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
_,*A = map(int,open(0).read().split())
A.sort()
M = 10**6 + 1
l = [0] * (M)
for a in A:
    if l[a] == 0:
        l[a] = 2
        for x in range(a*2, M, a):
            l[x] = 1
    elif l[a] == 2:
        l[a] += 1
print(l.count(2))
