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 C {

	public static void main(String[] args) throws Exception{
		BufferedReader f = new BufferedReader(new InputStreamReader(System.in));
		PrintWriter out = new PrintWriter(new BufferedWriter(new OutputStreamWriter(System.out)));
		
		
		int n = Integer.parseInt(f.readLine());
		
		int[] dp = new int[n+5];
		int counter = 1;
		for(int i = 2; i <= n; i ++) {
			int smallest_prime_factor = i;
			for(int j = 2; j <= Math.sqrt(i); j ++) {
				if(i % j == 0) {
					smallest_prime_factor = j;
					break;
				}
			}
			
			if(smallest_prime_factor == i) {
				dp[i] = counter ++;
			}
			else {
				dp[i] = dp[smallest_prime_factor];
			}
		}
		
		for(int i = 2; i <= n; i ++) {
			out.print(dp[i] + " ");
		}
		
		out.close();

	}

}