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 not_divisible
  implicit none
  integer :: n, a(200000) = 0, c(1000000) = 0, m = 0, i, j
  read(*,*) n
  read(*,*) a(1:n)
  do i = 1, n
    c(a(i)) = c(a(i))+1
  end do
  select case(c(1))
  case(1)
    write(*,'(i0)') 1
    stop
  case(2:)
    write(*,'(i0)') 0
    stop
  end select
  do i = 1, n
    if (c(a(i)) > 1) cycle
    do j = 2, a(i)
      if (j*j > a(i)) exit
      if (mod(a(i),j) /= 0) cycle
      if (c(j) > 0 .or. c(a(i)/j) > 0) goto 100
    end do
    m = m+1
  100 end do
  write(*,'(i0)') m
end program not_divisible