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:
import math

def get_ans(n):
    ans = [1, ]
    max_num = 1
    for i in range(3, n + 1):
        cur_num = max_num + 1
        for j in range(2, int(math.sqrt(i)) + 1):
            if i % j == 0:
                cur_num = min(cur_num, ans[j - 2])
                
        max_num = max(max_num, cur_num)
        ans.append(cur_num) 

    return ans
    

def main():
    n = int(input())
    print(' '.join(str(i) for i in get_ans(n)))


if __name__ == '__main__':
    main()