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.
#!/usr/bin/env python3
import sys
import math

n = int(sys.stdin.readline())


def mpd(num):
    border = math.floor(num ** (1 / 2.0))
    c = 2
    is_found = False
    while c <= border and not is_found:
        if num % c == 0:
            border2 = math.floor(c ** (1 / 2.0))
            is_not_found = False
            sc = 2
            while sc <= border2 and not is_not_found:
                if c % sc == 0:
                    is_not_found = True
                sc += 1
            if sc > border2:
                is_found = True
        if not is_found:
            c += 1
    if is_found:
        return c
    else:
        return num


n = n - mpd(n)
i = int(n / 2 + 1)
print(i)
