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: Wrong Answer)

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

public class Main {
    public static void main(String[] args) throws Exception {
        Graph g = input();
        boolean[] bools = new boolean[g.getSize()];
        Arrays.fill(bools,false);
        System.out.println(dfs(g,0,0,bools));
    }

    private static Graph input(){
        Scanner sc = new Scanner(System.in);
        int n = sc.nextInt();
        int m = sc.nextInt();
        Graph ret = new Graph(n);
        for(int i = 0; i < m;i++){
            int a = sc.nextInt()-1;
            int b = sc.nextInt()-1;
            ret.addEdge(a,b);
            ret.addEdge(b,a);
        }
        sc.close();
        return ret;
    }

    private static int dfs(Graph g, int s, int dist, boolean[] bools){
        if(dist == bools.length){
            return 1;
        }
        if(bools[s]){
            return 0;
        }
        bools[s] = true;
        int ans = 0;
        LinkedList<Integer> al = g.getAdjacencyList(s);
        for(int i: al){
            ans += dfs(g,i,dist+=1,bools);
        }
        bools[s] = false;
        return ans;
    }
}

     class Graph {
        private ArrayList<LinkedList<Integer>> adjacencyList;
        public Graph(int numberNodes) {
            adjacencyList = new ArrayList<LinkedList<Integer>>(numberNodes);
            for (int i = 0; i < numberNodes; i++) {
                adjacencyList.add(new LinkedList<Integer>());
            }
        }
        private boolean isValidNode(int index) {
            return index >= 0 && index < adjacencyList.size();
        }
        public void addEdge(int to, int from) {
            if (!isValidNode(to) || !isValidNode(from)) {
                throw new IndexOutOfBoundsException();
            }
            adjacencyList.get(from).addLast(to);
        }
        public int getSize(){
            return adjacencyList.size();
        }
        public LinkedList<Integer> getAdjacencyList(int i){
            return adjacencyList.get(i);
        }
    }