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 sqrt, floor

def isPrime(x):
    for i in range(2,floor(sqrt(x))+1):
        if x%i == 0:
            return False
    return True

def divsub(n):
    if n == 0:
        return 0
    for i in range(2,floor(sqrt(n)+1)):
        if n%i == 0 and isPrime(i):
            n = n-i
            return 1+n//2
    return 1        

def main():
    n = int(input())
    print(divsub(n))            

main()    