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:
def isPrime(n):
    for i in range(2,int(n**0.5)+1):
        if n%i==0:
            return False
        
    return True
n=int(input())
b=[]
c=[]
s=0
for i in range(2,n+1):
    if(isPrime(i)):
        b.append([i,s+1])
        s=s+1
        c.append(s)
        #print("in",s)
    else:
        for j in range(s):
            #print(b[j][0])
            if(i%b[j][0]==0):
                c.append(b[j][1])
                break
print(*c)