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
#include<bits/stdc++.h>
using namespace std;
int ara[200005], freq[1000006], val[1000006];
int main()
{
    int n;
    scanf("%d", &n);
    for(int i=0; i<n; i++)
    scanf("%d", &ara[i]), freq[ ara[i] ]++;
    for(int i=1; i<=1000000; i++)
    for(int j=i; j<=1000000; j+= i)
    val[j]+= freq[i], val[j]= min(val[j], 2);
    int res= 0;
    for(int i=0; i<n; i++)res+= (val[ ara[i] ]==1);
    printf("%d\n", res);
    return 0;
}
