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:

prime = [-1 for i in range(100005)]
p = 2
avail = 1
while (p * p <= 100005): 
    if (prime[p] == -1):
        for i in range(p, 100005, p):
            if prime[i] == -1:
                prime[i] = avail
        avail += 1
    p += 1

#print(avail)
for i in range(2, 100005):
    if prime[i] == -1:
        #print(i, "id unmakred")
        prime[i] = avail
        avail += 1
        
n = int(input())
print(*prime[2 : n + 1])