(10) [10 marks] Consider a race with 2n horses labeled 1,2,...,2n. The horses may cross the finish line either individually or in pairs, but no more than two horses may finish at the same time. In how many distinct ways can the race conclude under this constraint? For example, with 2 horses, there are exactly three possible outcomes: 1. Horse 1 finishes before horse 2; 2. Horse 2 finishes before horse 1; 3. Horses 1 and 2 finish simultaneously. As another example, in a race with 6 horses, one possible outcome is: horses 1 and 5 tie for first place, followed by horse 3, then horse 4, and finally horses 2 and 6 tie for last