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:
n=int(input())


def computeGCD(x, y):
	while(y): 
		x, y = y, x % y 
	return x

def smallestDivisor(n): 
  
    # if divisible by 2 
    if (n % 2 == 0): 
        return 2; 
  
    # iterate from 3 to sqrt(n) 
    i = 3;  
    while(i * i <= n): 
        if (n % i == 0): 
            return i; 
        i += 2; 
  
    return n


def is_prime(n):
    """
    Assumes that n is a positive natural number
    """
    # We know 1 is not a prime number
    if n == 1:
        return False

    i = 2
    # This will loop from 2 to int(sqrt(x))
    while i*i <= n:
        # Check if i divides x without leaving a remainder
        if n % i == 0:
            # This means that n has a factor in between 2 and sqrt(n)
            # So it is not a prime number
            return False
        i += 1
    # If we did not find any factor in the above loop,
    # then n is a prime number
    return True

cur_max = 0
results = []
for i in range(2, n+1):
	if is_prime(i):
		cur_max += 1
		results.append(cur_max)
	else:
		results.append(results[smallestDivisor(i)-2])

# print(*range(2,n+1))
print(*results)

# for i in range(2, n+1):
# 	for j in range(i+1, n+1):
# 		if computeGCD(i, j) == 1:
# 			if results[i-2] == results[j-2]:
# 				print(i, j)

# 2 3 4 5 6 7 8 9 10

# 1 2 1 3 1 4 1 1 1