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:
from math import ceil, sqrt
N = int(input())
Visited = [False] * (N+3)
Ans = [-1] * (N+3)
mark = 1
for i in range(2,int(ceil(sqrt(N)))+1):
    if(Visited[i]==False):
        Ans[i] = mark
        for j in range(2*i,N+3,i):
            if(Ans[j]==-1):
                Ans[j]=mark
                Visited[j] = True
        mark+=1
for x in range(2,N+1):
    if(Ans[x]==-1):
        Ans[x] = mark
        mark+=1
print(*Ans[2:N+1])