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 function(n):
    if n==2 or n==3:
        return 1
    condition=True
    if n%2==0:
        return int(n/2)
    for i in range(2, math.floor(math.sqrt(n))):
        if i%2==0:
            condition=False
            break
    if condition:
        return 1
    if not condition:
        for j in range(2, math.floor(math.sqrt(n))):
            if n%j==0:
                return int(int((n-j)/2)+1)




if __name__=="__main__":
    n=int(input())
    print(function(n))