write a go solution for Description:
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:   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;  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.

Input Format:
The first line contains three integers n, m and q (1<=n,m<=1000; 1<=q<=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<=x<=n; 1<=y<=m) — the description of each query.

Output Format:
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.

Note:
None. Output only the code with no comments, explanation, or additional text.