Problem Statement

You are given an undirected unweighted graph with $N$ vertices and $M$ edges that contains neither self-loops nor double edges.

Here, a self-loop is an edge where $a_i​=b_i​(1≤i≤M)$, and double edges are two edges where $(a_i​,b_i​)=(a_j​,b_j​)$ or $(a_i​,b_i​)=(b_j​,a_j​)(1≤i<j≤M)$.

How many different paths start from vertex $1$ and visit all the vertices exactly once?

Here, the endpoints of a path are considered visited.

For example, let us assume that the following undirected graph shown in Figure $1$ is given.

Figure $1$: an example of an undirected graph

The following path shown in Figure $2$ satisfies the condition.

Figure $2$: an example of a path that satisfies the condition

However, the following path shown in Figure $3$ does not satisfy the condition, because it does not visit all the vertices.

Figure $3$: an example of a path that does not satisfy the condition

Neither the following path shown in Figure $4$, because it does not start from vertex $1$.

Figure $4$: another example of a path that does not satisfy the condition

Constraints

• $2≤N≤8$
• $0≤M≤N(N−1)/2$
• $1≤a_i​<b_i≤N$
• The given graph contains neither self-loops nor double edges.

Input

The input is given from Standard Input in the following format:

N M  
a1​ b1​  
a2​ b2​
:  
aM​ bM​  

Output

Print the number of the different paths that start from vertex $1$ and visit all the vertices exactly once.

Samples

3 3
1 2
1 3
2 3

2

The given graph is shown in the following figure:

The following two paths satisfy the condition:

7 7
1 3
2 7
3 4
4 5
4 6
5 6
6 7

1

This test case is the same as the one described in the problem statement.