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: Time Limit Exceeded)

program D
read*,in

call sub(in)
end program

subroutine sub(in)
implicit double precision(a-h,o-z)
integer::na(1:in)
integer::ic(1:200000)
do k=1,200000
ic(k)=0
end do
read*,(na(j),j=1,in)
icou=0
do i=in,1,-1
id=0
if (ic(i)==1)then
id=1
goto 90
end if
do j=1,i-1
if(id==0)then
if (abs(dble(na(i)/na(j))-(dble(na(i))/dble(na(j))))<1.E-6)then
id=1
end if
end if
if(ic(j)==0)then
if (abs(dble(na(j)/na(i))-(dble(na(j))/dble(na(i))))<1.E-6)then
ic(j)=1
end if
end if
end do
90 if(id==0)then
icou=icou+1
end if
end do
print*,icou
end subroutine