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.Generic;
using System.Linq;
using static Input;

public class Prog
{
    private const int INF = 1000000007;
    public static void Main()
    {
        int N = Cin<int>();
        int M = Cin<int>();
        List<bool> visit = Enumerable.Repeat(false, N).ToList();
        Glaph glaph = new Glaph(visit);
        glaph.visit[0] = true;
        glaph.now_Node = 0;
        List<int>[] edge = new List<int>[N];
        for (int i = 0; i < N; i++) edge[i] = new List<int>();
        for (int i = 0; i < M; i++)
        {
            int[] inp = Line<int[]>().Select(v => v - 1).ToArray();
            edge[inp[0]].Add(inp[1]);
            edge[inp[1]].Add(inp[0]);
        }
        long ans = 0;
        Stack<Glaph> stack = new Stack<Glaph>();
        stack.Push(glaph);
        while (stack.Count() != 0)
        {
            Glaph now_state = stack.Pop();
            if (now_state.visit.All(v => v == true)) ans++;
            foreach (var i in edge[now_state.now_Node])
            {
                if (!now_state.visit[i])
                {
                    Glaph next_state = new Glaph(now_state.visit);
                    next_state.visit[i] = true;
                    next_state.now_Node = i;
                    stack.Push(next_state);
                }
            }
        }
        Console.WriteLine(ans);
    }
}

public class Glaph
{
    public List<bool> visit;
    public int now_Node { get; set; }
    public Glaph(List<bool> b) { visit = new List<bool>(b); }
}

public class Input
{
    private static Queue<string> queue = new Queue<string>();
    public static T Cin<T>()
    {
        if (queue.Count == 0) foreach (var s in Console.ReadLine().Split(' ')) queue.Enqueue(s);
        if (typeof(T) == typeof(int)) return (T)(object)int.Parse(queue.Dequeue());
        else if (typeof(T) == typeof(long)) return (T)(object)long.Parse(queue.Dequeue());
        else if (typeof(T) == typeof(string)) return (T)(object)(queue.Dequeue());
        else if (typeof(T) == typeof(double)) return (T)(object)double.Parse(queue.Dequeue());
        else return (T)(object)(-1);
    }
    public static T Line<T>()
    {
        if (typeof(T) == typeof(int[]))
        {
            return (T)(object)Console.ReadLine().Split(' ').Select(int.Parse).ToArray();
        }
        else if (typeof(T) == typeof(long[]))
        {
            return (T)(object)Console.ReadLine().Split(' ').Select(long.Parse).ToArray();
        }
        else if (typeof(T) == typeof(string[]))
        {
            return (T)(object)Console.ReadLine().Split(' ').ToArray();
        }
        else if (typeof(T) == typeof(double[]))
        {
            return (T)(object)Console.ReadLine().Split(' ').Select(double.Parse).ToArray();
        }
        else return (T)(object)(-1);
    }
}