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)

n=gets.to_i
l2=[]
l5=[]
n.times do
  a=gets.chomp
  if a.include?(".")
    d=a.split(".")[1].size
  else
    d=0
  end
  a=a.delete(".").to_i
  c2,c5=0,0
  while a%2==0
    a/=2
    c2+=1
  end
  l2 << c2-d
  while a%5==0
    a/=5
    c5+=1
  end
  l5 << c5-d
end
c=0
n.times do |i|
  i.times do |j|
    c+=1 if l2[i]+l2[j]>=0&&l5[i]+l5[j]>=0
  end
end
puts c