Number of Cycles

Problem Description

Given a simple graph with $n$ vertices and $m$ edges, count the number of simple cycles.

Input Format

The first line contains two integers $n$ and $m$. Lines $2$ through $m+1$ each contain two integers $x, y$, indicating an edge between vertices $x$ and $y$.

Output Format

Output one line containing the number of cycles in the graph.

Sample Input

4 6
1 2
1 3
1 4
2 3
2 4
3 4

Sample Output

7

Constraints

For $100\%$ of the data, it is guaranteed that $1\le n \le 19, m \le \frac{n\times (n-1)}{2}$.