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 {

	static boolean[] passed;
	static int N;
	static int[][] adj;

	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);

		N = sc.nextInt();
		int M = sc.nextInt();
		adj = new int[N][N];
		passed = new boolean[N];

		int a, b;
		for (int i = 0; i < M; i++) {
			a = sc.nextInt() - 1;
			b = sc.nextInt() - 1;
			adj[a][b] = 1;
			adj[b][a] = 1;
		}

		passed[0] = true;
		System.out.println(dfs(0));
	}

	static int dfs(int node) {
		boolean allPassed = true;
		for(int i = 0; i < N; i++) {
			allPassed = allPassed && passed[i];
		}
		if(allPassed) {
			return 1;
		}

		int ret = 0;

		for(int i = 0; i < N; i++) {
			if(adj[node][i] < 1) continue;
			if(passed[i]) continue;

			passed[i] = true;
			ret += dfs(i);
			passed[i] = false;
		}

		return ret;
	}
}