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 Fortran (GNU Fortran 9.2.1) (judge verdict: Accepted)

program main
    use,intrinsic :: iso_fortran_env
    implicit none
    integer(int32):: n,i,j,l,ans=0
    integer(int32), allocatable:: a(:),divisor(:)

    read*, n
    allocate(a(n))
    read*, a(:)

    l = maxval(a)
    allocate(divisor(l),source=0)

    do i=1,n
        divisor(a(i))=divisor(a(i))+1
        if (divisor(a(i)) > 1) cycle
        j=2
        do while(a(i)*j <= l)
            divisor(a(i)*j)=divisor(a(i)*j)+1
            j=j+1
        end do
    end do

    do i=1,n
        if (divisor(a(i)) == 1) ans=ans+1
    end do
    print'(i0)', ans
end program main