Let S be the portion of the cylinder y = ln x in the first octant whose projection parallel to the y-axis onto the xz-plane is the rectangle R_xz: 1 ≤ x ≤ e, 0 ≤ z ≤ 1. Let n be the unit vector normal to S that points away from the xz-plane. Find the flux of F = 2yj + zk through S in the direction of n.