Given right hexagon $H$ with side length $1$. On the sides of $H$ points $A_1$,$A_2$,$\ldots$,$A_k$ such that at least one of them is the midpoint of some side and for every $1 \leq i \leq k$ lines $A_{i-1}A_i$ and $A_iA_{i+1}$ form equal angles with the side, that contains the point $A_i$ (let $A_0=A_k$ and $A_{k+1}=A_1$. It is known that the length of broken line $A_1A_2\ldots A_kA_1$ is a positive integer Prove that $n$ is divisible by $3$ M. Zorka