NL-NWO 1976 Problem 2

Given $\vartriangle ABC$ and a point $P$ inside that triangle. The parallelograms $CPBL$ , $APCM$ and $BPAN$ are constructed. Prove that $AL$ , $BM$ and $CN$ pass through one point $S$ , and that $S$ is the midpoint of $AL$ , $BM$ and $CN$ .