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

n = int(input())

result = 0
flag = False

i = 2
while (i < math.sqrt(n) + 1):
    if (n % i == 0):
        flag = True
        n -= i
        result += 1
        break
    i += 1

if flag:
    result += n // 2
else:
    result = 1

print(result)
		  	   		 	     			 		     	