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 PyPy3 (7.3.0) (judge verdict: Runtime Error)

import math
n = int(input())
integer = []
decimal = []
cnt = 0

for i in range(n):
  f = float(input())
  if f.is_integer():
    integer += [f]
  else:
    _f = f*10000
    if _f.is_integer():
      decimal += [f]

cnt += math.factorial(len(integer)-1)

for i in decimal:
  for j in integer:
    tmp = i*j
    if tmp.is_integer():
      cnt += 1
  for j in decimal:
    tmp = i*j
    if tmp.is_integer():
      cnt += 1
      

print(cnt)