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: Wrong Answer)

N = int(input())
A = list(map(int, input().split()))

import math
import bisect

ans = [True] * N
A.sort()

A_cnt = {}
for i, Ai in enumerate(A):
    A_cnt.setdefault(str(Ai), 0)
    A_cnt[str(Ai)] += 1

for i, Ai in enumerate(A):
    if A_cnt[str(Ai)] > 1: ans[i] = False

inA = [False] * (10 ** 6 + 1)
for i, Ai in enumerate(A):
    inA[Ai] = True

for i, Ai in enumerate(A):
    for p in range(1, int(math.sqrt(Ai)) + 1):
        if Ai % p == 0:
            if inA[p]:
                ans[i] = False
                break
            if p == 1: continue
            elif inA[Ai // p]:
                ans[i] = False
                break

ans = ans.count(True)
print(ans)