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 Main {
	public static void main(String[] args) {
		try(Scanner input = new Scanner(System.in)){
			int n = input.nextInt();
			input.nextLine();
			boolean prime[] = new boolean[n+1];
			for(int i =0; i < prime.length;i++) {
				prime[i] = true;
			}
			prime[0] = false;
			prime[1] = false;
			sieveOfEratosthenes(squareRoot(n), prime);
			System.out.println(specialColoring(n,prime));
		}
	}
	private static void sieveOfEratosthenes(int n, boolean[] prime) { 
        for(int p = 2; p <=n; p++) {
            if(prime[p] == true) { 
                for(int i = p*p; i < prime.length; i += p) {
                    prime[i] = false;
                }
            } 
        } 
    }
	private static int squareRoot(int x) {
		int root = (int) Math.pow(x, 0.5) - 1;
		if(root*root == x) {return root;}
		root++;
		if(root*root>x) {
			return root-1;
		}
		if(root*root == x) {return root;}
		root++;
		if(root*root>x) {
			return root-1;
		}
		if(root*root == x) {return root;}

		return -1;
	}
	private static String specialColoring(int n, boolean[] prime) {
		int[] coloring = new int[n-1];
		int number = 0;
		for(int i = 2; i <= n;i++) {
			if(prime[i]) {
				number++;
  				coloring[i-2] = number;
				int j = 2;
				while(i*j<=n) {

					coloring[i*j - 2] = number;
					j++;
				}
			}
		}
		StringBuilder output = new StringBuilder();
		for(int s = 0; s <n-1;s++) {
			if(s==n-2) {
				output.append(coloring[s]);
			}else {
				output.append(coloring[s]);
				output.append(" ");

			}
		}
		return output.toString();
	}
}