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))
         (m 1)
         (a (make-array `(,(1+ n)) :initial-element 0))
         (c (make-array `(,(1+ n)) :initial-element 1))
         (b (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 #'<))
    ;;
    (setf (aref b 1) (aref a 1))
    (loop :for i :from 2 :to n
          :do (let* ((x (aref a i))
                     (flag t))
                (loop :named inner
                      :for j :from 1 :to m
                      :do (let* ((y (aref b j))
                                 (gcd (gcd x y)))
                            (when (/= gcd 1)
                              (if (= gcd y)
                                  (setf (aref c j) 0)
                                  (setf (aref b j) (min gcd y)))
                              (setf flag nil)
                              (return-from inner))))
                (when flag
                  (setf (aref b (incf m)) x))))
    ;;
    (loop :for i :from 1 :to n
          :if (> (* (aref b i) (aref c i)) 0)
          :do (incf r))
    (format t "~A~%" r)))
(main)