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.BufferedReader;
import java.io.InputStreamReader;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Collections;
import java.util.StringTokenizer;

public class Main {
	final static long MOD = 1000000007L;
	public static void main(String[] args) {
		Reader in = new Reader();
		int n = in.nextInt();
		int[] ans = new int[n+1];
		int num = 2;
		for(int i = 2; i<=n; i++) {
			if(i%2==0) {
				ans[i] = 1;
			}else {
				if(ans[i]==0) {
					int cur = i;
					while(cur<n+1) {
						ans[cur] = num;
						cur+=i;
					}
					num++;
				}
			}
		}
		for(int i = 2; i<=n; i++) System.out.print(ans[i]+" ");
	}
	static int gcd(int a, int b) {
		 if (b==0) return a;
		  return gcd(b,a%b);
	}
	static class Reader {
		static BufferedReader br;
		static StringTokenizer st;
		private int charIdx = 0;
		private String s;

		public Reader() {
			this.br = new BufferedReader(new InputStreamReader(System.in));
		}

		public int[] na(int n) {
			int[] a = new int[n];
			for (int i = 0; i < n; i++)
				a[i] = nextInt();
			return a;
		}
		public double[] nd(int n) {
			double[] a = new double[n];
			for (int i = 0; i < n; i++)
				a[i] = nextDouble();
			return a;
		}
		public char nextChar() {
			if (s == null || charIdx >= s.length()) {
				if (st == null || !st.hasMoreTokens())
					try {
						readLine();
					} catch (Exception e) {
					}
				s = st.nextToken();
				charIdx = 0;
			}
			return s.charAt(charIdx++);
		}

		public long[] nl(int n) {
			long[] a = new long[n];
			for (int i = 0; i < n; i++)
				a[i] = nextLong();
			return a;
		}

		public char[] nca() {
			return next().toCharArray();
		}

		public String[] nS(int n) {
			String[] a = new String[n];
			for (int i = 0; i < n; i++)
				a[i] = next();
			return a;
		}

		public int nextInt() {
			if (st == null || !st.hasMoreTokens())
				try {
					readLine();
				} catch (Exception e) {
				}
			return Integer.parseInt(st.nextToken());
		}

		public double nextDouble() {
			if (st == null || !st.hasMoreTokens())
				try {
					readLine();
				} catch (Exception e) {
				}
			return Double.parseDouble(st.nextToken());
		}

		public Long nextLong() {
			if (st == null || !st.hasMoreTokens())
				try {
					readLine();
				} catch (Exception e) {
				}
			return Long.parseLong(st.nextToken());
		}

		public String next() {
			if (st == null || !st.hasMoreTokens())
				try {
					readLine();
				} catch (Exception e) {
				}
			return st.nextToken();
		}

		public static void readLine() {
			try {
				st = new StringTokenizer(br.readLine());
			} catch (Exception e) {
			}
		}
	}
}