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;
using System.Linq;
using System.IO;
using System.Text;
using static System.Console;
using static System.Math;

namespace CP
{
    class Atria
    {
        //訪問済みかどうかを保存する配列
        static bool[] vs;
        static long ans;
        static bool[,] graph;
        static void Main(string[] args)
        {
            int[] s = ReadLine().Split(' ').Select(int.Parse).ToArray();
            int n = s[0];
            int m = s[1];
            //無向グラフを隣接行列を用いて受け取る
            graph = new bool[n, n];
            for (int i = 0; i < m; i++)
            {
                int[] scan = ReadLine().Split(' ').Select(x => int.Parse(x)-1).ToArray();
                graph[scan[0], scan[1]] = true;
                //graph[scan[1], scan[0]] = true;
            }
            //訪問済みかどうかを保存する配列
            vs = new bool[n];
            ans = 0;
            DFS(0);
            WriteLine(ans);
        }

        static void DFS(int v)
        {
            if (vs.Distinct().Count(x => x == true) == 1)
            {
                ans++;
                return;
            }

            for (int i = 0; i < vs.Count(); i++)
            {
                if (graph[v,i]&&vs[i] == false)
                {
                    vs[i] = true;
                    DFS(i);
                    vs[i] = false;
                }
            }

            return;
        }
    }
}