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 = int(raw_input())
ais = map(int,raw_input().split())
cc = collections.Counter(ais)
s = {ai:True for ai in ais}
m = max(ais)
for a in cc:
	c = a if cc[a] > 1 else 2 * a
	while(c <= m):
		if a in s: s[c] = False
		c+= a
count = 0
for ai in s:
	if s[ai]:
		count +=1

print count