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 <cstdio>
#include <algorithm>
#include <iostream>
#include <vector>
#include <map>
#include <unordered_map>
#include <cmath>
#include <queue>
#include <set>

using namespace std;
typedef long long ll;
typedef pair<int, int> P;
#define INF int(1e9)
#define REP(i, n) for(int i = 0; i < (int)(n); i++)
#define REPR(i, n) for(int i = n - 1; i >= 0; i--)
#define REPONE(i, n) for(int i = 1; i <= (int)(n); i++)
#define EACH(i, mp) for(auto i:mp)
#define FOR(i, m, n) for(int i = m;i < n;i++)
int dx[4] = {1, 0, -1, 0}, dy[4] = {0, 1, 0, -1};

const int MAX_N = 8, MAX_M = 8 * 7 / 2;
bool G[MAX_N][MAX_N];
bool visited[MAX_N];
int N, M;

int dfs(int v) {
    bool all_visited = true;
    REP(i, N) if (!visited[i]) all_visited = false;
    if (all_visited) return 1;

    int ret = 0;
    REP(i, N) {
        if (!G[v][i]) continue;
        if (visited[i]) continue;
        visited[i] = true;
        ret += dfs(i);
        visited[i] = false;
    }
    return ret;
}

void solve() {
    visited[0] = true;
    int ans = dfs(0);
    cout << ans << endl;
}

int main() {
    cin >> N >> M;
    for (int i = 0; i < M; ++i) {
        int a, b;
        cin >> a >> b;
        a--, b--;
        G[a][b] = G[b][a] = true;
    }
    solve();
    return 0;
}