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.Text;
using static MyIO;


public class C
{
	public static void Main()	
	{
		int N = GetInt();
		int M = GetInt();
		int[,] graph = new int[N+1,N+1];
		for(int i = 0; i < M; i++)
		{
			int a = GetInt();
			int b = GetInt();
			graph[a,b] = 1;
			graph[b,a] = 1;
		}

		int ans = 0;
		int[] perm = new int[N-1];
		for(int i = 2; i <= N; i++)
			perm[i-2] = i;
		do
		{
			if(graph[1, perm[0]] == 0)
				continue;

			bool isOK = true;
			for(int i = 1; i <= N-2; i++)
			{
				if(graph[perm[i-1], perm[i]] == 0)
				{
					isOK = false;
					break;
				}
			}
			if(isOK)
				ans++;

		} while (nextPermutation(ref perm));

		Console.WriteLine(ans);
	}


	private static bool nextPermutation(ref int[] array)
	{
		int len = array.Length;
		int i = len - 2;
		while((i >= 0) && (array[i] > array[i + 1]))
			i--;
		if(i < 0)
			return false;

		int pivot = array[i];
		int j = i + 1;
		while((j < len - 1) && (array[j + 1] > pivot))
			j++;
		
		int tmp = array[i];
		array[i] = array[j];
		array[j] = tmp;
		
		Array.Reverse(array, i + 1, len - i - 1);

		return true;
	}
}


public static class MyIO
{
	private static string[] args = null;
	private static int num = -1;
	private static int used = -1;

	private static string getArg()
	{
		if(used == num)
		{
			args = Console.ReadLine().Split(' ');
			num = args.Length;
			used = 0;
		}
		return args[used++];
	}

	public static int GetInt(){ return int.Parse(getArg()); }
	public static long GetLong(){ return long.Parse(getArg()); }
	public static double GetDouble(){ return double.Parse(getArg()); }
	public static string GetString(){ return getArg(); }
}