100 sums of the pairs of numbers at the endpoints of the chosen chords are equal

There are given N = (2.2.2.......500 times) points on a circle labeled 1, 2, . . . , N in some order.
Prove that one can choose 100 pairwise disjoint chords joining some of these points so that the
100 sums of the pairs of numbers at the endpoints of the chosen chords are equal.