Problem Description

Given a connected undirected graph with n nodes and m edges, the capacity of each edge is 1.
Define maxflow(s, t) as the maxflow from s to t.
Calculate
n i-1
∑ ∑ min(maxflow(i, j), 3)
i=1 j=1

Input

The first line of the input contains an integer T , denoting the number of test cases.
In each test case, there are two integers n, m in the first line, denoting the number of vertices and edges of the graph.
Then followed m lines, each line contains two integers ui, vi, denoting an undirected edge (ui, vi).
1 ≤ T ≤ 20, 1 ≤ n ≤ 100000, 0 ≤ m ≤ 300000, ∑ n ≤ 400000, ∑ m ≤ 700000, ui不等于vi

Output

For each test case, output one line contains a single integer, denoting the answer.

1
5 7
1 4
1 2
2 3
2 3
3 4
4 5
4 5

21