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.
from math import ceil
a = int(input())
steps = 0

def minprime(x):
    for i in range(2, ceil(x**0.5)+1):
        if x % i == 0:
            return i
    return x
while a != 0:
    t = minprime(a)
    if t == 2:
        steps += a // t
        a = 0
    else:
        a -= t
        steps += 1
print(steps)
