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;

class program
{

    static bool[,] graph = new bool[10, 10];
    static Stack stack = new Stack();
    static int ans = 0;

    static void dps(int root, int N)
    {
        stack.Push(root);

        if (stack.Count == N)
        {
            ans++;
            stack.Pop();
            return;
        }

        for(int i = 1; i <= N; i++)
        {
            if (graph[root, i] == true)//rootからiへの辺が存在する
            {
                if (!stack.Contains(i))//そのパスでiを訪問したことがない
                {
                    dps(i, N);
                }
            }
        }

        stack.Pop();
        return;

    }


    static void Main(string[] args)
    {
        string[] input = Console.ReadLine().Split();
        int N = int.Parse(input[0]);
        int M = int.Parse(input[1]);


        for (int i = 0; i < 10; i++)
        {
            for (int j = 0; j < 10; j++)
            {
                graph[i, j] = false;
            }
        }

        for(int i = 0; i < M; i++)
        {
            input = Console.ReadLine().Split();
            int a = int.Parse(input[0]);
            int b = int.Parse(input[1]);
            graph[a, b] = true;
            graph[b, a] = true;

        }

        int root = 1;
        dps(root, N);

        Console.WriteLine(ans);

    }
}