BALKAN-SL 2014 G1

Let $ABC$ be an isosceles triangle, in which $AB=AC$ , and let $M$ and $N$ be two points on the sides $BC$ and $AC$ , respectively such that $\angle BAM = \angle MNC$ . Suppose that the lines $MN$ and $AB$ intersects at $P$ . Prove that the bisectors of the angles $\angle BAM$ and $\angle BPM$ intersects at a point lying on the line $BC$