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 find_divisor(n):
    sqrt = int(n ** 0.5)
    for i in range(2, sqrt +1):
        if n % i == 0:
            return i

def is_prime(n):
    sqrt = int(n ** 0.5)
    divisors = 0
    
    for i in range(1, sqrt + 1):
        if n % i == 0:
            divisors += 1

        if divisors > 1:
            return False

    return True   


n = int(input())

numbers = [i for i in range(2, n+1)]
result = [0] * len(numbers)
dic = {}
index = 1

for i in range(len(numbers)):
    if is_prime(numbers[i]):
        dic[numbers[i]] = index
        result[i] = str(index)
        index += 1
    else:
       result[i] = str(dic[find_divisor(numbers[i])])

print(' '.join(result))