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 prime(n):
    if(n<2): 
        return False;
    else:
        if(n%2==0):
            return False;
        else:
            for i in range(3,int(math.sqrt(n))+1,2):
                if(n%i==0):
                    return False;
    return True;
    
a = int(input());

if(prime(a)):
	print(1);
	exit(0);

for i in range(2,int(math.sqrt(a))+1):
    if(prime(i) and a%i==0):
        print(a/i);
        exit(0);
                
        