Surface Integrals, Stokes & Divergence · Hard problem

Let $\mathbf F=(-y,x,0)$ and let the annular washer plate be $1\le x^2+y^2\le9$ in the plane $z=0$. Its boundary consists of the outer circle $C_1$ (radius $3$, counterclockwise) and the inner circle $C_2$ (radius $1$, clockwise) — together oriented to match the washer's upward normal by the right-hand rule. Use Stokes' theorem to find $\displaystyle\oint_{C_1}\mathbf F\cdot d\mathbf r+\oint_{C_2}\mathbf F\cdot d\mathbf r$.