Surface Integrals, Stokes & Divergence · Superchallenge problem

Let $S$ be the ellipsoid $x^2 + \dfrac{y^2}{4} + \dfrac{z^2}{9} = 1$. Compute $\displaystyle\iint_S \sqrt{x^2 + \frac{y^2}{16} + \frac{z^2}{81}}\;dS$. Give an exact answer in terms of $\pi$.