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.Generic;

class OneStroke
{
	
	static int N, M;
	static bool[] visited;
	static int count;
	static int answer;
	static List<int>[] dest;

	static public void Main(string[] args)
	{
		string[] vals = Console.ReadLine().Split(' ');
		N = int.Parse(vals[0]);
		M = int.Parse(vals[1]);
		dest = new List<int>[N+1];
		for(int i=1; i<=N; i++)
			dest[i] = new List<int>();
		int a, b;
		for(int i=0; i<M; i++)
		{
			vals = Console.ReadLine().Split(' ');
			a = int.Parse(vals[0]);
			b = int.Parse(vals[1]);
			dest[a].Add(b);
			dest[b].Add(a);
		}
		visited = new bool[N+1];
		count = answer = 0;
		search(1);
		Console.WriteLine(answer);
	}

	static void search(int n)
	{
		visited[n] = true;
		if(++count == N)
		{
			answer++;
			return;
		}

		for(int i=0; i<dest[n].Count; i++)
		{
			if(visited[dest[n][i]] == false)
			{
				search(dest[n][i]);
				visited[dest[n][i]] = false;
				count--;
			}
		}
	}

}