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
import os
import sys
from atexit import register
from io import BytesIO
sys.stdin = BytesIO(os.read(0, os.fstat(0).st_size))
sys.stdout = BytesIO()
register(lambda: os.write(1, sys.stdout.getvalue()))
input = lambda: sys.stdin.readline().rstrip('\r\n')
raw_input = lambda: sys.stdin.readline().rstrip('\r\n')


n = int(input())
seq = [int(x) for x in input().split()]
ans = 0
d = {}
for val in seq:
    try:
        d[val] += 1
    except:
        d[val] = 1
mm  = max(seq)
lst = [True for _ in range(mm+1)]
for val in seq:
    f = 2
    while val*f <= mm:
        lst[val*f] = False
        f += 1
ans = 0
for val in seq:
    if lst[val] and d[val] == 1:
        ans += 1
print(ans)