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 as m
import collections as clt

number_of_elements = 0
arr = []

def Input(number_of_elements):
    number_of_elements = int(input())

    return number_of_elements

def Is_prime(number):
    
    for index in range(2,int(m.sqrt(number)+1)):
        if number % index == 0:
            return 0

    return 1

def Smallest_divisor(number):
    # result is always different one
    for index in range(2,int(m.sqrt(number)+1)):
        if number % index == 0:
            return index

    return number

def Processing(number_of_elements):
    arr.append(0)
    arr.append(0)

    count = 0;

    for index in range(2, number_of_elements + 1):
        if Is_prime(index):
            count += 1
            arr.append(count)
        else:
            arr.append(0)

    for index in range(2, number_of_elements + 1):
        if arr[index] == 0:
            arr[index] = arr[Smallest_divisor(index)]

    for index in range(2, number_of_elements + 1):
        print(arr[index], end = " ")


if __name__ == "__main__":
    number_of_elements = Input(number_of_elements)
    number_of_elements = Processing(number_of_elements)