Evaluate Flux through upper hemisphere

Question

The problem: Evaluate the flux through the surface $x^2+y^2+z^2=1$, $ z\geq0$, of the vectorfield $\mathbf{F}=(xz, yz, z^2)$. When I try to solve this problem either with the divergence theorem or by parameterizing the surface I get the value $\pi$. The answer in the text book says it is $\frac{\pi}{2}$. I would appreciate if anyone could take a look at this problem! Thanks in advance!