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 gra[10][10];
int visited[10];
int N,M,ans;

int all_visited(){
	int a=1;
	for(int i=1;i<=N;i++)a*=visited[i];
	if(a>0)return 1;
	return 0;
}

void DFS(int v){
	if(all_visited()==1){
		ans++;
		return;
	}
	for(int i=1;i<=N;i++){
		if(gra[v][i]==1 && visited[i]==0){
			visited[i]=1;
			DFS(i);
			visited[i]=0;
		}
	}
	return;
}

int main(){
	scanf("%d%d",&N,&M);
	
	for(int i=0;i<M;i++){
		int a,b;
		scanf("%d%d",&a,&b);
		gra[a][b]=gra[b][a]=1;
	}
	
	visited[1]=1;
	DFS(1);
	
	printf("%d\n",ans);
	return 0;
}