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.io.IOException;
import java.io.InputStream;
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) {
        FastScanner fs = new FastScanner();
        int N = fs.nextInt();
        int M = fs.nextInt();
        int[][] matrix = new int[N][M];
        for (int i = 0; i < N; ++i) Arrays.fill(matrix[i], 0);
        for (int i = 0; i < M; ++i) {
            int a = fs.nextInt() - 1;
            int b = fs.nextInt() - 1;
            matrix[a][b] = 1;
            matrix[b][a] = 1;
        }

        Integer[] arr = new Integer[N];
        for (int i = 0; i < N; ++i) arr[i] = i;
        int cnt = 0;
        do {
            if (arr[0] != 0) continue;

            boolean flag = true;
            for (int i = 0; i < N-1; ++i) {
                if (matrix[arr[i]][arr[i+1]] == 0) flag = false;
            }

            if (flag) ++cnt;
        } while (nextPermutation(arr));

        System.out.println(cnt);
    }




    static class FastScanner {
        private final InputStream in = System.in;
        private final byte[] buffer = new byte[1024];
        private int ptr = 0;
        private int buflen = 0;

        private boolean hasNextByte() {
            if (ptr < buflen) {
                return true;
            }else{
                ptr = 0;
                try {
                    buflen = in.read(buffer);
                } catch (IOException e) {
                    e.printStackTrace();
                }
                if (buflen <= 0) {
                    return false;
                }
            }
            return true;
        }

        private int readByte() { if (hasNextByte()) return buffer[ptr++]; else return -1;}
        private static boolean isPrintableChar(int c) { return 33 <= c && c <= 126;}
        public boolean hasNext() { while(hasNextByte() && !isPrintableChar(buffer[ptr])) ptr++; return hasNextByte();}

        public String next() {
            if (!hasNext()) throw new NoSuchElementException();
            StringBuilder sb = new StringBuilder();
            int b = readByte();
            while(isPrintableChar(b)) {
                sb.appendCodePoint(b);
                b = readByte();
            }
            return sb.toString();
        }

        public long nextLong() {
            if (!hasNext()) throw new NoSuchElementException();
            long n = 0;
            boolean minus = false;
            int b = readByte();
            if (b == '-') {
                minus = true;
                b = readByte();
            }
            if (b < '0' || '9' < b) {
                throw new NumberFormatException();
            }
            while(true){
                if ('0' <= b && b <= '9') {
                    n *= 10;
                    n += b - '0';
                }else if(b == -1 || !isPrintableChar(b)){
                    return minus ? -n : n;
                }else{
                    throw new NumberFormatException();
                }
                b = readByte();
            }
        }

        public int nextInt() {
            long nl = nextLong();
            if (nl < Integer.MIN_VALUE || nl > Integer.MAX_VALUE) throw new NumberFormatException();
            return (int) nl;
        }

        public double nextDouble() { return Double.parseDouble(next());}
    }

}