Did you know that the length of your arm can be used to find your height, just like the ratios in a person's face can be used to identify them? Math and forensic science work together again in this fun experiment!

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  1. FATKING 6:23 PM February 19, 2019

    ⠀⠀⠀⠀⣀⣤
    ⠀⠀⠀⠀⣿⠿⣶
    ⠀⠀⠀⠀⣿⣿⣀
    ⠀⠀⠀⣶⣶⣿⠿⠛⣶
    ⠤⣀⠛⣿⣿⣿⣿⣿⣿⣭⣿⣤
    ⠒⠀⠀⠀⠉⣿⣿⣿⣿⠀⠀⠉⣀
    ⠀⠤⣤⣤⣀⣿⣿⣿⣿⣀⠀⠀⣿
    ⠀⠀⠛⣿⣿⣿⣿⣿⣿⣿⣭⣶⠉
    ⠀⠀⠀⠤⣿⣿⣿⣿⣿⣿⣿
    ⠀⠀⠀⣭⣿⣿⣿⠀⣿⣿⣿
    ⠀⠀⠀⣉⣿⣿⠿⠀⠿⣿⣿
    ⠀⠀⠀⠀⣿⣿⠀⠀⠀⣿⣿⣤
    ⠀⠀⠀⣀⣿⣿⠀⠀⠀⣿⣿⣿
    ⠀⠀⠀⣿⣿⣿⠀⠀⠀⣿⣿⣿
    ⠀⠀⠀⣿⣿⠛⠀⠀⠀⠉⣿⣿
    ⠀⠀⠀⠉⣿⠀⠀⠀⠀⠀⠛⣿
    ⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣿⣿
    ⠀⠀⠀⠀⣛⠀⠀⠀⠀⠀⠀⠛⠿⠿⠿
    ⠀⠀⠀⠛⠛

    ⠀⠀⠀⣀⣶⣀
    ⠀⠀⠀⠒⣛⣭
    ⠀⠀⠀⣀⠿⣿⣶
    ⠀⣤⣿⠤⣭⣿⣿
    ⣤⣿⣿⣿⠛⣿⣿⠀⣀
    ⠀⣀⠤⣿⣿⣶⣤⣒⣛
    ⠉⠀⣀⣿⣿⣿⣿⣭⠉
    ⠀⠀⣭⣿⣿⠿⠿⣿
    ⠀⣶⣿⣿⠛⠀⣿⣿
    ⣤⣿⣿⠉⠤⣿⣿⠿
    ⣿⣿⠛⠀⠿⣿⣿
    ⣿⣿⣤⠀⣿⣿⠿
    ⠀⣿⣿⣶⠀⣿⣿⣶
    ⠀⠀⠛⣿⠀⠿⣿⣿
    ⠀⠀⠀⣉⣿⠀⣿⣿
    ⠀⠶⣶⠿⠛⠀⠉⣿
    ⠀⠀⠀⠀⠀⠀⣀⣿
    ⠀⠀⠀⠀⠀⣶⣿⠿

    ⠀⠀⠀⠀⠀⠀⠀⠀⣤⣿⣿⠶⠀⠀⣀⣀
    ⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣶⣿⣿⣿⣿⣿⣿
    ⠀⠀⣀⣶⣤⣤⠿⠶⠿⠿⠿⣿⣿⣿⣉⣿⣿
    ⠿⣉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣤⣿⣿⣿⣀
    ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣿⣿⣶⣤
    ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣿⣿⣿⣿⠿⣛⣿
    ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠛⣿⣿⣿⣿
    ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⣿⠿⠀⣿⣿⣿⠛
    ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⣿⣿⣿
    ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⣿⠀⠀⣿⣶
    ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠛⠀⠀⣿⣿⣶
    ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⠤
    ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿
    ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
    ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣀
    ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿

    ⠀⠀⣀
    ⠀⠿⣿⣿⣀
    ⠀⠉⣿⣿⣀
    ⠀⠀⠛⣿⣭⣀⣀⣤
    ⠀⠀⣿⣿⣿⣿⣿⠛⠿⣶⣀
    ⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⣉⣶
    ⠀⠀⠉⣿⣿⣿⣿⣀⠀⠀⣿⠉
    ⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿
    ⠀⣀⣿⣿⣿⣿⣿⣿⣿⣿⠿
    ⠀⣿⣿⣿⠿⠉⣿⣿⣿⣿
    ⠀⣿⣿⠿⠀⠀⣿⣿⣿⣿
    ⣶⣿⣿⠀⠀⠀⠀⣿⣿⣿
    ⠛⣿⣿⣀⠀⠀⠀⣿⣿⣿⣿⣶⣀
    ⠀⣿⣿⠉⠀⠀⠀⠉⠉⠉⠛⠛⠿⣿⣶
    ⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿
    ⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉
    ⣀⣶⣿⠛

    ⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
    ⠀⠀⠀⠀⠀⠀⣿⣿⣿⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
    ⠀⠀⠀⠀⠀⠀⠉⣿⣿⣿⣶⣿⣿⣿⣶⣶⣤⣶⣶⠶⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
    ⠀⠀⠀⠀⠀⠀⣤⣿⠿⣿⣿⣿⣿⣿⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
    ⠛⣿⣤⣤⣀⣤⠿⠉⠀⠉⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
    ⠀⠉⠉⠉⠉⠉⠀⠀⠀⠀⠉⣿⣿⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
    ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
    ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
    ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
    ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
    ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣛⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
    ⠀⠀⠀⠀⠀⠀⠀⣶⣿⣿⠛⠿⣿⣿⣿⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
    ⠀⠀⠀⠀⠀⠀⠀⣿⠛⠉⠀⠀⠀⠛⠿⣿⣿⣶⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
    ⠀⠀⠀⠀⠀⠀⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
    ⠀⠀⠀⠀⠀⠛⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
    ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

    ⠀⠀⠀⠀⠀⠀⣤⣶⣶
    ⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣀⣀
    ⠀⠀⠀⠀⠀⣀⣶⣿⣿⣿⣿⣿⣿
    ⣤⣶⣀⠿⠶⣿⣿⣿⠿⣿⣿⣿⣿
    ⠉⠿⣿⣿⠿⠛⠉⠀⣿⣿⣿⣿⣿
    ⠀⠀⠉⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣤⣤
    ⠀⠀⠀⠀⠀⠀⠀⣤⣶⣿⣿⣿⣿⣿⣿
    ⠀⠀⠀⠀⠀⣀⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿
    ⠀⠀⠀⠀⣀⣿⣿⣿⠿⠉⠀⠀⣿⣿⣿⣿
    ⠀⠀⠀⠀⣿⣿⠿⠉⠀⠀⠀⠀⠿⣿⣿⠛
    ⠀⠀⠀⠀⠛⣿⣿⣀⠀⠀⠀⠀⠀⣿⣿⣀
    ⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠿⣿⣿
    ⠀⠀⠀⠀⠀⠉⣿⣿⠀⠀⠀⠀⠀⠀⠉⣿
    ⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣀⣿
    ⠀⠀⠀⠀⠀⠀⣀⣿⣿
    ⠀⠀⠀⠀⠤⣿⠿⠿⠿

    ⠀⠀⠀⠀⣀
    ⠀⠀⣶⣿⠿⠀⠀⠀⣀⠀⣤⣤
    ⠀⣶⣿⠀⠀⠀⠀⣿⣿⣿⠛⠛⠿⣤⣀
    ⣶⣿⣤⣤⣤⣤⣤⣿⣿⣿⣀⣤⣶⣭⣿⣶⣀
    ⠉⠉⠉⠛⠛⠿⣿⣿⣿⣿⣿⣿⣿⠛⠛⠿⠿
    ⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠿
    ⠀⠀⠀⠀⠀⠀⠀⠿⣿⣿⣿⣿
    ⠀⠀⠀⠀⠀⠀⠀⠀⣭⣿⣿⣿⣿⣿
    ⠀⠀⠀⠀⠀⠀⠀⣤⣿⣿⣿⣿⣿⣿
    ⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠿
    ⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠿
    ⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿
    ⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣿⣿
    ⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣿⣿
    ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⠛⠿⣿⣤
    ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⠀⠀⠀⣿⣿⣤
    ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣶⣿⠛⠉
    ⠀⠀⠀⠀⠀⠀⠀⠀⣤⣿⣿⠀⠀⠉
    ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

    ⠀⠀⠀⠀⠀⠀⣶⣿⣶
    ⠀⠀⠀⣤⣤⣤⣿⣿⣿
    ⠀⠀⣶⣿⣿⣿⣿⣿⣿⣿⣶
    ⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿
    ⠀⠀⣿⣉⣿⣿⣿⣿⣉⠉⣿⣶
    ⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿
    ⠀⣤⣿⣿⣿⣿⣿⣿⣿⠿⠀⣿⣶
    ⣤⣿⠿⣿⣿⣿⣿⣿⠿⠀⠀⣿⣿⣤
    ⠉⠉⠀⣿⣿⣿⣿⣿⠀⠀⠒⠛⠿⠿⠿
    ⠀⠀⠀⠉⣿⣿⣿⠀⠀⠀⠀⠀⠀⠉
    ⠀⠀⠀⣿⣿⣿⣿⣿⣶
    ⠀⠀⠀⠀⣿⠉⠿⣿⣿
    ⠀⠀⠀⠀⣿⣤⠀⠛⣿⣿
    ⠀⠀⠀⠀⣶⣿⠀⠀⠀⣿⣶
    ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣭⣿⣿
    ⠀⠀⠀⠀⠀⠀⠀⠀⣤⣿⣿⠉

    ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶
    ⠀⠀⠀⠀⠀⣀⣀⠀⣶⣿⣿⠶
    ⣶⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤
    ⠀⠉⠶⣶⣀⣿⣿⣿⣿⣿⣿⣿⠿⣿⣤⣀
    ⠀⠀⠀⣿⣿⠿⠉⣿⣿⣿⣿⣭⠀⠶⠿⠿
    ⠀⠀⠛⠛⠿⠀⠀⣿⣿⣿⣉⠿⣿⠶
    ⠀⠀⠀⠀⠀⣤⣶⣿⣿⣿⣿⣿
    ⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠒
    ⠀⠀⠀⠀⣀⣿⣿⣿⣿⣿⣿⣿
    ⠀⠀⠀⠀⠀⣿⣿⣿⠛⣭⣭⠉
    ⠀⠀⠀⠀⠀⣿⣿⣭⣤⣿⠛
    ⠀⠀⠀⠀⠀⠛⠿⣿⣿⣿⣭
    ⠀⠀⠀⠀⠀⠀⠀⣿⣿⠉⠛⠿⣶⣤
    ⠀⠀⠀⠀⠀⠀⣀⣿⠀⠀⣶⣶⠿⠿⠿
    ⠀⠀⠀⠀⠀⠀⣿⠛
    ⠀⠀⠀⠀⠀⠀⣭⣶

    ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤
    ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
    ⠀⠀⣶⠀⠀⣀⣤⣶⣤⣉⣿⣿⣤⣀
    ⠤⣤⣿⣤⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣀
    ⠀⠛⠿⠀⠀⠀⠀⠉⣿⣿⣿⣿⣿⠉⠛⠿⣿⣤
    ⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⣿⣿⠛⠀⠀⠀⣶⠿
    ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣿⣿⣿⣤⠀⣿⠿
    ⠀⠀⠀⠀⠀⠀⠀⣶⣿⣿⣿⣿⣿⣿⣿⣿
    ⠀⠀⠀⠀⠀⠀⠀⠿⣿⣿⣿⣿⣿⠿⠉⠉
    ⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣿⣿⠿
    ⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠉
    ⠀⠀⠀⠀⠀⠀⠀⠀⣛⣿⣭⣶⣀
    ⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿
    ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠉⠛⣿
    ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⣿⣿
    ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣉⠀⣶⠿
    ⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⠿
    ⠀⠀⠀⠀⠀⠀⠀⠛⠿⠛

