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
import collections
n = map(int, raw_input().split(' '))
ais = map(int, raw_input().split(' '))
cc = collections.Counter(ais)
ais.sort()
m = max(ais)
p = [True for _ in range(m + 1)]

count = 0
for ai in ais:
	if p[ai] is True:
		x = 2 * ai
	 	while(x < len(p)): 
	 		p[x] = False
	 		x += ai
for ai in ais:
	if p[ai] is True:
		if cc[ai] == 1:
			count +=1
print count