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())


def my(n):
    xx = []
    for i in range(1, int(math.sqrt(n) + 1)):
        if n % i == 0:
            yield i
            if i * i != n:
                xx.append(n / i)
    for divisor in reversed(xx):
        yield divisor


all_div = my(n)

def get():
    for elem in all_div:
        if(len(list(my(elem)))==2):
            return elem







if(n%2==0):
    print(int(n/2))
else:
    print(int(1+ (n-get())/2))



