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++ (GCC 9.2.1) (judge verdict: Time Limit Exceeded)

#include <iostream>

long long A[200001];

int main() {
    long long N;
    std::cin >> N;
    for (long long i=1; i<=N; i++) {
        std::cin >> A[i];
    }
    qsort(A+1, N, sizeof(long long), [](void const* a, void const* b) {
        return *(int*)a - *(int*)b;
        });

    long long count = 0;
    for (long long i=1; i<=N; i++) {
        if (A[i] < 0)
            continue;
        for (int j=i+1; j<=N; j++) {
            if (A[j] > 0 && A[j]%A[i] == 0)
                A[j] *= -1;
        }
        if (A[i] != -A[i+1]) {
            count++;
        }
    }
    std::cout << count << std::endl;
}