Surface Integrals, Stokes & Divergence · Hard problem

Let $\mathbf F=(y^2,z^2,x^2)$ and let $C$ be the unit circle $x^2+y^2=1$, $z=0$, traversed counterclockwise viewed from above. Using Stokes' theorem with whichever capping surface — the flat disk or the upper unit hemisphere — makes the integral easiest, find $\displaystyle\oint_C \mathbf F\cdot d\mathbf r$.