In a certain kingdom there were 32 knights. Some of them were vassals of others $($ a vassal can have only one suzerain, and the suzerain is always richer than his vassal $)$. A knight with at least four vassals is given the title of Baron. What is the largest number of barons that can exist under these conditions?
$($ In the kingdom the following law is enacted: ” the vassal of my vassal is not my vassal”$)$.