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())

if n%2==0:
    print(n//2)
else:
    pr = -1
    for i in range(2,math.ceil(math.sqrt(n))+1):
        if n%i==0:
            pr = i
            break
    #print(pr)
    if pr==-1:
        pr = n
        

    x = n//pr
    m = (x-1)*pr
    #print(m)
    print(1+m//2)
    
