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;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using static System.Console;
using static System.Math;
using static AtCoderTemplate.MyLibrary;

namespace AtCoderTemplate
{
    class Program
    {
        static int N, M, i;
        static bool[, ] connect;
        static bool[] reached;
        static int count = 0, length = 0;
        static void Main (string[] args)
        {
            string[] str1 = Console.ReadLine ().Split (' ');
            N = int.Parse (str1[0]);
            M = int.Parse (str1[1]);

            reached = new bool[N];
            connect = new bool[N, N];

            //辺の読み込み
            for (i = 0; i < N; i++)
            {
                string[] str2 = Console.ReadLine ().Split (' ');
                connect[int.Parse (str2[0]) - 1, int.Parse (str2[1]) - 1] = true;
                connect[int.Parse (str2[1]) - 1, int.Parse (str2[0]) - 1] = true;
            }
            reached[0] = true;
            Search (0);

            Console.WriteLine (count);

        }

        static void Search (int n)
        {
            for (int k = 0; k < N; k++)
            {
                if (connect[n, k] == true && reached[k] == false)
                {
                    length++;
                    reached[k] = true;
                    Search (k);

                    reached[k] = false;
                }

            }

            if (length == N - 1) count++;
            length--;
        }

    }

    class MyLibrary
    {

        // 自作の関数
        public static int MyFunction (int n)
        {
            return 0;
        }
    }
}