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.
n = int(input())
import math
pr = []
if n%2 == 0:
    print(n//2)
else:
    for num in range(3,200000,2):
        if all(num%i!=0 for i in range(2,int(math.sqrt(num))+1)):
              pr.append(num)
    found = True
    for p in pr:
        if n%p == 0:
            found = True
            break
    if found:
        n = n - p
    else:
        n = 0
    print(n//2+1)