You are given an integer number n. The following algorithm is applied to it:

  1. if n = 0, then end algorithm; 
  2. find the smallest prime divisor d of n; 
  3. subtract d from n and go to step 1. 



Determine the number of subtrations the algorithm will make.

Input

The only line contains a single integer n (2 ≤ n ≤ 10^{10}).

Output

Print a single integer — the number of subtractions the algorithm will make.

Examples

Input


5


Output


1


Input


4


Output


2

Note

In the first example 5 is the smallest prime divisor, thus it gets subtracted right away to make a 0.

In the second example 2 is the smallest prime divisor at both steps.
import math

n = int(input())

num_steps = 0

while n != 0:
    a = 2
    poss_dict = {i: True for i in range(2, int(math.sqrt(n))+1)}
    
    is_prime = True
    for i in range(2, int(math.sqrt(n))+1):
        if not poss_dict[i]:
            continue
        if not n % i:
            max_fits_in = n // i
            num_steps += max_fits_in
            n -= i * max_fits_in
            is_prime = False
            for j in range(i, int(math.sqrt(n))+1):
                poss_dict[j] = False
            break

    if is_prime:
        num_steps += 1
        break

print(num_steps)
            
