Directed Graphs and Network Flows · Hard problem

A digraph has vertices $A,B,C,D,E$ and arcs $A\to C$, $C\to D$, $D\to E$, $E\to A$, $A\to D$, $B\to C$. What is the minimum number of new arcs that must be added so every vertex has equal in-degree and out-degree (as needed for an Eulerian circuit)?