CF1598E 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.