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.
def factorize(n):  # o(sqr(n))
    c, ans = 2, []
    while (c * c < n):
        if n % c == 0:
            return c
        c += 1

    if c * c == n:
        return c
    return n


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