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++14 (GCC 5.4.1) (judge verdict: Wrong Answer)

#include <bits/stdc++.h>
using namespace std;
#define r(i,a,n) for(int i=a;i<n;i++)
int a[9][9],n,v[9][9];
int dfs(int s,int d){
	int ss=0;
	if(d==n-2)return 1;
	r(i,1,n+1){
		r(j,1,n+1)v[s][j]=1;
		if(a[s][i]&&!v[s][i])ss+=dfs(i,d+1);
		r(j,1,n+1)v[s][j]=0;
	}
	return ss;
}
int main(){
	int m,qq,ww,s;
	cin>>n>>m;
	r(i,0,m){
		cin>>qq>>ww;
		a[qq][ww]=1;
		a[ww][qq]=1;
	}
	r(i,1,n+1){
		r(j,0,n+1)r(k,0,n+1)v[i][j]=0;
		if(a[1][i]){
			r(k,1,n+1)v[k][1]=1;
			s+=dfs(i,1);		}
	}
	cout<<s<<endl;
}