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)

(let* ((n (read))
       (m (sort (loop :repeat n :collect (read)) #'<))
       (ll (make-array (+ 2 (expt 10 6)) :element-type 'bit :initial-element 1))
       (ans 0))
  (loop :for k :in m
        :with x = -1
        :do(if (and (= k x) (= 1 (aref ll k))) (incf ans))
        :do(loop :for j :from k :upto (1+ (expt 10 6)) :by k
                 :if (= 1 (aref ll j)) :do(setf (aref ll j) 0))
        :do(setf x k))
  (princ ans))