Number of Islands II

Given an empty 2D grid of size \(m \times n\) where each cell is initially water (denoted by 0), you are asked to perform a sequence of operations. Each operation converts a water cell into land (denoted by 1). Two land cells are considered connected if they are adjacent horizontally or vertically. An island is defined as a maximal set of connected lands.

After each operation, you are required to output the current number of islands in the grid.

Note: If an operation is attempted on a cell that is already land, the number of islands remains unchanged.

Example:

Input:
3 3 5
0 0
0 1
1 2
2 1
1 1
Output:
1 1 2 3 1

</p>

inputFormat

The input is given via standard input and has the following format:

• The first line contains three integers: \(m\) \(n\) \(k\) where \(m\) and \(n\) are the grid dimensions and \(k\) is the number of operations.
• The following \(k\) lines each contain two integers \(x\) and \(y\), representing the row and column indices to convert to land (0-indexed).

outputFormat

Print a single line with \(k\) integers separated by a space. Each integer is the number of islands after the corresponding operation.

## sample

3 3 5
0 0
0 1
1 2
2 1
1 1

1 1 2 3 1