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.
#!/usr/bin/python

from __future__ import print_function
import math
import sys

from math import sqrt
from itertools import count, islice

def isPrime(n):
    return n > 1 and all(n%i for i in islice(count(2), int(sqrt(n)-1)))

def sub(n):
    s = 0

    if isPrime(n):
        s += 1
        n -= n

    while n != 0:
        if n%2 == 0:
            s += n//2
            n = 0
        else:
            p = 3
            while p < (n + 1):
                if isPrime(p):
                    if n%p == 0:
                        n -= p
                        s += 1
                        break
                p += 1

    print(s)


def main():
    n = int(raw_input())
    sub(n)

if __name__ == '__main__':
    main()