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;
const int maxn=1e6+111;
int v[maxn], N, p[maxn];
map<int, int> cnt;
int main(){
    scanf("%d", &N);
    for (int i=1; i<=N; i++) scanf("%d", &p[i]), cnt[p[i]]++;
    sort(p+1, p+1+N);
    int ans=0;
    for (int i=1; i<=N; i++){
        if (v[p[i]]) continue;
        if (cnt[p[i]]==1)ans++;
        for (int j=1; j*p[i]<=p[N]; j++) v[j*p[i]]=1;
    }
    printf("%d", ans);
}