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>
int fn[10][10]={};
int flag[10]={};
int n;
int ans=0;
 
int check(int num){
    int flaga=1;
    for(int i=1;i<=n;i++){
        if(flag[i]==0) flaga=0;
    }
    return flaga;
}
 
void route(int j,int i,int num){
    if (fn[j][i]==1&&flag[i]==0){
        flag[i]=num;
        int a=check(num);
        ans+=a;
        for (int k=2;k<=n;k++){
            route(i,k,num+1);
        }
        flag[i]=0;
    }
}
 
int main(){
    int m,i,j;
    scanf("%d %d",&n,&m);
    for (int k=0;k<m;k++){
        scanf("%d %d",&i,&j);
        fn[i][j]=1;
        fn[j][i]=1;
    }
    for (i=2;i<=n;i++){
        flag[1]=1;
        route(1,i,2);
        for (j=1;j<=n;j++)flag[j]=0;
    }
    printf("%d\n",ans);
}