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 math import ceil


def is_prime(num):
    sq = ceil(num ** (1/2))
    if num == 2:
        return True
    for i in range(2,sq+1):
        if num % i == 0:
            return False
    return True


def first_divisor(num):
    for i in range(2,num):
        if num % i == 0:
            return i


n = int(input())
counter = 0
lst_of_nums = []
for i in range(2, n+1):
    if is_prime(i):
        counter += 1
        print(counter, end=' ')
        lst_of_nums.append(counter)
    else:
        FD = first_divisor(i)
        print(lst_of_nums[FD - 2], end=' ')
        lst_of_nums.append(lst_of_nums[FD - 2])