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 sys
input = sys.stdin.readline


class Problem:
    def __init__(self):
        pass

    def solve(self):
        print(self._solve())

    def _solve(self):
        n = int(input())
        done = [0] * (n + 1)
        v = 1
        for i in range(2, n + 1):
            if done[i]:
                continue
            k = 1
            while k * i <= n:
                done[k * i] = v
                k += 1
            v += 1

        return ' '.join(str(x) for x in done[2:])


def main():
    problem = Problem()
    problem.solve()


if __name__ == "__main__":
    main()