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.lang.*;
import java.io.*;

/* Name of the class has to be "Main" only if the class is public. */
public class Main
{
	public static void main (String[] args) throws java.lang.Exception
	{
		// your code goes here
		FastReader sc=new FastReader();
		int n=sc.I();
		int[] a=new int[n+1];
		int c=0;
		for(int i=2;i<=n;i++)
		{
		    if(a[i]==0){
		    c++;
		    for(int j=i;j<=n;j+=i)
		    if(a[j]==0)
		    a[j]=c;}
		}
		for(int i=2;i<=n;i++)
		System.out.print(a[i]+" ");
	 }
	 
	 
	  static class FastReader 
    { 
        BufferedReader br; 
        StringTokenizer st; 
  
        public FastReader() 
        { 
            br = new BufferedReader(new
                     InputStreamReader(System.in)); 
        } 
  
        String next() 
        { 
            while (st == null || !st.hasMoreElements()) 
            { 
                try
                { 
                    st = new StringTokenizer(br.readLine()); 
                } 
                catch (IOException  e) 
                { 
                    e.printStackTrace(); 
                } 
            } 
            return st.nextToken(); 
        } 
  
        int I() 
        { 
            return Integer.parseInt(next()); 
        } 
  
        long L() 
        { 
            return Long.parseLong(next()); 
        } 
  
        double D() 
        { 
            return Double.parseDouble(next()); 
        } 
  
        String nextLine() 
        { 
            String str = ""; 
            try
            { 
                str = br.readLine(); 
            } 
            catch (IOException e) 
            { 
                e.printStackTrace(); 
            } 
            return str; 
        } 
    } 
    static int gcd(int a,int b)
		{
		    if(a%b==0)
		    return b;
		    return gcd(b,a%b);
		}
	static float power(float x, int y) 
    { 
        float temp; 
        if( y == 0) 
            return 1; 
        temp = power(x, y/2);  
          
        if (y%2 == 0) 
            return temp*temp; 
        else
        { 
            if(y > 0) 
                return x * temp * temp; 
            else
                return (temp * temp) / x; 
        } 
    } 
    static long pow(int a,int b)
    {
        long result=1;
        if(b==0)
        return 1;
        long x=a;
        while(b>0)
        {
            if(b%2!=0)
            result*=x;
            
            x=x*x;
            b=b/2;
        }
        return result;
    }
    
    static ArrayList<Integer> sieveOfEratosthenes(int n) 
    { 
        ArrayList<Integer> arr=new ArrayList<Integer>();
        boolean prime[] = new boolean[n+1]; 
        for(int i=2;i<n;i++) 
            prime[i] = true; 
          
        for(int p = 2; p*p <=n; p++) 
        { 
            if(prime[p] == true) 
            { 
                arr.add(p);
                for(int i = p*p; i <= n; i += p) 
                    prime[i] = false; 
            } 
        } 
        return arr;
    } 
}