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: Accepted)

using System;
using System.Linq;
using System.Collections.Generic;


public class HelloWorld
{
    
    
    static List<long>[] Hedge;
    static long ans = 0;
    static Queue<long> que;
    
    static long N;
    
    static public void Main ()
    {
        var NM = Console.ReadLine().Split().Select(a => long.Parse(a)).ToArray();
        N = NM[0];
        var M = NM[1];
        Hedge = new List<long>[N+1];
        for(long i = 0;i <= N ;i++){
            Hedge[i] = new List<long>();
        }
        
        for(long i = 0;i < M ;i++){
            var AB = Console.ReadLine().Split().Select(a => long.Parse(a)).ToArray();
            var A = AB[0];
            var B = AB[1];
            Hedge[A].Add(B);
            Hedge[B].Add(A);
        }
       // Console.WriteLine(ans);
        que = new Queue<long>();
        var Used = new long[N+1];
        que.Enqueue(1);
        CountPath(Used,0);
        Console.WriteLine(ans);
    }
    
    static void CountPath(long[] Used,long count){
        if(que.Count == 0){
            return;
        }
      // Console.WriteLine(String.Join(" ",Used));
        var top = que.Dequeue();
        Used[top] = 1;
        count++;
        if(count == N){
            ans++;
            return;
        }else if(count > N){
            return;
        }
        foreach(long item in Hedge[top]){
            if(Used[item] == 0){
                que.Enqueue(item);
            var copy = new long[N+1];
            Used.CopyTo(copy, 0);
            CountPath(copy,count);
            }
            
        }
        
    }

}