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:
from bisect import bisect_left#,insort_left
n = int(input())
a = [None]*(n-1)
a[0] = 1
prime = [2]
for i in range(3,n+1):
    flag = False
    i_sqrt = int(i**0.5)
    i2 = bisect_left(prime,i_sqrt)
    for pi,p in enumerate(prime[:i2+1]):
        if i%p==0:
            flag = True
            break
    #pi = bisect_left(prime,i)
    if flag:
        a[i-2]=pi+1
    else:
        a[i-2]=len(prime)+1
        prime.append(i)
print(*a)