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E. Staircases

time limit per test

2 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputYou 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

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.

Output

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.

Examples

Input

2 2 8 1 1 1 1 1 1 2 2 1 1 1 2 2 1 1 1

Output

5 10 5 2 5 3 1 0

Input

3 4 10 1 4 1 2 2 3 1 2 2 3 3 2 1 3 3 4 1 3 3 1

Output

49 35 24 29 49 39 31 23 29 27

Input

1000 1000 2 239 634 239 634

Output

1332632508 1333333000

Codeforces (c) Copyright 2010-2022 Mike Mirzayanov

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