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 PYTHON):

Solution:
import sys
range = xrange
input = raw_input

n = int(input())

big = 10**5+10
P = [1]*big
P[0] = P[1] = 0
biggest_factor = [0]*big
for i in range(big):
    if P[i]:
        biggest_factor[i] = i
        j = i + i
        while j<big:
            P[j] = 0
            biggest_factor[j] = i
            j += i

B = [0]*(n+1)
count = 1
for i in range(n+1):
    if P[i]:
        B[i] = count
        count += 1
    else:
        B[i] = B[biggest_factor[i]]

print ' '.join(str(b) for b in B[2:])