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>
#define mp make_pair
#define pb push_back
#define rep(i,n) for(int i=0;i<(n);i++)
#define reps(i,n,s) for(int i=(s);i<(n);i++)
typedef long long int ll;
using namespace std;
bool G[10][10]={false};

int main(){
cin.tie(0);
ios::sync_with_stdio(false);

int N,M;
cin>>N>>M;
rep(i,M){
    int a,b;
    cin>>a>>b;
    G[a][b]=G[b][a]=true;
}

vector<int> ord(N);
rep(i,N)ord[i]=i;
int res=0;
do{
    if(ord[0]!=0) break;

    bool ok=true;
    rep(i,N-1){
        int from=ord[i];
        int to=ord[i+1];
        if(!G[from][to]) ok = false;
    }
    if(ok) res++;
}while(next_permutation(ord.begin(),ord.end()));
cout<<res<<endl;
//system("pause");
return 0;
}