The problem of the court.

The king does not trust his courtiers. He compiled a complete list of all the courtiers and ordered each of them to follow someone else. At the same time, the first courtier from the list follows who follows the second. The second keeps track of who follows the third, and so on. The penultimate one follows the one who follows the latter. The latter follows those who follow the first.

Question: an even or odd number of courtiers at the king?