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:
n = int(input())
prime = [True for i in range(n + 1)] 
p = 2
while (p * p <= n): 
    if (prime[p] == True): 
        for i in range(p * 2, n + 1, p): 
            prime[i] = False
    p += 1
prime[0]= False
prime[1]= False
allp = []
for p in range(n + 1): 
    if prime[p]: 
        allp.append(p)
res = [1]*(n+1)
counter = 1
for elem in allp:
    i = 0
    while i <= n:
        res[i] = counter
        i += elem
    counter += 1
print(*res[2:])