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 Test{
	
	static int prime[]=   new int[100001];
	
	static void load(){
		
		prime[0] = 1;
		prime[1] = 1;
		
		for(int i=2;i<=Math.sqrt(prime.length);i++){
			if(prime[i] == 1){
				continue;
			}
			for(int j=2*i;j<prime.length;j=j+i){
				 prime[j] = 1;
			}
		}
	}
	public static void main(String args[]){
		load();
		Scanner s = new Scanner(System.in);
		int n = s.nextInt();
		int a[] = new int[n+1];
		int c = 1;
		for(int i=2;i<=n;i++){
			if(prime[i] == 0){
				a[i] = c++;
			}
		}
		
		for(int i=2;i<=n;i++){
			if(a[i] == 0){
				
				for(int j=2;j<=Math.sqrt(i);j++){
					if(i%j == 0){
						a[i] = a[j];
						break;
					}
				}
			}
		}
		
		for(int i=2;i<=n;i++){
			System.out.print(a[i]+" ");
		}
	}
}