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

见题面

见题面