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<bits/stdc++.h>
using namespace std;
int main(){
    int n;
    cin >> n;
    double a[n];
    vector<pair<int,int> >apair(n);
    map<long,map<long,long> >pair; //2^x,5^y -> pair[x][y]
    for(int i=0;i<n;i++){
        cin >> a[i];
        double tmp = a[i];
        int x = -9;
        int y = -9;
        
        
        long tmpi = (long)floor(1000000000.0 * a[i]);
        cerr << tmpi<<endl;
        while(tmpi%2==0){
            tmpi /= 2;
            x++;
        }
        while(tmpi%5==0){
            tmpi /= 5;
            y++;
        }
        apair[i].first = x;
        apair[i].second = y;
        pair[x][y]++;

        


    }

    // for(int i=0;i<n;i++){
    //     cerr<<a[i]<<" "<<apair[i].first<<" "<<apair[i].second<<endl;
    // }


    long ans = 0;

    for(int i=-70;i<=70;i++){
        for(int j=-30;j<=30;j++){

            for(int ii = -70;ii<=70;ii++){
                for(int jj = -30;jj<=30;jj++){
                    if(i+ii<0 || j+jj<0)continue;

                    long tmpp = 0;
                    
                    if(i==ii && j==jj)tmpp = pair[i][j] * (pair[i][j]-1);
                    else tmpp = pair[i][j] * pair[ii][jj];

                    ans += tmpp;
                    if(tmpp != 0)cerr<<i<<" "<<j<<" "<<ii<<" "<<jj<<" "<<tmpp<<endl;

                    
                }
            }
        }
    }
    cout << ans/2 << endl;



}