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 is_prime(i):
    return True

def get_next_prime():
    i = 2
    while True:
        if is_prime(i):
            yield(i)
            i += 1

def run():
    n = eval(input())
    nums = [0] * (n-1)
    g = get_next_prime()
    current = next(g)
    last = current
    for i in range(2, n+1):
        j = i
        enter = False
        while j < n+1:
            if nums[j-2] == 0:
                enter = True
                last = current
                nums[j-2] = current
            j += i
        # last = current
        # print(i, nums)
        if enter:
            current = next(g)
    
    for i in range(n-1):
        if nums[i] == last:
            nums[i] = 1  

    print(' '.join(list(map(str, nums))))

if __name__ == '__main__':
    run()