Trees · Challenge problem

Graph $B$ has a triangle $1\text{-}2\text{-}3\text{-}1$, then a path $3\text{-}4\text{-}5$, then a second triangle $5\text{-}6\text{-}7\text{-}5$ (vertices $1,\ldots,7$; edges $12,23,31,34,45,56,67,75$). How many of $B$'s edges are bridges?