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: Wrong Answer)

using System;
using System.Collections.Generic;
using System.Linq;
class Method
{
    bool[] seen;
    int sum;
    int count = 0;
  
    public Method(int s, int n){
        seen = new bool[n];
        for(int i=0; i<n; i++){
            seen[i] = false;
        }
        sum = s;
    }
  
  	public int get(){
  		return count;    
    }
  
    public void dfs(int[,] pass, int v, int c){
        seen[v-1] = true;
        for(int i=0; i<pass.Length/2; i++){
            int thisV = pass[i,0];
            if(thisV != v) continue;
            int nextV = pass[i,1];
            if(seen[nextV-1]) continue;
            dfs(pass, nextV, c+nextV);
        }
        //Console.WriteLine(c);
        if(c == sum) count++;
    }
}

class Program
{
	static void Main(string[] args)
	{
		string[] input = Console.ReadLine().Split(' ');
        int n = int.Parse(input[0]);
        int m = int.Parse(input[1]);
        int s = 0;
        for(int i=1; i<=n; i++){
            s += i;
        }
        int[,] pass = new int[m*2, 2];
        for(int i=0; i<m; i++){
            string[] input2 = Console.ReadLine().Split(' ');
            pass[i,0] = int.Parse(input2[0]);
            pass[i,1] = int.Parse(input2[1]);
            pass[i+m,0] = int.Parse(input2[1]);
            pass[i+m,1] = int.Parse(input2[0]);
        }
        /*int start = 0;
        for(int i=0; i<m; i++){
            if(pass[i,0] == 1) {
                start = pass[i,1];
                break;
            }
        }*/
        Method me = new Method(s, n);
        me.dfs(pass, 1, 1);
        Console.WriteLine(me.get());
	}
}