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.
from math import sqrt

def get_first_divisor(n):
    s = set()
    for d in range(3, int(sqrt(n)) + 1, 2):
        if n % d == 0:
            return d
    return 1

n = int(input())
if n % 2 == 0:
    print(n // 2)
else:
    p = get_first_divisor(n)
    if p == 1:
        print(1)
    else:
        print((n - p) // 2 + 1)