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())
# n = 4
def get_prime(n):
    is_p = [0] * (n+1)
    prime = []
    for i in range(2, n+1):
        if is_p[i] == 0:
            prime.append(i)
        for j in prime:
            if i * j >= n: break
            is_p[i*j] = 1
            if i % j == 0: break
    return prime


def solve(n):
    res = [0] * (n+1)
    prime = get_prime(n)
    seq = 1
    for x in prime:
        tmp = x
        while x < n+1:
            if res[x] == 0:
                res[x] = seq
            x += tmp
        seq += 1

    return ' '.join(map(str, res[2:]))

print(solve(n))