Conway's Game of Life Simulation

You are given an initial grid representing cells in Conway's Game of Life. Each cell is either alive ('*') or dead ('.'). The grid evolves in discrete iterations according to the following rules:

• If a cell is alive and has 2 or 3 live neighbors, it remains alive; otherwise, it dies.
• If a cell is dead and has exactly 3 live neighbors, it becomes alive; otherwise, it remains dead.

These rules can be written in LaTeX as follows:

For a live cell: it survives if $2 \leq N \leq 3$, otherwise it dies.
For a dead cell: it becomes live if $N = 3$.

Your task is to simulate the game for k iterations on each given grid and output the number of live cells remaining at the end.

inputFormat

The input is read from standard input (stdin) and has the following format:

T
n m k
row1
row2
...
rown
... (repeated for T test cases)

Where:

• T is the number of test cases.
• For each test case, the first line contains three integers n, m, and k representing the number of rows, the number of columns, and the number of iterations, respectively.
• Each of the next n lines contains a string of length m consisting only of the characters . (dead cell) and * (live cell), representing the initial grid configuration.

outputFormat

For each test case, output a single integer on a new line representing the number of live cells remaining after k iterations. The output is written to standard output (stdout).

## sample

1
3 3 1
.*.
*.*
.*.

4

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