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 Python (3.8.2) (judge verdict: Accepted)

import numpy as np
from decimal import Decimal

N = int(input())

nums = [Decimal(input()) for _ in range(N)]

two_fives = []


for i, num in enumerate(nums):
    int_converted = int(num * (10**9))
    
    two_div_count = 0
    while int_converted % 2 == 0:
        two_div_count += 1
        int_converted //= 2
    
    five_div_count = 0
    while int_converted % 5 == 0:
        five_div_count += 1
        int_converted //= 5

    two_fives.append((two_div_count,five_div_count))


ok_count = 0

two_five_exists = np.zeros((19,19), dtype=int)

for i in range(N):    
    two_count, five_count = two_fives[i]
    two_count = min(18, two_count)
    five_count = min(18, five_count)
    ok_count += two_five_exists[two_count, five_count]

    two_pair = 18 - two_count
    five_pair = 18 - five_count
    two_five_exists[two_pair:, five_pair:] += 1

print(ok_count)