Directed Graphs and Network Flows · Superchallenge problem

A digraph has two groups: $\{1,2,3\}$ with arcs $1\to2$, $2\to3$, $3\to1$, and $\{4,5,6\}$ with arcs $4\to5$, $5\to6$, $6\to4$, plus a single extra arc $3\to4$ (and NO other arcs between the groups – most pairs across the two groups never play at all, so this is not a complete tournament). Call a vertex a king if it reaches every other vertex within two steps. How many kings does this digraph have?