RMO, INMO 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.
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