Problem:
Score : 300 points

Problem Statement

You are given N real values A_1, A_2, \ldots, A_N.
Compute the number of pairs of indices (i, j)
such that i < j and the product A_i \cdot A_j is integer.

Constraints

2 \leq N \leq 200\,000

0 < A_i < 10^4

A_i is given with at most 9 digits after the decimal.

Input

Input is given from Standard Input in the following format.

N
A_1
A_2
\vdots
A_N

Output

Print the number of pairs with integer product A_i \cdot A_j (and i < j).

Sample Input 1

5
7.5
2.4
17.000000001
17
16.000000000

Sample Output 1

3

There are 3 pairs with integer product:

7.5 \cdot 2.4 = 18

7.5 \cdot 16 = 120

17 \cdot 16 = 272

Sample Input 2

11
0.9
1
1
1.25
2.30000
5
70
0.000000001
9999.999999999
0.999999999
1.000000001

Sample Output 2

8

Solution in C++ (GCC 9.2.1) (judge verdict: Wrong Answer)

#include <iostream>
#include<bits/stdc++.h>
#define int long long int
#define vi vector<int>
#define vvi vector<vector<int>>
using namespace std;
int P=10002;
int mp[10002];
int gcd(int a,int b)
{
     if (b == 0) 
        return a; 
    return gcd(b, a % b); 
}
int32_t main() {
	// your code goes here
	
	  //cout<<"Case #"<<x++<<":\n";
	 int n,i,j,k;
	 cin>>n;
	 vector<double> a(n);
	 for(i=0;i<n;i++)
	 cin>>a[i];
	 vvi nd(n,vi(2));
	 for(i=0;i<n;i++)
	 {
	     int num=a[i]*pow(10,9),den=pow(10,9);
	     int gc=gcd(num,den);
	     num/=gc,den/=gc;
	     nd[i][0]=num,nd[i][1]=den;
	     if(den<P)
	     mp[den]++;
	 }
	 int sum=mp[1]*(mp[1]-1)/2,cnt=1;
	 for(i=0;i<n;i++)
	 {
	     if(nd[i][1]==1)
	     {
	         for(j=2;j<=sqrt(nd[i][0]);j++)
	         {
	             if(nd[i][0]%j==0)
	             {
	                 if(j*j==nd[i][0])
	                 sum+=mp[j];
	                 else sum+=mp[j]+mp[nd[i][0]/j];
	             }
	         }
	     }
	 }
	  cout<<(sum)<<"\n";
	return 0;
}