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:
/* package whatever; // don't place package name! */

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 Ideone
{ 
	static boolean prime[]=new boolean[100006];; 
	static void sieve()
{      
        for(int i=0;i<100005;i++) 
            prime[i] = true; 
            
            
        for(int p = 2; p*p <=100005; p++) 
        { 
            if(prime[p] == true) 
            {  
                for(int i = p*p; i <=100005; i += p) 
                    prime[i] = false; 
            } 
        } 
}
	public static void main (String[] args) throws java.lang.Exception
	{
		// your code goes here
		Scanner sc=new Scanner(System.in);
		int n=sc.nextInt();
		sieve();
		
		int[] arr=new int[n+1];
		int val=1;
		for(int i=2;i<=n;i++)
    {
        if(prime[i])
        {
            arr[i]=val;
                for(int j=2*i;j<=n;j+=i)
                {
                    if(arr[j]==0)
                        arr[j]=val;
                }
                val++;
        }
    }
		
		for(int i=2;i<n+1;i++)
		System.out.println(arr[i]);
		
	}
}