Golden Plate

1000ms

262144K

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 $$$(w - 4(i - 1))\times(h - 4(i - 1))$$$.

$\text{[math]}$ 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.

Sample Input:

3 3 1

Sample Output:

Sample Input:

7 9 1

Sample Output:

Sample Input:

7 9 2

Sample Output:

Note:

The first example is shown on the picture below.

$\text{[math]}$

The second example is shown on the picture below.

$\text{[math]}$

The third example is shown in the problem description.

Informação

Provedor Codeforces

Código CF1031A