The task of the courtiers.

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

Question: Even or odd number of courtiers with the king?