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: Accepted)

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

class Program
{
    static void Main(string[] args)
    {
        new Magatro().Solve();
    }
}

public class Scanner
{
    private StreamReader Sr;

    private string[] S;
    private int Index;
    private const char Separator = ' ';

    public Scanner(Stream source)
    {
        Index = 0;
        S = new string[0];
        Sr = new StreamReader(source);
    }

    private string[] Line()
    {
        return Sr.ReadLine().Split(Separator);
    }

    public string Next()
    {
        string result;
        if (Index >= S.Length)
        {
            S = Line();
            Index = 0;
        }
        result = S[Index];
        Index++;
        return result;
    }
    public int NextInt()
    {
        return int.Parse(Next());
    }
    public double NextDouble()
    {
        return double.Parse(Next());
    }
    public long NextLong()
    {
        return long.Parse(Next());
    }
    public decimal NextDecimal()
    {
        return decimal.Parse(Next());
    }
    public string[] StringArray(int index = 0)
    {
        Next();
        Index = S.Length;
        return S.Skip(index).ToArray();
    }
    public int[] IntArray(int index = 0)
    {
        return StringArray(index).Select(int.Parse).ToArray();
    }
    public long[] LongArray(int index = 0)
    {
        return StringArray(index).Select(long.Parse).ToArray();
    }
    public bool EndOfStream
    {
        get { return Sr.EndOfStream; }
    }
}

public class Magatro
{
    private Scanner Cin;
    private int N, M;
    private int[] A, B;

    private List<int>[] L;
    private void Scan()
    {
        Cin = new Scanner(Console.OpenStandardInput());
        N = Cin.NextInt();
        M = Cin.NextInt();
        A = new int[M];
        B = new int[M];
        for (int i = 0; i < M; i++)
        {
            A[i] = Cin.NextInt();
            B[i] = Cin.NextInt();
        }
    }

    public void Solve()
    {
        Scan();
        L = new List<int>[N + 1];
        for (int i = 0; i <= N; i++)
        {
            L[i] = new List<int>();
        }
        for (int i = 0; i < M; i++)
        {
            L[A[i]].Add(B[i]);
            L[B[i]].Add(A[i]);
        }

        int[] temp = new int[N - 1];
        for (int i = 2; i <= N; i++)
        {
            temp[i - 2] = i;
        }
        int cnt = 0;
        int loop = (int)Math.Pow(N-1, N - 1);
        for (int i = 0; i < loop; i++)
        {
            HashSet<int> h=new HashSet<int>();
            int p = i;
            bool flag = true;
            for (int j = 0; j < N-1; j++)
            {
                if (!h.Add(p % (N-1) + 2))
                {
                    flag = false;
                    break;
                }
                p /= N - 1;
            }
            if (!flag) continue;

            int[] a = h.ToArray();
          //  Console.WriteLine(string.Join(" ", a));
            if (!L[1].Contains(a[0])) continue;
            bool flagb = true;
            for (int j = 1; j < N-1; j++)
            {
                if (!L[a[j - 1]].Contains(a[j]))
                {
                    flagb = false;
                    break;
                }
            }
            if (flagb) cnt++;
        }
        Console.WriteLine(cnt);
    }
}