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.*;
public class Main {
    static StreamTokenizer in=new StreamTokenizer(new BufferedReader(new InputStreamReader(System.in)));
    static int inf=(int)1e9+7;
    static PrintWriter out=new PrintWriter(new OutputStreamWriter(System.out));
    public static void main(String args[])throws Exception{
        int n=getInt();
        int arr[]=new int[n+1];
        int now=1;
        for(int i=2;i<=n;i++){
            if(arr[i]==0){
                arr[i]=now;
                for(int j=2;i*j<=n;j++){
                    arr[i*j]=now;
                }
                now++;
            }
        }
        for(int i=2;i<=n;i++){
            if(i!=2)out.write(" ");
            out.write(arr[i]+"");
        }
        out.flush();
        out.close();
    }
    public static void ssort(int arr[]){
        int len=arr.length;
        for(int i=0;i<len;i++){
            int t=(int)(Math.random()*len);
            int temp=arr[t];
            arr[t]=arr[i];
            arr[i]=temp;
        }
        Arrays.sort(arr);
    }
    public static int getInt() throws Exception{
        in.nextToken();
        return (int)in.nval;
    }
}