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.Arrays;
import java.util.Scanner;

public class P1174C {

    public static void main(String[] args) {

        Scanner in = new Scanner(System.in);
        // Scanner in = new Scanner(new File("input.txt"));
        int n = in.nextInt();

        int[] arr = new int[n + 1];
        arr[2] = 1;

        int[] primes = new int[10000];
        primes[0] = 2;
        int top = 0;

        int cur = 1;

        for (int i = 3; i <= n; i++) {

            boolean isPrime = true;

            for (int j = 0; j <= top; j++) {
                if (i % primes[j] == 0) {
                    arr[i] = arr[primes[j]];
                    isPrime = false;
                    break;
                }
            }

            if (isPrime) {
                primes[++top] = i;
                arr[i] = ++cur;
            }

        }

        Arrays.stream(arr).skip(2).forEach(System.out::println);

    }

}