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 as m


n = int(input())

if n % 2 == 0:
    print(n // 2)
else:
    sq = int(m.sqrt(n))
    d = 3
    while d <= sq and n % d != 0:
        d += 1
    if d <= sq:
        print(1 + (n - d) // 2)
    else:
        print(1)
