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.Scanner;

public class Main {
	static boolean[][] connected;
	static boolean[] arrived;
	static int ans = 0;
	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);

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

		// make a map
		connected = new boolean[n][n];
		for (int i = 0; i < m; i++) {
			int a = sc.nextInt() - 1; // start at 0
			int b = sc.nextInt() - 1;
			connected[a][b] = true;
			connected[b][a] = true;
		}

		arrived = new boolean[n];
		search(arrived, 0);

		System.out.println(ans);

		sc.close();
	}

	// search
	static void search(boolean[] arrived, int arrive) {
		if (arrived[arrive]) {
			return;
		} else {
			arrived[arrive] = true;
		}

		if (isAccomplish(arrived)) {
			ans++;
			return;
		}

		for (int i = 0; i < connected.length; i++) {
			if (connected[arrive][i]) {
				search(copyArray(arrived), i);
			}
		}
	}

	// copy a array
	static boolean[] copyArray(boolean[] arr1) {

		boolean[] arr2 = new boolean[arr1.length];
		for (int i = 0; i < arr1.length; i++) {
			arr2[i] = arr1[i];
		}

		return arr2;
	}

	// check accomplish
	static boolean isAccomplish(boolean[] arr) {
		for (int i = 0; i < arr.length; i++) {
			if (!arr[i]) {
				return false;
			}
		}
		return true;
	}

}