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_Ehab_and_a_Special_Coloring_Problem{
    
    @SuppressWarnings("unchecked")
    public static void main(String[] args) throws Exception{
        int n = in.readInt();
        int[] A = new int[n+1];
        int cval = 0;
        for(int i = 2; i*i <= n; i++){
            if(A[i] == 0){
                cval++;
                A[i] = cval;
                for(int j = i*i; j <= n; j+=i){
                    A[j] = cval;
                }
            }
        }

        for(int i = 2; i <= n; i++){
            if(A[i] == 0)
                A[i] = ++cval;
            System.out.print(A[i] +" ");
        }
    }

    static Inputer in;
    static {
        in = new Inputer();
    }

    static class Inputer{
        BufferedReader br;
        Inputer(){
            try{
                br = new BufferedReader(new InputStreamReader(System.in));
            }
            catch(Exception e){}
        }
        public int readInt() throws Exception{
            return Integer.parseInt(readLine());
        }
        public long readLong() throws Exception{
            return Long.parseLong(readLine());
        }
        public int[] readA(String delim) throws Exception{
            String[] s = readLine().split(delim);
            int[] A = new int[s.length];
            for(int i = 0; i < s.length; i++)
                A[i] = Integer.parseInt(s[i]);
            return A;
        }
        public int[] readA() throws Exception{
            String[] s = readLine().split("\\s+");
            int[] A = new int[s.length];
            for(int i = 0; i < s.length; i++)
                A[i] = Integer.parseInt(s[i]);
            return A;
        }
        public long[] readLA() throws Exception{
            String[] s = readLine().split("\\s+");
            long[] A = new long[s.length];
            for(int i = 0; i < s.length; i++)
                A[i] = Long.parseLong(s[i]);
            return A;
        }
        public String readLine() throws Exception{
            return br.readLine();
        }
        public int[] copyA(int[] A){
            int[] B = new int[A.length];
            for(int i= 0 ; i < A.length; i++)
                B[i] = A[i];
            return B;
        }
    }
    static void shuffle(int[] A){
        int n = A.length;
        Random rand = new Random();
        for(int t = 0; t < A.length; t++){
            int i1 = rand.nextInt(n);
            int i2 = rand.nextInt(n);
            int tmp = A[i1];
            A[i1] = A[i2];
            A[i2] = tmp;
        }
    }
    static class Pair{
        int first, second;
        Pair(){
        }
        Pair(int a, int b){
            first = a;
            second = b;
        }
        @Override
        public String toString() {
            return "{"+first+","+second+"}";
        }
    }
}