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,m=map(int,input().split())
from collections import deque
n=int(input())

pr=[0]*(1+n)
p=[0]
def mind(x):
    for i in range(2,int(x**0.5)+1):
        if x%i==0:
            return pr[i]
    p.append(p[-1]+1)
    pr[x]=p[-1]
    return p[-1]

a=[]
b=[]
for i in range(2,n+1):
    t=mind(i)
    a.append(t)
    #b.append((i,t))
print(*a)
#print(*b)

def gcd(x,y):
    if x%y==0:
        return y
    while x%y!=0:
        x,y=y,x%y
    return y