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: Accepted)

(let* ((n (read))
       (a (make-array `(,(+ n 1)) :initial-element 0))
       (m 0)
       (dp)
       (c)
       (r 0))
  ;; read
  (loop :for i :from 1 :to n
        :do (setf (aref a i) (read)))
  ;;
  (setf a (sort a #'<))
  (setf m (aref a (1- (length a))))
  (setf dp (make-array `(,(1+ m)) :initial-element t))
  (setf c (make-array `(,(1+ m)) :initial-element nil))
  ;;
  (loop :for i :from 1 :to n
        :do (let ((x (aref a i)))
              (when (and (null (aref c x)) (aref dp x))
                (setf (aref c x) t)
                (loop :for y :from (* x 2) :upto m :by x
                      :do (setf (aref dp y) nil)))))
  ;;
  (loop :for i :from 1 :to n
        :if (and (or (= i n) (/= (aref a i) (aref a (1+ i))))
                 (or (= i 1) (/= (aref a (1- i)) (aref a i)))
                 (aref dp (aref a i)))
        :do (incf r))
  (format t "~A~%" r))