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 sqrt
def get_int():
    from sys import stdin
    return int(stdin.readline().replace('\n', ''))

def smallest_prime_factor(n):
    from math import sqrt
    if n % 2 == 0:
        return 2
    for i in range(3,int(sqrt(n))+1,2):
        if n % i == 0:
            return i
    if n > 2:
        return n


def algo(n):
    subtractions = 0
    spf = smallest_prime_factor(n)
    n -= spf
    subtractions +=1
    if n != 0:
        multiple = int(n/2)
        subtractions += multiple
    return subtractions


n = get_int()
print(algo(n))

    			 		 	  				  		 				 			