Surface Integrals, Stokes & Divergence · Superchallenge problem

Let $\mathbf F = \left(yz + 3z - y,\ x - z,\ 2y + x^2\right)$. Consider every circle $C$ of radius $1$ centred at the origin, lying in any plane through the origin and traversed in either direction. Find the largest possible value of $\oint_C \mathbf F\cdot d\mathbf r$. Give an exact answer.