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

lines = []
for line in sys.stdin:
	lines.append(line.rstrip('\n'))

aNumber = int(lines.pop(0))

def decompose (n): 
    i=2
    result = []
    while n > 1:
        while n%i==0:
            result.append(i)
            n=n/i
        i=i+1
    return result

if aNumber == 0:
    print(aNumber)
else:
    print(len(decompose(aNumber)))