406565: GYM102441 G Sum of Distances in Cactus

Find the sum of the distances between all pairs of vertices in a cactus graph. A cactus graph is a graph in which every edge belongs to at most one simple cycle. The distance between vertices is calculated as the number of edges in the shortest path connecting a given pair of vertices.

First line contains two integers $$$n$$$ and $$$m$$$ — the number of vertices and the number of edges in the cactus.

Each of the following $$$m$$$ lines contains two integers $$$u_i$$$ $$$v_i$$$ — the numeric labels of vertices connected by an edge.

It is guaranteed that the graph is connected and does not have self-loops and multiple edges.

$$$$$$ 1 \le n \le 10^5$$$$$$ $$$$$$ n - 1 \le m \le 2 \times n$$$$$$ $$$$$$ 1 \le u_i, v_i \le n$$$$$$

Output a single line containing the sum of the distances between all pairs of vertices.

3 3
1 2
2 3
3 1

3

7 8
2 1
3 1
5 1
3 2
4 3
5 7
6 3
4 6

42