Each square in a grid can be in one of two states; it either contains a living cell or does not contain a living cell. The

arrangement of living cells on a grid is called a generation. Given a generation, the next generation is computed by

examining each square in the generation and applying the following rules:

$1.$ If a square has a living cell and $2$ or $3$ of its neighbors have living cells, then the square continues to have a

living cell in the next generation.

$2.$ If a square has a living cell and less than $2$ or more than $3$ of its neighbors have living cells, then in the next

generation, the square does not contain a living cell.

$3.$ If a square does not have a living cell and exactly $3$ of its neighbors have living cells, then the square will have

a living cell in the next generation.

$4.$ If a square does not have a living cell and does not have exactly $3$ neighbors with living cells, then the square

continues to not have a living cell in the next generation.