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


def checkPrime(d):
    tgt = int(math.ceil(math.sqrt(d))) + 1
    # print("tgt : " + str(tgt))

    for i in range(2, tgt):
        # print("i : " + str(i))
        if d % i == 0:
            return False
    return True

def solve(n):
    ret = 0

    if checkPrime(n):
        return 1

    while n > 0:
        if n % 2 == 0:
            return ret + n // 2
        for d in range(2, n + 1):
            if n % d == 0 and checkPrime(d):
                # print("d : " + str(d))
                ret += 1
                n -= d
                break
            elif (n - d) % 2 == 0 and checkPrime(d):
                return ret + (n - d) // 2
    return ret

def driver():
    n = int(input())
    print(solve(n))

driver()