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.
from math import sqrt
sol=0
n=int(input())
while(n%2!=0):
    ok=0
    for i in range (3,min(int(sqrt(n)+2),n+1)):
        if(n%i ==0):
            n=n-i
            sol=sol+1
            ok=1
            break
    if(ok==0):
        n=0
        sol=sol+1
        break
print(n//2+sol)