Show an altitude of triangle is angle bisector

Question

Points $M$ and $N$ are on sides $\overline{AC}$ and $\overline{AB}$ of $\triangle ABC$. Lines $\overline{BM}$ and $\overline{CN}$ intersect each other on altitude of $\overline{AD}$ of $\triangle ABC$.

Show that $\overline{AD}$ bisects $\angle MDN$.