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-mcs 6.8.0.105) (judge verdict: Accepted)

using System;
using System.Collections;
using System.Collections.Generic;
using System.Collections.Specialized;
using System.ComponentModel.Design;
using System.Globalization;
using System.Linq;
using System.Numerics;
using System.Text;
using System.Threading;
using System.Threading.Tasks;
using System.Xml.Schema;
using static System.Console;

namespace ConsoleApp2
{
    class Program
    {
        static public int[] Sarray() { return ReadLine().Split().Select(int.Parse).ToArray(); }
        static public List<int> Slist() { return new List<int>(ReadLine().Split().Select(int.Parse)); }
        static bool[,] graph = new bool[8, 8];
        static void Main(string[] args)
        {
            var NM = Sarray();
            var N = NM[0];
            var M = NM[1];
            for(var i=0;i<M;i++)
            {
                var AB = Sarray();
                graph[AB[0] - 1, AB[1] - 1] = graph[AB[1] - 1, AB[0] - 1] = true;
            }
            var visited = new bool[8];
            visited[0] = true;
            WriteLine(dfs(0, N, visited));
        }

        static int dfs(int v,int N,bool[] visited)
        {
            var all = true;
            for(var i=0;i<N;i++)
            {
                if (!visited[i]) all = false;
            }
            if (all) return 1;
            var ret = 0;
            for(var i=0;i<N;i++)
            {
                if (!graph[v, i]) continue;
                if (visited[i]) continue;
                visited[i] = true;
                ret += dfs(i, N, visited);
                visited[i] = false;
            }
            return ret;
        }
    }
}