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)

END { load __FILE__ unless $stdin.eof? }

def e25(n)
  e2 = e5 = 0
  loop do
    d, m = n.divmod(2)
    break if m != 0
    e2 += 1
    n = d
  end
  loop do
    d, m = n.divmod(5)
    break if m != 0
    e5 += 1
    n = d
  end
  [e2, e5]
end

n = gets.to_i
a = Array.new(n) do
  x, y = gets.chomp.split(".")
  y ||= "0"
  z = (x << (y << "000000000")[0, 9]).to_i
  e25(z)
end.sort!

b = a.tally.map { |k, v| k << v }

cnt = 0
until b.empty?
  e2, e5, m = b.shift
  cnt += m * m.pred / 2 if e2 >= 9 && e5 >= 9
  l = b.select { |f2, f5, *| e2 + f2 >= 18 && e5 + f5 >= 18 }.sum(&:last)
  cnt += m * l
end

p cnt