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 Ruby (2.7.1) (judge verdict: Accepted)

n = gets.to_i
 
nums = []
n.times do
  f = gets.to_f
  nums << (f * 1e9).round # 2^9 * 5^9
end 
 
candidates = Hash.new(0)
nums.each do |num|
  raise if num == 0

  i2 = 0
  while num % 2 == 0
    i2 += 1
    num /= 2
  end

  i5 = 0
  while num % 5 == 0
    i5 += 1
    num /= 5
  end

  candidates[[i2, i5]] += 1
end 

res = 0
keys = candidates.keys
i = 0
while i < keys.size
  j = i
  i2_0, i5_0 = keys[i]
  while j < keys.size
    i2_1, i5_1 = keys[j]
    i2 = i2_0 + i2_1
    i5 = i5_0 + i5_1
    if i2 >= 18 && i5 >= 18
      vi = candidates[keys[i]]
      vj = candidates[keys[j]]
      raise unless vi > 0 && vj > 0
      if i == j
        res += vi * (vi - 1) / 2
      else
        res += vi * vj
      end
    end
    j += 1
  end
  i += 1
end
puts res