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 Java7 (OpenJDK 1.7.0) (judge verdict: Accepted)

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

/**
 * Created by guoxiang.li on 2017/02/13.
 */
public class Main {

    private int count=0;
    private ArrayList[] graph;
    boolean[] visited;
    public int undirectedGraphTraversalWays(int[][] nums,int n){

       graph=new ArrayList[n];

        for(int i=0;i<n;i++){
            graph[i]=new ArrayList();
        }

        visited=new boolean[n];

        for(int i=0;i<nums.length;i++){
            graph[nums[i][0]-1].add(nums[i][1]-1);
            graph[nums[i][1]-1].add(nums[i][0]-1);
        }


        visited[0]=true;
        undirectedGraphTraversalWaysHelper(graph[0]);
        return count;

    }


    private boolean undirectedGraphTraversalWaysHelper(ArrayList nodes){


        boolean flag=true;
        for(boolean visitedFlag:visited){
            flag&=visitedFlag;
        }

        if(flag){
            return true;
        }


        for(Object node:nodes){

            int index=((Integer) node).intValue();

            if(visited[index]){
                continue;
            }
            visited[index]=true;

            if(undirectedGraphTraversalWaysHelper(graph[index])){
                count++;
            }

            visited[index]=false;
        }

        return false;



    }

    public static void main(String[] args) {



        Main sol=new Main();
        Scanner sc = new Scanner(System.in);
        // get a integer
        int n = sc.nextInt();
        // get two integers separated with half-width break
        int m = sc.nextInt();

        int[][] edges=new int[m][2];
        for(int i=0;i<m;i++) {
            edges[i][0] = sc.nextInt();
            edges[i][1] = sc.nextInt();
        }

        System.out.println(sol.undirectedGraphTraversalWays(edges,n));


    }


}