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())
P = [2]
for k in range(3,N+1):
    f = 1
    for l in range(2,int(math.sqrt(k))+1):
        if k % l == 0:
            f = 0
            break
    if f==1:
        P.append(k)

a = [0 for k in range(N+1)]
t = 0
for p in P:
    t += 1
    s = 0
    while (s+1)*p <= N:
        s += 1
        if a[s*p] == 0:
            a[s*p] = t

print(*a[2:N+1], sep=" ")