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 mp():
    return map(int, input().split())

def gcd(a, b):
    if a == 0:
        return b
    return gcd(b % a, a)

def check():
    global n, a
    for i in range(2, n + 1):
        for j in range(2, n + 1):
            if gcd(i, j) == 1 and a[i] == a[j]:
                return False
    return True

n = int(input())

a = [10 ** 9] * (n + 1)

x = 1
d = 2
while d <= n:
    f = 0
    for i in range(d, n + 1, d):
        if x < a[i]:
            a[i] = x
            f = 1
    x += f
    d += 1

for i in range(2, n + 1):
    print(a[i], end = ' ')
    
#print(check())