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.*;

import static java.lang.Math.*;

public class C {
    public static void main(String[] args) throws Exception {
        Scanner in = new Scanner(System.in);
        PrintWriter pw = new PrintWriter(System.out);
        int n = in.nextInt();
        int a[] = solve(n);
        for (int i = 2; i <= n; i++) {
            pw.print(a[i] + " ");
        }
        pw.println();
        pw.close();
    }

    static int[] solve(int n) {
        int a[] = new int[n + 1];
        int x = 0;
        for (int i = 2; i <= n; i++) {
            if (a[i] != 0) continue;
            a[i] = ++x;
            for (int j = i; j <= n; j += i) {
                a[j] = a[i];
            }
        }
        return a;
    }


    static void debug(Object... obj) {
        System.err.println(Arrays.deepToString(obj));
    }
}