A vector field $\vec{F}$ is given by $\vec{F} = \langle z^2, x^2, y^2 \rangle$. Using Stokes' Theorem, compute $\iint_S (\nabla \times \vec{F}) \cdot d\vec{S}$ where $S$ is the portion of the paraboloid $z = 1 - x^2 - y^2$ that lies above the $xy$-plane, oriented upwards.