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
import math
number = int(input())
if number % 2 == 0:
    print(number // 2)
    sys.exit(0)
first_div = -1
counter = 3
divisors = []
for i in range(1, int(math.sqrt(number)) + 1):
    if number % i == 0:
        divisors.append(i)
        divisors.append(number // i)
if len(divisors) == 2:
    print(1)
else:
    print((number - divisors[2] // 2 + 1))