Eulerian and Hamiltonian Graphs · Medium problem

A tree has a path $1\text{-}2\text{-}3\text{-}4\text{-}5$ (edges $12,23,34,45$) with an extra leaf $6$ attached to vertex $2$ and another extra leaf $7$ attached to vertex $4$ (edges $26, 47$). What is the minimum number of new edges that must be added so the resulting graph has an Euler circuit?