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 PYTHON):

Solution:
from sys import stdout

def min_prime(num):
	for k in xrange(len(primes)):
		if num % primes[k] == 0:
			return primes[k]

n = int(raw_input())

criv = 300000 * [True]
primes = []
Max = int (pow(300000, 0.5) + 1)

for k in xrange(2, Max):
	if criv[k]:
		primes.append(k)
		for l in xrange(k * k, 300000, k):
			criv[l] = False
			
ar = [1] * (n-1)
		
		
i = 2
dici = {}
for k in xrange(1, n-1, 2):
	
	if criv[k + 2]:
		dici[k + 2] = i
		ar[k] = dici[k + 2]
		i += 1
	else:
		menor_primo = min_prime(k+2)
		ar[k] = dici[menor_primo]
		
	
for k  in xrange(len(ar)):
	ar[k] = str(ar[k])

stdout.write( " ".join(ar))