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.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.OutputStreamWriter;
import java.io.PrintWriter;
import java.io.StreamTokenizer;
import java.util.Arrays;
import java.util.HashMap;
import java.util.Map;
import java.util.Scanner;

public class Main {
	public static StreamTokenizer input = new StreamTokenizer(new BufferedReader(new InputStreamReader(System.in),19999999));
	public static int nextInt() throws IOException{ input.nextToken(); return (int)input.nval; }
	public static PrintWriter out = new PrintWriter(new OutputStreamWriter(System.out));
    static int[] prime=new int[1000009];
    static int tot=0;
    static boolean[] notprime=new boolean[1000009];

    static void pony_prime(int n){ 
        notprime[0]=true;
        notprime[1]=true;
        for(int i=2;i<=n;++i){
            if(!notprime[i])
                prime[tot++]=i;
            for(int j=0; j<tot && i*prime[j]<=n;++j){ 
                notprime[i*prime[j]]=true; 
                if(i%prime[j]==0) break;
            }
         }
    }

    public static void main(String[] args) throws Exception {
       
    	try {       
        int count =1;
        int n=nextInt();
        pony_prime(n+10);
        Map<Integer,Integer> map = new HashMap<>();
        for(int i=1;i<=n;++i){
            if(!notprime[i]) {
            	map.put(i, count);
            	count++;
            }
        }
        
        String str1 = new String("");
        for(int i=2;i<=n;i++) {
        	if(map.containsKey(i)) {
        		out.print(map.get(i)+" ");
        	}else {
        		for(int j=2;j<i;j++) {
        			if(i%j==0) {
        				out.print(map.get(j)+" ");
        				break;
        			}
        		}
        	}
        }
       
		out.flush();

    }catch(Exception e){
		
	}
	}
}