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: Runtime Error)

import java.util.Arrays;
import java.util.Scanner;

public class Main {
    private static boolean[][] graph;
    public static void main(String[] ans) {
        Scanner scanner = new Scanner(System.in);
        int N = scanner.nextInt();
        int M = scanner.nextInt();
        graph = new boolean[N][N];
        for (int i = 0; i < N; i++) {
            Arrays.fill(graph[i], false);
        }

        for (int i = 0; i < N; i++) {
            int a = scanner.nextInt();
            int b = scanner.nextInt();
            graph[a-1][b-1] = true;
            graph[b-1][a-1] = true;
        }
        boolean[] visited = new boolean[N];
        Arrays.fill(visited, false);
        System.out.println(dfs(1, N,visited ));
    }

    private static int dfs(int currentNode, int N, boolean[] visited) {
        boolean allVisited = true;
        for (int i = 0; i < N; i++) {
            if (!visited[i]) {
                allVisited = false;
            }
        }
        if (allVisited) {
            return 1;
        }

        int ans = 0;
        for (int i = 0; i < N; i++) {
            if(!graph[currentNode][i]) {
                continue;
            }

            if(visited[i]) {
                continue;
            }
            visited[i] = true;
            ans += dfs(i, N, visited);
            visited[i] = false;
        }

        return ans;
    }
}