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: Wrong Answer)

#include <iostream>
#include<string>
#include<time.h>
#include<math.h>
#include<stdlib.h>
#include<map>
using namespace std;
 
int main() {
	long long N;
	cin >> N;
	long long A[200000];
 
	long long i,j;
	long long C = 0;
	long long z=0;
	for (i = 0; i < N; i++) {
		cin >> A[i];
	}
	for (i = 0; i < N; i++) {
		C = 0;
		for (j = 0; j < N; j++) {
			if (i != j) {
				if (A[i] % A[j] == 0)break;
				else C++;
			}
			if (C == N - 1)z++;
		}
	}
	cout << z << endl;
	return 0;
}