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.*;
import java.io.*;

public class a 
{
	int n, cnt = 0;
	int[] a;
	boolean[] v;
	
	a(Scanner in, PrintWriter out)
	{
		n = in.nextInt();
		a = new int[n+1];
		v = new boolean[n+1];
		for (int i = 2; i <= n; i++)
			if (!v[i])
			{
				cnt++;
				for (int j = i; j <= n; j += i)
				{
					a[j] = cnt;
					v[j] = true;
				}
			}
		
		for (int i = 2; i <= n; i++)
			out.print(a[i]+" ");
	}
	
	public static void main(String[] args) 
	{
		Scanner in = new Scanner(System.in);
		PrintWriter out = new PrintWriter(System.out);
		new a(in, out);
		out.close();
	}
	
}