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 sys
N=int(sys.stdin.readline().strip())
A=map(int, sys.stdin.readline().split())
A.sort()
max_A=A[-1]

L=[ 0 for _ in range(max_A+1) ]
for a in A:
    L[a]+=1

for i,x in enumerate(L):
    if 1<x:
        L[i]=0

for a in A:
    for i in range(a*2,max_A+1,a):
        L[i]=0

print sum(L)