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.Collections.Generic;
using System.Text;

class Program
{
    public static int Main()
    {
        do
        {
            new Program().solve();
        } while (true);
        return 0;
    }
    public int dfs(bool[,] matrix, bool[] check, int N, int row, int depth)
    {
        if (depth >= N - 1)
            return 1;

        int count = 0;
        for (int i = 1; i < N; ++i)
        {
            if (!check[i] && matrix[row, i])
            {
                check[i] = true;
                count += dfs(matrix, check, N, i, depth + 1);
                check[i] = false;
            }
        }
        return count;
    }
    public void solve()
    {
        string[] str = Console.ReadLine().Split(' ');
        int N = int.Parse(str[0]);
        int M = int.Parse(str[1]);

        bool[,] matrix = new bool[N, N];
        bool[] check = new bool[N];
        for (int i = 0; i < M; ++i)
        {
            str = Console.ReadLine().Split(' ');
            int a = int.Parse(str[0]) - 1;
            int b = int.Parse(str[1]) - 1;
            matrix[a, b] = true;
            matrix[b, a] = true;
        }

        Console.WriteLine(dfs(matrix, check, N, 0, 0));
    }
}