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:
# 1 2 1 3 1 4 1 5 1  6
# 2 3 4 5 6 7 8 9 10 11

simp = [2]
n = int(input())
# n = 10 ** 5
arr = [-1] * (n + 1)
arr[2] = 1
curr = 2
for i in range(3, n + 1):
    for s in simp:
        if s > i ** 0.5:
            simp.append(i)
            arr[i] = curr
            curr += 1
            break
        elif (i / s).is_integer():
            arr[i] = arr[s]
            break

print(*arr[2:])