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
n=int(input())
sub=0
k=0
if  not n&1:
    print(n//2)
    k+=1
for j in range(3,int(math.sqrt(n))+1,2):
    if not n%j:
        n-=j
        sub+=1
    if not n&1 and n!=0 and k!=1:
        k+=1
        print(sub+(n//2))
        break
    if n==0:
        break
if n>1:
    sub+=1
if k<1:
    print(sub)
    


    