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

def smallestDividor(n):
  if(n%2 == 0):
    return 2

  for j in range(3,n+2,2):
    if(n%j == 0):
      return j

def powerN(n,prime):
  return math.log(n)//math.log(p)


n = int(input())
compt = 0
dep = 2

p = smallestDividor(n)
compt = int(powerN(n,p))
print(compt)