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 get_min_divisor(x):
    for i in range(2, int(pow(x, 1/2) + 1)):
        if x % i == 0:
            return i
    return 1


out = (n + 1) * [-1]

curr = 1
out[2] = curr
for i in range(3, n + 1):
    min_div = get_min_divisor(i)
    if out[min_div] == -1:
        curr += 1
        out[i] = curr
    else:
        out[i] = out[min_div]

print(' '.join([str(x) for x in out[2:]]))