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 specialColoring {
 
	public static void main(String[] args) {
		Scanner s = new Scanner (System.in);
		int n = s.nextInt();
		int[] arr = new int[n+1];
		int p = 1;
		for (int i=2;i<=n;i++)
		{
			if (arr[i]==0) {
				arr[i] = p;
			for (long j=1l*i*i;j<=n;j=j+i)
				arr[(int)j] = p;
			p++;
			}
		}
		StringBuilder res = new StringBuilder();
		for (int i=2;i<=n;i++)
			res.append(arr[i]+" ");
		System.out.println(res);
	}
 
}