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
val_dict = dict()
def smallest(n): 
    while n % 2 == 0: 
        return 2 
        n = n / 2 
    for i in range(3,int(math.sqrt(n))+1,2): 
        while n % i== 0: 
            return i
            n = n / i
    if n > 2: 
        return n
assign = 1
n = int(input())
for i in range(2, n+1):
    x= smallest(i)
    if x==i:
        val_dict[i]=assign
        assign+=1
    else:
        val_dict[i] = val_dict[x]
for k, v in val_dict.items():
    print(v, end = " ")