The vertices of a convex $1991$-gon are enumerated with integers from $1$ to $1991$. Each side and diagonal of the $1991$-gon is colored either red or blue. Prove that, for an arbitrary renumeration of vertices, one can find integers $k$ and $l$ such that the segment connecting the vertices numbered $k$ and $l$ before the renumeration has the same color as the segment connecting the vertices numbered $k$ and $l$ after the renumeration.