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:
sieve=[0]*(10**5+10)
prime=[]
for i in range(2,10**5+10):
    j=2*i
    while j<len(sieve):
        sieve[j]=-1
        j+=i
for i in range(2,len(sieve)):
    if sieve[i]==0:
        prime.append(i)
from sys import stdout
#print(prime)
ans=[0]*(10**5+10)
n=int(input())
for i in range(0,len(prime)):
    #print('i',i)
    j=prime[i]
    while j < len(ans):
        if ans[j]!=0:
            j+=prime[i]
            continue
        ans[j]=i+1
        j+=prime[i]
#print(ans)
for i in range(2,n+1):
    stdout.write(str(ans[i])+' ')
    #pass