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.Arrays;
import java.util.Scanner;

public class Main {
	public static int MAX;
	public static boolean[] primes;
	public static int[] a;

	public static void main(String[] args) {
		Scanner s = new Scanner(System.in);
		MAX = s.nextInt();
		sieve();
		for (int i = 2; i <= MAX; i++) {
			System.out.print(a[i] + " ");
		}
	}

	public static void sieve() {
		primes = new boolean[MAX + 1];
		a = new int[MAX + 1];
		Arrays.fill(primes, true);
		primes[1] = false;
		primes[0] = false;
		int curr = 1;
		for (int i = 2; i <= MAX; i++) {
			if (!primes[i])
				continue;
			primes[i] = true;
			a[i] = curr;
			curr++;
			for (int j = i; j <= MAX / i; j++) {
				primes[i * j] = false;
				a[i * j] = a[i];
			}
		}
	}

	public static void printArray(int[] array) {
		for (int i : array) {
			System.out.print(i + " ");
		}
		System.out.println();
	}

	public static void printMatrix(int[][] matrix) {
		for (int[] is : matrix) {
			printArray(is);
		}
		System.out.println();
	}

	public static void printArray(long[] array) {
		for (long i : array) {
			System.out.print(i + " ");
		}
		System.out.println();
	}

	public static void printMatrix(long[][] matrix) {
		for (long[] is : matrix) {
			printArray(is);
		}
		System.out.println();
	}
}