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:
#imgur.com/Pkt7iIf.png

#n, m = map(int, input().split())
#n = int(input())
#d = list(map(int, input().split()))

def sieve(n):
    res = []
    prime = [True for i in range(n+1)] 
    p = 2
    while (p * p <= n): 
        if (prime[p] == True): 
            for i in range(p * 2, n+1, p): 
                prime[i] = False
        p += 1
    for p in range(2, n): 
        if prime[p]: res.append(p)
    return res

n = int(input())
primes = sieve(n+1)
primes.reverse()

r = [0]*(n+1)
color = 1

while len(primes) > 0:
    a = primes.pop()
    t = a
    while a < n+1:
        if r[a] == 0:
            r[a] = color
        a += t
    color +=1

[print(i, end = ' ') for i in r[2:]]