1997 AIME Problem 13

Let S be the set of points in the Cartesian plane that satisfy

|||x|-2|-1|+|||y|-2|-1|=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.