Walks, Paths and Connectivity · Hard problem

Let $G$ have vertices $1,\ldots,9$ with edges $12,23,13$ (a triangle), $34,45,35$ (a triangle sharing vertex $3$), $56,67,57$ (a triangle sharing vertex $5$), and two pendant edges $78$ and $79$. $G$ has exactly three cut vertices. For the cut vertex whose removal leaves the MOST separate pieces, find the product of the sizes of those pieces.