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.*;

public class C {
    public static void main(String[] args) throws IOException {
        Scanner f = new Scanner(System.in);
        PrintWriter out = new PrintWriter(new OutputStreamWriter(System.out));

        int n = f.nextInt();
        int[] output = new int[n + 1];
        List<Integer> primes = Sieve(n);
        for (int i=0; i<primes.size(); ++i) {
            int p = primes.get(i);
            int mult = n / p;
            for (int j=1; j<=mult; ++j) {
                output[p * j] = i + 1;
            }
        }
        for (int i=2; i<=n; ++i) {
            out.print(output[i] + " ");
        }
        out.close();
    }

    static List<Integer> Sieve(int n) {
        List<Integer> primes = new ArrayList<>();
        Boolean[] arr = new Boolean[n + 1];

        for (int l = 0; l < n + 1; l++) {
            arr[l] = true;
        }

        arr[0] = false;
        arr[1] = false;

        for (int p = 2; p * p < n + 1; p++) {
            for (int k = p * p; k < n + 1; k += p) {
                arr[k] = false;
            }
        }

        for (int j = 2; j < n + 1; j++) {
            if (arr[j]) {
                primes.add(j);
            }
        }

        return primes;
    }

    static class Scanner {
        StringTokenizer st;
        BufferedReader br;

        public Scanner(InputStream s) {
            br = new BufferedReader(new InputStreamReader(s));
        }

        public Scanner(String s) throws FileNotFoundException {
            br = new BufferedReader(new FileReader(s));
        }

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

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

        public String nextLine() throws IOException {
            return br.readLine();
        }

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

        public double nextDouble() throws IOException {
            return Double.parseDouble(next());
        }

        public boolean ready() throws IOException {
            return br.ready();
        }
    }
}