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())

count = 0
while True:
  if n == 0:
    break
  if n % 2 == 0:
    count += (n // 2) 
    break

  i = 2
  d = n
  while i < int(math.sqrt(n)) + 1:
    if n % i == 0:
      d = i
      break
    i += 1
  n -= d
  count += 1
print(count)
