Limak is a little bear who loves to play with graphs. Recently, he defined a new structure in a graph and called it a stickman.
A stickman is a set of 7 different vertices and 6 edges. Vertices should be connected by edges as in the image below.
You can see here two legs, two arms and a head. Formally, one vertex (the one between arms) must be connected to four other vertices and one of these four must be connected to two more vertices.
Limak has an undirected graph with N vertices and M edges.
He asks you a favor.
Could you count how many stickmen there are in Limak's graph, modulo 10^9+7?
A stickman is defined by a set of 7 vertices and 6 edges - order doesn't matter here. It means that we shouldn't distinguish legs. Moreover, we shouldn't distinguish head and arms.
Input format:
The first line contains two integers N and M, denoting number of vertices and number of edges, respectively.
Vertices are numbered 1 through N.
Each of the next M lines contains two different vertices connected by an edge.
There is at most one edge between every two vertices.
Output format:
In the single line print the number of stickmen modulo 10^9+7.
Constraints:
7 <= N <= 200
0 <= M <= N * (N-1) / 2