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 sieve():
    vis = [1 for i in range(n + 1)]
    vis[0] = vis[1] = 0
    for i in range(n + 1):
        if vis[i]:
            prime.append(i)
            for j in range(i << 1, n + 1, i):
                vis[j] = 0


global prime
global n
n = eval(input())
prime = []
sieve()
a = [0 for i in range(n + 1)]
for i in range(len(prime)):
    now = prime[i]
    a[now] = i + 1
    val = now << 1
    while val <= n:
        a[val] = i + 1
        val += now
for i in range(2, n + 1):
    print(a[i], end=" ")