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)

def divisors(n,x)
  i = 0
  while n % x == 0
    n = n / x
    i += 1
  end
  i
end
N = gets.to_i
a = N.times.map{gets.to_f}
arr = Array.new(14){Array.new(4){Hash.new(0)}}
a.each do |xx|
  bit = 9
  x = xx * (10 ** 9).floor
  while x % 10 == 0
    bit -= 1
    x /= 10
  end
  y = x
  while y % 10 == 0
    bit -= 1
    y /= 10
  end
  if y % 5 == 0
    arr[bit%14][2][divisors(y,5)] += 1
  elsif y % 2 == 0
    arr[bit%14][1][divisors(y,2)] += 1
  else
    arr[bit%14][0][0] += 1
  end
  arr[bit%14][3][0] += 1
end
cnt = 0
(-4).upto(9) do |i|
  i.upto(9) do |j|
    be = cnt
    if i + j <= 0
      if i == j
        cnt += arr[i%14][3][0] * (arr[i%14][3][0]-1) / 2
      else
        cnt += arr[i%14][3][0] * arr[j%14][3][0]
      end
    else
      if i == j
        inum = 0
        jnum = 0
        arr[i%14][1].each do |k,v|
          if k >= i+j
            inum += v
          end
        end
        arr[i%14][2].each do |k,v|
          if k >= i+j
            jnum += v
          end
        end
        cnt += inum * jnum
      else
        inum = 0
        arr[i%14][1].each do |k,v|
          if k >= i+j
            inum += v
          end
        end
        jnum = 0
        arr[j%14][2].each do |k,v|
          if k >= i+j
            jnum += v
          end
        end
        cnt += inum * jnum
        inum = 0
        arr[i%14][2].each do |k,v|
          if k >= i+j
            inum += v
          end
        end
        jnum = 0
        arr[j%14][1].each do |k,v|
          if k >= i+j
            jnum += v
          end
        end
        cnt += inum * jnum
      end
    end
  end
end
puts cnt