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())
A = [*map(int, input().split())]
mx = max(A)
c = [0]*(mx+1)
l = [0]*(mx+1)
for a in A:
    c[a] += 1
    for i in range(a*2, mx+1, a): l[i] = 1
ans = 0
for a in A:
    if not l[a] and c[a] <= 1: ans += 1
print(ans)
