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 is_prime(n):
    sqrt = int(n ** 0.5)
    divisors = 0
    
    for i in range(1, sqrt + 1):
        if n % i == 0:
            divisors += 1

        if divisors > 1:
            return False

    return True

n = int(input())

i = 2
while i <= n:
    if n % i == 0 and is_prime(i):
        print(n//i)
        break
    i += 1