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Let $C$ be the circle $y^{2}+z^{2}=2$, where $x=0$, oriented counterclockwise when viewed from the positive $x$ axis, and let $S$ be any oriented capping surface of $C$ such that $C$ is positively oriented with respect to the surface $S$. Let the vector field $\mathbf{F}$ be defined as $\nabla \times(x y z \mathbf{i}+z \mathbf{j}-y \mathbf{k})$. Then the flux of $\mathbf{F}$ through such a surface $S$ is a multiple of $\pi$, that is, $\iint_{S} \nabla \times(x y z \mathbf{i}+z \mathbf{j}-y \mathbf{k}) \cdot d \mathbf{S}=n \pi$ for some number $n$. What is the number $n$ ? Select one: a. -2 b. 2 c. -4 d. 8 e. 16 f. -16

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GANI86 The First Answerer