Defense of a Kingdom

Theodore is building a new strategy game called "Defense of a Kingdom". On each level the player defends a Kingdom represented by a rectangular grid of cells. The player builds crossbow towers in some cells of the grid. A tower defends every cell in its own row and its own column. No two towers share a row or a column.

The penalty of a position is the number of cells in the largest undefended rectangle. For example, the position shown in the picture below has penalty 12.

Help Theodore write a program that computes the penalty of a given position.

The first line contains three integers: w — the width of the grid, h — the height of the grid, and n — the number of crossbow towers (1 ≤ w, h ≤ 40000; 0 ≤ n ≤ min(w, h)).

Each of the next n lines contains two integers xi and yi — the coordinates of the cell occupied by a tower (1 ≤ xi ≤ w; 1 ≤ yi ≤ h).

Print a single integer — the number of cells in the largest rectangle that is not defended by any tower.