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:
/* package codechef; // don't place package name! */
// package rishabh;
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();
// 		constructST(a,n);RMQ(n, qs, qe)
        // sieveOfEratosthenes();
		int n=sc.nextInt(),a[]=new int[n+3],value=1;
		Arrays.fill(a, 0);
		
		for(int i=2; i<=n; i++) {
			if(a[i]!=0) {
				continue;
			}
			a[i]=value;
			for(int j=i; j<=n; j+=i) {
				a[j]=value;
			}
			value++;
		}
		for(int i=2; i<=n; i++)
			System.out.print(a[i]+" ");
		System.out.println();
	}
    static int lower_bound(long a[],long x){
	    int n=a.length,low=0,high=n-1,res=-1;
	    while(low<=high){
	    	int mid=(low+high)>>1;
         
	    	if(a[mid]>=x){
	    		res=mid;
	    		high=mid-1;
	    	}
	    	else 
	    		low=mid+1;
	    }
	    return res;
	}
    static int upper_bound(int a[],int x){
         int n=a.length,low=0,high=n-1,res=-1;
         while(low<=high){
             int mid=(low+high)>>1;
             if(a[mid]<=x){
                 res=mid;low=mid+1;
             }
             else 
                 high=mid-1;
         }
         return res;
     }
    //   static int MAX=1000001;boolean prime[] = new boolean[MAX]; 
      
    //   static void sieveOfEratosthenes() { 
    //       for(int m9=0;m9<MAX;m9++) prime[m9]=true;
    //     for(int p = 2; p*p <=n; p++) { 
    //         if(prime[p] == true) 
    //         { 
    //             // Update all multiples of p 
    //             for(int i = p*2; i <= n; i += p) 
    //                 prime[i] = false; 
    //         } 
    //     } 
    //   }
      
      static long modexpo(long x,long n,long m){
        if(n==0)
            return 1;
        else if(n%2==0)
            return (modexpo(((x%m)*(x%m))%m,n/2,m))%m;
        else
            return ((x%m)*((modexpo(((x%m)*(x%m))%m,(n-1)/2,m))%m))%m;
      } 
       static int gcd(int a,int b){
           if(b==0)
              return a;
           else 
              return gcd(b,a%b);
       }
       static long gcd(long a,long b){
           if(b==0)
              return a;
           else 
              return gcd(b,a%b);
       }
	 static class FastReader{
          BufferedReader in;
          StringTokenizer st;
          public FastReader(){
              in=new BufferedReader(new InputStreamReader(System.in));
          }
          String next(){
              while(st==null || !st.hasMoreElements()){
                  try{
                      st=new StringTokenizer(in.readLine());
                  }
                  catch(IOException e){
                      e.printStackTrace();
                  }
               }
               return st.nextToken();
            }
            int nextInt(){
                return Integer.parseInt(next());
            }
            long nextLong(){
                return Long.parseLong(next());
            }
            double nextDouble(){
                return Double.parseDouble(next());
            }
            String nextLine(){
            String str19 = "";
            try{
                str19 = in.readLine();
            }
            catch (IOException e){ 
                e.printStackTrace();
             }
            return str19;
        }
      }    
}