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: Runtime Error)

(let* ((n (read))
       (s 1)
       (j (1+ s))
       (m n)
       (a (make-array `(,(1+ n)) :initial-element 0))
       (r 0))
  ;; 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 (>= s m)
               (return-from main)))
  (loop :for i :from 1 :to m
        :if (/= 0 (aref a m))
        :do (incf r))
  (format t "~A~%" r))