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: Runtime Error)

import java.util.Scanner;
public class Main{
	
	public static void main(String[] args) {
		Scanner sc  = new Scanner(System.in);
		
		int n = sc.nextInt();
		int m = sc.nextInt();
		boolean [][]g = new boolean [n][n];
		
		for(int i = 0 ; i < n ; i++) {
			int a = sc.nextInt()-1;
			int b = sc.nextInt()-1;
			
			g[a][b] = true;
			g[b][a] = true;
			
		}
		boolean visit [] = new boolean [n];
		
		visit[0] = true;
		int count = dfs(n,0,g,visit);
		System.out.println(count);

	}
		private static int dfs(int n,int v ,boolean [][]g,boolean []visit) {
			
			boolean Allvisit = true;
			
			for(int i = 0 ;i < n ; i++) {
				if(!visit[i]) {
					Allvisit = false;
				}
			}
			
			if(Allvisit) {
				return 1;
			}
			int sum = 0;
			
			for(int i = 0; i < n ; i++) {
				if(!visit[i] && g[v][i]) {
					visit[i] = true;
					sum += dfs(n,i,g,visit);
					visit[i] = false;
				}
				
			}
			
			return sum;
			
			
			}
}