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: Runtime Error)

/**
 * code generated by JHelper
 * More info: https://github.com/AlexeyDmitriev/JHelper
 * @author TM
 */


#include <iostream>
#include <algorithm>
#include <vector>
#include <string>
#include <queue>
#include <map>
#include <set>
#include <functional>
#include <cmath>
#include <numeric>
#include <iterator>

#define SIZE 100005
#define MOD 1000000007
#define INF 100000000

using namespace std;

class COneStrokePath {
public:
    int dfs(int now, vector<bool> visited) {
        if (visited[now]) return 0;
        visited[now] = true;
        if (count(visited.begin(), visited.end(), false) == 1) {
            return 1;
        }
        int ans = 0;
        for (int i = 0; i < to_vec[now].size(); ++i) {
            ans += dfs(to_vec[now][i], visited);
        }
        return ans;

    }

    void solve(std::istream &cin, std::ostream &cout) {
        int n, m;
        cin >> n >> m;
        to_vec.resize(m + 1);
        vector<bool> visited(m + 1);

        for (int i = 0; i < m; ++i) {
            visited[i] = false;
            int a, b;
            cin >> a >> b;
            to_vec[a].push_back(b);
            to_vec[b].push_back(a);
        }

        cout << dfs(1, visited) << endl;
    }

    vector<vector<int>> to_vec;
};


int main() {
    COneStrokePath solver;
    std::istream &in(std::cin);
    std::ostream &out(std::cout);
    solver.solve(in, out);
    return 0;
}