The Great Secret

Once, a famous candy wrapper collector held a presentation of his collection. It was so impressive that all his friends, except for one, decided to become candy wrapper collectors too. Just collecting is not very interesting; the main thing is exchanging. At first, the exchange process was chaotic, which led to constant disputes among the friends. One wise friend decided to organize the exchange process by creating a list showing who gives their wrappers to whom. To avoid further disputes, the list was made so that each person gives their wrappers to exactly one person and receives wrappers from exactly one person (the person they give to and receive from may be the same).

The friend who was excluded was very upset about being forgotten. She decided to disrupt the exchange process, but to do this she needed to know the organizer's list, which was kept secret. Therefore, she decided to consider all possible exchange options. However, she did not realize how many options there were. Help her count the number of such exchange variants.