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:
N = int(input())
def prime_list(num):
    """
    This function returns a list of prime numbers less than natural number entered.
    :param num: natural number
    :return result:  List of primes less than natural number entered
    """
    prime_table = [True for _ in range(num+1)]
    i = 2
    while i ** 2 <= num:
        if prime_table[i]:
            j = i + i
            while j <= num:
                prime_table[j] = False
                j += i
        i += 1

    result = [i for i in range(num) if prime_table[i] and i >= 2]
    return result

ans = []
prime = prime_list(N+1)

def check(num, dic):
    for p in prime:
        if num % p == 0:
            return dic[p]

p_set = set(prime)
r_prime = list(reversed(prime))
inc = 2
res = dict()
for i in range(2, N+1):
    if i % 2 == 0:
        ans.append(1)
    else:
        if i in p_set:
            ans.append(inc)
            res[i] = inc
            inc += 1
        else:
            ans.append(check(i, res))
for a in ans:
    print(a, end=" ")
print()