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.io.*;
import java.math.*;
import java.util.*;
 
public class Main {
    private static boolean debug = false;
    private static boolean elapsed = false;
 
    private static PrintWriter _out = new PrintWriter(System.out);
    private static PrintWriter _err = new PrintWriter(System.err);
 
    private void solve(Scanner sc) {
        int N = sc.nextInt();
        int M = sc.nextInt();
        List<List<Integer>> list = new ArrayList<>();
        for (int i = 0; i < N; ++i) {
            list.add(new ArrayList<>());
        }
        for (int i = 0; i < M; ++i) {
            int a = sc.nextInt() - 1;
            int b = sc.nextInt() - 1;
            list.get(a).add(b);
            list.get(b).add(a);
        }
 
        List<Integer> route = new ArrayList<>();
        route.add(0);
        _out.println(search(0, N, list, route, new HashSet<>()));
    }
    private int search(int cur, int N, List<List<Integer>> list, List<Integer> route, Set<List<Integer>> set) {
        if (route.size() >= N) {
            if (route.size() == N && !set.contains(route)) {
                set.add(new ArrayList<>(route));
                return 1;
            }
            return 0;
        }
 
        int res = 0;
 
        for (int next : list.get(cur)) {
            if (!route.contains(next)) {
                route.add(next);
                res += search(next, N, list, route, set);
                route.remove(route.size() - 1);
            }
        }
 
        return res;
    }
    private static BigInteger C(long n, long r) {
        BigInteger res = BigInteger.ONE;
        for (long i = n; i > n - r; --i) {
            res = res.multiply(BigInteger.valueOf(i));
        }
        for (long i = r; i > 1; --i) {
            res = res.divide(BigInteger.valueOf(i));
        }
        return res;
    }
    private static BigInteger P(long n, long r) {
        BigInteger res = BigInteger.ONE;
        for (long i = n; i > n - r; --i) {
            res = res.multiply(BigInteger.valueOf(i));
        }
        return res;
    }
    /*
     * 10^10 > Integer.MAX_VALUE = 2147483647 > 10^9
     * 10^19 > Long.MAX_VALUE = 9223372036854775807L > 10^18
     */
    public static void main(String[] args) {
        long S = System.currentTimeMillis();
 
        Scanner sc = new Scanner(System.in);
        new Main().solve(sc);
        _out.flush();
 
        long G = System.currentTimeMillis();
        if (elapsed) {
            _err.println((G - S) + "ms");
        }
        _err.flush();
    }
}