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>
#define rep(i,n) for(int i=0;i<n;i++)
#define loop(i,x,n) for(int i=x;i<n;i++)
#define pb push_back
#define mp make_pair
#define fir first
#define sec second
#define MAX 100005
#define int long long
using namespace std;
const int MOD=1000000007;
const int INF=1000000009;

vector<vector<int>> tree;
int n,m,sum=0;

int dfs(int s,vector<int> used){
  bool flag=true;
  rep(i,n)if(used[i]==0)flag=false;
  if(flag)sum++;
  rep(i,tree[s].size()){
    int u=tree[s][i];
    if(used[u]==1)continue;
    used[u]=1;
    dfs(u,used);
    used[u]=0;
  }
  return sum;
}

signed main(){
  cin>>n>>m;
  tree=vector<vector<int>>(n);
  rep(i,m){
    int a,b;
    cin>>a>>b;
    a--;b--;
    tree[a].pb(b);
    tree[b].pb(a);
  }
  vector<int> used(n);
  used[0]=1;
  cout<<dfs(0,used)<<endl;


  return 0;
}