RU-ALLRUSSIAN 2010

Let $O$ be the circumcentre of the acute non-isosceles triangle $ABC$ . Let $P$ and $Q$ be points on the altitude $AD$ such that $OP$ and $OQ$ are perpendicular to $AB$ and $AC$ respectively. Let $M$ be the midpoint of $BC$ and $S$ be the circumcentre of triangle $OPQ$ . Prove that $\angle BAS =\angle CAM$ .