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 main():
    buf = input()
    n = int(buf)
    prime_map = dict()
    a = []
    for i in range(2, n+1):
        first_prime = first_prime_factor(i)
        if first_prime not in prime_map:
            prime_map[first_prime] = len(prime_map)+1
        a.append(prime_map[first_prime])
    print(' '.join(list(map(str, a))))

def first_prime_factor(x):
    n = x
    i = 2
    while i * i <= n:
        if n % i == 0:
            return i
        i += 1
    return x

if __name__ == '__main__':
    main()