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 generate(n):
	l=[0 for j in range(n+1)]
	p=2
	prime=1
	while(p*p<=n):
		if(l[p]==0):
			l[p]=prime
			#print(l[p],p)
			prime=prime+1
			for i in range(p*p,n+1,p):
				l[i]=l[p]
		p=p+1
	l=l[2:]
	for k in range(0,len(l)):
		if(l[k]==0):
			l[k]=prime
			prime=prime+1
	print(*l)



t=int(input())
generate(t)