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
def isprime(n):
    for i in range(2,n):
        if(n%i==0):
            return False
    return True
n=int(input())
if(n%2==0):
    print(n//2)
else:

    i = 3
    f=0
    while (i * i <= n):
        if (n % i == 0):
            f=1
            n -= i
            break
        i += 2
    if(f==0):
        n=0
    print(1 + (n) // 2)