    ⠀⠀⠀⣶⣿⣶
    ⠀⠀⠀⣿⣿⣿⣀
    ⠀⣀⣿⣿⣿⣿⣿⣿
    ⣶⣿⠛⣭⣿⣿⣿⣿
    ⠛⠛⠛⣿⣿⣿⣿⠿
    ⠀⠀⠀⠀⣿⣿⣿
    ⠀⠀⣀⣭⣿⣿⣿⣿⣀
    ⠀⠤⣿⣿⣿⣿⣿⣿⠉
    ⠀⣿⣿⣿⣿⣿⣿⠉
    ⣿⣿⣿⣿⣿⣿
    ⣿⣿⣶⣿⣿
    ⠉⠛⣿⣿⣶⣤
    ⠀⠀⠉⠿⣿⣿⣤
    ⠀⠀⣀⣤⣿⣿⣿
    ⠀⠒⠿⠛⠉⠿⣿
    ⠀⠀⠀⠀⠀⣀⣿⣿
    ⠀⠀⠀⠀⣶⠿⠿⠛ ⠀⠀⠀⠀⣀⣤
    ⠀⠀⠀⠀⣿⠿⣶
    ⠀⠀⠀⠀⣿⣿⣀
    ⠀⠀⠀⣶⣶⣿⠿⠛⣶
    ⠤⣀⠛⣿⣿⣿⣿⣿⣿⣭⣿⣤
    ⠒⠀⠀⠀⠉⣿⣿⣿⣿⠀⠀⠉⣀
    ⠀⠤⣤⣤⣀⣿⣿⣿⣿⣀⠀⠀⣿
    ⠀⠀⠛⣿⣿⣿⣿⣿⣿⣿⣭⣶⠉
    ⠀⠀⠀⠤⣿⣿⣿⣿⣿⣿⣿
    ⠀⠀⠀⣭⣿⣿⣿⠀⣿⣿⣿
    ⠀⠀⠀⣉⣿⣿⠿⠀⠿⣿⣿
    ⠀⠀⠀⠀⣿⣿⠀⠀⠀⣿⣿⣤
    ⠀⠀⠀⣀⣿⣿⠀⠀⠀⣿⣿⣿
    ⠀⠀⠀⣿⣿⣿⠀⠀⠀⣿⣿⣿
    ⠀⠀⠀⣿⣿⠛⠀⠀⠀⠉⣿⣿
    ⠀⠀⠀⠉⣿⠀⠀⠀⠀⠀⠛⣿
    ⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣿⣿
    ⠀⠀⠀⠀⣛⠀⠀⠀⠀⠀⠀⠛⠿⠿⠿
    ⠀⠀⠀⠛⠛

    ⠀⠀⠀⣀⣶⣀
    ⠀⠀⠀⠒⣛⣭
    ⠀⠀⠀⣀⠿⣿⣶
    ⠀⣤⣿⠤⣭⣿⣿
    ⣤⣿⣿⣿⠛⣿⣿⠀⣀
    ⠀⣀⠤⣿⣿⣶⣤⣒⣛
    ⠉⠀⣀⣿⣿⣿⣿⣭⠉
    ⠀⠀⣭⣿⣿⠿⠿⣿
    ⠀⣶⣿⣿⠛⠀⣿⣿
    ⣤⣿⣿⠉⠤⣿⣿⠿
    ⣿⣿⠛⠀⠿⣿⣿
    ⣿⣿⣤⠀⣿⣿⠿
    ⠀⣿⣿⣶⠀⣿⣿⣶
    ⠀⠀⠛⣿⠀⠿⣿⣿
    ⠀⠀⠀⣉⣿⠀⣿⣿
    ⠀⠶⣶⠿⠛⠀⠉⣿
    ⠀⠀⠀⠀⠀⠀⣀⣿
    ⠀⠀⠀⠀⠀⣶⣿⠿

    ⠀⠀⠀⠀⠀⠀⠀⠀⣤⣿⣿⠶⠀⠀⣀⣀
    ⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣶⣿⣿⣿⣿⣿⣿
    ⠀⠀⣀⣶⣤⣤⠿⠶⠿⠿⠿⣿⣿⣿⣉⣿⣿
    ⠿⣉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣤⣿⣿⣿⣀
    ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣿⣿⣶⣤
    ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣿⣿⣿⣿⠿⣛⣿
    ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠛⣿⣿⣿⣿
    ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⣿⠿⠀⣿⣿⣿⠛
    ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⣿⣿⣿
    ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⣿⠀⠀⣿⣶
    ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠛⠀⠀⣿⣿⣶
    ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⠤
    ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿
    ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
    ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣀
    ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿

    ⠀⠀⣀
    ⠀⠿⣿⣿⣀
    ⠀⠉⣿⣿⣀
    ⠀⠀⠛⣿⣭⣀⣀⣤
    ⠀⠀⣿⣿⣿⣿⣿⠛⠿⣶⣀
    ⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⣉⣶
    ⠀⠀⠉⣿⣿⣿⣿⣀⠀⠀⣿⠉
    ⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿
    ⠀⣀⣿⣿⣿⣿⣿⣿⣿⣿⠿
    ⠀⣿⣿⣿⠿⠉⣿⣿⣿⣿
    ⠀⣿⣿⠿⠀⠀⣿⣿⣿⣿
    ⣶⣿⣿⠀⠀⠀⠀⣿⣿⣿
    ⠛⣿⣿⣀⠀⠀⠀⣿⣿⣿⣿⣶⣀
    ⠀⣿⣿⠉⠀⠀⠀⠉⠉⠉⠛⠛⠿⣿⣶
    ⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿
    ⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉
    ⣀⣶⣿⠛

    ⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
    ⠀⠀⠀⠀⠀⠀⣿⣿⣿⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
    ⠀⠀⠀⠀⠀⠀⠉⣿⣿⣿⣶⣿⣿⣿⣶⣶⣤⣶⣶⠶⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
    ⠀⠀⠀⠀⠀⠀⣤⣿⠿⣿⣿⣿⣿⣿⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
    ⠛⣿⣤⣤⣀⣤⠿⠉⠀⠉⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
    ⠀⠉⠉⠉⠉⠉⠀⠀⠀⠀⠉⣿⣿⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
    ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
    ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
    ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
    ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
    ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣛⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
    ⠀⠀⠀⠀⠀⠀⠀⣶⣿⣿⠛⠿⣿⣿⣿⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
    ⠀⠀⠀⠀⠀⠀⠀⣿⠛⠉⠀⠀⠀⠛⠿⣿⣿⣶⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
    ⠀⠀⠀⠀⠀⠀⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
    ⠀⠀⠀⠀⠀⠛⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
    ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

    ⠀⠀⠀⠀⠀⠀⣤⣶⣶
    ⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣀⣀
    ⠀⠀⠀⠀⠀⣀⣶⣿⣿⣿⣿⣿⣿
    ⣤⣶⣀⠿⠶⣿⣿⣿⠿⣿⣿⣿⣿
    ⠉⠿⣿⣿⠿⠛⠉⠀⣿⣿⣿⣿⣿
    ⠀⠀⠉⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣤⣤
    ⠀⠀⠀⠀⠀⠀⠀⣤⣶⣿⣿⣿⣿⣿⣿
    ⠀⠀⠀⠀⠀⣀⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿
    ⠀⠀⠀⠀⣀⣿⣿⣿⠿⠉⠀⠀⣿⣿⣿⣿
    ⠀⠀⠀⠀⣿⣿⠿⠉⠀⠀⠀⠀⠿⣿⣿⠛
    ⠀⠀⠀⠀⠛⣿⣿⣀⠀⠀⠀⠀⠀⣿⣿⣀
    ⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠿⣿⣿
    ⠀⠀⠀⠀⠀⠉⣿⣿⠀⠀⠀⠀⠀⠀⠉⣿
    ⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣀⣿
    ⠀⠀⠀⠀⠀⠀⣀⣿⣿
    ⠀⠀⠀⠀⠤⣿⠿⠿⠿

    ⠀⠀⠀⠀⣀
    ⠀⠀⣶⣿⠿⠀⠀⠀⣀⠀⣤⣤
    ⠀⣶⣿⠀⠀⠀⠀⣿⣿⣿⠛⠛⠿⣤⣀
    ⣶⣿⣤⣤⣤⣤⣤⣿⣿⣿⣀⣤⣶⣭⣿⣶⣀
    ⠉⠉⠉⠛⠛⠿⣿⣿⣿⣿⣿⣿⣿⠛⠛⠿⠿
    ⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠿
    ⠀⠀⠀⠀⠀⠀⠀⠿⣿⣿⣿⣿
    ⠀⠀⠀⠀⠀⠀⠀⠀⣭⣿⣿⣿⣿⣿
    ⠀⠀⠀⠀⠀⠀⠀⣤⣿⣿⣿⣿⣿⣿
    ⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠿
    ⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠿
    ⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿
    ⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣿⣿
    ⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣿⣿
    ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⠛⠿⣿⣤
    ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⠀⠀⠀⣿⣿⣤
    ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣶⣿⠛⠉
    ⠀⠀⠀⠀⠀⠀⠀⠀⣤⣿⣿⠀⠀⠉
    ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

    ⠀⠀⠀⠀⠀⠀⣶⣿⣶
    ⠀⠀⠀⣤⣤⣤⣿⣿⣿
    ⠀⠀⣶⣿⣿⣿⣿⣿⣿⣿⣶
    ⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿
    ⠀⠀⣿⣉⣿⣿⣿⣿⣉⠉⣿⣶
    ⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿
    ⠀⣤⣿⣿⣿⣿⣿⣿⣿⠿⠀⣿⣶
    ⣤⣿⠿⣿⣿⣿⣿⣿⠿⠀⠀⣿⣿⣤
    ⠉⠉⠀⣿⣿⣿⣿⣿⠀⠀⠒⠛⠿⠿⠿
    ⠀⠀⠀⠉⣿⣿⣿⠀⠀⠀⠀⠀⠀⠉
    ⠀⠀⠀⣿⣿⣿⣿⣿⣶
    ⠀⠀⠀⠀⣿⠉⠿⣿⣿
    ⠀⠀⠀⠀⣿⣤⠀⠛⣿⣿
    ⠀⠀⠀⠀⣶⣿⠀⠀⠀⣿⣶
    ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣭⣿⣿
    ⠀⠀⠀⠀⠀⠀⠀⠀⣤⣿⣿⠉

    ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶
    ⠀⠀⠀⠀⠀⣀⣀⠀⣶⣿⣿⠶
    ⣶⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤
    ⠀⠉⠶⣶⣀⣿⣿⣿⣿⣿⣿⣿⠿⣿⣤⣀
    ⠀⠀⠀⣿⣿⠿⠉⣿⣿⣿⣿⣭⠀⠶⠿⠿
    ⠀⠀⠛⠛⠿⠀⠀⣿⣿⣿⣉⠿⣿⠶
    ⠀⠀⠀⠀⠀⣤⣶⣿⣿⣿⣿⣿
    ⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠒
    ⠀⠀⠀⠀⣀⣿⣿⣿⣿⣿⣿⣿
    ⠀⠀⠀⠀⠀⣿⣿⣿⠛⣭⣭⠉
    ⠀⠀⠀⠀⠀⣿⣿⣭⣤⣿⠛
    ⠀⠀⠀⠀⠀⠛⠿⣿⣿⣿⣭
    ⠀⠀⠀⠀⠀⠀⠀⣿⣿⠉⠛⠿⣶⣤
    ⠀⠀⠀⠀⠀⠀⣀⣿⠀⠀⣶⣶⠿⠿⠿
    ⠀⠀⠀⠀⠀⠀⣿⠛
    ⠀⠀⠀⠀⠀⠀⣭⣶

    ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤
    ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
    ⠀⠀⣶⠀⠀⣀⣤⣶⣤⣉⣿⣿⣤⣀
    ⠤⣤⣿⣤⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣀
    ⠀⠛⠿⠀⠀⠀⠀⠉⣿⣿⣿⣿⣿⠉⠛⠿⣿⣤
    ⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⣿⣿⠛⠀⠀⠀⣶⠿
    ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣿⣿⣿⣤⠀⣿⠿
    ⠀⠀⠀⠀⠀⠀⠀⣶⣿⣿⣿⣿⣿⣿⣿⣿
    ⠀⠀⠀⠀⠀⠀⠀⠿⣿⣿⣿⣿⣿⠿⠉⠉
    ⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣿⣿⠿
    ⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠉
    ⠀⠀⠀⠀⠀⠀⠀⠀⣛⣿⣭⣶⣀
    ⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿
    ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠉⠛⣿
    ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⣿⣿
    ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣉⠀⣶⠿
    ⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⠿
    ⠀⠀⠀⠀⠀⠀⠀⠛⠿⠛

