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.lang.reflect.Array;
import java.math.BigInteger;
import java.util.*;

import static java.lang.Math.*;

public class Main {
    BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
    StringTokenizer st = new StringTokenizer("");
    PrintWriter pw = new PrintWriter(System.out);

    int nextInt() throws IOException {
        return Integer.parseInt(next());
    }

    String next() throws IOException {
        if (!st.hasMoreTokens()) {
            st = new StringTokenizer(br.readLine());
        }
        return st.nextToken();
    }

    long nextLong() throws IOException {
        return Long.parseLong(next());
    }

    public static void main(String[] args) throws IOException {
        new Main().run();
    }

    void run() throws IOException {
        int n;
        n = nextInt();
        boolean[] prost = new boolean[n + 1];
        for (int i = 1; i < n + 1; i++) {
            int count = 0;
            for (int j = 1; j <= sqrt(i); j++) {
                if (i % j == 0) {
                    count += 2;
                }
            }
            if (count == 2) {
                prost[i] = true;
            }
        }
        int[] ans = new int[n + 1];
        int t = 1;
        for (int i = 2; i <= n; i++) {
            if (prost[i]) {
                ans[i] = t;
                t++;
            } else {
                for (int j = 1; j <= sqrt(i); j++) {
                    if (i % j == 0 && j != 1) {
                        ans[i] = ans[j];
                        break;
                    }
                }
            }
        }
        for (int i = 2; i < ans.length; i++) {
            System.out.print(ans[i] + " ");
        }
        pw.close();
    }
}