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 sys
input=sys.stdin.readline
from math import *
n=int(input())
for i in range(2,int(sqrt(n))+1):
    if n%i==0 and i==2:
        print(n//i)
        exit(0)
    if n%i==0:
        print(1+((n-i)//2))
        exit(0)
print(1)        
