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 Julia (1.4.0) (judge verdict: Time Limit Exceeded)

parseInt(x) = parse(Int, x)
parseFloat(x) = parse(BigFloat, x)
#parseFloat(x) = parse(Float64, x)
parseMap(x::Array{SubString{String},1}) = map(parseFloat, x)
function main()
  N = parseInt(readline())
  A = zeros(BigFloat,N)
  for i in 1:N
    A[i] = parseFloat(readline())
  end
  #println(A)
  count=0
  for i in 1:N
    for j in i+1:N
      if A[i]*A[j]-div(A[i]*A[j],1)==0
        count+=1
      end
    end
  end

  println(count)
end
main()