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.*;
import java.io.*;

public class C {
	public static void main(String[] args) {
		Scanner console = new Scanner(System.in);
		int n = console.nextInt();
		boolean[] isprime = new boolean[n + 1];
		Arrays.fill(isprime, true);
		isprime[0] = isprime[1] = false;
		for (int i = 2; i <= n; i++) {
			if (isprime[i] && i * i <= n) {
				if (i * i < 0)
					break;
				for (long j = (long) (i * i); j <= n; j += i) {
					isprime[(int) j] = false;
				}
			}
		}
		int[] ans = new int[n + 1];
		Arrays.fill(ans, -1);
		int cur = 1;
		for (int i = 2; i <= n; i++) {
			if (isprime[i]) {
				for (int j = i; j <= n; j += i) {
					ans[j] = cur;
				}
				cur++;
			}
		}
		for (int i = 2; i <= n; i++) {
			System.out.print(ans[i] + " ");
		}
	}
}