Lu
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠆⢰⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣀⠴⢾⡉⠙⠛⠲⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣶⢋⠀⢠⡇⠀⠀⢀⠈⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⡇⠀⠀⢨⠃⠀⠀⠐⠂⡄⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢸⠁⠀⠀⠁⠀⠀⠁⠀⠐⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢠⠎⠀⠀⠀⠀⠀⠂⠁⠀⠂⡄⠰⢻⠀⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢀⡞⠀⠐⠀⠀⢀⠠⠄⠀⠀⡀⠀⠰⡄⣧⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣨⣭⠤⡄⠀⠀⠀⢠⡄⠀⠰⠀⠈⠟⠀⢧⢘⢧⡀⠀⠀⠀⠀⠀⠀
⣤⣾⡋⣅⡀⢿⣄⠀⡀⢸⠃⣰⣐⣷⡀⢀⡧⠀⢧⠙⢧⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣷⡄⢹⣷⣷⡟⢸⣯⣿⣿⣷⣼⡇⠐⠘⣶⠘⣇⠀⠀⠀⠀⠀
⢻⠿⡼⣿⣿⠇⠀⠘⢿⠃⠀⢿⣿⣿⡟⢻⣇⠀⠀⠈⡶⣼⠀⠀⠀⠀⠀
⢸⡆⠙⢄⠀⠀⠀⡖⠈⠀⠀⠀⠈⠁⠁⣸⠉⠡⢤⠈⠳⢿⠀⠀⠀⠀⠀
⢉⡻⣄⠀⠁⠀⣬⣓⣂⣠⡤⠀⠀⠀⠠⡯⡄⠀⠀⠀⣀⡞⠀⠀⠀⠀⠀
⠀⠸⡎⣦⡀⠀⠉⠩⠍⠉⠀⠀⢀⡴⠞⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀
⠀⠀⠈⠺⡍⠳⣤⣀⣀⣀⡠⣾⠋⠈⠁⠀⠁⢀⣠⠏⠀⠈⠑⠒⠒⠠⠄
⠀⠀⠀⠀⠈⠳⢯⣏⠋⠉⣁⣀⡀⣀⣈⣠⣷⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣶⣾⣿⡿⠿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠧⠭⣈⡙⠉⠉⠉⠨⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠠⠤⠀⠀⠀⠀⠀⠀