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 <string>
#include <vector>
#include <queue>
#include <deque>
#include <stack>
#include <set>
#include <map>
#include <unordered_map>
#include <unordered_set>
#include <cstring>
#include <cmath>
#include <cstdlib>
#include <algorithm>
#include <random>
#include <iomanip>
#include <functional>
#include <cassert>

using namespace std;

typedef long long ll;

const int K = 1e9;

int main() {
  ios_base::sync_with_stdio(false); cin.tie(0);
#ifdef LOCAL
  freopen("input.txt", "r", stdin);
#endif
  int n;
  cin >> n;
  map <pair <int, int>, int> cnt;
  for (int i = 0; i < n; ++i) {
    double c;
    cin >> c;
    ll x = (ll)(c * K);
    int c2 = 0, c5 = 0;
    while (x % 2 == 0) {
      ++c2;
      x /= 2;
    }
    while (x % 5 == 0) {
      ++c5;
      x /= 5;
    }
    ++cnt[{c2, c5}];
  }
  ll ans = 0;
  for (auto a : cnt) {
    for (auto b : cnt) {
      if (a.first.first + b.first.first >= 18 && a.first.second + b.first.second >= 18) {
        if (a != b) {
          ans += (ll)a.second * b.second;
        } else {
          ans += (ll)a.second * (a.second - 1);
        } 
      }
    }
  }
  ans /= 2;
  cout << ans << '\n';
}