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.util.ArrayList;
import java.util.Arrays;
public class codeforces{

    public static boolean isprime(int a){
        if(a<4)
        return true;
        for(int i=2;i<=(int) Math.sqrt(a);i++)
        {
            if(a%i==0)
            return false;
        }
        return true;
    }
    public static void main(String[] args) throws IOException{
        InputStreamReader isr=new InputStreamReader(System.in);
        BufferedReader br=new BufferedReader(isr);
        StringBuilder str=new StringBuilder();
        int t=Integer.parseInt(br.readLine());
        int[] a=new int[t-1];
        ArrayList<Integer> arrayList=new ArrayList<>();
        for(int i=2;i<=t;i++)
        {
            if(isprime(i))
            arrayList.add(i);
        }
        int i1=0;
        while(i1<arrayList.size()){
            for(int i=arrayList.get(i1);i<t+1;i+=(arrayList.get(i1)))
            a[i-2]=i1+1;
            i1++;
        }
        for(int i=0;i<t-1;i++)
        System.out.print(a[i]+" ");
        System.out.println();
    }
}