    ⠀⠀⠀⣶⣿⣶
    ⠀⠀⠀⣿⣿⣿⣀
    ⠀⣀⣿⣿⣿⣿⣿⣿
    ⣶⣿⠛⣭⣿⣿⣿⣿
    ⠛⠛⠛⣿⣿⣿⣿⠿
    ⠀⠀⠀⠀⣿⣿⣿
    ⠀⠀⣀⣭⣿⣿⣿⣿⣀
    ⠀⠤⣿⣿⣿⣿⣿⣿⠉
    ⠀⣿⣿⣿⣿⣿⣿⠉
    ⣿⣿⣿⣿⣿⣿
    ⣿⣿⣶⣿⣿
    ⠉⠛⣿⣿⣶⣤
    ⠀⠀⠉⠿⣿⣿⣤
    ⠀⠀⣀⣤⣿⣿⣿
    ⠀⠒⠿⠛⠉⠿⣿
    ⠀⠀⠀⠀⠀⣀⣿⣿
    ⠀⠀⠀⠀⣶⠿⠿⠛ ⠀⠀⠀⠀⣀⣤
    ⠀⠀⠀⠀⣿⠿⣶
    ⠀⠀⠀⠀⣿⣿⣀
    ⠀⠀⠀⣶⣶⣿⠿⠛⣶
    ⠤⣀⠛⣿⣿⣿⣿⣿⣿⣭⣿⣤
    ⠒⠀⠀⠀⠉⣿⣿⣿⣿⠀⠀⠉⣀
    ⠀⠤⣤⣤⣀⣿⣿⣿⣿⣀⠀⠀⣿
    ⠀⠀⠛⣿⣿⣿⣿⣿⣿⣿⣭⣶⠉
    ⠀⠀⠀⠤⣿⣿⣿⣿⣿⣿⣿
    ⠀⠀⠀⣭⣿⣿⣿⠀⣿⣿⣿
    ⠀⠀⠀⣉⣿⣿⠿⠀⠿⣿⣿
    ⠀⠀⠀⠀⣿⣿⠀⠀⠀⣿⣿⣤
    ⠀⠀⠀⣀⣿⣿⠀⠀⠀⣿⣿⣿
    ⠀⠀⠀⣿⣿⣿⠀⠀⠀⣿⣿⣿
    ⠀⠀⠀⣿⣿⠛⠀⠀⠀⠉⣿⣿
    ⠀⠀⠀⠉⣿⠀⠀⠀⠀⠀⠛⣿
    ⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣿⣿
    ⠀⠀⠀⠀⣛⠀⠀⠀⠀⠀⠀⠛⠿⠿⠿
    ⠀⠀⠀⠛⠛

    ⠀⠀⠀⣀⣶⣀
    ⠀⠀⠀⠒⣛⣭
    ⠀⠀⠀⣀⠿⣿⣶
    ⠀⣤⣿⠤⣭⣿⣿
    ⣤⣿⣿⣿⠛⣿⣿⠀⣀
    ⠀⣀⠤⣿⣿⣶⣤⣒⣛
    ⠉⠀⣀⣿⣿⣿⣿⣭⠉
    ⠀⠀⣭⣿⣿⠿⠿⣿
    ⠀⣶⣿⣿⠛⠀⣿⣿
    ⣤⣿⣿⠉⠤⣿⣿⠿
    ⣿⣿⠛⠀⠿⣿⣿
    ⣿⣿⣤⠀⣿⣿⠿
    ⠀⣿⣿⣶⠀⣿⣿⣶
    ⠀⠀⠛⣿⠀⠿⣿⣿
    ⠀⠀⠀⣉⣿⠀⣿⣿
    ⠀⠶⣶⠿⠛⠀⠉⣿
    ⠀⠀⠀⠀⠀⠀⣀⣿
    ⠀⠀⠀⠀⠀⣶⣿⠿

    ⠀⠀⠀⠀⠀⠀⠀⠀⣤⣿⣿⠶⠀⠀⣀⣀
    ⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣶⣿⣿⣿⣿⣿⣿
    ⠀⠀⣀⣶⣤⣤⠿⠶⠿⠿⠿⣿⣿⣿⣉⣿⣿
    ⠿⣉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣤⣿⣿⣿⣀
    ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣿⣿⣶⣤
    ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣿⣿⣿⣿⠿⣛⣿
    ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠛⣿⣿⣿⣿
    ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⣿⠿⠀⣿⣿⣿⠛
    ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⣿⣿⣿
    ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⣿⠀⠀⣿⣶
    ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠛⠀⠀⣿⣿⣶
    ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⠤
    ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿
    ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
    ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣀
    ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿

    ⠀⠀⣀
    ⠀⠿⣿⣿⣀
    ⠀⠉⣿⣿⣀
    ⠀⠀⠛⣿⣭⣀⣀⣤
    ⠀⠀⣿⣿⣿⣿⣿⠛⠿⣶⣀
    ⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⣉⣶
    ⠀⠀⠉⣿⣿⣿⣿⣀⠀⠀⣿⠉
    ⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿
    ⠀⣀⣿⣿⣿⣿⣿⣿⣿⣿⠿
    ⠀⣿⣿⣿⠿⠉⣿⣿⣿⣿
    ⠀⣿⣿⠿⠀⠀⣿⣿⣿⣿
    ⣶⣿⣿⠀⠀⠀⠀⣿⣿⣿
    ⠛⣿⣿⣀⠀⠀⠀⣿⣿⣿⣿⣶⣀
    ⠀⣿⣿⠉⠀⠀⠀⠉⠉⠉⠛⠛⠿⣿⣶
    ⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿
    ⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉
    ⣀⣶⣿⠛

    ⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
    ⠀⠀⠀⠀⠀⠀⣿⣿⣿⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
    ⠀⠀⠀⠀⠀⠀⠉⣿⣿⣿⣶⣿⣿⣿⣶⣶⣤⣶⣶⠶⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
    ⠀⠀⠀⠀⠀⠀⣤⣿⠿⣿⣿⣿⣿⣿⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
    ⠛⣿⣤⣤⣀⣤⠿⠉⠀⠉⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
    ⠀⠉⠉⠉⠉⠉⠀⠀⠀⠀⠉⣿⣿⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
    ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
    ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
    ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
    ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
    ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣛⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
    ⠀⠀⠀⠀⠀⠀⠀⣶⣿⣿⠛⠿⣿⣿⣿⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
    ⠀⠀⠀⠀⠀⠀⠀⣿⠛⠉⠀⠀⠀⠛⠿⣿⣿⣶⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
    ⠀⠀⠀⠀⠀⠀⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
    ⠀⠀⠀⠀⠀⠛⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
    ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

    ⠀⠀⠀⠀⠀⠀⣤⣶⣶
    ⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣀⣀
    ⠀⠀⠀⠀⠀⣀⣶⣿⣿⣿⣿⣿⣿
    ⣤⣶⣀⠿⠶⣿⣿⣿⠿⣿⣿⣿⣿
    ⠉⠿⣿⣿⠿⠛⠉⠀⣿⣿⣿⣿⣿
    ⠀⠀⠉⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣤⣤
    ⠀⠀⠀⠀⠀⠀⠀⣤⣶⣿⣿⣿⣿⣿⣿
    ⠀⠀⠀⠀⠀⣀⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿
    ⠀⠀⠀⠀⣀⣿⣿⣿⠿⠉⠀⠀⣿⣿⣿⣿
    ⠀⠀⠀⠀⣿⣿⠿⠉⠀⠀⠀⠀⠿⣿⣿⠛
    ⠀⠀⠀⠀⠛⣿⣿⣀⠀⠀⠀⠀⠀⣿⣿⣀
    ⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠿⣿⣿
    ⠀⠀⠀⠀⠀⠉⣿⣿⠀⠀⠀⠀⠀⠀⠉⣿
    ⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣀⣿
    ⠀⠀⠀⠀⠀⠀⣀⣿⣿
    ⠀⠀⠀⠀⠤⣿⠿⠿⠿

    ⠀⠀⠀⠀⣀
    ⠀⠀⣶⣿⠿⠀⠀⠀⣀⠀⣤⣤
    ⠀⣶⣿⠀⠀⠀⠀⣿⣿⣿⠛⠛⠿⣤⣀
    ⣶⣿⣤⣤⣤⣤⣤⣿⣿⣿⣀⣤⣶⣭⣿⣶⣀
    ⠉⠉⠉⠛⠛⠿⣿⣿⣿⣿⣿⣿⣿⠛⠛⠿⠿
    ⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠿
    ⠀⠀⠀⠀⠀⠀⠀⠿⣿⣿⣿⣿
    ⠀⠀⠀⠀⠀⠀⠀⠀⣭⣿⣿⣿⣿⣿
    ⠀⠀⠀⠀⠀⠀⠀⣤⣿⣿⣿⣿⣿⣿
    ⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠿
    ⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠿
    ⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿
    ⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣿⣿
    ⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣿⣿
    ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⠛⠿⣿⣤
    ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⠀⠀⠀⣿⣿⣤
    ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣶⣿⠛⠉
    ⠀⠀⠀⠀⠀⠀⠀⠀⣤⣿⣿⠀⠀⠉
    ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

    ⠀⠀⠀⠀⠀⠀⣶⣿⣶
    ⠀⠀⠀⣤⣤⣤⣿⣿⣿
    ⠀⠀⣶⣿⣿⣿⣿⣿⣿⣿⣶
    ⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿
    ⠀⠀⣿⣉⣿⣿⣿⣿⣉⠉⣿⣶
    ⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿
    ⠀⣤⣿⣿⣿⣿⣿⣿⣿⠿⠀⣿⣶
    ⣤⣿⠿⣿⣿⣿⣿⣿⠿⠀⠀⣿⣿⣤
    ⠉⠉⠀⣿⣿⣿⣿⣿⠀⠀⠒⠛⠿⠿⠿
    ⠀⠀⠀⠉⣿⣿⣿⠀⠀⠀⠀⠀⠀⠉
    ⠀⠀⠀⣿⣿⣿⣿⣿⣶
    ⠀⠀⠀⠀⣿⠉⠿⣿⣿
    ⠀⠀⠀⠀⣿⣤⠀⠛⣿⣿
    ⠀⠀⠀⠀⣶⣿⠀⠀⠀⣿⣶
    ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣭⣿⣿
    ⠀⠀⠀⠀⠀⠀⠀⠀⣤⣿⣿⠉

    ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶
    ⠀⠀⠀⠀⠀⣀⣀⠀⣶⣿⣿⠶
    ⣶⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤
    ⠀⠉⠶⣶⣀⣿⣿⣿⣿⣿⣿⣿⠿⣿⣤⣀
    ⠀⠀⠀⣿⣿⠿⠉⣿⣿⣿⣿⣭⠀⠶⠿⠿
    ⠀⠀⠛⠛⠿⠀⠀⣿⣿⣿⣉⠿⣿⠶
    ⠀⠀⠀⠀⠀⣤⣶⣿⣿⣿⣿⣿
    ⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠒
    ⠀⠀⠀⠀⣀⣿⣿⣿⣿⣿⣿⣿
    ⠀⠀⠀⠀⠀⣿⣿⣿⠛⣭⣭⠉
    ⠀⠀⠀⠀⠀⣿⣿⣭⣤⣿⠛
    ⠀⠀⠀⠀⠀⠛⠿⣿⣿⣿⣭
    ⠀⠀⠀⠀⠀⠀⠀⣿⣿⠉⠛⠿⣶⣤
    ⠀⠀⠀⠀⠀⠀⣀⣿⠀⠀⣶⣶⠿⠿⠿
    ⠀⠀⠀⠀⠀⠀⣿⠛
    ⠀⠀⠀⠀⠀⠀⣭⣶

    ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤
    ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
    ⠀⠀⣶⠀⠀⣀⣤⣶⣤⣉⣿⣿⣤⣀
    ⠤⣤⣿⣤⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣀
    ⠀⠛⠿⠀⠀⠀⠀⠉⣿⣿⣿⣿⣿⠉⠛⠿⣿⣤
    ⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⣿⣿⠛⠀⠀⠀⣶⠿
    ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣿⣿⣿⣤⠀⣿⠿
    ⠀⠀⠀⠀⠀⠀⠀⣶⣿⣿⣿⣿⣿⣿⣿⣿
    ⠀⠀⠀⠀⠀⠀⠀⠿⣿⣿⣿⣿⣿⠿⠉⠉
    ⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣿⣿⠿
    ⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠉
    ⠀⠀⠀⠀⠀⠀⠀⠀⣛⣿⣭⣶⣀
    ⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿
    ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠉⠛⣿
    ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⣿⣿
    ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣉⠀⣶⠿
    ⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⠿
    ⠀⠀⠀⠀⠀⠀⠀⠛⠿⠛

