Pigeonhole and Extremal Arguments · Hard problem

Five players $A, B, C, D, E$ play a round-robin. $A$ beats $B$ and $C$; $B$ beats $C$, $D$ and $E$; $C$ beats $D$ and $E$; $D$ beats $A$ and $E$; $E$ beats $A$. A KING is a player who, for every other player $Q$, beat $Q$ or beat someone who beat $Q$. How many kings are there?