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.io.* ;

public class CF_1110 {
      
    public static void main(String[] args) throws IOException{
        FastReader scn = new FastReader() ;
        int n = scn.nextInt() ;
        int[] arr = new int[n + 1] ;
        int x = 1 ;
        for(int i = 2 ; i * i <= n ;i++){
            if(arr[i] == 0){
                arr[i] = x ;
                for(int j = i*i ; j <= n ; j += i){
                    if(arr[j] == 0){
                        arr[j] = x ;
                    }
                }
                x++ ;
            }
        }
        for(int i = 2 ; i <= n ;i++){
            if(arr[i] == 0){
                arr[i] = x ;
                x++ ;
            }
        }
        for(int i = 2 ; i <= n ; i++){
            System.out.print(arr[i] + " ");
        }  
        System.out.println();

     }
     /*
     TreeMap<Integer , Integer> even = new TreeMap<>() , odd = new TreeMap<>();
       for(int i = 0 ;i < n ;i++){
           if(arr[i] % 2 == 0){
               even.put(arr[i], even.getOrDefault(arr[i], 0) + 1) ;
           } else {
            odd.put(arr[i], odd.getOrDefault(arr[i], 0) + 1) ;
           }
       }
       for(int i = 0 ; i < n ; i++){
        if(arr[i] % 2 == 0){
            // remove 
            if(even.get(arr[i]) == 1){
                even.remove(arr[i]) ;
            }  else {
                even.put(arr[i] , even.get(arr[i]) - 1) ;
            }
            // smallest 
            Entry<Integer , Integer>  k = odd.pollFirstEntry() ;
            if(k == null || k.getKey() > arr[i]){
                continue ;
            }  
            // swap 
            arr[i] = k.getKey() ;
            // delete and add 
         } else {
            if(odd.get(arr[i]) == 1){
                odd.remove(arr[i]) ;
            }  else {
                odd.put(arr[i] , odd.get(arr[i]) - 1) ;
            }
        }
        
       }
     */
    
     static class Pair 
     {
        int f ; 
        int s ;
        Pair(int f , int s)
        {
            this.f = f ; 
            this.s = s ;
        }
    }
    static 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;
        }
    }
     
 }