Surface Integrals, Stokes & Divergence · Superchallenge problem

Let $\mathbf F = \left(\dfrac{y^3}{3},\ x - \dfrac{x^3}{3},\ 0\right)$. Among all simple closed curves $C$ in the $xy$-plane, oriented counterclockwise, find the largest possible value of $\oint_C \mathbf F\cdot d\mathbf r$. Give an exact answer in terms of $\pi$.