Group of Strangers

In an online social networking service, a user creates an account and connects to other users. Some services use one way follows, but in this problem every connection is bidirectional: if A is connected to B, then B is connected to A.

You are given the connections among $N$ users. Count the ways to choose three users who are strangers to each other. No two of the chosen three may be connected. If even one pair among them is connected, that group is not counted.

Two groups are different if and only if they differ in at least one member.

The first line contains an integer $T$ ($T \le 60$), the number of test cases.

The first line of each test case contains two integers $N$ ($3 \le N \le 5000$) and $M$ ($0 \le M \le 20000$), the number of users and the number of connections. Each of the next $M$ lines contains two integers $A$ and $B$ ($1 \le A, B \le N$, $A \ne B$), meaning that users $A$ and $B$ are connected. The same connection is never given twice.

For each test case, print one line in the form Case #X: Y, where $X$ is the test case number starting from 1 and $Y$ is the number of ways to choose three users who are strangers to each other.