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:
def generate_primes(n):
    primes = [True for i in range(n+1)]
    p = 2
    while p * p <= n:
        if primes[p]:
            for i in range(p * 2, n+1, p):
                primes[i] = False
        p += 1

    prime_numbers = []
    for i in range(len(primes)):
        if primes[i]:
            prime_numbers.append(i)

    # 0, 1 not prime
    return prime_numbers[2:]


def run():
    n = int(input())

    primes = generate_primes(n)
    prime_hash = {}
    for number in primes:
        prime_hash[number] = True

    prime_counter = 1
    # this part is slow
    result = []
    for i in range(2, n+1):
        if i in prime_hash:
            result.append(prime_counter)
            prime_counter += 1
        else:
            for index, prime in enumerate(primes):
                if i % prime == 0:
                    result.append(index + 1)
                    break

    str_numbers = map(str, result)
    return ' '.join(str_numbers)


print(run())