Instability

Long long ago, there was a prosperous kingdom which consisted of n cities and every two cites were connected by an undirected road.

However, one day a big monster attacked the kingdom and some roads were destroyed. In order to evaluate the influence brought by the catastrophe, the king wanted to know the instability of his kingdom. Instability is defined as the number of the unstable subset of {1, 2,$\cdots $,n}.

A set S is unstable if and only if there exists a set A such that $A\subseteq S(|A|\geq 3$) and A is a clique or an independent set, namely that cites in A are pairwise connected directly or they are pairwise disconnected.

Archaeologist has already restored themroads that were not destroyed by the monster. And they want you to figure out the instability.

Since the answer may be tremendously huge, you are only required to write a program that prints the answer modulo 1000000007.

The first line contains only one integer T, which indicates the number of test cases.

For each test case, the first line contains two integers n ($3\leq n \leq 50$) and m ($1\leq m\leq n(n - 1)/2$), indicating the number of cities and the number of roads.

Then the following are m lines, each of which contains two integers x and y, indicating there is a road between the city x and the city y.

It is guarenteed that there does not exist a road connecting the same city and there does not exist two same roads.

For each test case, print a line “Case #x: y”, where x is the case number (starting from 1) and y is an integer indicating the instability modulo 1000000007.

2
4 3
1 2
2 3
1 3
3 0

Case #1: 2
Case #2: 1

• In the first example, {1,2,3} and {1,2,3,4} , containing the subset {1,2,3} which is connected
directly, are considered unstable.
• In the second example, {1,2,3} is considered unstable because they are not pairwise connected
directly.

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