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>

int ri() {
	int n;
	scanf("%d", &n);
	return n;
}

int main() {
	int n = ri();
	int cnt[1000001] = { 0 };
	bool mult[1000001] = { 0 };
	for (int i = 0; i < n; i++) {
		int a = ri();
		if (!cnt[a]++) for (int j = a + a; j <= 1000000; j += a) mult[j] = true;
	}
	int res = 0;
	for (int i = 0; i <= 1000000; i++) if (cnt[i] == 1 && !mult[i]) res++;
	printf("%d\n", res);
	return 0;
}
