Glass cutting

Artūras built a frame for a new greenhouse and plans to glaze it. He bought a glass pane of size $M \times N$ (length $M$, width $N$), but at home he found $K$ defects in it. All defects are small, so treat each one as a point where the glass is slightly cracked.

Artūras does not want to use poor-quality glass, so he plans to cut out the largest possible rectangle from the pane that contains no defects.

Artūras has a device that holds the pane and makes straight cuts parallel to its edges, that is, horizontal and vertical cuts. The device is precise enough that a cut can pass through a defect without the glass breaking.

Compute the maximum area of a defect-free rectangle that Artūras can cut from the pane.

A defect may lie on the edge of the cut rectangle, but no defect may lie inside it.

The first line contains three integers $M$, $N$, and $K$. Each of the next $K$ lines contains two integers $X$ and $Y$, the coordinates of one defect.

The lower left corner of the original pane has coordinates $(0, 0)$, and the upper right corner has coordinates $(M, N)$.

It is always true that $1 \le X \le M-1$ and $1 \le Y \le N-1$. All defect coordinates are distinct.

Print one integer: the maximum area of a defect-free rectangle that Artūras can cut from the pane.

$2 \le M, N \le 30000$, $1 \le K \le 500$