ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠶⠤⠤⠤⠤⠴⠖⠛⠉⠀