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 C# (Mono 4.6.2.0) (judge verdict: Accepted)

using System;
using System.Linq;
using System.Collections.Generic;
class P
{
    static void Main()
    {
        int[] nm = Console.ReadLine().Split().Select(int.Parse).ToArray();
        bool[][] path = Enumerable.Repeat(0, 8).Select(_ => new bool[8]).ToArray();
        for (int i = 0; i < nm[1]; i++)
        {
            int[] ab = Console.ReadLine().Split().Select(int.Parse).ToArray();
            path[ab[0] - 1][ab[1] - 1] = true;
            path[ab[1] - 1][ab[0] - 1] = true;
        }
        int res = 0;
        int[] perm = Enumerable.Range(0, nm[0]).ToArray();
        do
        {
            //Console.WriteLine(string.Join(" ", perm));
            if (perm[0] != 0) break;
            for (int j = 0; j < nm[0] - 1; j++)
            {
                if (!path[perm[j]][perm[j + 1]])
                {
                    goto end;
                }
            }
            res++;
            end:;
        }
        while (NextPermutation(perm));
        Console.WriteLine(res);
    }

    public static void Swap<T>(ref T x, ref T y) { T tmp = x; x = y; y = tmp; }

    public static bool NextPermutation<T>(T[] array, int index, int length, Comparison<T> comp)
    {
        if (length <= 1) return false;
        for (int i = length - 1; i > 0; i--)
        {
            int k = i - 1;
            if (comp(array[k], array[i]) < 0)
            {
                int j = Array.FindLastIndex(array, delegate (T x) { return comp(array[k], x) < 0; });
                Swap(ref array[k], ref array[j]);
                Array.Reverse(array, i, length - i);
                return true;
            }
        }
        Array.Reverse(array, index, length);
        return false;
    }

    public static bool NextPermutation<T>(T[] array) where T : IComparable
    {
        return NextPermutation(array, 0, array.Length, Comparer<T>.Default.Compare);
    }
}