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 Java8 (OpenJDK 1.8.0) (judge verdict: Accepted)

import java.util.ArrayList;
import java.util.Scanner;




class Main{


	static	ArrayList<Integer> one ;
	static	ArrayList<Integer> two ;
	static	ArrayList<Integer> three ;
	static	ArrayList<Integer> four ;
	static long pow = 1000000007;

	static int n;
	static int m;
	static int ans  = 0;
	static int[][] g;
	static boolean[] used;



	public static void main(String[] args) {

		Scanner sc = new Scanner(System.in);			//文字の入力
		n =sc.nextInt();
		m =sc.nextInt();
		g = new int[n+1][n+1];
		for(int i = 0;i < m;i++){
			int a  = sc.nextInt();
			int b = sc.nextInt();
			g[a][b] = 1;
			g[b][a] = 1;
		}
//
//		for(int i = 1;i <= m;i++){					//mapの確認
//			for(int j = 1;j <= m;j++){
//				System.out.print(g[i][j]);
//			}
//			System.out.println();
//		}

		used = new boolean[n+1];
	
		used[1] = true;
		dfs(1,1);
		System.out.println(ans);


	}
	static void dfs(int p,int num){			//numは通った頂点の個数
		if(num == n){
			ans++;
		}

		for(int i = 1;i <= n;i++){
			if(!(used[i]) && g[p][i] == 1){
				num++;
				used[i] = true;
				dfs(i, num);
				num--;
				used[i] = false;
			}

		}


	}

}



class Pair implements Comparable{
	Character from;
	int end;
	@Override
	public int compareTo(Object other) {
		Pair otherpair = (Pair)other;

		return end - otherpair.end;
	}
}