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 prime(a):
	for i in range(2,int(math.sqrt(a))+1):
		if a%i==0:
			return 0
	return 1

n = int(input())

if prime(n)==1:
	print("1")
	
elif n%2==0:
	print(int(n/2))
	
else:
	for i in range(2,n):
		if n%i==0 and prime(i):
			d =i;
			break;
	print(1+((n-d)//2))
