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.HashSet;
import java.util.Scanner;
import java.util.Set;

public class Main {

    private static int N;
    private static int M;
    private static int[] A;
    private static int[] B;

    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        N = sc.nextInt();
        M = sc.nextInt();
        A = new int[M];
        B = new int[M];
        for (int i = 0; i < M; i++) {
            A[i] = sc.nextInt();
            B[i] = sc.nextInt();
        }
        System.out.println( solve() );
    }

    private static int solve() {
        Set<Integer> path = new HashSet<>();
        path.add(1);
        return _solve(1, path);
    }

    private static int _solve(int node, Set<Integer> path) {
        if( path.size() == N ) return 1;

        int ans = 0;
        for (int i = 0; i < M; i++) {
            if( A[i] == node ) {
                int to = B[i];
                if( !path.contains(to) ) {
                    Set<Integer> newPath = new HashSet<>(path);
                    newPath.add(to);
                    ans += _solve(to, newPath);
                }
            }

            if( B[i] == node ) {
                int to = A[i];
                if( !path.contains(to) ) {
                    Set<Integer> newPath = new HashSet<>(path);
                    newPath.add(to);
                    ans += _solve(to, newPath);
                }
            }
        }
        return ans;
    }
}