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 math
def sieve(x):
	if(x%2==0):
		return 2
	root=math.sqrt(x)
	root=int(root)+1
	for i in range(3,root,2):
		if(x%i==0):
			return i
	return 0
n=int(input())
ans=0
while(n>0):
	div=sieve(n)
	if(div==0):
		ans+=1
		break
	else:
		l=int(math.log(n,div))
		ans+=l
		n-=div**l
print(ans)