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

namespace Tasks
{
    public class C
    {
        static void Main(string[] args)
        {
            var sw = new StreamWriter(Console.OpenStandardOutput()) { AutoFlush = false };
            Console.SetOut(sw);
            Solve();
            Console.Out.Flush();
        }

        static int N;
        static int M;
        static bool[][] graph;

        public static void Solve()
        {
            var NM = Console.ReadLine().Trim().Split(' ').Select(int.Parse).ToArray();
            (N, M) = (NM[0], NM[1]);
            graph = new bool[N][].Select(x => x = new bool[N]).ToArray();
            for (var i = 0; i < M; i++)
            {
                var ab = Console.ReadLine().Trim().Split(' ').Select(int.Parse).ToArray();
                var a = ab[0] - 1;
                var b = ab[1] - 1;
                graph[a][b] = graph[b][a] = true;
            }
            var visit = new bool[N];
            visit[0] = true;
            Console.WriteLine(Dfs(0, visit));
        }

        public static int Dfs(int current, bool[] visit)
        {
            if (visit.All(x => x)) return 1;
            var count = 0;
            for (var i = 0; i < N; i++)
            {
                if (!graph[current][i]) continue;
                if (visit[i]) continue;
                visit[i] = true;
                count += Dfs(i, visit);
                visit[i] = false;
            }

            return count;
        }
    }
}