Score : $300$ points

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 $a_i = b_i (1 \leq i \leq M)$, 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 \leq i. 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

• $2 \leq N \leq 8$
• $0 \leq M \leq N(N-1)/2$
• $1 \leq a_i
• 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.

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.