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)

#pragma warning disable

using System;
using System.Collections.Generic;
using System.IO;
using System.Linq;
using System.Runtime.Serialization.Formatters.Binary;
using System.Text;
using System.Text.RegularExpressions;
using System.Diagnostics;
using System.Numerics;
using System.Collections;
using System.Timers;

static class MainClass
{
    public static void Main(string[] args)
    {
        var NM = Console.ReadLine().SplittedStringToInt32List();
        var N = NM[0];
        var M = NM[1];
        var edges = new List<Edge>();
        for (int i = 0; i < M; i++)
        {
            var item = Console.ReadLine().SplittedStringToInt32List();
            var ed = new Edge() {  From = item[0], To = item[1] };

            edges.Add(ed);
        }
        var ls = new List<int>();
        for (int i = 1; i <= N; i++)
        {
            ls.Add(i);
        }
        var nums = ls.Perm().Select(x => x.ToArray()).Where(x => x[0] == 1);

        var count = 0;
        foreach (var item in nums)
        {
            var isok = true;
            var before = -1;
            foreach (var item2 in item)
            {
                if (before == -1)
                {
                    before = item2;
                    continue;
                }
                if (edges.Where(x => (x.From == item2 && x.To == before) || (x.To == item2 && x.From == before)).Count() <= 0)
                {
                    isok = false;
                    break;
                }
                before = item2;
            }
            if (isok)
            {
                count++;
            }
        }
        Console.WriteLine(count);

        Console.ReadLine();

    }
    public static IEnumerable<IEnumerable<T>> Perm<T>(this IEnumerable<T> items, int? k = null)
    {
        if (k == null)
            k = items.Count();

        if (k == 0)
        {
            yield return Enumerable.Empty<T>();
        }
        else
        {
            var i = 0;
            foreach (var x in items)
            {
                var xs = items.Where((_, index) => i != index);
                foreach (var c in Perm(xs, k - 1))
                    yield return c.Before(x);

                i++;
            }
        }
    }

    // 要素をシーケンスに追加するユーティリティ
    public static IEnumerable<T> Before<T>(this IEnumerable<T> items, T first)
    {
        yield return first;

        foreach (var i in items)
            yield return i;
    }
    class Edge
    {
        public int From;
        public int To;
    }



    #region ライブラリ
    public static long ToInt64(this string str) => long.Parse(str);
    public static int ToInt32(this string str) => int.Parse(str);
    public static BigInteger ToBigInteger(this string str) => BigInteger.Parse(str);
    public static List<string> SplittedStringToList(this string str) => str.Split(new[] { ' ' }, StringSplitOptions.RemoveEmptyEntries).ToList();
    public static List<int> SplittedStringToInt32List(this string str) => str.Split(new[] { ' ' }, StringSplitOptions.RemoveEmptyEntries).Select(x => int.Parse(x)).ToList();
    public static List<BigInteger> SplittedStringToBigInteger(this string str) => str.Split(new[] { ' ' }, StringSplitOptions.RemoveEmptyEntries).Select(x => BigInteger.Parse(x)).ToList();

    public const int INF = int.MaxValue / 2;
    #endregion
}