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.Text;
using System.Threading.Tasks;

namespace Cs
{

    class hutatu
    {
        int a, b = 0;
        public hutatu(int a,int b)
        {
            this.a = a;this.b = b;
        }
        public bool doti(int c)
        {
            return a == c || b == c;
        }
        public int gyaku(int c)
        {
            if (a == c) { return b; }
            if (b == c) { return a; }
            return -1;
                    }
    }
    class Program
    {
        static void Main(string[] args)
        {
            var str = Console.ReadLine().Split(' ');
            int n = int.Parse(str[0]);
            int m = int.Parse(str[0]);
            List<hutatu> ab = new List<hutatu>();

            int[] dye = new int[n];
            for (int i = 0; i < m; i++)
            {
                var str2 = Console.ReadLine().Split(' ');
                ab.Add(new hutatu(int.Parse(str2[0]), int.Parse(str2[1])));
            }
            Console.WriteLine(mycheck(1, dye, ab));

        }

        static int mycheck(int me, int[] die,List<hutatu>newab)
        {
            die[me-1] = 1;
            if (die.All(c => c == 1)) { return 1; }
            int count = 0;
            List<hutatu> ne = newab.ToList();
            ne.RemoveAll(c => c.doti(me));
            bool botti = true;
            for (int i = 0; i < newab.Count; i++)
            {
                int k = newab[i].gyaku(me);
                if (k == -1) { continue; }
                botti = false;
                count += mycheck(k, die.ToArray(), ne);
            }
            if (botti) { return 0; }
            return count;
        }


    }
}