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.Text;
using System.Numerics;
using System.IO;

namespace SolutionCS
{
    class Program
    {
        static void Main(string[] args)
        {
            string[] s = Console.ReadLine().Split(' ');
            int N = int.Parse(s[0]);
            int M = int.Parse(s[1]);

            List<int>[] lists = new List<int>[N];
            for (int i = 0; i < N; i++)
            {
                lists[i] = new List<int>();
            }

            for (int i = 0; i < M; i++)
            {
                s = Console.ReadLine().Split(' ');
                int f = int.Parse(s[0]) - 1;
                int t = int.Parse(s[1]) - 1;

                lists[f].Add(t);
                lists[t].Add(f);
            }

            bool[] reach = new bool[N];

            int ans = CanAllReach(0, N, lists, reach);

            Console.WriteLine(ans);
        }

        static int CanAllReach(int from, int nodeNum, List<int>[] edgeList, bool[] reachFlas)
        {
            reachFlas[from] = true;

            bool allreach = true;
            for (int i = 0; i < nodeNum; i++)
            {
                allreach &= reachFlas[i];
            }
            if (allreach)
            {
                return 1;
            }

            int ans = 0;
            foreach(int t in edgeList[from])
            {
                if (!reachFlas[t])
                {
                    bool[] newReach = new bool[nodeNum];
                    Array.Copy(reachFlas, newReach, nodeNum);

                    ans += CanAllReach(t, nodeNum, edgeList, newReach);
                }
            }

            return ans;
        }
    }
}