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.BufferedReader;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.util.StringTokenizer;
import java.io.*;

public class Main {
        
        
    public static void main(String[] args) throws Exception{
        // TODO Auto-generated method stub
        //Reader.init(System.in);
       // Scanner sc=new Scanner(System.in);
        FastReader sc=new FastReader(); 
        OutputStream outputStream = System.out;
        PrintWriter out = new PrintWriter(outputStream);
        ArrayList<Integer> list=new ArrayList<Integer>();
        int n=sc.nextInt();
        int[] ans=new int[n+1];
        int[] sie=new int[n+1];
        int counter=1;
        for(int i=2;i<=n;i++) {
            if(sie[i]==0) {
                int c=1;
                while(c*i<=n) {
                    sie[c*i]=1;
                    ans[c*i]=counter;
                    c++;
                }
                counter++;
            }
        }
        for(int i=2;i<=n;i++) {
            System.out.print(ans[i]+" ");
        }
    }
}  

class pair{
    int f;int s;
    pair(int f,int s){
        this.f=f;
        this.s=s;
    }
}
class a implements Comparator<pair>{
    public int compare(pair p1,pair p2) {
        return (int)(p1.f-p2.f);
    }
}
class FastReader 
{ 
    BufferedReader br; 
    StringTokenizer st; 

    public FastReader() 
    { 
        br = new BufferedReader(new
                 InputStreamReader(System.in)); 
    } 

    String next() 
    { 
        while (st == null || !st.hasMoreElements()) 
        { 
            try
            { 
                st = new StringTokenizer(br.readLine()); 
            } 
            catch (IOException  e) 
            { 
                e.printStackTrace(); 
            } 
        } 
        return st.nextToken(); 
    } 

    int nextInt() 
    { 
        return Integer.parseInt(next()); 
    } 

    long nextLong() 
    { 
        return Long.parseLong(next()); 
    } 

    double nextDouble() 
    { 
        return Double.parseDouble(next()); 
    } 

    String nextLine() 
    { 
        String str = ""; 
        try
        { 
            str = br.readLine(); 
        } 
        catch (IOException e) 
        { 
            e.printStackTrace(); 
        } 
        return str; 
    } 
}