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.io.*;
import java.util.*;
import java.text.*;
import java.math.*;
import java.util.regex.*;

public class Solution 
{
	static class InputReader
	{
	    private final InputStream stream;
	    private final byte[] buf = new byte[8192];
	    private int curChar, snumChars;

	    public InputReader(InputStream st) {
	      this.stream = st;
	    }

	    public int read() {
	      if (snumChars == -1)
	        throw new InputMismatchException();
	      if (curChar >= snumChars) {
	        curChar = 0;
	        try {
	          snumChars = stream.read(buf);
	        } catch (IOException e) {
	          throw new InputMismatchException();
	        }
	        if (snumChars <= 0)
	          return -1;
	      }
	      return buf[curChar++];
	    }

	    public int nextInt() {
	      int c = read();
	      while (isSpaceChar(c)) {
	        c = read();
	      }
	      int sgn = 1;
	      if (c == '-') {
	        sgn = -1;
	        c = read();
	      }
	      int res = 0;
	      do {
	        res *= 10;
	        res += c - '0';
	        c = read();
	      } while (!isSpaceChar(c));
	      return res * sgn;
	    }

	    public long nextLong() {
	      int c = read();
	      while (isSpaceChar(c)) {
	        c = read();
	      }
	      int sgn = 1;
	      if (c == '-') {
	        sgn = -1;
	        c = read();
	      }
	      long res = 0;
	      do {
	        res *= 10;
	        res += c - '0';
	        c = read();
	      } while (!isSpaceChar(c));
	      return res * sgn;
	    }

	    public int[] nextIntArray(int n) {
	      int a[] = new int[n];
	      for (int i = 0; i < n; i++) {
	        a[i] = nextInt();
	      }
	      return a;
	    }

	    public String readString() {
	      int c = read();
	      while (isSpaceChar(c)) {
	        c = read();
	      }
	      StringBuilder res = new StringBuilder();
	      do {
	        res.appendCodePoint(c);
	        c = read();
	      } while (!isSpaceChar(c));
	      return res.toString();
	    }

	    public String nextLine() {
	      int c = read();
	      while (isSpaceChar(c))
	        c = read();
	      StringBuilder res = new StringBuilder();
	      do {
	        res.appendCodePoint(c);
	        c = read();
	      } while (!isEndOfLine(c));
	      return res.toString();
	    }

	    public boolean isSpaceChar(int c) {
	      return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
	    }

	    private boolean isEndOfLine(int c) {
	      return c == '\n' || c == '\r' || c == -1;
	    }
	}
   	public static class pair implements Comparable<pair>
    {
        int first;
        int second;
        public pair(int a,int b)
        {
            this.first = a;
            this.second = b;
        }
        public int compareTo(pair u)
        {
            return (u.first - u.second) - (first - second);
        }
    }
    public static long gcd(long a,long b)
    {
        if(b == 0)
            return a;
        return gcd(b,a%b);
    }
    public static ArrayList<Integer> sieve(int[] lps,int n)
	{
		ArrayList<Integer> arr = new ArrayList<>();
		for(int i = 2;i <= n;i++)
		{
			if(lps[i] == 0)
			{
				lps[i] = i;
				arr.add(i);
			}
			for(int j = 0;j < arr.size() && arr.get(j) <= lps[i] && i*arr.get(j) <= n;j++)
				lps[i*arr.get(j)] = arr.get(j);
		}
		return arr;
	}
    public static void main(String[] args) throws Exception
    {
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        PrintWriter out = new PrintWriter(System.out);
       	int n = Integer.parseInt(br.readLine());
        int count = 1;
        int[] lps = new int[n + 1];
        ArrayList<Integer> primes = sieve(lps, n);
        int[] ans = new int[n + 1];
        for(int i = 0; i < primes.size(); i++)
        {
        	//System.out.println(primes.get(i));
        	int a = primes.get(i);
        	for(int j = a; j <= n; j += a)
        		ans[j] = count;
        	count++;
        }
        for(int i = 2; i <= n; i++)
        {
        	out.print(ans[i] + " ");
        }
        out.println();
       	out.close(); 
    }	
}