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 primes(n): 
	allp=[]
	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
	for p in range(2, n): 
		if prime[p]: 
			allp.append(p)
	return allp
n=int(input())
l=[0]*(n-1)
k=1
allp=primes(n+1)
for i in allp:
	for j in range(i,n+1,i):
		if l[j-2]==0:
			l[j-2]=k
	k+=1
for i in l:
	print (i,end=" ")