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 :initial-element 0))
    (cnt (make-array 1000005 :initial-element 0))
    (ans 0))
    (dotimes (i n)
        (incf (aref a i) (read))
    )
    (loop for x across a do
        (if (not (= (aref cnt x) 0))
            (setf (aref cnt x) 2)
            (loop for i from x by x while (< i 1000005) do
                (incf (aref cnt i))
            )
        )
    )

    (loop for x across a do
        (if (= (aref cnt x) 1)
        (incf ans))
    )
    (princ ans)
)