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
import math
#f=open("test.txt","r")
f=sys.stdin
n=int(f.readline().rstrip())
if n%2==0:
    print(n//2)
else:
    count=0
    temp=0
    sq=int(math.sqrt(n))
    if sq>=3:
        for i in range(3,sq+1,2):
            if n % i == 0:
                n = n - i
                count += 1
                i = 3
                if n % 2 == 0:
                    print((n // 2) + count)
                    temp=1
                    break
    if temp==0:
        print(1)


