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 com.example.programmingpractice;

import java.io.BufferedReader;
import java.io.InputStreamReader;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Comparator;
import java.util.HashMap;
import java.util.HashSet;
import java.util.List;
import java.util.Scanner;

public class CodeforcesNT {

    public static void main (String[] args) throws Exception{
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        String[] inputs = br.readLine().trim().split(" ");
        int n = Integer.parseInt(inputs[0]);
        int[] arr = new int[n+1];
        int num = 1;
        for(int i = 2; i<=n; i++) {
            if(arr[i] == 0) {
                for (int j = 1; i * j <= n; j++) {
                    if (arr[i * j] == 0) arr[i * j] = num;
                }
                num++;
            }

        }
        StringBuilder ans = new StringBuilder();
        for(int i = 2; i<n; i++) ans.append(arr[i]).append(' ');
        ans.append(arr[n]);
        System.out.println(ans);
    }
}