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 is_prime(n):
    if n == 1:
        return False
    if n == 2:
        return True
    for d in range(2, int(sqrt(n)) + 1):
        if n % d == 0:
            return False
    return True

def get_first_prime(n):
    for d in range(2, int(sqrt(n)) + 1):
        if n % d == 0 and is_prime(d):
            return d
    return n

n = int(input())
if is_prime(n):
    print(1)
elif n % 2 == 0:
    print(n // 2)
else:
    n -= get_first_prime(n)
    print(1 + n // 2)