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:
# code from https://www.geeksforgeeks.org/sieve-of-eratosthenes/
def SieveOfEratosthenes(n): 
    prime = [True for i in range(n+1)]
    vals = []
    p = 2
    while (p * p <= n): 
        if (prime[p] == True): 
            for i in range(p * p, n+1, p): 
                prime[i] = False
        p += 1
    for p in range(2, n): 
        if prime[p]: 
            vals.append(p)
    return vals
n = int(input())
vals = SieveOfEratosthenes(n+1)
x = [1 for i in range(n-1)]
num = 1
for i in range(len(vals)):
	x[vals[i]-2] = num
	for i in range(vals[i] * vals[i], n+1, vals[i]): 
		x[i-2] = num
	num+=1
s = ""
for i in x:
	s+=str(i)+" "
print(s[:-1])