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Conway's Game of Life

There is an infinite two dimensional grid.

Each cell in the grid can either be "alive" or "dead".

Given the current state of the grid calculate the next "generation" of the grid given the following rules:

  1. Any live cell with fewer than two live neighbours dies, as if caused by under-population.
  2. Any live cell with two or three live neighbours lives on to the next generation.
  3. Any live cell with more than three live neighbours dies, as if by over-population.
  4. Any dead cell with exactly three live neighbours becomes a live cell, as if by reproduction.

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