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: Memory Limit Exceeded)

import java.util.*;

public class Main{

		public static boolean[][] isPath;
		public static boolean[] visited;
		public static int ans = 0;
		public static int n;
		public static int m;

	public static void main(String args[]){
		
		Scanner scan = new Scanner(System.in);
		
		//N頂点M辺
		n = scan.nextInt();
		m = scan.nextInt();
		

		//頂点カウント
		visited = new boolean[n];

		//組み合わせ格納
		isPath = new boolean[n][n];
		for(int i=0; i<m; i++){
			int a = scan.nextInt();
			int b = scan.nextInt();
			isPath[a-1][b-1] = true;
			isPath[b-1][a-1] = true; 
		}

		//最初の1は訪問済み
		visited[0] = true;

		dfs(0);

		System.out.println(ans);
		//dfsメソッド

		
	}
	public static void dfs(int v){
			
			//すべての頂点を訪問済みならans++
			int t = 0;
			for(int i=0; i<n; i++){
				if(visited[i]==true){t++;}
			}
			if(t==n){ans++;}

			for(int i=0; i<n; i++){
				//隣接してるならtrue 未訪問ならfalse
				if(isPath[v][i]==true && visited[i]==false){continue;}
				visited[i] = true;
				dfs(i);
				visited[i] = false;
			}
		}
}