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 sys import stdin, stdout
from math import *

def nStep(n):
    if (n==0):
        return 0
    for i in range(2,floor(sqrt(n)+2),1):
        if (n % i == 0):
            return floor(n/i)+nStep(n % i)
    return 1
def main():
    global n
    n=int(stdin.readline())
    stdout.write(str(nStep(n)))
    return 0



if __name__ == "__main__":
    main()