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.HashSet;
import java.util.Scanner;

public class Main {
    static int N;
    static int M;
    static int[][] graph;
    static int INF = Integer.MAX_VALUE;

    public static void main(String args[]) {
        Scanner scanner = new Scanner(System.in);
        N = scanner.nextInt();
        M = scanner.nextInt();

        graph = new int[N][N];
        for (int i = 0; i < N; i++) {
            for (int j = 0; j < N; j++) {
                graph[i][j] = INF;
            }
        }

        for (int i = 0; i < M; i++) {
            int from = scanner.nextInt() - 1;
            int to = scanner.nextInt() - 1;
            graph[from][to] = to;
            graph[to][from] = from;
        }

        scanner.close();

        System.out.println(dfs(0, 1, new HashSet<>(1)));
    }

    private static int dfs(int i, int passCount, HashSet<Integer> passedVertetes) {
        if (N <= passCount) return 1;

        int ret = 0;
        for (int to: graph[i]) {
            if (to != INF) {
                if (!passedVertetes.contains(to)) {
                    passedVertetes.add(to);
                    passCount++;
                    ret += dfs(to, passCount, passedVertetes);
                }
            }
        }

        return ret;
    }
}