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 <cstdio>
#include <algorithm>
#include <vector>
using namespace std;
int main() {
	int N;
	scanf("%d", &N);
	double A[N];
	for (int i = 0; i < N; ++i) scanf("%lf", &A[i]);
	long long B[N], ans = 0;
	for (int i = 0; i < N; ++i) B[i] = A[i] * 1000000000;
	vector<long long> p5[19];
	int p2[44];
	fill_n(p2, 44, 0);
	for (int i = 0; i < N; ++i) {
		int x = 0;
		long long temp = B[i];
		while (temp % 5 == 0) ++x, temp /= 5;
		p5[x].push_back(B[i]);
	}
	for (int i = 0; i < 19; ++i) {
		for (int j: p5[18 - i]) {
			int x = 0;
			long long temp = j;
			while (temp % 2 == 0) ++x, temp /= 2;
			++p2[x];
		}
		for (int j: p5[i]) {
			int x = 0;
			long long temp = j;
			while (temp % 2 == 0) ++x, temp /= 2;
			for (int k = max(0, 18 - x); k < 44; ++k) ans += p2[k];
			if (i * 2 >= 18 && x * 2 >= 18) --ans;
		}
	}
	printf("%lld", ans / 2);
	return 0;
}