# Problem #305

 305 Let $S$ be the set of points in the Cartesian plane that satisfy $\Big|\big| |x|-2\big|-1\Big|+\Big|\big| |y|-2\big|-1\Big|=1.$ If a model of $S$ were built from wire of negligible thickness, then the total length of wire required would be $a\sqrt{b}$, where $a$ and $b$ are positive integers and $b$ is not divisible by the square of any prime number. Find $a+b$. This problem is copyrighted by the American Mathematics Competitions.
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