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)

#define _GLIBCXX_DEBUG
#include <bits/stdc++.h>
using namespace std;
#define rep(i, n) for (int i = 0; i < (int)(n); i++)


template <typename T>
void cout_vector(vector<T> A){
    for (T a : A) cout << a +1 << " ";
    cout << endl;
}





bool in(vector<int> A, int key){
    for (int a : A){
        if (a == key) return true;
    }
    return false;
}


int main(){
    int N,M;
    cin >> N >> M;
    if (M < N - 1){
        cout << 0 << endl;
        return 0;
    }
    vector<vector<int>> Graph(N);
    rep(i,M){
        int a,b;
        cin >> a >> b;
        a--;
        b--;
        Graph[a].push_back(b);
        Graph[b].push_back(a);
    }
    vector<int> A(N - 1);
    rep(i,N - 1) A[i] = i + 1;
    int ans = 0;
    /*cout << "----------" << endl;
    for(int idx = 0; idx < N; idx++){
        cout_vector(Graph[idx]);
    }
    cout << "----------" << endl;*/
    do {
        bool flag = true;
        int start = A[0];
        if (!(in(Graph[0],start))) {      
            flag = false;
            continue;
        }
        for (int j = 1; j < N - 1; j++)  {
            int goal = A[j];        
            //cout << start << endl;    
            if (!(in(Graph[start],goal))){ 
                //cout << (start + 1) << " to " << (goal + 1) << " is not exits." << endl;
                flag = false;
                continue;
            } else {
                //cout << (start + 1) << " to " << (goal + 1) << " is exits." << endl;
            }
            start = goal;
        }
        //cout << "---" << endl;
        (flag) && (ans++);
    } while(next_permutation(A.begin(),A.end()));
    cout << ans << endl;
    return 0;
}