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: Time Limit Exceeded)

parseline(str) = parse.(Int, split(str))
function NotDivisible()
    N = readline()
    A = parseline(readline())
    ans = 0
    for i in 1:length(A)
        flag = true
        for j in 1:length(A)
            i==j && continue
            A[i]%A[j] == 0 && (flag=false; break)
        end
        flag && (ans+=1)
    end
    println(ans)
end
NotDivisible()