The Happy Worm

A happy worm lives in an $m \times n$ rectangular field. Some cells of the field contain a stone; every other cell is empty (each cell is either empty or holds exactly one stone).

When the worm sleeps it lies in a straight line: either horizontally, along a single row, or vertically, along a single column. It then stretches so that its length is as large as possible, extending from where it lies in both directions until it is stopped by a stone or by the edge of the field. The worm may never occupy a cell that contains a stone or a cell outside the field, and while sleeping it must be at least $2$ cells long.

A sleeping position is therefore a maximal straight run of empty cells (in one row or one column) whose length is at least $2$. Two positions are different when they cover different sets of cells; a horizontal run and a vertical run are always different positions.

Count how many different positions the worm can be in while sleeping.

The first line contains an integer $t$ ($1 \le t \le 11$), the number of test cases. Each test case is given as follows.

The first line of a test case contains three integers $m$, $n$, and $k$ ($1 \le m, n, k \le 100000$): the number of rows, the number of columns, and the number of stones. Each of the next $k$ lines contains two integers $r$ and $c$, the row and column of one stone ($1 \le r \le m$, $1 \le c \le n$). No stone is listed more than once.

For each test case, print a single line containing the number of different positions in which the happy worm can sleep.