1209_A. Paint the Numbers
You are given a sequence of integers a_1, a_2, ..., a_n. You need to paint elements in colors, so that: 

  * If we consider any color, all elements of this color must be divisible by the minimal element of this color. 
  * The number of used colors must be minimized. 



For example, it's fine to paint elements [40, 10, 60] in a single color, because they are all divisible by 10. You can use any color an arbitrary amount of times (in particular, it is allowed to use a color only once). The elements painted in one color do not need to be consecutive.

For example, if a=[6, 2, 3, 4, 12] then two colors are required: let's paint 6, 3 and 12 in the first color (6, 3 and 12 are divisible by 3) and paint 2 and 4 in the second color (2 and 4 are divisible by 2). For example, if a=[10, 7, 15] then 3 colors are required (we can simply paint each element in an unique color).

Input

The first line contains an integer n (1 ≤ n ≤ 100), where n is the length of the given sequence.

The second line contains n integers a_1, a_2, ..., a_n (1 ≤ a_i ≤ 100). These numbers can contain duplicates.

Output

Print the minimal number of colors to paint all the given numbers in a valid way.

Examples

Input


6
10 2 3 5 4 2


Output


3


Input


4
100 100 100 100


Output


1


Input


8
7 6 5 4 3 2 2 3


Output


4

Note

In the first example, one possible way to paint the elements in 3 colors is:

  * paint in the first color the elements: a_1=10 and a_4=5, 
  * paint in the second color the element a_3=3, 
  * paint in the third color the elements: a_2=2, a_5=4 and a_6=2. 



In the second example, you can use one color to paint all the elements.

In the third example, one possible way to paint the elements in 4 colors is:

  * paint in the first color the elements: a_4=4, a_6=2 and a_7=2, 
  * paint in the second color the elements: a_2=6, a_5=3 and a_8=3, 
  * paint in the third color the element a_3=5, 
  * paint in the fourth color the element a_1=7. 
```python
n=int(input())
arr = list(map(int,input().split()))
elem = {}
arr.sort()
for i in arr:
  f=0
  for k in elem:
    if i%k == 0:
      elem[k]+=1
      f=1
      break
  if not f:
    elem[i] = 1
print(len(elem))
```