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:
n = int(input())
a_i = [0]*(n-1)
asig = 0
for i in range(2,n+1):
    if a_i[i-2]==0:#se le resta 2 a los indices pq para i = 2 nuestro primer numero corresponde la posicion 0 en a_i
        asig +=1
        a_i[i-2]=asig
        for j in range(i,n+1,i):
           if a_i[j-2]==0 and (j)%i==0:
               a_i[j-2]= a_i[i-2]
for i in range(0,n-1):
    print(a_i[i])