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:
a=int(input())
n=2
f=1
arr=[]


def prime(n):

    if (n <= 1):
        return False
    if (n <= 3):
        return True


    if (n % 2 == 0 or n % 3 == 0):
        return False

    i = 5
    while (i * i <= n):
        if (n % i == 0 or n % (i + 2) == 0):
            return False
        i = i + 6

    return True

def smallestFactor(n):

    if (n % 2 == 0):
        return 2;


    i = 3;
    while (i * i <= n):
        if (n % i == 0):
            return i;
        i += 2;

    return n;
while(n<=a):
    if (prime(n)==True):
        arr.append(f)
        f+=1
    else:
        u=smallestFactor(n)
        arr.append(arr[u-2])
    n+=1
print(*arr)