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.ArrayList;
import java.util.List;
import java.util.Scanner;

public class Main {
	Scanner sc = new Scanner(System.in);
	int n,m;
	List<List<Integer>> graph;
	List<Integer> V;


	public static void main(String[] args) {
		Main main = new Main();
		main.solve();
	}

	void solve() {
		n = nextInt();
		m = nextInt();
		graph = new ArrayList<List<Integer>>();
		V = new ArrayList<Integer>();

		for(int i=0;i<=n;i++) {
			V = new ArrayList<Integer>();
			graph.add(V);
		}

		for(int i=0;i<m;i++) {
			int a = nextInt();
			int b = nextInt();
			graph.get(a).add(b);
			graph.get(b).add(a);
		}
		sc.close();

		int res = 0;
		for(int i=1;i<=1;i++)res += SearchforAllVerticesPass(i);

		System.out.println(res);
	}

	private int SearchforAllVerticesPass(int gi) {
		int[] f = new int[n+1];
		return SearchforAllVerticesPass(gi,0+1,f);
	}

	private int SearchforAllVerticesPass(int gi,int cnt, int[] f) {
		List<Integer> VL=graph.get(gi);

		f[gi]=1;
		int sum=0;

		for(int i=0;i<VL.size();i++) {
			if(f[VL.get(i)]==1)continue;
			if(cnt+1==n)sum++;
			else sum+=SearchforAllVerticesPass(VL.get(i),cnt+1,f);
		}

		f[gi]=0;
		return sum;
	}


	private int nextInt() {
		return Integer.parseInt(sc.next());
	}
	private long nextLong() {
		return Long.parseLong(sc.next());
	}
	private String next() {
		return sc.next();
	}

}