p02642 AtCoder Beginner Contest 170 - Not Divisible
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
```python
n,*a=map(int,open(0).read().split())

ma=1001001
nums=[0]*ma

for i in a:
    nums[i]+=1
    if nums[i]==1: # 一回だけ出てきた場合
        for j in range(i+i,ma,i):
            nums[j]+=2
            
ans=nums.count(1)
print(ans)

```