Game of Life: Next State Generation

You are given a grid representing the current state of Conway's Game of Life. Your task is to compute the next state of the grid according to the following rules:

• Any live cell (represented by a 1) with fewer than 2 live neighbours dies, as if by underpopulation.
• Any live cell with 2 or 3 live neighbours lives on to the next generation.
• Any live cell with more than 3 live neighbours dies, as if by overpopulation.
• Any dead cell (represented by a 0) with exactly 3 live neighbours becomes a live cell, as if by reproduction.

In mathematical terms, let \(N(c)\) be the number of live neighbours of a cell. Then:

• If the cell is live: it remains live if \(2 \leq N(c) \leq 3\); otherwise it dies.
• If the cell is dead: it becomes live if \(N(c) = 3\); otherwise it remains dead.

The grid is provided as a 2D array with R rows and C columns. The first line of input contains two integers: R and C, followed by R lines each containing C space-separated integers.

Your program should output the next state of the grid in the same format.

inputFormat

The input starts with a line containing two integers R and C (the number of rows and columns). The next R lines each contain C integers (each either 0 or 1) separated by spaces, representing the current state of the grid.

Example:

4 3
0 1 0
0 0 1
1 1 1
0 0 0

outputFormat

Output the next state of the grid with the same dimensions. Each of the R lines should contain C space-separated integers.

For the input above, the correct output is:

0 0 0
1 0 1
0 1 1
0 1 0

## sample

4 3
0 1 0
0 0 1
1 1 1
0 0 0

0 0 0
1 0 1
0 1 1
0 1 0

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