Eulerian and Hamiltonian Graphs · Superchallenge problem

Split $8$ people into two groups of four, $L=\{1,2,3,4\}$ and $R=\{5,6,7,8\}$. Suppose everyone in $L$ is friends with everyone in $R$ EXCEPT for the four pairs $(1,5),(2,6),(3,7),(4,8)$ (so $12$ of the $16$ possible cross-friendships exist). This graph has Hamiltonian cycles. What is the minimum number of friendships that must end so that NO circular seating works (every neighbor pair friends)?