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Fill a 2×n2\times n grid with each integer from 11 to 2n2n such that every cell with a neighboring cell above or to the left of it has a greater number in it than those neighbors.

If the number of ways to fill the grid this way is f(n),f(n), then what is limnf(n)f(n1)?\displaystyle\lim_{n\to \infty}\frac{f(n)}{f(n-1)}?

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