The Association of Tennis Professionals (ATP) ranks 200 men's tennis players and separately ranks 200 women's tennis players. There are no ties in either ranking. Now, suppose that there is a mixed doubles tournament (ie. a tournament in which each team consists of one man and one woman). Further suppose that the participants of this tournament are comprised of exactly 20 men from the 200 ATP-ranked men and exactly 20 women from the 200 ATP-ranked women. That is, a total of 40 players will compete in the tournament, half men and half women. And the organizers of the tournament will form mixed doubles teams among those 40 players that will compete in the tournament. Prove that, for any group of 40 ATP-ranked players (half men, half women) that participates in the tournament, the organizers of the tournament will always be able to form two mixed doubles teams with the same average ranking. That is, prove that in this tournament, there will always be two distinct men m1 (whose ranking is rank(m1)) and m2 (whose ranking is rank(m2)) and two distinct women w1 (whose ranking is rank(w1)) and w2 (whose ranking is rank(w2)), such that the average of rank(m1) and rank(w1) is equal to the average of rank(m2) and rank(w2).