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)

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

k = 0
b = 0
for l in range(n):
    if a[l] == 1:
        b = b + 1
        
if b == 0:
    for i in range(n):
        for j in range(n):
            if a[j] != 0:
                if i != j:            
                    if a[i] % a[j] == 0:
                        a[i] = 0
                        break
            if j == n-1:
                k = k + 1          
    print(k)
elif b == 1:
    print('1')
else:
    print('0')