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.*;

public class Main {

    static <T extends Comparable<? super T>> boolean nextPermutation(T[] sequence) {
        int first = getFirst(sequence);
        if (first == -1) return false;
        int toSwap = sequence.length - 1;
        while (sequence[first].compareTo(sequence[toSwap]) >= 0) --toSwap;
        swap(sequence, first++, toSwap);
        toSwap = sequence.length - 1;
        while (first < toSwap) swap(sequence, first++, toSwap--);
        return true;
    }

    static <T extends Comparable<? super T>> int getFirst(T[] sequence) {
        for (int i = sequence.length - 2; i >= 0; --i)
            if (sequence[i].compareTo(sequence[i + 1]) < 0) return i;
        return -1;
    }

    static <T extends Comparable<? super T>> void swap(T[] sequence, int i, int j) {
        T tmp = sequence[i];
        sequence[i] = sequence[j];
        sequence[j] = tmp;
    }

    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        int N = sc.nextInt();
        int M = sc.nextInt();
        Integer[][] graph = new Integer[N][N];
        for (int i = 0; i < N; ++i) Arrays.fill(graph[i], 0);
        for (int i = 0; i < M; ++i) {
            int a = sc.nextInt() - 1;
            int b = sc.nextInt() - 1;
            graph[a][b] = 1;
            graph[b][a] = 1;
        }

        Integer[] arr = new Integer[N];
        for (int i = 0; i < N; ++i) arr[i] = i;

        int res = 0;
        do {
            if (arr[0] != 0) break;
            boolean flag = true;
            for (int i = 0; i < N-1; ++i) {
                if (graph[arr[i]][arr[i+1]] == 0) flag = false;
            }
            if (flag) ++res;
        } while(nextPermutation(arr));

        System.out.println(res);
    }
}