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 Common Lisp (SBCL 2.0.3) (judge verdict: Time Limit Exceeded)

(let ((n (read))
      (x nil)
      (ans 0))
  (push (read) x)
  (loop :for i :from 2 :to n
        :for a := (read-from-string (format nil "~Ad0" (read-line)))
        :do (loop :for b :in x
                  :if (= (- (* a b) (floor (* a b))) 0)
                  :do (incf ans))
        :do (push a x))
  (format t "~A~%" ans))