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: Wrong Answer)

import java.util.*;

public class Main {
    
   static int N;
   static int count;
   static ArrayList<ArrayList<Integer>> al;       
    
  public static void main(String[] args) {
      
       Scanner sc = new Scanner(System.in);              
              
       int N = sc.nextInt();
       int M = sc.nextInt();
       
       al = new ArrayList<>();
       
       for(int i = 0; i < N; i++){
	   al.add(new ArrayList<>());
       } 
       
       for(int i = 0; i < M; i++) {
	   int a = sc.nextInt() - 1;
	   int b = sc.nextInt() - 1;
	   al.get(a).add(b);
	   al.get(b).add(a);
       }

       count = 0;
       boolean[] reach = new boolean[N];
       dfs(0, 0, reach);
       System.out.println(count);           
  } 
  
   static void dfs(int now, int num, boolean[] reach) {
		if (num == N - 1) {
			count++;
			return;
		}
                
		for (Integer v : al.get(now)) {
			reach[now] = true;
			if (!reach[v]) dfs(v, num + 1, reach);
			reach[now] = false;
		}               
   }

   
}