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 smallest_div(x):
    for i in range(2, int(math.sqrt(x) + 1)):
        if x % i == 0:
            return i
    return x


def prime(x):
    for i in range(2, int(math.sqrt(x) + 1)):
        if x % i == 0:
            return i == x
    return True


def main():
    n = int(input())
    if prime(n):
        return 1
    else:
        div = smallest_div(n)
        return n // 2 - max(0, (div - 3) // 2)


if __name__ == '__main__':
    main()
