Surface Integrals, Stokes & Divergence · Easy problem

Let $\mathbf F = (-y, x, z)$ and let $S$ be the upper hemisphere $x^2 + y^2 + z^2 = 4$, $z \ge 0$, 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 $\pi$.