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.Diagnostics;
using System.Text;
using System.Linq;
class Program
{
    private static int n, m;
    private static bool[,] edge;
    static void Main()
    {
        int[] inputs = Console.ReadLine().Split().Select(int.Parse).ToArray();
        n = inputs[0];
        m = inputs[1];
        edge = new bool[n, n];
        for (int i = 0; i < m; i++)
        {
            inputs = Console.ReadLine().Split().Select(int.Parse).ToArray();
            int a = inputs[0] - 1, b = inputs[1] - 1;
            edge[a, b] = true;
            edge[b, a] = true;
        }
        Console.WriteLine(Search(0, 0));
    }
    static int Search(int s, int f)
    {
        f = f | 1 << s;
        if (f == (int)Math.Pow(2, n) - 1)
            return 1;
        int v = 0;
        for (int i = 0; i < m; i++)
            if (edge[s, i] && ((f >> i & 1) == 0))
                v += Search(i, f);
        return v;
    }
}