Graph Algorithms · Easy problem

A graph has vertices $a, b, c, d, e$ and edges $ab, bc, cd, de, ea, bd$. Running a DFS from $a$ that visits each vertex's unvisited neighbors in alphabetical order reaches $d$ for a second time through the edge $bd$, which turns out to be a back edge. What is the length (number of edges) of the cycle that this back edge forms together with the DFS tree path between $b$ and $d$?