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
import java.util.*;
import java.io.*;
import java.math.BigInteger;

public class Main {	

	private static void solve(){
		//Implement solution here.
		int N = ni();
		int[] A = na(N);
		boolean[] filter = new boolean[1000001];
		Arrays.sort(A);
		int result = 0;
		
		for(int i = 0; i < N; i++) {			
			int thisA = A[i];
			if(!filter[thisA]) {
				if(i < N -1 && A[i] == A[i + 1]) {
						filter[thisA] = true;
					} else {
						result++;
					}
			} else {
				continue;
			}
			
			int tmp = thisA;
			while(tmp <= 1000000) {
				filter[tmp] = true;
				tmp += thisA;
			}
		}
		System.out.println(result);
	}

	//Switch input source (stdin/file)
	private static BufferedReader br;
	public static void main(String[] args){
		br = new BufferedReader(new InputStreamReader(System.in));
		String debugDataPath = System.getenv("DD_PATH");        
		if(debugDataPath != null){
			try{
				br = new BufferedReader(new InputStreamReader(new FileInputStream(new File(debugDataPath))));
			}catch(Exception e){
				throw new RuntimeException(e);
			}
		}
		boolean hasNext = true;
		while(hasNext){
			solve();	
			try{
				br.mark(1);
				if(br.read() > 0){
					br.reset();			
					System.out.println("---");
				} else {
					hasNext = false;
				}
			}catch(Exception e){
				throw new RuntimeException(e);
			} 
		}
	}

	//Input read utility
	private static StringTokenizer tokenizer = null;
	public static String next() {
		while (tokenizer == null || !tokenizer.hasMoreTokens()) {
			try {
				tokenizer = new StringTokenizer(br.readLine());
			} catch (Exception e) {
				throw new RuntimeException(e);
			}
		}
		return tokenizer.nextToken();
	}
	//Get next single int
	private static int ni() {
		return Integer.parseInt(next());
	}
	//Get next single long
	private static long nl() {
		return Long.parseLong(next());
	}
	//Get next single double
	private static double nd() {
		return Double.parseDouble(next());
	}
	//Get next int array from one line
	private static int[] na(int n) {
		int[] a = new int[n];
		for (int i = 0; i < n; i++)
			a[i] = ni();
		return a;
	}
	//Get next char array from one line
	private static char[] ns() {
		return next().toCharArray();
	}
	//Get next long array from one line
	private static long[] nal(int n) {
		long[] a = new long[n];
		for (int i = 0; i < n; i++)
			a[i] = nl();
		return a;
	}
}
