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 math import *
from sys import stdin,stdout
z=int(stdin.readline())
if (z%2==0):
    stdout.write(str(z//2))
else:
    for i in range(2,ceil(sqrt(z))+1):
        if (z%i==0):stdout.write(str(1+(z-i)//2));exit()
    stdout.write('1')
