Walks, Paths and Connectivity · Hard problem

A graph has two connected components with no edges between them. Component $A$ is the $5$-cycle $1\text{-}2\text{-}3\text{-}4\text{-}5\text{-}1$ together with the chord $13$. Component $B$ is the complete graph $K_4$ on vertices $6,7,8,9$. How many triangles does the whole graph contain?