CN-SMO 2013 Problem 2

$\triangle ABC$ , $AB>AC$ . the incircle $I$ of $\triangle ABC$ meet $BC$ at point $D$ , $AD$ meet $I$ again at $E$ . $EP$ is a tangent of $I$ , and $EP$ meet the extension line of $BC$ at $P$ . $CF\parallel PE$ , $CF\cap AD=F$ . the line $BF$ meet $I$ at $M,N$ , point $M$ is on the line segment $BF$ , the line segment $PM$ meet $I$ again at $Q$ . Show that $\angle ENP=\angle ENQ$