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.*;
public class Main { 
    public static void main(String[] args) {
        FastScanner sc=new FastScanner();
        int o=0;
        int n=sc.nextInt();
        PriorityQueue<Integer> q=new PriorityQueue<>();
		for(int i=0;i<n;i++){
        		int p=sc.nextInt();
        		q.add(p);
		}
      	int[] a=new int[n];
      	for(int i=0;i<n;i++){
        	a[i]=q.poll();
        }
      	int la=a.length;
      	int max_a=(int)a[la-1];
      	boolean[] dp=new boolean[max_a+1];
      Arrays.fill(dp,true);
      	for(int i=0;i<la;i++){ 
          	if(dp[(int)a[i]]){
              for(int j=1;j<=max_a/(int)a[i];j++){
              	dp[(int)a[i]*j]=false;
                
              }
              if(i<la-1&&a[i]!=a[i+1]){
                	o++;
                }else if(i==la-1){
                	o++;
                }
            }                     	
        }
      System.out.println(o);
    }
}

    class FastScanner {
  private final InputStream in = System.in;
  private final byte[] buffer = new byte[1024];
  private int ptr = 0;
  private int buflen = 0;
  private boolean hasNextByte() {
      if (ptr < buflen) {
          return true;
      }else{
          ptr = 0;
          try {
              buflen = in.read(buffer);
          } catch (IOException e) {
              e.printStackTrace();
          }
          if (buflen <= 0) {
              return false;
          }
      }
      return true;
  }
  private int readByte() { if (hasNextByte()) return buffer[ptr++]; else return -1;}
  private static boolean isPrintableChar(int c) { return 33 <= c && c <= 126;}
  public boolean hasNext() { while(hasNextByte() && !isPrintableChar(buffer[ptr])) ptr++; return hasNextByte();}
  public String next() {
      if (!hasNext()) throw new NoSuchElementException();
      StringBuilder sb = new StringBuilder();
      int b = readByte();
      while(isPrintableChar(b)) {
          sb.appendCodePoint(b);
          b = readByte();
      }
      return sb.toString();
  }
  public long nextLong() {
      if (!hasNext()) throw new NoSuchElementException();
      long n = 0;
      boolean minus = false;
      int b = readByte();
      if (b == '-') {
          minus = true;
          b = readByte();
      }
      if (b < '0' || '9' < b) {
          throw new NumberFormatException();
      }
      while(true){
          if ('0' <= b && b <= '9') {
              n *= 10;
              n += b - '0';
          }else if(b == -1 || !isPrintableChar(b)){
              return minus ? -n : n;
          }else{
              throw new NumberFormatException();
          }
          b = readByte();
      }
  }
  public int nextInt() {
      long nl = nextLong();
      if (nl < Integer.MIN_VALUE || nl > Integer.MAX_VALUE) throw new NumberFormatException();
      return (int) nl;
  }
  public double nextDouble() { return Double.parseDouble(next());}
}