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.Text;
using System.Collections.Generic;
class Solve{
    int count;
    bool[] c;
    int N;
    List<int>[] G;
    public Solve(){}
    StringBuilder sb;
    public static int Main(){
        new Solve().Run();
        return 0;
    }
    void Run(){
        sb = new StringBuilder();
        Calc();
        Console.Write(sb.ToString());
    }
    void Calc(){
        string[] str = Console.ReadLine().Split(' ');
        N = int.Parse(str[0]);
        int M = int.Parse(str[1]);
        G = new List<int>[N];
        for(int i=0;i<N;i++){
            G[i] = new List<int>();
        }
        for(int i=0;i<M;i++){
            str = Console.ReadLine().Split(' ');
            int a = int.Parse(str[0])-1;
            int b = int.Parse(str[1])-1;
            G[a].Add(b);
            G[b].Add(a);
        }
        c = new bool[N];
        count = 0;
        dfs(0,0);
        sb.Append(count+"\n");
    }
    void dfs(int p,int n){
        if(n == N-1){
            count++;
            return;
        }
        c[p] = true;
        for(int i=0;i<G[p].Count;i++){
            int pn = G[p][i];
            if(!c[pn]){
                dfs(pn,n+1);
            }
        }
        c[p] = false;
    }
}