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.
def func():
    global x
    if x % 2 == 0:
        print(x // 2)
    else:
        count = 0
        for i in range(3, int(x**(1/2))+1, 2):
            if x % i == 0:
                x -= i
                count += 1
                break
        else:
            print(1)
            return
        print(count + x // 2)


x = int(input())
func()
