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.

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

• $1 \le n \le 10^5$
• $n - 1 \le m \le 2 \times n$
• $1 \le u\_i, v\_i \le n$