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<string>
#include<stdio.h>
#include<iostream>
#include<iomanip>
#include<ios>
#include<algorithm>
#include<stack>
#include<queue>
#include<cmath>
#include<type_traits>
#include<random>
#include<vector>
#include<map>


using namespace std;

bool flag = 0;

vector<bool> used;

int connect[10][10] = {};

int co;

int N,M;

void tansaku(int x,int depth)
{
	used[x] = 1;
	if(depth==N-1)
	{
		co = co + 1;
		used[x] = 0;
		return;
	}
	for(int i=0;i<N;i++)
	{
		if(connect[x][i]==1 && used[i]==0)
		{
			tansaku(i,depth+1);
		}
	}
	used[x] = 0;

}

int main()
{
	cin >> N >> M;
	vector<int> a(M);
	vector<int> b(M);
	for(int i=0;i<N;i++)
	{
		used.push_back(0);
	}
	for(int i=0;i<M;i++)
	{
		cin >> a[i] >> b[i];
		a[i] = a[i] - 1;
		b[i] = b[i] - 1;
		connect[a[i]][b[i]] = 1;
		connect[b[i]][a[i]] = 1;
	}
	co = 0;
	tansaku(0,0);
	cout << co << endl;
}