AT-OEMO-FED1 2018 Problem 2

Let $ABC$ be a triangle with incenter $I$ . The incircle of the triangle is tangent to the sides $BC$ and $AC$ in points $D$ and $E$ , respectively. Let $P$ denote the common point of lines $AI$ and $DE$ , and let $M$ and $N$ denote the midpoints of sides $BC$ and $AB$ , respectively. Prove that points $M, N$ and $P$ are collinear.

(Proposed by Karl Czakler)