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:
import sys
input = sys.stdin.readline

from collections import defaultdict
d = defaultdict(int)
i = 1
n = int(input())
primes = [2,3,5,7]
if n > 10:
	for j in range(11, n + 1):
		for x in primes:
			if j % x == 0:
				break
		else:
			primes.append(j)
#print(primes)

for x in primes:
	d[x] = i
	i += 1
l = []
for j in range(2, n + 1):
	for x in primes:
		if j % x == 0:
			l.append(d[x])
			break
print(*l)