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;

const int maxn = 200010;
int n, s1[maxn], s2[maxn], cnt[100][100];
long long a[maxn];

int main() {
    scanf("%d", &n);
    for (int i = 1; i <= n; i++) {
        double x; scanf("%lf", &x);
        a[i] = floor(x * 1e10);
        while (!(a[i] % 2)) s1[i]++, a[i] /= 2;
        while (!(a[i] % 5)) s2[i]++, a[i] /= 5;
        assert(s1[i] <= 60 && s2[i] <= 60);
    }
    long long ans = 0;
    for (int i = 1; i <= n; i++) {
        for (int j = 0; j <= 60; j++) {
            for (int k = 0; k <= 60; k++) {
                if (j + s1[i] >= 20 && k + s2[i] >= 20) ans += cnt[j][k];
            }
        }
        cnt[s1[i]][s2[i]]++;
    }
    printf("%lld\n", ans);
    return 0;
}