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.Scanner;

public class EhabandaSpecialColoringProblem {

	public static void main(String[] args) {
		// TODO Auto-generated method stub
		
		Scanner sc = new Scanner(System.in);
		int n = sc.nextInt();
		
		int a[] = new int[n+1];
		int k=1;
		
		for(int i=2;i*i<=n;i++) {
			
			boolean used = false;
			for(int j=1;j*i<=n;j++) {
				if(a[j*i]==0) {
					used=true;
					a[j*i]=k;
				}

			}
			if(used)
			k++;
		}
		
		for(int i=2;i<n;i++) {
			if(a[i]==0) {
				System.out.print(k+ " ");
				k++;
			}else {
				System.out.print(a[i]+" ");
			}

		}
		
		if(a[n]==0) {
			System.out.print(k);
		}else {
			System.out.print(a[n]);
		}
	}

}