UZ-MO 2013 Problem 2

Let $x$ and $y$ are real numbers such that $x^2y^2+2yx^2+1=0.$ If $S=\frac{2}{x^2}+1+\frac{1}{x}+y(y+2+\frac{1}{x})$ , find (a)max $S$ and (b) min $S$ .