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 B {

	static class Doit{

		static ArrayList<Integer> primes;

		public static void criba(int n) {

			primes = new ArrayList<>();

			boolean mark[] = new boolean[n + 1];

			for(int i = 2; i * i <= n; i++) {
				if(!mark[i]) {

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

						mark[j] = true;

					}	
				}
			}

			for(int i = 2; i <=n; i++) {
				if(!mark[i])primes.add(i);
			}

		}

		public void solve(InputReader in, PrintWriter out) {
			int n = Integer.parseInt(in.next());			

			criba(n);

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

			arr[1] = 1;

			int ind = 1;

			for(int w: primes) {

				for(int j = w; j <=n; j+= w) {
					arr[j] = ind;
				}

				ind++;		

			}


			for(int i = 2; i <= n; i++) {
				System.out.print(arr[i]+ " ");
			}

			System.out.println();


		}	
	}


	public static void main(String[] args) {
		InputStream inputStream = System.in;
		OutputStream outputStream = System.out;
		InputReader in = new InputReader(inputStream);
		PrintWriter out = new PrintWriter(outputStream);
		Doit solver = new Doit();
		solver.solve(in, out);
		out.close();
	}	

	static class InputReader {
		public BufferedReader reader;
		public StringTokenizer tokenizer;

		public InputReader(InputStream stream) {
			reader = new BufferedReader(new InputStreamReader(stream), 32768);
			tokenizer = null;
		}

		public String next() {
			while (tokenizer == null || !tokenizer.hasMoreTokens()) {
				try {
					tokenizer = new StringTokenizer(reader.readLine());
				} catch (IOException e) {
					throw new RuntimeException(e);
				}
			}
			return tokenizer.nextToken();
		}

	}
}