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:
from sys  import stdin,stdout
from math import floor
st=lambda:list(stdin.readline().strip())
li=lambda:list(map(int,stdin.readline().split()))
mp=lambda:map(int,stdin.readline().split())
inp=lambda:int(stdin.readline())
pr=lambda n: stdout.write(str(n)+"\n")

mod=1000000007
'''
prime=[]
i=2
l=[True for i in range(10**5+1)]
while i*i <= 10**5 :
    if l[i]:
        for j in range(i*i,10**5+1,i):
            l[j]=False
    i+=1
for i in range(2,10**5+1):
    if l[i]:
        prime.append(i)
'''

def solve():
    n=inp()
    dp=[-1 for i in range(n+10)]
    i=2
    val=1
    while i<=n:
        if dp[i]==-1:
            dp[i]=val
            for j in range(2*i,n+1,i):
                dp[j]=val
            val+=1
        i+=1
    print(*dp[2:n+1])
            
    
    
for _ in range(1):
    solve()