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B. Divisor Subtraction
time limit per test
2 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output

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 $$$n$$$ ($$$2 \le n \le 10^{10}$$$).

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.