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 $$a+b$$.

(第十五届AIME1997 第13题)