Find the Flux Of $\vec { F }$ Through the Surface $S$

Multiple Choice

Find the flux of $\vec { F }$ through the surface $S$ in the positive z direction. Let $S = \{ ( u + v , 3 u + 2 v , 6 v ) : 0 \leq u \leq 1 \text { and } 1 \leq v \leq 3 \}$ and $\vec { F } ( x , y , z ) = \langle z , x , y \rangle$

A) $378$
B) $- 791$
C) $- 409$
D) $0$