Use the Divergence Theorem to evaluate the surface integral $\iint_{\mathcal{S}} \mathbf{F}\cdot d\mathbf{S}$ .

$\mathbf{F} = \left<6 x+y, z,4 z-x\right>$, $\mathcal{S}$ is the boundary of the region between the paraboloid $z=9-x^2-y^2$ and the $xy$-plane.

$\iint_{\mathcal{S}} \mathbf{F}\cdot d\mathbf{S}=$