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.io.*;
import java.util.ArrayList;
import java.util.List;

public class Main {

    public static void main(String[] args) throws IOException {
        new Main().run();
    }

    private void run() throws IOException {
        
        BufferedReader reader = new BufferedReader(new InputStreamReader(System.in));
        int n = Integer.parseInt(reader.readLine());

        List<Integer> list = new ArrayList<>(n-1);
        List<Integer> primeNumbers = new ArrayList<>();
        primeNumbers.add(2); list.add(1);

        for (int i = 3; i <= n; i++) {
            int primeIndex = -1;
            for (int j = 0; j < primeNumbers.size(); j++) {
                if(i % primeNumbers.get(j) == 0){
                    primeIndex = j;
                    break;
                }
            }
            if(primeIndex == -1){
                primeNumbers.add(i);
                list.add(primeNumbers.size());
            }else{
                list.add(primeIndex+1);
            }
        }

        BufferedWriter writer = new BufferedWriter(new OutputStreamWriter(System.out));
        for (int val: list) {
            writer.write(val + " ");
        }
        writer.flush();

    }

}