Surface Integrals, Stokes & Divergence · Challenge problem

Let $\mathbf F = (z, x, y)$ and let $C$ be the circle $x^2 + y^2 = 1$, $z = 0$, oriented counterclockwise seen from above. Compute $\oint_C \mathbf F\cdot d\mathbf r$ via Stokes' theorem. Give the answer as $k\pi$.