    ⠀⠀⠀⣶⣿⣶
    ⠀⠀⠀⣿⣿⣿⣀
    ⠀⣀⣿⣿⣿⣿⣿⣿
    ⣶⣿⠛⣭⣿⣿⣿⣿
    ⠛⠛⠛⣿⣿⣿⣿⠿
    ⠀⠀⠀⠀⣿⣿⣿
    ⠀⠀⣀⣭⣿⣿⣿⣿⣀
    ⠀⠤⣿⣿⣿⣿⣿⣿⠉
    ⠀⣿⣿⣿⣿⣿⣿⠉
    ⣿⣿⣿⣿⣿⣿
    ⣿⣿⣶⣿⣿
    ⠉⠛⣿⣿⣶⣤
    ⠀⠀⠉⠿⣿⣿⣤
    ⠀⠀⣀⣤⣿⣿⣿
    ⠀⠒⠿⠛⠉⠿⣿
    ⠀⠀⠀⠀⠀⣀⣿⣿
    ⠀⠀⠀⠀⣶⠿⠿⠛ ⠀⠀⠀⠀⣀⣤
    ⠀⠀⠀⠀⣿⠿⣶
    ⠀⠀⠀⠀⣿⣿⣀
    ⠀⠀⠀⣶⣶⣿⠿⠛⣶
    ⠤⣀⠛⣿⣿⣿⣿⣿⣿⣭⣿⣤
    ⠒⠀⠀⠀⠉⣿⣿⣿⣿⠀⠀⠉⣀
    ⠀⠤⣤⣤⣀⣿⣿⣿⣿⣀⠀⠀⣿
    ⠀⠀⠛⣿⣿⣿⣿⣿⣿⣿⣭⣶⠉
    ⠀⠀⠀⠤⣿⣿⣿⣿⣿⣿⣿
    ⠀⠀⠀⣭⣿⣿⣿⠀⣿⣿⣿
    ⠀⠀⠀⣉⣿⣿⠿⠀⠿⣿⣿
    ⠀⠀⠀⠀⣿⣿⠀⠀⠀⣿⣿⣤
    ⠀⠀⠀⣀⣿⣿⠀⠀⠀⣿⣿⣿
    ⠀⠀⠀⣿⣿⣿⠀⠀⠀⣿⣿⣿
    ⠀⠀⠀⣿⣿⠛⠀⠀⠀⠉⣿⣿
    ⠀⠀⠀⠉⣿⠀⠀⠀⠀⠀⠛⣿
    ⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣿⣿
    ⠀⠀⠀⠀⣛⠀⠀⠀⠀⠀⠀⠛⠿⠿⠿
    ⠀⠀⠀⠛⠛

    ⠀⠀⠀⣀⣶⣀
    ⠀⠀⠀⠒⣛⣭
    ⠀⠀⠀⣀⠿⣿⣶
    ⠀⣤⣿⠤⣭⣿⣿
    ⣤⣿⣿⣿⠛⣿⣿⠀⣀
    ⠀⣀⠤⣿⣿⣶⣤⣒⣛
    ⠉⠀⣀⣿⣿⣿⣿⣭⠉
    ⠀⠀⣭⣿⣿⠿⠿⣿
    ⠀⣶⣿⣿⠛⠀⣿⣿
    ⣤⣿⣿⠉⠤⣿⣿⠿
    ⣿⣿⠛⠀⠿⣿⣿
    ⣿⣿⣤⠀⣿⣿⠿
    ⠀⣿⣿⣶⠀⣿⣿⣶
    ⠀⠀⠛⣿⠀⠿⣿⣿
    ⠀⠀⠀⣉⣿⠀⣿⣿
    ⠀⠶⣶⠿⠛⠀⠉⣿
    ⠀⠀⠀⠀⠀⠀⣀⣿
    ⠀⠀⠀⠀⠀⣶⣿⠿

    ⠀⠀⠀⠀⠀⠀⠀⠀⣤⣿⣿⠶⠀⠀⣀⣀
    ⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣶⣿⣿⣿⣿⣿⣿
    ⠀⠀⣀⣶⣤⣤⠿⠶⠿⠿⠿⣿⣿⣿⣉⣿⣿
    ⠿⣉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣤⣿⣿⣿⣀
    ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣿⣿⣶⣤
    ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣿⣿⣿⣿⠿⣛⣿
    ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠛⣿⣿⣿⣿
    ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⣿⠿⠀⣿⣿⣿⠛
    ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⣿⣿⣿
    ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⣿⠀⠀⣿⣶
    ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠛⠀⠀⣿⣿⣶
    ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⠤
    ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿
    ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
    ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣀
    ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿

    ⠀⠀⣀
    ⠀⠿⣿⣿⣀
    ⠀⠉⣿⣿⣀
    ⠀⠀⠛⣿⣭⣀⣀⣤
    ⠀⠀⣿⣿⣿⣿⣿⠛⠿⣶⣀
    ⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⣉⣶
    ⠀⠀⠉⣿⣿⣿⣿⣀⠀⠀⣿⠉
    ⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿
    ⠀⣀⣿⣿⣿⣿⣿⣿⣿⣿⠿
    ⠀⣿⣿⣿⠿⠉⣿⣿⣿⣿
    ⠀⣿⣿⠿⠀⠀⣿⣿⣿⣿
    ⣶⣿⣿⠀⠀⠀⠀⣿⣿⣿
    ⠛⣿⣿⣀⠀⠀⠀⣿⣿⣿⣿⣶⣀
    ⠀⣿⣿⠉⠀⠀⠀⠉⠉⠉⠛⠛⠿⣿⣶
    ⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿
    ⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉
    ⣀⣶⣿⠛

    ⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
    ⠀⠀⠀⠀⠀⠀⣿⣿⣿⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
    ⠀⠀⠀⠀⠀⠀⠉⣿⣿⣿⣶⣿⣿⣿⣶⣶⣤⣶⣶⠶⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
    ⠀⠀⠀⠀⠀⠀⣤⣿⠿⣿⣿⣿⣿⣿⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
    ⠛⣿⣤⣤⣀⣤⠿⠉⠀⠉⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
    ⠀⠉⠉⠉⠉⠉⠀⠀⠀⠀⠉⣿⣿⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
    ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
    ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
    ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
    ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
    ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣛⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
    ⠀⠀⠀⠀⠀⠀⠀⣶⣿⣿⠛⠿⣿⣿⣿⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
    ⠀⠀⠀⠀⠀⠀⠀⣿⠛⠉⠀⠀⠀⠛⠿⣿⣿⣶⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
    ⠀⠀⠀⠀⠀⠀⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
    ⠀⠀⠀⠀⠀⠛⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
    ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

    ⠀⠀⠀⠀⠀⠀⣤⣶⣶
    ⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣀⣀
    ⠀⠀⠀⠀⠀⣀⣶⣿⣿⣿⣿⣿⣿
    ⣤⣶⣀⠿⠶⣿⣿⣿⠿⣿⣿⣿⣿
    ⠉⠿⣿⣿⠿⠛⠉⠀⣿⣿⣿⣿⣿
    ⠀⠀⠉⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣤⣤
    ⠀⠀⠀⠀⠀⠀⠀⣤⣶⣿⣿⣿⣿⣿⣿
    ⠀⠀⠀⠀⠀⣀⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿
    ⠀⠀⠀⠀⣀⣿⣿⣿⠿⠉⠀⠀⣿⣿⣿⣿
    ⠀⠀⠀⠀⣿⣿⠿⠉⠀⠀⠀⠀⠿⣿⣿⠛
    ⠀⠀⠀⠀⠛⣿⣿⣀⠀⠀⠀⠀⠀⣿⣿⣀
    ⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠿⣿⣿
    ⠀⠀⠀⠀⠀⠉⣿⣿⠀⠀⠀⠀⠀⠀⠉⣿
    ⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣀⣿
    ⠀⠀⠀⠀⠀⠀⣀⣿⣿
    ⠀⠀⠀⠀⠤⣿⠿⠿⠿

    ⠀⠀⠀⠀⣀
    ⠀⠀⣶⣿⠿⠀⠀⠀⣀⠀⣤⣤
    ⠀⣶⣿⠀⠀⠀⠀⣿⣿⣿⠛⠛⠿⣤⣀
    ⣶⣿⣤⣤⣤⣤⣤⣿⣿⣿⣀⣤⣶⣭⣿⣶⣀
    ⠉⠉⠉⠛⠛⠿⣿⣿⣿⣿⣿⣿⣿⠛⠛⠿⠿
    ⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠿
    ⠀⠀⠀⠀⠀⠀⠀⠿⣿⣿⣿⣿
    ⠀⠀⠀⠀⠀⠀⠀⠀⣭⣿⣿⣿⣿⣿
    ⠀⠀⠀⠀⠀⠀⠀⣤⣿⣿⣿⣿⣿⣿
    ⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠿
    ⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠿
    ⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿
    ⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣿⣿
    ⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣿⣿
    ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⠛⠿⣿⣤
    ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⠀⠀⠀⣿⣿⣤
    ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣶⣿⠛⠉
    ⠀⠀⠀⠀⠀⠀⠀⠀⣤⣿⣿⠀⠀⠉
    ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

    ⠀⠀⠀⠀⠀⠀⣶⣿⣶
    ⠀⠀⠀⣤⣤⣤⣿⣿⣿
    ⠀⠀⣶⣿⣿⣿⣿⣿⣿⣿⣶
    ⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿
    ⠀⠀⣿⣉⣿⣿⣿⣿⣉⠉⣿⣶
    ⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿
    ⠀⣤⣿⣿⣿⣿⣿⣿⣿⠿⠀⣿⣶
    ⣤⣿⠿⣿⣿⣿⣿⣿⠿⠀⠀⣿⣿⣤
    ⠉⠉⠀⣿⣿⣿⣿⣿⠀⠀⠒⠛⠿⠿⠿
    ⠀⠀⠀⠉⣿⣿⣿⠀⠀⠀⠀⠀⠀⠉
    ⠀⠀⠀⣿⣿⣿⣿⣿⣶
    ⠀⠀⠀⠀⣿⠉⠿⣿⣿
    ⠀⠀⠀⠀⣿⣤⠀⠛⣿⣿
    ⠀⠀⠀⠀⣶⣿⠀⠀⠀⣿⣶
    ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣭⣿⣿
    ⠀⠀⠀⠀⠀⠀⠀⠀⣤⣿⣿⠉

    ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶
    ⠀⠀⠀⠀⠀⣀⣀⠀⣶⣿⣿⠶
    ⣶⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤
    ⠀⠉⠶⣶⣀⣿⣿⣿⣿⣿⣿⣿⠿⣿⣤⣀
    ⠀⠀⠀⣿⣿⠿⠉⣿⣿⣿⣿⣭⠀⠶⠿⠿
    ⠀⠀⠛⠛⠿⠀⠀⣿⣿⣿⣉⠿⣿⠶
    ⠀⠀⠀⠀⠀⣤⣶⣿⣿⣿⣿⣿
    ⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠒
    ⠀⠀⠀⠀⣀⣿⣿⣿⣿⣿⣿⣿
    ⠀⠀⠀⠀⠀⣿⣿⣿⠛⣭⣭⠉
    ⠀⠀⠀⠀⠀⣿⣿⣭⣤⣿⠛
    ⠀⠀⠀⠀⠀⠛⠿⣿⣿⣿⣭
    ⠀⠀⠀⠀⠀⠀⠀⣿⣿⠉⠛⠿⣶⣤
    ⠀⠀⠀⠀⠀⠀⣀⣿⠀⠀⣶⣶⠿⠿⠿
    ⠀⠀⠀⠀⠀⠀⣿⠛
    ⠀⠀⠀⠀⠀⠀⣭⣶

    ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤
    ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
    ⠀⠀⣶⠀⠀⣀⣤⣶⣤⣉⣿⣿⣤⣀
    ⠤⣤⣿⣤⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣀
    ⠀⠛⠿⠀⠀⠀⠀⠉⣿⣿⣿⣿⣿⠉⠛⠿⣿⣤
    ⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⣿⣿⠛⠀⠀⠀⣶⠿
    ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣿⣿⣿⣤⠀⣿⠿
    ⠀⠀⠀⠀⠀⠀⠀⣶⣿⣿⣿⣿⣿⣿⣿⣿
    ⠀⠀⠀⠀⠀⠀⠀⠿⣿⣿⣿⣿⣿⠿⠉⠉
    ⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣿⣿⠿
    ⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠉
    ⠀⠀⠀⠀⠀⠀⠀⠀⣛⣿⣭⣶⣀
    ⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿
    ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠉⠛⣿
    ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⣿⣿
    ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣉⠀⣶⠿
    ⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⠿
    ⠀⠀⠀⠀⠀⠀⠀⠛⠿⠛

