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.Web;

namespace Competitive
{
    internal class Solution
    {
        public int N, M;
        public bool[,] AD;
        public int ret;
        public void Run()
        {
            {
                var line = Input.ReadIntArray();
                N = line[0];
                M = line[1];
            }

            AD = new bool[N, N];

            for (int i = 0; i < M; i++)
            {
                var line = Input.ReadIntArray();
                int a = line[0] - 1;
                int b = line[1] - 1;
                AD[a, b] = true;
                AD[b, a] = true;
            }

            ret = 0;
            var pm = new Permutation(N, Process);
            pm.DFSRun();

            Console.WriteLine(ret);
        }

        public void Process(int[] order)
        {
            if (order[0] != 0) return;
            for (int i = 0; i < N - 1; i++)
            {
                if (!AD[order[i], order[i + 1]]) return;
            }

            ret++;
        }
    }

    // libs ----------
    // Permutationを全通り列挙
    class Permutation
    {
        public int N;
        public bool[] F;
        public int[] V;
        public Action<int[]> Process;

        public Permutation(int N, Action<int[]> process)
        {
            this.N = N;
            Process = process;
        }

        public void DFSRun()
        {
            F = new bool[N];
            V = new int[N];
            DFS(0);
        }

        private void DFS(int i)
        {
            if (i == N)
            {
                Process(V);
            }
            else
            {
                for (int k = 0; k < N; k++)
                    if (!F[k])
                    {
                        F[k] = true;
                        V[i] = k;
                        DFS(i + 1);
                        F[k] = false;
                    }
            }
        }

    }

    // common ----------

    internal static class Input
    {
        public static string ReadString()
        {
            string line = Console.ReadLine();
            return line;
        }

        public static int ReadInt()
        {
            string line = Console.ReadLine();
            return int.Parse(line);
        }

        public static int[] ReadIntArray()
        {
            string line = Console.ReadLine();
            return line.Split(' ').Select(int.Parse).ToArray();            
        }

        public static long ReadLong()
        {
            string line = Console.ReadLine();
            return long.Parse(line);
        }

        public static long[] ReadLongArray()
        {
            string line = Console.ReadLine();
            return line.Split(' ').Select(long.Parse).ToArray();
        }

        public static double[] ReadDoubleArray()
        {
            string line = Console.ReadLine();
            return line.Split(' ').Select(double.Parse).ToArray();
        }
    }
    
    internal class Program
    {
        public static void Main(string[] args)
        {
            var s = new Solution();
            s.Run();
        }
    }
}