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.*;

/**
 * @author kenpen
 */
public class EhabColor
{
    public static void main(String... args)
    {
        int n = getInt();
        System.out.println(arrayToString(colorIt(n)));
    }

    static int[] primes;
    static int count = 0;

//    static void primes(int n) {
//        boolean [] isPrime = new boolean[n + 1];
//        for (int i = 2 ; i <= n ; ++i) isPrime[i] = true;
//        for (int i = 2; i <= n; ++i) {
//            if (isPrime[i]) {
//                count++;
//                int j = i + i;
//                while (j <= n) {
//                    isPrime[j] = false;
//                    j += i;
//                }
//            }
//        }
//        primes = new int[count];
//        int c = 0;
//        for (int i = 2; i <= n; ++i) {
//            if (isPrime[i]) primes[c++] = i;
//        }
//    }

    static int[] colorIt(int n) {
        int[] colors = new int[n - 1];
        int color = 1;
        for (int i = 2; i <= n; ++i) {
            if (colors[i - 2] == 0) {
                colors[i - 2] = color;
                long j = (long) i * i;
                while (j <= n) {
                    colors[(int) j - 2] = color;
                    j += i;
                }
                color++;
            }
        }
        return colors;
    }

    // ===== Printing code ===== 
    static StringBuilder buf = new StringBuilder();
    static int bufSize = 5000;

    static void print(String s)
    {
        print(s, false);
    }

    static void print(String s, boolean newLine)
    {
        buf.append(s);
        if (newLine) {
            buf.append("\n");
        }
        if (buf.length() >= bufSize) {
            System.out.print(buf);
            buf.delete(0, buf.length());
        }
    }

    static void flush()
    {
        System.out.print(buf);
        buf.delete(0, buf.length());
    }

    static String arrayToString(int[] arr) {
        StringBuilder sb = new StringBuilder();
        for (int a : arr) sb.append(a).append(" ");
        if (arr.length > 0) sb.deleteCharAt(sb.length() - 1);
        return sb.toString();
    }

    // ===== INPUT TAKING CODE ==== 
    static BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
    static StringTokenizer st;

    static void checkSt()
    {
        if (st == null || !st.hasMoreTokens()) {
            try {
                st = new StringTokenizer(br.readLine());
            } catch (IOException e) {
                System.out.println("Error parsing input");
            }
        }
    }

    static int getInt()
    {
        checkSt();
        return Integer.valueOf(st.nextToken());
    }

    static int getLong()
    {
        checkSt();
        return Integer.valueOf(st.nextToken());
    }

    static long getNewLineLong()
    {
        try {
            return Long.valueOf(br.readLine());
        } catch (IOException e) {
            System.out.println("Error parsing input");
            return 0;
        }
    }

    static int getNewLineInt()
    {
        try {
            return Integer.valueOf(br.readLine());
        } catch (IOException e) {
            System.out.println("Error parsing input");
            return 0;
        }
    }

    static char getChar()
    {
        checkSt();
        return st.nextToken().charAt(0);
    }

    static String getStr()
    {
        checkSt();
        return st.nextToken();
    }

}