BG-MO 1979 Problem 2

Points $P,Q,R,S$ are taken on respective edges $AC$ , $AB$ , $BD$ , and $CD$ of a tetrahedron $ABCD$ so that $PR$ and $QS$ intersect at point $N$ and $PS$ and $QR$ intersect at point $M$ . The line $MN$ meets the plane $ABC$ at point $L$ . Prove that the lines $AL$ , $BP$ , and $CQ$ are concurrent.