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>
#define IT map<pair<int,int> , ll>::iterator
using namespace std;

typedef long long ll;
const int NMAX = 2e5 + 10;
const int MOD = 1e9 + 7;
int main(int argc, char const *argv[])
{
	int n;
	double a;
	scanf("%d",&n);
	map<pair<int,int> , ll>val_map;
	for(register int i = 0;i < n;i++)
	{
		scanf("%lf",&a);
		ll denominator = 1000000000;
		ll numerator = (ll)(a * denominator) + 0.1;
		ll gcd = __gcd(denominator,numerator);
		denominator /= gcd;
		numerator /= gcd;
		int two = 0,five = 0;
		while(denominator % 2 == 0) two--,denominator /= 2;
		while(denominator % 5 == 0) five--,denominator /= 5;
		while(numerator % 2 == 0) two++,numerator /= 2;
		while(numerator % 5 == 0) five++,numerator /= 5;
		val_map[make_pair(two,five)]++;
	}
	ll ans = 0;

	for(IT it1 = val_map.begin();it1 != val_map.end();it1++)
		for(IT it2 = val_map.begin();it2 != val_map.end();it2++)
			if(it1->first.first + it2->first.first >= 0 && it1->first.second + it2->first.second >= 0)
			{
				if(it1->first == it2->first)
					ans += it1->second * (it1->second - 1) / 2;
				else if(it1->first < it2->first)
					ans += it1->second * it2->second;
			}
	printf("%lld\n",ans);
	return 0;
}