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B. Divisor Subtraction

time limit per test

2 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputYou are given an integer number $$$n$$$. The following algorithm is applied to it:

- if $$$n = 0$$$, then end algorithm;
- find the smallest prime divisor $$$d$$$ of $$$n$$$;
- 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.

Codeforces (c) Copyright 2010-2020 Mike Mirzayanov

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