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.ArrayList;
import java.util.List;
import java.util.Scanner;

public class Contest {

    //private static List<Integer> results = new ArrayList<>();
    //private static Map<Integer, List<Integer>> map = new HashMap<>();
    /**
     * @param args the command line arguments
     */
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        String line = sc.nextLine();
        //String line = "100000";
        String[] split = line.split(" ");

        int n = Integer.valueOf(split[0]);

        Integer[] arrayMap = new Integer[n + 1];
        for (int i = 0; i < arrayMap.length; i++) {
            arrayMap[i] = 0;
        }

        List<Integer> primeList = new ArrayList<>();

        outerloop:
        for (int i = 2; i <= n; i++) {
            if (isPrime(i)) {
                primeList.add(i);
                arrayMap[i] = primeList.indexOf(i) + 1;
            }
        }

        outerloop:
        for (int i = 2; i <= n; i++) {
            if (arrayMap[i] == 0) {
                for (Integer prime : primeList) {
                    if (i % prime == 0) {
                        arrayMap[i] = primeList.indexOf(prime) + 1;
                        continue outerloop;
                    }
                }
                throw new IllegalStateException("wtf?");
            }
        }

        doneArray(arrayMap);
    }

    public static boolean isPrime(int num) {
        if (num > 2 && num % 2 == 0) {
            //System.out.println(num + " is not prime");
            return false;
        }
        int top = (int) Math.sqrt(num) + 1;
        for (int i = 3; i < top; i += 2) {
            if (num % i == 0) {
                //System.out.println(num + " is not prime");
                return false;
            }
        }
        //System.out.println(num + " is prime");
        return true;
    }

    public static boolean CheckPrime(int numberToCheck) {
        int remainder;
        for (int i = 2; i <= numberToCheck / 2; i++) {
            remainder = numberToCheck % i;
            if (remainder == 0) {
                return false;
            }
        }
        return true;

    }

    /*private static boolean checkPresense(Integer i, Integer ai) {
        List<Integer> list = map.get(ai);
        for (Integer outer : list) {
            if (gcd(i, outer) == 1) {
                //System.out.println("gcd: " + String.valueOf(ai) + "/" + String.valueOf(outer));
                return true;
            }
        }
        return false;
    }*/

 /*private static int gcd(Integer a, Integer b) {
        int t;
        while (b != 0) {
            t = a;
            a = b;
            b = t % b;
        }
        return a;
    }*/

 /*private static void addToMap(Integer i, Integer ai) {
        if (map.get(ai) == null) {
            map.put(ai, new ArrayList<>());
        }
        map.get(ai).add(i);
    }*/
    private static void doneList(List<Integer> a) {
        StringBuilder builder = new StringBuilder("");
        for (int i = 0; i < a.size(); i++) {
            builder.append(a.get(i)).append(" ");
        }
        System.out.println(builder.toString().substring(0, builder.toString().length() - 1));
    }

    private static void doneArray(Integer[] a) {
        StringBuilder builder = new StringBuilder("");
        for (int i = 2; i < a.length; i++) {
            builder.append(a[i]).append(" ");
        }
        System.out.println(builder.toString().substring(0, builder.toString().length() - 1));
    }

    private static void done() {
        System.out.println("-1");
    }

    private static int lowerBound(int[] a, int low, int high, int element) {
        while (low < high) {
            int middle = low + (high - low) / 2;
            if (element > a[middle]) {
                low = middle + 1;
            } else {
                high = middle;
            }
        }
        return low;
    }

    private static int upperBound(int[] a, int low, int high, int element) {
        while (low < high) {
            int middle = low + (high - low) / 2;
            if (a[middle] > element) {
                high = middle;
            } else {
                low = middle + 1;
            }
        }
        return low;
    }

}