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 *
n = int(input())

def cp(m):
    for i in range(2,int(sqrt(m))+1):
        if (m % i == 0):
            return False
    return True

def sp(m):
    for i in range(2,int(sqrt(m))+1):
        if (m % i == 0 and cp(i)):
            return i
    return 0

def lala(m):
    if (m % 2 == 0): return int(m/2)

    prm = cp(m)
    if (prm): return 1
    
    spm = sp(m)
    return 1+lala(m-spm)

print(lala(n))