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 (Clang 3.8.0) (judge verdict: Accepted)

#include <iostream>
#include <vector>

using namespace std;

int dfs(vector<vector<int> > G, int n, bool *visited, int u) {
    bool all_visited = true;
    for (int i = 0; i < n; i++) {
        if (visited[i] == false)
            all_visited = false;
    }

    if (all_visited) {
        return 1;
    }

    int ret = 0;

    for (int i = 0; i < G[u].size(); i++) {
        int v = G[u][i];
        if (visited[v])
            continue;
        
        visited[v] = true;
        ret += dfs(G, n, visited, v);
        visited[v] = false;
    }

    return ret;
}

int main() {
    int n, m;   cin >> n >> m;
    vector<vector<int> > G(n);
    int a, b;   
    for (int i = 0; i < m; i++) {
        cin >> a >> b;
        G[a-1].push_back(b-1);
        G[b-1].push_back(a-1);
    }

    bool *visited = new bool[n];
    for (int i = 0; i < n; i++)
        visited[i] = false;
    visited[0] = true;

    int ans = dfs(G, n, visited, 0);

    cout << ans << endl;

    return 0;
}