Circumcircle

Let $ABC$ be a triangle with $\angle BAC = 70^\circ$. Points $D$ and $E$ are chosen on side $BC$ such that $\angle DAC = \angle ABC$ and $\angle EAB = \angle ACB$. Let $M$ and $N$ be the midpoints of $AD$ and $AE$, respectively. The circumcircle of triangle $AMN$ meets $AB$ and $AC$ again at $Q$ and $P$, respectively ($Q, P \neq A$). Find $\angle AQM$, in degrees.