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 SieveOfEratosthenes(n):
    prime = ['TRUE' for i in range(n+1)] 
    p = 2
    t=1
    while(p * p <= n):
        if(prime[p] == 'TRUE'):
            for i in range(p,n+1,p):
                prime[i] = t
            t = t+1
        p += 1
        
    for p in range(2,n+1):
        if prime[p] == 'TRUE':
            prime[p] = t
            t = t+1
    return prime[2:]
    
        
n = int(input())
arr = SieveOfEratosthenes(n)
print(' '.join(str(i) for i in arr))