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 int n, m;
	static int[] a, b;
	static boolean[] vis;
	static boolean[][] connect;

	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];
		vis = new boolean[n];
		connect = new boolean[n][n];
		for(int i = 0 ; i < m ; i++) {
			a[i] = sc.nextInt() - 1;
			b[i] = sc.nextInt() - 1;
			connect[a[i]][b[i]] = connect[b[i]][a[i]] = true;
		}
		vis[0] = true;
		int ans = dfs(0);
		System.out.println(ans);
	}

	public static int dfs(int x) {
		boolean all_vis = true;
		for(int i = 0 ; i < n ; i++) {
			if(!vis[i]) all_vis = false;
		}
		if(all_vis) return 1;
		int ret = 0;
		for(int i = 0 ; i < n ; i++) {
			if(vis[i]) continue;
			if(!connect[x][i]) continue;
			vis[i] = true;
			ret += dfs(i);
			vis[i] = false;
		}
		return ret;
	}

}