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.ArrayList;
import java.util.Scanner;

public class EhabColor {

    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        int n = sc.nextInt();
//        int[] primes = sieve(n);
        int k = 1;
        int[] ret = new int[n+1];
        for(int i=2; i<=n; i++) {
            if(ret[i] == 0) {
                for(int j=i; j<=n; j+=i) {
                    if(ret[j] == 0) {
//                        ret[j] = primes[k];
                        ret[j] = k;
                    }
                }
                k++;
            }
        }
        for(int i=2; i<=n; i++) {
            System.out.print(ret[i] + " ");
        }
    }

    public static int[] sieve(int n) {
        int[] toCheck = new int[n+1];
        for(int i=2; i<=n; i++) {
            if(toCheck[i] == 0) {
                for(int j=i+i; j<=n; j+=i) {
                    toCheck[j] = 1;
                }
            }
        }
        ArrayList<Integer> primes = new ArrayList<>();
        primes.add(1);
        for(int i=2; i<=n; i++) {
            if(toCheck[i] == 0){
                primes.add(i);
            }
        }
        int[] ret = primes.stream().mapToInt(i->i).toArray();
        return ret;
    }
}