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.Linq;
using System.Collections.Generic;
using System;

public class C
{
    public int c { get; set; }
}

public class Info
{
    public int node { get; set; }
    public string via { get; set; }
}

public class Hello
{
    public static void Main()
    {
        string[] line = Console.ReadLine().Trim().Split(' ');
        var n = int.Parse(line[0]);
        var m = int.Parse(line[1]);
        var map = new bool[n, n];
        for (int i = 0; i < m; i++)
        {
            line = Console.ReadLine().Trim().Split(' ');
            var a = int.Parse(line[0]) - 1;
            var b = int.Parse(line[1]) - 1;
            map[a, b] = true;
            map[b, a] = true;
        }
        var c = new C();
        goBfs(map, c);
        Console.WriteLine(c.c);
    }
    public static void goBfs(bool[,] map, C c)
    {
        var n = map.GetLength(0);
        var q = new Queue<Info>();
        q.Enqueue(new Info { node = 0, via = "" });
        while (q.Count() > 0)
        {
            var a = q.Dequeue();
            if (a.via.Length + 1 == n && !a.via.Contains(a.node.ToString())) { c.c++; goto next; }
            for (int i = 0; i < n; i++)
                if (map[a.node, i] && !(a.via + a.node.ToString()).Contains(i.ToString()))
                    q.Enqueue(new Info { node = i, via = a.via + a.node.ToString() });
            next:;
        }
    }
}