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 get_least_prime_div(a):
    for div in range(2, int(math.sqrt(a)) + 2):
        if a % div == 0:
            return div
    return 1

a = int(input())
total_steps = 0
if a % 2 == 0:
    total_steps += a // 2
    a = 0
if a % 2 != 0:
    div = get_least_prime_div(a)
    total_steps = 1
    a -= div
    total_steps += a // 2
    a = 0

print(total_steps)