Question 46
$2N$ points are marked on a circle ($N$ is a positive integer) so that no point in the interior of the circle belongs to three chords with the endpoints at marked points. A collection of $N$ chords with the endpoints at marked points is called a matching if every marked point is the endpoint of exactly one of these chords. A matching is called even if the number of intersection points of its chords is even, and odd otherwise. Find the difference between the quantities of even and odd matchings.
