Description

You have a plate and you want to add some gilding to it. The plate is a rectangle that we split into $w\times h$ cells. There should be $k$ gilded rings, the first one should go along the edge of the plate, the second one — $2$ cells away from the edge and so on. Each ring has a width of $1$ cell. Formally, the $i$-th of these rings should consist of all bordering cells on the inner rectangle of size $(w - 4(i - 1))\times(h - 4(i - 1))$.

The picture corresponds to the third example.

Your task is to compute the number of cells to be gilded.

Input

The only line contains three integers $w$, $h$ and $k$ ($3 \le w, h \le 100$, $1 \le k \le \left\lfloor \frac{min(n, m) + 1}{4}\right\rfloor$, where $\lfloor x \rfloor$ denotes the number $x$ rounded down) — the number of rows, columns and the number of rings, respectively.

Output

Print a single positive integer — the number of cells to be gilded.

Samples

3 3 1

8

7 9 1

28

7 9 2

40

Note

The first example is shown on the picture below.

The second example is shown on the picture below.

The third example is shown in the problem description.