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.

#n = 123456789987654321
#m = 1987654321
def solve(n,c):
    if(n==0):
      return c
    if(n%2==0):
      return c+n//2
    for i in range(3,int(n**0.5)+1):
      if(n%i==0):
        return solve(n - i,c+1)
    return 1
    

print(solve(int(input()),0))
    