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: Wrong Answer)

using System;
using System.Collections.Generic;

namespace ABC054_C
{
    class Program
    {
        static void Main(string[] args)
        {
            var nm = Array.ConvertAll(Console.ReadLine().Split(' '), int.Parse);
            var n = nm[0];
            var m = nm[1];
            var gra = new int[n, n];
            for (var i = 0; i < m; i++)
            {
                var hen = Array.ConvertAll(Console.ReadLine().Split(' '), int.Parse);
                gra[hen[0] - 1, hen[1] - 1] = 1;
                gra[hen[1] - 1, hen[0] - 1] = 1;
            }
            Console.WriteLine(dfs(0, n, gra));
        }
        static int dfs(int v, int n, int[,] mmm)
        {
            var ans = 0;
            var s = new Stack<int>();
            for (var j = 0; j < n; j++)
            {
                if (mmm[v, j] == 1)
                {
                    var bo = new int[n];
                    bo[v]++;
                    s.Push(j);
                    while(s.Count != 0)
                    {
                        var c = s.Pop();
                        for(var k=0;k<n;k++)
                        {
                            if(mmm[c,k] == 1 && bo[k] == 0)
                            {
                                s.Push(k);
                                bo[k]++;
                            }
                        }
                    }
                    foreach(var ch in bo)
                    {
                        if(ch != 1)
                        {
                            break;
                        }
                    }
                    ans++;
                }
            }
            return ans;
        }
    }
}