    ⠀⠀⠀⣶⣿⣶
    ⠀⠀⠀⣿⣿⣿⣀
    ⠀⣀⣿⣿⣿⣿⣿⣿
    ⣶⣿⠛⣭⣿⣿⣿⣿
    ⠛⠛⠛⣿⣿⣿⣿⠿
    ⠀⠀⠀⠀⣿⣿⣿
    ⠀⠀⣀⣭⣿⣿⣿⣿⣀
    ⠀⠤⣿⣿⣿⣿⣿⣿⠉
    ⠀⣿⣿⣿⣿⣿⣿⠉
    ⣿⣿⣿⣿⣿⣿
    ⣿⣿⣶⣿⣿
    ⠉⠛⣿⣿⣶⣤
    ⠀⠀⠉⠿⣿⣿⣤
    ⠀⠀⣀⣤⣿⣿⣿
    ⠀⠒⠿⠛⠉⠿⣿
    ⠀⠀⠀⠀⠀⣀⣿⣿
    ⠀⠀⠀⠀⣶⠿⠿⠛ ⠀⠀⠀⠀⣀⣤
    ⠀⠀⠀⠀⣿⠿⣶
    ⠀⠀⠀⠀⣿⣿⣀
    ⠀⠀⠀⣶⣶⣿⠿⠛⣶
    ⠤⣀⠛⣿⣿⣿⣿⣿⣿⣭⣿⣤
    ⠒⠀⠀⠀⠉⣿⣿⣿⣿⠀⠀⠉⣀
    ⠀⠤⣤⣤⣀⣿⣿⣿⣿⣀⠀⠀⣿
    ⠀⠀⠛⣿⣿⣿⣿⣿⣿⣿⣭⣶⠉
    ⠀⠀⠀⠤⣿⣿⣿⣿⣿⣿⣿
    ⠀⠀⠀⣭⣿⣿⣿⠀⣿⣿⣿
    ⠀⠀⠀⣉⣿⣿⠿⠀⠿⣿⣿
    ⠀⠀⠀⠀⣿⣿⠀⠀⠀⣿⣿⣤
    ⠀⠀⠀⣀⣿⣿⠀⠀⠀⣿⣿⣿
    ⠀⠀⠀⣿⣿⣿⠀⠀⠀⣿⣿⣿
    ⠀⠀⠀⣿⣿⠛⠀⠀⠀⠉⣿⣿
    ⠀⠀⠀⠉⣿⠀⠀⠀⠀⠀⠛⣿
    ⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣿⣿
    ⠀⠀⠀⠀⣛⠀⠀⠀⠀⠀⠀⠛⠿⠿⠿
    ⠀⠀⠀⠛⠛

    ⠀⠀⠀⣀⣶⣀
    ⠀⠀⠀⠒⣛⣭
    ⠀⠀⠀⣀⠿⣿⣶
    ⠀⣤⣿⠤⣭⣿⣿
    ⣤⣿⣿⣿⠛⣿⣿⠀⣀
    ⠀⣀⠤⣿⣿⣶⣤⣒⣛
    ⠉⠀⣀⣿⣿⣿⣿⣭⠉
    ⠀⠀⣭⣿⣿⠿⠿⣿
    ⠀⣶⣿⣿⠛⠀⣿⣿
    ⣤⣿⣿⠉⠤⣿⣿⠿
    ⣿⣿⠛⠀⠿⣿⣿
    ⣿⣿⣤⠀⣿⣿⠿
    ⠀⣿⣿⣶⠀⣿⣿⣶
    ⠀⠀⠛⣿⠀⠿⣿⣿
    ⠀⠀⠀⣉⣿⠀⣿⣿
    ⠀⠶⣶⠿⠛⠀⠉⣿
    ⠀⠀⠀⠀⠀⠀⣀⣿
    ⠀⠀⠀⠀⠀⣶⣿⠿

    ⠀⠀⠀⠀⠀⠀⠀⠀⣤⣿⣿⠶⠀⠀⣀⣀
    ⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣶⣿⣿⣿⣿⣿⣿
    ⠀⠀⣀⣶⣤⣤⠿⠶⠿⠿⠿⣿⣿⣿⣉⣿⣿
    ⠿⣉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣤⣿⣿⣿⣀
    ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣿⣿⣶⣤
    ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣿⣿⣿⣿⠿⣛⣿
    ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠛⣿⣿⣿⣿
    ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⣿⠿⠀⣿⣿⣿⠛
    ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⣿⣿⣿
    ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⣿⠀⠀⣿⣶
    ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠛⠀⠀⣿⣿⣶
    ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⠤
    ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿
    ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
    ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣀
    ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿

    ⠀⠀⣀
    ⠀⠿⣿⣿⣀
    ⠀⠉⣿⣿⣀
    ⠀⠀⠛⣿⣭⣀⣀⣤
    ⠀⠀⣿⣿⣿⣿⣿⠛⠿⣶⣀
    ⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⣉⣶
    ⠀⠀⠉⣿⣿⣿⣿⣀⠀⠀⣿⠉
    ⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿
    ⠀⣀⣿⣿⣿⣿⣿⣿⣿⣿⠿
    ⠀⣿⣿⣿⠿⠉⣿⣿⣿⣿
    ⠀⣿⣿⠿⠀⠀⣿⣿⣿⣿
    ⣶⣿⣿⠀⠀⠀⠀⣿⣿⣿
    ⠛⣿⣿⣀⠀⠀⠀⣿⣿⣿⣿⣶⣀
    ⠀⣿⣿⠉⠀⠀⠀⠉⠉⠉⠛⠛⠿⣿⣶
    ⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿
    ⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉
    ⣀⣶⣿⠛

    ⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
    ⠀⠀⠀⠀⠀⠀⣿⣿⣿⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
    ⠀⠀⠀⠀⠀⠀⠉⣿⣿⣿⣶⣿⣿⣿⣶⣶⣤⣶⣶⠶⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
    ⠀⠀⠀⠀⠀⠀⣤⣿⠿⣿⣿⣿⣿⣿⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
    ⠛⣿⣤⣤⣀⣤⠿⠉⠀⠉⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
    ⠀⠉⠉⠉⠉⠉⠀⠀⠀⠀⠉⣿⣿⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
    ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
    ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
    ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
    ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
    ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣛⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
    ⠀⠀⠀⠀⠀⠀⠀⣶⣿⣿⠛⠿⣿⣿⣿⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
    ⠀⠀⠀⠀⠀⠀⠀⣿⠛⠉⠀⠀⠀⠛⠿⣿⣿⣶⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
    ⠀⠀⠀⠀⠀⠀⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
    ⠀⠀⠀⠀⠀⠛⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
    ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

    ⠀⠀⠀⠀⠀⠀⣤⣶⣶
    ⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣀⣀
    ⠀⠀⠀⠀⠀⣀⣶⣿⣿⣿⣿⣿⣿
    ⣤⣶⣀⠿⠶⣿⣿⣿⠿⣿⣿⣿⣿
    ⠉⠿⣿⣿⠿⠛⠉⠀⣿⣿⣿⣿⣿
    ⠀⠀⠉⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣤⣤
    ⠀⠀⠀⠀⠀⠀⠀⣤⣶⣿⣿⣿⣿⣿⣿
    ⠀⠀⠀⠀⠀⣀⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿
    ⠀⠀⠀⠀⣀⣿⣿⣿⠿⠉⠀⠀⣿⣿⣿⣿
    ⠀⠀⠀⠀⣿⣿⠿⠉⠀⠀⠀⠀⠿⣿⣿⠛
    ⠀⠀⠀⠀⠛⣿⣿⣀⠀⠀⠀⠀⠀⣿⣿⣀
    ⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠿⣿⣿
    ⠀⠀⠀⠀⠀⠉⣿⣿⠀⠀⠀⠀⠀⠀⠉⣿
    ⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣀⣿
    ⠀⠀⠀⠀⠀⠀⣀⣿⣿
    ⠀⠀⠀⠀⠤⣿⠿⠿⠿

    ⠀⠀⠀⠀⣀
    ⠀⠀⣶⣿⠿⠀⠀⠀⣀⠀⣤⣤
    ⠀⣶⣿⠀⠀⠀⠀⣿⣿⣿⠛⠛⠿⣤⣀
    ⣶⣿⣤⣤⣤⣤⣤⣿⣿⣿⣀⣤⣶⣭⣿⣶⣀
    ⠉⠉⠉⠛⠛⠿⣿⣿⣿⣿⣿⣿⣿⠛⠛⠿⠿
    ⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠿
    ⠀⠀⠀⠀⠀⠀⠀⠿⣿⣿⣿⣿
    ⠀⠀⠀⠀⠀⠀⠀⠀⣭⣿⣿⣿⣿⣿
    ⠀⠀⠀⠀⠀⠀⠀⣤⣿⣿⣿⣿⣿⣿
    ⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠿
    ⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠿
    ⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿
    ⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣿⣿
    ⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣿⣿
    ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⠛⠿⣿⣤
    ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⠀⠀⠀⣿⣿⣤
    ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣶⣿⠛⠉
    ⠀⠀⠀⠀⠀⠀⠀⠀⣤⣿⣿⠀⠀⠉
    ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

    ⠀⠀⠀⠀⠀⠀⣶⣿⣶
    ⠀⠀⠀⣤⣤⣤⣿⣿⣿
    ⠀⠀⣶⣿⣿⣿⣿⣿⣿⣿⣶
    ⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿
    ⠀⠀⣿⣉⣿⣿⣿⣿⣉⠉⣿⣶
    ⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿
    ⠀⣤⣿⣿⣿⣿⣿⣿⣿⠿⠀⣿⣶
    ⣤⣿⠿⣿⣿⣿⣿⣿⠿⠀⠀⣿⣿⣤
    ⠉⠉⠀⣿⣿⣿⣿⣿⠀⠀⠒⠛⠿⠿⠿
    ⠀⠀⠀⠉⣿⣿⣿⠀⠀⠀⠀⠀⠀⠉
    ⠀⠀⠀⣿⣿⣿⣿⣿⣶
    ⠀⠀⠀⠀⣿⠉⠿⣿⣿
    ⠀⠀⠀⠀⣿⣤⠀⠛⣿⣿
    ⠀⠀⠀⠀⣶⣿⠀⠀⠀⣿⣶
    ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣭⣿⣿
    ⠀⠀⠀⠀⠀⠀⠀⠀⣤⣿⣿⠉

    ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶
    ⠀⠀⠀⠀⠀⣀⣀⠀⣶⣿⣿⠶
    ⣶⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤
    ⠀⠉⠶⣶⣀⣿⣿⣿⣿⣿⣿⣿⠿⣿⣤⣀
    ⠀⠀⠀⣿⣿⠿⠉⣿⣿⣿⣿⣭⠀⠶⠿⠿
    ⠀⠀⠛⠛⠿⠀⠀⣿⣿⣿⣉⠿⣿⠶
    ⠀⠀⠀⠀⠀⣤⣶⣿⣿⣿⣿⣿
    ⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠒
    ⠀⠀⠀⠀⣀⣿⣿⣿⣿⣿⣿⣿
    ⠀⠀⠀⠀⠀⣿⣿⣿⠛⣭⣭⠉
    ⠀⠀⠀⠀⠀⣿⣿⣭⣤⣿⠛
    ⠀⠀⠀⠀⠀⠛⠿⣿⣿⣿⣭
    ⠀⠀⠀⠀⠀⠀⠀⣿⣿⠉⠛⠿⣶⣤
    ⠀⠀⠀⠀⠀⠀⣀⣿⠀⠀⣶⣶⠿⠿⠿
    ⠀⠀⠀⠀⠀⠀⣿⠛
    ⠀⠀⠀⠀⠀⠀⣭⣶

    ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤
    ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
    ⠀⠀⣶⠀⠀⣀⣤⣶⣤⣉⣿⣿⣤⣀
    ⠤⣤⣿⣤⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣀
    ⠀⠛⠿⠀⠀⠀⠀⠉⣿⣿⣿⣿⣿⠉⠛⠿⣿⣤
    ⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⣿⣿⠛⠀⠀⠀⣶⠿
    ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣿⣿⣿⣤⠀⣿⠿
    ⠀⠀⠀⠀⠀⠀⠀⣶⣿⣿⣿⣿⣿⣿⣿⣿
    ⠀⠀⠀⠀⠀⠀⠀⠿⣿⣿⣿⣿⣿⠿⠉⠉
    ⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣿⣿⠿
    ⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠉
    ⠀⠀⠀⠀⠀⠀⠀⠀⣛⣿⣭⣶⣀
    ⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿
    ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠉⠛⣿
    ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⣿⣿
    ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣉⠀⣶⠿
    ⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⠿
    ⠀⠀⠀⠀⠀⠀⠀⠛⠿⠛

