Defense of a Kingdom#2261
Manunya is implementing a new strategy game called "Defense of a Kingdom." In each level, the player defends a kingdom represented as a rectangular grid of cells. The player can place towers in certain cells of the grid.
Each tower defends all cells in its row and column. No two towers are placed in the same row or column.
The penalty for a given tower placement is the number of cells in the largest rectangle not defended by any tower. For example, in the position shown in the picture, the penalty is .
Help Manunya write a program that calculates the penalty for the given position.
The first line contains three integers: — the width of the grid, — the height of the grid, and — the number of towers (1 \leq w, h \leq 40000; 0 \leq n \leq \min(w, h)).
Each of the following lines contains two integers x_i and y_i — the coordinates of the cell where a tower is placed (1 \leq x_i \leq w; 1 \leq y_i \leq h).
Output a single integer — the number of cells in the largest rectangle that is not defended by any tower.
Example 1