Compute the flux of the vector field $\vec{F}(x,y,z) = 5 \vec{i} + 3 \vec{j} + 2 \vec{k}$ through the rectangular region with corners at $(0,0,1)$, $(1,0,1)$, $(1,1,1)$, and $(0,1,1)$ oriented in the positive z-direction, as shown in the figure. Flux =

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