Directed Graphs and Network Flows · Hard problem

A digraph has vertices $1,\dots,6$ and arcs $1\to2$, $2\to1$, $3\to4$, $4\to3$, $5\to6$, $6\to5$, $1\to5$, $3\to5$ — three separate $2$-cycles, with two of them pointing into the third. What is the minimum number of arcs that must be added to make this digraph strongly connected?