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.
A = [False for _ in range(10**6+40)]

n = int(input())

f = 0

for i in range(2, len(A)):
    if A[i] == False:
        if n%i == 0:
            f = i
            break
        j = 2*i
        while j < len(A):
            A[j] = True
            j += i

if f == 0:
    print(1)
else:
    print(((n-f)//2 + 1))