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 mysol(n):
    minDiv = 987654321
    off = 2

    ret = 0

    while n > 0:
        tgt = int(math.ceil(math.sqrt(n))) + 1
        while off < tgt:
            if n % off == 0:
                minDiv = off
                break
            off += 1

        if off == tgt:
            return 1  # prime number.

        n -= minDiv
        ret += 1
        divided = n // 2
        if n % 2 == 0:
            return ret + divided
        else:
            ret += divided
            n = divided
    return ret

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

driver()