⠀⣠⣶⡿⠿⠿⠷⢦⡀⠀⢀⡴⠾⠿⠿⢿⣶⣄⠀
⣼⡿⠁⢀⣤⣶⣦⣤⡙⠤⢋⣤⣴⣶⣦⡄⠈⢿⣧
⣿⡇⢀⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⡀⢸⣿
⢹⣇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣸⡏
⠀⠻⣆⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⣰⠟⠀
⠀⠀⠈⠳⣄⠙⢿⣿⣿⣿⣿⣿⡿⠛⣡⠞⠁⠀⠀
⠀⠀⠀⠀⠈⠻⣦⡙⢿⣿⣿⠋⣠⠞⠁⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⠻⣆⠛⣡⠞⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠃⠀

⢠⠊⣉⠒⠤⢀⡀          ⡐⢁⠴⢜⢄
 ⡎⢸  ⠉⠐⠢⢌⠑⢄    ⡸  ⡆    ⠣⠱⡀
 ⡇⢸        ⣀⠗  ⠉⠉⠁  ⠙⠢⠤⡀⢃⢱
 ⡇⠘⣄⢀⠔⠉                    ⠈⠁⠘⡄
 ⢇    ⠁                       ⠘⡄
 ⢸            ⢀⣀⣀⡀      ⢀⣀⣀⡀   ⢣
 ⡸        ⢴⣾⡿⠿⠽⠇        ⠘⠛⠛⠛   ⠈⢄
⠰⡁              ⢠⠒⠢⡀⠈⠒⠊   ⡠⢄  ⡘
 ⠱⣀          ⢀⠜    ⠇        ⢀⠔⠁  ⡏
     ⠑⠤⢄⣀⠔⠁    ⡜        ⠊⠁  ⢀⠜

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⢾⣿⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⢿⡿⢦⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠟⠟⠛⢸⣿⣾⡇⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠃⠀⠀⠀⠙⢻⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡄⠀⠐⠂⢀⣼⡿⠻⣇⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⢑⠒⢒⡻⠿⠃⠀⢸⡄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠟⠉⢻⡄⠐⠏⠁⣀⠀⢢⠀⠈⣧⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣀⠔⠊⠉⠁⠀⠀⠱⠁⠀⠹⢽⠗⠈⡆⠀⣿⡄⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠘⣯⠂⠀⠀⠀⠀⡀⠱⡀⠀⠀⠀⠀⢀⠃⢨⣿⡇⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢰⡀⣀⢀⡤⠊⠀⠀⠀⠈⠉⠐⠢⡜⠀⣼⣿⡇⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⡠⡜⣿⠃⠀⠀⢀⠀⠀⠀⠀⠘⠀⠇⢀⣿⣿⠳⡄⠀⠀⠀⠀
⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢠⠃⡄⢿⣷⡄⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⡌⠀⠘⣸⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢹⡄⢀⡟⢳⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢦⣈⣿⣾⣾⡼⠀⠀⠀⠀⠀⠀
⠀⠀⢺⠀⢀⣺⣷⣿⣿⡧⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣴⡻⣿⣿⣿⣗⠄⠀⠠⠆⠀⠀
⠀⠀⠀⣠⣭⣷⣿⣿⣿⣻⡧⣠⣤⣀⠀⠀
⠀⢠⣺⣿⣟⡿⡧⡏⣋⢕⢍⣿⢮⣝⣲⠤
⠈⠁⢉⡴⠛⠟⠛⣏⠉⠈⠳⡙⠂⠈⠙⠀
⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