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

def check_prime(n):
    for i in range(2,int(sqrt(n))+1):
        if(n%i==0):
            return 0
    else:
        return 1

def smallest_prime(n):
    for i in range(2,int(sqrt(n))+1):
        if(check_prime(i)):
            if(n%i == 0):
                return i
    else:
        return n
        
        
    

n = int(input())
count = 0
while(n!=0):
    if(n%2==0):
        count = count + (n//2)
        break
    d = smallest_prime(n)
    n = n-d
    count += 1
print(count)
