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 is_prime(n):
    if(n == 2):
        return True
    elif(n % 2 == 0 or n == 1):
        return False
    
    max_divisor = math.floor(math.sqrt(n))
    for d in range(3, 1 + max_divisor, 2):
        if(n % d == 0):
            return False
    return True

n = int(input())
if(n % 2 == 0):
    print(int(n / 2))
elif(is_prime(n)):
    print(1)
else:
    for i in range(3, n + 1):
        if(n % i == 0):
            print(int(1 + (n - i) / 2))
            break
	 			 	  	  		    		 	 	  					