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 PyPy3 (7.3.0) (judge verdict: Time Limit Exceeded)

import sys
def input():
    return sys.stdin.readline()[:-1]

def main():
    N = int(input())
    A = list(map(int, input().split()))
    
    A_dict = {}
    for a in A:
        if a in A_dict.keys():
            A_dict[a] += 1
        else:
            A_dict[a] = 1

    black_list = set()
    ans = 0
    for a in sorted(A_dict.keys()):
        for b in black_list:
            if a % b == 0:
                break
        else:
            if A_dict[a] == 1:
                ans += 1
            black_list.add(a)
    print(ans)
main()