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 math
N = int(input())
c = 0
while N%2 and N != 0:
    f= 1
    for i in range(2,math.ceil(N**0.5)+1):
        if N % i == 0:
            N -= i
            c+=1
            f=0
            break
    if f:
        N = 0;c = 1
print(c + N//2)
