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.io.*;
public class HelloWorld
{   static long z=(long)Math.pow(10,9)+7;
     public static void main(String []args)throws IOException
     {  int i,j;
        BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
        int n=Integer.parseInt(br.readLine());
        int a[]=new int[n+1];
        ArrayList<Integer> arr=new ArrayList<Integer>();
        arr.add(2);
        int flag=0;
        for(i=3;i<=n;i++)
        {   flag=0;
            for(j=2;j<=Math.sqrt(i)+1;j++)
            {
                if(i%j==0)
                {flag=-1;break;}
            }
            if(flag==0)
                arr.add(i);
        }
        //System.out.println(arr);
        
        int counter=1;
        for(int p:arr)
        {   for(i=1;i*p<=n;i++)
            {
                if(a[i*p]==0)
                    a[i*p]=counter;
            }
            counter++;
        }
        for(i=2;i<=n;i++)
        {
            if(a[i]==0)
                a[i]=counter++;
        }
        for(i=2;i<=n;i++)
            System.out.print(a[i]+" ");
     }
}