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 helper(x):
    up = math.floor(math.sqrt(x))
    i = 2
    while i <= up:
        if x % i == 0:
            return i
        i += 1
    return x


n = int(input())
if n // 2 == 0:
    print(n // 2)
else:
    print(1 + (n - helper(n)) // 2)
 	   	 	  	 					  		 				 		 	