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# (.NET Core 3.1.201) (judge verdict: Accepted)

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

class MainClass
{
    static List<int>[] G;
    static int N;
    static void Main()
    {
        var NM = Console.ReadLine().Split().Select(int.Parse).ToArray();
        N = NM[0];
        int M = NM[1];
        G = new List<int>[N];
        for (int i = 0; i < N; i++)
        {
            G[i] = new List<int>();
        }

        for (int i = 0; i < M; i++)
        {
            var r = Console.ReadLine().Split().Select(_ => int.Parse(_) - 1).ToArray();
            G[r[0]].Add(r[1]);
            G[r[1]].Add(r[0]);
        }

        int ans = Search(0, Enumerable.Repeat(false, N).ToArray());

        Console.WriteLine(ans);
    }
    static int Search(int now,bool[] frags)
    {
        int ans = 0;
        if (frags[now]) return 0;

        bool[] nfrags = new bool[N];
        Array.Copy(frags, nfrags, N);
        nfrags[now] = true;
        if (nfrags.All(_ => _)) return 1;
        foreach(int i in G[now])
        {
            ans += Search(i, nfrags);
        }

        return ans;
    }
}