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.Scanner;
public class Main {

	public static void main(String[] args) {
		// TODO 自動生成されたメソッド・スタブ
		Scanner scan = new Scanner(System.in);
        int N = scan.nextInt();
        int M =scan.nextInt();
		int a[][]= new int[N+1][N+1];
		int count =0;
		int c =0;
		int v[] = new int[N+1];
		v[1]=1;
		int red = 0;
		for(int i=0;i<M;i++){
			a[scan.nextInt()][scan.nextInt()]=1;
		}
		for(int i=0;i<N+1;i++){
			for(int j=0;j<i;j++){
				a[i][j]=a[j][i];
			}
		}
		c = dfs(1,N,count,red,a,v);
		System.out.println(c);
	}
	
	public static int dfs(int l,int N,int t,int red,int a[][],int v[]){
		if(red==N-1){
			t++;
		}for(int j=1;j<=N;j++){
			if(a[l][j]==1 && v[j]==0){
				v[j]=1;
				red++;
				t = dfs(j,N,t,red,a,v);
				v[j]=0;
				red--;
			}
		}return t;
	}
}