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: Accepted)

import java.util.*;

public class Main {
  static int N = 0;
  static int[][] edge;
  static int ans = 0;
  static int[] permutation = new int[8];
  public static void main(String[] args) {
    Scanner sc = new Scanner(System.in);
    N = sc.nextInt();
    edge = new int[N][N];
    int M = sc.nextInt();
    for(int i = 0; i < M; i++) {
      int a = sc.nextInt() - 1;
      int b = sc.nextInt() - 1;
      edge[a][b] = 1;
      edge[b][a] = 1;
    }
    dfs(1, 1);
    System.out.println(ans);
  }

  public static void dfs(int pos, int mask) {
    if(pos == N) {
      int count = 0;
      for(int i = 0; i < N - 1; i++) {
        if(edge[permutation[i]][permutation[i + 1]] == 0) count++;
      }
      if(count == 0) ans++;
    } else {
      for(int i = 0; i < N; i++) {
        if((mask & (1 << i)) == 0) {
          permutation[pos] = i;
          dfs(pos + 1, mask ^ (1 << i));
        } 
      }
    }
  }
}