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.io.*;
import java.util.Arrays;
import java.util.Scanner; 

public class Tester { 
    public static void main(String[] args)  
    {
    	Scanner s=new Scanner(System.in);
    	int n=s.nextInt();
        int a[]=new int[n+1];
        for(int j=1;j<=n;j++)
        	a[j]=-1;
        int val=1;
        for(int j=2;j<=n;j++)
        {
        	if(a[j]==-1)
        	{
        		for(int k=j;k<=n;k+=j)
        		{
        			if(a[k]==-1)
        				a[k]=val;
        		}
        		val++;
        	}
        }
        for(int j=2;j<=n;j++)
        	System.out.print(a[j]+" ");
    
    		
    } 
}