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 Java (OpenJDK 11.0.6) (judge verdict: Accepted)

import java.util.*;

public class Main {

	public static void main(String[] args) {
		Main main = new Main();
		main.run();
	}

	ArrayList<ArrayList<Integer>>g = new ArrayList<>();
	boolean used[];
	int n;
	int ans;
	public void run() {
		Scanner sc = new Scanner(System.in);
		n=sc.nextInt();
		int m=sc.nextInt();
		for(int i=0; i<n; i++) {
			g.add(new ArrayList<>());
		}
		used = new boolean[n];
		for(int i=0; i<m; i++) {
			int a=sc.nextInt();
			int b=sc.nextInt();
			a--;
			b--;
			g.get(a).add(b);
			g.get(b).add(a);
		}
		used[0]=true;
		dfs(0, 1);
		System.out.println(ans);
		sc.close();
	}

	private void dfs(int u, int cnt) {
		for(int i=0; i<g.get(u).size(); i++) {
			int v = g.get(u).get(i);
			if(! used[v]) {
				used[v]=true;
				dfs(v, cnt+1);
				used[v]=false;
			}
		}
		if(cnt == n) {
			ans++;
		}
	}
}