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())
a = [True]*1000002
for i in range(2,1000002):
    if (a[i] == True):
        for j in range(i**2,1000002,i):
            a[j] = False
if (n % 2 == 0):
    print(n // 2)
    exit()
count = 0
if (n % 2 != 0):
        for i in range(2, 1000002):
            if (a[i] == True and n % i == 0):
                n -= i
                break
print(n // 2 + 1)
