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.ArrayDeque;
import java.util.Deque;
import java.util.Scanner;

public class Main {
  
  public static void main(String[] args) {
    
    Scanner sc = new Scanner(System.in);
    
    int N = Integer.parseInt(sc.next());
    int M = Integer.parseInt(sc.next());
    
    if (M < N - 1) {
      System.out.println(0);
      return;
    }
    
    int a[] = new int[M];
    int b[] = new int[M];
    for (int i = 0; i < M; i++) {
      a[i] = Integer.parseInt(sc.next());
      b[i] = Integer.parseInt(sc.next());
    }
    boolean ok[][] = new boolean[N][N];
    for (int i = 0; i < M; i++) {
      ok[a[i] - 1][b[i] - 1] = true;
      ok[b[i] - 1][a[i] - 1] = true;
    }
    
    int ans = 0;
    
    Deque<state> stack = new ArrayDeque<state>();
    boolean flag[] = new boolean[N];
    int count = N;
    stack.addLast(new state(0, flag, count));
    while (!stack.isEmpty()) {
      state now = stack.removeLast();
      now.flag[now.num] = true;
      if (--now.left == 0) {
        ans++;
        continue;
      }
      for (int i = 0; i < N; i++) {
        if (ok[now.num][i] && !now.flag[i]) {
          stack.addLast(new state(i, now.flag, now.left));
        }
      }
    }
    System.out.println(ans);
  }
  
  public static class state {
    public int     num;
    public boolean flag[];
    public int     left;
    
    public state(int x, boolean list[], int count) {
      num = x;
      flag = list.clone();
      left = count;
    }
  }
}