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++ (GCC 9.2.1) (judge verdict: Wrong Answer)

#include<bits/stdc++.h>
#define lln long long int
#define llu unsigned lln
#define sc(n) scanf("%d",&n);
#define scl(n) scanf("%lld",&n);
#define scd(n) scanf("%lf",&n);
#define pf(res) printf("%d\n",res);
#define pfl(res) printf("%lld\n",res);
#define pfd(res) printf("%lf\n",res);
#define maxii 100005
using namespace std;
typedef pair<int,int> pii;
typedef pair<lln,lln> pll;
vector<int> vi[maxii];
vector<int>:: iterator child;
typedef vector<lln> vl;
typedef vector<pii> vii;
typedef vector<pll> vll;


int arr[maxii];
int arr2[maxii];
bool check[maxii];
int cnt=0,n,maxi;
void dfs(int node,int c)
{
    check[node]=true;
    //cout<<node<<" "<<c<<endl;
    maxi=max(c,maxi);
    if(vi[node].size()==n-1)cnt++;
    for(int child=0;child<vi[node].size();child++)
    {
        if(check[vi[node][child]]==false)
        {
            dfs(vi[node][child],c+1);
        }
    }
}

int main()
{
   int m,x,y;
   sc(n)
   sc(m)
   for(int i=0;i<m;i++)
   {
       sc(x)
       sc(y)
       vi[x].push_back(y);
       vi[y].push_back(x);
   }
   int res=0;
   for(int i=2;i<=n;i++)
   {
       memset(check,false,sizeof(check));
       int c=0;
       maxi=0;
       dfs(i,c);
       if(maxi==n-1)
       {
           res++;
       }
       cout<<i<<" "<<maxi<<endl;

   }
   if(res==0)cout<<"1";
   else  cout<<res;
}