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:
entrada = int(raw_input())
array = [''] * 100050
valor = 1
teste = 0
cont = 0
i = 2

def verifica(array,valor,teste,cont):
	valor  = 1
	while(valor*teste <= entrada):
		if not(array[teste*valor]):
			array[teste*valor] = cont
		valor += 1
	return True
	
while(i <= entrada):
    if not(array[i]):
        cont += 1
        teste = i
        verifica(array,valor, teste, cont)
    i += 1

result = ''    

for i in range(2,entrada):
    result += str(array[i]) + " "
result += str(array[entrada])

print result