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())
def pr(x):
    for i in range(2, x):
        if x % i == 0:
            return False
    else:
        return True
z=1
l=[0]*(n-1)
# q=list(filter(lambda x: (pr(x)==True) , range(2,n+1)))
# print(q)
for i in range(2,n+1):#list(filter(lambda x: (pr(x)) , range(2,n+1))):
	if(l[i-2]>0):
		continue
	else:	
		f=1
		while(i*f<=n):
			if(l[i*f-2]==0):
				l[i*f-2]=z
			f+=1
		z+=1
print(*l)