Surface Integrals, Stokes & Divergence · Superchallenge problem

Let $T$ be the torus obtained by revolving the circle $(x - 2)^2 + z^2 = 1$ (in the $xz$-plane) about the $z$-axis. Find the outward flux of $\mathbf F = (x, y, z)$ through $T$. Give an exact answer in terms of $\pi$.