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;

const int Max = 8;
bool g[Max][Max];

int dfs(int k, int n, bool vis[])
{
	bool check = true;
  	for(int i = 0; i < n; i++)
      if(vis[i] == false)
        check = false;
  	if(check)
      return 1;
  	int res = 0;
  	for(int i = 0; i < n; i++)
    {
    	if(g[k][i] == false)
          	continue;
      	if(vis[i])
          	continue;
      	vis[i] = true;
      	res += dfs(i, n, vis);
      	vis[i] = false;
    }
  	return res;
}

int main()
{
	int n, m;
  	cin>>n>>m;
  	for(int i = 0; i < m; i++)
    {
    	int a, b;
      	cin>>a>>b;
      	g[a-1][b-1] = g[b-1][a-1] = true;
    }
  	bool vis[n];
  	memset(vis, false, sizeof(vis));
  	cout<<dfs(0, n, vis)<<"\n";
}