Directed Graphs and Network Flows · Superchallenge problem

A digraph has vertices $1,2,3,4$ and arcs $1\to2$, $1\to3$, $2\to3$, $2\to4$, $3\to1$, $3\to4$, $4\to1$, $4\to2$ (every vertex has in-degree $2$ and out-degree $2$). How many different Eulerian circuits start and end at vertex $1$, using each of the $8$ arcs exactly once (two circuits count as different if they use the arcs in a different order)?