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: Wrong Answer)

from bisect import bisect_left
n = int(input())
a = [int(i) for i in input().split()]
from collections import Counter
a_cnt = Counter(a)
a = []
for k, v in a_cnt.items():
    if v == 1:
        a.append(k)
a.sort()
ans = 0
while a:
    min_a = a[0]
    b = []
    ans += 1
    index = bisect_left(a, min_a * 2)
    m_i = max(index, 1)
    for i in range(m_i, len(a)):
        if a[i] % min_a != 0:
            b.append(a[i])
    a = a[1:index] + b 
print(ans)