IMO Team Selection Test

Let $ABCD$ be an inscribed quadrangle, and let $BC$ and $AD$ intersect at point $P$. The point $Q$ belongs to the line $BP$ in such a way that $\overline{PQ}=\overline{BP}$, and $CAQR$ and $DBCS$ are parallelograms. Prove that the points $C,Q,R$ and $S$ are concyclic.