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: Time Limit Exceeded)

require 'prime'

class Array
  def imos
    n = size

    ret = map(&:dup)

    (n - 1).downto(0) do |i|
      (n - 2).downto(0) do |j|
        ret[i][j] += ret[i][j + 1]
      end
    end

    (n - 2).downto(0) do |i|
      (n - 1).downto(0) do |j|
        ret[i][j] += ret[i + 1][j]
      end
    end

    ret
  end
end

M = 10 ** 9
N = gets.to_i
A = N.times.map { gets.to_f }

table = Array.new(19) { Array.new(19, 0) }

A.each do |a|
  primes = (a * M).to_i.prime_division.to_h

  cnt_2 = primes[2] || 0
  cnt_5 = primes[5] || 0

  cnt_2 = 18 if 18 < cnt_2
  cnt_5 = 18 if 18 < cnt_5

  table[cnt_2][cnt_5] += 1
end

table = table.imos
ans = 0

A.each do |a|
  v = a * M
  cnt_2 = 0
  cnt_5 = 0

  while v % 2 == 0
    cnt_2 += 1
    v /= 2
  end

  while v % 5 == 0
    cnt_5 += 1
    v /= 5
  end

  cnt_2 = 18 if 18 < cnt_2
  cnt_5 = 18 if 18 < cnt_5

  ni = 18 - cnt_2
  nj = 18 - cnt_5

  if 9 <= cnt_2 && 9 <= cnt_5
    ans -= 1
  end

  ans += table[ni][nj]
end

puts ans / 2