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 Solution{

	public static void main(String args[])throws IOException{

		//BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
		
		Scanner in=new Scanner(System.in);
	
		int n=in.nextInt();

		int a[]=new int[n+1];

		int k=1;
		for(int i=2; i<=n; i++)
			if(a[i]==0){
				for(int j=i; j<=n; j+=i)
					a[j]=k;
				k+=1;
			}

		StringBuffer out=new StringBuffer();
		for(int i=2; i<=n; i++)
			out.append(a[i]+" ");

		System.out.println(out);
	}
}