KöMaL 2006 B3914

$P$ is an arbitrary point on the side $AB$ of the parallelogram ABCD , and $Q$ is an arbitrary point of side $CD$. Let $M$ denote the intersection of the lines $DP$ and $AQ$, and let $N$ denote the intersection of the lines $CP$ and $BQ$. Show that the line $MN$ is passing through the centre of the parallelogram.