Given a undirected graph with $$$N (N \leq 100)$$$ vertices, $$$M (M \leq N * (N + 1) / 2)$$$ edges (there can be edge connect a vertex with itself but all edges are distinct).

Find the number of minimum paths that every edge is in exactly 1 path.

Thanks.

UPD: I just realized it is sum of (odd vertices / 2) for every connected component (and some special case like m = 0, odd vertices = 0).