Directed Graphs and Network Flows · Superchallenge problem

Seven teams $1,\dots,7$ play a round robin. For every pair $i<j$, team $i$ beats team $j$, EXCEPT that team $7$ beats team $1$, and team $6$ beats team $2$ (two upsets). Call a team a king if it beats every other team directly or beats some team that beat that team. How many kings does this tournament have?