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()))
M=max(a)
num=[0]*M
for x in a:
	num[x-1]+=1
for i in range(M):
	if num[i]>=2:
		num[i]=0
ret=[1]*M
for i in range(M):
	if num[i]:
		j=i+i+1
		while j<M:
			ret[j]=0 
			j+=i+1
	else:
		ret[i]=0
print(ret.count(1))