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.
p = []
f = 0
n = int(input())
if n % 2 == 0:
    c = n // 2
else:
    for i in range(2, n + 1):
        for j in range(2, i//2 + 2):
            if i % j == 0:
                f = 1
                t = j
                break
            else:
                if j == (i // 2 + 1):
                    p.append(i)
    if f == 1:
        c = 1 + ((n - t) // 2)
    else:
        c = 1
print(c)
