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.BufferedReader;
import java.io.BufferedWriter;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.io.OutputStreamWriter;
import java.io.PrintWriter;
import java.util.Arrays;
import java.util.StringTokenizer;
/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 */
public class Main {
	public static void main(String[] args) {
		InputReader in = new InputReader(System.in);
		PrintWriter out = new PrintWriter(new BufferedWriter(new OutputStreamWriter(System.out)),true);
		TaskB solver = new TaskB();
		solver.solve(1, in, out);
		out.flush();
		out.close();
	}
}

class TaskB {
    public void solve(int testNumber, InputReader in, PrintWriter pw) {
    	boolean sieve[]=new boolean[100001];
    	Arrays.fill(sieve, true);
    	sieve[0]=false;
    	sieve[1]=false;
    	for(int i=2;i<=Math.sqrt(sieve.length);i++) {
    		if(sieve[i]){
    			for(int j=i*i;j<100001;j+=i) {
    				sieve[j]=false;
    			}
    		}
    	}
    	int n=in.nextInt();
    	int ans[]=new int[n+1];
    	Arrays.fill(ans, 0);
    	int temp=1;
    	for(int i=2;i<=n;i++) {
    		if(sieve[i]) {
    			ans[i]=temp;
    			temp++;
    		}
    	}
    	for(int i=2;i<=Math.sqrt(n);i++) {
    		if(sieve[i]) {
    			temp=ans[i];
    			for(int j=i*i;j<=n;j+=i) {
    				ans[j]=temp;
    			}
    			temp++;
    		}
    	}
    	for(int i=2;i<=n;i++) {
    		pw.print(ans[i]+" ");
    	}
    	
}
}
class Pair<A,B>{	
	A first;
	B second;
	Pair(A first,B second){
		this.first=first;
		this.second=second;
	}
}


class InputReader{
    BufferedReader br;
    StringTokenizer st;
    public InputReader(InputStream in){
        br=new BufferedReader(new InputStreamReader(in));
        st=null;
    }
    public String next(){
    while(st==null||!st.hasMoreTokens()){
        try{
            st=new StringTokenizer(br.readLine());
        }catch(IOException e){
            throw new RuntimeException(e);
        }
    }
   return st.nextToken();
    }
    public int nextInt(){
        return Integer.parseInt(next());
    }
    public long nextLong() {
    	return Long.parseLong(next());
    }
    public double nextDouble() {
    	return Double.parseDouble(next());
    }
}