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

numero = int(input())

aux = True
if(numero % 2 == 0):
  print(int(numero/2))
else:
  raiz = math.floor(math.sqrt(numero))
  for i in range(2, raiz + 1):
    if(numero % i == 0):
      print(int((numero - i) / 2) + 1)
      aux = False
      break
  if(aux):
    print(1)
	      	    			  				 		  			 	