Problem:
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≤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.

Sample Input 1

3 3
1 2
1 3
2 3

Sample Output 1

2

The given graph is shown in the following figure:

The following two paths satisfy the condition:

Sample Input 2

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

Sample Output 2

1

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

Solution in C (GCC 5.4.1) (judge verdict: Accepted)

#include<stdio.h>
#include<string.h>
int s1[10][10];
int vis[10];
int judge[10][10];
int n,m;
int sum,all;
void dfs(int num)
{
    int a,b;
    if(sum==n)
    {
        all++;
        return;
    }
    for(a=1;a<=n;a++)
    {
        if(s1[num][a]==1&&vis[a]==0)
        {
            vis[a]=1;sum++;
            dfs(a);
            vis[a]=0;sum--;
        }
    }
    return;
}
int main()
{
    int a,b,x,y;
    while(scanf("%d%d",&n,&m)!=EOF)
    {
        sum=0;all=0;
        memset(s1,0,sizeof(s1));
        memset(vis,0,sizeof(vis));
        for(a=1;a<=m;a++)
        {
            scanf("%d%d",&x,&y);
            s1[x][y]=s1[y][x]=1;
        }
        vis[1]=1;sum++;
        dfs(1);
        printf("%d\n",all);
    }
    return 0;
}