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: Accepted)

#include<bits/stdc++.h>
using namespace std;
typedef long long ll;
const ll mod=1e9+7;
const ll INF=mod*mod;
#define rep(i, n) for (ll i = 0; i < (ll)(n); i++)
#define all(x) (x).begin(),(x).end()
ll min(ll a,ll b){
  if(a>b){
    return b;
    }
      else{
        return a;
      }
  }
  
  ll max(ll a,ll b){
    if(a>b){
      return a;
    }
    else{
      return b;
    }
  }

ll power(ll a,ll b){
 ll ans=1;
 for(ll i=1;i<=b;i++){
ans*=a;
  }
  return ans;
}

 ll gcd(ll m,ll n){
 	if(n==0){
       return m;
     }
   return gcd(n,m%n);
 }
ll lcm(ll a,ll b){
  ll g=gcd(a,b);
  return a/gcd(a,b)*b;
		

}
const ll limit=28;
ll a[limit];
ll b[limit];
bool G[limit][limit];
ll N,M;

ll dfs(ll v,bool visited[limit]){
  bool ALL=true;
  rep(i,N){
    if(visited[i]==false){
      ALL=false;
    }
  }

  if(ALL){
    return 1;//+1はすべてのdfsに共通に足される？
  }
  
  ll ret=0;
  
  rep(i,N){
    
    if(G[v][i]==true&&visited[i]==false){
      visited[i]=true;
      ret+=dfs(i,visited);
      visited[i]=false;
    }

  }
  
  return ret;
}
 
    
      
    
    
int main(){
  
  cin>>N>>M;
  
  rep(i,M){
cin>>a[i]>>b[i];
    
    G[a[i]-1][b[i]-1]=G[b[i]-1][a[i]-1]=true;
  }
  bool visited[limit];
rep(i,N){
  visited[i]=false;
  
}
 
  visited[0]=true;//0スタート固定？
  

  cout<<dfs(0,visited)<<endl;
}