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.Linq;
using System.Text;
using System.Text.RegularExpressions;
using System.Collections.Generic;
using System.Threading.Tasks;

class Program
{
	//繋がっている地点を格納するリストの配列
	static List<int>[] pathArray;
	//合計
	static int N;
	//答え
	static int ans;

	//次の地点に進む関数
	static void GoForward(int x, int cnt, bool[] arrived){
			//現在地点を記録
			cnt ++;
			bool[] arr = new bool[N];
			Array.Copy(arrived, arr, N);
			arr[x-1] = true;

			//N回以上の経路を通った場合
			if(cnt == N){
					ans ++;
					return;
			}
			else{
					//次の地点へ進む
					foreach(int next in pathArray[x-1]){
							//まだ到達していなければ次へ
							if(arr[next-1] == false){
									GoForward(next, cnt, arr);
							}
					}
			}
	}

	//Main
	static void Main(string[] args)
	{
		//読み込む
		string[] line = Console.ReadLine().Split(' ');
		N = int.Parse(line[0]);
		int M = int.Parse(line[1]);

		//配列を初期化
		pathArray = new List<int>[N];
		for(int i=0; i<N; i++){
				pathArray[i] = new List<int>();
		}

		//辺を読み込み、リストに追加
		for(int i=0; i<M; i++){
				string[] line1 = Console.ReadLine().Split(' ');
				int a = int.Parse(line1[0]);
				int b = int.Parse(line1[1]);

				pathArray[a-1].Add(b);
				pathArray[b-1].Add(a);
		}

		//全探索
		GoForward(1, 0, new bool[N]);

		//答えを出力
		Console.WriteLine(ans);

	}
}