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.lang.*;
import java.io.*;

public class A3 {
    public static void main(String[] Args){
        Scanner scan=new Scanner(System.in);
        int n=scan.nextInt();
        int[] arr=new int[n+1];
        for (int i = 2; i <=n ; i++) {
            arr[i]=-1;
        }
        for (int i = 2; i <=n ; i++) {
            if(i%2==0){
                arr[i]=1;
            }
        }
        boolean[] ar=new boolean[n+1];
        for (int i = 2; i*i <=n ; i++) {
            if(ar[i]){
                continue;
            }
            for (int j = i*i; j <=n ; j+=i) {
                if(j%i==0){
                    ar[j]=true;
                }
            }
        }
        ArrayList<Integer> arrr=new ArrayList<>();
        for (int i = 2; i <=n ; i++) {
            if(!ar[i]){
                arrr.add(i);
            }
        }
        int num=2;
        for (int i = 1;i<arrr.size();i++) {
            int prime=arrr.get(i);
            for (int j = prime; j <=n ; j+=2) {
                if(j%prime==0&&arr[j]==-1){
                    arr[j]=num;
                }
            }
            num++;
        }
        StringBuilder build=new StringBuilder();
        for (int i = 2; i <=n ; i++) {
            build.append(arr[i]+" ");
        }
        System.out.println(build);
    }
}