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 Julia (1.4.0) (judge verdict: Accepted)

parseInt(x) = parse(Int, x)
parseMap(x::Array{SubString{String},1}) = map(parseInt, x)

function main()
    n::Int=parseInt(readline())
    a::Vector{Int}=parseMap(split(readline()))
    cnt::Vector{Int}=[0 for i in 1:10^6]
    for i in a
        cnt[i]+=1
    end
    if cnt[1]==1
        println(1)
    elseif cnt[1]>2
        println(0)
    else
        ans::Int=0
        for i in a
            flag::Bool=true
            for j in 2:trunc(Int,sqrt(i))+1
                if i%j==0 && i>j && (cnt[i÷j]>0 || cnt[j]>0)
                    flag=false
                    break
                end
            end
            if cnt[i]>1
                flag=false
            end
            if flag
                ans+=1
            end
        end
        println(ans)
    end
end
main()