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: Accepted)

n = int(input())
a = list(map(int, input().split()))
a = sorted(a)
dp = [1 for i in range(10**6+10)]
for i in range(n):
    if dp[a[i]] == 1:
        dp[a[i]] = 2
        for j in range(2*a[i], 10**6+10, a[i]):
            dp[j] = 0
    elif dp[a[i]] == 2:
        dp[a[i]] = 0
res = 0
for i in range(n):
    if dp[a[i]] == 2:
        res += 1
print(res)