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())
MAX = 10**6
table = [0]*(MAX+1)
for x in map(int,input().split()):
    table[x] += 1
for i in range(MAX+1):
    if table[i]:
        for j in range(2*i if table[i] == 1 else i, MAX+1, i):
            table[j] = 0
print(sum(table))