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: Wrong Answer)

n = gets.to_i

ints = []
floats = []
n.times do
  f = gets.to_f
  i = f.to_i
  if i == f
    ints << i
  else
    floats << (f * 1000000000).to_i
  end
end

# ints の組み合わせ全て
res = 0
if ints.size > 1
  res += ints.size * (ints.size - 1) / 2
end


candidates = Hash.new(0)
ints.each do |i|
  max2 = -1
  max5 = -1
  13.downto(0) do |k2|
    5.downto(0) do |k5|
      break if max2 >= k2 && max5 >= k5
      k = (2 ** k2) * (5 ** k5)
      next if k == 1 || k >= 10000
      next unless i % k == 0
      candidates[k] += 1
      max2 = k2
      max5 = k5
      break
    end
  end
end

# ints と floats を1つずつ選んだ際に整数になる組み合わせ
keys = candidates.keys.select{|k| candidates[k] > 0 }.sort
floats.each do |f|
  keys.each do |k|
    m = f * k
    if m % 1000000000 == 0
      res += candidates[k]
    end
  end
end

puts res