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: Time Limit Exceeded)

import sys
input = sys.stdin.readline

def main():
  n = int(input())
  a = [float(input()) for _ in range(n)]
  
  ans = 0
  count = 0
  
  for i in range(n):
    listJ = list(range(i + 1, n))
    for j in listJ:
      if a[i] - int(a[i]) == 0 and a[j] - int(a[j]) == 0:
        count += 1
      else:
        ans = (a[i]*10000) * (a[j]*10000)
        ans = ans*0.00000001
      if ans - int(ans) == 0:
        count += 1
  print(count)

main()