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: Accepted)

n, *a = map(int, open(0).read().split())
a.sort()
am = a[-1] + 1
dp = [True] * am
ans = 0
dup = set()
for x in a:
    d = dp[x]
    if d:
        ans += 1
        for i in range(x, am, x):
            dp[i] = False
        dp[x] = None
    elif d == None:
        dup.add(x)

print(ans - len(dup))