A14596 | Staircases

You are given a matrix, consisting of $n$ rows and $m$ columns. The rows are numbered top to bottom, the columns are numbered left to right.

Each cell of the matrix can be either free or locked.

Let's call a path in the matrix a staircase if it:

- starts and ends in the free cell;
- visits only free cells;
- has one of the two following structures:
1. the second cell is $1$ to the right from the first one, the third cell is $1$ to the bottom from the second one, the fourth cell is $1$ to the right from the third one, and so on;
2. the second cell is $1$ to the bottom from the first one, the third cell is $1$ to the right from the second one, the fourth cell is $1$ to the bottom from the third one, and so on.

In particular, a path, consisting of a single cell, is considered to be a staircase.

Here are some examples of staircases:

Initially all the cells of the matrix are free.

You have to process $q$ queries, each of them flips the state of a single cell. So, if a cell is currently free, it makes it locked, and if a cell is currently locked, it makes it free.

Print the number of different staircases after each query. Two staircases are considered different if there exists such a cell that appears in one path and doesn't appear in the other path.

The first line contains three integers $n$ , $m$ and $q$ ( $1 \le n, m \le 1000$ ; $1 \le q \le 10^4$ ) — the sizes of the matrix and the number of queries.

Each of the next $q$ lines contains two integers $x$ and $y$ ( $1 \le x \le n$ ; $1 \le y \le m$ ) — the description of each query.

Print $q$ integers — the $i$ -th value should be equal to the number of different staircases after $i$ queries. Two staircases are considered different if there exists such a cell that appears in one path and doesn't appear in the other path.