Bacterial Colony Growth Simulation

This problem involves simulating the growth of a bacterial colony in a petri dish following rules similar to Conway's Game of Life. The petri dish is represented as a grid of n rows and m columns. Each cell in the grid can either be alive (represented by 1) or dead (represented by 0).

The simulation is performed for k generations. In each generation, the next state of the grid is computed according to the following rules:

• If a cell is alive and it has $N$ live neighbors, then it survives if and only if $N = 2$ or $N = 3$. Otherwise, it dies.
• If a cell is dead and it has exactly 3 live neighbors (i.e. $N = 3$), then it becomes alive.

Note that a neighbor is any cell adjacent in one of the 8 directions (horizontal, vertical, and diagonal).

Your task is to simulate this process, taking the initial state of the grid as input, and output the state of the grid after k generations.

inputFormat

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

n m k
row1
row2
...
rown

Here:

• n is the number of rows in the grid.
• m is the number of columns in the grid.
• k is the number of generations to simulate.
• Each of the next n lines contains m integers (each either 0 or 1) separated by spaces representing the initial state of the grid.

outputFormat

Output to standard output the final state of the grid after k generations. The output should have n lines, each containing m integers separated by spaces.

## sample

3 3 1
0 1 0
0 1 0
0 1 0

0 0 0
1 1 1
0 0 0

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