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
def smallest_divisor(x):
    for i in range (2,int(sqrt(x)+2)):
        if x % i == 0:
            return i
    return x

        
x = int(raw_input())

d = smallest_divisor(x)
res = 0
if x == 0:
    print 0
else:
    x -= d
    print 1 + x//2
