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: Runtime Error)

using System;
using System.Collections.Generic;
using System.Linq;
using System.Threading;
using System.Threading.Tasks;
namespace Capp
{
    class Program
    {
        public enum En
        {
            a
            ,b
            ,c
            ,d
            ,e
            ,f
        }

        
        static void Main(string[] args)
        {
            var c = new Solve();
            c.S();

        }
    }

    public class Solve
    {
        List<int>[] es = new List<int>[10];
        List<List<int>> es2;
        int n;
        int m;
        int res = 0;
        // 訪問管理
        int t = 0;
        bool[] visit = new bool[10];
        private void rec(int x)
        {
            bool ok = true;
            for (int i = 0; i < n; i++)
            {
                if (!visit[i])
                    ok = false;
            }
            if (ok)
            {
                res++;
                return;
            }

            if (t == (1 << n) - 1)
            {
                res++;
                return;
            }

            foreach (var v in es[x])
            {
                if (visit[v]) continue;
                // t = 3
                // t & (1 << 0) = 1
                // t & (1 << 1) = 2
                // t & (1 << 2) = 0
                if ((t & (1 << v)) > 0)
                    continue;

                visit[t] = true;
                t |= (1 << v);

                rec(v);
                visit[t] = false;
                t ^= (1 << v);
            }
        }
        public void S()
        {
            var nm = Console.ReadLine().Split(' ').Select(x => int.Parse(x)).ToArray();
            n = nm[0];
            m = nm[1];
            es2 = new List<List<int>>();
            for (int i = 0; i < 10; i++)
            {
                es2.Add(new List<int>());
                es[i] = new List<int>();
            }
            for (int i = 0; i < m; i++)
            {
                var s = Console.ReadLine().Split(' ').Select(x => int.Parse(x)).ToArray();
                var a = s[0] - 1;
                var b = s[1] - 1;
                es[a].Add(b);
                es[b].Add(a);

                es2[a].Add(b);
                es2[b].Add(a);
            }
            t = 1;
            rec(0);
            Console.WriteLine(res);
        }
    }

    public class Test<T> : ITest<T>
    {
        public string S { get; set; }
    }

    public interface ITest<out T>
    {
        string S { get; set; }
    }

    struct c
    {
        public string s { get; set; }
        private dynamic _d;
        public dynamic d { get { return _d; }}
        public void Setd(dynamic d)
        {
            _d = d;
        }
    }
    class AsTest
    {
        internal async Task<int> AsyncMethod(int x)
        {
            var t1 = Task.Run(() =>
            {
                Thread.Sleep(10000);
                return 10 * x;
            });
            var res = await t1;
            Console.WriteLine($"asyncmethod {res}");


            return res;
        }

    }
}