APMO 2012 Problem 1

Let $P$ be a point in the interior of a triangle $ABC$ , and let $D, E, F$ be the point of intersection of the line $AP$ and the side $BC$ of the triangle, of the line $BP$ and the side $CA$ , and of the line $CP$ and the side $AB$ , respectively. Prove that the area of the triangle $ABC$ must be $6$ if the area of each of the triangles $PFA, PDB$ and $PEC$ is $1$ .