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
A = []
max = 0
N.times{
    a = Rational(gets)
    A << a
    if max < a
        max = a
    end
}
#warn A.inspect
A.reject!{|x|x.denominator > max}
A.sort_by!{|x|x.denominator}
#warn A.inspect
count = 0
(0 .. A.size - 2).each{|i|
    (i + 1 .. A.size - 1).each{|j|
        if A[i].numerator < A[j].denominator
            break
        end
        r = A[i] * A[j]
        if r.denominator == 1
            count += 1
        end
    }
}
puts count