Walks, Paths and Connectivity · Challenge problem

Let $G$ have a central vertex $1$ with three branches: a path $1\text{-}2\text{-}3$ ending in a triangle on $3,11,12$; a path $1\text{-}4\text{-}5\text{-}6$; and a path $1\text{-}7\text{-}8\text{-}9\text{-}10$. Find the number of bridges of $G$ plus the number of cut vertices of $G$.