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<iostream>
#include <fstream>
#include <vector>
#include <algorithm>

using namespace std;

int counter = 0;
void findP(vector<int> points);
int n, m;
vector<pair<int, int>> edge;

int main()
{
#ifdef LOCAL
    std::ifstream in("input.txt");
    std::cin.rdbuf(in.rdbuf());
#endif
    cin >> n >> m;
    
    for(int i=0;i<m;i++){
        int p1, p2;
        cin >> p1 >> p2;
        edge.push_back({p1, p2});
    }

    vector<int> points = {1};
    findP(points);

    cout << counter << endl;

    return 0;
}
void findP(vector<int> points){
    if(points.size() >= n){
        counter++;
    }
    else{
        for(auto iter:edge){
            vector<int> tmpPoint = points;
            if(iter.first == tmpPoint[points.size()-1] && std::count(tmpPoint.begin(), tmpPoint.end(), iter.second) == 0){
                tmpPoint.push_back(iter.second);
                findP(tmpPoint);
            }
            else if(iter.second == tmpPoint[points.size()-1] && std::count(tmpPoint.begin(), tmpPoint.end(), iter.first) == 0){
                tmpPoint.push_back(iter.first);
                findP(tmpPoint);
            }
        }
    }
}