Trees · Hard problem

Graph $G$ has vertices $1, \ldots, 8$ and edges $12, 23, 34, 45, 56, 67, 78, 25$ (the path $1\text{-}2\text{-}\cdots\text{-}8$ together with one extra edge joining $2$ and $5$). How many edges of $G$ are bridges (edges whose removal disconnects $G$)?