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())
s=[]
count=1
def isprime (i, count):
    x= int(math.sqrt(i)) +1
    for y in  range(2, x+1):
        if i%y==0: 
            return y-1
    count+=1
    return count
for i in range(2, n+1):
    z=isprime(i,count)
    if count<z:
        count+=1
        s.append(str(z))
    else:
        if z>len(s)-1:
            s.append(str(z))
        else:
            s.append(str(s[z-1]))
print(" ".join(s))