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 java.util.*;

public class Solution {
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        long input = sc.nextLong();
        System.out.println(solve(input));
    }

    public static int solve(long input) {
        long smallestDiv = getSmallestDiv(input);
        if(smallestDiv==input) return 1;
        if(input%2==0) return (int)(input/2);
        return (int)(input/2+1);
    }

    public static long getSmallestDiv(long input) {
        int i = 2;

        while (input >= (long) i * i) {
            if(input%i==0) return i;
            i++;
        }
        return input;
    }
}