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++14 (GCC 5.4.1) (judge verdict: Accepted)

#include <stdio.h>
#include <iostream>
#include <algorithm>
#include <cmath>
#include <numeric>
#include <vector>
#include <set>
#include <map>
#include <cstring>
#include <unordered_map>
#define lld long long int
#define DBG1(vari1) cerr<<#vari1<<" = "<<(vari1)<<endl;
#define DBG2(vari1,vari2) cerr<<#vari1<<" = "<<(vari1)<<" "<<#vari2<<" = "<<(vari2)<<endl;
#define DBG3(vari1,vari2,vari3) cerr<<#vari1<<" = "<<(vari1)<<" "<<#vari2<<" = "<<(vari2)<<" "<<#vari3<<" = "<<(vari3)<<endl;
using namespace std;
int visited[100];
vector <int> adj[100];
int ans=0;
int nv=0;
int n,m;
void dfs(int s)
{
	visited[s]=1;
	nv++;
	if(nv==n)
		ans++;
	for(int i=0;i<adj[s].size();i++)
	{
		if(!visited[adj[s][i]])
			dfs(adj[s][i]);
	}
	visited[s]=0;
	nv--;
}
int main()
{
	ios_base::sync_with_stdio(false);
	cin.tie(NULL);
	// freopen("input.txt", "r", stdin);  
	cin >> n >> m;
	for(int i=0;i<m;i++)
	{
		int a,b;
		cin >> a >> b;
		adj[a].push_back(b);
		adj[b].push_back(a);
	}
	dfs(1);
	cout << ans;
}