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 collections, heapq, math, sys

n= int(sys.stdin.readline().rstrip())

isPrime = [True for _ in range(n+1)]
vals = [1 for _ in range(n+1)]
curr = 1
for i in range(2, n+1):
    j = i * i
    if isPrime[i]:
        vals[i] = curr
        for k in range(j, n+1, i):
            isPrime[k] = False
            vals[k] = curr
        curr += 1

for i in range(2, n+1):
    sys.stdout.write(str(vals[i]) + ' ')