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.HashMap;
import java.util.HashSet;
import java.util.Map;
import java.util.Set;
import java.util.TreeSet;

public class Main {
	
	private static int count = 0;
	private static Map<Integer, Set<Integer>> pass;
	private static Set<Integer> visited = new HashSet<Integer>();
	private static int n;
	
	public static void main(String[] args) {
		java.util.Scanner scanner = new java.util.Scanner(System.in);
		n = scanner.nextInt();
		int m = scanner.nextInt();
		int[][] ab = new int[m + 1][2];
		for (int i = 1; i <= m; i++) {
			ab[i] = new int[]{scanner.nextInt(), scanner.nextInt()};
		}
		pass = new HashMap<Integer, Set<Integer>>();
		for (int i = 1; i <= m; i++) {
			for (int j = 1; j <= n; j++) {
				if (ab[i][0] == j) {
					Set<Integer> set = pass.get(j);
					if (set == null) {
						set = new TreeSet<Integer>();
						pass.put(j, set);
					}
					set.add(ab[i][1]);
				} else if (ab[i][1] == j) {
					Set<Integer> set = pass.get(j);
					if (set == null) {
						set = new TreeSet<Integer>();
						pass.put(j, set);
					}
					set.add(ab[i][0]);
				}
			}
		}
		visited.add(1);
		next(1);
		System.out.println(count);
	}

	private static void next(int current) {
		if (allVisited()) {
			count++;
			return;
		}
		
		for (Integer end : pass.get(current)) {
			if (!visited.contains(end)) {
				visited.add(end);
				next(end);
				visited.remove(end);	// 1つ戻る
			}
		}
	}
	
	private static boolean allVisited() {
		return visited.size() == n;
	}
}