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# (Mono 4.6.2.0) (judge verdict: Runtime Error)

using System;
using System.Linq;
public class Hello{//imit
    static int N,M;
    static bool[,] path;
    static bool[] visited;
    
    public static void Main(){
        var line = Console.ReadLine().Split(' ').Select(int.Parse).ToArray();
        N = line[0];
        M = line[1];
        var allArrived = false;
        visited = new bool[N];
        visited[0] = true;
        path = new bool[M,M];
        for(var i = 0;i < M;i++){
                var input = Console.ReadLine().Split(' ').Select(int.Parse).ToArray();
                path[input[0] - 1,input[1] - 1] = path[input[1] - 1,input[0] - 1] = true;
        }
        
        Console.WriteLine(dfs(0,N,visited));
    }
    
    static int dfs(int v, int n, bool[] visited){
        bool allvisited = true;
        for(var i = 0;i < n;i++){
            if(!visited[i]){
                allvisited = false;
            }
        }
        
        if(allvisited){
            return 1;
        }
        
        int ret = 0;
        
        for(var i = 0;i < n;i++){
            if(!path[v,i]){
                continue;
            }
            if(visited[i]){
                continue;
            }
            
            visited[i] = true;
            ret += dfs(i,n,visited);
            visited[i] = false;
        }
        
        return ret;
        
    }
}