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 IsPrime(n):
    if n == 1:
        return False
    if n == 2:
        return True
    for i in range(2,int(n**0.5)+1):
        if n%i == 0:
            return False
    if n%i != 0 and i == int(n**0.5):
        return True

def SmallestDivisor(n):
    if n % 2 == 0:
        return 2   
    else:
        squareRootOfn = math.floor(math.sqrt(n))
        for i in (3,squareRootOfn,2):
            if n % i == 0:
                return i
                break
            else:
                if i == squareRootOfn:
                   return i

def Divisor():
    n = int(raw_input())
    if n%2 == 0:
        subs = n/2
    else:
        if IsPrime(n):
            subs = 1
        else:
            d = SmallestDivisor(n)
            print d
            subs = n/d
    print int(subs)

Divisor()