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

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

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

    private static int dfs(boolean[][] g, int s, boolean[] bools){
        boolean all_true = true;
        for(boolean b: bools){
            if(!b){
                all_true = false;
                break;
            }
        }
        if(all_true){
            return 1;
        }
        int ans = 0;
        for(int i = 0; i < bools.length; i++){
            if(!g[s][i] || bools[i]) continue;
                bools[i] = true;
                ans += dfs(g,i,bools);
                bools[i] = false;
        }
        return ans;
    }
}