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)

/*
* @Author Silviase(@silviasetitech)
* For ProCon
*/

import java.util.*;
import java.lang.*;
import java.math.*;

class Main{

    static int n;
    static int m;
    static int ans;
    static int[] w;
    static int[] ww;
    static boolean[] visit;
    public static void main(String[] args){
        Scanner sc = new Scanner(System.in);
        
        n = sc.nextInt();
        m = sc.nextInt();
        w = new int[m];
        ww = new int[m];
        
        for (int i = 0; i < m; i++) {
            int tmp = sc.nextInt();
            int tmpp = sc.nextInt();
            w[i] = tmp-1;
            ww[i] = tmpp-1;
        }

        visit  = new boolean[n];
        Arrays.fill(visit, false);
        dfs(0);
        System.out.println(ans);
        sc.close();
    }

    public static void dfs(int placenow) {
        visit[placenow] = true;
        boolean success = true;
        for (int i = 0; i < n; i++) {
            if (visit[i] == false) { // not go all place
                success = false;
                break;
            }
        }
        if (success) {
            ans++;
            visit[placenow] = false;
            return;
        }

        for (int i = 0; i < m; i++) {
            if (w[i] == placenow && visit[ww[i]] == false ) {
                dfs(ww[i]);
            }else if(ww[i] == placenow && visit[w[i]] == false){
                dfs(w[i]);
            }else{
                continue;
            }
        }
        visit[placenow] = false;
        return;
    }

}