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 Problem {

	public static void main(String[] args) throws IOException {
		// TODO Auto-generated method stub
		Scanner in = new Scanner(System.in);
		
		int length = in.nextInt();
		int [] hasSet = new int [length+1];
		int count=1;
		int index=-1;
		for(int i=2;i<=length;i++) {
			boolean found=false;
			for(int j=2;j<=Math.sqrt(i);j++) {
				if(i%j==0) {
					index = j;
					found=true;
					break;
				}
			}
			if(!found) {
				hasSet[i]=count;
				System.out.print(count + " ");

				count++;
			}
			else
				System.out.print(hasSet[index] + " ");
			
			
		}
		in.close();

	}

}