E. Staircasestime limit per test2 secondsmemory limit per test256 megabytesinputstandard inputoutputstandard 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.InputThe 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.OutputPrint 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.ExamplesInput
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

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

5 10 5 2 5 3 1 0 
['brute force', 'combinatorics', 'data structures', 'dfs and similar', 'dp', 'implementation', 'math', '*2100']