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 sqrt

def SPD(n)->int:
    if n % 2 == 0:
        return 2
    for i in range(3,int(sqrt(n))+1,2):
        if n%i==0:
            return i
    return -1

n = int(input())
cnt = 0
if (SPD(n)==-1):
    print(1)
    exit(0)
while (True):
    if n%2==0:
        print(n//2 + cnt)
        exit(0)
    else:    
        n -= SPD(n)
        cnt+=1
        
    
