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())

least_prime = [0] * (n + 1) 
  
    # We need to print 1 for 1. 
least_prime[1] = 1
cnt = 1 
    
  
for i in range(2, n + 1) : 
          
        # least_prime[i] == 0 
        # means it i is prime 
    if (least_prime[i] == 0) : 
              
            # marking the prime number 
            # as its own lpf 
        least_prime[i] = cnt 
  
            # mark it as a divisor for all its 
            # multiples if not already marked 
        for j in range(i * i, n + 1, i) : 
            if (least_prime[j] == 0) : 
                least_prime[j] = cnt 
        cnt += 1 
print(*least_prime[2:])