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.HashMap;
import java.util.Map;
import java.util.Scanner;

public class C1174 {

    public static void main(String[] args) {
        Scanner in = new Scanner(System.in);
        int N = in.nextInt();
        int[] A = new int[N+1];
        int nextLabel = 1;
        Map<Integer,Integer> map = new HashMap<>();
        for (int n=2; n<=N; n++) {
            int minD = n;
            for (int d=2; d*d<=n; d++) {
                if (n%d == 0) {
                    minD = d;
                    break;
                }
            }
            Integer label = map.get(minD);
            if (label == null) {
                label = nextLabel++;
                map.put(minD, label);
            }
            A[n] = label;
        }
        StringBuilder output = new StringBuilder();
        for (int n=2; n<=N; n++) {
            output.append(A[n]).append(' ');
        }
        System.out.println(output);
    }

}