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.*;

public class Codeforces1174C {

	public static void main(String[] args) throws IOException {
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
		StringTokenizer st = new StringTokenizer(br.readLine());
		int n = Integer.parseInt(st.nextToken());

		boolean[] isPrime = new boolean[n+1];
		for (int i = 1; i <= n; i++) {
			isPrime[i] = true;
		}
		
		for (int i = 2; i <= n; i++) {
			if (isPrime[i]) {
				for (int j = i; j <= (n/i); j++) {
					isPrime[i*j] = false;
				}
			}
		}
		
		int[] primeList = new int[n];
		primeList[0] = 1;
		int ctr = 1;
		for (int i = 2; i <= n; i++) {
			if (isPrime[i]) {
				primeList[ctr] = i;
				ctr++;
			}
		}

		int[] ans = new int[n+1];
		for (int i = 1; i < ctr; i++) {
			int prime = primeList[i];
			for (int j = 1; j <= (n/prime); j++) {
				ans[prime*j] = i;
			}
		}
		
		for (int i = 2; i <= n; i++) {
			System.out.print(ans[i] + " ");
		}
	}
}