Problem:
Score : 400 points

Problem Statement

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.

Sample Input 1

5
24 11 8 3 16

Sample Output 1

3

The integers with the property are 2, 3, and 4.

Sample Input 2

4
5 5 5 5

Sample Output 2

0

Note that there can be multiple equal numbers.

Sample Input 3

10
33 18 45 28 8 19 89 86 2 4

Sample Output 3

5

Solution in C++ (Clang 10.0.0) (judge verdict: Time Limit Exceeded)

#include <iostream>
#include <algorithm>
using namespace std;

int main() {
    int n, a[200010];
    cin >> n;
    for (int i = 0; i < n; ++i) {
        cin >> a[i];
    }
    sort(a, a + n);
    int ans = 0;
    for (int i = 0; i < n; ++i) {
        bool isCounted = true;
        for (int j = 0; j < n; ++j) {
            if (i == j) continue;
            else if (a[i] < a[j]) break;
            else if (a[i] % a[j] == 0) {
                isCounted = false;
                break;
            }
        }
        if (isCounted) ++ans;
    }
    cout << ans << endl;
    return 0;
}