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)throws Exception
	{
		Scanner sc=new Scanner(System.in);
		int n = sc.nextInt();
	    int ar[]=new int[n+1];
		int value=1;
		int i,j;
		for(i=2;i<=n;i++)
		{
		    if(ar[i]==0)
		    {
		        ar[i]=value;
		        if(!(i>(Math.sqrt(n)+1)))
		        for(j=i*i;j<=n;j+=i)
		        {
		    
		        ar[j]= value;
		        }
		        value++;
		    }
		}
		if(ar[n]==0)
		ar[n]=value;
		for(i=2;i<=n;i++)
		System.out.print(ar[i] + " ");
	}
}