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
n=int(input())
def func(n):
    isprime=True
    count=0
    if n%2==0:
        count=n//2
        return count
    z=int(math.floor(math.sqrt(n)))+1
    for i in range(2,z):
        if n%i==0:
            isprime=False
            break
    if isprime:
        return 1
    n=n-i
    count = 1 + (n//2)
    return count
print(func(n))