RS-SMO 2010 Problem 2

In an acute-angled triangle $ABC$ , $M$ is the midpoint of side $BC$ , and $D, E$ and $F$ the feet of the altitudes from $A, B$ and $C$ , respectively. Let $H$ be the orthocenter of $\Delta ABC$ , $S$ the midpoint of $AH$ , and $G$ the intersection of $FE$ and $AH$ . If $N$ is the intersection of the median $AM$ and the circumcircle of $\Delta BCH$ , prove that $\angle HMA = \angle GNS$ .

Proposed by Marko Djikic