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())
compound={}
compound[0]=1
compound[1]=1
compound=[0]*100000
for i in range(2,int(sqrt(100000))+1):
	for p in range(2*i,100000,i):
		compound[p]=1
def min_div(x):
	for i in range(2,100000):
		if not(compound[i]) and not(x%i):
			return i
	return x
if n%2:
	print(((n-min_div(n))//2)+1)
else:
	print(n//2)
	