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: Wrong Answer)

import java.util.*;
public class Main {
    static List<String> list;
    public static void main(String[] args) {
        Scanner scan = new Scanner(System.in);
        int N = scan.nextInt();
        int M = scan.nextInt();
        int sum = 0;
        List<Integer> list1 = new ArrayList<>();
        List<Integer> list2 = new ArrayList<>();
        for(int i = 0; i < M; i++){
            int a = scan.nextInt();
            int b = scan.nextInt();
            list1.add(a);
            list2.add(b);
        }
        list = new ArrayList<>();
        //ここで全列挙を行う
        f(N, "1");
        int count = 0;
        for(int i = 0; i < list.size(); i++){
            count = 0;
            for(int m = 0; m < N-1; m++){
                int cur = list.get(i).charAt(m) - '0';
                int next = list.get(i).charAt(m+1) - '0';
                if(list1.contains(cur)){
                    for(int j = 0; j < M; j++){
                        //System.out.println("a");
                        if(list1.get(j) == cur && list2.get(j) == next){
                            count++;
                        }
                    }
                }else if(list2.contains(cur)){
                    for(int j = 0; j < M; j++){
                        if(list1.get(j) == next && list2.get(j) == cur){
                            count++;
                        }
                    }
                }else{
                    continue;
                }
            }
            //System.out.println(count);
            if(count == N-1){
                //System.out.println(list.get(i));
                sum++;
            }
        }
        System.out.println(sum);
    }
    
    public static void f(int N, String str){
        if(str.length() == N){
            list.add(str);
        }
        for(int i = 2; i <= N; i++){
            if(!str.contains(Integer.toString(i))){
                f(N, str+Integer.toString(i));
            }
        }
    }
}