Rectangle Cutting

In a small historic village, a popular wedding-ceremony activity is called rectangle cutting. Each close relative of the bride comes up and cuts a rectangle into the wedding cake (but does not take a piece). The cake has a rectangular shape, and the task is to count how many pieces the cake is divided into after all the cuts.

For example, in the figure below the cake is 3×5 (height × width) and three people have each made a rectangular cut. As a result, the cake is split into six pieces.

Each rectangular cut is described by the $(x, y)$ coordinates of two opposite corners. Only the outline (the four edges) of each rectangle is cut; no cake is removed. The cuts in the figure correspond to the first sample test case. Because families here can be large, the number of pieces can also be large, so a program is needed to compute it.

The input contains several test cases. Each test case spans several lines. The first line contains two integers $h$ and $w$ ($1 \le h, w \le 20$) — the height and the width of the cake. The second line contains a single integer $n$ ($0 \le n \le 50$) — the number of people who cut a rectangle. Each of the following $n$ lines contains four integers $x_1$, $y_1$, $x_2$, $y_2$, the coordinates of two opposite corners of one cut, where $0 \le x_1, x_2 \le w$ and $0 \le y_1, y_2 \le h$ (the $x$-axis runs along the width, the $y$-axis along the height). The input ends with a line containing two zeros, which is not processed.

For each test case, output a single line containing the number of pieces the cake is cut into.