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.
def get_least_prime_div(a, left):
    for div in range(left, a + 1):
        if a % div == 0:
            return div
    return 1

def steps_in_row(a, div):
    d2 = a // div
    # d2 * div -> (div - 1) * div # div вычли div - d2 раза
    steps = max(d2 - div + 1, 0)
    return steps

a = int(input())
total_steps = 0
div = 1
while a > 0:
    div = get_least_prime_div(a, 2)
    steps = steps_in_row(a, div)
    if steps == 0:
        total_steps += 1
        a = 0
    else:
        a = div * (div - 1)
        total_steps += steps

print(total_steps)