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 mindel(n):
    if n % 2 == 0:
        return 2
    d = 3
    while d * d <= n and n % d != 0:
        d += 2
    return d


if __name__ == "__main__":
    n = int(input())
    data = [1]*(n-1)
    isPrime = [1]*(n-1)
    i = 2
    while i**2 <= n:
        if isPrime[i-2]:
            j = i**2
            while j <= n:
                isPrime[j-2] = 0
                j += i
        i += 1
    curc = 1
    for i in range(2, n+1):
        if isPrime[i-2]:
            data[i-2] = curc
            curc += 1
        else:
            data[i-2] = data[mindel(i)-2]
    for i in data:
        print(i, end=' ')