Problem: You're given an integer n. For every integer i from 2 to n, assign a positive integer a_i such that the following conditions hold:

  * For any pair of integers (i,j), if i and j are coprime, a_i ≠ a_j. 
  * The maximal value of all a_i should be minimized (that is, as small as possible). 



A pair of integers is called [coprime](https://en.wikipedia.org/wiki/Coprime_integers) if their [greatest common divisor](https://en.wikipedia.org/wiki/Greatest_common_divisor) is 1.

Input

The only line contains the integer n (2 ≤ n ≤ 10^5).

Output

Print n-1 integers, a_2, a_3, …, a_n (1 ≤ a_i ≤ n). 

If there are multiple solutions, print any of them.

Examples

Input


4


Output


1 2 1 

Input


3


Output


2 1

Note

In the first example, notice that 3 and 4 are coprime, so a_3 ≠ a_4. Also, notice that a=[1,2,3] satisfies the first condition, but it's not a correct answer because its maximal value is 3.

Solution (in JAVA):

Solution:
import java.util.*;
public class Main {
  public static void main(String[] args) {
    Scanner s = new Scanner(System.in);
    int n = s.nextInt();
    ArrayList<Integer> a = new ArrayList<Integer>();
    a.add(1);
    a.add(2);
    for(int i=2;i<=n;i=i+1)
    {
      int flag = 0;
      for(int j=1;j<a.size();j++)
      {
        if(i%a.get(j)==0)
        {
          System.out.print(j+" ");
          flag=1;
          break;
        }
      }
      if(flag==0)
      {
        System.out.print(a.size()+" ");
        a.add(i);
      }
    }
  }
}