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 time
import collections
import math

class Time_test:
    def __enter__(self):
        self.enter_time = time.time()
    def __exit__(self, exc_type, exc_val, exc_tb):
        print("Command was executed in", time.time()-self.enter_time)

n = int(input())
counter = 0
if n % 2 == 1:
    for i in range(3, math.floor(math.sqrt(n))+1):
        if n % i == 0:
            n -= i
            counter += 1
            break

for i in range(2, math.floor(math.sqrt(n))+1):
    if n % i == 0:
        counter += n // i
        n -= n // i * i
        break

if n != 0:
    counter += 1
print(counter)
