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
N = int(input())
AList = list(map(int, input().split()))

sortList = sorted(AList)
Amax = max(sortList)

dp = [0]*(Amax+1)

for n in sortList:
  dp[n] += 1
  if dp [n] == 1:
    for i in range(n*2, Amax+1, n):
      dp[i] += 2

print(dp.count(1))