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.

5
24 11 8 3 16

3

The integers with the property are $2$, $3$, and $4$.

4
5 5 5 5

0

Note that there can be multiple equal numbers.

10
33 18 45 28 8 19 89 86 2 4

5