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.
while True:
    n=int(input("Ввести целое число ",))
    k=0
    if n<2:
        print("некорректное значение")
    elif 2<=n<10**10:
        while n>2:
            if n%2==0:
                d=2
                n=n-d
                k=k+1
            elif n%3==0:
                d=3
                n=n-d
                k=k+1
            elif n%n==0:
                d=n
                n=n-d
                k=k+1
        print(k)
        break
    else:
        print("значение вне допустимого диапазона")