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.ArrayList;
import java.util.Arrays;
import java.util.Collections;
import java.util.HashSet;
import java.util.LinkedList;
import java.util.List;
import java.util.Scanner;
import java.util.Set;
import java.util.stream.Collectors;
import java.util.stream.IntStream;

public class Main
{
    private static int solve(Set<int[]> nodes, Set<Integer> vertexes, int pos)
    {
        /*
        System.out.println(
                String.format(
                        "pos=%d, vertexes=%s, nodes=%s",
                        pos,
                        Arrays.toString(vertexes.stream().toArray()),
                        Arrays.toString(nodes.stream()
                                .map(node -> String.format("(%d->%d)", node[0], node[1]))
                                .toArray())
                )
        );
         */

        if (vertexes.contains(pos)) {
            if (vertexes.size() == 1) {
                return 1;
            }
        }
        else {
            return 0;
        }

        int count = 0;
        for (int[] node : nodes) {
            if (node[0] == pos) {
                count += solve(nodes,
                        vertexes.stream()
                                .filter(x -> x != pos)
                                .collect(Collectors.toSet()),
                        node[1]);
            }
            else if (node[1] == pos) {
                count += solve(nodes,
                        vertexes.stream()
                                .filter(x -> x != pos)
                                .collect(Collectors.toSet()),
                        node[0]);
            }
        }

        return count;
    }

    public static void main(String[] args)
    {
        Scanner scanner = new Scanner(System.in);
        int n = scanner.nextInt();
        int m = scanner.nextInt();
        Set<int[]> xs = new HashSet<>();
        for (int i = 0; i < m; i++) {
            int[] node = new int[2];
            node[0] = scanner.nextInt();
            node[1] = scanner.nextInt();
            xs.add(node);
        }

        Set<Integer> vertexes = IntStream.rangeClosed(1, n).boxed().collect(Collectors.toSet());

        System.out.println(solve(xs, vertexes, 1));
    }
}