    ⠀⠀⠀⣶⣿⣶
    ⠀⠀⠀⣿⣿⣿⣀
    ⠀⣀⣿⣿⣿⣿⣿⣿
    ⣶⣿⠛⣭⣿⣿⣿⣿
    ⠛⠛⠛⣿⣿⣿⣿⠿
    ⠀⠀⠀⠀⣿⣿⣿
    ⠀⠀⣀⣭⣿⣿⣿⣿⣀
    ⠀⠤⣿⣿⣿⣿⣿⣿⠉
    ⠀⣿⣿⣿⣿⣿⣿⠉
    ⣿⣿⣿⣿⣿⣿
    ⣿⣿⣶⣿⣿
    ⠉⠛⣿⣿⣶⣤
    ⠀⠀⠉⠿⣿⣿⣤
    ⠀⠀⣀⣤⣿⣿⣿
    ⠀⠒⠿⠛⠉⠿⣿
    ⠀⠀⠀⠀⠀⣀⣿⣿
    ⠀⠀⠀⠀⣶⠿⠿⠛ ⠀⠀⠀⠀⣀⣤
    ⠀⠀⠀⠀⣿⠿⣶
    ⠀⠀⠀⠀⣿⣿⣀
    ⠀⠀⠀⣶⣶⣿⠿⠛⣶
    ⠤⣀⠛⣿⣿⣿⣿⣿⣿⣭⣿⣤
    ⠒⠀⠀⠀⠉⣿⣿⣿⣿⠀⠀⠉⣀
    ⠀⠤⣤⣤⣀⣿⣿⣿⣿⣀⠀⠀⣿
    ⠀⠀⠛⣿⣿⣿⣿⣿⣿⣿⣭⣶⠉
    ⠀⠀⠀⠤⣿⣿⣿⣿⣿⣿⣿
    ⠀⠀⠀⣭⣿⣿⣿⠀⣿⣿⣿
    ⠀⠀⠀⣉⣿⣿⠿⠀⠿⣿⣿
    ⠀⠀⠀⠀⣿⣿⠀⠀⠀⣿⣿⣤
    ⠀⠀⠀⣀⣿⣿⠀⠀⠀⣿⣿⣿
    ⠀⠀⠀⣿⣿⣿⠀⠀⠀⣿⣿⣿
    ⠀⠀⠀⣿⣿⠛⠀⠀⠀⠉⣿⣿
    ⠀⠀⠀⠉⣿⠀⠀⠀⠀⠀⠛⣿
    ⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣿⣿
    ⠀⠀⠀⠀⣛⠀⠀⠀⠀⠀⠀⠛⠿⠿⠿
    ⠀⠀⠀⠛⠛

    ⠀⠀⠀⣀⣶⣀
    ⠀⠀⠀⠒⣛⣭
    ⠀⠀⠀⣀⠿⣿⣶
    ⠀⣤⣿⠤⣭⣿⣿
    ⣤⣿⣿⣿⠛⣿⣿⠀⣀
    ⠀⣀⠤⣿⣿⣶⣤⣒⣛
    ⠉⠀⣀⣿⣿⣿⣿⣭⠉
    ⠀⠀⣭⣿⣿⠿⠿⣿
    ⠀⣶⣿⣿⠛⠀⣿⣿
    ⣤⣿⣿⠉⠤⣿⣿⠿
    ⣿⣿⠛⠀⠿⣿⣿
    ⣿⣿⣤⠀⣿⣿⠿
    ⠀⣿⣿⣶⠀⣿⣿⣶
    ⠀⠀⠛⣿⠀⠿⣿⣿
    ⠀⠀⠀⣉⣿⠀⣿⣿
    ⠀⠶⣶⠿⠛⠀⠉⣿
    ⠀⠀⠀⠀⠀⠀⣀⣿
    ⠀⠀⠀⠀⠀⣶⣿⠿

    ⠀⠀⠀⠀⠀⠀⠀⠀⣤⣿⣿⠶⠀⠀⣀⣀
    ⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣶⣿⣿⣿⣿⣿⣿
    ⠀⠀⣀⣶⣤⣤⠿⠶⠿⠿⠿⣿⣿⣿⣉⣿⣿
    ⠿⣉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣤⣿⣿⣿⣀
    ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣿⣿⣶⣤
    ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣿⣿⣿⣿⠿⣛⣿
    ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠛⣿⣿⣿⣿
    ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⣿⠿⠀⣿⣿⣿⠛
    ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⣿⣿⣿
    ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⣿⠀⠀⣿⣶
    ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠛⠀⠀⣿⣿⣶
    ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⠤
    ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿
    ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
    ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣀
    ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿

    ⠀⠀⣀
    ⠀⠿⣿⣿⣀
    ⠀⠉⣿⣿⣀
    ⠀⠀⠛⣿⣭⣀⣀⣤
    ⠀⠀⣿⣿⣿⣿⣿⠛⠿⣶⣀
    ⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⣉⣶
    ⠀⠀⠉⣿⣿⣿⣿⣀⠀⠀⣿⠉
    ⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿
    ⠀⣀⣿⣿⣿⣿⣿⣿⣿⣿⠿
    ⠀⣿⣿⣿⠿⠉⣿⣿⣿⣿
    ⠀⣿⣿⠿⠀⠀⣿⣿⣿⣿
    ⣶⣿⣿⠀⠀⠀⠀⣿⣿⣿
    ⠛⣿⣿⣀⠀⠀⠀⣿⣿⣿⣿⣶⣀
    ⠀⣿⣿⠉⠀⠀⠀⠉⠉⠉⠛⠛⠿⣿⣶
    ⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿
    ⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉
    ⣀⣶⣿⠛

    ⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
    ⠀⠀⠀⠀⠀⠀⣿⣿⣿⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
    ⠀⠀⠀⠀⠀⠀⠉⣿⣿⣿⣶⣿⣿⣿⣶⣶⣤⣶⣶⠶⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
    ⠀⠀⠀⠀⠀⠀⣤⣿⠿⣿⣿⣿⣿⣿⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
    ⠛⣿⣤⣤⣀⣤⠿⠉⠀⠉⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
    ⠀⠉⠉⠉⠉⠉⠀⠀⠀⠀⠉⣿⣿⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
    ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
    ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
    ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
    ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
    ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣛⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
    ⠀⠀⠀⠀⠀⠀⠀⣶⣿⣿⠛⠿⣿⣿⣿⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
    ⠀⠀⠀⠀⠀⠀⠀⣿⠛⠉⠀⠀⠀⠛⠿⣿⣿⣶⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
    ⠀⠀⠀⠀⠀⠀⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
    ⠀⠀⠀⠀⠀⠛⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
    ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

    ⠀⠀⠀⠀⠀⠀⣤⣶⣶
    ⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣀⣀
    ⠀⠀⠀⠀⠀⣀⣶⣿⣿⣿⣿⣿⣿
    ⣤⣶⣀⠿⠶⣿⣿⣿⠿⣿⣿⣿⣿
    ⠉⠿⣿⣿⠿⠛⠉⠀⣿⣿⣿⣿⣿
    ⠀⠀⠉⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣤⣤
    ⠀⠀⠀⠀⠀⠀⠀⣤⣶⣿⣿⣿⣿⣿⣿
    ⠀⠀⠀⠀⠀⣀⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿
    ⠀⠀⠀⠀⣀⣿⣿⣿⠿⠉⠀⠀⣿⣿⣿⣿
    ⠀⠀⠀⠀⣿⣿⠿⠉⠀⠀⠀⠀⠿⣿⣿⠛
    ⠀⠀⠀⠀⠛⣿⣿⣀⠀⠀⠀⠀⠀⣿⣿⣀
    ⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠿⣿⣿
    ⠀⠀⠀⠀⠀⠉⣿⣿⠀⠀⠀⠀⠀⠀⠉⣿
    ⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣀⣿
    ⠀⠀⠀⠀⠀⠀⣀⣿⣿
    ⠀⠀⠀⠀⠤⣿⠿⠿⠿

    ⠀⠀⠀⠀⣀
    ⠀⠀⣶⣿⠿⠀⠀⠀⣀⠀⣤⣤
    ⠀⣶⣿⠀⠀⠀⠀⣿⣿⣿⠛⠛⠿⣤⣀
    ⣶⣿⣤⣤⣤⣤⣤⣿⣿⣿⣀⣤⣶⣭⣿⣶⣀
    ⠉⠉⠉⠛⠛⠿⣿⣿⣿⣿⣿⣿⣿⠛⠛⠿⠿
    ⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠿
    ⠀⠀⠀⠀⠀⠀⠀⠿⣿⣿⣿⣿
    ⠀⠀⠀⠀⠀⠀⠀⠀⣭⣿⣿⣿⣿⣿
    ⠀⠀⠀⠀⠀⠀⠀⣤⣿⣿⣿⣿⣿⣿
    ⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠿
    ⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠿
    ⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿
    ⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣿⣿
    ⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣿⣿
    ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⠛⠿⣿⣤
    ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⠀⠀⠀⣿⣿⣤
    ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣶⣿⠛⠉
    ⠀⠀⠀⠀⠀⠀⠀⠀⣤⣿⣿⠀⠀⠉
    ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

    ⠀⠀⠀⠀⠀⠀⣶⣿⣶
    ⠀⠀⠀⣤⣤⣤⣿⣿⣿
    ⠀⠀⣶⣿⣿⣿⣿⣿⣿⣿⣶
    ⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿
    ⠀⠀⣿⣉⣿⣿⣿⣿⣉⠉⣿⣶
    ⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿
    ⠀⣤⣿⣿⣿⣿⣿⣿⣿⠿⠀⣿⣶
    ⣤⣿⠿⣿⣿⣿⣿⣿⠿⠀⠀⣿⣿⣤
    ⠉⠉⠀⣿⣿⣿⣿⣿⠀⠀⠒⠛⠿⠿⠿
    ⠀⠀⠀⠉⣿⣿⣿⠀⠀⠀⠀⠀⠀⠉
    ⠀⠀⠀⣿⣿⣿⣿⣿⣶
    ⠀⠀⠀⠀⣿⠉⠿⣿⣿
    ⠀⠀⠀⠀⣿⣤⠀⠛⣿⣿
    ⠀⠀⠀⠀⣶⣿⠀⠀⠀⣿⣶
    ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣭⣿⣿
    ⠀⠀⠀⠀⠀⠀⠀⠀⣤⣿⣿⠉

    ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶
    ⠀⠀⠀⠀⠀⣀⣀⠀⣶⣿⣿⠶
    ⣶⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤
    ⠀⠉⠶⣶⣀⣿⣿⣿⣿⣿⣿⣿⠿⣿⣤⣀
    ⠀⠀⠀⣿⣿⠿⠉⣿⣿⣿⣿⣭⠀⠶⠿⠿
    ⠀⠀⠛⠛⠿⠀⠀⣿⣿⣿⣉⠿⣿⠶
    ⠀⠀⠀⠀⠀⣤⣶⣿⣿⣿⣿⣿
    ⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠒
    ⠀⠀⠀⠀⣀⣿⣿⣿⣿⣿⣿⣿
    ⠀⠀⠀⠀⠀⣿⣿⣿⠛⣭⣭⠉
    ⠀⠀⠀⠀⠀⣿⣿⣭⣤⣿⠛
    ⠀⠀⠀⠀⠀⠛⠿⣿⣿⣿⣭
    ⠀⠀⠀⠀⠀⠀⠀⣿⣿⠉⠛⠿⣶⣤
    ⠀⠀⠀⠀⠀⠀⣀⣿⠀⠀⣶⣶⠿⠿⠿
    ⠀⠀⠀⠀⠀⠀⣿⠛
    ⠀⠀⠀⠀⠀⠀⣭⣶

    ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤
    ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
    ⠀⠀⣶⠀⠀⣀⣤⣶⣤⣉⣿⣿⣤⣀
    ⠤⣤⣿⣤⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣀
    ⠀⠛⠿⠀⠀⠀⠀⠉⣿⣿⣿⣿⣿⠉⠛⠿⣿⣤
    ⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⣿⣿⠛⠀⠀⠀⣶⠿
    ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣿⣿⣿⣤⠀⣿⠿
    ⠀⠀⠀⠀⠀⠀⠀⣶⣿⣿⣿⣿⣿⣿⣿⣿
    ⠀⠀⠀⠀⠀⠀⠀⠿⣿⣿⣿⣿⣿⠿⠉⠉
    ⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣿⣿⠿
    ⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠉
    ⠀⠀⠀⠀⠀⠀⠀⠀⣛⣿⣭⣶⣀
    ⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿
    ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠉⠛⣿
    ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⣿⣿
    ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣉⠀⣶⠿
    ⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⠿
    ⠀⠀⠀⠀⠀⠀⠀⠛⠿⠛

