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 Java (OpenJDK 11.0.6) (judge verdict: Wrong Answer)

import java.util.*;
public class Main {
  
	public static void main(String[] args){
        Scanner sc = new Scanner(System.in);

		int N = sc.nextInt();
		int M = sc.nextInt();
      
      	boolean[][] connectingNumsArray2 = new boolean[N][N];
        for(int i = 0; i < N; i++){
            for(int j = 0; j < N; j++){
                // 初期値はfalse
                connectingNumsArray2[i][j] = false;
            }
        }
		
      	for(int i = 0; i < M; i++){
            int a = sc.nextInt();
            int b = sc.nextInt();
          
            //0から始まるから、1ずれる
          	connectingNumsArray2[a -1][b - 1] = true;
            connectingNumsArray2[b - 1][a - 1] = true;
        }
      
        List<Integer> pathList = new ArrayList<>();
      	pathList.add(1);
      	int ans = 0;
      	makePathList(1, pathList, N, ans, connectingNumsArray2);
      
        System.out.println(ans);
    }
  
  	public static void makePathList(
        int currentNum, List<Integer> pathList,int N, int ans, boolean[][] connectingNumsArray2){
        for(boolean[] nextNumCandidate : connectingNumsArray2){
            for(int i = 0; i < N; i++){
                if(nextNumCandidate[i] == false){
                    if(pathList.size() == N - 1){
                        ans = ans + 1;
                    }
                } else {
                    if(pathList.contains(i + 1) == false){
                        pathList.add(i + 1);
                        makePathList(i + 1, pathList, N, ans, connectingNumsArray2);
                    }
                }     
            }
        }
    }
}