………⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣾⣿⣿⣿⣿⣷⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡄⠐⣤⡀⠀⠀⣀⣤⠴⠶⠶⠶⠦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣇⡜⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⢳⠱⡄⠀⠀⠉⠙⠲⣄⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⣿⣿⣿⡿⣿⣿⣿⣿⡄⠀⡝⣿⡿⠿⠛⠛⠛⠛⠿⣿⣿⠀⠹⡄⠀⠀⠀⠀⠈⢷⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⡿⠟⠋⢁⣾⣿⣿⣿⣿⣿⣾⣞⣁⣀⡀⠀⠀⠐⣦⣤⣈⠻⠀⠀⠛⠓⢦⡀⠀⠀⢘⡇⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠉⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣷⡀⣠⡯⠽⠷⢦⣄⠘⡆⠈⠙⢦⡀⠀⢀⠜⠋⠹⣄⡼⠁⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠁⠀⠀⠀⠀⠈⢳⡇⠀⠀⠀⠀⡠⠋⡀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣯⡉⠉⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠁⠀⢀⣠⠞⠁⢠⠀⠀⡆⡿⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣦⣤⣀⣀⣠⣤⡴⠚⠉⣀⣠⡴⠞⠋⠁⠀⠀⠈⠀⢠⠁⡇⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣇⣼⢿⢠⣞⡤⣶⠿⠛⢻⣟⠓⢦⠀⣠⠀⢀⠀⠁⣸⡇⠀⠠⠴⡎⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⠻⠍⡏⠞⠉⣼⣇⠀⢀⣾⡿⠀⠈⣿⠵⢊⠀⢀⣴⣿⡇⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣀⠈⠈⠀⢸⢹⣿⣷⢟⡿⠃⠀⠀⠉⠉⠁⢰⣿⣿⣿⡇⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣟⠉⡁⠀⠀⠀⠘⡀⠻⠿⠬⠄⣀⠀⠀⠀⠀⣠⣿⣿⣿⣿⠁⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣤⣀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣠⣼⣿⣿⣿⣿⡏⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⢖⡿⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⣤⣴⣾⣿⣿⣿⣿⣿⠏⢰⠇⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⢠⡾⠖⠚⠛⠲⢦⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣶⣦⣤⣤⡤⠄⠀⢀⣿⣿⣿⣿⡿⠁⠀⣿⠀⠀⠀⠀⠀⠀⣴⠋⣀⣤⣶⣷⣦⣤⣤⡤⠂⠀⢻⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣷⠀⠀⠘⣿⣿⣿⣿⡇⠀⡀⢹⡀⣠⠤⠤⠤⣼⣵⣾⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⣧ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⡿⠹⡄⠀⠀⠹⣿⣿⣿⣇⠀⠐⢄⢻⡀⠀⠀⢀⢠⣙⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⢹ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠟⠀⠀⢣⠀⠀⠀⠈⠻⣿⣿⣦⡀⠈⡗⠻⠄⠀⢸⢏⡗⠘⡆⠀⠙⢿⣿⣿⣿⣿⠙⢇⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠋⠀⠀⠀⠈⢆⠀⠀⠀⠀⠙⢿⣿⣿⡄⢸⠀⠀⠀⠀⢃⡷⢄⢳⠀⠀⢸⣿⣿⣿⡿⠀⠈⠀⣼ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠁⠀⠀⠀⠀⠀⠈⢦⢀⣠⠤⣄⠀⢻⣿⣿⣸⠀⠀⠀⠀⠊⠐⠑⢸⠀⠀⣼⣿⣿⡿⠁⠂⠀⠀⡟ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⠀⠀⠈⢳⠂⣿⡟⡏⠀⠀⢠⢎⠀⠀⠀⢸⠀⣸⣿⣿⣿⠃⠀⢰⠀⢰⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⢀⡿⠁⣀⡤⠞⢧⠈⢆⠀⠀⠸⣤⣿⣿⣿⣿⠀⠀⣸⠀⣼⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⢰⣄⠀⠚⠀⢠⡃⠀⠀⠈⣇⠈⣆⠀⠀⠑⠹⣿⣿⣿⠀⠀⣿⢰⠇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠸⡜⡗⠲⠖⠋⢱⡀⠀⠀⠸⡄⠘⡆⠀⠀⠀⠹⣿⡿⡄⢰⢿⠏⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⡇⠸⡄?