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(n):
  if n == 2 or n == 3: return True
  if n < 2 or n%2 == 0: return False
  if n < 9: return True
  if n%3 == 0: return False
  r = int(n**0.5)
  f = 5
  while f <= r:
    #print '\t',f
    if n%f == 0: return False
    if n%(f+2) == 0: return False
    f +=6
  return True


import math
n = int(input())
c = 2
l = []
for i in range(n-1):
    #print(l)
    if i%2 == 0:
        l += [1]
    elif is_prime(i+2) or i == 1:
        l += [c]
        c+=1
    else:
        j = 2
        while (i+2)%j != 0:
            j+=1
        l += [l[j-2]]
        #print(j)
for x in l:
    print(x, end= ' ')

print()