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.*;
import java.lang.*;

public class Rextester{
    public static void main(String[] args)throws IOException{
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        int n = new Integer(br.readLine());
        br.close();
        int[] prime = new int[n+1];
        Arrays.fill(prime,-1);
        for(int i=2;i<=n;i++){
            if(prime[i]==-1){
                for(int j=2*i;j<=n;j+=i){
                    if(prime[j]==-1){
                        prime[j]=i;
                    }
                }
            }
        }
        //for(int i=2;i<=n;i++){
          //  System.out.print(prime[i]+" ");
        //}
        //System.out.println();
        StringBuffer sb = new StringBuffer();
        int[] array = new int[n+1];
        int[] array2 = new int[n+1];
        int p=2;
        for(int i=2;i<=n;i++){
            if(i%2==0){
                array2[i]=1;
            }
            else if(prime[i]==-1){
                array2[i]=p++;
            }
            else{
                array2[i]=array2[prime[i]];
            }
        }
        for(int i=2;i<=n;i++){
            sb.append(array2[i]).append(" ");
        }
        System.out.println(sb);
    }
}