Surface Integrals, Stokes & Divergence · Hard problem

At a certain instant, a balloon occupies the ellipsoid $\dfrac{x^2}{9}+\dfrac{y^2}{4}+z^2\le 1$ (meters), and every point of its surface is moving outward with velocity $\mathbf F=(2x,2y,2z)$ m/s. Find the outward flux of $\mathbf F$ through the balloon's surface, in m$^3$/s.