Bobo has points arranged into a matrix with n rows and m columns. The points in the intersection of the i-th row and the j-th column is labeled with (i, j).
He is going to perform q operations of the following 2 kinds.
1. Given parameters a, b, add edges between points (i, j) and (i, j + 1) for all and .
2. Given parameters a, b, add edges between points (i, j) and (i + 1, j) for all and .
Bobo would like to know the number of connected components after each operation.

The input consists of several test cases and is terminated by end-of-file.
The first line of each test case contains three integers n, m and q.
The i-th of the following q lines contains three integers ,  and  where  is the kind of the operation i and ,  are corresponding parameters.

For each test case, print q integers which denote the number of connected components after each operation.

2 3 3
2 1 1
2 3 3
1 1 1
1000000000 1000000000 1
1 1 2

5
4
2
999999998000000002

* 
* 
* 
* If , . If , .
* The sum of q does not exceed .