Vector Calculus · Hard problem

Let $S$ be the part of the paraboloid $z = 4 - x^2 - y^2$ with $z\ge 0$, oriented upward. Compute the flux $\displaystyle\iint_S \mathbf F\cdot d\mathbf S$ of $\mathbf F = (x,\; y,\; z)$. Give your answer in terms of $\pi$.