    ⠀⠀⠀⣶⣿⣶
    ⠀⠀⠀⣿⣿⣿⣀
    ⠀⣀⣿⣿⣿⣿⣿⣿
    ⣶⣿⠛⣭⣿⣿⣿⣿
    ⠛⠛⠛⣿⣿⣿⣿⠿
    ⠀⠀⠀⠀⣿⣿⣿
    ⠀⠀⣀⣭⣿⣿⣿⣿⣀
    ⠀⠤⣿⣿⣿⣿⣿⣿⠉
    ⠀⣿⣿⣿⣿⣿⣿⠉
    ⣿⣿⣿⣿⣿⣿
    ⣿⣿⣶⣿⣿
    ⠉⠛⣿⣿⣶⣤
    ⠀⠀⠉⠿⣿⣿⣤
    ⠀⠀⣀⣤⣿⣿⣿
    ⠀⠒⠿⠛⠉⠿⣿
    ⠀⠀⠀⠀⠀⣀⣿⣿
    ⠀⠀⠀⠀⣶⠿⠿⠛ ⠀⠀⠀⠀⣀⣤
    ⠀⠀⠀⠀⣿⠿⣶
    ⠀⠀⠀⠀⣿⣿⣀
    ⠀⠀⠀⣶⣶⣿⠿⠛⣶
    ⠤⣀⠛⣿⣿⣿⣿⣿⣿⣭⣿⣤
    ⠒⠀⠀⠀⠉⣿⣿⣿⣿⠀⠀⠉⣀
    ⠀⠤⣤⣤⣀⣿⣿⣿⣿⣀⠀⠀⣿
    ⠀⠀⠛⣿⣿⣿⣿⣿⣿⣿⣭⣶⠉
    ⠀⠀⠀⠤⣿⣿⣿⣿⣿⣿⣿
    ⠀⠀⠀⣭⣿⣿⣿⠀⣿⣿⣿
    ⠀⠀⠀⣉⣿⣿⠿⠀⠿⣿⣿
    ⠀⠀⠀⠀⣿⣿⠀⠀⠀⣿⣿⣤
    ⠀⠀⠀⣀⣿⣿⠀⠀⠀⣿⣿⣿
    ⠀⠀⠀⣿⣿⣿⠀⠀⠀⣿⣿⣿
    ⠀⠀⠀⣿⣿⠛⠀⠀⠀⠉⣿⣿
    ⠀⠀⠀⠉⣿⠀⠀⠀⠀⠀⠛⣿
    ⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣿⣿
    ⠀⠀⠀⠀⣛⠀⠀⠀⠀⠀⠀⠛⠿⠿⠿
    ⠀⠀⠀⠛⠛

    ⠀⠀⠀⣀⣶⣀
    ⠀⠀⠀⠒⣛⣭
    ⠀⠀⠀⣀⠿⣿⣶
    ⠀⣤⣿⠤⣭⣿⣿
    ⣤⣿⣿⣿⠛⣿⣿⠀⣀
    ⠀⣀⠤⣿⣿⣶⣤⣒⣛
    ⠉⠀⣀⣿⣿⣿⣿⣭⠉
    ⠀⠀⣭⣿⣿⠿⠿⣿
    ⠀⣶⣿⣿⠛⠀⣿⣿
    ⣤⣿⣿⠉⠤⣿⣿⠿
    ⣿⣿⠛⠀⠿⣿⣿
    ⣿⣿⣤⠀⣿⣿⠿
    ⠀⣿⣿⣶⠀⣿⣿⣶
    ⠀⠀⠛⣿⠀⠿⣿⣿
    ⠀⠀⠀⣉⣿⠀⣿⣿
    ⠀⠶⣶⠿⠛⠀⠉⣿
    ⠀⠀⠀⠀⠀⠀⣀⣿
    ⠀⠀⠀⠀⠀⣶⣿⠿

    ⠀⠀⠀⠀⠀⠀⠀⠀⣤⣿⣿⠶⠀⠀⣀⣀
    ⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣶⣿⣿⣿⣿⣿⣿
    ⠀⠀⣀⣶⣤⣤⠿⠶⠿⠿⠿⣿⣿⣿⣉⣿⣿
    ⠿⣉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣤⣿⣿⣿⣀
    ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣿⣿⣶⣤
    ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣿⣿⣿⣿⠿⣛⣿
    ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠛⣿⣿⣿⣿
    ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⣿⠿⠀⣿⣿⣿⠛
    ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⣿⣿⣿
    ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⣿⠀⠀⣿⣶
    ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠛⠀⠀⣿⣿⣶
    ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⠤
    ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿
    ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
    ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣀
    ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿

    ⠀⠀⣀
    ⠀⠿⣿⣿⣀
    ⠀⠉⣿⣿⣀
    ⠀⠀⠛⣿⣭⣀⣀⣤
    ⠀⠀⣿⣿⣿⣿⣿⠛⠿⣶⣀
    ⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⣉⣶
    ⠀⠀⠉⣿⣿⣿⣿⣀⠀⠀⣿⠉
    ⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿
    ⠀⣀⣿⣿⣿⣿⣿⣿⣿⣿⠿
    ⠀⣿⣿⣿⠿⠉⣿⣿⣿⣿
    ⠀⣿⣿⠿⠀⠀⣿⣿⣿⣿
    ⣶⣿⣿⠀⠀⠀⠀⣿⣿⣿
    ⠛⣿⣿⣀⠀⠀⠀⣿⣿⣿⣿⣶⣀
    ⠀⣿⣿⠉⠀⠀⠀⠉⠉⠉⠛⠛⠿⣿⣶
    ⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿
    ⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉
    ⣀⣶⣿⠛

    ⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
    ⠀⠀⠀⠀⠀⠀⣿⣿⣿⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
    ⠀⠀⠀⠀⠀⠀⠉⣿⣿⣿⣶⣿⣿⣿⣶⣶⣤⣶⣶⠶⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
    ⠀⠀⠀⠀⠀⠀⣤⣿⠿⣿⣿⣿⣿⣿⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
    ⠛⣿⣤⣤⣀⣤⠿⠉⠀⠉⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
    ⠀⠉⠉⠉⠉⠉⠀⠀⠀⠀⠉⣿⣿⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
    ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
    ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
    ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
    ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
    ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣛⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
    ⠀⠀⠀⠀⠀⠀⠀⣶⣿⣿⠛⠿⣿⣿⣿⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
    ⠀⠀⠀⠀⠀⠀⠀⣿⠛⠉⠀⠀⠀⠛⠿⣿⣿⣶⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
    ⠀⠀⠀⠀⠀⠀⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
    ⠀⠀⠀⠀⠀⠛⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
    ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

    ⠀⠀⠀⠀⠀⠀⣤⣶⣶
    ⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣀⣀
    ⠀⠀⠀⠀⠀⣀⣶⣿⣿⣿⣿⣿⣿
    ⣤⣶⣀⠿⠶⣿⣿⣿⠿⣿⣿⣿⣿
    ⠉⠿⣿⣿⠿⠛⠉⠀⣿⣿⣿⣿⣿
    ⠀⠀⠉⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣤⣤
    ⠀⠀⠀⠀⠀⠀⠀⣤⣶⣿⣿⣿⣿⣿⣿
    ⠀⠀⠀⠀⠀⣀⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿
    ⠀⠀⠀⠀⣀⣿⣿⣿⠿⠉⠀⠀⣿⣿⣿⣿
    ⠀⠀⠀⠀⣿⣿⠿⠉⠀⠀⠀⠀⠿⣿⣿⠛
    ⠀⠀⠀⠀⠛⣿⣿⣀⠀⠀⠀⠀⠀⣿⣿⣀
    ⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠿⣿⣿
    ⠀⠀⠀⠀⠀⠉⣿⣿⠀⠀⠀⠀⠀⠀⠉⣿
    ⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣀⣿
    ⠀⠀⠀⠀⠀⠀⣀⣿⣿
    ⠀⠀⠀⠀⠤⣿⠿⠿⠿

    ⠀⠀⠀⠀⣀
    ⠀⠀⣶⣿⠿⠀⠀⠀⣀⠀⣤⣤
    ⠀⣶⣿⠀⠀⠀⠀⣿⣿⣿⠛⠛⠿⣤⣀
    ⣶⣿⣤⣤⣤⣤⣤⣿⣿⣿⣀⣤⣶⣭⣿⣶⣀
    ⠉⠉⠉⠛⠛⠿⣿⣿⣿⣿⣿⣿⣿⠛⠛⠿⠿
    ⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠿
    ⠀⠀⠀⠀⠀⠀⠀⠿⣿⣿⣿⣿
    ⠀⠀⠀⠀⠀⠀⠀⠀⣭⣿⣿⣿⣿⣿
    ⠀⠀⠀⠀⠀⠀⠀⣤⣿⣿⣿⣿⣿⣿
    ⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠿
    ⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠿
    ⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿
    ⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣿⣿
    ⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣿⣿
    ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⠛⠿⣿⣤
    ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⠀⠀⠀⣿⣿⣤
    ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣶⣿⠛⠉
    ⠀⠀⠀⠀⠀⠀⠀⠀⣤⣿⣿⠀⠀⠉
    ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

    ⠀⠀⠀⠀⠀⠀⣶⣿⣶
    ⠀⠀⠀⣤⣤⣤⣿⣿⣿
    ⠀⠀⣶⣿⣿⣿⣿⣿⣿⣿⣶
    ⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿
    ⠀⠀⣿⣉⣿⣿⣿⣿⣉⠉⣿⣶
    ⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿
    ⠀⣤⣿⣿⣿⣿⣿⣿⣿⠿⠀⣿⣶
    ⣤⣿⠿⣿⣿⣿⣿⣿⠿⠀⠀⣿⣿⣤
    ⠉⠉⠀⣿⣿⣿⣿⣿⠀⠀⠒⠛⠿⠿⠿
    ⠀⠀⠀⠉⣿⣿⣿⠀⠀⠀⠀⠀⠀⠉
    ⠀⠀⠀⣿⣿⣿⣿⣿⣶
    ⠀⠀⠀⠀⣿⠉⠿⣿⣿
    ⠀⠀⠀⠀⣿⣤⠀⠛⣿⣿
    ⠀⠀⠀⠀⣶⣿⠀⠀⠀⣿⣶
    ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣭⣿⣿
    ⠀⠀⠀⠀⠀⠀⠀⠀⣤⣿⣿⠉

    ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶
    ⠀⠀⠀⠀⠀⣀⣀⠀⣶⣿⣿⠶
    ⣶⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤
    ⠀⠉⠶⣶⣀⣿⣿⣿⣿⣿⣿⣿⠿⣿⣤⣀
    ⠀⠀⠀⣿⣿⠿⠉⣿⣿⣿⣿⣭⠀⠶⠿⠿
    ⠀⠀⠛⠛⠿⠀⠀⣿⣿⣿⣉⠿⣿⠶
    ⠀⠀⠀⠀⠀⣤⣶⣿⣿⣿⣿⣿
    ⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠒
    ⠀⠀⠀⠀⣀⣿⣿⣿⣿⣿⣿⣿
    ⠀⠀⠀⠀⠀⣿⣿⣿⠛⣭⣭⠉
    ⠀⠀⠀⠀⠀⣿⣿⣭⣤⣿⠛
    ⠀⠀⠀⠀⠀⠛⠿⣿⣿⣿⣭
    ⠀⠀⠀⠀⠀⠀⠀⣿⣿⠉⠛⠿⣶⣤
    ⠀⠀⠀⠀⠀⠀⣀⣿⠀⠀⣶⣶⠿⠿⠿
    ⠀⠀⠀⠀⠀⠀⣿⠛
    ⠀⠀⠀⠀⠀⠀⣭⣶

    ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤
    ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
    ⠀⠀⣶⠀⠀⣀⣤⣶⣤⣉⣿⣿⣤⣀
    ⠤⣤⣿⣤⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣀
    ⠀⠛⠿⠀⠀⠀⠀⠉⣿⣿⣿⣿⣿⠉⠛⠿⣿⣤
    ⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⣿⣿⠛⠀⠀⠀⣶⠿
    ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣿⣿⣿⣤⠀⣿⠿
    ⠀⠀⠀⠀⠀⠀⠀⣶⣿⣿⣿⣿⣿⣿⣿⣿
    ⠀⠀⠀⠀⠀⠀⠀⠿⣿⣿⣿⣿⣿⠿⠉⠉
    ⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣿⣿⠿
    ⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠉
    ⠀⠀⠀⠀⠀⠀⠀⠀⣛⣿⣭⣶⣀
    ⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿
    ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠉⠛⣿
    ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⣿⣿
    ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣉⠀⣶⠿
    ⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⠿
    ⠀⠀⠀⠀⠀⠀⠀⠛⠿⠛

