Surface Integrals, Stokes & Divergence · Superchallenge problem

Let $\mathbf F = \dfrac{(x,\ y,\ z - 1)}{\left(x^2 + y^2 + (z - 1)^2\right)^{3/2}}$, the inverse-square field of a point source at $(0, 0, 1)$. Let $S$ be the part of the paraboloid $z = 4 - x^2 - y^2$ with $z \ge 0$, oriented with upward normal. Find $\iint_S \mathbf F\cdot d\mathbf S$. Give an exact answer.