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;
using System.Collections.Generic;
using System.Linq;
using System.IO;
using System.Text;

public class Don
{
    public Don() { }
    private Reader r = new Reader();

    private static List<bool> visited;
    private static List<List<int>> G;
    private static int ret = 0;

    // 深さ優先探索
    void dfs(int p, int n, int goal)
    {
        if (n == goal)
        {
            ret++;
        }
        else
        {
            for (var i = 0; i < G[p].Count() ; i++)
            {
                var y = G[p][i];
                if (!visited[y])
                {
                    visited[y] = true;
                    dfs(G[p][i], n + 1, goal);
                    visited[y] = false;
                }
            }
        }
    }

    public void Solve()
    {
        int N = r.nextInt();
        int M = r.nextInt();

        G = new List<List<int>>();
        visited = new List<bool>();

        for (var i = 0; i <= N; i++) G.Add(new List<int>());
        for (var i = 0; i <= N + 1; i++) visited.Add(false);

        for (var i = 0; i < N; i++)
        {
            G[r.nextInt()].Add(r.nextInt());
        }

        visited[1] = true;

        dfs(1, 1, N - 1);

        Console.WriteLine(ret);
    }

    public static void Main(string[] args)
    {
        new Don().Solve();
    }

}

class Reader
{
    string[] s;
    int i;
    char[] cs = new char[] { ' ' };

    public Reader()
    {
        s = new string[0];
        i = 0;
    }

    public string next()
    {
        if (i < s.Length)
            return s[i++];
        var input = Console.ReadLine();
        while (input == "")
            input = Console.ReadLine();
        s = input.Split(cs, StringSplitOptions.RemoveEmptyEntries);
        i = 0;
        return next();
    }

    public int nextInt()
    {
        return int.Parse(next());
    }

    public long nextLong()
    {
        return long.Parse(next());
    }

    public double nextDouble()
    {
        return double.Parse(next());
    }

}