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
a_1 b_1
a_2 b_2
:
a_M b_M

Output

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