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.Text;
using System.Threading.Tasks;

namespace c
{
    class Program
    {
        static void Main(string[] args)
        {
            var strnm = Console.ReadLine().Split(' ');
            var n = int.Parse(strnm[0]);
            var m = int.Parse(strnm[1]);

            var graph = new List<int>[n];
            for (int i = 0; i < n; i++)
            {
                graph[i] = new List<int>();
            }

            for (int i = 0; i < m; i++)
            {
                var strab = Console.ReadLine().Split(' ');
                var a = int.Parse(strab[0]);
                var b = int.Parse(strab[1]);
                graph[a - 1].Add(b);
                graph[b - 1].Add(a);
            }

            var isPassed = new bool[n];
            for (int i = 0; i < n; i++)
            {
                isPassed[i] = false;
            }

            var pathCount = search(1, graph, isPassed);

            Console.WriteLine(pathCount.ToString());
        }

        static int search(int start, List<int>[] graph, bool[] isPassed)
        {
            var workIsPassed = new bool[isPassed.Length];
            for (int i = 0; i < isPassed.Length; i++)
            {
                workIsPassed[i] = isPassed[i];
            }

            workIsPassed[start - 1] = true;

            var isAllPassed = true;
            foreach (var b in workIsPassed)
            {
                if (!b)
                {
                    isAllPassed = false;
                    break;
                }
            }
            if (isAllPassed)
            {
                return 1;
            }

            int pathCount = 0;
            foreach (int i in graph[start - 1])
            {
                if (!workIsPassed[i - 1])
                {
                    pathCount += search(i, graph, workIsPassed);
                }
            }

            return pathCount;
        }
    }
}