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.Collections.Generic;
using System.Linq;
using System.Text;

public class AtCoderA
{
    static void Main()
    {
        var sc = new Scanner();

        int n = sc.NextInt();
        int m = sc.NextInt();

        bool[,] route = new bool[n + 1, n + 1];
        for (int i = 0; i < m; i++)
        {
            int a = sc.NextInt();
            int b = sc.NextInt();
            route[a, b] = true;
            route[b, a] = true;
        }

        List<int[]> nums = AllPermutation<int>(Enumerable.Range(1, n).ToArray());

        int answer = 0;

        foreach (var num in nums)
        {
            if (num[0] != 1)
            {
                continue;
            }

            bool ok = true;
            for (int i = 0; i < n - 1; i++)
            {
                if (!route[num[i], num[i + 1]])
                {
                    ok = false;
                    break;
                }
            }
            if (ok)
            {
                answer++;
            }
        }

        Console.WriteLine(answer);
    }

    // 順列生成
    private static List<T[]> AllPermutation<T>(params T[] array) where T : IComparable
    {
        var arr = new List<T>(array).ToArray();
        var ret = new List<T[]>();
        ret.Add(new List<T>(arr).ToArray());
        var length = arr.Length;
        var next = true;
        while (next)
        {
            next = false;
            int i;
            for (i = length - 2; i >= 0; i--)
            {
                if (arr[i].CompareTo(arr[i + 1]) < 0)
                {
                    break;
                }
            }
            if (i < 0)
            {
                break;
            }
            var j = length - 1;
            while (arr[i].CompareTo(arr[j]) > 0)
            {
                j--;
            }
            if (arr[i].CompareTo(arr[j]) < 0)
            {
                var tmp = arr[i];
                arr[i] = arr[j];
                arr[j] = tmp;
                Array.Reverse(arr, i + 1, length - i - 1);
                ret.Add(new List<T>(arr).ToArray());
                next = true;
            }
        }
        return ret;
    }

    class Scanner
    {
        private string[] _line;
        private int _index;
        private const char Separator = ' ';

        public Scanner()
        {
            _line = new string[0];
            _index = 0;
        }

        public string Next()
        {
            while (_index >= _line.Length)
            {
                _line = Console.ReadLine().Split(Separator);
                _index = 0;
            }

            return _line[_index++];
        }

        public int NextInt() => int.Parse(Next());
        public long NextLong() => long.Parse(Next());
        public double NextDouble() => double.Parse(Next());
        public decimal NextDecimal() => decimal.Parse(Next());
        public char NextChar() => Next()[0];
        public char[] NextCharArray() => Next().ToCharArray();

        public string[] Array()
        {
            _line = Console.ReadLine().Split(Separator);
            _index = _line.Length;
            return _line;
        }

        public int[] IntArray() => Array().Select(int.Parse).ToArray();
        public long[] LongArray() => Array().Select(long.Parse).ToArray();
        public double[] DoubleArray() => Array().Select(double.Parse).ToArray();
        public decimal[] DecimalArray() => Array().Select(decimal.Parse).ToArray();
    }
}