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 <bits/stdc++.h>
using namespace std;
typedef long long ll;
typedef pair<int, int> pii;
const int maxn = 200000 + 10;
const int maxm = 100;
ll ans;
int C[maxm][maxm];
inline int lowbit(const int & x) { return x & (-x);}
int sum(int x, int y)
{
	int ret = 0;
	x += 50;
	y += 50;
	for(int i = x; i < maxm; i += lowbit(i))
		for(int j = y; j < maxm; j += lowbit(j))
			ret += C[i][j];
	return ret;
}
void add(int x, int y)
{
	x += 50;
	y += 50;
	for(int i = x; i; i -= lowbit(i))
		for(int j = y; j; j -= lowbit(j))
			++C[i][j];
}
int main()
{
	int n;
	scanf("%d", &n);
	for(int i = 1; i <= n; ++i)
	{
		double q;
		cin >> q;
		ll x = q * 1e9 + 0.5;
		int cnt2 = 0, cnt5 = 0;
		while(x % 2 == 0) x /= 2, ++cnt2;
		while(x % 5 == 0) x /= 5, ++cnt5;
		cnt2 -= 9;
		cnt5 -= 9;
		ans += sum(-cnt2, -cnt5);
		add(cnt2, cnt5);
	}
	cout << ans << endl;
	return 0;
}