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:

def isPrime(n):
    p = 2
    while p*p <= n:
        if n % p == 0:
            return False
        p+=1
    return True

def nextPrime(n):
    n+=1
    while not isPrime(n):
        n+=1
    return n

n = int(input())
nums = [0] * (n-1)

p = 2
for i in range(len(nums)):
    m = 1
    while p <= n:
        k = 1
        while k*p <= n:
            if nums[k*p-2] == 0:
                nums[k*p-2] = m
            k+=1
        p = nextPrime(p)
        m += 1

for e in nums:
    print(e, end=" ")
print("")