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.BufferedReader;
import java.io.InputStreamReader;
import java.util.ArrayList;
import java.util.HashMap;
import java.util.List;
import java.util.Scanner;

public class Main {
    public static void main(String[] args) {
        Main main = new Main();
        main.solve();
    }
    public void solve() {
        Scanner scan = new Scanner(new BufferedReader(new InputStreamReader(System.in)));
        int N = scan.nextInt();
        int M = scan.nextInt();
        boolean[] done = new boolean[N];
        HashMap<Integer, List<Integer>> edges = new HashMap<>();
        for (int i = 0; i < M; i++) {
            int a = scan.nextInt()-1;
            int b = scan.nextInt()-1;
            if (!edges.containsKey(a)) {
                edges.put(a, new ArrayList<Integer>());
            }
            if (!edges.containsKey(b)) {
                edges.put(b, new ArrayList<Integer>());
            }
            edges.get(a).add(b);
            edges.get(b).add(a);
        }
        int answer = dfs(0, done, edges);
        System.out.println(answer);
    }
    public int dfs(int current, boolean[] done, HashMap<Integer, List<Integer>> edges) {
        if (done[current]) {
            return 0;
        }
        done[current] = true;
        boolean all_visited = true;
        for (int i = 0; i < done.length; i++) {
            if (!done[i]) {
                all_visited = false;
                break;
            }
        }
        if (all_visited) {
            return 1;
        }
        List<Integer> neighbors = edges.get(current);
        int answer = 0;
        for (int next : neighbors) {
            if (done[next]) {
                continue;
            }
            answer += dfs(next, done, edges);
            done[next] = false;
        }
        return answer;
    }
}