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.Scanner;

public class Main {
    public static void main(String args[]) {
        try (Scanner in = new Scanner(System.in)) {
            int N = in.nextInt();
            int M = in.nextInt();
            int[] a = new int[M];
            int[] b = new int[M];
            ArrayList<ArrayList<Integer>> adj = new ArrayList<>();
            for (int i = 0; i < N; i++) {
                adj.add(new ArrayList<>());
            }
            for (int i = 0; i < M; i++) {
                a[i] = in.nextInt() - 1;
                b[i] = in.nextInt() - 1;
                adj.get(a[i]).add(b[i]);
                adj.get(b[i]).add(a[i]);
            }
            dfs(0, adj, 1 << 0, N);
            System.out.println(count);
        }
    }

    private static int count = 0;

    private static void dfs(int index, ArrayList<ArrayList<Integer>> adj, int used, int N) {
        if ((used & ((1 << N) - 1)) == ((1 << N) - 1)) {
            count++;
            return;
        }

        for (Integer i : adj.get(index)) {
            if ((used & (1 << i)) == (1 << i)) {
                continue;
            }
            dfs(i.intValue(), adj, used | (1 << i.intValue()), N);
        }
    }
}