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 PYTHON3):

Solution:
from sys import stdin
from collections import defaultdict
input = stdin.readline
# ~ T = int(input())
def is_prime(n):
	if n < 2:
		return False
	if n == 2:
		return True
	if n % 2 == 0:
		return False
	for i in range(3,n + 1):
		if i * i > n:
			break
		else:
			if n % i == 0:
				return False
	return True
T = 1
for t in range(1,T + 1):
	n = int(input())
	res = [0 for x in range(n + 2)]
	count = 1
	for i in range(2,n + 1):
		if is_prime(i):
			res[i] = count
			count += 1
			for j in range(i * i,n + 1,i):
				res[j] = res[i]
	for i in range(2,n + 1):
		print(res[i],end = " ")