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 Python (3.8.2) (judge verdict: Time Limit Exceeded)

from collections import defaultdict


n = int(input())
A = list(map(int, input().split()))


def divisor(n):
    div_list = set()
    limit = int(n**0.5) + 1
    for div in range(1, limit):
        if n % div == 0:
            div2 = n // div
            div_list.add(div)
            div_list.add(div2)
    
    return list(div_list)


        
A_dict = defaultdict(int)
for a in A:
    A_dict[a] += 1

    
ans = n
for a in A:
    A_dict[a] -= 1
    divs = divisor(a)
    for div in divs:
        if A_dict[div] >= 1:
            ans -= 1
            break
            
    A_dict[a] += 1


print(ans)