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: Accepted)

#include <iostream>
using namespace std;
typedef long long ll;
int t[20][20];
int main() {
  int n;
  cin>>n;
  ll ans = 0;
  for(int i = 0; i < n; ++i) {
    string s;
    cin>>s;
    int has_dot = 0;
    for(int i = 0; i < s.size(); ++i) {
      if(s[i] == '.') has_dot = 1;
    }
    if(!has_dot) {
      s.push_back('.');
    }
    while(s.size() < 10 || s[s.size()-10] != '.') {
      s.push_back('0');
    }
    ll y = 0;
    for(int i = 0; i < s.size(); ++i) {
      if(s[i] == '.') continue;
      y *= 10;
      y += s[i] - '0';
    }
    // cout<<s<<' '<<y;

    int d2 = 0;
    int d5 = 0;
    while(y % 2 == 0) {
      y /= 2;
      ++d2;
    }
    while(y % 5 == 0) {
      y /= 5;
      ++d5;
    }
    d2 = min(19, d2);
    d5 = min(19, d5);
    for(int p2 = 0; p2 < 20; ++p2) {
      for(int p5 = 0; p5 < 20; ++p5) {
        if(d2 + p2 >= 18 && d5 + p5 >= 18) {
          ans += t[p2][p5];
        }
      }
    }
    // cout<<' '<<d2<<' '<<d5<<endl;
    ++t[d2][d5];
  }
  cout<<ans<<endl;
}