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.*;
import java.math.*;

public class CP{
  public static OutputStream out=new BufferedOutputStream(System.out);
  static Scanner sc=new Scanner(System.in);
  static long mod=1000000007l;
  static int INF=1000000;

  //nl-->neew line; //l-->line;  //arp-->array print;  //arpnl-->array print new line
  public static void nl(Object o) throws IOException{out.write((o+"\n").getBytes()); }
  public static void l(Object o) throws IOException{out.write((o+"").getBytes());}
  public static void arp(int[] o) throws IOException{for(int i=0;i<o.length;i++) out.write((o[i]+" ").getBytes()); out.write(("\n").getBytes());}
  public static void arpnl(int[] o) throws IOException{for(int i=0;i<o.length;i++) out.write((o[i]+"\n").getBytes());}
  public static void scanl(long[] a,int n) {for(int i=0;i<n;i++) a[i]=sc.nextLong();}
  public static void scani(int[] a,int n) {for(int i=0;i<n;i++) a[i]=sc.nextInt();}
  public static void scan2D(int[][] a,int n,int m) {for(int i=0;i<n;i++) for(int j=0;j<m;j++) a[i][j]=sc.nextInt();}
  //
  static long cnt;
  static TreeSet<Integer> ans;
  static int n,m;
  static boolean[][] dp,vis;
  static HashMap<Pair,Boolean> arrl;
  static Stack<Integer> stk;
  static Queue<Integer> queue;
  static HashSet<Integer> mtrnode;
  static ArrayList<Integer> arrlans;


  public static void main(String[] args) throws IOException{
    long sttm=System.currentTimeMillis();
    long mod=1000000007l;

    int n=sc.nextInt();
    int[] a=new int[n+1];
    int cnt=1;
    for(int i=2;i<=n;i++){
        if(a[i]==0){
            for(int j=i;j<=n;j+=i){
                a[j]=cnt;
            }
            cnt++;
        }
    }
    for(int i=2;i<=n;i++){
        l(a[i]+" ");
    }
    nl("");

    out.flush();
  }

}

class Pair{
  int x,y;
  Pair(int x,int y){
    this.x=x;
    this.y=y;
  }
}