Use  Stokes Theorem to compuet a surface integral 

Let $F=y i- x j +zx^3y^2 k$. Evaluate 
\[\iint_S (\nabla \times F) \cdot n dA,\]
where $S$ is the surface defined by $x^2+y^2+z^2=1,$  $z \leq 0$. 

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