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)

;小数の形の文字列を入力すると
;分数にして返す関数
(defun dec2frac (str)
  (loop for x across str
        with den = 0 and num = 0 and bool = nil
        
        if #1=(digit-char-p x)
        do (setf num (+ (* 10 num) #1#))
        
        if bool do (incf den)
        else do (setf bool (eq x #\.))
        
        finally 
        (setf den (expt 10 den))
        (return (/ num den))))


(defun solve (l)
  (loop for l2 on l
        for x in l
        sum (loop for y in (cdr l2)
                  count (integerp (* x y)))))

(princ (solve (loop repeat (read)
                    collect (dec2frac (read-line)))))