JBMO 2014 Problem 2

Consider an acute triangle $A B C$ with area S. Let $C D \perp A B (D \in A B)$, $D M \perp A C (M \in A C)$ and $D N \perp B C (N \in B C)$. Denote by $H_{1}$ and $H_{2}$ the orthocentres of the triangles $M N C$ and $M N D$ respectively. Find the area of the quadrilateral $\mathrm{AH}_{1} \mathrm{BH}_{2}$ in terms of $S$.