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:
prime=[2,3,5,7,11]
for i in range(12,100010):
    for j in prime:
        if i%j==0:
            break
        if j*j>i:
            prime.append(i)
            break
    else:
        prime.append(i)
d={}
for i in range(1,len(prime)+1):
    d[prime[i-1]]=i

#print(prime)

n=int(input())
for i in range(2,n+1):
    if i in d:
        print(d[i],end=" ")
    else:
        for j in range(len(prime)):
            if i%prime[j]==0:
                print(j+1,end=" ")
                break