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: Runtime Error)

#include <bits/stdc++.h>

#define rep(i, n) for(int (i)=0; (i)<(n); (i)++)

using namespace std;

typedef long long ll;
typedef pair<int, int> P;

template<class T>bool chmax(T &a, const T &b) { if (a<b) { a=b; return 1; } return 0; }
template<class T>bool chmin(T &a, const T &b) { if (b<a) { a=b; return 1; } return 0; }


vector<vector<bool>> G;

bool solve(vector<int> v, int index)
{
  if(index==v.size()-1)
    return true;
  else if(G[v[index]][v[index+1]]==true)
    return solve(v, index+1);
  else
    return false;
}


int main()
{
  int N, M;
  cin >> N >> M;

 G.resize(N);
  for(int i=0; i<N; i++)
    G[i].resize(N);

  
  for(int i=0; i<N; i++)
    for(int j=0; j<N; j++)
      G[i][j] = false;
  
  for(int i=0; i<M; i++)
    {
      ll v1, v2;
      cin >> v1 >> v2;
      G[v1-1][v2-1]=true;
      G[v2-1][v1-1]=true;
    }
  
  vector<int> v(N);
  for(int i=0; i<M; i++)
    v[i]=i;

  ll count = 0;
  do
    {
      if(solve(v, 0))
	{
	  //	  for(int i=0; i<v.size(); i++)
	  //cout << v[i] <<" " ;
	  cout << endl;
	  count++;
	}
    }
  while(next_permutation(v.begin()+1, v.end()));


  cout << count << endl;
  
  return 0;
}


//cout << setprecision(13);
//next_permutation();
//__gcd();
//reverse();
//set ,tuple ,pair;
//bitset
//vector.find
//vector.count