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.*;
 
public class ehab3 {
    public static void main( String[] args ) {
	Scanner in = new Scanner( System.in );
	int n = in.nextInt(), c = 0;
	int[] a = new int[n + 1];
	for ( int i = 2; i <= n; i++ ) {
	    if ( a[i] == 0 ) {
		a[i] = ++c;
		for ( int j = i; j <= n; j += i ) 
		    a[j] = a[i];
	    }
	    System.out.print( a[i] + " " );
	}
    }
}