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: Accepted)

#include <bits/stdc++.h>

using namespace std;

typedef long long ll;
#define mems(p) memset(p,-1,sizeof(p))
#define mp make_pair
#define pb push_back
#define eb emplace_back
#define nl "\n"

const int mxN = 1e6 + 1;
const ll MOD = 1e9 + 7;

void fast()
{ios_base::sync_with_stdio(false);cin.tie(0);cout.tie(0);}

ll gcd(ll a, ll b) {
	return b ? gcd(b, a%b) : a;
}

int found[mxN];
int a[mxN];

int main() {
	fast();
	int n;
	cin >> n;
	for (int i = 0; i < n; ++i)
	{
		cin >> a[i];
		found[a[i]]++;
	}
	int ans = 0;
	for (int i = 0; i < n; ++i)
	{
		bool success = true;
		if (found[a[i]] > 1) continue;
		if (a[i] > 1 && found[1] > 0) continue;
		for (int j = 2; j*j <= a[i]; ++j)
		{
			if (a[i] % j == 0) {
				if (found[j] || found[a[i]/j]) {
					success= false;
					break;
				}
			}
		}
		if (success) {
			++ans;
		}
	}
	cout << ans << nl;
}