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>

std::vector<std::vector<int>> vec;
void dfs(int edge, std::vector<bool> bool_vec, int& c) {
    if (bool_vec[edge]) {
        return;
    }
    bool_vec[edge] = true;
    bool all_true = true;
    for (int i = 1; i <= bool_vec.size(); i++) {
       if (vec[edge][i] == 1 && bool_vec[i] == false) {
           all_true = false;
           bool_vec[i] = true;
           dfs(i, bool_vec, c);
           bool_vec[i] = false;
       }
    }
    if (all_true) {
        c++;
    }
}

int n, m, x, y;


int main() {
    std::cin >> n >> m;
    vec.assign(n+1, std::vector<int>(n+1, 0));
    for (int i = 0; i < m; i++) {
        std::cin >> x >> y;
        vec[x][y] = 1;
    }
    int c = 0;
    for (int i = 1; i <= n; i++) {
        std::vector<bool> bv(n+1, false);
        bv[1] = true;
        if (vec[1][i] == 1) {
            dfs(i, bv, c);
        }
    }
    std::cout << c << std::endl;
}