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())
if n==2:
    print(1)
elif n==3:
    print(1,2)
else:
    L=[True]*(n+1)
    L[0]=0
    L[1]=0
    i=2
    temp=1
    while i*i<=n:
        if L[i] is True:
            L[i]=temp
            temp+=1
            x=i*i
            while x<=n:
                L[x]=L[i]
                x+=i
        i+=1
    counter=1
    x=1
    m=1
    #print(L)
    for i in range(2,n+1):
        if L[i] is True:
            print(m+1,end=" ")
            m+=1
        else:
            print(L[i],end=" ")
            m=max(m,L[i])