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 HelloWorld{

     public static void main(String []args){
        Scanner sc=new Scanner(System.in);
        int n=sc.nextInt();
       
        long prime[] = new long[n+1]; 
        for(int i=0;i<n;i++) 
            prime[i] = 0; 
          long x=1;
        for(int p = 2; p<=n; p++) 
        { 
           
            if(prime[p-1] == 0) 
            { 
                prime[p-1]=x;
                
                for(int i = p; i <= n; i += p) 
                    prime[i-1] = x; 
                    x=x+1;
            } 
        } 
          
        
        for(int i = 1; i <n; i++) 
        { 
             
                System.out.print(prime[i]+" "); 
        } 
    } 
      
   
}