JBMO 2011 Problem 4

Let $ABCD$ be a convex quadrilateral and points $E$ and $F$ on sides $AB,CD$ such that $$\tfrac{AB}{AE}=\tfrac{CD}{DF}=n$$

If $S$ is the area of $AEFD$ show that ${S\leq\frac{AB\cdot CD+n(n-1)AD^2+n^2DA\cdot BC}{2n^2}}$