Directed Graphs and Network Flows · Superchallenge problem

Six teams $1,\dots,6$ play a round robin. Teams $1,2,3$ beat each other cyclically ($1$ beats $2$, $2$ beats $3$, $3$ beats $1$); teams $4,5,6$ play transitively ($4$ beats $5$ and $6$; $5$ beats $6$); and each of $1,2,3$ beats each of $4,5,6$, EXCEPT that team $6$ beats team $1$ instead of the reverse. What is the minimum number of games whose outcome would have to be reversed to make the overall results transitive (acyclic)?