Problem:
Score : 400 points

Problem Statement

Given is a number sequence A of length N.

Find the number of integers i \left(1 \leq i \leq N\right) with the following property:

For every integer j \left(1 \leq j \leq N\right) such that i \neq j , A_j does not divide A_i.

Constraints

All values in input are integers.

1 \leq N \leq 2 \times 10^5

1 \leq A_i \leq 10^6

Input

Input is given from Standard Input in the following format:

N
A_1 A_2 \cdots A_N

Output

Print the answer.

Sample Input 1

5
24 11 8 3 16

Sample Output 1

3

The integers with the property are 2, 3, and 4.

Sample Input 2

4
5 5 5 5

Sample Output 2

0

Note that there can be multiple equal numbers.

Sample Input 3

10
33 18 45 28 8 19 89 86 2 4

Sample Output 3

5

Solution in Common Lisp (SBCL 2.0.3) (judge verdict: Wrong Answer)

(defun main ()
  (let* ((n (read))
         (s 1)
         (j (1+ s))
         (m n)
         (a (make-array `(,(1+ n)) :initial-element 0))
         (r 0))
    (when (= n 1)
      (format t "~A~%" 1)
      (return-from main))
    ;; read
    (loop :for i :from 1 :to n
          :do (setf (aref a i) (read)))
    ;;
    (setf a (sort a #'<))
    ;;
    (loop :named main
          :do  (loop :for i :from (1+ s) :to m
                     :do (when (/= 0 (mod (aref a i) (aref a s)))
                           (setf (aref a j) (aref a i))
                           (incf j)))
               (when (= (aref a s) (aref a (1+ s)))
                 (setf (aref a s) 0))
               (incf s)
               (setf m (1- j))
               (setf j (1+ s))
               (when (or (>= s m) (> (aref a s) 500000))
                 (return-from main)))
    (loop :for i :from 1 :to m
          :if (/= 0 (aref a m))
          :do (incf r))
    (format t "~A~%" r)))
(main)