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

n = int(input())

counter = 0
i = 2

min_div = -1
ans = 0
while i <= sqrt(n):
	if n % i == 0:
		min_div = i
		n -= i
		ans += 1
		break 
	i += 1	

if min_div > 0:
	ans += n // 2
else: 
	ans = 1

print ans