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
n = int(input())

primes = {2: True}
for v in range(3, n + 1):
    a = 2
    b = False
    while a <= int(math.sqrt(v) + 1):
        if v % a == 0:
            b = True
            break
        a += 1
    if not b:
        primes[v] = True

ans = [0] * (n + 1)
for i, p in enumerate(primes):
    if p > (n + 1):
        break
    for j in range(0, n + 1, p):
        if ans[j] == 0:
            ans[j] = i + 1

ans = ans[2:]
print(" ".join([str(v) for v in ans]))