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.
from math import sqrt


def smallest_prime(x):
	if x % 2 == 0:
		return 2
	else:
		n = int(sqrt(x)+1)
		for i in range(3, n, 2):
			if x % i == 0:
				return i
	return x


num = int(input())
count = 0
while smallest_prime(num) != 2:
	count += 1
	num -= smallest_prime(num)
print(count+num//2)