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
def isPrime(n):
    l = 0
    for i in range(2,int(math.sqrt(n))+1):
        if(n%i==0):
            l+=1
            break
    if(l==0):
        return True
    else:
        return False
def lowest_divisor(n):
    for i in range(2,int(math.sqrt(n))+1):
        if(n%i==0):
            return i
n = int(input())
a = [0]*(n-1)
p = 2
for i in range(len(a)):
    if(i%2==0):
        a[i] = 1
    else:
        if(isPrime(i+2)):
            a[i] = p
            p+=1
        else:
            k = lowest_divisor(i+2)
            a[i] = a[k-2]
print(*a)