BALTIC-WAY 2015 Problem 12

A circle passes through vertex $B$ of the triangle $A B C$, intersects its sides $A B$ and $B C$ at points $K$ and $L$, respectively, and touches the side $A C$ at its midpoint $M$. The point $N$ on the $\operatorname{arc} B L$ (which does not contain $K)$ is such that $\angle L K N=\angle A C B$. Find $\angle B A C$ given that the triangle $C K N$ is equilateral.