Compute the flux of $\vec F = 2 x\vec i + 2 y\vec j + 3 z\vec k$ over the quarter cylinder $S$ given by $x^2+y^2=1$, $0\leq x\leq 1$, $0\leq y\leq 1$, $0\leq z\leq 1$, oriented outward.

flux =