AZ-MO 2020 Problem 4

There is a non-equilateral triangle $ABC$ .Let $ABC$ 's Incentri $I$ .Point $D$ is on the $BC$ side.The circle drawn outside the triangle $IBD$ and $ICD$ intersects the sides $AB$ and $AC$ at points $E$ and $F.$ The circle drawn outside the triangle $DEF$ intersects the sides $AB$ and $AC$ at $N$ and $M$ .Prove that $EM\parallel FN$ .