Directed Graphs and Network Flows · Hard problem

Five teams $A,B,C,D,E$ play a round robin (every pair meets exactly once). The results are $A\to B$, $B \to C$, $C \to A$, $D \to E$, and each of $A,B,C$ beats both $D$ and $E$ (an arrow points from winner to loser). Call a team a king if, for every other team, it beat that team directly or beat some team that beat that team. How many kings does this tournament have?