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:
def isPrime(n):
	# a prime(except 2 or 3) is of the form 6k-1 or 6k+1
	if n == 2 or n == 3:
		return True
	if n % 2 == 0 or n % 3 == 0:
		return False
	i = 5
	w = 2
	sqN = int(pow(n, .5))
	while i <= sqN:
		if n % i == 0:
			return False
		i += w
		w = 6 - w
	return True

n = int(input().strip())
arr = [0]*(n+1)
c = 1
for i in range(2, n+1):
	if isPrime(i):
		arr[i] = c
		for j in range(i+i, n+1, i):
			if not arr[j]:
			   arr[j] = c
		c += 1
print(*arr[2:])