In this previous note about [Placing Square in a Grid], Chung Kevin posed the question of "How many distinct ways are there to layer four 2 by 2 squares on a grid?"

Siddhartha Srivastava came up with an ingenious bijection, to show that the answer was 16. Brock Brown came up with a code to count the number of approaches.

I'm wondering, can we generalize this even further? What is the answer for the \( 4 \times 4 \) grid with 9 squares placed?

How about the \( n \times n \) grid?

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