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
n = int(input()) #Guarda el dato de entrada.
r = sqrt(n)      #Guarda la raíz del número de entrada.
d = 2            #posible menor primo divisor de n(dato de la entrada).
while(d < r and n%d != 0): #Busca el menor divisor primo de n.
    d+=1   
    
if(d>r): d = n #significa que n es primo y por tanto es el mismo,su menor primo divisor.
    
print(int(1+(n-d)/2)) #cantidad de restas que se hacen con su divisor hasta que n=0.