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.io.*;
import java.util.*;

public class Main{
	static class FastReader{
		BufferedReader br;
		StringTokenizer st;
		public FastReader(){
			br = new BufferedReader(new InputStreamReader(System.in));
		}
		public String next(){
			try{
				while(st==null||!st.hasMoreElements()){
					st = new StringTokenizer(br.readLine());
				}
			}catch(Exception e){
				e.printStackTrace();
			}
			return st.nextToken();

		}
		public int nextInt(){
			return Integer.parseInt(next());
		}
		public long nextLong(){
			return Long.parseLong(next());
		}
		public double nextDouble(){
			return Double.parseDouble(next());
		}
		public String nextLine(){
			String s = "";
			try{
				s = br.readLine();
			}catch(Exception e){
				e.printStackTrace();
			}	
			return s;		
		}
	} 
	static ArrayList<Node> nodes = new ArrayList<>();
	static int count = 0;
	static int n;
	static class Node{
		ArrayList<Node> adj = new ArrayList<>();
		int i;
		Node(int i ){
			this.i = i;
		}
		
	}
	static void dfs(int src,boolean[] visited,int size){
		if(size==n)count++;
		for(Node adj :nodes.get(src).adj){
			if(!visited[adj.i]){
				visited[adj.i] = true;
				dfs(adj.i,visited,size+1);
				visited[adj.i] = false;
			}
		} 
	}
	public static void main(String[] args){
		FastReader in = new FastReader();
		PrintWriter out = new PrintWriter(System.out);
		n = in.nextInt();
		int m = in.nextInt();
		for(int i = 0 ; i < n; i++)nodes.add(new Node(i));
		for(int i = 0 ; i<m;i++){
			int v1 = in.nextInt()-1;
			int v2 = in.nextInt()-1;
			nodes.get(v1).adj.add(nodes.get(v2));
			nodes.get(v2).adj.add(nodes.get(v1));

		}
		int size = 1;
		boolean visited[] = new boolean[n];
		visited[0] = true;
		dfs(0,visited,size);
		out.println(count);
		out.flush();
		out.close();  
	}

}