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.Scanner;
import java.util.List;
import java.util.ArrayList;

public class Main{
  static int n, m;
  static List< List< Integer > > graph;

  static int count;

  public static void main(String[] args){
    Scanner sc = new Scanner(System.in);

    n = sc.nextInt();
    m = sc.nextInt();
    graph = new ArrayList< >(n);
    for(int i = 0; i < n; i++){
      graph.add(new ArrayList< >());
    }
    for(int i = 0; i < m; i++){
      int a = sc.nextInt() - 1, b = sc.nextInt() - 1;
      graph.get(a).add(b);
      graph.get(b).add(a);
    }

    count = 0;
    backTrack(0, 0, new boolean[n]);

    System.out.println(count);
  }

  static void backTrack(int i, int v, boolean[] visited){
    if(i == n - 1){
      ++count;
      return;
    }
    visited[v] = true;
    for(int w : graph.get(v)){
      if(!visited[w]){
        backTrack(i + 1, w, visited);
      }
    }
    visited[v] = false;
  }
}