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 PYTHON):

Solution:
def primes(n):

    prime = [True for i in range(n+1)] 

    p = 2

    while (p * p <= n): 

        if (prime[p] == True): 

            for i in range(p * p, n+1, p): 

                prime[i] = False

        p += 1

    return [i for i in range(2, n) if prime[i]]

n = input()

k = primes(n+1)

l = [0]*(n+1)

coprime = 1

for i in k:

    l[i] = coprime

    for q in range(i * i, n+1, i): 

        l[q] = coprime

    coprime += 1

for i in l[2::]:

    print i,