KZ-MO 2016 Problem 4

In isosceles triangle $ABC$ ( $CA=CB$ ), $CH$ is altitude and $M$ is midpoint of $BH$ .Let $K$ be the foot of the perpendicular from $H$ to $AC$ and $L=BK \cap CM$ .Let the perpendicular drawn from $B$ to $BC$ intersects with $HL$ at $N$ .Prove that $\angle ACB=2 \angle BCN$ .(M. Kunhozhyn)