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.*;

//数字の順列全列挙まで作成（まだ同じものを含まない場合に限る）
public class Main {
	
	static Set<String> permutations = new HashSet<String>();
	static int N;
	static char base[]; 
	
	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
		N = sc.nextInt();
		sc.close();
			
		//1~Nの順列を全列挙する。
		
		StringBuilder sb = new StringBuilder();
 
		
		base = new char[N];
		for(int i=1;i<=N;i++) base[i-1]= (char)(i+'0');
		
		for(int i=0;i<N;i++) {
			char start[] = new char[N];
			start[0] = base[i];
			dfs(start);
		}
		
		for(String tmp : permutations) {
			System.out.println(tmp);
		}
		
		
	}
	
	static void dfs(char c[]) {
		if(finished(c)) {
			permutations.add(new String(c));
			return;
		}
		for(int i=0;i<N;i++) {
			char nextChar = base[i];
			if(isContain(c, nextChar)) continue;
			char nextC[] = c.clone();
			nextC[depth(c)]=nextChar;
			dfs(nextC);
		}
	}
	
	static boolean isContain(char target[], char c) {
		for(char t :target) if(c==t) return true;
		return false;
	}
	
	static boolean finished(char target[]) {
		if(isContain(target, '\u0000'))return false;
		return true;
	}
	
	static int depth(char target[]) {
		int cnt = N;
		for(char t:target) {
			if(t=='\u0000')cnt--;
		}
		return cnt;
	}
	
}