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.*;

public class Main {
    static Integer res = 0;
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        int n =sc.nextInt();
        int m =sc.nextInt();
        boolean[] visited = new boolean[n];
        List<List<Integer>> g = new ArrayList<>();

        for (int i = 0; i < m; i++) {
            g.add(new ArrayList<>());
        }

        for (int i = 0; i < m; i++) {
            int a = sc.nextInt() - 1;
            int b = sc.nextInt() - 1;
            g.get(a).add(b);
            g.get(b).add(a);
        }

        visited[0] = true;
        dfs(g, n, visited, 0);
        System.out.println(res);
    }

    private static void dfs(List<List<Integer>> graph, int n, boolean[] visited, int cur) {
        if (allVisited(n, visited)) {
            res++;
            return;
        }

        List<Integer> next = graph.get(cur);
        for (Integer next1 : next) {
            if (visited[next1]) {
                continue;
            }

            visited[next1] = true;
            dfs(graph, n, visited, next1);
            visited[next1] = false;
        }
    }

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

        return true;
    }
}