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 EhabandaSpecialColoringProblem {

	public static void main(String[] args) throws IOException, FileNotFoundException {
		BufferedReader in = new BufferedReader(new InputStreamReader(System.in));
		//BufferedReader in = new BufferedReader(new FileReader("EhabandaSpecialColoringProblem.in"));
		// INPUT //

		int n = Integer.parseInt(in.readLine());  
		ArrayList<Integer> a = new ArrayList<>();

		int numprimes = 0;
		for (int i = 2; i <= n; i++) {
			int b = smallestprime(i);
			if (b == -1) {
				numprimes++;
				a.add(numprimes);
			}
			else a.add(a.get(b-2));
		}
			
		
		in.close();

		for (int i = 0; i < a.size(); i++) {
			System.out.print(a.get(i) + " ");
		}

	}

	public static int smallestprime(int a) {
		// finds the smallest prime factor
		// if a is prime, returns -1
		
		for (int i = 2; i <= Math.sqrt(a); i++) {
			if (a % i == 0) return i;
		}
		return -1;
	}
	
}