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.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.Scanner;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 *
 * @author Akash
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        Scanner in = new Scanner(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        CEhabAndASpecialColoringProblem solver = new CEhabAndASpecialColoringProblem();
        solver.solve(1, in, out);
        out.close();
    }

    static class CEhabAndASpecialColoringProblem {
        public void solve(int testNumber, Scanner in, PrintWriter out) {
            int n = in.nextInt();
            n++;
            int a[] = new int[n];
            boolean primes[] = new boolean[n];
            for (int i = 0; i < n; i++) {
                primes[i] = true;
                a[i] = Integer.MAX_VALUE;
            }
            primes[1] = false;
            int k = 1;
            for (int i = 2; i < n; i++) {
                if ((i & 1) == 0) {
                    a[i] = 1;
                    continue;
                }
                if (primes[i]) {
                    k++;
                    a[i] = Math.min(a[i], k);
                    for (int j = 2 * i; j < n; j += i) {
                        a[j] = Math.min(a[j], k);
                        primes[j] = false;
                    }
                }
            }

            for (int i = 2; i < n; i++) {
                out.print(a[i] + " ");
            }
        }

    }
}