1997 AIME Problem 13

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.

Leading zeroes must be inputted, so if your answer is 34, then input 034

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.