Eulerian and Hamiltonian Graphs · Superchallenge problem

Split $8$ people into two groups of four, $L=\{0,1,2,3\}$ and $R=\{4,5,6,7\}$, and suppose every person in $L$ is friends with every person in $R$ (and no one is friends within their own group) — the complete bipartite graph $K_{4,4}$. Counting two seating arrangements around a circular table as the same whenever one is a rotation or reflection of the other, how many distinct Hamiltonian cycles (seating arrangements where every neighbor pair are friends) does $K_{4,4}$ have?