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.

Examples

Input

5
24 11 8 3 16


Output

3


Input

4
5 5 5 5


Output

0


Input

10
33 18 45 28 8 19 89 86 2 4


Output

5
n=int(input())
l=list(map(int,input().split()))
c=0
d={}
f=[0]*(max(l)+1)
for i in l:
	if i in d:
		d[i]+=1
	else:
		d[i]=1
x=sorted(list(set(l)))
for i in x:
	if d[i]==1 and f[i]==0:
		c+=1
	for j in range(2*i,len(f),i):
		f[j]=1 

print(c)