Surface Integrals, Stokes & Divergence · Medium problem

Let $\mathbf F = (z - y,\ x + z,\ xy)$ and let $S$ be the paraboloid $z = 4 - x^2 - y^2$, $z \ge 0$, with upward normal. Use Stokes' theorem to find $\iint_S (\nabla\times\mathbf F)\cdot d\mathbf S$. Give an exact answer in terms of $\pi$.