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 <bits/stdc++.h>
#include<string>
#include<algorithm>
#include<utility>
#include<map>
using namespace std;
bool graph[8][8];

int dfs(int node,int N,bool visited[8]){

    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 < N; ++i){
        if(graph[node][i]==false) continue;
        if(visited[i]) continue;
        visited[i]=true;
        ret += dfs(i,N,visited);
        visited[i]=false;//次のノードに繰り返すから、もとに戻しておく
    }
    return  ret;
}


int main(){
    int N, M;
    cin >> N >> M;
    for(int i =0 ; i < M; ++i){
        int A, B;
        cin >> A >> B;
        graph[A-1][B-1]=graph[B-1][A-1]=true;
    }
    bool visited[8];
    for(int i = 0; i < N; ++i){
        visited[i]=false;
    }

    visited[0]=true;
    cout << dfs(0,N,visited) << endl;
    return 0;
}