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 divisors(num):
    for i in range(2, int(sqrt(num)) + 1):
        if num % i == 0:
            return i
    return num


def resulting(n):
    count = 0
    if n % 2 != 0:
        n -= divisors(n)
        count += 1
    return count + (n // 2)


print(resulting(int(input())))
