Evaluate the surface integral ${}_S$vec$(F)*dS$ for the given vector field vec$(F)$ and the oriented surface $S,$ where

vec$(F)(x,y,z)=$xvec$(i)-$zvec$(j)+$yvec$(k)$

$S$ is the part of the sphere $x^2+y^2+z^2=4$ in the first octant, with orientation away from the origin. Proceed until you have an iterated double integral and then stop. DO NOT evaluate this integral.