Directed Graphs and Network Flows · Challenge problem

A digraph has two separate pieces: $\{1,2,3\}$ with arcs $1\to2$, $2\to3$, $3\to1$, and $\{4,5,6\}$ with arcs $4\to5$, $5\to6$, $6\to4$ (no arcs at all between the two pieces, and every vertex already has equal in-degree and out-degree within its own piece). What is the minimum number of new arcs that must be added so the whole digraph has an Eulerian circuit?