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 System.Numerics;
using static System.Console;
using static System.Convert;
using static System.Math;

class Program
{
    class P
    {
        public int index;
        public List<int> ad;

        public P(int index)
        {
            this.index = index;
            ad = new List<int>();
        }
    }

    static void Main(string[] args)
    {
        var nm = Array.ConvertAll(ReadLine().Split(' '), int.Parse);
        var ps = new P[nm[0]];
        var set = new HashSet<int>();
        for(var i = 0; i < nm[1]; i++)
        {
            var ab = Array.ConvertAll(ReadLine().Split(' '), int.Parse);
            for(var j = 0; j <2; j++)
            {
                if (set.Contains(ab[j]))
                    ps[ab[j]-1].ad.Add(ab[1 - j]-1);
                else
                {
                    set.Add(ab[j]);
                    ps[ab[j]-1] = new P(ab[j]-1);
                    ps[ab[j]-1].ad.Add(ab[1 - j]-1);
                }
            }
        }
        set.Clear();
        var result = 0;
        get(ps, ref result, set,0);
        WriteLine(result);
    }

    private static void get(P[] ps,ref int result,HashSet<int> set,int i)
    {
        set.Add(i);
        for(var j = 0; j < ps[i].ad.Count; j++)
        {
            if (!set.Contains(ps[i].ad[j]))
                get(ps, ref result, set, ps[i].ad[j]);
        }
        if (set.Count == ps.Length) result++;
        set.Remove(i);
    }
}