Directed Graphs and Network Flows · Superchallenge problem

A digraph has vertices $1,\dots,6$ with arcs $1\to2$, $2\to1$ (a $2$-cycle), $5\to6$, $6\to5$ (another $2$-cycle), and also $2\to3$, $1\to4$, $2\to5$. What is the minimum number of new arcs that must be added so the digraph becomes strongly connected?