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.*;
import java.text.DecimalFormat;

public class programA {
	public static int isprime(int n) {
		for(int i =2; i*i<=n;i++) {
			if(n%i == 0) {
				return(i);
			}
		}
		return(-1);
	}
	public static void main(String[] args) throws IOException {
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
		int n = Integer.parseInt(br.readLine());
		int arr[] = new int[n+1];
		int j = 2;
		for (int i = 2; i <= n; i++) {
			if (i % 2 == 0) {
				System.out.print("1 ");
				arr[i] = 1;
			}else {
				int g = isprime(i);
						if(g!=-1) {
							System.out.print(arr[g]+" ");
							arr[i] = arr[g];
						}else {
							System.out.print(j+" ");
							arr[i]=j;
							j++;
						}
			}
		}

	}
}