Bipartite Graphs and Matchings · Hard problem

A relay network has a $5$-station ring $0\text{-}1\text{-}2\text{-}3\text{-}4\text{-}0$, with an additional chain of stations $5,6,7,8$ hanging off station $4$ (links $45,56,67,78$). What is the size of a maximum matching (disjoint active links, no station in more than one)?