CN-TST 2012 Problem 2

Given a scalene triangle $ABC$ . Its incircle touches $BC,AC,AB$ at $D,E,F$ respectvely. Let $L,M,N$ be the symmetric points of $D$ with $EF$ ,of $E$ with $FD$ ,of $F$ with $DE$ ,respectively. Line $AL$ intersects $BC$ at $P$ ,line $BM$ intersects $CA$ at $Q$ ,line $CN$ intersects $AB$ at $R$ . Prove that $P,Q,R$ are collinear.