Walks, Paths and Connectivity · Hard problem

Let $G$ have vertices $1,\ldots,6$ with edges $12$, $13$, $23$, $14$, $24$, $15$, $25$ (so $1$ and $2$ are joined directly and also by a path through each of $3$, $4$, and $5$), plus one more edge $36$. How many bridges does $G$ have?