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 math


def array(dt=int):
    return map(dt, raw_input().split())


M = 10 ** 5

P = [-1 for _ in range(10 ** 5 + 1)]

P[2] = 2

for i in range(4, M + 1, 2):
    P[i] = 2

for i in range(3, int(math.sqrt(M + 1)) + 1):
    if P[i] == -1:
        P[i] = i
        for j in range(i * i, M + 1, i):
            P[j] = i

for i in range(2, M + 1):
    if P[i] == -1:
        P[i] = i


def factors(k):
    f = 0
    while k > 1:
        k = k // P[k]
        f += 1
    return f


# for i in range(2, 12):
#     print i, factors(i)


n = input()
C = [-1 for i in range(n + 1)]
c = 1
for i in range(2, n + 1):
    if P[i] == i:
        C[i] = c
        c += 1
    else:
        C[i] = C[P[i]]

print " ".join(map(str, C[2:]))