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.Text;
    using System.Collections.Generic;
    using static System.Math;
    using System.Linq;
    using static System.Array;
    
    namespace ConsoleApp2
    {
    class Program
    {
        static string S;
        static long ans = 0;
        static long N;
        static long M;
        static Node[] Nodes;
        static void Main(string[] args)
        {

            //var N = long.Parse(Console.ReadLine());
            var NK = Console.ReadLine().Split(' ').Select(x => long.Parse(x)).ToArray();
            N = NK[0];
            M = NK[1];
            Nodes = new Node[N + 1];
            for (int i = 1; i <= N; i++)
            {
                Nodes[i] = new Node(i);
            }

            for (int i = 0; i < M; i++)
            {
                var AB = Console.ReadLine().Split(' ').Select(x => long.Parse(x)).ToArray();
                var A = AB[0];
                var B = AB[1];

                Nodes[A].adj.Add(B);
                Nodes[B].adj.Add(A);
            }

            cul(1, new bool[N + 1]);

            Console.WriteLine(ans);
        }

        static void cul(long st,bool[] used)
        {
            used[st] = true;
            foreach (var item in Nodes[st].adj)
            {
                if (!used[item])
                {
                    var nused = new bool[N + 1];
                    Copy(used, nused, N + 1);
                    cul(item,nused);
                }
            }

            var fl = true;

            for (int i = 1; i <= N; i++)
            {
                if (!used[i])
                {
                    fl = false;
                    break;
                }
            }

            if (fl) ans++;

        }
    }

    class Node
    {
        long num = -1;
        public List<long> adj;
        public Node(long inp)
        {
            this.num = inp;
            adj = new List<long>();
        }
    }
}