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.*;
import java.lang.*;
import java.io.*;

/* Name of the class has to be "Main" only if the class is public. */
public class Codechef
{
	public static void main (String[] args) throws java.lang.Exception
	{
	    Scanner sc = new Scanner(System.in);
	    int n = sc.nextInt();
	    int count = 1;
	    int t = 0;
	    int[] a = new int[n];
	    int[] prime = new int[n];
	    int v = 0;
	    for(int i=1;i<n;i++)
	    {
	        t = 0;
	        for(int j=0;j<v && j<i-1;j++)
	        {
	            if((i+1)%prime[j] != 0)
	            {
	                t++;
	            }
	            else{
	                a[i] = a[prime[j]-1];
	                break;
	            }
	        }
	        if(t == v)
	        {
	            a[i] = count;
	            prime[v] = a[i]+1;
	            v++;
	            count++;
	        }
	    }
	    for(int i=1;i<n;i++)
	    {
	        System.out.print(a[i]+" ");
	    }
	}
}