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 isPrime(n) : 
    if (n == 2) : 
        return 2,True
    if (n == 3):
    	return 3,True
    if (n % 2 == 0):
        return 2,False
    if (n%3 == 0):
    	return 3,False
    i = 5
    while(i * i <= n) : 
        if (n % i == 0):
            return i,False
        if (n%(i+2) == 0):
        	return i+2,False
        i = i + 6
  
    return n,True



n = int(raw_input())
z = []
c = 0
for i in range(n-1):
	sp,isp = isPrime(i+2)
	if isp == True:
		c += 1
		z.append(c)
	else:
		z.append(z[sp-2])
print ''.join(str(i) + " " for i in z)