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.*;

public class Main {

    public static void main(String[] args) {
        // write your code here
        Scanner sc = new Scanner(System.in);

        int n = sc.nextInt();
        int m = sc.nextInt();

        boolean[][] meiro = new boolean[n][n];

        for (int i = 0; i < m; i++) {
            int left = sc.nextInt() - 1;
            int right = sc.nextInt() - 1;
            meiro[left][right] = true;
            meiro[right][left] = true;
        }

        StringBuilder builder = new StringBuilder();

        for (int i = 1; i < n; i++) {
            builder.append(i);
        }

        String base = builder.toString();
        permutation(base, "");

        int count = 0;

        top : for (String target: list
             ) {
            String[] values = target.split("");
            int lastValue = 0;
            for (String value : values) {
                int start = lastValue;
                int end = Integer.parseInt(value);
                if (!meiro[start][end]) {
                    continue top;
                }
                lastValue = end;
            }
            count++;
        }

        System.out.println(count);
    }

    private static ArrayList<String> list = new ArrayList<>();

    private static void permutation(String q, String ans){
        // Base Case
        if(q.length() <= 1) {
            list.add(ans + q);
        }
        // General Case
        else {
            for (int i = 0; i < q.length(); i++) {
                permutation(q.substring(0, i) + q.substring(i + 1),
                        ans + q.charAt(i));
            }
        }
    }
}