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: Time Limit Exceeded)

from numba import njit, int32, int64
from numba.typed import Dict

@njit
def solve(B):
    A = Dict.empty(
        key_type=int64,
        value_type=int64)
    for b in B:
      A[b] = A.get(b, 0) + 1
    r = 0
    if 1 in A:
        if A[1] == 1:
            return 1
        return 0
    for a, v in A.items():
        if v > 1:
            continue
        i = 2
        while i * i <= a:
            if a % i == 0:
                if i in A:
                    break
                if a // i in A:
                    break
            i += 1
        else:
            r += 1
    return r

def main():
    N = int(input())
    A = list(map(int, input().split()))
    return solve(A)

print(main())