Bipartite Graphs and Matchings · Superchallenge problem

Take the graph with three $5$-cycles sharing the common edge $1\text{-}2$: cycle $A = 1\text{-}2\text{-}3\text{-}4\text{-}5\text{-}1$, cycle $B = 1\text{-}2\text{-}6\text{-}7\text{-}8\text{-}1$, and cycle $C = 1\text{-}2\text{-}9\text{-}10\text{-}11\text{-}1$. After removing the single edge $1\text{-}2$ (the minimum needed to make the graph bipartite), what is the size of a maximum matching in the resulting graph?