    ⠀⠀⠀⣶⣿⣶
    ⠀⠀⠀⣿⣿⣿⣀
    ⠀⣀⣿⣿⣿⣿⣿⣿
    ⣶⣿⠛⣭⣿⣿⣿⣿
    ⠛⠛⠛⣿⣿⣿⣿⠿
    ⠀⠀⠀⠀⣿⣿⣿
    ⠀⠀⣀⣭⣿⣿⣿⣿⣀
    ⠀⠤⣿⣿⣿⣿⣿⣿⠉
    ⠀⣿⣿⣿⣿⣿⣿⠉
    ⣿⣿⣿⣿⣿⣿
    ⣿⣿⣶⣿⣿
    ⠉⠛⣿⣿⣶⣤
    ⠀⠀⠉⠿⣿⣿⣤
    ⠀⠀⣀⣤⣿⣿⣿
    ⠀⠒⠿⠛⠉⠿⣿
    ⠀⠀⠀⠀⠀⣀⣿⣿
    ⠀⠀⠀⠀⣶⠿⠿⠛ ⠀⠀⠀⠀⣀⣤
    ⠀⠀⠀⠀⣿⠿⣶
    ⠀⠀⠀⠀⣿⣿⣀
    ⠀⠀⠀⣶⣶⣿⠿⠛⣶
    ⠤⣀⠛⣿⣿⣿⣿⣿⣿⣭⣿⣤
    ⠒⠀⠀⠀⠉⣿⣿⣿⣿⠀⠀⠉⣀
    ⠀⠤⣤⣤⣀⣿⣿⣿⣿⣀⠀⠀⣿
    ⠀⠀⠛⣿⣿⣿⣿⣿⣿⣿⣭⣶⠉
    ⠀⠀⠀⠤⣿⣿⣿⣿⣿⣿⣿
    ⠀⠀⠀⣭⣿⣿⣿⠀⣿⣿⣿
    ⠀⠀⠀⣉⣿⣿⠿⠀⠿⣿⣿
    ⠀⠀⠀⠀⣿⣿⠀⠀⠀⣿⣿⣤
    ⠀⠀⠀⣀⣿⣿⠀⠀⠀⣿⣿⣿
    ⠀⠀⠀⣿⣿⣿⠀⠀⠀⣿⣿⣿
    ⠀⠀⠀⣿⣿⠛⠀⠀⠀⠉⣿⣿
    ⠀⠀⠀⠉⣿⠀⠀⠀⠀⠀⠛⣿
    ⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣿⣿
    ⠀⠀⠀⠀⣛⠀⠀⠀⠀⠀⠀⠛⠿⠿⠿
    ⠀⠀⠀⠛⠛

    ⠀⠀⠀⣀⣶⣀
    ⠀⠀⠀⠒⣛⣭
    ⠀⠀⠀⣀⠿⣿⣶
    ⠀⣤⣿⠤⣭⣿⣿
    ⣤⣿⣿⣿⠛⣿⣿⠀⣀
    ⠀⣀⠤⣿⣿⣶⣤⣒⣛
    ⠉⠀⣀⣿⣿⣿⣿⣭⠉
    ⠀⠀⣭⣿⣿⠿⠿⣿
    ⠀⣶⣿⣿⠛⠀⣿⣿
    ⣤⣿⣿⠉⠤⣿⣿⠿
    ⣿⣿⠛⠀⠿⣿⣿
    ⣿⣿⣤⠀⣿⣿⠿
    ⠀⣿⣿⣶⠀⣿⣿⣶
    ⠀⠀⠛⣿⠀⠿⣿⣿
    ⠀⠀⠀⣉⣿⠀⣿⣿
    ⠀⠶⣶⠿⠛⠀⠉⣿
    ⠀⠀⠀⠀⠀⠀⣀⣿
    ⠀⠀⠀⠀⠀⣶⣿⠿

    ⠀⠀⠀⠀⠀⠀⠀⠀⣤⣿⣿⠶⠀⠀⣀⣀
    ⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣶⣿⣿⣿⣿⣿⣿
    ⠀⠀⣀⣶⣤⣤⠿⠶⠿⠿⠿⣿⣿⣿⣉⣿⣿
    ⠿⣉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣤⣿⣿⣿⣀
    ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣿⣿⣶⣤
    ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣿⣿⣿⣿⠿⣛⣿
    ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠛⣿⣿⣿⣿
    ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⣿⠿⠀⣿⣿⣿⠛
    ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⣿⣿⣿
    ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⣿⠀⠀⣿⣶
    ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠛⠀⠀⣿⣿⣶
    ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⠤
    ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿
    ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
    ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣀
    ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿

    ⠀⠀⣀
    ⠀⠿⣿⣿⣀
    ⠀⠉⣿⣿⣀
    ⠀⠀⠛⣿⣭⣀⣀⣤
    ⠀⠀⣿⣿⣿⣿⣿⠛⠿⣶⣀
    ⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⣉⣶
    ⠀⠀⠉⣿⣿⣿⣿⣀⠀⠀⣿⠉
    ⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿
    ⠀⣀⣿⣿⣿⣿⣿⣿⣿⣿⠿
    ⠀⣿⣿⣿⠿⠉⣿⣿⣿⣿
    ⠀⣿⣿⠿⠀⠀⣿⣿⣿⣿
    ⣶⣿⣿⠀⠀⠀⠀⣿⣿⣿
    ⠛⣿⣿⣀⠀⠀⠀⣿⣿⣿⣿⣶⣀
    ⠀⣿⣿⠉⠀⠀⠀⠉⠉⠉⠛⠛⠿⣿⣶
    ⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿
    ⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉
    ⣀⣶⣿⠛

    ⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
    ⠀⠀⠀⠀⠀⠀⣿⣿⣿⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
    ⠀⠀⠀⠀⠀⠀⠉⣿⣿⣿⣶⣿⣿⣿⣶⣶⣤⣶⣶⠶⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
    ⠀⠀⠀⠀⠀⠀⣤⣿⠿⣿⣿⣿⣿⣿⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
    ⠛⣿⣤⣤⣀⣤⠿⠉⠀⠉⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
    ⠀⠉⠉⠉⠉⠉⠀⠀⠀⠀⠉⣿⣿⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
    ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
    ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
    ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
    ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
    ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣛⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
    ⠀⠀⠀⠀⠀⠀⠀⣶⣿⣿⠛⠿⣿⣿⣿⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
    ⠀⠀⠀⠀⠀⠀⠀⣿⠛⠉⠀⠀⠀⠛⠿⣿⣿⣶⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
    ⠀⠀⠀⠀⠀⠀⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
    ⠀⠀⠀⠀⠀⠛⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
    ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

    ⠀⠀⠀⠀⠀⠀⣤⣶⣶
    ⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣀⣀
    ⠀⠀⠀⠀⠀⣀⣶⣿⣿⣿⣿⣿⣿
    ⣤⣶⣀⠿⠶⣿⣿⣿⠿⣿⣿⣿⣿
    ⠉⠿⣿⣿⠿⠛⠉⠀⣿⣿⣿⣿⣿
    ⠀⠀⠉⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣤⣤
    ⠀⠀⠀⠀⠀⠀⠀⣤⣶⣿⣿⣿⣿⣿⣿
    ⠀⠀⠀⠀⠀⣀⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿
    ⠀⠀⠀⠀⣀⣿⣿⣿⠿⠉⠀⠀⣿⣿⣿⣿
    ⠀⠀⠀⠀⣿⣿⠿⠉⠀⠀⠀⠀⠿⣿⣿⠛
    ⠀⠀⠀⠀⠛⣿⣿⣀⠀⠀⠀⠀⠀⣿⣿⣀
    ⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠿⣿⣿
    ⠀⠀⠀⠀⠀⠉⣿⣿⠀⠀⠀⠀⠀⠀⠉⣿
    ⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣀⣿
    ⠀⠀⠀⠀⠀⠀⣀⣿⣿
    ⠀⠀⠀⠀⠤⣿⠿⠿⠿

    ⠀⠀⠀⠀⣀
    ⠀⠀⣶⣿⠿⠀⠀⠀⣀⠀⣤⣤
    ⠀⣶⣿⠀⠀⠀⠀⣿⣿⣿⠛⠛⠿⣤⣀
    ⣶⣿⣤⣤⣤⣤⣤⣿⣿⣿⣀⣤⣶⣭⣿⣶⣀
    ⠉⠉⠉⠛⠛⠿⣿⣿⣿⣿⣿⣿⣿⠛⠛⠿⠿
    ⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠿
    ⠀⠀⠀⠀⠀⠀⠀⠿⣿⣿⣿⣿
    ⠀⠀⠀⠀⠀⠀⠀⠀⣭⣿⣿⣿⣿⣿
    ⠀⠀⠀⠀⠀⠀⠀⣤⣿⣿⣿⣿⣿⣿
    ⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠿
    ⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠿
    ⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿
    ⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣿⣿
    ⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣿⣿
    ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⠛⠿⣿⣤
    ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⠀⠀⠀⣿⣿⣤
    ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣶⣿⠛⠉
    ⠀⠀⠀⠀⠀⠀⠀⠀⣤⣿⣿⠀⠀⠉
    ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

    ⠀⠀⠀⠀⠀⠀⣶⣿⣶
    ⠀⠀⠀⣤⣤⣤⣿⣿⣿
    ⠀⠀⣶⣿⣿⣿⣿⣿⣿⣿⣶
    ⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿
    ⠀⠀⣿⣉⣿⣿⣿⣿⣉⠉⣿⣶
    ⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿
    ⠀⣤⣿⣿⣿⣿⣿⣿⣿⠿⠀⣿⣶
    ⣤⣿⠿⣿⣿⣿⣿⣿⠿⠀⠀⣿⣿⣤
    ⠉⠉⠀⣿⣿⣿⣿⣿⠀⠀⠒⠛⠿⠿⠿
    ⠀⠀⠀⠉⣿⣿⣿⠀⠀⠀⠀⠀⠀⠉
    ⠀⠀⠀⣿⣿⣿⣿⣿⣶
    ⠀⠀⠀⠀⣿⠉⠿⣿⣿
    ⠀⠀⠀⠀⣿⣤⠀⠛⣿⣿
    ⠀⠀⠀⠀⣶⣿⠀⠀⠀⣿⣶
    ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣭⣿⣿
    ⠀⠀⠀⠀⠀⠀⠀⠀⣤⣿⣿⠉

    ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶
    ⠀⠀⠀⠀⠀⣀⣀⠀⣶⣿⣿⠶
    ⣶⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤
    ⠀⠉⠶⣶⣀⣿⣿⣿⣿⣿⣿⣿⠿⣿⣤⣀
    ⠀⠀⠀⣿⣿⠿⠉⣿⣿⣿⣿⣭⠀⠶⠿⠿
    ⠀⠀⠛⠛⠿⠀⠀⣿⣿⣿⣉⠿⣿⠶
    ⠀⠀⠀⠀⠀⣤⣶⣿⣿⣿⣿⣿
    ⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠒
    ⠀⠀⠀⠀⣀⣿⣿⣿⣿⣿⣿⣿
    ⠀⠀⠀⠀⠀⣿⣿⣿⠛⣭⣭⠉
    ⠀⠀⠀⠀⠀⣿⣿⣭⣤⣿⠛
    ⠀⠀⠀⠀⠀⠛⠿⣿⣿⣿⣭
    ⠀⠀⠀⠀⠀⠀⠀⣿⣿⠉⠛⠿⣶⣤
    ⠀⠀⠀⠀⠀⠀⣀⣿⠀⠀⣶⣶⠿⠿⠿
    ⠀⠀⠀⠀⠀⠀⣿⠛
    ⠀⠀⠀⠀⠀⠀⣭⣶

    ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤
    ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
    ⠀⠀⣶⠀⠀⣀⣤⣶⣤⣉⣿⣿⣤⣀
    ⠤⣤⣿⣤⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣀
    ⠀⠛⠿⠀⠀⠀⠀⠉⣿⣿⣿⣿⣿⠉⠛⠿⣿⣤
    ⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⣿⣿⠛⠀⠀⠀⣶⠿
    ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣿⣿⣿⣤⠀⣿⠿
    ⠀⠀⠀⠀⠀⠀⠀⣶⣿⣿⣿⣿⣿⣿⣿⣿
    ⠀⠀⠀⠀⠀⠀⠀⠿⣿⣿⣿⣿⣿⠿⠉⠉
    ⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣿⣿⠿
    ⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠉
    ⠀⠀⠀⠀⠀⠀⠀⠀⣛⣿⣭⣶⣀
    ⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿
    ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠉⠛⣿
    ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⣿⣿
    ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣉⠀⣶⠿
    ⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⠿
    ⠀⠀⠀⠀⠀⠀⠀⠛⠿⠛

    ⠀⠀⠀⣶⣿⣶
    ⠀⠀⠀⣿⣿⣿⣀
    ⠀⣀⣿⣿⣿⣿⣿⣿
    ⣶⣿⠛⣭⣿⣿⣿⣿
    ⠛⠛⠛⣿⣿⣿⣿⠿
    ⠀⠀⠀⠀⣿⣿⣿
    ⠀⠀

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