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 menor_fator_primo(num):
    fatores = []
    if num % 2 == 0:
        return 2

    i = 3
    while i <= math.sqrt(num):
        if num % i == 0:
            return i
        i += 2
    return num

num = int(input())

cont = 0
while num > 0:
    if num % 2 == 0:
        cont += num // 2
        break
    else:
        cont += 1
        num -= menor_fator_primo(num)

print(cont)
 		 	 			 				  	 	  						  	