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.io.File;
import java.io.FileNotFoundException;
import java.util.ArrayList;
import java.util.LinkedList;
import java.util.List;
import java.util.Scanner;

public class Main {
    static int sum;
    static List<LinkedList<Integer>> graph;
    static boolean[] isVisited;

    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        int n = Integer.parseInt(sc.next());
        int m = Integer.parseInt(sc.next());
        graph = new ArrayList<LinkedList<Integer>>();
        isVisited = new boolean[n];
        int s ,t;
        for(int i=0;i<n;i++)graph.add(new LinkedList<>());
        for(int i=0;i<m;i++){
            s = Integer.parseInt(sc.next())-1;
            t = Integer.parseInt(sc.next())-1;
            graph.get(s).add(t);
            graph.get(t).add(s);
        }
        sc.close();
        sum = 0;
        bfs(0,n,0);
        System.out.println(sum);

    }

    public static void bfs(int pos,int n,int v){
        if(pos == n-1){
            sum++;
        }else{
            isVisited[v] = true;
            for(Integer i : graph.get(v)){
                if(!isVisited[i]){
                    bfs(pos+1,n,i);
                }
            }
            isVisited[v] = false;
        }
    }
}