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 sys
from os import path
if (path.exists('input.txt') and path.exists('output.txt')):
    sys.stdout = open('output.txt', 'w')
    sys.stdin = open('input.txt', 'r')

def main():
    n = int(input())
    ans = 0
    while n > 0:
        sm_p = n
        if n % 2 == 0:
            ans += n // 2
            break
        else:
            i = 3
            while i * i <= n:
                if n % i == 0:
                    sm_p = i
                    break
                i += 2
        n -= sm_p
        ans += 1
    print(ans)

main()