SILK-ROAD 2019 Problem 1

The altitudes of the acute-angled non-isosceles triangle $ABC$ intersect at the point $H$ . On the segment $C_1H$ , where $CC_1$ is the altitude of the triangle, the point $K$ is marked. Points $L$ and $M$ are the feet of perpendiculars from point $K$ on straight lines $AC$ and $BC$ , respectively. The lines $AM$ and $BL$ intersect at $N$ . Prove that $\angle ANK = \angle HNL$ .