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 as m

def nextPrime(x):
    ans = x
    size = int(m.sqrt(x))
    for j in range(2, size+1):
        if x % j == 0:
            ans = j
            break
    return ans

# Main
def run():

    n = int(input())

    p = nextPrime(n)

    ans = ((n - p) // 2) + 1

    print(ans)

# end main


# Program Start
if __name__ == "__main__":
    run()