Toggle Grid Cells

You are given a grid with n rows and m columns. Initially, all cells in the grid are empty. You will be given q queries, each query contains a pair of integers (x, y) indicating the cell at row x and column y (1-indexed). For each query, you need to toggle the state of the cell at position (x, y). Toggling means that if the cell is empty, it becomes filled; if it is filled, it becomes empty.

After processing each query, output the total number of filled cells. Formally, if we define the filled cells as a set, after each toggle operation, print \( |S| \) (the size of the set of filled cells).

Example:

Input:
3 3 3
1 1
3 1
1 1
Output:
1
2
1

</p>

inputFormat

The first line contains three space-separated integers \(n\), \(m\), and \(q\), representing the number of rows, columns, and queries respectively.

Each of the following \(q\) lines contains two space-separated integers \(x\) and \(y\) representing the row and column indices of the cell to toggle.

outputFormat

For each query, print on a new line the number of filled cells after performing the toggle operation.

## sample

3 3 3
1 1
3 1
1 1

1
2
1

</p>