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;

namespace ProgramingStudying2
{
    class Program
    {
        static int n;
        static int m;
        static List<List<int>> G;
        static int ans;

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

            G = new List<List<int>>();

            for(int i = 0; i < n; i++)
            {
                G.Add(new List<int>());
            }

            for(int i = 0; i < m; i++)
            {
                var ab = Console.ReadLine().Split().Select(int.Parse).ToArray();
                var a = ab[0] - 1;
                var b = ab[1] - 1;

                G[a].Add(b);
                G[b].Add(a);
            }

            var visited = new bool[n];
            visited[0] = true;
            ans = 0;

            dfs(0, 1, visited);

            Console.WriteLine(ans);
        }

        static void dfs(int x, int count, bool[] visited)
        {
            if(count == n)
            {
                ans++;
            }

            else
            {
                foreach(int nx in G[x])
                {
                    if (visited[nx])
                    {
                        continue;
                    }
                    var newCount = count + 1;

                    visited[nx] = true;

                    dfs(nx, newCount, visited);
                }
            }
            visited[x] = false;
        }
    }
}