Hard Geometry Problem

In a quadrilateral ABCD, P and R are the midpoints of AB and CD respectively. Also Q and S are points on the sides BC and DA respectively such that BQ = 2QC and DS = 2SA. Prove that the area of the quadrilateral PQRS equals S/2 where S is the area of the quadrilateral ABCD.

I've tried ages to solve this but it seems I'm not good enough. Let's see who can.

[elaslawek]

Hope the attachment helps!