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: Runtime Error)

import java.util.*;

public class Main{
  public static void main(String[] args){
    Scanner scan = new Scanner(System.in);
    int n = scan.nextInt();
    int m = scan.nextInt();

    ArrayList<ArrayList<Integer>> a = new ArrayList<ArrayList<Integer>>();
    for (int i=0;i<m;i++){
      ArrayList<Integer> b = new ArrayList<Integer>();
      a.add(b);
    }

    for (int i=0;i<m;i++){
      int a1 = scan.nextInt();
      int a2 = scan.nextInt();

      ArrayList<Integer> c1 = a.get(a1-1);
      c1.add(a2);

      ArrayList<Integer> c2 = a.get(a2-1);
      c2.add(a1);
    }

    int ret = 0;
    boolean[] g = new boolean[n+1];

    for (int j=0;j<=n;j++){
      g[j] = false;
    }
    ret = find(a,0,1,g,1,n);
    System.out.println(ret);
  }

  static int find(ArrayList<ArrayList<Integer>> a, int sum, int current, boolean[] b, int where, int target){
    if (current == target){
      sum += 1;
      return sum;
    }

    ArrayList<Integer> n = a.get(where-1);
    b[where] = true;

    for (int k : n){
      if (b[k] == true){
        continue;
      }
      sum = find(a,sum,current+1,b,k,target);
    }

    b[where] = false;

    return sum;

  }

}